18th EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING
COMPUTER-AIDED CHEMICAL ENGINEERING Advisory Editor: R. Gani Volume 1: Volume 2: Volume 3: Volume 4: Volume 5:
Volume 6: Volume 7: Volume 8: Volume 9: Volume 10: Volume 11: Volume 12: Volume 13: Volume 14: Volume 15: Volume 16: Volume 17: Volume 18: Volume 19: Volume 20: Volume 21:
Volume 22: Volume 23: Volume 24: Volume 25:
Distillation Design in Practice (L.M. Rose) The Art of Chemical Process Design (G.L. Wells and L.M. Rose) Computer Programming Examples for Chemical Engineers (G. Ross) Analysis and Synthesis of Chemical Process Systems (K. Hartmann and K. Kaplick) Studies in Computer-Aided Modelling. Design and Operation Part A: Unite Operations (I. Pallai and Z. Fonyó, Editors) Part B: Systems (I. Pallai and G.E. Veress, Editors) Neural Networks for Chemical Engineers (A.B. Bulsari, Editor) Material and Energy Balancing in the Process Industries - From Microscopic Balances to Large Plants (V.V. Veverka and F. Madron) European Symposium on Computer Aided Process Engineering-10 (S. Pierucci, Editor) European Symposium on Computer Aided Process Engineering-11 (R. Gani and S.B. Jørgensen, Editors) European Symposium on Computer Aided Process Engineering-12 (J. Grievink and J. van Schijndel, Editors) Software Architectures and Tools for Computer Aided Process Engineering (B. Braunschweig and R. Gani, Editors) Computer Aided Molecular Design: Theory and Practice (L.E.K. Achenie, R. Gani and V. Venkatasubramanian, Editors) Integrated Design and Simulation of Chemical Processes (A.C. Dimian) European Symposium on Computer Aided Process Engineering-13 (A. Kraslawski and I. Turunen, Editors) Process Systems Engineering 2003 (Bingzhen Chen and A.W. Westerberg, Editors) Dynamic Model Development: Methods, Theory and Applications (S.P. Asprey and S. Macchietto, Editors) The Integration of Process Design and Control (P. Seferlis and M.C. Georgiadis, Editors) European Symposium on Computer-Aided Process Engineering-14 (A. Barbosa-Póvoa and H. Matos, Editors) Computer Aided Property Estimation for Process and Product Design (M. Kontogeorgis and R. Gani, Editors) European Symposium on Computer-Aided Process Engineering-15 (L. Puigjaner and A. Espuña, Editors) 16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering (W. Marquardt and C. Pantelides) Multiscale Modelling of Polymer Properties (M. Laso and E.A. Perpète) Chemical Product Design: Towards a Perspective through Case Studies (K.M. Ng, R. Gani and K. Dam-Johansen, Editors) 17th European Symposium on Computer Aided Process Engineering (V. Plesu and P.S. Agachi, Editors) 18th European Symposium on Computer Aided Process Engineering (B. Braunschweig and X. Joulia, Editors)
COMPUTER-AIDED CHEMICAL ENGINEERING, 25
18th EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING Edited by
Bertrand Braunschweig IFP, France
and
Xavier Joulia LGC - ENSIACET - IPT, France
Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi International Scientific Committee. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxiii National Organising Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvi
Plenary Lectures Model Parameterization Tailored to Real-Time Optimization Benoît Chachuat, Bala Srinivasan and Dominique Bonvin. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Challenges for Multi-Scale Modeling of Multiple Failure Modes in Microelectronics Juergen Auersperg, Bernhard Wunderle, Rainer Dudek, Hans Walter and Bernd Michel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Design and Integration of Policies to Achieve Environmental Targets René Bañares-Alcántara. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Computational Chemical Engineering Modeling Applied to Energy and Reactor Design Luc Nougier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Curricular and Pedagogical Challenges for Enhanced Graduate Attributes in CAPE Ian T. Cameron and Daniel R. Lewin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Topic 1 – Off-Line Systems Keynote Lectures Chemical Product Engineering: The 3rd Paradigm Michael Hill.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Simulation in Nuclear Engineering Design Christian Latgé. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Oral Communications Supply Chain Risk Management Through HAZOP and Dynamic Simulation Arief Adhitya, Rajagopalan Srinivasan and I.A. Karimi.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 A New Approach for the Design of Multicomponent Water/Wastewater Networks Débora C. Faria and Miguel J. Bagajewicz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Effect of Catalytic Reactor Design on Plantwide Control Strategy: Application to VAM Plant Costin S. Bildea and Alexandre C. Dimian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
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Model of the Product Properties for Process Synthesis Peter M.M. Bongers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model André B. de Haan, Norbert J.M. Kuipers and Maartje Steensma. . . . . . . . . . . . . . . . . . . . . .61 Synthesis of Cryogenic Energy Systems Frank Del Nogal, Jin-Kuk Kim, Simon Perry and Robin Smith . . . . . . . . . . . . . . . . . . . . . . . 67 Study of a Novel Heat Integrated Hybrid Pervaporation Distillation Process: Simulation and Experiments M.T. Del Pozo Gómez, P. Ruiz Carreira, J.-U. Repke, A. Klein, T. Brinkmann and G. Wozny. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 A Novel Network-Based Continuous-time Formulation for Process Scheduling Diego M. Giménez, Gabriela P. Henning and Christos T. Maravelias. . . . . . . . . . . . . . . . . . 79 Excipient Interaction Prediction: Application of the Purdue Ontology for Pharmaceutical Engineering (POPE) Leaelaf Hailemariam, Pradeep Suresh, Venkata Pavan Kumar Akkisetty, Girish Joglekar, Shuo-Huan Hsu, Ankur Jain, Kenneth Morris, Gintaras Reklaitis, Prabir Basu and Venkat Venkatasubramanian. . . . . . . . . . . . . . . . . . . . 85 Optimal Column Sequencing for Multicomponent Mixtures Andreas Harwardt, Sven Kossack and Wolfgang Marquardt. . . . . . . . . . . . . . . . . . . . . . . . . 91 Systematic Design of Production Processes for Enantiomers with Integration of Chromatography and Racemisation Reactions Malte Kaspereit, Javier García Palacios, Tania Meixús Fernández and Achim Kienle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 The Application of a Task-Based Concept for the Design of Innovative Industrial Crystallizers Richard Lakerveld, Herman J.M. Kramer, Peter J. Jansens and Johan Grievink. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Cell Cycle Modelling for Off-line Dynamic Optimisation of Mammalian Cultures Carolyn M. Lam, Kansuporn Sriyudthsak, Cleo Kontoravdi, Krunal Kothari, Hee-Ho Park, Efstratios N. Pistikopoulos and Athanasios Mantalaris. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 New Configuration for Hetero-Azeotropic Batch Distillation: I. Feasibility Studies Peter Lang, Ferenc Denes and Xavier Joulia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Integrated Design of Solvent-Based Extractive Separation Processes P. Lek-utaiwan, B. Suphanit, N. Mongkolsiri and R. Gani. . . . . . . . . . . . . . . . . . . . . . . . . . 121 Development of a Novel Petri Net Tool for Process Design Selection Based on Inherent Safety Assessment Method Fakhteh Moradi and Parisa A. Bahri.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
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Population Balance Modeling of Influenza Virus Replication in MDCK Cells During Vaccine Production Thomas Müller, Josef Schulze-Horsel, Yury Sidorenko, Udo Reichl and Achim Kienle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A Population Balance Model Approach for Crystallization Product Engineering via Distribution Shaping Control Zoltan K. Nagy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Uncertainty Patterns and Sensitivity Analysis of an Indicator Based Process Design Framework Stavros Papadokonstantakis, Agarwal Siddharta, Hirokazu Sugiyama and Konrad Hungerbühler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Batch Scheduling with Intermediate Due Dates Using Timed Automata Models Subanatarajan Subbiah, Thomas Tometzki and Sebastian Engell. . . . . . . . . . . . . . . . . . . . 151 A Decomposition Approach to Short-Term Scheduling of Multi-Purpose Batch Processes Norbert Trautmann, Rafael Fink, Hanno Sagebiel and Christoph Schwindt . . . . . . . . . . . 157
Posters Combined Nitrogen and Phosphorus Removal. Model-Based Process Optimization Noelia Alasino, Miguel C. Mussati, Nicolás Scenna and Pío Aguirre. . . . . . . . . . . . . . . . . 163 A Systematic Procedure for Optimizing Crude Oil Distillation Systems Hasan Y. Alhammadi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Evaluation of Pervaporation Process for Recovering a Key Orange Juice Flavour Compound: Modeling and Simulation W.A. Araujo, M.E.T. Alvarez, E.B. Moraes and M.R. Wolf-Maciel . . . . . . . . . . . . . . . . . . . 175 A Microeconomics-Based Approach to Product Design Under Uncertainty Craig Whitnack, Ashley Heller and Miguel J. Bagajewicz. . . . . . . . . . . . . . . . . . . . . . . . . . 181 Model Predictive Control Based Planning in the Fruit Industry Aníbal Blanco, Guillermo Masini, Noemi Petracci and Alberto Bandoni . . . . . . . . . . . . . . 187 Optimize Process Condensate Reusing System for Ammonia Plant by the Synthesis of MEN Li Chen, Jian Du, Zhihui Gao, Pingjing Yao and Warren D. Seider. . . . . . . . . . . . . . . . . . 193 Entrainer-Based Reactive Distillation versus Conventional Reactive Distillation for the Synthesis of Fatty Acid Esters M.C. de Jong, A.C. Dimian and A.B. de Haan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Supply Chain Optimization with Homogenous Product Transport Constraints Tivadar Farkas, Zoltán Valentinyi, Endre Rév and Zoltán Lelkes. . . . . . . . . . . . . . . . . . . . 205 A Sensitivity Analysis on Optimal Solutions Obtained for a Reactive Distillation Column Rui M. Filipe, Steinar Hauan, Henrique A. Matos and Augusto Q. Novais . . . . . . . . . . . . 211
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Synthesis of Zero Effluent Multipurpose Batch Processes Using Effective Scheduling Jacques F. Gouws and Thokozani Majozi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Design of a Syngas Infrastructure Paulien M. Herder, Rob M. Stikkelman, Gerard P.J. Dijkema and Aad F. Correljé. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Implementation of a Reactive Dividing Wall Distillation Column in a Pilot Plant Rodrigo Sandoval-Vergara, Fabricio Omar Barroso-Muñoz, Héctor Hernández-Escoto, Juan Gabriel Segovia-Hernández, Salvador Hernández and Vicente Rico-Ramírez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Optimisation of a Bio-ethanol Purification Process Using Conceptual Design and Simulation Tools Patricia M. Hoch and José Espinosa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Improvement of Operating Procedures through the Reconfiguration of a Plant Structure Satoshi Hoshino, Hiroya Seki, Tomoya Sugimoto and Yuji Naka. . . . . . . . . . . . . . . . . . . . . 241 Graph-Theoretic Approach to Optimal Synthesis of Supply Networks: Distribution of Gasoline from a Refinery Young Kim, L.T. Fan, Choamun Yun, Seung Bin Park, Sunwon Park, Botond Bertok and Ferenc Friedler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications Mohamed T. Mahmud, Iqbal M. Mujtaba and Mansour Emtir. . . . . . . . . . . . . . . . . . . . . . . 253 An Integrated Framework for Operational Scheduling of a Real-World Pipeline Network Suelen Neves Boschetto, Luiz Carlos Felizari, Lia Yamamoto, Leandro Magatão, Sérgio Leandro Stebel, Flávio Neves-Jr, Lúcia Valéria Ramos de Arruda, Ricardo Lüders, Paulo César Ribas and Luiz Fernando de Jesus Bernardo . . . . . . . . . . . . 259 An Optimization Framework of Multibed Pressure Swing Adsorption Systems Dragan Nikolic, Michael C. Georgiadis and Eustathios S. Kikkinides . . . . . . . . . . . . . . . . 265 Multi-Objective Design of Multipurpose Batch Facilities Using Economic Assessments Tânia Rute Pinto, Ana Paula F.D. Barbósa-Póvoa and Augusto Q. Novais . . . . . . . . . . . . 271 Oil Products Pipeline Scheduling with Tank Farm Inventory Management Susana Relvas, Henrique A. Matos, Ana Paula F.D. Barbosa-Póvoa and João Fialho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Methodology of Conceptual Process Synthesis for Process Intensification Ben-Guang Rong, Eero Kolehmainen and Ilkka Turunen . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Process Plant Knowledge Based Simulation and Design Jelenka B. Savkovic-Stevanovic, Snezana B. Krstic, Milan V. Milivojevic and Mihailo B. Perunicic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
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Study of Arrangements for Distillation of Quaternary Mixtures Using Less Than N-1 Columns Dulce María Méndez-Valencia, María Vázquez-Ojeda, Juan Gabriel Segovia-Hernández, Héctor Hernández and Adrián Bonilla-Petriciolet. . . . . . . . . . . . . . . 295 A Hybrid Meta-Heuristic Method for Logistics Optimization Associated with Production Planning Yoshiaki Shimizu, Yoshihiro Yamazaki and Takeshi Wada . . . . . . . . . . . . . . . . . . . . . . . . . 301 Model-Based Investment Planning Model for Stepwise Capacity Expansions of Chemical Plants Andreas Wiesner, Martin Schlegel, Jan Oldenburg, Lynn Würth, Ralf Hannemann and Axel Polt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Divided Wall Distillation Column: Dynamic Modeling and Control Alexandru Woinaroschy and Raluca Isopescu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Topic 2 – On-Line Systems Oral Communications Optimization of Preventive Maintenance Scheduling in Processing Plants DuyQuang Nguyen and Miguel Bagajewicz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 Predictive Optimal Management Method for the Control of Polygeneration Systems Andrés Collazos and François Maréchal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Comparison of Model Predictive Control Strategies for the Simulated Moving Bed Adrian Dietz and Jean-Pierre Corriou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Model Reduction Techniques for Dynamic Optimization of Chemical Plants Operation Bogdan Dorneanu, Costin Sorin Bildea and Johan Grievink . . . . . . . . . . . . . . . . . . . . . . . 337 A Mathematical Programming Framework for Optimal Model Selection/Validation of Process Data Belmiro P. Duarte, Maria J. Moura, Filipe J.M. Neves and Nuno M.C. Oliveira. . . . . . . . 343 Towards On-line Model-Based Design of Experiments Federico Galvanin, Massimiliano Barolo and Fabrizio Bezzo . . . . . . . . . . . . . . . . . . . . . . 349 Sensor Placement for Fault Detection and Localization Carine Gerkens and Georges Heyen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 Using Kriging Models for Real-Time Process Optimisation Marcos V.C. Gomes, I. David L. Bogle, Evaristo C. Biscaia Jr. and Darci Odloak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements Héctor Hernández-Escoto, Ricardo Aguilar-López, María Isabel Neria-González and Alma Rosa Domínguez-Bocanegra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
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Optimal Control of Batch Processes Using Particle Swam Optimisation with Stacked Neural Network Models Fernando Herrera and Jie Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Online LQG Stabilization of Unstable Gas-Lifted Oil Wells Esmaeel Jahanshahi, Karim Salahshoor and Riyaz Kharrat . . . . . . . . . . . . . . . . . . . . . . . . 381 Analysis of the Constraint Characteristics of a Sheet Forming Control Problem Using Interval Operability Concepts Fernando V. Lima, Christos Georgakis, Julie F. Smith and Phillip D. Schnelle . . . . . . . . . 387 Real-Time Optimization via Adaptation and Control of the Constraints Alejandro Marchetti, Benoît Chachuat and Dominique Bonvin . . . . . . . . . . . . . . . . . . . . . . 393 Integration of Engineering Process Control and Statistical Control in Pulp and Paper Industry Ana S. Matos, José G. Requeijo and Zulema L. Pereira . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 A Combined Balanced Truncation and Multi-Parametric Programming Approach for Linear Model Predictive Control Diogo Narciso and Efstratios Pistikopoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Fault Detection and Isolation Based on the Model-Based Approach: Application on Chemical Processes Nelly Olivier-Maget, Gilles Hétreux, Jean-Marc Le Lann and Marie-Véronique Le Lann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Computer Aided Operation of Pipeless Plants Sabine Piana and Sebastian Engell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Off-line Design of PAT Systems for On-line Applications Ravendra Singh, Krist V. Gernaey and Rafiqul Gani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
Posters New Method for Sensor Network Design and Upgrade for Optimal Process Monitoring Miguel J. Bagajewicz, DuyQuang Nguyen and Sanjay Kumar Sugumar . . . . . . . . . . . . . . . 429 A Novel Proactive-Reactive Scheduling Approach in Chemical Multiproduct Batch Plants Elisabet Capón, Georgios M. Kopanos, Anna Bonfill, Antonio Espuña and Luis Puigjaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Model Predictive Control of the Waste Water Treatment Plant Based on the Benchmark Simulation Model No.1-BSM1 Vasile-Mircea Cristea, Cristian Pop and Paul Serban Agachi. . . . . . . . . . . . . . . . . . . . . . . 441 Load Balancing Control System of a Furnace from Atmospheric Distillation Unit Cristian Patrascioiu and Sanda Mihalache . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 Optimal Operation of Sublimation Time of the Freeze Drying Process by Predictive Control: Application of the MPC@CB Software N. Daraoui, P. Dufour, H. Hammouri and A. Hottot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
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Improving Steady-State Identification Galo A.C. Le Roux, Bruno Faccini Santoro, Francisco F. Sotelo, Mathieu Teissier and Xavier Joulia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 Application of Adaptive Neurofuzzy Control Using Soft Sensors to Continuous Distillation Javier Fernandez de Canete, Pablo del Saz-Orozco and Salvador Gonzalez-Perez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Correlation-Based Just-In-Time Modeling for Soft-Sensor Design Koichi Fujiwara, Manabu Kano and Shinji Hasebe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 Integrating Strategic, Tactical and Operational Supply Chain Decision Levels in a Model Predictive Control Framework José Miguel Laínez, Georgios M. Kopanos, Mariana Badell, Antonio Espuña and Luis Puigjaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 Hybrid Strategy for Real Time Optimization with Feasibility Driven for a Large Scale Three-Phase Catalytic Slurry Reactor Delba N.C. Melo, Adriano P. Mariano, Eduardo C. Vasco de Toledo, Caliane B.B. Costa and Rubens Maciel Filho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Adaptive Control of the Simultaneous Saccharification – Fermentation Process from Starch to Ethanol Silvia Ochoa, Velislava Lyubenova, Jens-Uwe Repke, Maya Ignatova and Günter Wozny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Advanced Control Monitoring in Petrobras’ Refineries: Quantifying Economic Gains on a Real-Time Basis Rafael Pinotti, Antonio Carlos Zanin and Lincoln Fernando Lautenschlager Moro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation Diego Martinez Prata, José Carlos Pinto and Enrique Luis Lima . . . . . . . . . . . . . . . . . . . 501 State Estimation for Dynamic Prediction of Hydrate Formation in Oil and Gas Production Systems J. Rodriguez Perez, C.S. Adjiman and C.D. Immanuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 RCS for Process Control: Is There Anything New Under the Sun? Manuel Rodríguez and Ricardo Sanz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Data Treatment and Analysis for On-line Dynamic Process Optimization Nina Paula G. Salau, Giovani Tonel, Jorge O. Trierweiler and Argimiro R. Secchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Nonlinear Model Predictive Control of a Swelling Constrained Industrial Batch Reactor Levente L. Simon, Z.K. Nagy and Konrad Hungerbühler . . . . . . . . . . . . . . . . . . . . . . . . . . 525 An Adapted SLAB Model Using Sensor Data for the Prediction on the Dispersion of Hazardous Gas Releases Won So, Dongil Shin and En Sup Yoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
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Topic 3 – Computational & Numerical Solutions Strategies Keynote Lecture Expanding Process Modelling Capability through Software Interoperability Standards: Application, Extension and Maintenance of CAPE OPEN Standards Ray Dickinson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
Oral Communications Optimization of WWTP Control by Means of Multi-Objective Genetic Algorithms and Sensitivity Analysis Benoit Beraud, Jean-Philippe Steyer, Cyrille Lemoine and Eric Latrille. . . . . . . . . . . . . . . 539 A Model Reduction-Based Optimisation Framework for Large-Scale Simulators Using Iterative Solvers Ioannis Bonis and Constantinos Theodoropoulos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Rigorous Flowsheet Optimization Using Process Simulators and Surrogate Models José A. Caballero and Ignacio E. Grossmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 MILP-Based Decomposition Method for the Optimal Scheduling of an Industrial Batch Plant Pedro M. Castro, Augusto Q. Novais and Alexandre Carvalho . . . . . . . . . . . . . . . . . . . . . . 557 Design of Constrained Nonlinear Model Predictive Control Based on Global Optimisation Michal C ižniar, Miroslav Fikar and M.A. Latifi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Biclustering of Data Matrices in Systems Biology via Optimal Re-ordering Peter A. DiMaggio Jr., Scott R. McAllister, Christodoulos A. Floudas, Xiao-Jiang Feng, Joshua D. Rabinowitz and Herschel A. Rabitz. . . . . . . . . . . . . . . . . . . . . 569 Optimum Experimental Design for Key Performance Indicators Stefan Körkel, Harvey Arellano-Garcia, Jan Schöneberger and Günter Wozny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 Inductive Data Mining: Automatic Generation of Decision Trees from Data for QSAR Modelling and Process Historical Data Analysis Chao Y. Ma, Frances V. Buontempo and Xue Z. Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 The Solution of Very Large Non-Linear Algebraic Systems Davide Manca and Guido Buzzi-Ferraris. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 Multi-Operations Time-Slots Model for Crude-Oil Operations Scheduling Sylvain Mouret, Ignacio E. Grossmann and Pierre Pestiaux . . . . . . . . . . . . . . . . . . . . . . . . 593 A Framework for Analysis of Computational Load of CAPE Tools Pablo A. Rolandi and Alejandro Cano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 An Implementation of Parallel Computing for Hierarchical Logistic Network Design Optimization Using PSO Yoshiaki Shimizu and Hiroshi Kawamoto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
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Service-Oriented CAPE: A New Direction for Software Applications Iain D. Stalker, Eric S. Fraga, Aidong Yang and Nikolay D. Mehandjiev . . . . . . . . . . . . . 611 Using Grid Computing to Solve Hard Planning and Scheduling Problems Michael C. Ferris, Christos T. Maravelias and Arul Sundaramoorthy . . . . . . . . . . . . . . . . 617 Benchmarking Numerical and Agent-Based Models of an Oil Refinery Supply Chain Koen H. van Dam, Arief Adhitya, Rajagopalan Srinivasan and Zofia Lukszo . . . . . . . . . . 623 Large-Scale Nonlinear Programming Strategies for the Operation of LDPE Tubular Reactors Victor M. Zavala and Lorenz T. Biegler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
Posters Simulis® Thermodynamics: An Open Framework for Users and Developers Olivier Baudouin, Stéphane Dechelotte, Philippe Guittard and Alain Vacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635 A New Approach for Chemical Transfer Reaction Models Zakia Benjelloun-Dabaghi, Renaud Cadours, Sylvie Cauvin and Pascal Mougin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641 Modeling and Simulation of the Particle Size Distribution for Emulsion Polymerization in a Tubular Reactor Ala Eldin Bouaswaig, Wolfgang Mauntz and Sebastian Engell . . . . . . . . . . . . . . . . . . . . . 647 Composite Zeolite Membranes Characterization by using a Transient State Experimental Technique and a Parameter Estimation Procedure Lucile Courthial, Arnaud Baudot, Mélaz Tayakout-Fayolle and Christian Jallut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 MPC@CB Software: A Solution for Model Predictive Control Bruno da Silva, Pascal Dufour, Nida Othman and Sami Othman . . . . . . . . . . . . . . . . . . . . 659 Detection of Multiple Structural Changes in Linear Processes Through Change Point Analysis and Bootstrapping Belmiro P.M. Duarte and P.M. Saraiva. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Applications of Grey Programming to Process Design Edelmira D. Gálvez, Luis A. Cisternas, Pamela S. Patiño and Kathy L. Ossandon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671 Flexible and Configurable MILP-Models for Meltshop Scheduling Optimization Iiro Harjunkoski and Guido Sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677 Functional Data Analysis for the Development of a Calibration Model for Near-infrared Data Cheng Jiang and Elaine B. Martin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683 Application of Global Sensitivity Analysis to Biological Models Alexandros Kiparissides, Maria Rodriguez-Fernandez, Sergei Kucherenko, Athanasios Mantalaris and Efstratios Pistikopoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689
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Development of a Sophisticated Framework for Complex Single- and Multi-Objective Optimization Tasks Matthias Leipold, Sven Gruetzmann, Georg Fieg, Dietrich Maschmeyer, Jörg Sauer and Holger Wiederhold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 Towards Resilient Supply Chains: Uncertainty Analysis Using Fuzzy Mathematical Programming Kishalay Mitra, Ravindra D. Gudi, Sachin C. Patwardhan and Gautam Sardar. . . . . . . . . 701 Modeling and Identification of the Bio-ethanol Production Process from Starch: Cybernetic vs. Unstructured Modeling Silvia Ochoa, Ahrim Yoo, Jens-Uwe Repke, Günter Wozny and Dae Ryook Yang. . . . . . . . 707 Particle Swarm Optimisation in Heat Exchanger Network Synthesis Including Detailed Equipment Design Aline P. Silva, Mauro A.S.S. Ravagnani and Evaristo C. Biscaia Jr. . . . . . . . . . . . . . . . . . 713 A Single Stage Approach for Designing Water Networks with Multiple Contaminants Krzysztof Walczyk and Jacek Jezowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719
Topic 4 – Integrated and Multiscale Modelling and Simulation Keynote Lecture Multiscale Molecular Modeling: A Tool for the Design of Nano Structured Materials Maurizio Fermeglia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
Oral Communications Energy-Preserving Method for Spatial Discretization: Application to an Adsorption Column Ahmed Baaiu, Françoise Couenne, Laurent Lefevre and Yann Le Gorrec . . . . . . . . . . . . . 727 MEXA goes CAMD – Computer-Aided Molecular Design for Physical Property Model Building André Bardow, Sven Kossack, Ernesto Kriesten and Wolfgang Marquardt. . . . . . . . . . . . . 733 Modeling the Phase Equilibria of Nitriles by the soft-SAFT Equation of State Abdelkrim Belkadi, Mohamed K. Hadj-Kali, Vincent Gerbaud, Xavier Joulia, Fèlix Llovell and Lourdes F. Vega . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Application of a Digital Packing Algorithm to Cylindrical Pellet-Packed Beds Richard Caulkin, Michael Fairweather, Xiaodong Jia, Abid Ahmad and Richard A. Williams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 Modelling and Simulation of a Membrane Microreactor Using Computational Fluid Dynamics Paris Chasanis, Eugeny Y. Kenig, Volker Hessel and Stefan Schmitt . . . . . . . . . . . . . . . . . 751 Modeling of Catalytic Hydrogen Generation from Sodium Borohydride André Gonçalves, Pedro Castro, Augusto Q. Novais, Carmen M. Rangel and Henrique Matos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757
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Towards a New Generation Heat Exchanger Models Geert W. Haarlemmer and Jérôme Pigourier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763 Brownian Dynamics and Kinetic Monte Carlo Simulation in Emulsion Polymerization Hugo F. Hernandez and Klaus Tauer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769 Biodiesel Production by Heat-Integrated Reactive Distillation Anton A. Kiss, Alexandre C. Dimian and Gadi Rothenberg . . . . . . . . . . . . . . . . . . . . . . . . 775 Modeling Comparison of High Temperature Fuel Cell Performance: Electrochemical Behaviours of SOFC and PCFC Jean-Marie Klein and Jonathan Deseure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781 An Integrated Framework for Model-Based Flow Assurance in Deep-Water Oil and Gas Production Eduardo Luna-Ortiz, Praveen Lawrence, Constantinos C. Pantelides, Claire S. Adjiman and Charles D. Immanuel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 Enhanced Modeling and Integrated Simulation of Gasification and Purification Gas Units Targeted to Clean Power Production Mar Pérez-Fortes, Aarón Bojarski, Sergio Ferrer-Nadal, Georgios M. Kopanos, José Ma Nougués, Enric Velo and Luis Puigjaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793 Absorption of Aromatic Hydrocarbons in Multicomponent Mixtures: A Comparison Between Simulations and Measurements in a Pilot Plant Diethmar Richter, Holger Thielert and Günter Wozny . . . . . . . . . . . . . . . . . . . . . . . . . . . . 799 A Comprehensive Population Balance Model of Emulsion Polymerisation for PSD & MWD: Comparison to Experimental Data S.J. Sweetman, C.D. Immanuel, T.I. Malik, S. Emmett and N. Williams . . . . . . . . . . . . . . . 805 Prediction of Partition Coefficients Between Food Simulants and Packaging Materials Using Molecular Simulation and a Generalized Flory-Huggins Approach Olivier Vitrac and Guillaume Gillet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811 Shape – The Final Frontier Xue Z. Wang, Caiyun Ma and Kevin J. Roberts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817
Posters Computational Fluid Dynamics: A Tool to the Formulation of Therapeutic Aerosols Nathalie Bardin-Monnier, Véronique Falk and Laurent Marchal-Heussler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 Large Eddy Simulation of Particle Dispersion in a Straight, Square Duct Flow Michael Fairweather and Jun Yao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829 Test Bench Dimensioned by Specific Numerical Tool Nicolas Gascoin, Philippe Gillard, Gregory Abraham and Marc Bouchez . . . . . . . . . . . . 835 Optimization of SOFC Interconnect Design Using Multiphysic Computation Dominique Grondin, Jonathan Deseure, Mohsine Zahid, Maria José Garcia and Yann Bultel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841
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Multi-Objective Scheduling for Environmentally-Friendly Batch Operations Iskandar Halim and Rajagopalan Srinivasan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 Operability Analysis and Conception of Microreactor by Integration of Reverse Engineering and Rapid Manufacturing André L. Jardini, Maria Carolina B. Costa, Aulus R.R. Bineli, Andresa F. Romão and Rubens Maciel Filho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853 Optimisations with Energy Recovery for Oxidative Desulphurization of Heavy Gas Oil Hamza A. Khalfalla, Iqbal M. Mujtaba, Mohamed M. El-Garni and Hadi A. El-Akrami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859 Ion-Specific Potential of Mean Force Between Two Aqueous Proteins Eduardo R.A. Lima, Frederico W. Tavares and Evaristo C. Biscaia Jr. . . . . . . . . . . . . . . . 865 A Heteronuclear Group Contribution Method for Associating Chain Molecules (SAFT-γ) Alexandros Lymperiadis, Claire S. Adjiman, Amparo Galindo and George Jackson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871 An Analytical-Numerical Method for Solving a Heap Leaching Problem of one or more Solid Reactants from Porous Pellets Mario E. Mellado and Luis A. Cisternas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 Thermochemical Multi-phase Models Applying the Constrained Gibbs Energy Method Risto Pajarre, Peter Blomberg and Pertti Koukkari . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883 Industrial Applications of Multi-Phase Thermochemical Simulation Risto Pajarre, Pertti Koukkari and Karri Penttilä . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889 Prediction of the Melting Point Temperature Using a Linear QSPR for Homologous Series Inga Paster, Mordechai Shacham and Neima Brauner . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895 A General Mathematical Model for a Moving Bed Gasifier Sauro Pierucci and Eliseo Ranzi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901 Modelling of an Hybrid Wastewater Treatment Plant Marie-Noëlle Pons, Maria do Carmo Lourenço da Silva, Olivier Potier, Eric Arnos and Philippe Battaglia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907 Dimension Reduction of Two-Dimensional Population Balances Based on the Quadrature Method of Moments Andreas Voigt, Wolfram Heineken, Dietrich Flockerzi and Kai Sundmacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913 Predictions of the Consequences of Natural Gas-Hydrogen Explosions Using a Novel CFD Approach Robert M. Woolley, Michael Fairweather, Samuel A.E.G. Falle and Jack R. Giddings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919
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Topic 5 – Cape for the Users! Oral Communications Support of Strategic Business Decisions at BASF’s Largest Integrated Production Site Based on Site-Wide Verbund Simulation Stefan Brüggemann, Nanette Bauer, Eberhard Fuchs, Axel Polt, Bernhard Wagner and Michael Wulkow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925 A Generic Scientific Information Management System for Process Engineering Sylvie Cauvin, Mireille Barbieux, Laurent Carrié and Benoît Celse. . . . . . . . . . . . . . . . . . 931 Rapid Process Design and Development of Complex Solution Copolymers Yadunandan L. Dar and Tahir I. Malik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937 Troubleshooting and Process Optimisation by Integrating CAPE Tools and Six Sigma Methodology Dr. Guido Dünnebier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943 A Compliance Management System for the Pharmaceutical Industry Julie Fisher, Arantza Aldea and René Bañares-Alcántara . . . . . . . . . . . . . . . . . . . . . . . . . 949 Business Process Model for Knowledge Management in Plant Maintenance Tetsuo Fuchino, Yukiyasu Shimada, Masazumi Miyazawa and Yuji Naka . . . . . . . . . . . . . 955 Practical Challenges in Developing Data-Driven Soft Sensors for Quality Prediction Jun Liu, Rajagopalan Srinivasan and P.N. SelvaGuru . . . . . . . . . . . . . . . . . . . . . . . . . . . . 961 Process Analytical Technologies (PAT) – The Impact for Process Systems Engineering Zeng Ping Chen, David Lovett and Julian Morris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967 Decision Support for Control Structure Selection During Plant Design Jan Oldenburg, Hans-Jürgen Pallasch, Colman Carroll, Veit Hagenmeyer, Sachin Arora, Knud Jacobsen, Joachim Birk, Axel Polt and Peter van den Abeel . . . . . . . 973 Production-Line Wide Dynamic Bayesian Network Model for Quality Management in Papermaking Aino Ropponen and Risto Ritala . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 979 OntoMODEL: Ontological Mathematical Modeling Knowledge Management Pradeep Suresh, Girish Joglekar, Shuohuan Hsu, Pavan Akkisetty, Leaelaf Hailemariam, Ankur Jain, Gintaras Reklaitis and Venkat Venkatasubramanian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985 OntoCAPE 2.0 – a (Re-)Usable Ontology for Computer-Aided Process Engineering Jan Morbach, Andreas Wiesner and Wolfgang Marquardt . . . . . . . . . . . . . . . . . . . . . . . . 991
Posters CAPE Methods and Tools for Systematic Analysis of New Chemical Product Design and Development Merlin Alvarado-Morales, Naweed Al-Haque, Krist V. Gernaey, John M. Woodley and Rafiqul Gani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997
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Hazop Support System and its Use for Operation Koji Kwamura, Yuji Naka, Tetsuo Fuchino, Atsushi Aoyama and Nobuo Takagi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003 Acceleration of the Retrieval of Past Experiences in Case Based Reasoning: Application for Preliminary Design in Chemical Engineering Stephane Negny and Jean-Marc Le Lann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1009 Visual Exploration of Multi-State Operations Using Self-Organizing Map Yew Seng Ng and Rajagopalan Srinivasan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015 Multi-Criteria Decision Making in Product-driven Process Synthesis Kristel de Ridder, Cristhian Almeida-Rivera, Peter Bongers, Solke Bruin and Simme Douwe Flapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1021 Improvement of the Production Process of Leached Optical Fibers in a Technological and Organizational Context Daniëlle T. Stekelenburg, Zofia Lukszo and Jeff Lowe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027 Quality Assurance of Simulation Results Laurent Testard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033 Decision Tree Based Qualitative Analysis of Operating Regimes in Industrial Production Processes Tamás Varga, Ferenc Szeifert, József Réti and János Abonyi . . . . . . . . . . . . . . . . . . . . . . 1039 Mobatec Modeller – A Flexible and Transparent Tool for Building Dynamic Process Models Mathieu R. Westerweele and Jan Laurens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045
Topic 6 – Cape and Society Keynote Lecture Sustainable Energy Futures, and what we can do about it Cav. Prof. Sandro Macchietto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051
Oral Communications A Methodology for Designing and Evaluating Biomass Utilization Networks Nasser Ayoub, Hiroya Seki and Yuji Naka . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053 Integrated Gasification Combined Cycle (IGCC) Process Simulation and Optimization F. Emun, M. Gadalla and L. Jiménez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059 IDEF0 Activity Modeling for Integrated Process Design Considering Environmental, Health and Safety (EHS) Aspects Masahiko Hirao, Hirokazu Sugiyama, Ulrich Fischer and Konrad Hungerbühler . . . . . . 1065 A Prototype Agent-Based Modeling Approach for Energy System Analysis Bri-Mathias Hodge, Selen Aydogan-Cremaschi, Gary Blau, Joseph Pekny and Gintaras Reklaitis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1071
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A Systematic Framework for Biorefinery Production Optimization Norman E. Sammons, Jr., Wei Yuan, Mario R. Eden, Burak Aksoy and Harry T. Cullinan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077 Economic Analysis and Process Integration of Hydrogen Production Strategies Wei Yuan, Norman E. Sammons Jr., Kristin H. McGlocklin and Mario R. Eden . . . . . . . 1083 Design of Heat-integrated Power Systems with Decarbonisation Xuesong Zheng, Jin-Kuk Kim and Robin Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1089
Posters Mathematical Modeling of Limestone Dissolution in Batch Stirred Tank Reactors in Presence of a Diluted Strong Acid Cataldo De Blasio, Jarl Ahlbeck and Frej Bjondahl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095 Biodiesel Production from Vegetable Oils: Operational Strategies for Large Scale Systems Nívea de Lima da Silva, Elmer Ccopa Rivera, César Benedito Batistella, Danilo Ribeiro de Lima, Rubens Maciel Filho and Maria Regina Wolf Maciel . . . . . . . . 1101 Minimization of Life Cycle Greenhouse Emissions and Cost in the Operation of Steam and Power Plants Pablo E. Martinez and Ana Maria Eliceche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1107 Developing a Lake Eutrophication Model and Determining Biogeochemical Parameters: A Large Scale Parameter Estimation Problem Vanina Estrada, Elisa R. Parodi and M. Soledad Diaz . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113 Computer Aided Design of Occupationally Healthier Processes Mimi H. Hassim and Markku Hurme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1119 Energy Management in a Stand-Alone Power System for the Production of Electrical Energy with Long Term Hydrogen Storage Dimitris Ipsakis, Spyros Voutetakis, Panos Seferlis, Fotis Stergiopoulos, Simira Papadopoulou, Costas Elmasides and Chrysovalantis Keivanidis . . . . . . . . . . . . 1125 Mapping Environmental Issues within Supply Chains: A LCA Based Approach José Miguel Laínez, Aarón Bojarski, Antonio Espuña and Luis Puigjaner . . . . . . . . . . . 1131 Exergy Analysis of Biological Hydrogen Production Ala Modarresi, Walter Wukovits and Anton Friedl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137 Sensitivity Analysis of a Model for Atmospheric Dispersion of Toxic Gases Nishant Pandya, Eric Marsden, Pascal Floquet and Nadine Gabas. . . . . . . . . . . . . . . . . 1143 A Generic Framework for Modeling, Design and Optimization of Industrial Phosphoric Acid Production Processes Athanasios I. Papadopoulos and Panos Seferlis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149 Fisher Information: A Generalized Sustainability Index? Vicente Rico-Ramirez, Pedro A. Quintana-Hernandez, Jesus A. Ortiz-Cruz and Salvador Hernandez-Castro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155 Towards Improved Cleaning of FMCG Plants: A Model-Based Approach A. Yang, E.B. Martin, G.A. Montague and P.J. Fryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161
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Contents
Topic 7 – Cape in Education Oral Communications Development of Sustainable Energy Systems: A New Challenge for Process Systems Engineering Education Catherine Azzaro-Pantel, Christophe Gourdon, Xavier Joulia, Jean-Marc Le Lann, Stéphan Astier, Guillaume Fontes, Maria David and Alain Ayache. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167 Enhancing the Understanding and Insights of Students and Industry Operators in Process Engineering Principles via Immersive 3D Environments Christine Norton, Ian Cameron, Caroline Crosthwaite, Nicoleta Balliu, Moses Tade, David Shallcross, Andrew Hoadley, Geoff Barton and John Kavanagh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175 CAPE Tools in Biotechnology: Why, When, What, Who, Which Ones and Where? L. Jiménez, I. Katakis, A. Fabregat, T. Schafer, S. Rodriguez, J.M. Mateo, M. Giamberini, B. Rivera, P. Argüeso, E. Calero, L. Vico, F. Hernandez, R. Genc, M. Medir, J.R. Alabart and G. Guillén-Gosálbez . . . . . . . . . . . . . . . . . . . . . . . . 1181 What is “In” and What is “Out” in Engineering Problem Solving Mordechai Shacham, Michael B. Cutlip and Neima Brauner . . . . . . . . . . . . . . . . . . . . . . 1187
Poster Virtual and Remote Laboratory for Robotics E-Learning Carlos A. Jara, Francisco A. Candelas and Fernando Torres . . . . . . . . . . . . . . . . . . . . . 1193 Author Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199
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Preface This book contains papers presented at the 18th European Symposium on Computer Aided Process Engineering, ESCAPE-18, held in Lyon, France, June 1–4, 2008. A complementary CD-Rom contains all the papers presented at the symposium. ESCAPE-18 is the 40th event of the CAPE (Computer Aided Process Engineering) Working Party of the European Federation of Chemical Engineering (EFCE). The ESCAPE series started in 1992 at Elsinore, Denmark, on a strong foundation of 23 events of the CAPE WP. The first event was organized in Tutzing, Germany, in 1968. The most recent symposia were organized in Barcelona, Spain, 2005, Garmisch-Partenkirchen, Germany, 2006 and Bucharest, Romania, 2007. The ESCAPE series brings the latest innovations and achievements by leading professionals from the industrial and academic communities. The series serves as a forum for engineers, scientists, researchers, managers and students from academia and industry to: – present new computer aided methods, algorithms, techniques related to process and product engineering, – discuss innovative concepts, new challenges, needs and trends in the area of CAPE. This research area bridges fundamental sciences (physics, chemistry, thermodynamics, applied mathematics and computer sciences) with the various aspects of process and product engineering. The main theme for ESCAPE-18 is CAPE for the Users! CAPE systems are to be put in the hands of end users who need functionality and assistance beyond the scientific and technological capacities which are at the core of the systems. User-friendliness, on-line or web-based advice, decision support, knowledge management, organisational issues, are important points that must be taken care of when deploying a CAPE system. These issues were addressed in a special session and industrial case studies illustrating CAPE methods and tools were encouraged. The other four main topics cover the usual scope of ESCAPE series: – – – –
off-line systems for synthesis and design, on-line systems for control and operation, computational and numerical solutions strategies, integrated and multi-scale modelling and simulation,
and two general topics address the impact of CAPE tools and methods on Society and Education. More than 580 abstracts were submitted to the conference. Out of them 420 were invited to submit a full paper and 342 were finally selected for oral or poster presentation. Their authors came from 41 different countries. The review of abstracts, review of manuscripts and final selection
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of revised manuscripts were carried out by an International Scientific Committee (ISC). We are very grateful to the 84 members of the ISC for their efficient and fruitful collaboration. In addition to the accepted papers, eleven outstanding speakers were invited for giving plenary or keynote lectures on state-of-the art, challenges and future needs in all main topics. ESCAPE celebrates its 18th anniversary this year, reaching the adult stage! It is true that ESCAPE is quite an established conference in the realm of computer-aided process engineering, but it continues to attract innovative young researchers from around the world. We are confident that it will go on as such in the forthcoming year, keeping the young spirit together with the experience acquired over its first eighteen years. We hope that this book will serve as a valuable reference document to the scientific and industrial community and will contribute to the progress in computer aided process and product engineering.
Bertrand Braunschweig Xavier Joulia ESCAPE-18 Co-Chairmen
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International Scientific Committee
Conference Co-Chairpersons Bertrand Braunschweig, IFP, France Xavier Joulia, LGC – ENSIACET – INPT, France
Topic Area Co-Chairpersons Off-line Systems Rafiqul Gani, Technical University of Denmark, Denmark Jan van Schijndel, Shell Global Solutions International, The Netherlands
On-line Systems Chonghun Han, Seoul National University, South Korea Martin Wolf, Bayer Technology Services, Germany
Computational and Numerical Solution Strategies Lorens Biegler, Carnegie-Mellon University, USA Michel Pons, Michel Pons Technologie, France
Integrated and Multiscale Modelling and Simulation Luis Puigjaner, Universitat Politècnica de Catalunya, Spain Costas Pantelides, Process Systems Enterprise, UK
CAPE for the Users! Tahir I. Malik, ICI Strategic Technology Group, UK Wolfgang Marquardt, RWTH Aachen University, Germany
CAPE and Society Peter Glavic, University of Maribor, Slovenia Sophie Jullian, IFP, France
CAPE in Education Ian Cameron, University of Queensland, Australia Georges Heyen, University of Liège, Belgium
Members Off-line Systems Ana Barbosa-Póvoa, Instituto Superior Tecnico, Portugal David Bogle, University College London, UK Michael Doherty, University of California, USA
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International Scientific Committee Andrzej Gorak, University of Dortmund, Germany Johan Grievink, Delft University of Technology, The Netherlands Ignacio Grossmann, Carnegie Mellon University, USA Ludovit Jelemensky, Slovak University of Technology, Slovakia Zdravko Kravanja, University of Maribor, Slovenia Christian Latgé, CEA, France Henrique Matos, Instituto Superior Tecnico, Portugal Xuan Meyer, LGC – ENSIACET – INPT, France Ka Ming Ng, Hongkong University of Science and Technology, China (Hongkong) Sauro Pierucci, Politecnico di Milano, Italy Heinz Preisig, Norwegian University of Science and Technology, Norway Eva Sorensen, University College London, UK Petr Srehlik, BRNO University of Technology, Czech Republic
On-line Systems Dominique Bonvin, Ecole Polytechnique Fédérale de Lausanne, Switzerland Didier Caudron, Sanofi Pasteur, France Yann Creff, IFP, France Sebastian Engell, University of Dortmund, Germany Antonio Espuña, Universitat Politècnica de Catalunya, Spain Sten Bay Jorgensen, Technical University of Denmark, Denmark Marie-Véronique Le Lann, LAAS, France Iqbal Mujtaba, University of Bradford, UK Jose Pinto, Universidade de São Paulo, Brazil Sigurd Skogestad, Norwegian University of Science and Technology, Norway Venkat Venkatasubramanian, Purdue University, USA Günter Wozny, Technical University of Berlin, Germany Toshko Zhelev, University of Limerick, Ireland
Computational and Numerical Solution Strategies Guido Buzzi-Ferraris, Politecnico di Milano, Italy Benoit Chachuat, Ecole Polytechnique Fédérale de Lausanne, Switzerland Pascal Floquet, LGC – ENSIACET – INPT, France Christodoulos Floudas, Princeton University, USA Jacek Jezowski, Rzeszow Technical University, Poland François Maréchal, Ecole Polytechnique Fédérale de Lausanne, Switzerland Hervé Pingaud, ENSTIMAC, France Stratos Pistikopoulos, Imperial College London, UK Mordechai Shacham, Ben-Gurion University of the Negev, Israel Alain Vacher, ProSim, France Peter Verheijen, Delft University of Technology, The Netherlands
Integrated and Multiscale Modelling and Simulation Claire Adjiman, Imperial College London, UK Ana Maria Eliceche, Plapiqui, Argentina Christian Jallut, LAGEP – Université Lyon 1 – CPE, France Thokozani Majozi, University of Pretoria, South Africa Fernando Martins, FEUP, Portugal Natalia Menshutina, D.I. Mendeleev University of Chemical Technology, Russia
International Scientific Committee Gintaras Reklaitis, Purdue University, USA George Stephanopoulos, MIT, USA Jan Thullie, Politechnika Slaska, Poland Gilles Trystram, GénIAl – ENSIA, France
CAPE for the Users! Rafael Batres, Toyohashi University of Technology, Japan Sylvie Cauvin, IFP, France Gabriella Henning, INTEC, Argentina Andrzej Kraslawski, Lappeenranta University of Technology, Finland Jean-Marc Le Lann, LGC – ENSIACET – INPT, France Jack Ponton, University of Edinburgh, UK Rajagopalan Srinivasan, National University of Singapore, Singapore Lars Von Wedel, AixCAPE, Germany
CAPE and Society Arsène Isambert, LGPM-ECP, France Emilia Kondili, TEI of Piraeus, Greece Sandro Macchietto, Imperial College London, UK Peter Mizsey, Budapest University of Technology and Economics, Hungary Yuji Naka, Tokyo Institute of Technology, Japan Claudio Oller do Nascimento, Universidade de São Paulo, Brazil Valentin Plesu, University Politehnica of Bucharest, Romania En Sup Yoon, Seoul National University, Korea
CAPE in Education David Bogle, University College London, UK Marie Debacq, CNAM, France Urban Gren, Chalmers University of Technology, Sweden Daniel Lewin, Technion, Israel
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National Organising Committee
Chairman Bertrand Braunschweig, IFP
Members Didier Caudron, Sanofi Pasteur Stéphane Déchelotte, ProSim Pascal Floquet, LGC – ENSIACET – INPT Arsène Isambert, LGPM – ECP Christian Jallut, LAGEP – Université Lyon 1 – CPE Xavier Joulia, LGC – ENSIACET – INPT Christian Latgé, CEA Frédérique Léandri, IFP Francis Luck, Total Francis Nativel, Axens Hervé Roustan, Alcan Philippe Vacher, RSI
Symposium Secretariat ESCAPE 18 c/o COLLOQUIUM 12 rue de la Croix-Faubin 75011 Paris – France
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
1
Model Parameterization Tailored to Real-time Optimization Benoît Chachuat,a Bala Srinivasan,b Dominique Bonvina a
Laboratoire d’Automatique, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 9, CH-1015 Lausanne, Switzerland b Département de Génie Chimique, Ecole Polytechnique de Montréal, C.P. 6079 Succ. centre ville, Montréal (QC), H3C 3A7, Canada
Abstract Challenges in real-time process optimization mainly arise from the inability to build and adapt accurate models for complex physico-chemical processes. This paper surveys different ways of using measurements to compensate for model uncertainty in the context of process optimization. A distinction is made between model-adaptation methods that use the measurements to update the parameters of the process model before repeating the optimization, modifier-adaptation methods that adapt constraint and gradient modifiers, and direct-input-adaptation methods that convert the optimization problem into a feedback control problem. This paper argues in favor of modifier-adaptation methods, since it uses a model parameterization, measurements, and an update criterion that are tailored to the tracking of the necessary conditions of optimality. Keywords: Measurement-based optimization; Real-time optimization; Plant-model mismatch; Model adaptation; Model parameterization.
1. Introduction Optimization of process performance has received attention recently because, in the face of growing competition, it represents the natural choice for reducing production costs, improving product quality, and meeting safety requirements and environmental regulations. Process optimization is typically based on a process model, which is used by a numerical procedure for computing the optimal solution. In practical situations, however, an accurate process model can rarely be found with affordable effort. Uncertainty results primarily from trying to fit a model of limited complexity to a complex process. The model-fitting task is further complicated by the fact that process data are usually noisy and signals do not carry sufficient excitation. Therefore, optimization using an inaccurate model might result in suboptimal operation or, worse, infeasible operation when constraints are present [8]. Two main classes of optimization methods are available for handling uncertainty. The essential difference relates to whether or not measurements are used in the calculation of the optimal strategy. In the absence of measurements, a robust optimization approach is typically used, whereby conservatism is introduced to guarantee feasibility for the entire range of expected variations [18]. When measurements are available, adaptive optimization can help adjust to process changes and disturbances, thereby reducing conservatism [9]. It is interesting to note that the above classification is similar to that found in control problems with the robust and adaptive techniques. An optimal solution has to be feasible and, of course, optimal. In practice, feasibility is often of greater importance than optimality. In the presence of model uncertainty,
2
B. Chachuat et al.
feasibility is usually enforced by the introduction of backoffs from the constraints. The availability of measurements helps reduce these backoffs and thus improve performance [6]. Generally, it is easier to measure or infer constrained quantities (e.g. temperature or pressure) than estimate gradients of the cost and constrained quantities. These elements clearly set a priority of actions in the framework of adaptive optimization. This paper discusses three major approaches in adaptive optimization that differ in the way adaptation is performed, namely (i) model-adaptation methods, where the measurements are used to refine the process model, and the updated model is used subsequently for optimization [7,17]; (ii) modifier-adaptation methods, where modifier terms are added to the cost and constraints of the optimization problem, and measurements are used to update these terms [8,10,20]; and (iii) direct-input-adaptation methods, where the inputs are adjusted by feedback controllers, hence not requiring optimization but a considerable amount of prior information regarding control design [9,21,25]. These approaches are surveyed and compared in the first part of the paper. A critical discussion follows, which argues in favor of modifier-adaptation methods that share many advantages of the other methods. An important issue not addressed herein concerns the availability of reliable measurements. Also, note that the intended purpose of the models presented here is optimization and not prediction of the system behavior.
2. Static Optimization Problems For continuous processes operating at steady state, optimization typically consists in determining the operating point that minimize or maximize some performance of the process (such as minimization of operating cost or maximization of production rate), while satisfying a number of constraints (such as bounds on process variables or product specifications). In mathematical terms, this optimization problem can be stated as follows:
( ) ( ) := g ( , y ) 0
minimize: p ( ) := p , y p
subject to: G p where n and y p respectively; n
ny
ny ny
gp :
(1)
p
stand for the process input (set points) and output vectors,
p : n ng
p
is
the
plant
performance
index;
and
is the vector of constraints imposed on the input and output
variables. In contrast to continuous processes, the optimization of batch and semi-batch processes consists in determining time-varying control profiles, u(t), t 0 t t f . This typically involves solving a dynamic optimization problem, possibly with path and terminal constraints. A practical way of solving such problems is by parameterizing the control profiles using a finite number of parameters , e.g., a polynomial approximation of u(t) on finite elements. Although the process is dynamic in nature, a static map can be used to describe the relationship between the process inputs and the outcome of the batch y(t f ) . Hence, the problem can be regarded as a finite-dimensional static optimization problem similar to (1), and the optimization approaches discussed in the following sections can also be used in the framework of run-to-run optimization of
Model Parameterization Tailored to Real-Time Optimization
3
batch and semi-batch processes (see, e.g., [9]). In practice, the mapping relating the process inputs and outputs is typically unknown, and only an approximate model is available,
y = f ( , ) with y
ny
(2)
representing the model outputs, and n the model parameters, and n
f : n n y the input-output mapping. Accordingly, an approximate solution of problem (1) is obtained by solving the following model-based optimization problem:
minimize: ( , ) := ( , y, )
subject to: y = f ( , )
(3)
G ( , ) := g ( , y, ) 0
Provided that the objective and constraint functions in (1) and (3) are continuous and the feasible domains of these problems are nonempty and bounded, optimal solution points p and are guaranteed to exist for (1) and (3), respectively [2]. Note that such optimal points may not be unique due to nonconvexity. The KKT conditions – also called necessary conditions of optimality (NCO) – must hold at an optimal solution point provided that the active constraints satisfy a regularity condition at that point [2]. For Problem (3), the KKT conditions read:
(
)
G , 0, 0 ,
(
)
(
)
G , + , = 0, G , = 0
(
(4)
)
n
where g is the vector of Lagrange multipliers. The KKT conditions involve the G , which are denoted collectively by subsequently. quantities G, and
3. A Classification of Real-time Optimization Schemes Real-time optimization (RTO) schemes improve process performance by adjusting selected optimization variables using available measurements. The goal of this closedloop adaptation is to drive the operating point towards the true plant optimum in spite of inevitable structural and parameter model errors. RTO methods can be classified in different ways. This section presents one such classification based on the parameters that can be adapted, as illustrated in Fig. 1; note that repeated numerical optimization is used in the methods of columns 1 and 2, but not in those of column 3. 3.1. Model-Adaptation Methods The standard way of devising a RTO scheme is the so-called two-step approach [1], also referred to as repeated identification and optimization in the literature. In the first step, the values of (a subset of) the adjustable model parameters are estimated by using the available process measurements. This is typically done by minimizing the lack of closure in the steady-state model equations (2), such as the weighted sum of squared errors between measured outputs y p and predicted outputs y [17].
4
B. Chachuat et al.
Figure 1: Optimization scenarios that use measurements to adapt for feasibility and optimality.
A key, yet difficult, decision in the model-update step is to select the parameters to be updated. These parameters should be identifiable, represent actual changes in the process, and contribute to approach the process optimum; also, model adequacy proves to be a useful criterion to select candidate parameters for adaptation [8]. Clearly, the smaller the subset of parameters, the better the confidence in the parameter estimates, and the lower the required excitation. But too low a number of adjustable parameters can lead to completely erroneous models, and thereby to a false optimum. In the second step, the updated model is used to determine a new operating point, by solving an optimization problem similar to (3). Model-adaptation methods can be written generically using the following two equations (see Fig. 2):
(
)
k = k1 + upd y p ( k1 ) y( k1 , k1 ) ,
(5)
= opt (
(6)
k
k
)
where upd is the map describing the model-update step, such that upd (0) = 0 ; opt , the map describing the optimization step. Note that the handles for correction are a subset of the adjustable model parameters . The use of auxiliary measurements ( y p ) presents the advantage that any available measurement can be used.
Figure 2. Model-adaptation method: Two-step approach
5
Model Parameterization Tailored to Real-Time Optimization
It is well known that the interaction between the model-update and reoptimization steps must be considered carefully for the two-step approach to achieve optimal performance. In the absence of plant-model mismatch and when the parameters are structurally and practically identifiable, convergence to the plant optimum may be achieved in one iteration. However, in the presence of plant-model mismatch, whether the scheme converges, or to which operating point the scheme converges, becomes anybody's guess. This is due to the fact that the update objective might be unrelated to the cost or constraints in the optimization problem, and minimizing the mean-square error in y may not help in our quest for feasibility and optimality. To alleviate this difficulty, Srinivasan and Bonvin [23] presented an approach where the criterion in the update problem is modified to account for the subsequent optimization objective. Convergence under plant-model mismatch has been addressed by several authors [3,8]; it has been shown that an optimal operating point is reached if model adaptation leads to a matching of the KKT conditions for the model and the plant. Theorem 1. Let the parameter adaptation (5) be such that the plant measurements p match those predicted by the model, . Then, upon convergence, the model-adaptation scheme (5-6) reaches an (local) optimum operating point of the plant. A proof of this result is readily obtained from the assumption that the KKT conditions predicted by the model equal those achieved by the plant. With such a matching, the converged solution corresponds to a (local) plant optimum. Although Theorem 1 is straightforward, the KKT-matching assumption is difficult to meet in practice. It requires an “adequate” parameterization so that all the components of the KKT conditions can match, as well as “adequate” measurements and an “adequate” update criterion. 3.2. Modifier-Adaptation Methods In order to overcome the modeling deficiencies and to handle plant-model mismatch, several variants of the two-step approach have been presented in the literature. Generically, they consist in modifying for the cost and constraints of the optimization problem for the KKT conditions of the model and the plant to match. The optimization problem with modifiers can be written as follows: ( , ) := ( , ) + T minimize: ( , ) := G ( , ) + G + GT k 0 subject to: G
(
where G
ng
)
(7)
is the constraint bias, n the cost-gradient modifier, and
n n
G g the constraint-gradient modifier; these modifiers are denoted collectively by subsequently. • The constraint bias G represents the difference between the measured and predicted constraints, G := G p ( ) G( , ) , evaluated at the previous operating point k . Adapting only G leads to the so-called constraint-adaptation scheme [6,8]. Such a scheme is rather straightforward and corresponds to common industrial practice [17]. • The cost-gradient modifier represents the difference between the estimated and predicted values of the cost gradient, T := p , evaluated at the previous
6
B. Chachuat et al.
operating point k . The pertinent idea of adding a gradient modifier to the cost function of the optimization problem dates back to the work of Roberts [19] in the late 1970s. Note that it was originally proposed in the framework of two-step methods to better integrate the model update and optimization subproblems and has led to the so-called ISOPE approach [4]. • The constraint-gradient modifier G , finally, represents the difference between the estimated and predicted values of the constraint gradients, T := G p G , G
evaluated at the previous operating point k . The idea of adding such a first-order modifier term to the process-dependent constraints, in addition to the constraint bias G , was proposed recently by Gao and Engell [12]. This modification allows matching, not only the values of the constraints, but also their gradients. Overall, the update laws in modifier-adaptation methods can be written as (see Fig. 3):
(
k1 , ) k = k1 + upd p ( k1 ) (
= opt ( k
k
)
)
(8) (9)
:= G, G where , , with , G as defined in Problem (7); and the modifier update map, upd , is such that upd (0) = 0 . The handles for correction are the modifier parameters instead of used in the context of model-adaptation schemes. Also, the measurements p required to make the adaptation are directly related to the KKT conditions; auxiliary measurements are not used in this framework. Observe the one-toone correspondence between the number of measurements/estimates and the number of adjustable parameters. In particular, identifiability is automatically satisfied, and so are the KKT-matching conditions.
Figure 3. Modifier-adaptation method: Matching the KKT conditions
Modifier-adaptation methods possess nice theoretical properties, as summarized by the following theorem. Theorem 2. Let the cost and constraint functions be parameterized as in Problem (7). Also, let the information on the values of p be available and used to adapt the modifiers . Then, upon convergence, the modifier-adaptation scheme (8-9) reaches an (local) optimum operating point of the plant.
Model Parameterization Tailored to Real-Time Optimization
7
A proof of this result is easily obtained by noting that, upon convergence, the modified in (7) match the plant constraints G , and the gradients of the modified constraints G p cost and constraint functions match those of the plant (see also [10]). It follows that the active set is correctly determined and the converged solution satisfies the KKT conditions. Hence, there is a close link between the model- and modifier-adaptation methods in that the parameterization and the update procedure are both intended to match the KKT conditions. Essentially, modifier-adaptation schemes use a model-predictive control with a one-step prediction horizon. Such a short horizon is justified because the system is static. However, since the updated modifiers are valid only locally, modifieradaptation schemes require some amount of filtering/regularization (either in the modifiers or in the inputs) to avoid too aggressive corrections that may destabilize the system. 3.3. Direct-Input-Adaptation Methods This last class of methods provides a way of avoiding the repeated optimization of a process model by transforming it into a feedback control problem that directly manipulates the input variables. This is motivated by the fact that practitioners like to use feedback control of selected variables as a way to counteract plant-model mismatch and plant disturbances, due to its simplicity and reliability compared to on-line optimization. The challenge is to find functions of the measured variables which, when held constant by adjusting the input variables, enforce optimal plant performance [19,21]. Said differently, the goal of the control structure is to achieve a similar steadystate performance as would be realized by an (fictitious) on-line optimizing controller. In the presence of uncertainty, the inputs determined from off-line solution of problem (3) for nominal parameter values satisfy the NCO (4) but typically violate the NCO related to the plant itself. Hence, a rather natural idea is to correct the input variables so as to enforce the NCO for the plant [1,9,14]; in other words, the controlled variables are chosen as the NCO terms, with the corresponding set points equal to zero. Tracking of the NCO (4) consists of three steps: (i) determining the active set (positivity condition on Lagrange multipliers), (ii) following the active constraints, and (iii) pushing the sensitivity to zero. Determining the active set requires a switching strategy, whereby a constraint is included in the active set when it is attained, and deactivated when its Lagrange multiplier goes negative [29]. This switching logic renders the scheme more complex, and in the interest of simplicity, it may be assumed that the active constraints do not change. Note that such an assumption is always verified in the neighborhood of an optimal solution and is observed in many practical situations. Once the active set is known, the inputs are split into : (i) constraints-seeking directions that are used to track the active constraints, and (ii) sensitivity-seeking directions that are adapted to force the reduced gradients to zero. The active constraints G ap and the
G ap I P+ P , with P := , need to be measured. Since, in general, the constraint terms are easily measured, or can be reliably estimated, adjusting the inputs in the constraint-seeking directions to track the active constraints is rather straightforward [4,25,27]. Adjusting the sensitivity-seeking directions is more involved, mainly due to the difficulty in the measurement of the gradient terms. François et al. [9] proposed a two-time-scale adaptation strategy, wherein adaptation in the sensitivity-seeking directions takes place at a much slower rate than in the constraint-seeking directions.
reduced cost gradient r p :=
p
8
B. Chachuat et al.
Direct-input-adaptation methods obey the following equations (see Fig. 4):
(
k = k1 + con G ap ( k1 ), r p ( k1 )
(G
a p
)
(
( k ), r p ( k ) = swi p ( k )
)
)
(10) (11)
where con is the map describing the controller, such that con (0, 0) = 0 ; swi , the map describing the switching logic for determination of the active set. The handles for correction are the process inputs , i.e., no specific parameterization is required here. Both the active constraints and the reduced cost gradient are forced to zero, e.g., with a discrete integral-type controller.
Figure 4. Direct-input-adaptation method: Tracking the NCO using control
Direct-input-adaptation methods also possess nice theoretical properties, as summarized by the following theorem. Theorem 3. Let the information on the values of p be available and used to adapt the inputs and the active set given by (10-11). Then, upon convergence, the direct-inputadaptation scheme (10-11) reaches an (local) optimum operating point of the plant. Note that the active process constraints and reduced gradients are both zero upon convergence. Moreover, since the positivity of the Lagrange multipliers is guaranteed by the switching logic, the active set is correctly identified and the NCO are satisfied. The key question lies in the design of the controller. Unlike optimization-based schemes, the required smoothening is provided naturally via appropriate controller tuning. 3.4. Evaluation of the various methods A systematic approach for evaluating the performance of adaptive optimization schemes, named the extended cost design, has been presented in [30]. It incorporates measures of both the convergence rate and the effect of measurement noise. Interestingly, it is shown that in the presence of noise, a standard two-step algorithm may perform better, in terms of the proposed metric, than modified algorithms compensating for plant-model mismatch such as ISOPE. Another approach to performance characterization for adaptive optimization has been proposed in [15], which considers the backoff from active inequality constraints required to ensure feasibility. Therein, better adaptive optimization approaches produce smaller backoffs.
4. Use of Measurements for Feasible and Optimal Operation This section discusses the two main rows in Fig.1. The feasibility issue is addressed first, and various gradient estimation techniques are summarized next. 4.1. Feasible Operation In practical applications, guaranteeing feasible operation is often more important than achieving the best possible performance. Hence, first priority is given to meeting the
Model Parameterization Tailored to Real-Time Optimization
9
process constraints (such as safety requirements and product specifications) and only second priority to improving process performance in terms of the objective function. Interestingly, the results of a variational analysis in the presence of small parametric error support the priority given to constraint satisfaction over the sensitivity part of the NCO [6]. More specifically, it has been shown that, in addition to inducing constraint violation, failure to adapt the process inputs in the constraint-seeking directions results in cost variations in the order of the parameter variations ; in contrast, failure to adapt the inputs in the sensitivity-seeking directions gives cost variations in the order of 2 only. The ability to guarantee feasible operation is addressed next for the three classes of methods presented above. In model-adaptation methods, since the plant constraints are predicted by the process model, constraint matching – but not necessarily full KKT matching – is needed to guarantee feasibility; however, this condition may be difficult to meet, e.g., when the model is updated by matching a set of outputs not directly related to the active constraints. With modifier-adaptation methods, feasibility is guaranteed upon convergence, provided that all the constraint terms are measured [6]; yet, ensuring feasibility does not necessarily imply that the correct active set has been determined due to the use of possibly inaccurate cost and constraint gradients, e.g., when gradient modifiers are not considered. Finally, in direct-input-adaptation methods, feasibility is trivially established when the active set is known and does not change with the prevailing uncertainty. However, as soon as the active set changes, tracking the current set of active constraints may lead to infeasibility. A switching logic can be used to remove this limitation, but it requires experimental gradient information to be available; the use of a barrier-penalty function approach has also been proposed [26]. If feasibility cannot be guaranteed, conservatism can be introduced in the form of constraint backoffs. Such backoffs are also introduced to enforce feasibility when some of the constraints are difficult to measure. 4.2. Gradient Estimation Taking a system from a feasible to an optimal operating point requires accurate gradient information. In model-adaptation schemes, since the updated model is used to estimate the gradient, convergence is relatively fast. In the other two schemes, the gradient information has to be estimated experimentally, thereby slowing down convergence significantly. Perhaps the major bottleneck in modifier- and direct-input-adaptation schemes lies in the estimation of this gradient information. The finite-difference scheme used in the original ISOPE paper [19] is known to be inefficient for large-scale, slow and noisy processes. Hence, alternative techniques have been developed, which can be classified as either model-based approaches or perturbation-based approaches. Model-based approaches allow fast derivative computation by relying on a process model, yet only approximate derivatives are obtained. In self-optimizing control [12,21], the idea is to use a plant model to select linear combinations of outputs, the tracking of which results in “optimal“ performance, also in the presence of uncertainty; in other words, these linear combinations of outputs approximate the process derivatives. Also, a way of calculating the gradient based on the theory of neighbouring extremals has been presented in [13]; however, an important limitation of this approach is that it provides only a first-order approximation and that the accuracy of the derivatives depends strongly on the reliability of the plant model. The idea behind perturbation methods is to estimate process derivatives using variations in the operating point. Extremum-seeking control [1,14] attempts to obtain the cost
10
B. Chachuat et al.
sensitivity by superposing a dither signal to the plant inputs. In dynamic model identification, the plant is approximated by a dynamic model during the transient phase between two successive steady states [16,31,11]. Since the derivatives are calculated from the identified dynamic model, the waiting time needed for reaching a new steady state is avoided. Other perturbation-based approaches, which remove the disadvantage of requiring additional dynamic perturbations, consist in using current and past (steadystate) measurements to compute a gradient estimate based on Broyden’s formula [16]. For the case of multiple identical units operating in parallel, Srinivasan considered perturbations along the unit dimension rather than the time dimension, thereby allowing faster and more accurate derivative estimates [22]. In principle, the smaller the difference between the operating points, the more accurate the derivative approximation, but conditioning issues might arise due to measurement noise and plant disturbances. A way of avoiding this latter deficiency is presented in [10].
5. Discussion In this section, we take a critical look at the three classes of adaptive optimization methods described above in terms of various criteria. We also argue in favor of modifier-adaptation methods, in the sense that they provide a parameterization that is tailored to the matching of the KKT conditions. The analysis presented in Table 1 shows many facets of the problem. It is interesting to see that modifier-adaptation methods can be positioned between the model-adaptation methods and direct-input-tracking methods; several attractive features are shared between the first and second columns, while other features are shared between the second and third columns. The methods differ mainly in the handles and in the measurements that are used for correction. The major drawback of model-adaptation schemes is that KKT matching is required for convergence to a (local) plant optimum, which can be very difficult to satisfy with the (arbitrary) parameterization and (arbitrary) auxiliary measurements y p . In comparison, modifier-adaptation methods resolve the challenging task of selecting candidate parameters for adaptation by introducing the modifiers as handles. Also, the measurements p are directly related to the KKT conditions, and their number is equal to that of the handles , i.e., there results a square update problem. Hence, since these parameters are essentially decoupled, no sophisticated technique is required for the update of . Moreover, KKT matching becomes trivial, and reaching a (local) plant optimum is guaranteed upon convergence. This leads us to argue that modifier-adaptation methods possess the “adequate” parameterization and use the “adequate” measurements” for solving optimization problems on-line. Direct-input-adaptation methods differ from model- and modifier-adaptation methods in that a process model is not used on-line, thus removing much of the on-line complexity. Another important element of comparison is the use of experimental gradient information. The modifier- and direct-input-adaptation methods make use of experimental gradients to guarantee (local) optimality. However, obtaining this information is usually time consuming and slows down the entire adaptation scheme. Note that the use of an updated process model gives the ability to determine changes in the active set and typically provides faster convergence. Yet, in practice, the convergence of the model- and modifier-adaptation methods is often slowed down by the introduction of filtering that is required to avoid unstable behavior that would result because the corrections are local in nature.
11
Model Parameterization Tailored to Real-Time Optimization
Model-adaptation methods
Modifier-adaptation methods
Direct-input adaptation methods
Adjustable parameters
Dimension of parameters
n
ng + n (ng + 1)
n
Measurements
yp
p
p
Dimension of measurements
ny
ng + n (ng + 1)
ng + n (ng + 1)
p
None
y yp
Update criterion
2
2
Exp. gradient estimation
No
Yes
Yes
Repeated optimization
Yes
Yes
No
On-line use of process model
Yes
Yes
No
Model predictive
Model predictive
Any
Smoothening
External filter
External filter
Controller tuning
Choice of active sets
Optimization
Optimization
Switching logic
Requirement for feasibility (no gradient information)
Constraint matching
None
Correct active set
Requirement for optimality (with gradient information)
KKT matching
None
None
Controller type
Table 1. Comparison of various real-time optimization schemes
6. Conclusions This paper provides a classification of real-time optimization schemes and analyzes their ability to use measurements to track the necessary conditions of optimality of the plant. The similarities and differences between the various schemes are highlighted, and it is shown that modifier-adaptation schemes use a parameterization, measurements, and an update criterion that are tailored to the matching of KKT conditions. To improve the performance of adaptive optimization, it may be useful to combine specific features of the various methods. For example, the combination of model adaptation (which ensures fast convergence for the first few iterations and detects changes in the active set) with direct-input adaptation (which provides the necessary gradients in the neighborhood of the plant optimum) has been demonstrated in [24]. Another interesting combination would be to use a modifier-adaptation approach at one time scale and perform model adaptation at a slower rate, thus giving rise to a two-timescale adaptation strategy.
References 1. Ariyur K. B. and Kristic M., “Real-Time Optimization by Extremum Seeking Feedback”, Wiley, 2003. 2. Bazaraa M. S., Sherali H. D. and Shetty C. M., “Nonlinear Programming: Theory and Algorithms”, second ed., John Wiley and Sons, New York, 1993. 3. Biegler L. T., Grossmann I. E. and Westerberg A. W., “A note on approximation techniques used for process optimization”, Comput Chem Eng 9(2):201-206, 1985.
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4. Bonvin D. and Srinivasan B., “Optimal operation of batch processes via the tracking of active constraints”, ISA Trans 42(1):123-134, 2003. 5. Brdys M. A. and Tatjewski P., “Iterative Algorithms For Multilayer Optimizing Control”, World Scientific Pub Co, London UK, 2005. 6. Chachuat B., Marchetti A. and Bonvin D., “Process optimization via constraints adaptation”, J Process Control, in press. 7. Chen C. Y. and Joseph B., “On-line optimization using a two-phase approach: an application study”, Ind Eng Chem Res 26:1924-1930, 1987. 8. Forbes J. F. and Marlin T. E., “Model accuracy for economic optimizing controllers: the bias update case”, Ind Eng Chem Res 33:1919-1929, 1994. 9. François G., Srinivasan B. and Bonvin D., “Use of measurements for enforcing the necessary conditions of optimality in the presence of constraints and uncertainty”, J Process Control 15:701-712, 2005. 10. Gao W. and Engell S., “Iterative set-point optimization of batch chromatography”, Comput Chem Eng 29(6):1401-1409, 2005. 11. Golden M. P. and Ydstie B. E., “Adaptive extremum control using approximate process models”, AIChE J 35(7):1157-1169, 1989. 12. Govatsmark M. S. and Skogestad S., “Selection of controlled variables ans robust setpoints”, Ind Eng Chem Res 44(7):2207-2217, 2005. 13. Gros S., Srinivasan B. and Bonvin D., “Static optimization via tracking of the necessary conditions of optimality using neighboring extremals”, Proc ACC 2005, Portland OR, pp. 251-255, 2005. 14. Guay M. and Zang T., “Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainty”, Automatica 39:1283–1294, 2003. 15. de Hennin S. R., Perkins J. D. and Barton G. W., “Structural descisions in on-line optimization”, Proc Int Conf PSE‘94, pp. 297-302, 1994. 16. Mansour M. and Ellis J. E., “Comparison of methods for estimating real process derivatives in on-line optimization”, Appl Math Mod 27:275-291, 2003. 17. Marlin T. E. and Hrymak A. N., “Real-time operations optimization of continuous process”, Proc 5th Int Conf on Chemical Process Control (CPC-5), Tahoe City NV, 1997. 18. Mönnigmann M. and Marquardt W., “Steady-state process optimization with guaranteed robust stability and feasibility”, AIChE J 49(12):3110-3126, 2003. 19. Morari M., Stephanopoulos G. and Arkun Y., “Studies in the synthesis of control structures for chemical processes, Part I”, AIChE J 26(2):220-232, 1980. 20. Roberts P. D., “An algorithm for steady-state system optimization and parameter estimation”, Int J Syst Sci 10:719-734, 1979. 21. Skogestad S. “Plantwide control: The search for the self-optimizing control structure”. J Process Control 10:487–507, 2000. 22. Srinivasan B., “Real-time optimization of dynamic systems using multiple units”, Int J Robust Nonlinear Control 17:1183–1193, 2007. 23. Srinivasan B. and Bonvin D., “Interplay between identification and optimization in run-torun optimization schemes”, Proc ACC 2002, Anchorage AK, pp. 2174–2179, 2002. 24. Srinivasan B. and Bonvin D., “Convergence analysis of iterative identification and optimization schemes”, Proc ACC 2003, Denver CO, pp. 1956-1961, 2003. 25. Srinivasan B., Primus C. J, Bonvin D. and Ricker N. L., “Run-to-run Optimization via Constraint Control”, Control Eng Pract 9(8):911-919, 2001. 26. Srinivasan B., Biegler L.T. and Bonvin D., “Tracking the necessary conditions of optimality with changing set of active constraints using a barrier-penalty function”, Comput Chem Eng 32(3):572-579, 2008. 27. Stephanopoulos G. and Arkun Y., “Studies in the synthesis of control structures for chemical processes, Part IV”, AIChE J 26(6):975-991, 1980. 28. Tatjewski P., “Iterative optimizing set-point control–The basic principle redesigned”, Proc 15th IFAC World Congress, Barcelona, 2002.
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29. Woodward L., Perrier M. and Srinivasan B., “Multi-unit optimization with gradient projection on active constraints”, Proc 8th Int Symp on Dynamics and Control of Process Systems (DYCOPS), Vol 1, pp. 129-134, 2007. 30. Zhang Y. and Forbes J. F., “Extended design cost: A performance criterion for real-time optimization systems”, Comput Chem Eng 24:1829-1841, 2000. 31. Zhang Y. and Forbes J. F., “Performance analysis of perturbation-based methods for realtime optimization”, Can J Chem Eng 84:209-218, 2006.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Challenges for multi-scale modeling of multiple failure modes in microelectronics Juergen Auersperg, Bernhard Wunderle, Rainer Dudek, Hans Walter, Bernd Michel Abstract Design studies of electronics components on the basis of parameterized Finite Element Models and DoE/RSM-approaches (Design of Experiments/Response Surface Methods) are more and more performed for optimizations at early phases of the product development process. That is why electronics components especially in the field of RF (Radio Frequency), optoelectronics, high temperature and power applications are often exposed to extreme thermal environmental conditions, mechanical shock and vibrations. However, a continuous industry drive for miniaturization and function integration forces the development of feature sizes down to the nanometer regime. Simultaneously, the well known thermal expansion mismatch problem of the several materials, residual stresses generated by several steps of the manufacturing process and various kinds of inhomogeneity attribute to interface delamination, chip cracking and fatigue of interconnects, in particular. The applied methodologies typically base on classical stress/strain strength evaluations or/and life time estimations of solder interconnects using modified Coffin-Manson approaches. Recent studies show also how the evaluation of mixed mode interface delamination phenomena, classical strength hypotheses along with fracture mechanics approaches and thermal fatigue estimation of solder joints can simultaneously be taken into account. Over and above that, new materials will be introduced especially in Back-end of line (BEoL) layers of advanced Cu/Low-k 90, 45, … , 22 nanometer CMOS (Complementary Metal-Oxide Semiconductor) technologies. So, black diamond-I or black diamond-II as new materials are increasingly porous and interconnect materials or new functional layers come up as nano-particle filled high-tech compounds. Thus, it is to be checked whether it can be handled as homogeneous materials anymore. For sure, this will have most important impacts on the thermo-mechanical performance of the total IC (Integrated Circuit) tack. The problems appearing during packaging of CMOS-ICs at least showed that IC and package reliability are strongly interacted. Thus, the challenge for simulations in this field is not only the wide range of structural dimensions but also, the different approaches that have to be combined: Molecular or atomistic level simulations and “conventional” Finite Element Analysis (FEA) with global-local modeling, substructuring as well as fracture and damage mechanics, cohesive zone models, viscoelasticity, plasticity and creep of homogeneous constitutive models. Furthermore, it is known that multiple failure modes competitively act simultaneously wherefore, design optimizations have to incorporate all failure modes that are essential for the overall reliability. Moreover, considering that variables of the simulation models are naturally stochastic parameters leads to the consequence that all results show also scattering. First steps towards robust designs show the potential of the utilized FEA-based RSM/DOE approach to evaluate the thermo-mechanical reliability of various electronics assemblies in a more complex way giving at the same time a more solid basis for design optimizations.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Design and integration of policies to achieve environmental targets René Bañares-Alcántara Department of Engineering Science, University of Oxford, UK
Abstract Few problems are as urgent and important as climate change. Climate change mitigation policies are geographically and culturally dependent given the variability of resources, of access to technology and of national political constraints such as ensuring energy security, affordability and social acceptability. Thus, climate change mitigation hinges on devising integrated policies involving many mutually reinforcing and coordinated efforts in order to exploit synergies between policy tools and to avoid policy conflicts. The possible roles of chemical engineers in this problem are: • a traditional one, as providers of improved and new technologies, e.g. in the development of CO2 capture technologies, • a less conventional and recent one, as participants in the framing and development of policies, e.g. influencing the formulation of the UK energy policy [Clift 06], • a future role as providers of tools, methods and systems to support policy formulation, i.e. the development of effective and acceptable courses of action to reach explicit goals. The talk will address the last role. Important insights into a policy formulation methodology can be elicited from engineering design. It will be argued that engineering design and synthesis methodologies offer a productive framework and a suite of practical tools for supporting policy design and integration, i.e. providing alternative configurations of policy tools to use and how to schedule their phasing and implementation in order to achieve a reduction in greenhouse gas emissions. However, process and policy design are not identical and, as a result, complementary approaches have to be used to take into account their differences, in particular the pervasiveness of non-quantifiable factors. These ideas will be exemplified with two support systems being developed for energy and transport policy formulation.
References Clift, R. “Sustainable development and its implications for chemical engineering”. Chemical Engineering Science 61:4179-4187, 2006.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Computational chemical engineering modeling applied to energy and reactor design Luc Nougier IFP, France
Abstract Chemical engineering is the combination of physical, chemical, biological …operations on an energy or chemical plant. For process design, we have to carry out optimisations based on a multiple of parameters all the more so since the needs of processes in industry change very rapidly. These industries have to integrate new constraints linked to the energy cost and the environmental impact coupled with a need for more and more technical product. Chemical engineering will play a key role to maintain the efficiency of the industry in a global market in which the processes offer become more and more technological and has to take into account : . • higher system integration to minimised energy consumption by coupling different process steps (ie : coupling of endothermal and exothermal steps, reaction and separation….), . • better optimisation of units design, . • higher product selectivity to avoid or limit by-product, . • production of new products. To achieve these new developments the approach cover a large domain of technical disciplines and also a multiscale approach in time and length. This new complexity require to increase the relative weight of modeling and scientific calculation in the process development. For exemple, CFD calculation is currently used for the development of reactor technologies and reactor internal, but most of the time it is difficult to couple hydrodynamic modelisation and reaction modelisation. A lot of improvement are expected by coupling these two approaches. The molecular modelisation has also a large potential in process development and has to be coupled with more classical approach. For process integration, the thermodynamic optimisation is very useful mainly for developing new processes (pinch technology). The modeling tools have to be used in all the steps of process development taking into account a multiscale approach and without forgetting the measurement technologies needed for model validation.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Curricular and pedagogical challenges for enhanced graduate attributes in CAPE Ian T Camerona, Daniel R Lewinb a. School of Engineering, The University of Queensland, Brisbane, AUSTRALIA, 4072 b. PSE Research Group, Dept Chemical Engineering, Technion, Haifa 32000, ISRAEL
Extended Abstract Computer Aided Process Engineering (CAPE) undergirds and informs a wide range of decision making in the product and process life cycle. Life cycle phases that span the planning and conceptualization of product and process, through research and development and then onto design, construction, operation and decommissioning are permeated by CAPE activities. The importance of CAPE activities and their central role in the global engineering enterprise cannot be underestimated. These activities require the use of techniques and tools for informed decision making are shown in Figure 1.
EIA models
Finance models
Enviro
Prelim Elementary flowsheets flowsheets Pilot Physical properties
Logistics Optimization RCM models models
Flowsheet models
Planning Decon
Control models
Bioremed
at e R em ed i
D ec om
m
is si on
CFD
pe ra te
Molecular modelling C on ce pt
Nano
R &D
Reaction networks
CPM
Mechanical CFD
Micro
CPM
SCOR models
O
Meso
RMgt
D e de tail si ed gn
Macro
CPM
In st al l
Scenario planning
St ra te gi c
Length-time scale
Mega
Life cycle phase Figure 1 Some CAPE application areas across the life cycle phases
Yet, how well do we tackle the challenges of CAPE in curriculum design and deployment in higher education? What are the keys to effective development of graduate attributes and skills in the CAPE domain that can be achieved through innovative curricula and the learning environments that inform, challenge and prepare engineering graduates for work in a “model centric” world? What are the technological and informational forces that are rapidly shaping the way engineering is practised in the global context?
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I.T. Cameron and D.R. Lewin
In this presentation, the authors seek to address some of these questions by reference to current trends in educational practice and the application of active learning principles that have been developed, deployed and assessed at institutions in Australia, Israel and elsewhere. In most cases these approaches have found extensive use over many years. It is vital that the debate is centred not just on individual, isolated courses that touch on some aspects of the CAPE issue, but that we start with holistic or systems thinking on curriculum development that provides integration and cohesion in the curriculum and leads to graduate attributes and skills necessary for the next generation of engineers. The curriculum challenge is seen as a cohesive pathway that exercises a strong thread of CAPE activities. Pathways need to build upon basic concepts, integrate new content which illustrates the relationships amongst the principal learning components and then drives that learning with realism and relevance to maintain student engagement. The curriculum challenge has to address the major issues of: • • • •
WHAT has the be learned: the content issue WHY it is to be learned: the rationale HOW it is to be learned: the process and methods WHEN it has to be learned: the pathway to be adopted
In terms of processes, there are numerous options available with the most effective focusing on active learning strategies. Figure 2 illustrates some well documented pedagogic approaches that have been adopted into curriculum delivery. They include problem and project based learning (PBL), project centred curricula (PCC) and Conceive, Design, Implement and Operate (CDIO) approaches.
Figure 2 Active learning pedagogies in curriculum delivery
The authors will explore these key issues and illustrate holistic approaches that impact on curriculum innovation. They will draw examples from a range of applications of these important pedagogic concepts.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
23
Chemical Product Engineering: The 3rd Paradigm Michael Hill M Hill & Associates LLC, Mahwah, New Jersey 07430, USA, and Columbia University, New York, NY 10027, USA
Abstract New chemical products have historically been created by combining a broad knowledge of existing chemical products with scientific experimentation. Since a combinatorial explosion of product options will inevitably limit all experimental techniques, it should be preferable to minimize experimentation through a systematic consideration of product formulations prior to experimentation. This is the essence of product design and engineering. While the design of a chemical product and its manufacturing process are analogous, some critical differences are so fundamental that a new paradigm and new approaches are needed to successfully solve product design problems. In addition, chemical product design requires a methodology or algorithm to apply chemical engineering fundamentals. Product design techniques should draw largely on heuristics when data are limited, followed by more detailed calculations when data become available. Significant work is still needed to establish a comprehensive generic methodology for engineering chemical products in the absence of complete data. Keywords: Product Design, Product Engineering, Chemical Engineering Paradigm
1. Introduction Chemical Product Engineering and the related area of Chemical Product Design have recently received much attention within the chemical engineering community, with an exponential increase in published papers over the past decade. [1]. A chemical product may consist of an individual chemical, but more frequently it will be a mixture of chemicals with a set formulation and often a set microstructure. Chemical products of industrial interest include performance chemicals, semi-conductors, paints, cosmetics, inks, pharmaceuticals, personal care products, household products, and foods. [2,3] While new chemical product development has historically been the domain of chemists, the use of chemical products by consumers invariably involves some transformation of the product due to applied stresses, temperature gradients, physicochemical hydrodynamics, mass transfer, etc., making product use a “process” in the chemical engineering sense. [2,4] Thus the analysis of product behavior ultimately requires the same fundamentals as the analysis of process behavior, and is well suited to study by chemical engineers.
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M. Hill
Notwithstanding the commonalities in the engineering analyses of a chemical product’s behavior and its manufacturing process, there are fundamental differences between the design of a chemical product and its manufacturing process. For example, chemical process design primarily seeks to identify the lowest cost process. Even process related issues like reliability, controllability, and pollution control ultimately translate into costs that must be minimized. Thus, process design easily lends itself to a mathematical treatment. In contrast, chemical product design seeks to obtain the most added value for a product through enhanced product properties. This is far more complex than a mathematical treatment to maximize profit, as profit will depend in some unidentified way upon a complex set of product properties that may not even be identified at the outset. Thus, product design and engineering must not only require new chemical engineering approaches, but even more fundamentally, a new mindset. 2. The 3rd Paradigm While various comments on chemical engineering paradigms have appeared over the years [1,5-7], an overuse of the word paradigm by society in general may have led to some confusion over the meaning of the term. One is reminded of the Dilbert comic strip where every engineer says his project is a paradigm but no one seems to know what that means! The term paradigm was popularized by Thomas Kuhn in his book, The Structure of Scientific Revolutions, first published in 1962. Borrowing the word from linguistics, Kuhn used the term to indicate a specific way of viewing scientific reality, the mindset of a scientific community. Some of Kuhn’s examples include Copernican astronomy, Newtonian dynamics, and quantum mechanics. Each of these paradigms affected the choice of problems that were considered worthy of solution, as well as acceptable approaches to solving those problems. [8] As pointed out by Kuhn, even when paradigms are known to be inadequate, their inadequacies are frequently minimized or even ignored by a scientific community. But if and when a paradigm reaches a crisis where its technical inadequacies are brought into focus, perhaps driven by social requirements, a new paradigm will arise to explain what the prior paradigm could not. Thus the inadequacies of Newtonian mechanics in explaining some observations that had been viewed as anomalies eventually led to Einsteinian dynamics, and the success of this new paradigm in explaining those observations opened up an entirely new set of problems as worthy of consideration. [8] Of course Newtonian mechanics is still useful and may even be considered as a special case of Einsteinian dynamics.
Chemical Product Engineering: The 3rd Paradigm
25
From this perspective, it should be appreciated that originally chemical engineering had no paradigm. Chemical processes were studied within the context of various industries, and so engineers studied processes to make soap, dyestuffs, sugar, etc. Without the mindset of a unifying principle, engineers did not look for and hence failed to see commonality between these processes. [9] Chemical engineering received its first paradigm in 1915 with the introduction of the unit operations concept. [3,9,10] This mindset allowed engineers to recognize commonalities between elements of chemical processes despite their use in different industries. Under this paradigm, chemical engineering was no longer the study of how to manufacture a specific commodity, but rather the study of unit operations. As a consequence, chemical process design became a matter of deciding which sequence of unit operations was most appropriate to manufacture a desired product. While still useful to the present day, the unit operations paradigm proved inadequate for solving some important classes of problems. This awareness led to the emergence of chemical engineering science as a second paradigm in the late 1950’s, as best exemplified by the textbook Transport Phenomena. [3,9-11] This approach taught engineers to analyze problems by thinking in terms of their underlying fundamental chemical and physical sciences, writing mathematical equations to describe the phenomena, and then solving those equations. The chemical engineering science paradigm may also be described as the “first principles” approach. The chemical engineering science paradigm is widely used today. In fact, its application has been broadened by the incorporation of biological science and new information technology tools. But as important as these latter elements have been, they have been incorporated into the existing chemical engineering science paradigm rather than lead to a new mindset. Similarly, specific techniques for solving various classes of chemical engineering problems are not new paradigms, for they fall within the current chemical engineering way of thinking. On the other hand, until recently the chemical engineering community largely ignored all product issues other than purity as irrelevant, focusing exclusively on processing while leaving product development to chemists. In the minds of many, chemical engineering is synonymous with process engineering. Hence product engineering will require a new mindset in addition to new chemical engineering approaches, and should therefore be recognized as a third chemical engineering paradigm, as first hinted in 1988. [9] Of course, product engineering as a paradigm does not preclude other paradigms from emerging, nor does it replace previous paradigms. Process engineering may even be considered as a special case of product engineering.
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But a product engineering mindset is essential if chemical engineers are going to be able to solve problems where both the product and its manufacturing process must be identified, an entirely new and important class of problems. 3. Product Design Methodologies New chemical products have historically been created by combining a broad knowledge of existing chemical products with scientific experimentation. Product development is also at times accelerated through high-throughput experimentation, where large numbers of products are simultaneously made in small quantities, or through experimental design, where statistical techniques reduce the number of experiments performed. Nevertheless, these techniques have their limitations. For example, it is impractical to use high-throughput experimentation to make large numbers of structured products (like emulsions or composite powders) in small quantities. Similarly, experimental design can help determine optimal levels of a specified component but a combinatorial explosion will frequently prevent selection from a list of all potential components. Thus, chemical product development is all too often random trialand-error experimentation at present. However, the systematic identification of problem solutions should be superior to a random identification of solutions, either because better solutions can be identified or because acceptable solutions can be identified sooner or with less resource. So while it is unrealistic to eliminate all experimentation, it would be desirable to minimize experimentation through the introduction of a systematic consideration of product formulations prior to experimentation. From this perspective, the object of product design is to specify a small set of formulations likely to meet the product requirements, and which can be confirmed or refined through experimentation. Thus, chemical product design and engineering should be viewed as a phase of chemical product development that should precede a more focused experimental program. Analogous to chemical process design, chemical product design requires a methodology or algorithm to apply chemical engineering fundamentals. Cussler and Moggridge proposed a generic framework for chemical product design, suggesting a 4-step algorithm: (1) identify customer needs, (2) generate ideas to meet those needs, (3) select among the ideas, and (4) manufacture the product. They also admit that this framework is a simplification that tries to come down on the side of universal applicability rather than effectiveness in specific cases. [12] While this framework is an excellent starting point, it may be useful to expand on it. People who specialize in understanding consumers and market trends typically identify customer needs, often before chemical engineers are assigned to a product design project. Nevertheless, chemical engineers can help refine the
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understanding of consumer needs through their understanding of what is physically possible. Issues surrounding the design of a manufacturing process for complex chemical products have been discussed elsewhere [2,13,14], so I will focus on the remaining two steps, namely how ideas can be generated to meet customer needs, and how to best select from among those ideas. These steps must be at the heart of a chemical product design methodology. In practice, significant guidance is needed as to how to generate options and how to best select from among them. This is not simply a matter of brainstorming ideas and selecting the best option. While brainstorming and other creativity techniques are often useful for generating novel approaches to problems, a generic methodology is needed to systematically transform each novel approach into a specific set of product alternatives, and to quantitatively analyze those alternatives so as to select from among them. 4. Design of Homogeneous Products 4.1. Overview Having taught chemical product design to undergraduates at Columbia University, my colleagues and I have developed a useful methodology for designing homogeneous chemical products when limited data are available. This methodology has nine steps, and can guide a student team through a product design problem of moderate difficulty, each step requiring one week for a team of 3-4 students to complete, except steps 3, 4 and 5, which likely need two weeks each. Thus the course neatly fits into the time constraints of a university semester. The methodology assumes that the target behavior of the new chemical product has already been specified, eliminating the need for a step to determine customer needs. Also, since the required products are assumed homogeneous, their properties will result solely from their components and not a product microstructure generated during processing. This allows us to design the product and process sequentially rather than simultaneously, greatly simplifying the methodology and making it well within the grasp of undergraduates. Thus the procedure loosely follows the 4-step procedure of Cussler and Moggridge [12], but adds additional important details. For example, this procedure includes an analysis of market realities. A chemical product cannot be designed without a consideration of whether the proposed product will be profitable. Hence specific steps to assess the marketplace and determine profitability are included. In addition, recognizing that product design is only the first stage of product development and must be followed by a focused experimental program, the procedure includes an analysis of all uncertainties that should be followed up by experimentation.
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In addition, the methodology recognizes a key difference between the economics of commodities and specialty products that is easily overlooked. There is little risk that a commodity chemical manufactured by a new manufacturer or plant will go unsold if it is priced comparable to the competition. This is because manufacturers are generally unable to differentiate their commodity products from those of their competitors if they are priced the same, and so by the laws of supply and demand, any small increase in supply will lead to a small decrease in price for all manufacturers of the commodity as the market absorbs all the commodity produced by the new manufacturer. As all of the commodity manufactured at a new plant will sell at this new market price, the primary business decision is whether the investment in a new plant is justified by its return. On the other hand, since chemical products are differentiated by their performance specification, a new product will be governed by its own supply and demand equilibrium, and there will be no guarantee that a new chemical product can be sold at any price. There is no point in trying to calculate the return on investments (a cash flow transient) if the business proposition is not profitable in the steady state, i.e., with investments ignored. Hence before a prospective manufacturer considers whether the investment is justified by its return, ongoing profitability must be assessed first. This is typically a calculation of the market size that must be achieved for revenue to cover fixed costs, a situation referred to as “break-even”.1 [15] The methodology follows below. 4.1.1. Investigate Current Products The designer should begin by investigating current products, if any, in the marketplace – price, composition, the specific function of any components, strengths and weaknesses (from both a customer/consumer and a supplier perspective), any hidden costs, and total market size. Even if there is no product just like an intended product currently in the market, there may be other kinds of products indirectly fulfilling the same end function. For example, instead of using a device to purify drinking water, people may be drinking impure water and going more often to the doctor to treat water-borne illness. This will all be important information for setting an appropriate price for the new product, which in turn will be critical for determining whether the new product will be profitable.
1
Break-even, the market size size needed for revenues to cover ongoing fixed costs, is not the same as the payback period, the time required for cash flow to cover an investment. Break-even deals with steady state issues and is measured in either units of money or product volume; payback period deals with the cash flow transient and is measured in units of time.
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4.1.2. Initial Technical Analysis The mechanism(s) by which the new product may be able to work should be analyzed next. Consider the implications each mechanism will this have on the physical properties of the product. Also, identify the underlying chemical engineering phenomena (e.g. thermodynamics, reaction kinetics, transport phenomena, etc.) that will be relevant to understanding the behavior of the product. Where there are multiple properties that must be met simultaneously, consider if there are classes of compounds that can provide some of the required properties if they were present as components. If so, assume that the complete required property set can be decomposed into subsets of properties which can be achieved separately through their own components. This will allow the complete property set to be achieved by combining all components. Also identify any classes of compounds that would be inappropriate in the new product. This fundamental understanding will be later used to model the properties of the product. For example, consider the problem of formulating a biodegradable deicer for airplane wings. One would likely decide that freezing point depression is a more appropriate deicing mechanism than raising surface temperature by heat generation, as the latter effect would be temporary. This suggests that the product should contain a freezing point depressant. However, the product must also adequately wet and spread over the aircraft surface, not cause corrosion to wet metal surfaces, and biodegrade at acceptable rates. As it is unlikely that one compound will meet all these criteria, it can be assumed that the product will consist of (1) compounds that adequately depress the freezing point yet also biodegrade at acceptable rates, (2) compounds to ensure wetting, i.e. surfactants, and (3) compounds to prevent corrosion, i.e. anti-corrosion agents. 4.1.3. Build Product Property Models For each property subset, the understanding of the underlying chemical engineering phenomena can be used to derive a set of equations that can predict the relevant behavior as a function of composition. While simplifying assumptions may be made, be careful not to oversimplify. Verify qualitatively that the models will be useful for predicting the relevant behavior. Next, list all physical parameters that will be needed to apply the model with any candidate compound. In the absence of direct experimental data, decide how the needed physical parameters will be obtained (e.g. tabulated data, appropriate correlations, group contribution methods, etc.) For example, designing a biodegradable aircraft deicer would require a model of freezing point depression so that one could predict the mass of ice melted per mass of deicing compound at a given temperature. However, assuming ideal solution behavior leads to the unlikely conclusion that the only property governing freezing point depression is molecular weight, so solution ideality is
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clearly an oversimplification. In addition, the design would require a model of drainage rate off aircraft surfaces so that one could predict time to product failure, as well as a model of biodegradation. These models in turn lead to a need for various physical parameters, including activity coefficients, heats of fusion, and viscosity. 4.1.4. Generate Alternatives For each property subset, generate as large a list of potential candidates as is possible, based on an understanding of the underlying chemistry. This may be done by computer generation of alternatives or by searching through tabulated databases. Using the various product property models and any other relevant factors, cull each list by eliminating candidates that are inappropriate. 4.1.5. Select Product Composition For each property subset, define overall performance by assigning a weighting factor to each property in the set. In the example of the aircraft deicer, while there may minimum targets for freezing point depression and biodegradation that must be simultaneously achieved for a formulation to be given further consideration, assigning appropriate weighting factors to these properties will allow the product designer to consider performance tradeoffs in identifying the formulation with the best performance. Next obtain raw material costs for compounds that simultaneously meet all the important criteria within that property subset, and using the property models and weighting factors, rank all remaining candidates for their raw material costs on an equal overall performance basis. Identify any compounds that are less expensive than those used in current products on an equal overall performance basis, including hidden costs. Assuming that the complete required property set can be achieved by combining the components for each property subset, identify an overall composition to recommend for experimental study. 4.1.6. Design the Process For the preferred composition, chose a base case plant capacity and perform a preliminary process design. This preliminary process design should include a process flow sheet, a material balance for each stream, and sizing of all major equipment. Determine how much capital will be required to build this plant as a function of capacity. 4.1.7. Analyze the Risks Identify the key technical risks associated with this project, and recommend how these risks should be managed. This should include a listing of all key assumptions that were made in designing the product and its process, and an
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experimental plan for corroborating the conclusions drawn from these assumptions. 4.1.8. Analyze Finances for Ongoing Costs Based on cost/performance of the preferred composition and current products, identify a recommended selling price for the new product. Considering all available factors, identify the market share that may be expected at the recommended selling price. Making reasonable estimates, identify the expected variable costs and fixed costs associated with the new product.2 Identify the market share required for break-even, and compare to the expected market share to determine if the new product is likely to be profitable on an ongoing basis. Calculate the net profit expected on an ongoing basis. 4.1.9. Analyze Finances for Investments Making reasonable estimates, calculate the investment expenses that will be required. Given the expected market share and reasonable assumptions for the ramping up of sales, calculate how long will it take to recoup the initial investment while meeting the internally required discount rate. Based on this analysis, decide if the investment should be recommended. 4.2. Discussion This product design methodology will identify a product that meets the preliminary performance specification, and although it assesses both ongoing profitability and return on investments, it guarantees an acceptable level of neither. However, as with all design, product design should be approached iteratively. Once a product designer completes the last step of this method, he will know the various factors that influence product performance and economics. In addition, there may have been multiple product possibilities identified by the methodology, some of which may have been eliminated prematurely. Hence the product designer will be in a position to take a fresh look at all previous decisions and explore the impact of these decisions on ongoing profitability and return on investment. It is also possible that the product designed by this procedure can be the starting point for mathematical optimization. Since the product that offers maximum performance regardless of costs is unlikely to be the product that offers 2
Variable costs are ongoing costs proportional to sales volume, and include items like raw materials and delivery charges. Fixed costs are ongoing costs treated as independent of sales volume, although more correctly they are step functions of sales volume. These include items like depreciation and administrative overheads. [15] Some costs, like labor and utilities, fall somewhere in between these two idealizations, and may be treated as either. Note that a fixed capital investment, unlike depreciation, is not an ongoing cost, and hence is not a fixed cost.
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maximum profitability, there is value in simultaneously simulating and optimizing the effects of product performance, consumer response, and microeconomics. [16] As the focus of the product design must be sufficiently narrowed to permit this approach, the procedure outlined above is a good starting point. 5. Design of Structured Products The methodology proposed above assumes that a homogeneous product can achieve all the required product properties. This ignores the class of chemical products known as structured products, which achieve their properties through a microstructure that is determined by the interaction of its components and the manufacturing process. [17] Product engineering for structured products will be particularly difficult, as the product and process must be designed simultaneously. [2] Here again, a generic methodology is needed to systematically transform each novel approach into a specific set of product alternatives, and to quantitatively analyze those alternatives so as to select from among them. As with process design, this product design methodology would likely be hierarchical and iterative. Two primary approaches are possible: (1) generation and systematic reduction of the number of alternatives through heuristics, and (2) optimization of the set of all potential alternatives through mathematical programming. By analogy to what has been concluded about process design, it can be expected that product design techniques will draw largely on heuristics when data are limited, followed by more detailed calculations later on. [18] Where sufficient data to enable a complete mathematical representation of the product-engineering problem exists, mathematical techniques exist for their solution. However, significant work is still needed to establish a comprehensive generic methodology to generate and systematically reduce the number of alternatives through heuristics, so that product engineering can be accomplished even in the absence of complete data. Recent work has established how to mathematically represent the generic product-engineering problem [19], and mathematical programming has been successfully applied to these problems. [20] Of course, these techniques can only be applied where sufficient data are available to enable a complete mathematical representation of the product-engineering problem. Conversely, in the early stages of design when such data are generally lacking, heuristics are needed to systematically generate and analyze alternatives. Others have begun to identify product-engineering heuristics within specific product contexts [21-23], but a comprehensive generic methodology to generate and systematically reduce the number of alternatives through heuristics has yet to be established for the general problem.
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6. Conclusions The methodology for design of homogeneous products outlined in Section 4 highlights some of the real issues that chemical engineers face in product design. These problems may be quite rich despite the constraint that the product has no microstructure. On the other hand, a comprehensive generic methodology for structured products as suggested in Section 5 would be significantly more complex and would require significant work to develop. However, this methodology would allow structured products to be engineered even in the absence of complete data, accelerating new product development well beyond the capabilities of purely experimental techniques.
References [1] R. Costa, G. D. Moggridge, and P. M. Saraiva, AIChE J, 52 (2006) 1976 [2] M. Hill, AIChE J, 50 (2004) 1656 [3] E. Favre, L. Marchal-Heusler, and M. Kind, Trans IChemE, 80 (2002) 65 [4] M. F. Edwards, Chem. Eng. Res. Des., 84 (2006) 1 [5] J. Villermaux, Chem. Eng. Sci., 48 (1993) 2525 [6] R. A. Mashelkar, Chem. Eng. Sci., 50 (1995) 1 [7] G. Stephanopoulos and C. Han, Comp. Chem. Eng. 20 (1996) 143 [8] T. S. Kuhn, The Structure of Scientific Revolutions, University of Chicago Press, Chicago, 1996 [9] Committee on Chemical Engineering Frontiers, Frontiers in Chemical Engineering: Research Needs and Opportunities, National Academy Press, Washington, 1988 [10] J. Wei, ChemTech, 26 5 (1996) 16 [11] R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 2002 [12] E. L. Cussler and G. D. Moggridge, Chemical Product Design, Cambridge University Press, New York, 2001 [13] F. M. Meeuse, J. Grievink, P.J.T. Verheijen and M.L.M. Van der Stappen, “Conceptual Design of Processes for Structured Products” in M. F. Malone, J. A. Trainham and B. Carnahan (eds.) Fifth International Conference on Foundations of Computer Aided Process Design, AIChE Symp Ser No 323, 2000, pp. 324-328 [14] F. M. Meeuse, “Process Synthesis for Structured Food Products” in K. M. Ng, R. Gani, and K. Dam-Johansen (eds.) Chemical Product Design: Towards a Persepective Through Case Studies, Elsevier, Amsterdam, 2006, pp. 167-179 [15] W. C. Lawler, “Cost-Volume-Profit Analysis” in J. L. Livingstone and T. Grossman (eds.) The Portable MBA in Finance and Accounting, Wiley, New York, 2002, pp. 102-124 [16] M. J. Bagajewicz, AIChE J 53 (2007) 3155 [17] M. F. Edwards, IChemE North Western Branch Papers No. 9 (1998) [18] J. M. Douglas and and G. Stephanopoulos, “Hierarchical Approaches in Conceptural Process Design: Framework and Computer-Aided Implementation”, in L. T. Biegler and M. F. Doherty (eds.), Fourth International Conference on Foundations of Computer Aided Process Design, AIChE Symp Ser No 304, 1995, pp. 183-197 [19] R. Gani, Comp. Chem. Eng., 28 (2004) 2441 [20] A. K. Sunol, “A Mixed Integer (Non) Linear Programming Approach to Simultaneous Design of Product and Process”, in L. T. Biegler and M. F. Doherty (eds.), Fourth
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Ser No 304, 1995, pp. 276-279 [21] K. Y. Fung and K. M. Ng, AIChE J, 49 (2003), 1193 [22] C. Wibowo and K. M. Ng, AIChE J, 48 (2002) 1212 [23] C. Wibowo and K. M. Ng, AIChE J, 47 (2001) 2746
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Simulation in nuclear engineering design; Christian LATGE C.Latgé, Research Director, French Atomic Energy Commission, CEA-DEN-DTN , Cadarache Research Center, 13108 Saint Paul lez Durance FRANCE
Abstract The development of a new system or process in nuclear field requires generally first to select structural material and coolant and identify associated critical issues, which are inherent in the design and safe operation of the system or process which has to be developed. The design of a system or process has to deal with neutronics, thermal hydraulics, mass and heat transfer, and their consequences on heat deposition, materials structure mechanics, coolant technologies, control systems and operational procedures. All these related studies, using analytical, numerical and experimental approaches, have the following main objective: assessment of reliability and safety aspects which might endanger the integrity and operability of the system, during the life duration; this assessment contributes to the definition and evaluation of control systems, countermeasures, and more generally the preparation of licensing. Selection of best design options requires the use of simulation tools in order to size the individual components and demonstrate the reliability of the whole system or process. Thanks to some examples, ie the design of a spallation target for nuclear waste transmutation, within the framework of an international project, we will illustrate the design strategy of a prototypical integrated system. An extension to some other specific fields of research in chemical engineering for nuclear applications will be performed. Keywords: nuclear engineering, integrated prototypical systems, simulation tools
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Supply Chain Risk Management through HAZOP and Dynamic Simulation Arief Adhityaa, Rajagopalan Srinivasana, b, I.A. Karimib a
Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833, Singapore b Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore
Abstract In today’s globalized economy, supply chains strive to be increasingly efficient and effective by adopting strategies such as outsourcing, just-in-time practices, and lean inventory. However, these measures to operate the supply chain more efficiently often lead to increased fragility. As uncertainties become more prevalent and disruptions arise from many sources, supply chain risk management has become imperative. Considering the complexity of today’s supply chains and their operations, this paper proposes a systematic framework for supply chain risk management. Within the framework, this paper presents a structured methodology for risk identification and consequence analysis. Following the well-established HAZard and OPerability (HAZOP) analysis method in process safety, supply chain risk identification can be performed by systematically generating deviations in different supply chain parameters, and identifying their possible causes, consequences, safeguards, and mitigating actions. Consequence analysis can be conducted using a dynamic simulation model of the supply chain operations. The application and benefits of the proposed approach are demonstrated using a refinery supply chain case study. Keywords: Disruption Management, Uncertainty, Refinery, Supply Chain Modeling.
1. Introduction A supply chain (SC) comprises all the entities and activities required to deliver final products to end-customers – encompassing procurement, transportation, storage, conversion, packaging, etc. Present-day SCs involve numerous, heterogeneous, geographically distributed entities with varying dynamics, complexities, and uncertainties. Complex maze of the network, unpredictable dynamics, information delay, limited visibility, and involvement of disparate entities with varying goals complicate SC decision making. Furthermore, today’s SC operations are subject to various operational and disruption risks. Operational risks are uncertainties expected in day-to-day operations such as variations in supply, demand, production, transportation, and cost. Disruption risks arise from natural or man-made adverse events which cause variations beyond the expected range such as earthquakes and terrorist attacks. SC risk management is critical to ensure continuity of profitable operations amidst these risks. In this paper, we present a framework for SC risk management and demonstrate its application in a refinery SC. The refinery SC has many sub-processes such as crude procurement, planning, scheduling, oil trading, logistics, etc. At the center of this SC lie the oil refining operations. Refining is a complex process which involves a number of operations to transform crude oil into valuable products. The refinery SC begins from the oil
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reservoirs, found most abundantly in the Middle East region, and tapped via both ground fields and offshore platforms. Transportation of the crude to various processing plants/refineries around the world is carried out mostly by large ships called Very Large Crude Carriers (VLCCs) or pipelines. Even with extensive networks and carefully planned schedules, transportation times are relatively long; it takes 4-6 weeks for a VLCC carrying crude oil from the Middle East to reach refineries in Asia. Such long periods make crude supplies easily susceptible to disruptions, leading to failure to meet customers’ demands or a crude stock out. This is a critical problem as it would compel unit shutdowns and result in large losses. A single crude mix allows numerous products and their variants to be produced through a suitable alteration of processing conditions. Accordingly, refineries must adapt their operations to the different crude batches to maintain the required product specifications, which gives rise to differing operating costs. Further, since crude oil prices, product demands and prices fluctuate highly, optimization needs to be done frequently. Other key features of the refinery SC are large inventories, need for safety-first, sensitivity to socio-political uncertainties, environmental regulations, and extensive trading. Hence, there is clearly a need for risk management in the refinery SC. 1.1. Literature Review SC risk management is a growing research area. Chopra and Sodhi (2004) group SC risks into eight categories (disruptions, delays, systems, forecast, intellectual property, procurement, receivables, inventory, and capacity) and give general mitigating strategies for each category. Kleindorfer and Van Wassenhove (2004) discuss two types of risk management issues in global SCs: matching supply to demand and addressing disruptions to SC activity. Mishra, et al. (2003) present an agent-based decision support system to manage disruptions in a refinery SC. In the event of a disruption, agents collaborate to identify a holistic rectification strategy using heuristic rules. Since there is limited literature on structured and elaborate methodology for SC risk management, this paper attempts to propose one such methodology.
2. Framework and Methodology for Supply Chain Risk Management The proposed framework for SC risk management is illustrated in Figure 1 and comprises the following steps: 1. Risk identification: The first step is to recognize uncertainties and risks faced by the SC. With globalization and increased outsourcing practices, the number of parties involved in the SC and the links connecting them have increased significantly. Hence, some risks may not be obvious and it is important to have a structured method for risk identification, as presented in Section 2.1. 2. Consequence analysis: Once the risks have been identified, their consequences have to be analysed using an appropriate model of SC operations. The disruptions due to one particular risk or a combination of risks can be simulated and propagated through the SC model and the effects analysed. In a complex SC, there could be important domino effects. These should be explicitly considered in the analysis. Section 2.2 presents a dynamic simulation model of the integrated refinery SC which enables such analysis. 3. Risk estimation: Risk is usually quantified in financial terms and/or ranked according to some pre-defined criteria. The frequency or probability of each risk materializing is estimated. The risk is quantified in two dimensions: its frequency/probability and its severity/consequence, taking into account the effects of mitigating actions and safeguards, if any.
Supply Chain Risk Management Through HAZOP and Dynamic Simulation
Risk identification
List of detected risks
Consequence analysis
Risk estimation
List of risks and their estimates
List of risks, their safeguards and mitigating actions
Significant changes such that risk study is necessary
Risk monitoring
List of risks and their effects
KPIs and supply chain changes
Risk mitigation
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Risk assessment No
Supply chain operation
Risk acceptable? Yes
Figure 1. Proposed framework for SC risk management
4. Risk assessment: The risk management team decides whether the risk quantified in the previous step is acceptable based on experience, industry standards, benchmarks, or business targets. If not, additional mitigation actions or safeguards are required. 5. Risk mitigation: Mitigating actions and safeguards such as emergency procedures and redundancies have to be developed for the risks, based on both the SC model and inputs from the risk management team or relevant personnel. Two types of mitigating action can be differentiated – preventive and responsive. Once the risks have been deemed acceptable, SC operations proceed with the appropriate safeguards and mitigating actions in place. 6. Risk monitoring: The SC structure and operation do not remain stationary but changes regularly due to, for example, new suppliers, new regulations, new operating conditions, new products, etc. The risk management team should continually monitor the SC for new risks. The team might be required to start from step (1) to consider the new risks arising from these changes. 2.1. Risk Identification through HAZOP For risk identification, this paper proposes to employ the HAZard and OPerability (HAZOP) analysis method from chemical process risk management. SC networks are in many ways similar to chemical plants. Drawing from this analogy, we propose to represent SC structure and operations using flow diagrams, equivalent to process flow diagrams (PFDs). A simplified flow diagram of the refinery SC is shown in Figure 2. Following the well-established HAZOP method, SC risk identification can be performed by systematically generating deviations in different SC parameters, and identifying their possible causes, consequences, safeguards, and mitigating actions. The deviations are generated using a set of guidewords in combination with specific parameters from the flow diagrams. Table 1 gives a non-exhaustive list of these guidewords and parameters. The guideword “Low” can be combined with a flow to result in, for example, the deviation “Low demand”. Possible causes and consequences can be identified by tracing the flows in the diagram. Safeguards are any items or procedures which help to protect against a particular deviation. It could protect against the deviation before it occurs, i.e. reducing the frequency, or help to recover quickly and minimize impact after it occurs, i.e. reducing the severity. An example of the former is safety stock, which protects against demand uncertainty; an example of the latter is insurance. Mitigating actions are additional items or procedures on top of any existing safeguards which are deemed necessary to manage the deviation.
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Figure 2. Simplified refinery SC flow diagram Table 1. Sample guidewords and parameters for HAZOP
Guidewords No High Low Early/late Parameters Material flow Information flow Finance flow
Meaning None of the design intent is achieved Quantitative increase in a parameter Quantitative decrease in a parameter The timing is different from the intention Raw material, side product, energy, utility, etc Order, quote, forecast, message, signal for action, etc Cash, credit, share, receivables, pledge, contract, etc
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2.2. Consequence Analysis through Dynamic Simulation For consequence analysis, we have developed a dynamic simulation model of the refinery SC, called Integrated Refinery In-Silico (IRIS) (Pitty et al., 2007). It is implemented in Matlab/Simulink (MathWorks, 1996). Four types of entities are incorporated in the model: external SC entities (e.g. suppliers), refinery functional departments (e.g. procurement), refinery units (e.g. crude distillation), and refinery economics. Some of these entities, such as the refinery units, operate continuously while others embody discrete events such as arrival of a VLCC, delivery of products, etc. Both are considered here using a unified discrete-time model. The model explicitly considers the various SC activities such as crude oil supply and transportation, along with intra-refinery SC activities such as procurement planning, scheduling, and operations management. Stochastic variations in transportation, yields, prices, and operational problems are considered. The economics of the refinery SC includes consideration of different crude slates, product prices, operation costs, transportation, etc. The impact of any disruptions or risks such as demand uncertainties on the profit and customer satisfaction level of the refinery can be simulated through IRIS.
3. Case Study This case study is based on the refinery SC flow diagram in Figure 2. We consider the parameter “Crude arrival”, which is the material flow from the jetty to the refinery crude tanks (marked by a star in Figure 2), and the guideword “No” to derive the deviation “No crude arrival”. To study the possible causes of this deviation, we trace backward from the crude arrival flow and find the jetty, shipper, and supplier entities. No crude arrival could be caused by unavailability or disruption to any of these entities, e.g. jetty closure, shipper unreliability, or supplier stock-out. The possible consequences can be examined by tracing forward from the crude arrival flow, from which we find the crude tanks, processing units, product tanks, shipper, and customers. Thus, the possible consequences of no crude arrival are low inventory in the crude tanks, possible out-ofcrude situation which leads to operation being disrupted, low inventory in the storage tanks, low product shipment to customers, and unfulfilled demand. Safeguards for this deviation are required to cover for the crude which is not arriving. These could be in the form of crude safety stock or emergency crude procurement. Since shipper unreliability is one possible cause, a suitable mitigating action could be to consider engaging a more reliable shipper. Other mitigating actions include establishing better communication and transparency with suppliers and shippers for timely notice of any delay, and rescheduling to avoid shutdown by reducing throughput until the crude arrives. These HAZOP results are summarized in Table 2. Consequence analysis of no crude arrival due to delay in transportation is performed using IRIS simulations. In this case, the refinery would like to evaluate the mitigating action of engaging a more reliable shipper. The existing shipper has a 10% probability of late crude delivery while the new shipper is more reliable with a 5% probability of delay. However, the new shipper on average costs $30million more than the existing one. The refinery also considers having a safeguard in the form of safety stock. Hence, four cases are evaluated: with and without safety stock for each shipper option. The resulting profit and customer satisfaction from these cases are shown in Table 3. Safety stock can increase customer satisfaction to 95% despite low existing shipper reliability. However, profit suffers a lot from low shipper reliability. This is because of high shutdown costs. Demand backlog can be satisfied in the next immediate cycle, hence customer satisfaction does not suffer much from shutdown. Safety stock cannot make
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up for poor performance of shipper. In both cases (with and without safety stock), the new shipper increases the profit by more than $50million. Since the increase in profit is more than the increase in cost, it is recommended to switch to the new shipper. Further, safety stock is also recommended as it increases both customer satisfaction and profit.
4. Concluding Remarks Risk management is critical for today’s SCs. In this paper, we propose a systematic framework for SC risk management and structured methodology for risk identification and consequence analysis, demonstrated in a refinery SC. The proposed HAZOP method for risk identification has two notable advantages. It is systematic, because the deviations studied are generated using pre-defined guidewords and pertinent system parameters, as opposed to ad-hoc scenario analysis. It is also complete, because it is structured around a representation of the whole process in the form of flow diagrams, as opposed to other methods with limited scope such as checklist. Consequence analysis is performed through IRIS, a dynamic simulation model of the refinery SC. Risk probability estimation, cost-benefit analysis and optimization of risk management strategies are the direction of our current work.
References S., Chopra and M. S. Sodhi, 2004, Managing Risk to Avoid Supply Chain Breakdown, MIT Sloan Management Review, 46, 1, 53-61. P. R. Kleindorfer and L. N. Van Wassenhove, 2004, Managing Risk in Global Supply Chains, In H. Gatigon and J. Kimberly (eds.), The Alliance on Globalization, Cambridge University Press, Chapter 12. MathWorks, 1996, Using Simulink: Version 2. M. Mishra, R. Srinivasan, and I. A. Karimi, 2003, Managing disruptions in refinery supply chain using an agent-based decision support system, Presented at the AIChE annual meeting, San Francisco, CA, Nov 16-21. S. S. Pitty, W. Li, A. Adhitya, R. Srinivasan, and I. A. Karimi, 2007, Decision Support for Integrated Refinery Supply Chains. 1. Dynamic Simulation, Computers and Chemical Engineering (In Press). Table 2. HAZOP results for crude arrival delay
Deviation No crude arrival
Causes
Consequences
Safeguards
Jetty unavailability; Shipper disruption; Supplier stockout
Low stock, outof-crude; Operation disrupted; Demand unfulfilled
Safety stock; Emergency suppliers
Mitigating Actions More reliable shipper; Frequent check with supplier /logistics; Rescheduling
Table 3. Consequence analysis results for the risk of crude arrival delay
Safety Stock
Yes No
Average Customer Satisfaction (%) Shipper Existing New 95 98 91 95
Average Profit ($, million) Shipper Existing New 38 93 27 83
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
43
A new approach for the design of multicomponent water/wastewater networks Débora C. Faria and Miguel J. Bagajewicz University of Oklahoma, 100E. Boyd, Norman – OK 73019, USA
Abstract Water allocation problems have nonlinearities and non-convexities due to bilinear terms. To address this issue we propose to discretize one of the variables of the bilinear terms. As a result an MILP model is generated, which provides a lower bound. To reduce the gap between this lower bound and the upper bound (a feasible solution found using the original NLP model), an interval elimination procedure is proposed. As a result, the feasible space shrinks after each iteration and the global optimum is identified. We illustrate the methodology for minimum water allocation problems. Keywords: water networks, multicoponent, bilinearities, discretization, lower bound.
1. Introduction The design of water/wastewater networks where water is reused and/or regenerated in processes plants is one important problem in industry as it leads to important water and cost savings. To accomplish this task for multicomponent systesm, mathematical programming is needed (Bagajewicz , 2000). The models contain a large number of bilinear, non-convex terms, which make the identification of a global optimum cumbersome. To overcome this difficulty, some authors have presented methodologies to find feasible solutions for these systems (Bagajewicz et al.,2000; Alva-Argaez et al., 1998,2007; Ullmer et al.,2005). With the exception of the work presented by Karuppiah and Grossmann (2006), no other present a methodology to find the global optimum solution. In this paper we present a new discretization methodology based on an interval elimination procedure that guarantees global optimality. We present the nonlinear model first, followed by a description of the discretization model and the solution procedure. Finally, an example is presented.
2. The Nonlinear Model Problem statement: Given a set of water using units, freshwater sources, wastewater sink and available regeneration processes with their limiting data, a globally optimum for the freshwater consumption is sought. The corresponding non-liner model to solve this water allocation problem (WAP) written in terms of contaminant mass load is: Water balance at the water-using units
¦ FWU w,u + ¦ FUU u*,u + ¦ FRU r ,u w
u*
=
r
¦ FUS u ,s + ¦ FUU u ,u* + ¦ FURu*,r s
u*
∀u
(1)
r
FWU, FUU, FRU, FRR and FUR are the freshwater to unit, unit to unit, regeneration unit to units, regeneration to regeneration and unit to regeneration flowrates.
D.C. Faria and M.J. Bagajewicz
44
Water balance at the regeneration processes
¦ FURu ,r + ¦ FRRr*,r = ¦ FRU r ,u + ¦ FRRr ,r* + ¦ FRRr ,u u
r*
u
r*
∀r
(2)
u
Contaminant balance at the water-using units
¦ (CWw,c * FWw,u ) + ¦ ZUU u*,u ,d + ¦ ZRU r ,u,d w
u*
+ ΔM u ,c
r
= ¦ ZUU u ,u*,d + ¦ ZUS u , s ,d + ¦ ZURu ,r ,d u*
s
(3)
∀u, c
r
CWw,c is the pollutant c concentration in freshwater. In turn, ZUU, ZRU, ZUS and ZUR are mass flows of contaminants between units, regeneration to units, units to disposal and units to regeneration units. Finally ΔM u ,c is the mass load of component c. Maximum inlet concentration at the water-using units
¦ (CW w,c * FUW w,u ) + ¦ ZUU u*,u ,c + ¦ ZRU r ,u ,c w
u*
r
· § ≤ Cinmax u ,c * ¨¨ ¦ FUW w,u + ¦ FUU u*,u + ¦ FRU r ,u ¸¸ u* r ¹ ©w
(4) ∀u , c
Maximum outlet concentration at the water-using units
¦ (CW w,c * FUW w,u ) + ¦ ZUU u*,u ,c + ¦ ZRU r ,u ,c + ΔM u ,c w
u*
r
· § ≤ Coutmax u ,c * ¨¨ ¦ FUU u ,u* + ¦ FUR u , r + ¦ FUU u ,u* + ¦ FUS u , s ¸¸ ∀u , c r u* s ¹ © u*
(5)
Cinmax and Coutmax are maximum inlet and outlet concentrations. Contaminant balance at the regeneration processes
ª º ZRrout ,c = « ¦ ZURu , r ,c + ¦ ZRRr *, r ,c » *(1 − XCRr ,c ) r* ¬u ¼ ª º + « ¦ ZRU r ,u ,c + ¦ ZRRr ,r *,c + ¦ ZRRr ,r *,c » * XCRr ,c r* r* ¬u ¼
(6)
∀r , c
Here XCRr ,c is a binary parameter that determines is a contaminant is removed or not. Capacity (CAP) of the regeneration processes CAPr = ¦ FURu ,r + ¦ FRRr *,r ∀r u
(7)
r*
Contaminant mass loads These constraints are written in a general form where i can be any water using unit or any regeneration process; and j can be a water using unit, regeneration process or sink.
ZIJ i, j ,c = FIJ i, j * Couti, j
∀i ∈ {U , R}, j ∈ {U , R, S}, c
(8)
A New Approach for the Design of Multicomponent Water/Wastewater Networks
45
Freshwater consumption – Objective function
Min¦¦ FWU w,u w
(9)
u
3. The Discrete Methodology 3.1. Model Discretization The proposed approach discretizes one variable (concentrations used here or flowrates) of the bilinear term generated at the splitting points. As a result, a mixed integer linear programming (MILP) model is generated. The discretized concentrations are now parameters ( DC d,c,u for the water using units; DCR d,c,r for regeneration processes). Eq. 8 (the only bilinear one) is substituted by the following “big M” constraints, that force the outlet concentrations to be in between two discrete concentrations. ZIJ i , j ,c − DC d ,c ,i * FIJ i , j ≥ DC d ,c ,i * Fmax * (XI i,c,d − 1) ∀i ∈ {U , R}, j ∈ {U , R, S }, c, d < dmax ZIJ i , j ,c − DCd +1,c,i * FIJ i , j ≤ DCdmax,c,i * Fmax * (1 - XIi,c,d ) ∀i ∈ {U , R}, j ∈ {U , R, S }, c, d < dmax
(10)
(11)
To guarantee that only one interval is picked, we write:
¦ XIi,c,d = 1 d
∀i ∈ {U , R} , c
(12)
Thus, the contaminant mass load of each stream is calculated through a relaxation between two discrete points. Finally, to ensure that there is no contaminant mass load when flowrate does not exist, we write: ZIJ i , j ,c ≤ DC dmax ,c ,i * FIJ i, j
∀i ∈ {U , R}, j ∈ {U , R, S }, c
(13)
The discretized model provides a lower bound (because it is relaxing one constraint), but most important, it also points to a set of intervals that might contain the optimum. In addition, a good upper bound can be obtained using the solution of this lower bound as a starting point of the original NLP problem.
Once a lower bound and an upper bound of the problem are found, one can evaluate the lower bound solution and determine which intervals might be part of an optimum solution. The ones that are proved not to be in the optimum solution are eliminated and the remained intervals of the discrete concentration parameters are discretized again. This is done as follows. 3.2. Interval Eliminations In each iteration, after a lower and an upper bound are found, we implement the following procedure for each discrete concentration: 1. The interval selected by the lower bound model is forbidden to be selected (this means the correspondent binary is fixed to zero) 2. The discrete model is then run again. Two possibilities exist:
D.C. Faria and M.J. Bagajewicz
46
a.
The solution is feasible (a solution between the current lower and upper bound exists). In this case, it is possible to have an optimum solution outside of the investigated interval. Thus, nothing is done. The solution is infeasible (there is no feasible solution between the current lower and upper bound outside of the investigated interval). Thus, the optimum solution needs is inside of the investigated interval. Thus, the region outside of the investigated interval is disregarded.
b.
4. Illustration of The Methodology We now illustrate the method a small example with two water-using units and two contaminants (Wang and Smith, 1994) (Table 1). For this example, two intervals (dmax=3) are used. Figure 1 shows how the discrete concentrations are being divided at the beginning (initialization step). Process 1 2
Table 1 – Limiting data of illustrative example Mass Load Cin,max Contaminant (Kg/h) (ppm) A 4 0 B 2 25 A 5.6 80 B 2.1 30
Cout,max (ppm) 100 75 240 90
Figure 1 – Illustrative example of the discrete approach - initialization.
In this case, the lower bound is 52.895 ton/h and the upper bound is 54 ton/h. All the selected intervals of the discrete concentration are in the second interval. When the lower bound model is re-run forbidding the selected intervals (intervals evaluation), it is found that none of the first intervals have the possibility of hosting the optimum solutions. Thus, the intervals between the first and second discrete points can be eliminated and the second intervals re-discretized.
Figure 2 – Illustrative example of the discrete approach – 1st iteration.
A New Approach for the Design of Multicomponent Water/Wastewater Networks
47
With this new intervals in the second iteration the lower and upper bound do not change (LB = 52.895 ton/h and UB = 54 ton/h), but the intervals are smaller, so a new elimination procedure can be conducted. The same procedure is repeated until the lower bound solution is equal (or has a tolerance difference) to the upper bound solution. In this example, using two intervals, is solved in 11 iterations and 11.6 seconds. Note that hen the elimination is not possible more intervals are used.
5. Examples The proposed method is applied to a refinery case presented by Koppol et al. (2003). This example has four key contaminants (salts, H2S, Organics and ammonia), six water using units, and three regeneration processes. The limiting data of the water using units are shown in the original paper. The solution when freshawater consumption is minimized, without allowing the addition of regeneration processes, is presented in Figure 3. A freshwater consumption of 119.332 ton/h was achieved. Only one iteration is needed and the solution is found in 0.81 seconds. The solution when regeneration processes are introduced (Reverse osmosis, which reduces salts to 20 ppm; API separator followed by ACA, which reduces organics to 50 ppm; and, Chevron wastewater treatment, which reduces H2S to 5 ppm and ammonia to 30 ppm) has a freshwater consumption of 33.571 ton/h. Only one iteration is needed to find the solution in 2 seconds. However, the found solution present several regeneration recycles and very small flowrates. This is an undesirable situation for the practical point of view. To overcome this issue, we added binary variables to control a minimum allowed flowrate if the connection exits and to forbid recycles as well. The new solution (also 33.517 ton/h) is found in two iterations (34 seconds). The flowsheet obtained is not shown for space reasons.
Figure 3– Optimum for Multicomponent Example. No regeneration
Further, we no longer consider the regeneration processes with fixed outlet concentrations of the key contaminants. Instead, we evaluate what would be these concentrations if we want minimize the need for regenerations at the found freshwater consumption (33.571 ton/h). To translate this goal to a mathematical form, we use the total removed contaminant mass load (that is the combination between flowrate and concentration reduction) as the objective function. Now, the outlet concentrations of the keys contaminants in the regeneration processes can have any value higher than the ones previously presented. The optimum solution found after 2 iterations (66 Seconds) shows the regeneration processes having the following features: Reverse osmosis needs to reduce salts to 85 ppm instead 20 ppm originally proposed. The API separator
D.C. Faria and M.J. Bagajewicz
48
followed by ACA need to reduce organics to 50 ppm as before. Finaly, the Chevron wastewater treatment should keep the 5 ppm reductions for H2S, but can operate to reduce ammonia to 120 ppm instead 30ppm. The suggested network is presented in Figure 4.
Figure 4– Optimum for Multicomponent Example. With Regeneration
6. Conclusions The suggested approach has showed good results on the minimum water allocation problems. The methodology also allows handling the outlet concentration of the key contaminants of the regeneration processes as a variable. This arises to be important when one wants to determine optimum contaminats reduction without define the regeneration processes beforehand. As future work, the methodology will be extended to the optimization of WAP using other objective function.
References M. Bagajewicz, 2000, A review of recent design procedures for water networks in refineries and process plants, Computers and Chemical Engineering, 24, 2093-2113. M. Bagajewicz, M. Rivas and M. Savelski, 2000, A robust method to obtain optimal and suboptimal design and retrofit solutions of water utilization systems with multiple contaminants in process plants, Computers and Chemical Engineering, 24, 1461-1466. A.A. Alva-Argaez, C. Kokossis and R. Smith, 1998, Wastewater minimization of industrial system using an integrated approach, Computers and Chemical Engineering, 22, S741-S744. A.A. Alva-Argaez, C. Kokossis and R. Smith, 2007, A conceptual decomposition of MINLP models for the design of water-using systems, Int. J. of Env. and Pollution, 29(1-3), 177-205. C. Ullmer, N. Kunde, A. Lassahn, G. Gruhn and K. Schulz, 2005, WADO: water design optimization – methodology and software for the systhesis of process water systems, Journal of Cleaner Production, 13, 485-494. R.Karuppiah and I.E. Grassmann, 2006, Global optimization for the systhesis of integrated water systems in chemical processes, Computers and Chemical Engineering, 30,650-673. Y.P. Wang and R. Smith, 1994, Wastewater Minimization, Chem. Eng. Science, 49(7), 981-1006. A.P.R. Koppol, M.J. Bagajewicz, B.J. Dericks and M.J. Savelski, 2003, On zero water discharge solutions in the process industry, Advances in Environmental Research, 8, 151-171.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
49
Effect of catalytic reactor design on plantwide control strategy: Application to VAM plant Costin S. Bildea1 and Alexandre C. Dimian2 1
University “POLITEHNICA” of Bucharest, Polizu 1, Bucharest, Romania University of Amsterdam, Nieuwe Achtergracht 166, Amsterdam, The Netherlands
2
Abstract The paper demonstrates that the kinetic behaviour of a catalyst is a key element in developing a plantwide control strategy. The “inverse problem” is also important: design a catalyst whose kinetic behaviour fulfils at best the performance criteria of the plant. So far, these problems have not been systematically investigated. The methodological tool is based on the bifurcation analysis of the structure Reactor / Separation / Recycle. This analysis allows finding regions in the space of design parameters where performance criteria are met and stability is guaranteed. The catalytic chemical reactor must be a flexible unit. The recycling strategy is determined by the kinetic effect of each reactant, as well as by the sensitivity of the elementary reaction steps to concentration and temperature. When selectivity and catalyst properties require low per-pass conversion, manipulating the reactor temperature profile is an effective means for steering the plant between different operating points. Keywords: design, plantwide control, catalytic reactors, vinyl acetate
1. Introduction Controlling the inventory of reactants in plants with recycles can be performed in two ways [1]. The first one is evaluating the inventory of each reactant and controlling it by feedback, using the corresponding fresh feed as manipulated variable. A practical way is to fix the flow rates of reactants at reactor inlet. Production rate changes can be achieved a) by modifying the flow rates of reactants, which works when the process is designed for large conversion and b) by changing the reactor operation parameters, which is recommended at low values of conversion. The second approach is fixing the fresh feed rate of reactants and using the self-regulation property of the mass balance [2]. This strategy offers a direct way of changing the production rate. However, it can be applied only when the per-pass conversion of the limiting reactant has a high value. Previous studies [3] highlighted the interaction between reactor design and the control of plants with recycles and considered the generic Reactor / Separation / Recycle system as fundamental structure for developing plantwide control strategies. In the present paper, we consider the design and control of a process involving a complex LHHW catalytic reaction scheme. The Vinyl Acetate monomer (VAM) process has been proposed as benchmark for developing a plantwide control procedure [4], and received the attention of several studies [5-7]. However, our evaluation of these works indicates that the control strategy suffers of high sensitivity since the kinetics of the chemical reaction was implemented on a pre-determined reactor and plant design. Our approach considers the kinetics of the catalytic process as the starting point in designing the plant with recycles, as well as in developing the plantwide control strategy.
50
C.S. Bildea and A.C. Dimian
2. Process design The manufacturing of vinyl acetate by the oxy-acetylation of ethylene is described by the following gas-phase catalytic reaction: C2H4 + CH3COOH +0.5O2 ĺ C2H3OOCCH3 + H2O
ΔrH = -176.2 kJ/mol
A highly undesired secondary reaction is combustion of ethylene to CO2, which lowers the yield and complicates the removal of the reaction heat: ΔrH = -1322.8 kJ/mol
C2H4 + 3O2 ĺ 2CO2 + 2H2O
The catalyst plays a crucial role in the technology. A typical modern catalyst consists of 0.15-1.5 wt% Pd, 0.2-1.5 wt% Au, 4-10 wt% KOAc on silica spherical particles of 5 mm [8]. The very fast reaction takes place inside a thin layer (egg-shell catalyst). Preferred conditions are temperatures around 150 to 160 °C and pressures 8 to 10 bar. Hot spots above 200 °C lead to permanent catalyst deactivation. The excess of ethylene to acetic acid is 2:1 to 3:1. Because of explosion danger, the oxygen concentration in the reaction mixture should be kept below 8%. Small amount of water in the initial mixture are necessary for catalyst activation. The dilution of the reaction mixture with inert gas is necessary because of high exothermic effect. Accordingly, the reactor is designed at low values of the per-pass conversions, namely 15 – 35% for the acetic acid and 8-10% for ethylene. The above elements formulate hard constraints both for design and for plantwide control. Analyzing the mechanism of the catalytic reaction allows the identification of the major factors that affect the reactor design. The reaction kinetics is not sensitive to the concentration of the acetic acid, but the presence of some water is necessary to activate the catalyst. On the contrary, ethylene and oxygen are involved in kinetics through a complex adsorption/surface reaction mechanism. The catalyst manifests high activity and selectivity. The power-law kinetics involves only ethylene and oxygen [8]: α1 rVA = k1 pC p β1 H O 2
4
2
where Į1 is 0.35 - 0.38 and ȕ1 0.18 - 0.21. The reaction constant is given by k1 = A1 exp(− E1 / RT ) in which the energy of activation depends on the Pd content, for example 39 kJ/mol for Pd 1% and 17.3 kJ/mol for Pd 5%. A similar kinetic expression describes the secondary combustion reaction, but with reaction orders very different compared to the main reaction: α2 rCO2 = k 2 pC pβ2 H O 2
4
2
Table 1. Kinetic parameters for vinyl acetate synthesis over a Pd/Au/SiO2 catalyst [9,10]
Reactions
Power-law kinetics C2H4 O2 C2H4+CH3COOH+0.5O2 0.36 0.20 C2H4 +3O2 ĺ 2CO2 + 2H2O -0.31 0.82 * reaction rate in mol/litre-catalyst/sec.
Kinetic constants E (J/mol) 15000 21000
A1 2.65E-04 7.50E-04
A2 7.95E-05 2.25E-04
Effect of Catalytic Reactor Design on Plantwide Control Strategy
51
R-GAS HX R-IN SEP ETHENE MIX1
PFR
SEP
OXYGEN MIXER
ACETIC R-OUT R-ACETIC
Figure 1 Design of the reactor for vinyl acetate manufacturing in a recycle system
Figure 1 presents the Reactor / Separation / Recycle structure used for performing reactor design and bifurcation analysis. Because of incomplete conversion, both ethylene and acetic acid are recycled. The recycle policy should maintain an ethylene/acetic acid ratio of 3 : 1, as well as oxygen concentration at reactor inlet bellow 8 vol%. The choice of gaseous inert is a key design decision. Some reports [4-7] consider ethane (impurity in the fresh feed), but this solution is not adopted here. Because CO2 is produced by reaction in large amount, its use as inert in a concentration of 10-30 % vol is the most economical [8]. However, the presence of CO has to be prevented since this is a catalyst poison.
3. Plantwide control The main goals of the plantwide control system are to ensure safe operation, desired production rate and product quality, and to optimize the efficiency of using the material and energetic resources. Figure 2 presents the control structure around the chemical reactor. Safety is essential. Therefore, the oxygen is added under concentration control, in a mixing chamber placed behind concrete walls. Secondly, the cooling should avoid reaction runaway. Several temperature measurements are placed along the reactor bed and the highest value is selected as the process variable. The manipulated variable of the control loop is the steam generator pressure, which directly influences the coolant temperature. The water level in the steam generator is controlled by the water makeup. Note that using a simple feedback loop may not work. When the steam rate increases, the correct action is to add more water as makeup. However, the pressure simultaneously decreases. The lower pressure means that, initially, the steam bubbles will occupy a larger volume, and the liquid level will increase. A feedback levelcontroller will wrongly decrease the water make-up rate. Therefore, the steam rate is measured and the required water makeup is calculated. This feedforward action is combined with the feedback provided by the level controller. As recommended in previous works, the inventory of reactants in the plant is maintained by fixing the reactor-inlet flows. Acetic acid is taken with constant rate from a storage tank, and the fresh feed is added on level control. The gas rate going to the evaporator is a good estimation of the ethylene inventory. Therefore, this flow is kept constant by adjusting the fresh ethylene feed. The fresh oxygen rate is manipulated by a concentration control loop, as previously explained.
52
C.S. Bildea and A.C. Dimian
TC Steam
O2
F FF
C2H4 recycled
+
PC
TC
CC
+
LC
T
Reactor
T
HS
FC
T
Steam generator
C2H4 fresh
FC AcOH recycled
PC
TC
Evaporator
AcOH fresh
VAc crude to separation
FC
LC AcOH storage
FC AcOH to separation
Figure 2. Control structure for fresh feeds and around chemical reactor CO2 removal
CO2
C2H4 recycled
FC CC
AcOH
PC FC AcOH
C-4 C-1 LC
PC PC
TC
3Flash
C-1
Decanter
LC TC
FC
LC C-5
LC PC
TC LC
PC LC LC
VAc
C-3
T-1 VAc crude from reactor
PC
LC
TC
FC C-6 TC Water
Water AcOH to storage
Figure 3. Control structure of the separation section
Effect of Catalytic Reactor Design on Plantwide Control Strategy
53
The separation section takes advantage from the heterogeneous azeotrope formed by vinyl acetate and water. Significant energy saving, up to 70 %, can be obtained by making use of a dehydration gas pre-treatment. In this way the exothermic reaction can cover up to 90 % from the energy requirements of the distillations. The control of the separation section is presented in Figure 3. Because the distillate streams are recycled within the separation section, their composition is less important. Therefore, columns C-3, C-5 and C-6 are operated at constant reflux, while boilup rates are used to control some temperatures in the lower sections of the column. For the absorption columns C-1 and C-4, the flow rates of the absorbent (acetic acid) are kept constant. The concentration of CO2 in the recycle stream is controlled by changing the amount of gas sent to the CO2 removal unit. Temperature and pressure control loops are standard. In Reactor / Separation / Recycle systems, two strategies can be employed to achieve production rate changes. The first one, by manipulating the reactor inlet flows, does not work here: the acetic acid does not influence the reaction rate, the per-pass conversion of ethylene is very low (10%), while the reactor-inlet oxygen concentration is restricted by the safety concerns. Therefore, the second strategy manipulating the reaction conditions is applied.
4. Results Figure 4 shows results of simulation in Aspen DynamicsTM, for the following scenario: the plant is operated at the nominal steady state for 1 hour. Then, the coolant temperature is increased from 413 K to 425 K and simulation is continued for 2 hours. The maximum temperature inside the reactor increases from 455 K (at 0.8 m from reactor inlet) to 469 K (at 1.2 m from inlet). The higher temperature results in higher reaction rates, less reactants being recycled. The gas recycle is the fastest, and the ethylene feed is the first to be adjusted. Then, more oxygen is added by the concentration controller. The dynamics of the liquid recycle is slower and it takes about 0.5 hours until the acetic acid feed reaches the new stationary value. The vinyl acetate production rate increases from 154 kmol/h to 171 kmol/h. At time t = 3 hours, the coolant temperature is reduced to 400 K, and the simulation is run for another 2 hours. The maximum reactor temperature drops to 452 K (near reactor inlet) and the production rate is decreased to 134 kmol/h. During the entire simulation, the oxygen concentration stays very close to the setpoint of 6%. Moreover, the concentration of the vinyl acetate product is above the 99.98% specification. Similarly to our approach, Luyben and co-workers [4, 5] proposed to fix the reactorinlet flow rate of acetic acid and to use the fresh feed to control the inventory in the bottom of the acetic-acid distillation column. The two control strategies are equivalent (a)
(b)
Ethylene
180 160
Acetic acid 140 120
Oxygen
100 80
180
Water
160
Vinyl acetate
40 30
140 20
120
CO2 10
100 80
0
1
2
3
time / [h]
4
5
Flow rate / [kmol/h]
50
200
Flow rate / [kmol/h]
Flow rate / [kmol/h]
200
0 0
1
2
3
4
5
time / [h]
Figure 4. Dynamic simulation results as flow rates of a) fresh reactants and b) products
54
C.S. Bildea and A.C. Dimian
from a steady state point of view. However, Olsen et al. [6] showed that Luyben’s structure has an unfavourable dynamics due to the large lag between the manipulated and controlled variables. The other important control loops in [5] paired the oxygen feed with oxygen concentration, and ethylene feed with pressure in the system. The production rate was also manipulated by the setpoint of reactor temperature controller. Chen and McAvoy [7] applied a methodology where several control structures, generated on heuristic grounds, were evaluated using a linear dynamic model and optimal control. Their results also indicate that fixing the reactor-inlet flows is the recommended strategy.
4. Conclusion The case study of vinyl acetate synthesis emphasises the benefits of an integrated process design and plantwide control strategy based on the analysis of the Reactor / Separation / Recycles structure. The core is the chemical reactor, whose behaviour in recycle depends on the kinetics and selectivity of the catalyst, as well as on safety and technological constraints. Moreover, the recycle policy depends on the reaction mechanism of the catalytic reaction. The approach in steady state reactor design finds a dynamic equivalent in the plantwide control strategy. Because of low per pass conversion of both ethylene and acetic acid, manipulating the flow rate of reactant at reactor inlet has little power in adjusting the production rate. The reaction temperature profile becomes the main variables for changing the reaction rate and hence ensuring the flexibility in production. The inventory of reactants is adapted accordingly by fresh reactant make-up directly in recycles. Productivity higher than 1000 kg VAM/m3-catalyst/h can be achieved working at higher temperature and shorter residence time, as well as with good temperature control. This approach can be seen as generic for low per pass reactions.
References [1] Bildea C.S., Dimian A.C., Fixing flow rates in recycle systems: Luyben’s rule revisited. Industrial and Engineering Chemistry Research. 2003; 42: 4578. [2] Downs J., Distillation Control in a Plantwide Control Environment. In Practical Distillation Control; Luyben W., Ed.; van Nostrand Rheinhold: New York: 1992. [3] Bildea C.S., Dimian A.C., Cruz S.C., Iedema P.D., Design of tubular reactors in recycle systems, Computers & Chemical Engineering 28 (1-2): 63-72, 2004. [4] Luyben M.L. and Tyreus B.D., An industrial design / control study for the vinyl acetate monomer process, Comp. Chem. Eng., 1998, 22, 867 [5] Luyben M.L., Tyreus B.D., Luyben W.L. , Plantwide control design procedure, AIChE Journal, 43 (12), 3161-3174, 1997 [6] Olsen, D., Svrcek, W., Young, B., Plantwide control study of a vinyl acetate monomere process design, Chem. Eng. Comm, 192 (10), 1243-1257, 2005 [7] Chen, R. and McAvoy, T., Plantwide control system design: methodology and application to a vinyl acetate process, Ind. Eng. Chem. Res., 42, 4753 – 4771, 2003 [8] Renneke, R. et al., Development of a high performance catalyst for the production of vinyl acetate monomer, Topics in Catalysis, 38(4), 279-287, 2006 [9] Han, Y. F., Wang J. H., Kumar, D., Yan, Z., Goodman D. W., A kinetic study of vinyl acetate synthesis over Pd-based catalysts, J. Catalysis, 232, 467, 2005 [10] Han, Y. F., Kumar, D., Sivadinarayana C., Goodman, D. W., Kinetics of ethylene combustion in the synthesis of vinyl acetate, J. Catalysis, 224, 60, 2004
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
55
Model of the Product Properties for Process Synthesis Peter M.M. Bongers Unilever Food and Health Research Institute, Olivier van Noortlaan 130, 3130 AC,Vlaardingen, The Netherlands
Abstract In the hierarchical decomposition method, or, process synthesis one only looks at the input-output structure of the process at the first level. In subsequent levels more detail is added, finally ending with the entire flowsheet. Design decisions are made by using heuristics and models. The amount of detail in the models depend on the level at which the models are applied. The models are used to describe how processes behave in terms of bulk properties. However, during the product-process design, the product is judged on sensory attributes. The models need extension to sensory attributes (the property model). The sensory attributes depend on physical attributes, as can be predicted by the models, and ingredients. This dependency range from constant to highly non-linear. This paper describes how the problem of determining the lowest complexity model for the property function can be formulated and solved for an ice cream example. The estimated property function model provides a good estimation of the sensory attributes. In combination with a process function model we are able to related ingredients and process conditions with sensory attributes. Keywords: product-process design, sensory models, neural networks.
1. Background Process synthesis is regarded as the invention of conceptual process designs. These designs are expected to be reliable, economic attractive and generated within a limited time frame. Thus, process synthesis is the generation of alternatives and choices to reduce the number of alternatives in all conceptual process engineering steps within the innovation process. As the number of possible alternatives to perform a desired task can be easily about 104 to 109, methodologies are required to reduce this explosive number to manageable levels. The development of those methodologies to aid engineers to better design a process is not a novel challenge. In the chemical industry, first academic publications and successful industrial implementations related to process synthesis methodologies are well established, see Douglas (1988), Sirola (1996). In the hierarchical decomposition method developed by Douglas (1988) one only looks at the input-output structure of the process at the first level. In subsequent levels more detail is added, finally ending with the entire flowsheet. Design decisions are made by using heuristics and models. The amount of detail in the models depend on the level at which the models are applied. Historically, process models are used to describe how processes behave in terms of bulk properties such as flow, temperature, pressure, concentration, etc. However, our consumer goods, such as soups, mayonnaise or ice cream, are not bought on their bulk properties, but on how consumers perceive the products. During the product-process
P.M.M. Bongers
56
design stages, the product is judged on measured sensory attributes, such as mouth feel, bite, creamy texture, etc. Hence, there is a need to extend process models with sensory attributes. Figure 1 shows how the process model can be extended into a model chain from raw materials, equipment and operational conditions through sensory attributes to consumer liking. OPERATIONAL CONDITIONSL
EXTERNALDISTURBANCES
PROCESS FUNCTION
CONSUMER LIKING
SENSORY ATTRIBUTES
PHYSICAL ATTRIBUTES
RAWMATERIALS
PROPERTY FUNCTION
PRESSURE TEMPERATURE AIRCRYSTALSIZES
CONSUMER FUNCTION
SMOOTHNESS ICINESS CREAMINESS
Figure 1 Process, property and consumer function for ice cream
Products are bought by the consumers based on their perceived benefits. A product design should therefore aim at satisfying specific consumer benefits. To be more precise, one needs to be able to relate the ingredients, equipment and processing conditions to the consumer benefits. In the design phase there is the need to evaluate concepts without ‘large’ and expensive consumer trials. For this purpose sensory attributes measured by a trained QDA panel, are used to measure consumer benefits. Previously reported work describes dynamic process model for ice cream freezers (Bongers, 2006) and extruders (Bongers and Campbell, 2008) to relate operating conditions, equipment geometry with physical attributes, such as extrusion temperature. This leaves the property function as the unknown to be found. As no fundamental relations are currently available on which to develop a model, we have to revert to experimental relations. Then, for analysis purposes, the property function should be determined from physical attributes to sensory attributes. For synthesis purposes, the property function should be determined from sensory attributes back to physical attributes. In the past various attempts have been made to determine the property functions for all kinds of products. Almost all of these use linear regression techniques (see for example Powers and Moskovitz, 1974) to deal with the measured data. By the fact that most of the property function is highly non-linear, these techniques fail. In addition to the linear regression, a linear regression on non-linear functions of the attributes can be used. The drawback is that the non-linear functions of the attributes have to be defined by the user. At present this have to be done by trail-and-error and turns out to be a very tedious. Based on the above observations, a successful approach to determine the property function has to be based on a generic non-linear function description. One such approach is to use neural networks as a non-linear describing function.
Model of the Product Properties for Process Synthesis
57
2. Data manipulation 2.1. Data set The dataset of 30 experiments contains: • 1 equipment type (usage of a freezer or a freezer and single screw extruder) . This is a nominal parameter (-1 for only freezer, +1 for both freezer and single screw extruder) • 1 process parameter (exit temperature). This is a continuous parameter between -6oC and -13oC with a resolution of 0.1oC • 1 ingredients parameter (fat level). This is a continuous parameter between 8% and 12% with a resolution of 1% • 25 sensory properties of the icecream. These are ordered intervals between 0 and 10 with a resolution of 0.1 The property model has 3 independent inputs and 25 outputs. This multi-input-multioutput system can also be described as a multiple (decoupled) system of multi-inputssingle-output (Ljung, 1999). 2.1.1. Data analysis Basic statistical analysis on the sensory properties (variance, kurtosis and min-max) showed that 4 sensory parameters where not influenced by the inputs and hence excluded from the analysis (later on, they will be indicated as constant). Correlation analysis between the sensory attributes showed 3 sensory attributes having a correlation coefficient of 0.95 or higher with each other. For this cluster only one of the sensory attributes is taken forward in the analysis. As a result, only 17 sensory attributes will be analysed.
3. Property model The property model should be as simple as possible, but not too simplistic That means that for each of the senory parameters we need to determine the ‘simplest’ relation. On the data set two types of describing functions will be determined: a linear regression or neural network to describe the non-linearities. Which of the models to use will be determined by trading-off the prediction error against the number of parameters used, i.e. the AIC (Akaike, 1974). 3.1.1. Linear regression Multiple linear regression can be applied to determine a linear function having the following form: Sensory attribute(n) = p1 ⋅ Fatlevel + p2 ⋅ Temperature + p3 ⋅ FreezerType + p4 3.1.2. Neural network A neural network consists of a number of nodes, called neurons, connected to the inputs and outputs, having the following structure for this application.
P.M.M. Bongers
58
fat level extrusion temperature
sensory attribute
freezer type
The neurons weight all inputs and provide an output via the activation function. The complexity of the neural networks used will be determined by the number of nodes in the hidden layer (2,3,5 or 7). The activation applied in this application is a hyperbolic tangent function. In mathematical terms, the output of neuron j is defined by: output of neuron j With: yj n wiu i input from neuron i (or input i), weighted with wi y = tanh( Σ w u ) i i
j
i=1
The weightings wi in the neural network are determined by an optimisation algorithm using the error between the measured outputs and the outputs predicted by the neural network. The work of Rumelhart et.al. (1985) is recommended for more details about this type of neural networks and examples. In theory one hidden layer neural network is sufficient to describe all input/output relations. More hidden layers can be introduced to reduce the number of neurons compared to the number of neurons in a single layer neural network. The same argument holds for the type of activation function and the choice of the optimisation algorithm. However, the emphasis of this work is not directed on the selection of the best neural network structure, activation function and training protocol, but to the application of neural networks as a means of non-linear function fit.
4. Model parameter estimation 4.1. Training set In order to be able to perform validation of the model, not all 30 cases can be used to determine the model. Also care must be taken to which cases will be used for validation and which cases for determination of the model. Because it is easy with an experimental model to fit noise in the data, a ‘large’ validation set has been chosen (5 cases in the validation set and 25 cases remaining in the set to determine the model (=training set) ). To avoid coincidental results, the whole procedure is repeated 5 times with different training sets and validation sets, where the cases in the validation set have been selected randomly. 4.2. Error Criterion The next step is to determine the error criterion on which to decide the predictive value of the model and to decide which prediction type to use for which sensory attribute. For each of the sensory attribute, the root mean square of the prediction error, ε, will be used to evaluate the properties of the prediction model type. With: yˆ predicted output for case i N
ε :=
1 N −1
¦
i =1
( yi − yˆ i ) 2
i
yi N
measure output for case i number of cases
Model of the Product Properties for Process Synthesis
59
4.3. Results The whole analysis (including the penalty for over parametrising) has been implemented in Matlab (Mathworks 2007) using the public domain neural network tool of Norgaard (1995). The following predictor type, and mean square errors for the sensory attributes have been obtained. predictor type
Sensory attribute No Name . 1 Firmness on spooning
0.10
Neural (3*)
predictor type
Sensory attribute No Name . 14 powdery
0.02
Constant
2
Initial firmness
0.11
Neural (2)
15 vanilla pods
0.06
Neural (3)
3
Chewiness
0.05
Neural (3)
16 flavour melt
0.05
4
Coldness
0.18
Linear
17 creamy flavour 0.44
Correlated with 10 Linear
5
Crumbliness
0.08
Neural (2)
18 sweetness
0.03
Constant
6
inital smoothness
0.08
Neural (2)
19 sharp/yogurt
0.02
Constant
7
I/C quantity in mouth
0.11
Neural (7)
20 fruity
0.12
Neural (2)
8
I/C/ size in mouth
0.11
Neural (2)
21 vanilla flavour 0.07
Neural (2)
9
Rate of melt
0.17
Linear
22 boiled milk
0.14
Linear
10 Creamy texture
0.12
Neural (5)
23 other flavour
0.04
Constant
11 Thickness
0.14
12 final smoothness
0.15
Correlated with 10 Neural (2)
24 unexpected 0.15 flavour 25 final mouth- 0.16 coating
13 grittiness
0.07
Neural (2) sum of errors
Linear Neural (2)
2.78
As an example for the validation, one of the validation cases is shown below. It can be seen that almost all sensory attributes are predicted within the accuracy of the data. Sensory model validation (case 3) firmness on spooning initial firmness chewiness coldness crumbliness inital smoothness I/C quantity in mouth I/C/ size in mouth rate of melt creamy texture thickness final smoothness grittiness powdery vanilla pods creamy flavour sweetness sharp/yogurt fruity vanilla flavour boiled milk other flavour unexpected flavour final mouth-coating mouthdry/astringent
measured predicted 0
*
2
4 6 8 sensory score (st. dev.= 0.1242)
Denotes the number of neurons in the hidden layer.
10
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P.M.M. Bongers
5. Conclusions and future work The process models predicting bulk physical attributes have been augmented by a properties model describing the relations between the physical attribues and the sensory attributes. For each of the sensory attribute the lowest complexity model has been determined. Instead of an trial-and-error approach, a neural network with one hidden layer has been used as a generic non-linear function. The complexity of the neural network can thus be seen as the number of nodes in the hidden layer. The performance of the property function model obtained by the above described procedure has verified with the validation set and the property function model provides a good estimation of the sensory attributes.
References Akaike, H (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6): 716–723. Bongers, P.M.M. (2006) A Heat Transfer model of a scraped surface heat exchanger for Ice Cream, Proc. 16th European Symposium on Computer Aided Process Engineering Bongers, P.M.M., I. Campbell (2008) A Heat Transfer Model of an Ice Cream Single Screw Extruder, Proc. 18th European Symposium on Computer Aided Process Engineering Bruin, S. (2004) Lecture notes ‘Product design’, Technical University of Eindhoven, The Netherlands Douglas, J.M. (1988). Conceptual design of chemical process, McGraw Hill, New York. Lennart, L. (1999). System Identification — Theory For the User, 2nd ed, PTR Prentice Hall, Upper Saddle River, N.J. Matlab (2007). User guide, Norgaard, M. (1995). Neural Network based system identification toolbox, for use with MATLAB, Report 95-E-773, Institute of Automation, Technical University of Denmark. Powers, J.J., H.R. Moskowitz (1974). Correlating sensory objective measurements; new methods for answering old problems, Amer. Soc. Testing Materials, Philadelphia. Rumelhart, D.E., G.E. Hinton, R.J. Williams (1986). Learning internal representation by error propagation, Parallel Distributed Processing, MIT Press. Siirola, J.J. (1996). Industrial applications of chemical process synthesis, Advances in Chemical Engineering, 23, J.L. Anderson (Ed.), 1996 Wildmoser, J. (2004), Impact of Low Temperature Extrusion Processing on Disperse Microstructure in Ice Cream Systems, Dissertation ETH no. 15455.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
61
Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model André B. de Haan,a Norbert J.M. Kuipers, b Maartje Steensmac a
Eindhoven University of Technology, Faculty Chemical Engineering and Chemistry, PO Box 513, 5600 MD Eindhoven, The Netherlands b University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands c Akzo Nobel Salt bv,PO Box 10, 7400 AA Deventer, The Netherlands
Abstract Chiral compounds are important products in the pharmaceutical and fine chemical industry. Fractional reactive extraction (FREX) is a promising enantiomer separation method but knowledge on translation into industrial practice is very scarce. In this work the combinations of process and product parameters that generate a specified yield and product purity have been evaluated using a multi-stage equilibrium model. The simulations demonstrated that the influence of changes in process parameters (pH, T, concentrations) can be predicted with the multistage equilibrium model for reactive extraction of phenylglycinol and phenylethylamine. A higher pH, lower temperature, higher concentrations and a higher excess of extractant all result in higher purities. Implementation of reflux results in somewhat higher product purities (or less stages), but a significant loss in capacity. Recovery of product and extractant by backextraction should be carried out by pH shift, preferably with CO2 to prevent salt formation. For separating racemic mixtures with a minimal single stage selectivity of 1.5 a multiproduct extractor should contain 50 stages, evenly distributed over the wash and strip section. Keywords: Multistage modeling, Fractional extraction, Enantiomer
1. Introduction In the pharmaceutical and fine chemical industry, chiral compounds play an important role as intermediates and end products. Most of these products are produced in a multiproduct environment. Fractional reactive extraction (FREX) is a promising alternative to existing enantiomer separation methods. In this technique an enantioselective extractant is employed as separating agent in the fractional extraction scheme that employs a wash stream to remove the less strongly bonded enantiomer from the extract. [1]. So far, (fractional) reactive extraction has been studied by a number of authors for chiral separation of amino acids [2-7] and occasionally for other enantiomer classes [812]. However, knowledge on translation of lab-scale FREX into industrial practice or into a general multi-product design is very scarce. In our previous work, we have established an azophenolic crown ether based solvent system as a versatile, i.e. multiproduct, and highly selective extractant for various amines and amino alcohols [13]. The single-stage extraction equilibria including back-extraction were investigated [14] as well as the kinetics of the complexation reactions [15].
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As a step towards industrial implementation, this work aims to elucidate which combinations of process and product parameters generate a specified yield and product purity in a multistage extractor. To reach this goal, a multi-stage equilibrium model has been constructed based on a single stage description comprising the chemical and physical equilibria of the system. Simulations have been performed to study the effect of process parameters and the consequences for the design of a multi-product extractor. EXTRACT R, C
WASH
aq
org pK
HR+ HS+
pK
H+ + R H+ + S
P
P
R+C S+C
KR
KS
1
RC
FEED R,S
wash section
2
3
SC
strip section
4
RAFFINATE S
SOLVENT C
Figure 1: (left) Single extraction stage: main equilibria between enantiomers ‘R’ and ‘S’ and enantioselective extractant ‘C’; (right) fractional extraction scheme with wash stream (KR > KS).
2. Multi-Stage Equilibrium Model For the previously established azophenolic crown ether extractant a predictive single stage equilibrium model (Figure 1) was constructed and validated [14]. The extent of extraction is characterised by the distribution ratios DR and DS for each enantiomer:
DR =
[ R ]org ,allforms [ R ]aq ,allforms
=
[ R ]org + [ RC ]org +
[ R ]aq + [ HR ]aq
and
DS =
[ S ]org ,allforms [ S ]aq ,allforms
(1)
The operational selectivity αop is defined by the ratio of these distribution ratios. Its upper limit is the intrinsic selectivity αint, which is the ratio of the complexation constants:
α op =
DR DS
(assuming DR > DS)
and
α int =
KR KS
(2)
In fractional extraction equipment, additional degrees of freedom are the solvent-to-feed ratio (S/F), the wash flow (as W/F or W/S), the number of stages and the location of the feed stage. As measure for optical purity of the raffinate and the extract, the enantiomeric excess (e.e.) is used [16]. The e.e. and yield of the enatiomer R in the extract are given as:
e.e. =
[ R] − [ S ] [ R] + [ S ]
yield R , EXTRACT =
total R extract total R feed
[mol ] (3) [mol ]
The concentrations of extractant and enantiomer are characterised by the ‘concentration level’ and the ‘extractant excess’ defined as:
Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model
excess extractant =
63
S ⋅ [C ] solvent F ⋅ [rac] feed
(4)
In the multistage equilibrium model all single stages are connected countercurrently (Figure 1). The multistage model is implemented in gPROMS (PSE Ltd., London, UK). All equilibrium conditions and mass balances are solved simultaneously. To reduce the simulation time, the influence of process conditions is studied at a fixed number of stages of 4 (2 in each section) with the specification to ‘reach equal e.e. in each stream’. This specification is used to ensure that a ‘symmetrical’ separation (equal purity in extract and raffinate) is obtained. In each simulation the wash flow (expressed as W/S or W/F) is adapted to reach the point where the e.e. in the raffinate equals the e.e. in the extract.
3. Results and discussion 3.1. Influence of process parameters Figure 2 and 3 show that for both phenylglycinol (PG) and phenylethylamine (PEA) an increase in extractant excess, an increase in pH, a decrease in temperature or a higher overall concentration level all result in an ‘equal e.e.’ point at a higher e.e. in both streams and at a higher W/F ratio. By each of these changes, the extent of complexation between crown ether and both enantiomers increases (see Figure 1). If the wash stream is not adapted, the yield in the extract increases, but e.e. decreases. Vice-versa, the purity in the raffinate increases, but the yield decreases. If now the wash stream is increased as well, more enantiomer is washed back from the extract, and equal yield and purity are obtained in extract and raffinate. 3.2. Influence of number of stages The influence of pH and concentration level on the W/F ratio and required number of stages that yield a product purity of 0.98 e.e. are presented in Figure 4. It can be seen that lower pH or lower extractant excess results in a lower e.e. in four stages and thus also in a larger stage requirement to reach e.e. = 0.98. 1
PG
20
0.8
30
W/F
0.4
e.e.
W/F
0.6 PEA
0.8
PG
15
PEA
20
1
0.6
PEA
10 PEA
10
PG
0 0
10
20
T [°C]
30
0.2
5
0
0
0.2
PG
7.5
0.4
e.e.
40
8.5
9.5
0 10.5
pH
Figure 2: Influence of temperature (left) and pH (right) on ‘equal e.e.’ points (W/F, e.e.) for separation of PEA (pH=9.4) or PG (pH=9.1); S/F=2 with [rac] =0.01 M and [C]=0.01 M.
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A.B. de Haan et al. 20
0.9
40
1
30 [C]= 0.01
10 0.8
S/F=1
5
W/F
0.85 e.e.
W/F
15
PG
0.8
PEA
0.6
20 0.4
PEA
10
e.e.
S/F=1
0.2 PG
0
0
0.75 0
2
4
6
8
0
10
0 0.04
0.02 [C] = [rac], M
extractant excess [-]
40
40
30
30
30
20
20
10
10
10
0
0
15 20 10 5 0 8.5
9
9.5
N
W/F
20
40
W/F
25
10
N
Figure 3: Influence of extractant excess on PG separation (left, pH=9.1) and concentration level on equal e.e. points (W, e.e.) for separation of PEA (pH=9.4) or PG (right), S/F=2
0 0
pH
2
4
6
8
10
extractant excess [-]
Figure 4: Influence of pH (left) and extractant excess (right, pH=8.6) on W/F ratio and stage requirement N for PEA separation; e.e.=0.98 in both extract and raffinate, S/F=2, [rac]=0.02 M. 1
2.4
0.88
extract
0.87
0.9 raffinate
0.8
0.86
e.e.
W/F
e.e.
2.2
2 0.85
0.7
1.8 0
0.0005 [R-PG] in wash
0.001
0
0.0005
0.84 0.001
[R-PG] in wash
Figure 5: (left) Effect of reflux of R-PG in wash stream in PG separation on e.e. in extract and raffinate, fixed W/F=2.3, [rac]feed=0.01 M, S/F=2 with [C]=0.01 M (right) influence on location of equal e.e. points: W/F and e.e.
Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model
65
3.3. Minimal excess of extractant It was observed in the simulations that if there is no excess of extractant over the enantiomers, a full separation can never be obtained. Under these circumstances, the extractant will eventually become fully loaded, and adding more stages will not increase the product purity any further. Therefore, a minimal excess around 1.5 is required for the conditions and systems studied in this paper.
Wash stream W
3.4. Reflux The effect of reflux (addition of R-PG to wash stream) on e.e.’s in separation of PG is given in Figure 5(left) for a constant wash stream. It can be seen that the purity in the extract increases and the purity in the raffinate decreases. New ‘equal e.e.’ points were determined by adapting the wash stream. They are presented in Figure 5(right). It is concluded that reflux of the strongly bound enantiomer in the wash stream indeed results in a better e.e. (or lower stage requirement) and lower W/F ratio at the operating point. However, for an appreciable effect a rather large concentration of one enantiomer has to be present in the wash stream, so a large fraction of the W2 aq. stream product stream (raffinate 2) needs to be refluxed. Especially with a F high W/F ratio, application of fractional back Feed reflux may be uneconomical. extraction extraction (R,S) Figure 6: Conceptual flow sheet comprising fractional extraction and back-extraction unit with recycle of solvent stream. Assumption: R is preferentially extracted ( KR > KS)
solvent, C clean
solvent, R,C loaded
Raff. 2 R in water
Raff. 1: S in water
6
6
4
4
W2/F
W2/F
N=2 N=2
2
N=3
0
N=3
2 0
5.5
6 pH
6.5
5.5
6
6.5
pH
Figure 7: Back-extraction of PEA (left) and PG (right) by pH shift, aqueous stream W2 (as ratio to feed F) requirement for 99.5 % recovery. Data for N=2 and N=3, loading conditions: 5 °C, S/F=1.5, [C]=[rac]=0.02 M.
3.5. Back-extraction To recover the strongly bound enantiomer product and the extractant, the loaded solvent stream can be treated in a back-extraction unit (Figure 6). A convenient way to achieve back extraction by pH shift without producing salts is the addition of low-pressure CO2 [14]. The model results for back-extraction of PEA (left) and PG (right) by pH shift are
66
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presented in Figure 7 for 2 and 3 equilibrium stages. It can be seen that the W2/F ratio decreases with decreasing pH and increasing number of stages. W2/F determines the dilution of the product in raffinate 2 compared to the feed meaning that for W2/F 1.5 can be succesfully separated, and with 30 stages, all systems with αop > 2.0. Any ‘excess’ stages for a certain component opens possibilities to increase the capacity or reduce costs in that specific separation. The multistage model can be used as a tool for optimization.
5. Conclusions The availability of the versatile crown ether extractant in combination with the multistage model results in a unique separation tool in a multi-product environment. The influence of changes in process parameters (pH, T, concentrations) can be predicted with the multistage equilibrium model for reactive extraction of phenylglycinol and phenylethylamine. The purity and yield can be improved by each measure that results in a higher extent of complexation; a higher wash flow rate is required then to obtain a good yield and purity in both product streams. Implementation of reflux results in somewhat higher product purities (or less stages) at a slightly smaller W/F ratio, but a significant loss in capacity. Recovery of product and extractant by backextraction should be carried out by pH shift, preferably with CO2 to prevent salt formation.
References [1] T.C. Lo, M.H.I. Baird, C. Hanson, 1983, Handbook of Solvent Extraction. Wiley-Interscience, New York [2] T. Takeuchi, R. Horikawa, T. Tanimura, 1984, Anal. Chem., 56, 1152-1155. [3] H.B. Ding, P.W. Carr, E.W. Cussler, 1992, A.I.Ch.E.J., 38, 1493-1498. [4] Y. Yokouchi, Y. Ohno, K. Nakagomi, T. Tanimura, Y. Kabasawa, 1998, Chromatography, 19, 374-375 [5] H. Tsukube, J. Uenishi, T. Kanatani, H. Itoh, O. Yonemitsu, 1996, Chem. Comm., 4, 477-478. [6] M. Pietrasckiewicz, M. Kozbial, O. Pietraszkiewicz, 1998, J. Membr. Sci., 138, 109-113. [7] P.J. Pickering, J.B. Chaudhuri, 1997, Chem. Eng. Sci., 52, 377-386. [8] Y. Abe, T. Shoji, M. Kobayashi, W. Qing, N. Asai, H. Nishizawa, 1995, Chem. Pharm. Bull., 43, 262-265. [9] Y. Abe, T. Shoji, S. Fukui, M. Sasamoto, H. Nishizawa, 1996, Chem. Pharm. Bull., 44, 15211524. [10] V. Prelog, Z. Stojanac, K. Kovacevic, 1982, Helv. Chim. Acta, 65, 377-384. [11] V. Prelog, S. Mutak, K. Kovacevic, 1983, Helv. Chim. Acta, 66, 2279-2284. [12] V. Prelog, M. Kovacevic, M. Egli, 1989, Angew. Chem. Int. Ed. 28, 1147-1152. [13] M. Steensma, N.J.M. Kuipers, A.B. de Haan, G. Kwant, 2006, Chirality, 18, 314-328. [14] M. Steensma, N.J.M. Kuipers, A.B. de Haan, G. Kwant, 2006, J. Chem. Techn. Biotechn., 81. 588-597. [15] M. Steensma, N.J.M. Kuipers, A.B. de Haan, G. Kwant, 2007, Chem Eng. Sci., 62, 13951407. [16] R.A. Sheldon, Chirotechnology, Industrial synthesis of optically active compounds. Marcel Dekker Inc., 1993.
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Synthesis of Cryogenic Energy Systems Frank Del Nogal, Jin-Kuk Kim, Simon Perry and Robin Smith Centre for Process Integration, The University of Manchester, PO Box 88, Manchester, M60 1QD,United Kingdom
Abstract The use of cold energy should be systematically integrated with process streams in lowtemperature systems for energy savings and sustainable low-carbon society. In this paper, new design methodology for cascaded mixed refrigerant systems with multistage heat exchanges has been proposed, which systematically screens, evaluates and optimizes key decision variables in the design of refrigeration cycles (i.e. economic trade-off, partition temperature, refrigerant compositions, operating conditions, refrigerant flowrate). The integrated design and optimization for overall cryogenic energy systems is also addressed to reflect system interactions between driver selections and design of refrigeration systems. Two case studies are illustrated to demonstrate the advantage using developed design methods. Keywords: Low temperature energy systems, Mixed refrigerants, Power systems, Synthesis, Optimization
1. Provision of low-temperature cooling The provision of cold energy to process industries has gained far less attentions from process engineering community, compared to energy systems which is based on hightemperature energy carrier (e.g. steam), although sub-ambient cooling has a significant potential for energy saving in practice. Effective use of cold energy is vital to ensure the cost-effectiveness of low-temperature processes, as significant power requirement for compression is one of major energy consumptions in the provision of cryogenic cooling to process streams. One of widely-used techniques to save energy requirement in the cryogenic energy systems is to apply a heat integration technique, such that most appropriate levels and duties for refrigeration are determined to match them against GCC (grand composite curve), as shown in Figure 1 (Linnhoff et al., 1982; Linnhoff and Dhole, 1989; Smith 2005). The GCC represents overall characteristics of energy systems, and this provides better understanding how to design the refrigeration cycles. Figure 1 illustrates the cycle in which pure refrigerant is employed as a working fluid, and two levels of cooling for process streams are facilitated by using multiple expansion. If one level of refrigeration is provided, all the cooling duty is provided at Level 2, which results in large compressor shaftpower requirements. The thermodynamic efficiency of the simple cycle can be improved by introducing economizer, vapor cooler and inter-cooler with multi-level expansion (Wu, 2000, Smith 2005). The cascading two simple cycles, in which different refrigerant is used, is a useful way to reduce shaftpower requirements for compressor when large temperature range is to be covered by refrigeration. Another important degree of freedom for energy
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saving in refrigeration system is the decision for how to reject heat to or remove heat from process stream(s). These considerations often lead to have a complex cycle with multi-levels and/or cascaded arrangement, which consists of large number of unit.
T*
Level 1
Q1
Level 1 W
Q2
Level 2 Level 2
Q1
(A)
ΔH
Q2 (B)
Figure 1. Refrigeration with pure refrigerant The use of mixed refrigerants in the cycle can simplify the structure of refrigeration cycle as well as reduce compression duty significantly. As illustrated Figure 2a, the close match between hot (process) stream and cold (refrigeration) stream can be achieved by using mixed refrigerant, while pure refrigerant cannot avoid thermodynamic inefficiency due to large gap existed between two streams. The shape of refrigeration stream in Figure 2a depends on the composition of refrigerants and its operating conditions. When large temperature range is to be cooled by mixed refrigerant systems, cascade arrangement is also possible (Figure 2b). Other structural variations to obtain a better match between hot and cold stream profiles had been suggested, for example, repeated partial condensation and separation of the refrigerant stream (Finn et al., 1999), and a self-cooling mixed refrigerant cycle (Walsh, 1993). T
Process stream T
Process stream Upper cycle
Pinch Point Evaporator (mixed refrigerant)
Partition temperature
Lower cycle Evaporator (pure refrigerant) H
H (A)
(B)
Figure 2. Mixed refrigerant systems In order to explore the advantages from mixed refrigerant systems, it is aimed to develop a systematic design and optimization framework for mixed refrigerant systems, in which design interactions are systematically investigated, as well as all the available structural and operating options are fully screened to provide optimal and economic design. The developed new design method also overcomes shortcomings which had not
Synthesis of Cryogenic Energy Systems
69
been fully addressed in previous works done by Lee (2001) and Vaidyaraman and C. Maranas (2002): i) ii) iii) iv)
enforcement of minimum temperature difference (ΔTmin) throughout the heat recovery systematic trade-off between capital and operating cost multi-stage compression with inter-cooling, and avoiding being trapped in local optima.
2. Optimization of Mixed Refrigerant Systems Mixed refrigerant systems are optimized with the superstructure shown in Figure 3. The superstructure used in this work is arranged with multi-stage heat exchangers in which mixed refrigerant cycle provides not only cooling for a process stream, but also cooling of a hot gas stream. The liquid refrigerant is separated from hot refrigerant stream, and this can be further subcooled in the exchanger before expansion or can be expanded without subcooling. Both cases can be considered within the superstructure proposed in the study. The complexity of the multi-stage arrangement is further increased by introducing cascading of two cycles. The composition of refrigerants and operating conditions for each cycle can be chosen differently, which provides great flexibility in the design as the cooling profile can be closely matched with process stream. The heat recovery is integrated between upper and lower cycles. It should be noted that economic trade-off should be made to justify gains obtained from complex structures at the expense of capital cost.
.....
Process Stream
Figure 3. Superstructure for cascaded mixed refrigerant systems The key optimization variables in the design are: flowrate and composition of mixed refrigerants for each cycle, intermediate temperature between stages for each cycle, and operating pressures of stream after and before compressor for each cycle. The optimization formulation includes: •
Objective function
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• • •
Material and energy balances for each stage Pressure, temperature and enthalpy profiles Multistage compression arrangement with inter-cooling
The developed optimization is solved with genetic algorithm as the previous study based on deterministic optimization techniques showed that it is often trapped in local optima, due to highly non-linear nature of formulations in the model. The simulation model and genetic algorithm is interacted to produce high quality optimal solution(s), although computational time is relatively expensive. It should be mentioned that one of important features in the developed model is to ensure feasibility of heat recovery in every exchanger. The potential candidate (design) produced during optimization, is simulated, and cold and hot composite curves are produced. Then this is rigorously checked against given ΔTmin.
3. Case study 1 First case study is to liquefy gas stream from 25 oC to -163 oC by single mixed refrigerant cycle with a single stage. The energy data for process stream is given in Figure 4. The objective function is to minimize the shaftpower demand for compression. When 5 oC of ΔTmin is considered, the optimal cooling systems with 27.8 MW of minimum power demand are given in Figure 4, in which compositions of refrigerants and operating conditions (flowrate, pressure) are shown as well. The comparison between Lee’s (2001) method and new method is made, which shows 8 % of improvement in power demand from new method. 30 oC
2.81 kmol/s 45.1 bar 1.8 bar
Process Stream
25 oC
-163 oC
N 2 14.5 % C 1 19.5 % C 2 39.3% C 3 0.04% n-C4 26.67 %
Temp ( oC) ΔH (MW) 25 -6 -57.7 -74.6 -96.5 -163
20.2 18.3 14.5 10.2 5.9 0
Figure 4. Case study 1: Optimal design for single mixed refrigerant systems
4. Case study 2: Integrated design for low-temperature energy system with driver selection The second case study is to cool gas stream from 35 oC to -160 oC, and the detailed energy flow is given in Figure 5. In this example, cascade mixed refrigerant systems is optimized with 3 oC of ΔTmin.
Synthesis of Cryogenic Energy Systems
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As low-temperature energy systems employs a series of compressor, the driver selection (i.e. matching between mechanical power demands and available direct drivers) is very important in the overall system design. The design of refrigeration systems (i.e. number of compressor and its duty) inevitably affects the driver selection, and therefore, an integrated design between refrigeration and driver selection should be made. The simultaneous optimization between two design problems are carried out, which provides more realistic and applicable design. (Figure 6) The optimized variables are shown in the Figure 5, at the minimum power demand with 216.06 MW. It should be noted that the design results from an integrated optimization of overall low-temperature energy systems, with the full consideration of driver selections. It is clearly illustrated that the composition and operating conditions per each cycle are optimized to serve for each operating range. One stage for each cycle is chosen in this case, as multi-stage arrangement is not favored, due to large capital expenditure. F = 20.3 kmol/s N2 0.1 % C1 9.8 % C2 41.6 % C3 11.8 % n-C4 37.3 %
37.3 bar 4 bar 35 oC
Process Stream
Temp ( oC) ΔH (MW) 35 4.5 -21.9 -54.0 -80.0 -131.4 -160.0
42.2 bar
212 186 158 120 65 22 0
F = 12.9 kmol/s N 2 11.1 % C 1 40.1 % C 2 35.3 % C 3 13.0 % n-C4 0.5 %
1.9 bar -160 oC
Figure 5. Case study 2: Optimal design for cascade mixed refrigerant systems Genetic Algorithm
Objective function
Set of operating conditions with structural options
Refrigeration simulator Updated power demands
Driver selection
Integrated design
Figure 6. Integrated design for low-temperature energy systems
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5. Summary The developed new synthesis method for mixed refrigeration system provides not only energy saving in cryogenic systems but also conceptual understanding of the design problem in cold energy management. The effective way for providing cold energy is exploited from cascaded multi-stage mixed refrigeration cycles, which can be very effective to reduce compression power in low-temperature systems. Also the integrated design of refrigeration and driver selection is also developed and discussed from the case study.
References A. Finn, G. Johnson and T. Tomlinson (1999) Developments in Natural Gas Liquefaction, Hydrocarbon Processing, 78 (4) G. Lee (2001) Optimal design and analysis of refrigeration systems for low temperature processes, PhD Thesis, UMIST, Department of Process Integration, Manchester, UK B. Linnhoff and V. Dhole (1989) Shaftwork Targeting for Subambient Plants, AIChE Spring Meeting, Houston, US B. Linnhoff, D. Townsend, D. Boland, G. Hewitt, B. Thomas, A. Guy and R. Marsland (1982) User Guide on Process Integration for the Efficient Use of Energy. IChemE: Rugby, England, 1982 R. Smith (2005) Chemical Process Design and Integration, John Wiley & Sons, Ltd., UK S. Vaidyaraman and C. Maranas (2002) Synthesis of Mixed Refrigerant Cascade Cycles, Chemical Engineerng Communications, 189 (8) B. Walsh (1993) Mixed Refrigerant Process Design, Off. Proc. Comb. Conf., 6th Conf. Asia Pac. Confederation. Chemical Engineering, 1, 59/1-64/1 G. Wu (2000) Design and Retrofit of Integrated Refrigeration Systems, PhD Thesis, UMIST, Manchester, UK
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Study of a novel Heat Integrated Hybrid Pervaporation Distillation Process: Simulation and Experiments a b
M.T. Del Pozo Gómez, a P. Ruiz Carreira, a J.-U. Repke, a A. Klein, T. Brinkmann, a G.Wozny,
a
Institute for Process Engineering, Berlin University of Technology, Strasse des 17. Juni 135, Berlin 10623, Germany b GKSS Research Centre GmbH, Department of Process Engineering, Institute of Polymer Research, Max-Planck-Straße 1, Geesthacht D-21502, Germany
Abstract In the present work a new developed heat integrated hybrid pervaporation distillation process is modeled and experimental studies are carried out to analyze the effect of the heat integration in the process. With the results of the experiments, the model is validated and a comparison between industrial scale non heat integrated and heat integrated processes is done. As a result, three main advantages are presented in the approach: a) reduction of the necessary external energy supply into the process, b) improvement in the pervaporation separation performance and c) reduction in the necessary membrane surface. Keywords: heat integration, hybrid process, pervaporation, azeotropic mixtures
1. Introduction The separation of homogeneous azeotropic mixtures has always been a highly energy consuming process in the chemical industry. Many efforts have been done in the last decade to find new and more efficient processes that improve the thermal separation techniques in practice. Between the different studied alternatives outstands the hybridpervaporation distillation process [F. Lipzinski, 1999]. It has been seen in previous studies [P. Kreis, 2004] that this technique can lead to a considerable reduction in the process costs by decreasing the total energy consumption. But despite of these promising results, only the application in the field of organic solvents dehydration has gained a bigger importance in the chemical industry [A. Jonquières, 2001], and the only way to increase its use is with the improvement of the pervaporation technique using a more efficient module design or a better performance membrane. In the present paper, for the bettering of the pervaporation process, the necessary external energy supply will be reduced. The pervaporation process is a separation process, which is based on the selective transport through a dense membrane combined with a phase change of the permeating components from liquid to vapor [F. Lipnizki, 2001]. To make the change of state (liquid – vapor) possible, energy is required. That is normally reflected in a temperature drop between the inlet feed and the outlet retentate streams, what makes the use of external heat exchangers necessary after consecutive pervaporation modules. In previous studies [M. T. Del Pozo Gomez, 2007] it has been found, that the use of the saturated vapor going out at the top of the distillation column as a heating medium inside the pervaporation module (see fig.1) can lead to a lower energy consuming process avoiding the need of external heat exchangers minimizing
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the temperature drop along the module, and increasing the permeate flux. In the present work, the use of the heat integration in the process is studied in detail and experimentally demonstrated. For that aim, a heat exchanger has been built and integrated with a flat sheet membrane module and a model for the whole hybrid process has been built and experimentally validated. Finally, the total energy saving in an industrial scale heat integrated process is calculated.
Figure 1: Hybrid pervaporation distillation process flow sheet. Left with external heat exchangers, right with heat integration.
2. Study of the heat integration concept 2.1. Model of the process For the study of the process, a set of partial differential model equations for a flat sheet pervaporation membrane with an integrated heat exchanger (see fig.2) has been developed. The temperature dependence of the permeability coefficient is defined like an Arrhenius function [S. Sommer, 2003] and our new developed model of the pervaporation process is based on the model proposed by [Wijmans and Baker, 1993] (see equation 1). With this model the effect of the heat integration can be studied under different operating conditions and module geometry and material using a turbulent flow in the feed. The model has been developed in gPROMS® and coupled with the model of the distillation column described by [J.-U Repke, 2006], for the study of the whole hybrid system pervaporation distillation. § EA J p ,i = Qreference,i ⋅ exp¨ i ¨ R ©
§ 1 1 ⋅¨ − ¨T T feed © reference
·· ¸ ¸ ⋅ X i , feed ⋅ γ i , feed ⋅ p i0, feed − p i , permeate ¸¸ ¹¹
(
i Xi
Component in the mixture Mole fraction (mole/mole)
pi0 R Q
Pressure for the pure component (bar) Ideal gas constant (J/ mol K) Permeability (kg/m2 hr bar)
)
(1)
Jp
γi
Permeate flux (kg/m2 hr) Activity coefficient
pi T
Partial pressure (bar) Temperature (K)
Study of a Novel Heat Integrated Hybrid Pervaporation Distillation Process: Simulation and Experiments
75
Figure 2: Flat membrane module with heat integration. Left, whole module structure, right, picture of the heat integration part.
2.2. Experimental work For the model validation and the analysis of the heat integration in the hybrid pervaporation distillation process, a laboratory plant has been built at the TU -Berlin and prepared for the connection with the distillation column (see fig. 3). With this plant experiments with a flat PVA-based (Polyvinylalcohol from GKSS) hydrophilic membrane have been done. A heat exchanger has been built within the pervaporation module. The temperature in the heat exchanger has been necessary to avoid the temperature drop between feed and retentate streams in the pervaporation process. In the process a 2-Propanol/ Water mixture has been separated. The concentration of 2Propanol in the feed is between 80 and 90 % in weight and the temperature range in the experiments was between 70 and 90°C. The feed flow is turbulent and the system fully insulated to avoid heat looses. The pressure in the permeate side has been kept at 30 mbar and the feed pressure at 1.5 bar.
Figure 3: Pervaporation pilot plant in the TU- Berlin. Left process diagram, right pilot plant.
With help of a Freelance ABB process control system, the process was monitored and controlled and important variables of the system were recorded.
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3. Results and discussion 3.1. Membrane characterization and validation of the model After experimental work, the value of the activation energy (EA) and the reference permeability (Qref) for a PVA-based (from GKSS) pervaporation membrane and mixture in use have been obtained (see table1), and the model for the pervaporation process with and without heat integration has been successfully validated. The absolute error between the model and the experimental permeate fluxes is under 8% (see fig.4), and almost insignificant for the water purity in the permeate side (under 0.5%) obtaining a permeate stream with up to 99.9% in water. Table 1. Results of the membrane characterization for a reference temperature of 70°C. EA (J/mol)
Qref (kg/m2 hr bar)
2- Propanol
-69663.2
6.4E-4
Water
-230.73
1.483
Jp (kg/m 2 hr), model
Compound
8 % Absolute error
0.6 0.5 0.4
W ithout heat integration
0.3 0.2 0.1
W ith heat integration
0 0
0.1
0.2
0.3
0.4
0.5
0.6
2
Jp (kg/m hr), experimental Figure 4: Model validation. Permeate flux (Jp) experimental and model results, using a flat PVA based organic module by dehydratation of a 2- Propanol/ Water azeotropic mixture. The temperature was kept between 70 and 90°C and experiments with and without heat integration were done.
3.2. Influence of the heat integration in the pervaporation process Experiments with and without heat integration have been done under the same conditions in order to study the effects of the heat integration in the process. It has been found, that by supplying the energy necessary for the pervaporation, the total permeate flux increased more than 13% (see fig.5) and, if the total energy provided by the condensation of the vapor is supplied, even a higher increase in the permeate flux can be achieved (up to 22%) getting permeate fluxes around 0.36 kg/ m2 hr. The increase in the permeate flux has an important influence into the process, making possible, either the reduction of the necessary membrane area (for a desired product purity), or the increase of the product purity (if the membrane area is kept constant). No need of external heat exchangers between two pervaporation modules is required, and
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all the energy supplied into the pervaporation module can be obtained from the condensation of the distillate stream [A. Klein, 2006].
Jp (kg/m2 hr)
0.35 Experiments with heat integration Model with heat integration
0.33 0.31 0.29
Experiments without heat integration Model without heat integration
0.27 0.25 86.8
87
87.2
87.4
87.6
87.8
88
% wt. 2-Propanol in Feed
Increase in the permeate flux due to the heat integration
Figure 5: Influence of the heat integration in the permeate flux at a feed temperature of 70°C.
3.3. Comparative study of the industrial scale process with and without heat integration With the validated model, and on the basis of the industrial scale operation parameter presented by [S.Sommer, 2004] (see table 2), the configurations with and without heat integration have been compared for an industrial scale process. It has been found that the total energy supply in the process per kg final product can be reduced about 28% and that a higher product purity is obtained (see table 3) due to the heat integration effect. This is reflected not only in the reduction of the energy consumption, but also in a smaller necessary membrane area, if the desired purity of the product is constant. Table 2. Operation conditions of the industrial scale simulation processes. Pressure in the column
1.015 bar
Number of stages in the column
8
Feed wt% 2- Propanol in the column Feed wt% Water in the column
Feed flow rate in the column
1875 kg/hr
80
Bottom wt% Water in the column Membrane Area
99.8 125 m2
20
Permeate pressure
20 mbar
Table 3. Comparison between the energy conssumption in the two processes lay -out. [kW] Reboiler
[kW] External
[kW] Condenser
[kg/hr] product
[kJ/kg product]
With heat integration
509.87
46 (compressor)
311.63
1490.59 (90.6% wt. 2-Propanol)
2095.14
Without heat integration
525
170 (membrane feed reheating)
520
1500 (90% wt. 2Propanol)
2916
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4. Conclusions In the present paper, the influence of the novel heat integration concept has been successfully demonstrated and studied in detail. For that purpose, a heat exchanger has been built including a flat membrane module. A new model describing the heat integrated process has been developed in gPROMS® and experimentally validated. It has been proven that an important effect of the heat supply is the increase in the total permeate flux up to 22%. That will be directly reflected in higher product purity for a constant membrane area or in a smaller membrane surface requirement if the desired product purity is fixed, having a more profitable process. The concentration of water in the permeate side has been within the desired values (over 99.9%) and the model predictions of the separation process for the azeotropic mixture 2-Propanol/Water are adequate. The comparison of the industrial system with and without heat integration has been done. As a result, in the case with heat integration the total energy supply in the process can be reduced about 28% and the product purity can increase. In the presentation, the results of the model and experiments and the comparison of the process with and without heat integration will be shown in further detail and the advantages of the new heat integration concept will be proven.
5. Acknowledgements The authors would like to thank EFRE (request number 10134788) for sponsoring this project, and PolyAN GmbH for the cooperation in the present research work.
References M.T. Del Pozo Gómez, A. Klein, J.-U. Repke, G. Wozny, 2007, Study and Design of a Heatintegrated Hybrid Pervaporation-Distillation Process, ECCE-6 1357 Distillation, Absorption & Extraction. A. Klein, J.-U. Repke, M. T. Del Pozo Gómez, G.Wozny, 2006, Hybrid -PervaporationDistillation processes – a novel heat-integration approach, AJChE 409 Separation Design. J.-U. Repke, F. Forner, A Klein, 2006, Separation of Homogeneous Azeotropic Mixtures by Pressure Swing Distillation – Analysis of the Operation Performance, Chem. Eng. Techn., vol. 28, 1151-1557. S. Sommer, T. Melin, 2004, Design and Optimization of Hybrid Separation Processes for the Dehydration of 2-Propanol and Other Organics, Ind. Eng. Chem., vol. 43, 5248-5259. P. Kreis, 2004, Prozessanalyse hybrider Trennverfahren, Dissertation, Dortmund, Germany. S. Sommer, 2003, Pervaporation and vapour permeation with Microporous Inorganic Membranes, PhD Thesis, RWTH Aachen, Germany. J. Lipzinski, G. Trägardh, 2001, Modelling of Pervaporation, Models to analyze and predict the mass transfer transport in Pervaporation, Separation and Purification Methods, vol. 30(1), 4925. A. Jonquières, R. Clément, P. Lochon, J. Néel, M. Dresch, B. Chrétien, 2001, Industrial state-ofthe-art of pervaporation and vapour permeation in the western countries, Journal of Membrane Science, vol. 206, 87 -117. F. Lipzinski, R.W. Field and P.-K. Ten, 1999, Pervaporation-based hybrid process: a review of process design, applications and economics, Journal of Membrane Science vol. 153, 183 – 10. J.G. Wijmans, R.W. Baker, 1993, A simple predictive treatment of the permeation process in pervaporation, Journal of Membrane Science, vol. 79, 101-113.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
A Novel Network-based Continuous-time Formulation for Process Scheduling Diego M. Giménez,a Gabriela P. Henning,a Christos T. Maraveliasb a
INTEC (Universidad Nacional del Litoral - CONICET), Güemes 3450, S3000GLN Santa Fe, Argentina b Department of Chemical and Biological Engineering, University of Wisconsin – Madison, USA
Abstract We present a novel network-based continuous-time formulation for process scheduling that addresses multiple limitations of existing approaches. Specifically, it handles nonsimultaneous transfers of input/output materials to/from processing units; it employs a more flexible time representation; and it explicitly accounts for unit connectivity. This is accomplished via the modelling of two key issues: (i) the state of a processing/storage unit, and (ii) the material transfer between processing and storage units. The proposed formulation allows us to model many complexities associated with process scheduling and obtain solutions to problems that cannot be addressed by existing methods. Keywords: process scheduling; network-based continuous-time formulation.
1. Introduction Existing network-based scheduling formulations are based on the state-task network (STN) or the resource-task network (RTN) representation (Kondili et al., 1994; Pantelides, 1994). In these formulations it is implicitly assumed that: a) material transfer between units is always possible, i.e. all processing units are connected to all the vessels that are used for the storage of the corresponding input and output materials; b) all input/output materials of a task are transferred simultaneously to/from the processing unit when the task starts/ends; and c) stable output materials can be temporarily stored in a processing unit after a task is completed, but stable input materials cannot be temporarily stored before a task starts, i.e. in continuous time representations the beginning of a task must coincide with a time point and at such point all the materials should be available. However, these assumptions do not always hold. For example, in recovery and purification processes the solvent can be drained earlier. Similarly, in certain chemical reactions reactants are fed before the beginning of the task, which actually occurs when the catalyst is added. Interestingly, despite the large number of methods recently proposed to tackle process scheduling, there are very few attempts to address these limitations. Barbosa-Póvoa and Macchietto (1994) discuss the issue of connectivity and material transfer in the context of discrete-time formulations. However, to our knowledge none of the existing methods deals with the shortcomings due to assumption (c). The goal of this paper is the development of a novel approach that overcomes these shortcomings. The key ideas of the proposed method are presented in section 2. The main variables and constraints of the mixed-integer linear programming (MILP) formulation are presented in section 3. The advantages of the new method are illustrated through a small example problem in section 4.
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2. Proposed Approach 2.1. Time Representation We introduce a new global continuous-time representation: a set of global time points kK={1, 2, …K} span the scheduling horizon from 0 to H delimiting a set of K-1 time intervals of unknown length, where interval k starts at time point k and ends at k+1. The novelty of this new representation is that tasks do not have to start (or finish) exactly at a time point. In other words, a task assigned to start on a unit at time point k can actually start any time within interval k (late beginning) as Fig. 1a shows. Similarly, a task that is assigned to end at time point k can actually end at any time within interval k-1 (early end). Thus, the new representation can potentially lead to formulations with fewer time points. 2.2. Process States Unlike previous network-based models, a processing unit can be used both for carrying out process tasks or storing input/output materials before/after the start/end of a task. Furthermore, input/output materials do not have to be simultaneously transferred to/from a unit. Hence, a unit jJ can be in three different states during time interval k (Fig. 1b): a) idle state (Wj,k=1); b) storage state; and c) execution state (Ej,k=1). If used for storage, then it can either be used for input (SIj,k=1) or output (SOj,k=1) materials. The execution state is delimited by the formal task boundaries, which are given by the values of the event variables associated with task beginning and end. If a task iIj is assigned to start in unit j within interval k (at or after time point k) then Xi,j,k=1, where Ij is the set of tasks that can be carried out in unit j. If a task is assigned to end within interval k-1 (at or before time point k) then Yi,j,k=1. In addition, an auxiliary variable indicates when a task started before time point k is still being processed in unit j at such time (Zj,k=1). 2.3. Time Balances To accurately account for a late beginning or early end of a task in unit j after and before time point k, respectively, we introduce two new variables: a) T j LB , k that denotes the lateness within interval k in starting a task, and b) T j EE , k that denotes the earliness within interval k-1 in finishing a task. We also introduce variables to model the time a S processing unit remains idle ( T j ID , k ) or is used for storage T j , k , during interval k (Fig. 1c). Early end within [Tk’-2, Tk’-1] Output
Late beginning within Input [Tk+1,Tk+2] Task T: A + B o C + D storage
Idle
storage
Task T Tk-1
Tk
Tk+1
Tk+2
Tk’-2
Tk’-1
Tk’
(a) Proposed time representation W j ,k 1 1 S
I j ,k
O j , k ' 1
1 E j ,k 1 1 E j ,k 2 1 X T , j ,k 1 1 Z j ,k 2 1
Z j ,k' 2
E j ,k '2 1 S 1 Y j ,k' 1 1
1
Task T Tk-1
Tk
Tk+1
Tk+2
Tk’-2
Tk’-1
Tk’
(b) States of processing units T j ST ,k
T j ID , k 1
T
T
LB j , k 1
Processing Time
EE j ,k ' 1
T j ST , k ' 1
Task T Tk-1
Tk
Transfer of A at Tk
Tk+1 Transfer of B at Tk+1 B
A
Tk+2
Tk’-2
Tk’-1
Tk’
(c) Time balances Consumption of A & B by task T
Production of C & D by task T
Transfer of Transfer C at Tk’-1 of D at Tk’ D
C
Task T Tk-1
Tk
Tk+1
Tk+2
Tk’-2
(d) Material transfer
Figure 1. Key concepts of the proposed formulation
Tk’-1
Tk’
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2.4. Material Transfer and Material Balances Material transfer is formulated explicitly via flow variables. In the context of this contribution, the concept of flow represents an instantaneous transfer of material from a storage/processing unit to another physically connected storage/processing unit. Only one material can be stored in a storage unit vV in any time interval, but multiple input/output materials can be simultaneously stored in a processing unit before/after a task starts/ends. Material balance constraints in storage units include only incoming and outgoing flows. The corresponding balances in processing units include the incoming and outgoing flows as well as production and consumption terms that correspond to the transformation of materials by process tasks (Fig. 1d).
3. Mathematical Formulation In addition to the event ( X ijk ,Yijk ), state ( W jk , E jk , S Ijk , S Ojk ) and auxiliary ( Z jk ) binary variables, time corresponding to point k (Tk), and timing variables ( T jkLB , T jkEE , T jkID , T jkST ), the following continuous variables are defined: VV VU x Flows FmUV, j , v , k , FmUU , j , j ', k , Fm , v , v ', k , Fm , v , j , k to represent instantaneous transfers of material m at time point k between storage vessels (V) and processing units (U), where the letter sequence in the superscript denotes the direction of the transfer. x Batch-sizes BiS, j , k , BiP, j , k , BiF, j , k to denote the total amount of task i that starts to be processed, that keeps processing and finishes, respectively, in unit j at time point k. x Inventory I mV , v , k of material m in storage vessel v during time interval k, and inventory I mUI, j , k / I mUO, j , k of input/output material m in processing unit j during time interval k. To facilitate the presentation, in the remaining we use capital letters for variables, small letters for parameters (with the exception of horizon H) and bold capital letters for sets. 3.1. State Constraints Clearly, a processing unit has to be in exactly one state during each time interval:
E j ,k W j ,k S Ij ,k S Oj ,k
1, j ,k K
(1)
A unit is in the execution state during interval k if a task starts within such interval, i.e. at or after point k, or another task started in a previous interval is still being executed:
E j,k
Z j , k ¦ X i , j , k , j , k K
(2)
i I j
Finally, the Zj,k auxiliary variable (denoting that at time point k unit j continues executing a task previously started) can be defined as follows:
Z j ,k
Z j ,k 1 ¦ X i , j ,k 1 ¦ Yi , j ,k iI j
j, k ! 1
(3)
iI j
3.2. Timing Constraints A late beginning (early end) with respect to time point k can only occur if a task is assigned to start (end) in unit j at such time point, as the following inequalities indicate:
T j LB ,k d H
¦X
i, j,k
i I j , iI cZW
, j , k K ;
T j EE ,k d H
¦Y
i, j ,k i I j , i I pZW
, j , k ! 1
(4)
where IcZW/IpZW are the sets of tasks consuming/producing unstable materials for which late beginnings and early ends are forbidden. Similarly, storage and idle times occur only if the unit is in the corresponding state:
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T j ID j , k K , k d HW j , k ,
I O T j ST j , k K ; , k d H ( S j , k S j , k ),
(5)
In that case, the idle and storage times should be equal to the length of the time interval: ID Tk 1 Tk H (1 S Ij ,k S Oj ,k W j ,k ) d T j ST , k T j , k d Tk 1 Tk
j, k K
(6)
3.3. Time Balance Constraints Constraints (7)-(9) are used to define the continuous-time grid and enforce the appropriate timing constraints without resorting to big-M terms: LB ST ID Tk t ¦¦ (aijYi , j ,k ' bij BiF, j ,k ' ) ¦ T j EE j, k ! 1 ,k ' ¦ (T j ,k ' T j ,k ' T j ,k ' ), k 'dk iI j
k 'dk
(7)
k ' k
¦¦ (a
LB ST ID X i , j ,k ' bij BiS, j ,k ' ) ¦ T j EE j, k K (8) ,k ' ¦ (T j ,k ' T j ,k ' T j ,k ' ) d H Tk ,
¦ (T
ID ST F T j EE , k T j , k T j , k ) ¦¦ ( aijYi , j , k bij Bi , j , k )
ij
k 'tk iI j
k
LB j,k
k '!k
k 'tk
H , j
(9)
i I j k
where aij and bij are the fixed and proportional processing time constants. 3.4. Batching constraints Batch-size variables are constrained as follows:
E jMIN X i , j ,k d BiS, j ,k d E jMAX X i , j ,k , i I , j J i ,k K
(10)
BiF, j ,k d E jMAX Yi , j ,k , i I ; j J i ,k ! 1
(11)
BiS, j ,k BiP, j ,k
(12)
where
ȕjMIN/ȕjMAX
BiP, j ,k 1 BiF, j ,k 1 , i , j J i ,k K is the minimum/maximum capacity of unit j.
3.5. Material Balances 3.5.1. Storage Vessels The material balance constraint in storage vessels is expressed as follows:
I mV , v , k
I mV , v , k 1
¦F
VU m,v, j ,k
jJ v
¦F
VV m , v , v ', k
v 'V v
¦F
UV m, j ,v, k
j J v
¦F
VV m , v ', v , k
,
v 'V v
(13)
m ( M NIS M ZW ), v Vm , k where Jv/Vv are the sets of units/vessels connected to vessel v, MNIS/MZW are the sets of tasks for which non-intermediate storage/zero-wait storage policies are enforced, and Vm is the set of vessels that can be used to store up material m. The inventory is constrained not to exceed the maximum storage capacity 9m,vMAX by expression (14).
I mV , v , k d 9 mMAX m ( M NIS M ZW ), v Vm , k ,v ,
(14)
3.5.2. Processing Units The corresponding material balances in processing units for input and output materials are expressed via equations (15) and (16), respectively:
I mUI, j ,k
I mUI, j ,k
¦F
VU m ,v , j , k
vVi Vm
¦F
UU m , j ', j , k
j 'J j
¦J
C iI j I m
im
BiS, j ,k , m, j , k
(15)
A Novel Network-Based Continuous-time Formulation for Process Scheduling
I mUO, j ,k
I mUO, j ,k
¦J
iI j I mP
im
BiF, j ,k
¦F
PS m , j ,v , k
vV j Vm
¦F
PP m , j ', j , k
, m, j , k
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(16)
j 'J j
where ImC/ImP are the sets of tasks consuming/producing material m, Jj/Vj are the sets of units/vessels connected to unit j, and Ȗim is the stoichiometric coefficient of material m in task i (negative if consumed). Note that inventory level changes in processing units are due to material transfer as well as material consumption and production by processing tasks. Obviously, input/output materials can only be stored in a processing unit if the unit is in the corresponding state:
¦I
UI m, j , k
d E jMAX S Ij , k ,
j , k K ;
m
¦I
UO m , j ,k
d E jMAX S Oj ,k , j , k K
(17)
m
3.6. Utility Constraints The total amount Rr,k of utility r consumed at time interval k is calculated through equation (18), and constrained not to exceed the maximum availability ȡrMAX by (19):
Rr , k
Rr , k 1 ¦ ¦ [ f ijr ( X i , j , k Yi , j , k ) gijr ( BiS, j , k BiF, j , k )], r , k K (18) i I r jJ i
Rr ,k d U rMAX , r , k K
(19)
where Ir is the set of tasks requiring utility r, and fijr and gijr are the fixed and proportional, respectively, constants for the consumption of utility r by task i in unit j. 3.7. Objective function The proposed model consists of expressions (1)–(19) and can be used to tackle various objective functions. In this short communication the profit maximization is studied:
z
max
¦ ¦S
mM FP vVm
V m m ,v , K
I
(20)
where ʌm is the price of material m and MFP is the set of products that can be sold.
4. Example A scheduling problem corresponding to a simple multipurpose batch plant is studied in order to show the main advantages of the proposed formulation. The process structure, task information and material data are described in Fig. 2. The profit maximization for a time horizon of 8 hours (H=8) is pursued. The problem instance was solved with the aim of getting an optimal schedule in a case where existing models cannot even obtain a feasible solution. In this example it is easy to note that, since no intermediate initial inventory is held, the only way to obtain final products is by performing task T2 first (so INT1 and INT2 can be available), then executing T1 (so INT3 can be available), and finally either T3 or T4. Nevertheless, since a NIS policy is adopted for INT2, T4 should begin immediately after task T2 finishes. However, this is infeasible for current approaches because INT3 cannot be available at that time (INT3 is produced by T1, which cannot start until T2 finishes since it consumes INT1). The proposed formulation overcomes this limitation by allowing a temporal storage of INT2 in unit R-103 until INT3 becomes available. Thus, the material load/discharge is decoupled from the task beginning/end.
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Elements
Tasks Stoichiometric Relations
Processing Units: R-101, R-102, R-103 Tasks: T1, T2, T3, T4 Vessels: V-101, V-102, V-103, V-104, V-105, V-106 Materials: RM1, RM2, INT1, INT2, INT3, P1, P2 Utilities: Hot Steam (HS), Cooling Water (CW)
T1 T2 T3 T4
Material Data m ʌm ($/kg) v
Plant Topology 9 mMAX ,v
Inventory (kg)
RM1 RM2 INT1 INT2 INT3 P1 P2
UIS UIS FIS (200) NIS FIS (500) UIS UIS
1000 1000 0 0 0 0 0
0 0 0 0 0 30 40
V-101 V-102 V-103 V-104 V-105 V-106
0.8 RM1 + 0.2 INT1 o INT3 RM2 o 0.3 INT1 + 0.7 INT2 INT3 o P1 0.6 INT2 + 0.4 INT3 o P2
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Task Information i
j
aij (h)
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r
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T1
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0.5 0.5 0.75 0.75 0.25 0.5
0.025 0.04 0.0375 0.06 0.0125 0.025
40 25 40 25 40 40
HS HS CW CW HS CW
6 4 4 3 8 4
T2 T3 T4
80 50 80 50 80 80
0.25 0.25 0.3 0.3 0.2 0.5
(kg/min)
30 30 30 30 30 30
Figure 2. Example of a very simple multipurpose facility
Figure 3 presents the optimal schedule obtained by implementing the proposed MILP model in GAMS/CPLEX 10.0 on a Pentium IV (3.0 GHz) PC with 2 GB of RAM, adopting a zero integrality gap. It can be seen that six global time points (five time intervals) were required to obtain this optimal solution. The model instance involved 87 binary variables, 655 continuous ones, and 646 constraints. An optimal solution of $3592.2 was found in only 0.87 s by exploring 282 nodes. Units
T2
T1
T3
T4 INT3 (16.00) from V-104 T4 (46.67)
INT2 (28.00)
R-103
T5 T6 INT3 (5.33) from V-104 T4 (40.00) T3 (66.66)
INT2 (24.00) R-102
T2 (34.29) INT2 (28.00) T2 (40.00) INT1 (4.00) to V-103
R-101
2
INT3(61.33)
INT1 (10.29) INT3 (18.67) T1 (40.00) T1 (61.33) INT3 (21.33) INT1 (8.00) to V-104 INT1 (1.98) from V-103
2.250
0
INT2 (24.00)
3.750
5.417
4
Time (h)
6.917
6
Figure 3. Optimal schedule for the motivating example
References A. P. Barbosa-Póvoa and S. Macchietto, 1994, Detailed design of multipurpose batch plants, Comp. Chem. Eng., 18, 11/12, 1013-1042. E. Kondili, C. C. Pantelides, and W. H. Sargent, 1993, A general algorithm for short-term scheduling of batch operations-I. MILP formulation, Comp. Chem. Eng., 17, 2, 211-227. C. C. Pantelides, 1994, Unified frameworks for optimal process planning and scheduling. In: Foundations of computer-aided process operations, New York, 253-274.
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Excipient Interaction Prediction: application of the Purdue Ontology for Pharmaceutical Engineering (POPE) Leaelaf Hailemariama, Pradeep Suresha, Venkata Pavan Kumar Akkisettya, Girish Joglekarb, Shuo-Huan Hsub, Ankur Jaine, Kenneth Morrisc, Gintaras Reklaitisa, Prabir Basud and Venkat Venkatasubramaniana1 a
School of Chemical Engineering, Purdue University, West Lafayette IN 47907 USA Discovery Park, Purdue University, West Lafayette, IN 47907 USA c Department of Industrial and Physical Pharmacy, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907 USA d National Institute for Pharmaceutical Technology and Education, Purdue University, 315 Hovde Hall, 610 Purdue Mall, West Lafayette, IN 47907 USA e Enterprise Optimization, United Airlines, Chicago, IL 60007 USA b
Abstract A drug product consists of a drug substance and one or more excipients that play specific roles in rendering desired properties to that product, from improvement of flow to control of the release of the drug substance. Inter-excipient and drug substanceexcipient chemical reactions are to be avoided and formulators often use heuristics and past experience to avoid potential interactions during drug product development. Multiple tools are present to mechanistically predict chemical reactions: however their utility is limited due to the complexity of the domain and the need for explicit information. In this work, the Purdue Ontology for Pharmaceutical Engineering (POPE) was used to develop an excipient reaction prediction application that made use of structural, material and environmental information to predict reactions Keywords: Excipient Interaction, Product Development, Ontology, Rule Language
1. Introduction A drug product includes the drug substance along with compounds that enhance processing and effectiveness, called excipients, which perform such functions as improvement of flow or increase of tablet mass. The drug product is expected to be chemically stable to avoid formation of toxic compounds and loss of the drug substance: however reactions between the drug substance and excipients and amongst the excipients are possible. These interactions may be avoided by careful design based on experience, rigorous experimentation or using software packages to predict reactions. These packages include mechanistic tools and knowledge-based reaction prediction tools. Mechanistic tools that have been developed to predict reactions include the CAChe WorkSystem (see URL) and SPARTAN (see URL). Knowledge-based systems include reaction predictors like ROBIA (Reaction Outcomes By Informatics Analysis) 1
Corresponding author:
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(Socorro et al, 2005) and the LHASA (Logic and Heuristics Applied to Synthetic Analysis) software (see URL). However, the current solutions to chemical reaction prediction have several limitations. Secondary and tertiary interactions are rarely considered and there is little work on chemistry reasoning which is valuable for chemical stability analysis but would require an explicit information model. In addition, there is little scope for integration of the reaction information (which might describe conditions in microsolutions found between solid particles) with the solid information. In this work a prototypical reaction prediction system which makes use of known reaction information, the molecular structure of reactants and structural and environmental information, like the backbone of the molecule and the reaction pH, is presented. First the POPE ontology, which includes descriptions of the material, chemical reaction and structure descriptors, is briefly presented. The next section is dedicated to the description of the prototype reaction prediction system, followed by application examples. The last section discusses other potential applications of the ontological approach and future work.
2. Introduction to the Purdue Ontology for Pharmaceutical Engineering Several options exist for the explicit representation of information. XML (eXtensible Markup Language: see URL) is one. XML does not have a fixed set of tags but allows users to define tags of their own, much like the English language versus Chemistry or Biology. An example of XML Schema (glossary) examples is the Chemistry Markup Language (CML: see URL) for molecule information. XML does not provide any means of defining the semantics (meaning) of the information. The needs for explicit expression and capture of semantics are met by ontologies, which are defined as follows: “An ontology defines the basic terms and relations comprising the vocabulary of a topic area as well as the rules of combining terms and relations to define extensions to the vocabulary.” (Gomez-Perez et al., 2004). For the pharmaceutical domain, the ‘basic terms’ could be a ‘material’ and a ‘material property’ and their relations could be ‘<material> has <material property>’. An example of a simple ontology is shown in Figure 1. Figure 1: An ontology example The powder flow rate (a material property) of the API (a material) has an average value of 1 g/s within the range of [0.8, 1.2]. The source of the reported value was the experiment ‘API: Flow Measurement’ at a given context (78% relative humidity) The collection of the different concepts e.g. material, material property etc and their relation e.g. has Value, comprise an ontology. The Purdue Ontology for Pharmaceutical Engineering (POPE) was developed to address the information modeling needs mentioned previously. POPE includes several smaller interrelated ontologies; the Purdue Ontology for Material Entities (POME)
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which describes materials; the Purdue Ontology for Degradant Structures (PODS) which describes the chemical structure of materials with respect to molecular fragments; the Purdue Ontology for Reaction Expression (PORE) which describes the interactions between materials including chemical reactions; the Purdue Ontology for Material Properties (POMP) which describes the physical, chemical and mechanical properties of materials and the Purdue Ontology for Description of Experiments (PODE). 2.1. Material Ontology (POME) There had been some work done to describe materials in an explicit manner including the Standard for the Exchange of Product Data STEP (ISO 10303) and OntoCAPE, which included descriptions of phases, chemical components and reactions (Yang and Marquardt, 2004). However, in the data models above, experiments and solid properties get little treatment. POME builds on the concepts defined by OntoCAPE and includes solid and pharmaceutical properties. The material is described in terms of its substance entity (environment independent) and its phase system entity (environment dependent: solid, liquid, vapor, mixtures) and its role in a mixture (e.g. for solids: flow aid, dilunt etc). The phase system would be described by the fraction and identity of the phases comprising it (phase composition). Each phase would have a chemical composition, which describes the species and their relative abundance in the given phase as well as the environmental conditions e.g. temperature, pressure. For instance, the antibiotic Seromycin ® is manufactured as a tablet which may include several components like Cycloserine and Magnesium Stearate. The tablet is a solid mixture; the phase composition including phase, substance and amount information (e.g. Cycloserine: Solid: 83% m/m) and the role of Cycloserine being an Active Pharmaceutical Ingredient (API). The chemical composition describes a pure component. The substance aspect includes molecular structure information e.g. as a SMILES string (NC1CONC1=O). 2.2. Degradant Ontology (PODS) Previous work on representation of chemical structures includes the EcoCyc Ontology (http://ecocyc.org/) for metabolites and the Chemical Markup Language (CML) among others. Ontologies developed to describe molecules include those by Feldman et al (2005) and Villanueva-Rosales and Dumontier (2007). PODS builds on the above for the pharmaceutical domain by making use of common molecular fragments (shown in Figure 2). Each fragment is part of a ‘fragment-entity’ which might participate in a reaction and is connected to (or identified as) a backbone group. For Cycloserine, the fragment entities include a five- member ring, two amine groups and a carbonyl group. PODS can be coupled with the PORE to represent chemical systems and with POME to describe a material during product development. 2.3. Reaction Ontology (PORE) The concept of a reaction may include physical and chemical changes. Some work had been done previously to model chemical reactions including the EROS (Elaboration of Reactions for Organic Synthesis) system (Gasteiger et al, 2000) and work by Sankar and Aghila (2006). PORE was developed to represent reactions as interactions between functional groups/phase systems. Each reaction would have a reaction_context, which describes the pertinent descriptors of the reaction e.g. at what temperature it occurs, at
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what pressure, pH etc. For instance, the context for Cycloserine hydrolysis captures the temperature (600C), pH range (1-7) and phase (liquid). Several restrictions such as the requirement of at least one reactant and one product for a reaction were put in place. 2.4. Property Ontology (POMP) Previous work on explicit modeling of material properties includes CAPEC (Sousa et al, 1999) and OntoCAPE (Yang and Marquardt, 2004). POMP extends the properties in OntoCAPE to include interproperty relations and solid material properties. The property structure includes generic properties like heat, mass and momentum transfer properties (e.g. heat capacity, diffusivity and density respectively) as well as a separate description for solid properties. Solid properties were described at three levels; substance properties (pertaining to the molecular level e.g. molecular structure), particle properties (pertaining to single crystals or amorphous particles e.g. unit cell dimensions) and powder (bulk) properties (e.g. particle size distribution). Each property value would be correlated to a set of environmental conditions during measurement (e.g. temperature, pressure) and a source (experiment, mathematical model or literature). 2.5. Experiment Ontology (PODE) Noy and Hafner (2000) developed a representation of molecular biology experiments using ontologies. Hughes et al (2004) developed a laboratory ontology which captured the relationship between materials and processes through a hierarchy of actions. PODE links experiments to material properties. Experiments have some generic characteristics which include the time and place of the experiment as well as the experimenters. Equipment and experimental procedures were modeled as a collection of actions, which could be observation /measurement actions, processing actions or operation actions. For instance the measurement of Cycloserine bulk density involves a specific experimental procedure (put powder on top of sieve: (processing action); turn on sieve (operation action); observe powder volume (observation step)).
3. Prediction of reactions between drug product components POPE had previously been used to support a decision support system for pharmaceutical product development and modeling of solid unit operations (Venkatasubramanian et al, 2006). In this application, reactions between the drug substance and the excipients are predicted through the following steps. A survey of the drug degradation domain was made and a set of common molecular fragments are collected as in Figure 2. Once the chemical structure of the new drug substance is known, the active fragments are sought through the Chemistry Development Kit (CDK) tools. Figure 2: List of molecular fragments
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Reactions involving the identified active fragments are sought from among the reaction ontology instances which describe the participant active fragments. For user input including the molecular structure (described by PODS) and reaction conditions, the relevant reactions are returned. The reaction conditions would include the environment (temperature, pressure, pH: captured by PORE), phase information (described by POME and POMP) and reported experiment procedure (captured by PODE). The ontology was coded using OWL (Web Ontology Language) using the Protégé 3.3 interface. Search was performed using the Semantic Web Rule Language (SWRL) plugin of Protégé. The reaction database is populated from free online databases from SigmaAldrich® and Metasynthesis®. A schematic representation is shown in Figure 3.
Figure 3: Reaction prediction system (a) overall scheme (b) SWRL input The system was used to predict reactions for several drug compounds. For instance, the system correctly predicted the hydrolysis, oxidation and isomerization of Cycloserine based on the compound’s similarity to γ-Butyrolactone hydrolysis, Imipramine hydrochloride oxidation and Pilocarpine epimerization. Knowledge of the possibility of Cycloserine oxidation may exclude the use of Crospovidone, which has hydrogen peroxide, a strong oxidizing agent, as a common impurity. Capturing multiple types of information, possible through the ontological approach, is useful for interaction prediction in pharmaceutical product development.
4. Summary The Purdue Ontology for Pharmaceutical Engineering (POPE) was developed with its component ontologies for descriptions of materials, chemical structures, reactions, material properties and experiments. Based on POPE an excipient interaction prediction/diagnosis application which made use of structural and environmental information was presented. There are several challenges in the horizon, which include the consideration of rates of reaction to determine relevance and evaluation of multiple measures of molecular similarity.
Acknowledgements The work was done through the financial support of the Engineering Research Center for Structured Organic Particulate Systems (ERC-SOPS), the Indiana 21st Century Fund and Eli Lilly and Company. The authors thank Balachandra Krishnamurthy and researchers at Lilly Research Laboratories (Henry Havel, Brian Good, Gus Hartauer, Steve Baertschi, Ahmad Almaya, Aktham Aburub, and David Long) for their support.
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References S. Baertschi (2005) Pharmaceutical Stress Testing: Predicting Drug Degradation in Drugs and the Pharmaceutical Sciences, Vol. 153, Taylor and Francis Group, Boca Raton FL. Cache: http://www.cache.fujitsu.com/ CML: http://www.xml-cml.org H. J. Feldman, M. Dumontier, S. Ling,., N Haider, C.W.V. Hogue (2005) CO: A Chemical Ontology for Identification of Functional Groups and Semantic Comparison of Small Molecules, FEBS Letters, 579, 4685-4691. J. Gasteiger, M. Pförtner, M. Sitzmann, R. Höllering, O. Sacher, T. Kostka, N. Karg (2000) Computer-assisted synthesis and reaction planning in combinatorial chemistry, Perspectives in Drug Discovery and Design, 20, 245–264. A. Gomez-Perez., M. Fernandez-Lopez, O. Corcho. (2004) Ontological Engineering: with examples from the areas of knowledge management, e-Commerce and the Semantic Web. Springer-Verlag London. G. Hughes, H. Mills, D. de Roure, J. Frey, L. Moreau, M.C. Schraefel, G. Smith, E. Zaluska (2004) The semantic smart laboratory: a system for supporting the chemical eScientist, Organic and Biomolecular Chemistry, 2, 1-10. LHASA: http://www.lhasalimited.org N. Noy, C. Hafner (2000) Ontological foundations for experimental science knowledge bases, Applied Artificial Intelligence, 14, 565-618. N. Pandit (2007) Introduction to the pharmaceutical sciences Lippincott, Williams and Wilkins, Baltimore, MD. P. Sankar, G.J. Aghila (2006) Design and development of chemical ontologies for reaction representation, Journal of Chemical Information and Modeling, 46, 6, 2355-2368. I.M. Socorro, K. Taylor and J.M. Goodman (2005) ROBIA: A Reaction Prediction Program, Organic Letters, 7, 16, 3541-3544. SPARTAN : http://www.additive-net.de/software/spartan/index.shtml V. Venkatasubramanian, C. Zhao, G. Joglekar, A. Jain, L. Hailemariam, P. Suresh, V. Akkisetty, K. Morris, G.V. Reklaitis (2006) Ontological Informatics Infrastructure for chemical product design and process development, Computers and Chemical Engineering, CPC 7 Special Issue, 30(10-12), 1482-1496. N. Villanueva-Rosales, M. Dumontier (2007) Describing chemical functional groups in OWL-DL for the classification of chemical compounds, OWL: Experiences and Directions (OWLED 2007), co-located with European Semantic Web Conference (ESWC2007), Innsbruck, Austria. XML: http://www.w3.org/XML/ A. Yang, W Marquardt (2004) An Ontology-based Approach to Conceptual Process Modeling In: A. Barbarosa-Póvoa, H. Matos (Eds.): European Symposium on Computer Aided Process Engineering -14, 1159-1164.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimal column sequencing for multicomponent mixtures Andreas Harwardt,a Sven Kossack,a Wolfgang Marquardt a a
Lehrstuhl für Prozesstechnik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany,
[email protected] Abstract The separation of a multicomponent mixture using distillation is usually possible in a large number of different sequences, which will provide the same products but have different energy demand. In this contribution, we provide a systematic method to find the optimal column sequence based on exergy demand. The screening of design alternatives is done within a superstructure framework, which allows for the decomposition of the separation sequences into unique separation tasks. The use of the task concept significantly reduces the computational work. The individual separation tasks are evaluated using shortcut methods. For the application to azeotropic mixtures, the mixture topology is determined and feasibility checks are performed for every split. In this context, azeotropes are treated as pseudo-components. Keywords: sequence synthesis, multicomponent, rectification body method,
state task network 1. Introduction In distillation network synthesis, the separation of multicomponent mixtures is possible in a large number of different column sequences, where the sequences, although they result in the same products, have different energy demand. A nonoptimal choice of the separation sequence can lead to significant additional cost during the operation. Several approaches for column sequencing can be found in the literature. Hendry and Hughes [1] introduced the separation task concept, where the distillation network is decomposed into the individual separation tasks, which are evaluated using the ideal thermodynamic based UnderwoodFenske-Gilliland method. This idea was extended to complex distillation systems by Shah and Kokossis [2]. The idea of a superstructure for distillation column networks was introduced with the state task network by Sargent and Gaminibandara [3]. Thong and Jobson [4] suggested a sequential approach for the column sequencing for azeotropic mixtures. The major problem with column sequencing is the large number of possible sequences, which grows exponential by the number of products. This contribution presents a stepwise procedure to identify the optimal sequence.
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In the first step, the design alternatives are automatically generated using a superstructure. In the second step, the design alternatives are evaluated using the rectification body method (RBM) [5], a nonideal thermodynamic based shortcut method. Unlike simulation studies or MINLP optimization, shortcut methods allow fast evaluation of the single separation task without detailed specification of the distillation column. 2. Methodology 2.1. Zeotropic mixtures
Assuming a four component mixture and simple two product splits, Fig. 1 shows all possible separation sequences into the pure components under the assumption of sharp splits. If the number of components is increased, an exponential growth of the number of sequences is observed (Fig. 2, sequences). This behaviour is well known [6] and can be described by N=
(2(n − 1))! n!(n − 1)!
(1)
where n is the number of products and N is the number of sequences.
Figure 1: Sequence alternatives for the separation of a four component mixture
The same separation steps (same feed and product compositions) can occur in different sequences. This can be seen in Fig. 1, where the first and the second sequence have the first separation in common. This property is used in a superstructure to reduce the complexity of the multicomponent systems. The state task network [3] is applied. In this superstructure, every possible composition, which can be attained, is called a state. The states represent the feed, possible intermediate products and products of the separation sequence. A task is defined as an operation connecting three different states, the feed state and the two product states [1]. The tasks can be automatically generated by performing all possible separations of every state composition into the intermediate products or products. Every separation sequence can be seen as a
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valid combination of tasks. A combination of tasks is valid if it starts with the feed state and ends at the product states. The application of the state task network requires the specification of linearly independent products. If products are linearly dependent, which in this case means that they could be attained by mixing other products, the state task network formulation is not applicable. This is due to the fact that the tasks would not be independent from the sequence. The main advantage of superstructure is that the number of tasks only grows with the third power of the number of products, compared to the exponential growth of the number of sequences (Fig.1) [2]. 500 Sequences Tasks
400
300
200
100
0 2
3
4
5
6
7
8
Components
Figure 2: Growth of the number of tasks and sequences
2.2. Azeotropic mixtures
The application of the superstructure for the separation of azeotropic mixtures requires some modifications. Separation is limited by azeotropes and the corresponding distillation boundaries, which form distillation regions [7]. For a feasible separation, top and bottom product composition have to be in the same distillation region. Boundary crossing (where the feed and the two product compositions are located in different distillation regions) is possible in the presence of curved distillation boundaries, but is not considered in this work. The required information about the distillation boundary is obtained from the pinch distillation boundary (PDB) feasibility test [8]. The information is stored in the reachability matrix, as introduced by Rooks et al. [9], which represents the topology of the residue curve map of the mixture. A feasible set of linear independent products has to be selected, where products can be pure components, azeotropes or a chosen product composition. This set is feasible if all products are part of the same distillation region. The singular points of a distillation region usually provide a good set of possible product compositions. The azeotropes are treated as pseudo-components.
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2.3. Shortcut calculations
The evaluation of a separation sequences requires information about the feasibility and the cost of the individual separation tasks. Determining the minimum energy demand of a separation has been found to be a good way of estimating the cost of a distillation system, because operation cost are dominated by the energy demand and investment cost are closely related to the vapor flow rate in the column [10]. The minimum energy demand can be calculated using the RBM shortcut. The feasibility of the individual separation tasks can be checked with the application of PDB feasibility test. The sequence evaluation is performed sequentially. At first, the superstructure including states and tasks is generated automatically. For every task, the PDB feasibility test is performed. If the split is feasible, the RBM calculates the minimum energy demand for the separation of the feed into the top and the bottom product. Once the minimum energy demand (QB) has been calculated, the exergy demand (EB) can be determined. The exergy of the energy represents the part of the energy that can be converted into mechanical energy using the ideal Carnot cycle. The required information about the reboiler temperature (TB) is provided by the RBM calculations. The evaluation based on the exergy demand accounts for the different temperature levels of the energy requirement. Once all task energy and exergy requirements have been calculated, the sequence energy and exergy demand is determined. The feasible sequences are automatically generated for the given number of products. Information about the active tasks for every single sequence is provided by the algorithm. The separation of the mixture into n products requires n-1 tasks. The sequences are found by combinatorial search with all identified tasks, where invalid branches of the combinatorial tree are cut to significantly reduce the computational demand. The sequence evaluation is done by the summation of the energy or the exergy demands of the active task of the sequence, which is computationally inexpensive. This summation is done for every sequence. After all sequence exergy demands have been calculated, the sequence with the lowest exergy demand is selected to be the optimal one. 3. Case studies In a first case study, the zeotropic mixture of pentane, hexane, heptane and octane is supposed to be separated into the pure components. Five different sequences are possible (Fig. 1), which have ten individual separation tasks. They are referenced as sequence one to five according to the labeling in the figure. Assuming a pressure of 1.013 bar, an equimolar feed and a total flowrate of 10 mol/s, the energy and exergy demands are calculated for the ten tasks using the RBM shortcut. Sequence five, which corresponds to the direct sequence, is found to be optimal. Obviously, the optimal sequence depends on
Optimal Column Sequencing for Multicomponent Mixtures
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the feed composition. The sequence exergy requirement is calculated to be 157 kW, where the energy requirement is 637 kW. In a second case study, a zeotropic mixture is separated into ten products. The mixture contains the ten nalkanes from propane to dodecane. 4862 Sequences, with 165 shortcut calculations for the tasks, are evaluated in less than ten minutes (Windows 2003 Intel Xeon Dual 3.06 GHz 3840 MB RAM). In a third case study, the mixture of acetone, chloroform, benzene and toluene is investigated. Acetone and chloroform are known to form a high boiling azeotrope. The composition space is separated into two distillation regions. The superstructure is used to identify optimal sequences in both distillation regions. In this case, the feed is set to be of equimolar composition at a flowrate of 10 mol/s and a pressure of 1.013 bar. The separation takes place in the convex region of the composition space, which can be identified from the information in the reachability matrix. For the given feed composition all five separation sequences are feasible. Table 1 displays the task exergy (EB) and energy (QB) requirements for the separation using the RBM, the labeling corresponds to Fig.1. Table 1. Task energy and exergy requirements task #
feed
top
bottom
QB [kW]
EB [kW]
1
ABCD
ABC
D
366
91
2
ABCD
AB
CD
602
127
3
ABCD
A
BCD
242
42
4
ABC
AB
C
595
110
5
ABC
A
BC
257
40
6
AB
A
B
311
46
7
BCD
BC
D
329
82
8
BCD
B
CD
465
98
9
BC
B
C
476
88
10
CD
C
D
193
48
Table 2. Sequence energy and exergy requirements
active tasks
sequence #
QB [kW]
EB [kW]
6
1272
247
1
1
4
2
1
5
9
1100
219
3
2
6
10
1107
222
4
3
7
9
1047
211
5
3
8
10
900
188
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The reachable products are the pure components/pseudo-components of the convex distillation region, which are acetone (A), acetone/chloroform (B), benzene (C) and toluene (D). The information about the single task energy and exergy requirements provides a good insight in the behaviour of the system. The energy and exergy demand of a sequence can now easily be calculated by the summation of the energy and exergy demand of the present tasks of every sequence, the information is provided in Table 2. It can be seen, that in this case, sequence five, which consists of three direct splits, gives the optimal solution with the lowest exergy requirement. 4. Summary and conclusion This contribution aims to identify the optimal sequence for a distillation column network. The method for column sequencing presented here is based on ideas from previous contributions presented in the introduction. The application of a superstructure allows for the decomposition of the sequences into individual separation tasks, which significantly reduces the computational work. The use of the nonideal thermodynamic based RBM shortcut method has significant benefits over the use of the Underwood-Fenske-Gilliland method, since it allows the extension to azeotropic mixtures. The automatic generation of the superstructure and the fast evaluation with the shortcut allows the application on large systems up to 10 products (zeotropic system), which is significantly larger than other examples in the literature. Telling from the zeotropic and azeotropic case studies presented in this contribution, it can be seen that this superstructure generation and evaluation is a useful tool in distillation network design, because it allows for rapid evaluation of design alternatives. It provides a small selection of promising design alternatives, which can then be investigated in more detail. The method can be applied within the process syntheses framework [11] for process variant generation and evaluation.
References [1] Hendry, J.E., Hughes, R.R.: Chem. Eng. Prog. 1972, 68, 6, 71. [2] Shah, P.B., A.C. Kokossis: AIChE Journal 2002, 48, 527. [3] Sargent, R.W.H, K. Gaminibandara: Optimization in Action; L.C.W. Dixion, Ed.: Acadamic Press; London, 1976. [4] Thong, D.Y.C., Jobson, M.: Chem. Eng. Sci. 2001, 56, 4417. [5] Bausa J., R.v. Watzdorf, W. Marquardt: AIChE J. 1998, 44, 2181. [6] Thompson, R.W., C.J. King: AIChE J. 1972, 18, 941. [7] Doherty, M.F., M.F. Malone Conceptual Design of Distillation Systems, McGraw-Hill, New York, 2001. [8] Brüggemann, S.: PhD Thesis, RWTH Aachen 2005. [9] Rooks, R.E., V. Julka, M.F. Doherty, M.F. Malone: AIChE J. 1998, 44, 1382. [10] Bausa, J.: , PhD Thesis, RWTH Aachen 2001. [11] Kossack, S., K. Krämer, W. Marquardt: submitted to Chem. Eng. Res. Dev.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Systematic Design of Production Processes for Enantiomers with Integration of Chromatography and Racemisation Reactions Malte Kaspereit,a Javier García Palacios,a Tania Meixús Fernández,a Achim Kienle a,b a
Max-Planck-Institut für Dynamik komplexer technischer Systeme, Sandtorstr. 1, D-39106 Magdeburg, Germany b Otto-von-Guericke Universität, Lehrstuhl für Automatisierung/Modellbildung, Universitätsplatz 2, D-39106 Magdeburg, Germany
Abstract A systematic study is performed of integrated processes that combine chromatographic separation and racemisation reaction for production of pure enantiomers. In a theoretical case study, processes of different degrees of integration are investigated by optimization of corresponding models. Concepts studied range from reactor-separator-recycle systems to fully integrated schemes with distributed reactivity. Physico-chemical parameters were determined experimentally for a model system. Data are reported together with first results for a simple flowsheet-integrated process. Keywords: process integration, chromatography, racemisation, enantiomers
1. Introduction Enantiomers are stereoisomers structured like mirror-images (see Fig. 1). A main problem related to producing a pure single enantiomer is that selective synthesis is often not feasible or too expensive. In contrast, conventional synthetic procedures are less expensive but non-selective (they deliver the racemic 1:1 mixture). Since usually only one enantiomer has the desired physiological effect (the other might be ineffective or harmful), such mixtures need to be separated; for example, by kinetic resolution, crystallisation, or chromatography. However, the yield achievable by this approach is inherently limited to 50% only. a
a C b
d c
A
C
d
b
c
B
Figure 1: Schematic representation of two enantiomers (here denoted as A and B). The two forms differ only in the spatial arrangement of the functional groups
Against this background it appears highly desirable to combine enantioseparations with an interconversion (racemisation) of the undesired enantiomer. Ideally, this should allow for a yield of 100%. Since racemisations are equilibrium-limited (with 1:1
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equilibrium composition), process integration appears as viable concept. Here we will investigate processes that combine (continuous) chromatography and racemisation.
2. Theoretical Case Study 2.1. Problem statement Fig. 2 shows the task to be resolved by the processes considered here. The constraints resemble a pharmaceutical problem, where purity requirements are very high and – due to significant synthesis costs – a high conversion of the undesired form is desirable. (continuous) chromatography
50% A 50% B
≥ 99.9% A 0.1% B
racemisation A'B
Figure 2: Schematic problem statement for the production of enantiomer A.
Subject of the study are integrated processes without waste stream that yield the desired enantiomer with 99.9% purity. This corresponds to a conversion of 99.8%. Further, also a less restrictive case is investigated (90% purity and 80% conversion). Mail goal is here to identify general trends with respect to integrating continuous chromatography and racemisation. Therefore, we consider a countercurrent of stationary and mobile phases (i.e., True Moving Bed, TMB). While a feasible technology would require column switching (i.e., Simulated Moving Bed, SMB), the development of such system is out of scope here. Details on TMB/SMB systems are given in, e.g., [1]. 2.2. Processes investigated There is a rather large number of options to integrate continuous chromatography and racemisation reaction. Fig. 3 shows a selection of possible schemes for the production of the weaker adsorbing enantiomer A. a)
S SR
F
A
c)
S
b)
S
F
A
d)
S
reaction
separation
F
SR
F
A
A
reaction & separation
Figure 3: Selected schemes for the production of A (F – feed, S – solvent, SR – solvent removed). a) Reactor-separator-recycle system w/ four zones and solvent removal. b) Partially integrated process w/ three zones and side reactors. c) Fully integrated process w/ four zones, distributed reaction and solvent removal. d) Fully integrated scheme w/ three zones and distributed reaction.
Concerning the level of integration, classical flowsheet-integrated processes as reactorseparator-recycle systems (Fig. 3a) and the use of side reactors (“Hashimoto process”,
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Fig. 3b) are considered. Furthermore, fully integrated schemes are possible (i.e., chromatographic reactors). While one option is to apply a constant reaction rate parameter (i.e., Damköhler number, Da) throughout the unit, here we also consider the option to use different values for Da in the individual zones (Fig. 3c). Finally, since four-zone processes require a recycle (and the removal of solvent), also integrated processes with three zones are studied (Fig. 3d). Please note that here we focus on the schemes shown in Fig. 3 (and their corresponding “counterparts” for the production of enantiomer B). However, there are more options. For example, a four-zone Hashimoto system with internal recycles was suggested [2]. 2.3. Process model and optimisations All processes are modeled as series of countercurrent equilibrium cells. Parameters were determined experimentally (section 3). A liquid-phase reaction is accounted for by Da = (rate constant)x(cell volume)/(solid flow rate). Adsorption is described by the biLangmuir model. All equations were implemented in the simulation environment DIVA [3]; details on the implementation of a largely analogous model can be found in [1,4]. The following set of performance parameters were used to evaluate each process: ⋅ ⋅ ½ ⋅ ciout V SR ° VS ° out out , = , = , = SR PR V c EC ® Pi = out ¾ i PR ° PR c A + c Bout °¯ ¿
i = ( A, B)
(1)
with purity Pi, productivity PR, specific eluent consumption EC, specific solvent removal SR, and ciout as product concentrations. Note that PR can be scaled by the solid volumetric flow (here equal to unity). Furthermore, solvent removal is assumed ideal (i.e., no losses, obtains feed concentration level for higher concentrated solute) and that side reactors (Fig. 3a and 3c) are in reaction equilibrium. Optimisations were performed using an SQP algorithm in DIVA with EC as objective function and the purity as nonlinear constraint. Variables were Da-numbers and the relative zone flow rates, m j ( j=I...IV) (i.e., ratio of liquid and solid flow in each zone). 2.4. Results Table 1 lists the obtained optimisation results for the process schemes in Fig. 3. As expected, the conventional setup a) is a feasible option. It performs somewhat better for the strongly adsorbed component B. The reason is that for producing A, the recycle load is higher due to the strongly diluted stream of B at the extract port. The Hashimoto process (b) was found to be infeasible for 99.9% purity. In fact, the process is thermodynamically infeasible for the production of pure A. The scheme achieves only low performance for 90% purity. This is in agreement with literature [2]. The hypothetical option of a fully integrated process with distributed reactivity (c) allows for a significant improvement of process performance. This holds in particular for component A, where SR and EC are strongly reduced. The main reason is that here the required m I –value is 16% lower than in case (a); m I is even lower than the Henry constant of B. The explanation is that any B in the reactive zone I also reacts to produce A, which is desorbed more easily and transported towards the non-reactive zones. A similar benefical effect (which is somewhat less pronounced) is found for m IV, which is higher for the fully integrated schemes than for the flowsheet-integrated processes. As a last option, integrated three-zone processes (d) were studied. These cannot achieve a purity of 99.9%. However, a comparison of the results for 90% purity demonstrates a significant potential. Considering that these schemes have no recycle or solvent removal, they appear very attractive for tasks with limited purity requirements.
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Table 1: Optimisation results for the process options shown in Fig. 3. The first column marks the process scheme according for Fig. 3 and the target component. *) PR is scaleable by solid flux. P [%] 99.9 99.9 90.0 90.0 99.9 90.0 90.0 99.9 99.9 90.0 90.0 99.9 90.0 90.0
a) A a) B a) A a) B b) b) A b) B c) A c) B c) A c) B d) d) A d) B
m I / Da I [-] 23.47 / 19.33 / 19.47 / 18.03 / -
m II / Da II [-] 11.54 / 14.71 / 10.58 / 12.57 / -
m III / Da III m IV / Da IV EC [-] [-] [l/g] 17.34 / 13.26 / 11.7 20.22 / 12.24 / 9.67 18.67 / 13.54 / 5.30 20.41 / 13.20 / 5.01 not feasible 18.97 19.85 13.63 16.8 20.51 13.54 14.84 12.2 -4 -18 -18 19.69 / 1039 11.69 / 10 17.24 / 10 12.26 / 10 8.54 22.69 / 10-16 14.62 / 10-11 20.55 / 10- 3 15.05 / 10 9 8.94 16.37 / 1068 11.25 / 10- 4 18.49 / 10-18 13.09 / 10-18 2.87 19.29 / 10-18 13.03 / 10-18 20.56 / 10- 4 15.54 / 10 9 3.61 not feasible (max. PA= 98.9%, max. PB = 99.4%) 16.65 / 4061 19.04 / 10-18 13.08 / 10-18 4.19 19.85 / 10-18 12.79 / 10-18 15.68 / 458 4.10
SR [l/g] 9.54 5.56 3.50 2.13
PR [g/l]* 0.87 0.77 1.12 0.96
0 0 3.87 4.40 0.93 0.36
0.32 0.47 0.87 0.85 1.14 1.04
0 0
0.85 1.02
3. Investigations for a model system The model substance used in this work is chlorthalidone (CT), which has (in racemic form) some use as a diuretic and anti-hypertensive drug. CT is stereolabile (i.e., it can be racemised rather easily) [5]. Chemicals were purchased from Merck (Darmstadt, Germany), with the exception of CT (Sigma Aldrich, Steinheim, Germany). 3.1. Chromatographic parameters Experiments were performed using an analytical column (200x4mm) with a chiral stationary phase (Nucleodex β-OH, Macherey-Nagel, Germany) at 10°C with a flow rate of 0.5 ml/min. The mobile phase was 40/60 (v/v) methanol/water, 50mmol triethylamine at pH=5.0 (acetic acid). Conventional HPLC equipment was applied (Knauer, Berlin, Germany and DIONEX, Idstein, Germany). The porosity was determined from an acetone pulse. NTP-values were determined from small injections of 0.4 g/l racemic CT in mobile phase (corresponds to solubility). 0.4 0.3 c i [g/l]
t R,i [min]
16 14 12 10
0.2 0.1
0
0.05
0.1 0.15 c i [g/l]
0.2
0 10
20
30 t [min]
40
50
Figure 4: Determination of adsorption isotherms. Left – perturbation data and corresponding fit by isotherm model (lines). Right – overloading experiments (points, injection volume: 0.13...5ml) and simulations (lines).
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Adsorption isotherms of the bi-Langmuir-type were measured (see Tab. 2). An initial set of parameters was obtained by the perturbation method [6]. Subsequently, a “peak fitting” approach based on the equilibrium-dispersive model was used for refinement (for details, see [4]). Fig. 4 shows a good agreement between models and experiments. 3.2. Kinetics of racemisation reaction The thermal racemisation of CT was investigated using batch experiments. Since CT is available only in racemic form, first purified fractions (ca. 2ml each) were obtained from HPLC runs, which then were allowed to racemise at different temperatures (15°C to 60°C). Samples were taken for HPLC analysis. Fig. 5 (left) shows an example data set. -6
4
-8
3
ln k
c i [10-5 mol l-1]
5
2
-12
1 0
-10
0
100 200 t [min]
-14 29
300
31 33 1/T [10-4 K-1]
35
Figure 5: Left – example of a batch racemisation experiment at 40°C. Symbols: concentrations of the enantiomers (HPLC analysis). Lines: calculated from Eq. (2). Right – Arrhenius diagram obtained from batch experiments between 15°C and 60°C.
Data were fitted by adjusting the rate constant of the first-order kinetic expression
c1 (t ) =
c10 + c20 § 0 c10 + c20 · ¸ exp(− 2kt ) + ¨¨ c1 − 2 2 ¸¹ ©
(2)
Fig. 5 (right) shows the resulting Arrhenius plot from which activation parameters were determined (Tab. 2). Fig. 5 (left) shows the resulting fit obtained from these parameters and the rate expression (2). A good agreement was obtained for all experiments. Table 2: Summary of experimentally obtained parameters for chromatography and racemisation. Adsorption isotherms I
II
I
II
qS / qS bi / bi
length / diameter / porosity
B
A 94,17 / 0,244 20cm / 0,4 cm / 0,796
number of theoretical plates Racemisation kinetics
0,207 / 6,395
0,141 / 3,192 680 12 -1
k0 =3,77⋅10 s
/ EA = 99,9 kJ/mol
3.3. Recycling chromatography combined with thermal racemisation The above theoretical study shows that it is useful to fully integrate racemisation and continuous chromatography. However, corresponding technology is not yet available. Since the conventional reactor-separator setup was demonstrated to be feasible, as a first step single-column recycling chromatography was investigated experimentally. A thermostatted CSTR (40°C) was connected to the column in a recycle setup. A part of the front of each chromatogram was collected as product A; the rest was recycled to the
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reactor. To maximise productivity, the process was operated in “touching band” mode. Due to dispersion in the system, the product average product purity achieved was 95%. Reactor concentrations remained close to the 1:1 mixture. Since no solvent removal could be used at this small scale the process expectedly suffered from strong dilution. 100
5 0
0
10 cycle
20
100 yield [%]
10
EC [l/g]
PR [g/d/l]
15
50
0
0
10 cycle
20
50
0
0
10 cycle
20
Figure 6: Performance of single-column recycling with (open symbols) and without solvent removal (filled) in comparison to an SMB-based process with ISR in steady state (dashed lines).
Fig. 6 shows performance predictions obtained with the equilibrium-dispersive model for such single-column recycling with and without ideal solvent removal (ISR). The same requirements were used as in section 3. The process is basically infeasible without ISR. Also shown is the steady state performance of an SMB-based process (6 columns, ISR, cf. Fig. 3a). As is often found, the SMB process achieves a lower productivity, but at the same time allows for significantly lower solvent consumption.
4. Summary For the production of pure enantiomers from racemic mixtures it is desirable to combine the enantioseparation with an interconversion (racemisation) of the undesired form. Corresponding concepts that integrate chromatography and racemisation were studied theoretically, ranging from classical flowsheet integration to fully integrated processes with distributed reactivity. The latter options – although being hypothetical – have a significantly improved performance. However, it was also found that internal recycles and solvent removal are necessary if high purity is required. Parameters for racemisation kinetics and chromatographic separation of a model system were determined experimentally. Model predictions and first-stage experiments were performed for flowsheet integrated processes. Single-column systems were found to be an interesting alternative to SMB-based schemes. Current work focuses on theoretical investigations of further process schemes under a broader range of product and problem specifications. Furthermore, technological options are studied for fully integrated processes and intermediate solvent removal.
References [1] M. Kaspereit et al., J. Chromatogr. A (2007) 2 – 13 [2] T. Borren, Untersuchungen zu chromatographischen Reaktoren mit verteilten Funktionalitäten, PhD thesis, VDI Verlag, Düsseldorf, Germany, 2007 [3] M. Mangold et al., Chem. Eng. Sci. 55 (2000) 441 – 454 [4] M. Kaspereit, Separation of Enantiomers by a Process Combination of Chromatography and Crystallisation, PhD thesis, Shaker Verlag, Aachen, Germany, 2006 [5] K. Cabrera et al., J. Chromatogr. A 731 (1996) 315 – 321 [6] C. Blümel et al., J. Chromatogr. A 865 (1999) 51 – 71.
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The Application Of A Task-Based Concept For The Design Of Innovative Industrial Crystallizers Richard Lakervelda, Herman J.M. Kramera, Peter J. Jansensa, Johan Grievinka a
Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands
Abstract There is a need for a more synthesis-focused design approach for industrial crystallizers. In this paper a new task based design approach is applied to design a crystallization process unit. The approach aims to conceptually build-up the crystallization process from fundamental building blocks called physical tasks. Two lines of research are followed. First of all, the design and key results of several small scale experiments are discussed which demonstrate practical feasibility of the concept by isolating single tasks. Secondly, a model of a task based crystallizer consisting of two compartments has been developed. A dynamic optimization of the model shows that tight specifications on product quality can be achieved, because it is possible to control tasks independently from each other. This increase in flexibility for design and operation is of significant value for the development of future crystallizers. Keywords: Crystallization, Process synthesis, Task based design, Process optimization.
1. Introduction Crystallization is one of the oldest and economically most important separation technologies in chemical industry. The design of crystallization processes is complicated compared to liquid processes, because besides purity also properties like shape, polymorphic form and size distribution have to be taken into account. The selection of crystallisation equipment is traditionally done from a limited number of state-of-art industrial crystallizers followed by optimization of that particular type of equipment. This reduces the design space and creative input of a designer. This contribution discusses the application of a novel approach for the conceptual design of crystallization process units, which is called a task based design approach [1]. The aim of the work is twofold. Small scale experiments illustrate that by combining several technologies the task based design approach can be realized in practice. Secondly, a model based optimization study aims to illustrate the increase in flexibility for design and operation.
2. Task based design approach Current industrial crystallizers facilitate many physical phenomena. The control over each of these individual physical phenomena is not possible because in present industrial crystallizers these phenomena are strongly entangled. To improve on these drawbacks a more functionally-driven design approach is proposed called task-based design [1]. In the task-based design approach an attempt is made to conceptually construct the crystallization process from fundamental building blocks called physical tasks. A task is a design concept indicating a preferred change in the state of matter to a target state, to be effected by means of a physical or chemical event under a specified range of operating conditions and kinetics. The concept shows similarities with the state
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task network as was introduced by Kondili et. al [2] for process scheduling. Tasks can be connected in a network to accomplish the complete transition of a given feed into a desired product. The aim is to generate alternative ways of structuring the tasks, leading to a task superstructure that contains all possible and relevant tasks and their interconnectivity. Optimization of the task superstructure can be realized based on product quality, throughput or economic evaluation of the process and can be dependent on design constraints. The task based design approach is more flexible than traditional design approaches and allows for the optimization of individual crystallisation tasks. In this way a larger solution space is created which is needed to improve product quality.
3. Experimental isolation of single crystallization tasks One of the key challenges of the development of a task based design approach for crystallization processes is the ability to control crystallization tasks independently from each other, which makes optimization of that particular task possible. To demonstrate the practical feasibility of the approach an experimental program has been designed and conducted. The objectives of the experimental work are as follows: 1. Minimize attrition as it competes with growth 2. Keep supersaturation below nucleation threshold to isolate crystal growth 3. Evaluate technology which can induce nucleation at low supersaturation The next three sections discuss experiments which are each dedicated to one of these objectives. The focus will be on the design of the experiments and key results. 3.1. Experimental isolation of task crystal growth by minimizing attrition The setup that was selected to minimize attrition consists of a bubble column in which supersaturation is created by simultaneous cooling and evaporation of the solvent by sparging air. The crystals are kept in suspension by the upward velocity of the bubbles, eliminating the need for a stirrer or a circulation pump. In this way attrition caused by crystal-impeller collisions is absent. Seeded batch experiments on lab-scale show the feasibility of the concept by comparing the growth of a seeded population with so-called ideal growth behaviour. Ideal growth behaviour means that the number of crystals stays constant during the batch. In that case the final product size reaches a maximum, which can be estimated by setting up a mass balance over the seed population [3]. The results from the bubble column show a different trend compared to agitated crystallizers. In particular it can be said that the results are much closer to ideal growth behaviour, which means that the number of crystals stay constant during the batch and attrition is indeed minimized [4]. 3.2. Experimental isolation of task Supersaturation Generation with membranes The second objective of the experimental work is related to tight control of supersaturation at any place in a future crystallizer to prevent spontaneous nucleation bursts and to maximize crystal growth. Membranes offer an interesting opportunity to control supersaturation gradients in new crystallizer designs as a designer can move a boiling zone to any desired place. Furthermore additional process actuators are available by changing the conditions around a membrane, for example pressure or osmotic pressure at the permeate side in case of reverse osmosis. An experimental setup has been constructed and tested to assess the potential application of membranes for crystallization processes (Figure 1).
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105
flux [ kg m-2 h-1]
16
12
8
4
0 0
4
8
12
16
time [hours]
Figure 1: Process flow diagram setup combining crystallization and membranes
Figure 2: Measured flux for four successive experiments
It is concluded that a stable flux of approximately 2.5 kg m-2 h-1 can be achieved (Figure 2). This value will be an important input for the optimization studies of the design of a task based crystallizer in the next section. 3.3. Experimental isolation of task nucleation by using ultrasound Ultrasound is an interesting tool to induce nucleation at low supersaturation in a controlled way. It can be used to produce a large amount of nuclei with a narrow monodispersed distribution by applying pressure as a driving force [5]. An ultrasound generator is placed inside a supersaturated solution. An Ultrasonic field is applied for 2 minutes at various power inputs. The supersaturation is low to avoid spontaneous nucleation. The objective of the experiments is to evaluate the reproducibility of the production of nuclei and to relate the power output to the number of nuclei produced. During each experiment crystals were observed approximately one minute after insonation. It is concluded that nuclei can be generated at low supersaturation with a nucleation rate that is constant and not very sensitive for power input (Figure 3). The value of the nucleation rate will be used in the optimization studies. Produced crystals [#]
1.E+08
1.E+07
Gas Solvent
1.E+06
I
Ultrasound
M/L
G/L/S
1.E+05 40
50
60
70
80
Gas
Power input [W/l]
Figure 3: Measured number of crystals as function of ultrasonic power input.
I
Figure 4: compartmental structure task based crystallizer
4. Modeling and optimization of a task based crystallizer The experiments described in the previous chapter aim to demonstrate that the task based design approach is practically a feasible approach. Single crystallization tasks can be isolated, which makes optimization of that particular task possible. Combination of the technologies allows for the construction of a task based crystallizer in which each of the tasks can be controlled independently from each other. In this chapter an example of such a crystallizer is modeled and optimized.
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4.1. Modeling of a task based crystallizer A schematic drawing of the modeled system is given in figure 4. It involves a compartment with gas, liquid and solid phase which is used to grow crystals with negligible attrition. From this compartment a clear solution is taken which is fed to a second compartment which contains a membrane surface which is used to selectively remove solvent. Ultrasound can be applied within the GLS compartment to produce nuclei also at low supersaturation and with a constant rate. The system is operated in batch mode. The model will be used in an inverse problem and there exists a large difference in order of magnitude between the values of the moments of the crystal size distribution. Therefore special attention has been paid to proper scaling and simplification of the model. Therefore, instead of the full population balance the moments of the distribution are used, which yields a set of ordinary differential equations. The equations of the GLS compartment are written into dimensionless form to obtain a better scaled model. The component mass balance for the GLS compartment and the total mass and component balance for the ML compartment complete the model. This yields the following set of equations, where x0, .., x4 represent the scaled moments, y is the dimensionless solute concentration, İ is the liquid fraction and ș is the dimensionless time.
dx0 dT
K uD ,
dyGLS dT
UL
1
H
dVML dT
dx1 dT
yGLS x0 ,
dx2 dT
2 yGLS x1 , dH dT
1
yML yGLS J yGLS H
J AM W GLS
,
I
dCML dT
dx3 dT
VML
3 yGLS x2 ,
,H
dx4 dT
4 yGLS x3
1 kV x3
CGLS CML W GLS
(3)
(4)
CML dVML VML dT
(5)
Where Į represents the scaled nucleation rate, ȕ a growth rate constant, c0 and c* a reference and saturated concentration respectively, Ȗ is a dimensionless crystal density:
D
B W GLS E
3
E
0
* TGLS
kGW GLS c c
J
Ucrystal cT*
GLS
0
* TGLS
c c
W GLS
VGLS
I
(6)
The dimensionless state variables are defined as follows:
x0
yGLS
m0 E 3 , x1
m1E 2 , x2
cGLS cT*GLS c 0 cT*GLS
, yML
m2 E , x3
cML cT*GLS c 0 cT*GLS
m3 , x4
m4 E 1
(7)
(8)
4.2. Base case simulation The model of the task based crystallizer having two compartments has been implemented in gPROMS Modelbuilder 3.0.0. (PSE Enterprise, London). A base case simulation has been done with the settings as given in Table 1. The initial values correspond in both vessels to a clear saturated liquid.
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Table 1. Fixing degrees of freedom for base case simulation Parameter VML(t = 0) VGLS
Value
Unit
0.005
3
Physical meaning
m
Volume ML compartment
3
0.005
m
Volume GLS compartment -2
-1
J
2.5
kg m h
Mass flux from experiments (Figure 2)
Am
0.192
m2
Membrane surface area
B
3.5.108
# m-3 s-1
Maximum nucleation rate (Figure 3)
TGLS
298
K
Temperature GLS compartment
TML
323
K
Temperature ML compartment
ȝU
0.2 (t < 500 s)
-
20% of the reactor is insonated for 500s
0.0 (t > 500s) ij
l min-1
0.6 .
kG
6.0 10
-9
Flow rate between compartments
4 -1
-1
m s kg
-
The results of the base case simulation are depicted in Figure 5 and 6. It can be seen that crystals with a mean size of 265 ȝm can be produced with a solid fraction of 27%. The supersaturation and growth rate show a peak in the beginning which can be explained by the supersaturation build up from the increasing concentration in the ML compartment and supersaturation consumption by the increasing crystal surface area. 300
40
0.9
30 20
0.8
1.6 Mean size Supersaturation
Mean size [um]
50
1.2 200 0.8 100 0.4
10 0
0.7 0
2
4 Time [h] 6
8
Figure 5: Growth rate and liquid fraction in GLS compartment for the base case
0
Supersaturation [%]
1 Growth rate liquid fraction
liquid fraction [-]
Growth rate [nm/s]
60
0 0
2
4 Time [h] 6
8
Figure 6: Mean size and Supersaturation in GLS compartment for the base case
4.3. Model based optimization of a task based crystallizer The base case simulation can be optimized by introducing an objective function and by adding constraints to the model. The objective function of the dynamic optimization is the crystal mean size (m4/m3). The following constraints are subject to the simulation in addition to those indicating limits of the physical possible domain: x G = kg(C – C*) < 15.10-9 m s-1 (maximum growth rate, minimize defects) < 592 kg m-3 (prevent scaling on membrane surface) x CML = 0.75 (minimum liquid fraction) x İ(t = tend) The manipulated variables for the optimization are the mass flux over the membrane (J) and the ultrasound utilization (ȘU). Figure 7 shows the optimal trajectories of the manipulated variables. The results illustrate the strength of the task based design approach. In this case a very tight constraint on the growth rate has been imposed. It can be seen how both the flux and the utilization of ultrasound work together to maximize the crystal mean size. In the initial phase the ultrasound and flux are both high to create
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quickly a crystal population that can consume supersaturation and push the growth rate to its constraint (Figure 8). As the growth rate approaches the constraint the flux drops to reduce the supersaturation. At this point the utilization of ultrasound is still high to increase the surface area in the GLS compartment. As the crystals start to grow and consume more supersaturation, the flux can increase and the utilization of ultrasound can decrease to create less nuclei and therefore increase the mean size. Note that the total amount of solvent that has to be removed, which is proportional to the surface below the flux, is fixed because there is a constraint on the production. The flux therefore only has limited flexibility to force the growth rate below the constraint. It is possible to achieve the constraint on product quality, because now we are able to manipulate the task nucleation in addition to the task supersaturation generation. It should be noted that all the degrees of freedom are not explored yet, but already for this simple case a significant improvement in flexibility for design and operation is found. 20 Flux
16 12
Mean size [um]
1.5
10
8
0.5
4
40
0
0
0
1
2 Time [h] 3
4
Figure 7: Flux and insonation fraction maximizing mean size (only first 4 hours)
15
120
1
0
Mean size [um] Growth rate [m/s]
160
Fraction insonated
eta [%]
Flux [kg/m2/h]
2
20
200
80 5
Growth rate [nm/s]
2.5
0 0
2
4 Time [h] 6
8
Figure 8: Mean size (objective function) and growth rate (limiting constraint).
5. Conclusions In this paper a task based design approach is applied for the design of crystallization process units. The task based design approach considers fundamental crystallization tasks as building blocks for design. An experimental program and equipment have been identified which allows for the isolation of single crystallization tasks. It shows that the task based design approach is practically feasible. The experimental results are input for modeling and optimization of the design of a task based crystallizer, which consists of two compartments with different thermodynamic phases. A compartment in which the task crystal growth and nucleation are executed is connected to a compartment in which the task supersaturation generation can be executed. A dynamic optimization study shows that tight constraints on product quality can be achieved, because tasks can be controlled independently from each other. It allows for the design of novel crystallization equipment with improved flexiblity to manipulate product quality.
References [1] Menon, A.R. and A.A. Pande and H.J.M. Kramer and J. Grievink and P.J. Jansens, Ind.Eng.Chem.Res., 46 (2007) 3979 [2] E. Kondili and C.C. Pantelides and R.W.H. Sargent. Computers chem. Engng (1993), 17, 211 [3] N. Doki and N. Kubota and A. Sato et al., AIChE 45 (1999) 2527 [4] R. Lakerveld and A.N. Kalbasenka and H.J.M. Kramer and P.J. Jansens and J. Grievink, Proceedings of 14th Internationcal Workshop on Industrial Crystallization (2007) 221 [5] C. Virone and H.J.M. Kramer and G.M. van Rosmalen et al. Journal of Crystal Growth 294 (2006) 9
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Cell Cycle Modelling for Off-line Dynamic Optimisation of Mammalian Cultures Carolyn M. Lam,a Kansuporn Sriyudthsak,a Cleo Kontoravdi,a Krunal Kothari,a Hee-Ho Park,a Efstratios N. Pistikopoulos,a Athanasios Mantalarisa a
Centre for Process Systems Engineering, Dept. of Chem. Eng., Imperial College London, South Kensington Campus SW7 2AZ, UK.
Abstract Mammalian cell cultures producing high-value biopharmaceuticals are expensive and time-consuming to study due to their exclusive dependence on experimentation. A mathematical model has been developed that describes batch/fed-batch hybridoma suspension cultures under normal and chemically-arrested conditions, which is also used to optimise the fed-batch cultures. The optimised strategy was tested experimentally demonstrating that product concentration was closely predicted though the viable cell concentration was partly underestimated. Overall, the model has assisted in reducing the number of experiments required to determine optimal cell culture conditions. Further work is required to improve the model predictability. Keywords: mammalian, hybridoma, off-line, modelling, optimisation.
1. Introduction Biologicals, such as monoclonal antibodies (MAbs), are important drugs for the treatment of various diseases. The global market for MAbs is projected to increase to US$16.7 billion in 2008 (Reichert and Pavlou 2004). Mammalian cells are the preferred expression system in order to achieve functional products. However, large infrastructure investments, high costs of experimentation and long cultures necessitate the reduction in costs and time-to-market. Once the best cell-line and media composition have been selected, the feeding strategy for fed-batch cultures would need to be optimised to maximise the production potential of the cell culture. Continuous improvements in mammalian culture technologies are also important to maintain their competitiveness versus other alternatives such as transgenic plants and animals (Ma et al., 2003; Dyck et al., 2003). Modelling offers advantages in providing insight into the production process and guiding experimentation, thus elimination any unnecessary experiments. Furthermore, it also enables in silico determination of best and worst case scenarios, which help focusing resources on beneficial trials. In this study, modelling of a hybridoma suspension culture based on first principles for off-line optimisation of time-varying process strategies was performed. By tracking the population in various phases of the cell cycle (G0/G1, S, and G2/M), the specific productivity of each sub-population was taken into account, which reflected the culture’s intrinsic properties more accurately.
2. Materials and Methods 2.1. Batch and Fed-Batch Cultures The mouse-mouse hybridoma CRL-1606 cell line producing IgG1 monoclonal antibody (MAb) against human fibronectin was obtained from ATCC. Batch cultures
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were inoculated at 1.5-2.0x105 cell ml-1 in 100ml medium containing DMEM with 25mM glucose and 4mM glutamine (GIBCO), 2.5% CBS (ATCC) and 1% Pen-Strep (GIBCO) in shake-flask incubated at 37oC and 5% CO2. Samples were taken every 8 h. Three out of six batch cultures were arrested with 0.5% DMSO (Wang et al., 2004) at 44 h. A fed-batch culture was first tested in triplicates with the same initial conditions as the batch cultures and concentrated glutamine (Sigma) at 200 mM was added twice a day. Three sets of triplicate fed-batch cultures were then performed following an optimised feeding strategy with three different cell cycle-arrest times at 78 h, 96 h, and 126 h respectively. The feed contained DMEM (GIBCO) with 200mM glutamine and 500mM glucose (Sigma). 2.2. Cell Culture Analyses Cell concentration and viability were measured with a Neubauer haemocytometer (Assistant, Germany) and trypan-blue (Sigma). Glucose, glutamine, lactate, and ammonium were detected using BioProfile200 (NOVA Biomedical) pre-calibrated with internal standards. Cells were fixed and stained with propidium-iodide (Sigma-Aldrich) for cell cycle analysis with flow cytometry (Beckman Coulter). The concentration of MAb was measured using an in-house sandwich ELISA assay.
3. Modelling 3.1. Model Structure The model was adapted from Kontoravdi et al. (2005) for cell growth/death, nutrient uptake, and major metabolism. The model was further developed to include description of cell cycle sub-populations. The cell cycle representation was based on the yeast model of Uchiyama & Shioya (1999) and the tumour cell model of Basse et al. (2003). Eq.(1)-(4) express viable cell concentration(Xv[cell L-1]) in terms of cells in G0/G1, S, and G2/M phases. As a simplification in notation, G0/G1 cells will be indicated as G1 unless otherwise stated. XG1, XS, XG2/M [cell L-1] are concentrations of viable cells in G0/G1, S, and G2/M phase, respectively, whereas Fout[L h-1] is the outlet flowrate. V[L] is the cell culture volume; b, k1, k2 [h-1] are the transition rates of cells from G1 to S, S to G2, and M to G1 respectively; and μd[h-1] is the specific death rate. (1) X v = X G1 + X S + X G 2 / M dX G1 F = 2b ⋅ X G 2 / M − k1 ⋅ X G1 − μ d ⋅ X G1 − ( out ) ⋅ X G1 dt V dX S Fout = k1 ⋅ X G1 − k 2 ⋅ X S − μ d ⋅ X S − ( )⋅ XS V dt dX G 2 / M F = k 2 ⋅ X S − b ⋅ X G 2 / M − μ d ⋅ X G 2 / M − ( out ) ⋅ X G 2 / M V dt
(2) (3) (4)
k1, k2, b can be rearranged and expressed in terms of the specific growth rate, μ [h-1]: 2 − xG1 (5) k1 = ⋅μ
xG1 1 + xG 2 / M ⋅μ k2 = xS
b=
μ
(6) (7)
xG 2 / M
where xi is fraction of cells in cell cycle phase i. xi is related to the specific growth rate (Uchiyama & Shioya, 1999; Slater et al., 1977) and are expressed as follow:
Cell Cycle Modelling for Off-line Dynamic Optimisation of Mammalian Cultures
x G1 = 1 −
(t S + t G 2 / M ) ⋅ μ − θ S − θG2 / M log 2
111
(8)
tS ⋅ μ +θS log 2
(9)
x G 2 / M = 1 − x G1 − x S
(10)
xS =
where θi represents the fraction of cells in cell cycle phase i when growth rate is zero, and tS and tG2/M [h] represent the time spent in S and G2/M phase respectively. Eq.(11)-(12) are the specific glucose uptake rate, Qglc[mmol cell-1 h-1], and the specific lactate production rate, Qlac[mmol cell-1 h-1], modified from Kontoravdi et al. (2005) based on results of the initial fed-batch culture (see Fig.2). A maintenance term for glucose uptake was removed and the glucose uptake and lactate production rates were linked to glucose concentration. In the equations below, μ[h-1] is the specific growth rate, Yx,glc[cell mmol-1] is the cell-yield from glucose, KQglc[mM] is the halfsaturation constant for glucose uptake, [GLC] is the glucose concentration [mM], Ymax -1 lac,glc[mmol mmol ] is the maximum yield of lactate from glucose, Klac,glc[mM] is the half-saturation constant for lactate production with respect to glucose concentration. [GLC ]2 μ (11) ⋅ Q = glc
2 Yx , glc K Qglc + [GLC ]2
Qlac = Ymax lac , glc ⋅
[GLC ] K lac , glc + [GLC ]
(12)
Eq.(13)-(14) take into account the production of MAb by each cell cycle phase, where v(%) is viability, QMAb,G1 , QMAb,S , QMAb,G2/M[mg cell-1 h-1] are specific MAb production rates of the corresponding cell-cycle phases, [MAb] is the concentration of monoclonal-antibody [mg L-1], KMAb[%] is an inhibition constant for MAb production with respect to cell viability. The introduction of viability in QMAb was based on the results of Glacken et al. (1988) which demonstrated that cell culture productivity was affected by low viability; these findings were also observed in our experiments that specific productivity decreased for CRL-1606 during death phase. F d [ MAb] (13) = f (v) ⋅ (Q ⋅X +Q ⋅X +Q ⋅X ) − ( out ) ⋅ [ MAb] dt
where
MAb ,G1
0 ° ° 1 f (v ) = ® ° K MAb °¯1 + v
G1
, v ≥ 80%
MAb , S
S
MAb ,G 2 / M
G2 / M
V
(14)
, v < 80%
3.2. Parameter Estimation and Dynamic Optimisation The model was implemented in gPROMS (Process Systems Enterprise Ltd.) and the parameters were estimated based on the batch and initial fed-batch data. The same set of parameters was used to generate the simulation results for the batch, fed-batch, and cell growth arrested cultures. The model consists of 13 differential equations and 32 parameters of which 7 were altered in the arrested cultures with their values programmed to switch automatically in the model when the cell cycle-arresting chemical was introduced. As a case study for product yield optimisation, the amount of feed and the cell cycle-arrest time were varied while all other cell culture conditions, e.g. feed compositions, time intervals etc., were fixed. The model-based optimisation was done using a mixed-integer dynamic optimisation algorithm (Bansal et al., 2003) with a grid of initial values for the degrees of freedom concerned. The best fed-batch strategy was selected for experimental validation with a variation in cell cycle-arrest time in two additional fed-batch cultures to test the predictability of the model.
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4. Results and Discussion 4.1. Batch Cultures The model was able to capture the reduction in growth rate and the corresponding increase in the G0/G1 phase population when cells were arrested at 44 h (Fig.1). Although the viable cell concentration of the arrested culture at late exponential phase and the final MAb concentration of the normal culture were slightly lower than predicted, it is important to note that the relative growth rates and productivity in the two cultures were in accordance with model prediction. There was a time-lag of approximately 10 h in the change in G0/G1 and S phase distribution at the beginning of the cell culture as compared with the model simulation. This might suggest the need of a lag term in the model in order to represent the delayed response of the cells.
Fig.1: Batch culture data showing (a) viable cell (Xv) and antibody (MAb) concentration; and (b) cell cycle distribution for normal(n)/arrested(ar) cultures. Simulation results are shown by lines.
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4.2. Fed-batch Cultures
Fig.2: Initial fed-batch culture data showing (a) viable cell(Xv) and antibody(MAb) concentration; and (b) glutamine(Gln), ammonium(Amm), glucose(Glc), and lactate(Lac) concentration. Simulation results are shown by lines.
Fig.3: Optimised fed-batch data showing (a) viable cell(Xv) concentration; and (b) antibody (MAb) concentration for cell cycle-arrest at 126h and two other cell cycle-arrest times at 78h and 96h. Simulation results are shown by lines.
The initial fed-batch culture performed revealed a rich dynamic response of the cells when glutamine was continuously added throughout the cell culture. The simulated viable cell, MAb, glutamine, and ammonium concentrations followed the experimental trends (Fig.2). However, the cells appeared to consume less glucose and, consequently, produced less lactate after about 60 h. The model over-predicted the lactate production only near the end of the culture, suggesting that certain metabolic changes had taken place which has not been fully captured by Eq.(11)-(12). The model-based dynamic optimisation results that were obtained from a fixed feed composition, same initial condition as the batch culture, and a feeding interval of 6-12 h, suggested an optimal cell cycle-arrest time at 126 h and supplementation with feed from 48 h onwards. The results of three different fed-batch cultures with identical supplementation strategies but various cell cycle-arrest times are shown in Fig.3. The viable cell concentration, Xv, was closely predicted up to about 80 h. However, after 100h, Xv decreased significantly in all three cultures. The predicted MAb concentration was in accordance with the experimental results with only a slight under-prediction around 80-100 h. Both model predictions and experimental results indicated a small difference in MAb yield when the cultures were arrested at different times. The optimised fed-batch experiments involved a total of 9 shake flask cultures so the
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deviation between the data and model predictions for Xv appeared to suggest a deficiency in the model. Overall, with the aid of model predictions, fewer experiments were needed in order to explore the possible limits of the cell culture production capacity. In the optimised fed-batch culture, the culture life-time was extended as indicated by the Xv peaking at about 100 h while the corresponding peaking time for the initial fed-batch and batch cultures were about 90 h and 65 h respectively; and the MAb yield reached ~3.5x103 mg L-1 as compared to ~2.5x103 mg L-1 in the initial fed-batch culture and ~1.3x103 mg L-1 in the batch cultures.
5. Conclusion The model was able to predict the culture dynamics for batch, fed-batch, and cell growth arrested cultures, especially up to the exponential growth phase, after which certain variable predictions deviated from the experimental results in fed-batch cultures, e.g. the viable cell concentration in the optimised fed-batch culture tended to be overestimated, and the simulated glucose uptake rate near the end of the fed-batch cultures was higher than observed. The model closely predicted the monoclonal antibody concentration in the optimised fed-batch culture despite an underestimation of the viable cell concentration. The model developed was able to direct experimental efforts to a more focused area in this case study. The monoclonal antibody yield in the optimised fed-batch culture was ~3.5x103 mg L-1 which was about 40% higher than the initial fed-batch culture. Further improvement of the model structure may be necessary to enhance its predictive capability.
References V. Bansal, V. Sakizlis, R. Ross, J.D. Perkins, E.N. Pistikopoulos, 2003. New algorithms for mixed-integer dynamic optimization. Computers and Chemical Engineering, 27, 647-668. B. Basse, B.C. Baguley, E. S. Marshall, W. R. Joseph, B. van Brunt, G. Wake, D. J. N. Wall, 2003. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. Journal of Mathematical Biology, 47, 295-312. M.K. Dyck, D. Lacroix, F. Pothier, M.-A. Sirard, 2003. Making recombinant proteins in animals - different systems, different applications. Trends in Biotechnology, 21(9), 394-399. M.W. Glacken, E. Adema, A.J. Sinskey, 1988. Mathematical descriptions of hybridoma culture kinetics: I. Initial metabolic rates. Biotechnology and Bioengineering, 32(4), 491-506. C. Kontoravdi, S.P. Asprey, E.N. Pistikopoulos, A. Mantalaris, 2005. Application of global sensitivity analysis to determine goals for design of experiments: An example study on antibody-producing cell cultures. Biotechnology Progress, 21, 1128-1135. J.K.-C. Ma, P.M.W. Drake, P. Christou, 2003. The production of recombinant pharmaceutical proteins in plants. Nature Reviews Genetics, 4, 794-805. Process Systems Enterprise Ltd. 2007. URL: www.psenterprise.com. J.M. Reichert and A.K. Pavlou, 2004. Monoclonal antibodies market. Nature Reviews Drug Discovery, 3(5), 383-384. M. L. Slater, S. O. Sharrow, J. J. Gart, 1977. Cell cycle of Saccharomyces cerevisiae in populations growing at different rates. Proceedings of the National Academy of Sciences of the United States of America, 74, 3850-3854. K. Uchiyama and S. Shioya, 1999. Modeling and optimization of α-amylase production in a recombinant yeast fed-batch culture taking account of the cell cycle population distribution. Journal of Biotechnology, 71, 133-141. X. Wang, S. He, Y. Zhang, J. Xu, Q. Feng, L. Li, L. Mi, Z. Chen, 2004. DMSO Arrested hybridoma cells for enhanced antibody production. Sheng Wu Gong Cheng Xue Bao, 20, 568571.
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New Configuration For Hetero-Azeotropic Batch Distillation: I. Feasibility Studies Peter Langa , Ferenc Denesa and Xavier Jouliab a
BUTE Dept. of Building Services & Process Engineering, H-1521 Budapest, Muegyetem rkp. 3-5, bLGC-ENSIACET-INPT, 118 route de Narbonne, 31077 Toulouse, France
Abstract For heterogeneous batch distillation a new double column configuration operating in closed system is suggested. This configuration is investigated by feasibility studies based on the assumption of maximal separation and is compared with the traditional batch rectifier. The calculations are performed for a binary (n-butanol – water) and for a ternary heteroazeotropic mixture (isopropanol – water + benzene as entrainer). Keywords: heteroazeotrope, batch distillation, feasibility studies.
1. Introduction If components of a mixture form a heteroazeotrope or by the addition of an entrainer (E) a heteroazeotrope can be formed, the azeotropic composition can be crossed by decantation. In the pharmaceutical and fine chemical industries batch processes including the batch heteroazeotropic distillation (BHD) are widely applied. As far as we know the BHD was exclusively applied in the industry in batch rectifiers (equipped with a decanter) in open operation mode (with continuous top product withdrawal). The batch rectifier (BR) was investigated with variable decanter holdup by Rodriguez-Donis et al. (2002) and with continuous entrainer feeding by Modla et al. (2001, 2003) and Rodriguez-Donis et al. (2003), respectively. Recently the BHD was extensively studied for the BR and multivessel columns by Skouras et al. (2005a,b). The objectives of this paper are - to suggest a new double-column system (DCS) for the BHD, - to investigate this configuration by feasibility studies, - to compare its performance with that of the traditional BR. Calculations are performed for a binary (n-butanol – water) and for a ternary heteroazeotropic mixture (isopropanol – water + benzene).
2. The column configurations studied First the BR then the new DCS is studied by assuming maximal separation. 2.1. Batch rectifier (Fig. 1.) First the separation of the binary then that of the ternary mixture is presented. Separation of a binary mixture If the charge (feed) composition (xch,A (mole fraction of component A)) is in the Br Ar heterogeneous region ( x AZ, ) it is worth to separate it by decantation A < x ch,A < x AZ,A Ar into an A-rich ( x AZ, ) and a B-rich ( x Br ) phase before the start of the distillation. A AZ,A
One production cycle consists of two distillation steps. In the first step we select the phase to be distilled so that the overall quantity of the two products in the first cycle be
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Fig. 1. BR producing A from mixture A-B
Fig. 2. DCS for binary mixture
maximal. It can be derived (for pure products) that we have to distil the A-rich phase Br Ar Br first if x ch ,A > x AZ ,A /[1 − ( x AZ,A − x AZ,A )] . Step 1: Production of A: The A-rich phase ( x Ar ) of the heteroazeotrope (xAZ,A) is reAZ,A Br fluxed and the B-rich one ( x AZ, ) is withdrawn as distillate. The bottoms is product A. A
Step 2: Production of B: The B-rich phase(s) is (are) distilled. The B-rich phase of the azeotrope is refluxed and the A-rich one is withdrawn as distillate. The bottom residue is product B. The main disadvantages of the BR are that in one step only one component can be produced (in the residue) and that the recovery is limited since the other component in the distillate is saturated with this component. Separation of the ternary mixture The separation of a homoazeotropic isopropanol (A) – water (B) mixture is considered. Addition of an entrainer, in a small amount, is needed. The steps of a production cycle are: Er
Step 1: Production of A: The E-rich phase ( x TAZ ) of the ternary azeotrope ( x TAZ ) is Br
refluxed and the B-rich phase ( x TAZ ) is withdrawn as distillate, which is distilled in Step 2. The bottom residue is product A. Step 2: Removal of E: The B-rich phase of the azeotrope is refluxed and the E-rich phase is withdrawn as distillate. The bottom residue still contains some A. Step 3: Purification of B from A: A is removed (from the bottom residue of Step 2) in the form of binary A-B homoazeotrope ( x BAZ ) in the distillate and the bottom residue is product B. 2.2. The new double column system (Fig. 2.) The two column system is operated in closed mode (without continuous product withdrawal) with a single decanter. The two components are simultaneously produced as bottom residues. Separation of a binary mixture A heterogeneous charge is separated by decantation. The A-rich phase is filled in the reboiler of the column α (producing A) and a B-rich one to the other reboiler β. A homogeneous charge can be divided between the two reboilers. The top vapour of both columns is of azeotropic composition. The A-rich phase is sent to the top of column α and the B-rich one is fed to the top of column β.
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Separation of the ternary mixture The homogeneous charge can be arbitrarily divided between the two reboilers.The entrainer, which is filled at the start only in the reboiler of column α, circulates in the system. The top vapour of the column α is ternary azeotrope and that of column β is AB binary azeotrope. The E-rich phase is sent to the top of column α and the B-rich one (containing negligible amount of E) is fed to the top of column β.
3. Feasibility method Our aim is to estimate the duration of the processes and the amount of products. A simplified model was applied based on the following assumptions: maximal separation, negligible hold-up on the trays and in the decanter, constant molar overflow, the flow rates do not vary with the time, one-phase liquid streams leave the decanter, negligible duration of pumping between the operation steps (BR), no entrainer loss (in the case of the ternary mixture). The total and component material balances for one column and the decanter are analytically solved. For the DCS we assume that both products reach the prescribed purity at the same time, that is, the duration is minimal. The process time (τ) for both configurations and for the DCS the optimal division (vα) of total vapour flow rate (V) between the two reboilers and that of the charge (Ubα/Uch) are shown. 3.1. Equations for the BR Separation of a binary mixture jr ( x irAZ,i − x AZ U ,i )( x e ,i − x b ,i ) Duration of a step: τ = ir ⋅ b jr V ( x AZ,i − x AZ,i )( x e,i − x AZ ) ,i
where i, j: components (i is produced in the given step); x b,i , x e, i : mole fraction of i in the reboiler at the beginning and end of the step; U: molar holdup in the reboiler. Distillation of the ternary mixture Step 1: We suppose that product A does not contain E (it is polluted only by B). Er Br ( x TAZ U , A − x TAZ, A )( x spec, A − x ch , A ) ⋅ ch , Duration of this step: τ(1) = Er Br ( x TAZ, A − x TAZ, A )( x spec, A − x TAZ, A ) V where x spec,A is the specified purity of product A. Step 2: The top vapour has ternary azeotropic composition. Duration of this step: Br Br x Er ,A − x TAZ ,A x TAZ,E U b τ ( 2) = TAZ ⋅ ⋅ Er Er V x TAZ ,A − x TAZ,A x TAZ,E Step 3: In this step only A and B are present, the top vapour is the homoazeotrope. There is no need for a decanter. Duration of this step: x b,A − (1 − x spec,B ) U τ (3) = ⋅ (1 + R ) ⋅ b , where R is the reflux ratio. x BAZ,A − (1 − x spec,B ) V 3.2. Equations for the double column system Separation of the binary mixture β Br For a heterogeneous charge: x αb,A = x Ar AZ,A and x b ,A = x AZ,A . For a homogeneous one:
x αb, A = x βb, A = x ch , A , the number of independent equations is less by one than in the previous case, hence one of the unknowns ( U αb , U βb , v α ) must be specified. The value of the main operational parameters:
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τ=
Br Ar Δ( U α x αA ) − ΔU α x AZ − x Br Δ( U α x αA ) − ΔU α x AZ, A x Ar , A x AZ, A − x AZ, A AZ, A , vα = ⋅ Ar ⋅ AZ, A α α α Ar Br Δ( U x A ) − ΔU x AZ, A x AZ, A − x Br x AZ, A − x AZ, A x AZ, A − x AZ, A AZ, A
where ΔU α = U αe − U αb , Δ( U α ⋅ x αA ) = U eα ⋅ x spec,A − U αb ⋅ x αb,A , U αb =
x ch ,A − x βb,A x αb,A − x βb,A
⋅ U ch
Separation of a ternary mixture Initially only the reboiler α contains E. We neglect the content of E of the B-rich phase. Hence there is no E in column β whose top vapour is A-B binary azeotrope. The number of unknowns is more than the number of independent equations by one. Hence one of the unknowns must be specified. The composition of the phases is a function of vα but this function can be mathematically expressed with difficulty which would make the solution of the set of equations difficult. Hence we specify vα. The values of the main parameters of the operation: U αe ⋅ ( x spec,A − x ch ,A ) x Er − x , U αb = U eα + E ErTAZ, E ⋅ v α ⋅ V ⋅ τ , τ = Er α Er xE L ⋅ ( x A − x ch ,A ) + v ⋅ V ⋅ ( x ch ,A − x TAZ,A ) U eα =
x ch ,A − (1 − x spec,B ) x spec,A − (1 − x spec,B )
⋅ U ch
4. Calculation results The total vapour flow rate of the DCS was taken equal to that of the BR ( V = 20 kmol/h ). (The heat duty is proportional to the vapour flow rate.) For the DCS we determine the optimal division of the charge between the two reboilers (and the division of the total vapour flow rates belonging to it). In all cases the amount of charge is 100 kmol and the specified purity (xspec,i) is 99.5 mol% for both products. 4.1. Separation of binary mixtures (n-butanol(A) – water(B)) The composition of the heteroazeotrope and that of the A-rich and B-rich phases, Ar
Br
respectively: x AZ = [0.2562, 0.7438] , x AZ = [0.568, 0.432] , x AZ = [0.012, 0.988] All possible cases are studied: two homogeneous charges (one rich in A and the other rich in B) and a heterogeneous one. 4.1.1. Homogeneous charge rich in A a.Batch rectifier: x ch = [0.9, 0.1] . In Step 1 A is produced (Table 1). b. Double Column System We determine τ and vα for different ratios Ubα/Uch (Figs. 3. & 4.) The best operational policy (Table 1) is when the total amount of the charge is fed into reboiler α ( U αb / U ch = 1 ).The duration of the cycle is nearly equal for the two configuBR Step 1 Step 2 Ubα,β/Uch Div. of vap. fl.rate Duration [h] 0.862 0.014 Prod. A [kmol] 90.336 0.000 Prod. B [kmol] 0.000 9.544 Byprods. [kmol] 0.120 Byps. comp. [mol%] 56.80
DCS Col. α Col. β 1.00 0.00 0.9844 0.0156 0.880 90.404 0.000 0.000 9.596 0.000 -
BR Step 1 Step 2 Ubα,β/Uch Div. of vap. fl.rate Duration [h] 0.101 0.034 Prod. A [kmol] 0.502 0.000 Prod. B [kmol] 0.000 99.112 Byprods. [kmol] 0.386 Byps. comp. [mol%] 1.12
DCS Col. α Col. β 0.00 1.00 0.2538 0.7462 0.136 0.505 0.000 0.000 99.495 0.000 -
Table 1. Results (binary mixture rich in A) Table 2. Results (binary mixture rich in B)
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New Configuration for Hetero-Azeotropic Batch Distillation: I. Feasibility Studies
BR Step 1 Step 2 α,β Ub /Uch Div. of vap. fl.rate Duration [h] 2.006 0.100 Prod. A [kmol] 29.298 0.000 Prod. B [kmol] 0.000 69.823 Byprods. [kmol] 0.879 Byps. comp. [mol%] 56.80
DCS Col. α Col. β 0.5180 0.4820 0.9530 0.0470 2.141 29.798 0.000 0.000 70.202 0.000 -
Step 3 0.261 0.000 30.723 5.224 BAZ
DCS Col. α Col. β 0.9981 0.0019 0.9650 0.0350 8.494 67.576 0.000 0.000 32.424 0.000 -
Table 4. Results (ternary mixture)
25
1.0
20
0.8
15
0.6
10
0.4
5
0.2 0.0
0 0.0
0.2
0.4
0.6
U bα /U ch
0.8
0.0
1.0
0.2
0.4
0.6
U bα /U ch
0.8
1.0
Fig. 4. Rel. vap. flow rate of column α (binary mixture rich in A)
Fig. 3. Duration of the process (binary mixture rich in A)
1.0
16
0.8
U bα /U ch
12
τ [h]
BR Step 2 0.010 0.000 0.000 0.160 TAZ
vα
τ [h]
Table 3. Results (bin. heterogeneous mix.)
Step 1 Ubα,β/Uch Div. of vap. fl.rate Duration [h] 8.055 Prod. A [kmol] 64.001 Prod. B [kmol] 0.000 Byprods. [kmol] Byprods. compn. -
8 4
0.6 0.4 0.2 0.0
0 0.5
0.6
0.7
v
α
0.8
0.9
Fig. 5. Duration of the process (ternary mixture)
1.0
0.5
0.6
0.7
vα
0.8
0.9
1.0
Fig. 6. Division of the charge (ternary mixture)
rations. In the case of DCS by the best policy the whole amount of A is already in the reboiler α at the start and only B must be eliminated from it. The reason of the small value of vβ is that the B-rich phase flowing from the decanter into column β has very high B-content ( x Br AZ,B = 0.988 ). Hence only a small amount of A must be removed in the form of azeotrope for the purification of B. The main advantage of the DCS is that there is no residue at all. 4.1.2. Homogeneous charge rich in B a. Batch rectifier: x ch = [0.01, 0.99] . In Step 1 B is produced (Table 2). b. DCS: We determined τ and vα for different divisions of the charge. The best operational policy (Table 2) is when the total amount of the charge is fed into reboiler β. The duration of the cycle is nearly equal in the two cases. The ratio of the duration of the two steps for the BR: τ (1) / τ ( 2) = 2.971 The ratio of vapour flow rates of the two columns for the DCS: v β / v α = 2.940
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The values of these two ratios show that energy demand of the production of each component is nearly the same for the two configurations. The division of the charge can be explained similarly as in the case of the previous charge composition. 4.1.3. Heterogeneous charge Before the distillation the charge of composition x ch = [0.3, 0.7] is separated by decantation into an A-rich ( U Ar = 51.8 kmol ) and a B-rich ( U Br = 48.2 kmol ) phases. a. Batch rectifier: In Step 1 the A-rich phase is distilled and A is produced (Table 3). b. DCS: The preliminary decantation provides the division of the charge which determines the value of vA. Hence only one solution exists (Table 3). The duration of the cycle is nearly equal in the two cases. 4.2. Separation of the ternary mixture (isopropanol (A) – water (B) + benzene (E))
Binary azeotropic charge ( x BAZ = [0.674, 0.326,0] ) is separated by the application of an entrainer (E). The composition of the ternary IPA – water – benzene heteroazeotrope and those of its E-rich and B-rich phases: Er
Br
x TAZ = [0.238, 0.239, 0.523] , x TAZ = [0.277, 0.048, 0.675] , x TAZ = [0.103, 0.894, 0.003] a.Batch rectifier. Calculation results are shown in Table 4. b.DCS: We determine τ and U αb / U ch for different rel. vapour flow rates of column α (Figs. 5-6). Calculation results for the best operational policy are shown in Table 4. The duration of cycle is nearly equal in the two cases. The amount of the final residue is more than 5 % of the charge for the BR, whilst there is no residue at all by the DCR.
5. Conclusion We suggest using a new double column system (DCS) for heterogeneous batch distillation. It is operated in closed mode without continuous product withdrawal. This configuration was investigated by feasibility studies based on a simplified model (maximal separation, negligible holdup) and was compared with the traditional batch rectifier (BR). The calculations were performed for the mixtures n-butanol – water and isopropanol – water + benzene (entrainer). The performance of the DCS was compared with that of the BR. The main benefit of the DCS is that it produces no residue to be separated later. The DCS proved to be feasible and in the cases studied competitive with the BR. In comparison with the BR it gave for the ternary mixture better and for the binary one similar results, respectively. Feasibility studies were completed by rigorous simulations. The results of these calculations based on much less simplifying assumptions are published in a separate paper.
References Modla G., P. Lang and K. Molnar, (2001). Batch Heteroazeotropic Rectification … 6th WCCE, Melbourne, Australia, (10 pages on CD),. Modla G., P. Lang , B. Kotai and K. Molnar, (2003). AIChE J, 49 (10), 2533. Rodriguez-Donis I, V. Gerbaud, X. Joulia, (2002). AIChE J, 48 (6), 1168. Rodriguez-Donis Y., J. Equijarosa, V. Gerbaud, X. Joulia, (2003). AIChE J, 49, 3074. Skouras S., V. Kiva , S. Skogestad, (2005a). Chem. Eng. Sci., 60, 2895. Skouras S., S. Skogestad, V. Kiva, (2005b). AIChE Journal, 51 (4), 1144-1157.
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Integrated Design Of Solvent-Based Extractive Separation Processes P. Lek-utaiwana,b, B. Suphanita, N. Mongkolsirib, R. Ganic a
ChEPS, Dept of Chem Eng, King Mongkut’s Univ of Technical Thonburi, Bangkok , 10150, Thailand b SCG Chemicals, Rayong,21150, Thailand c CAPEC, Dept of Chem Eng, Technical Univ of Denmark, DK-2800 Lyngby, Denmark
Abstract The objective of this paper is to present a systematic methodology for integrated design of solvent-based extraction processes for recovery of desired chemicals and to highlight the application of this methodology through the solution of an industrial case study involving the recovery of two highly valued with high demand chemicals, ethylbenzene (EB) and mixed-xylenes, from a C8-aromatics mixture. The computer aided molecular design (CAMD) technique integrated with process design has been used to design the solvent-based extractive separation process. The details of the systematic methodology are presented and highlighted through the results from the industrial case study. A sensitivity analysis of the design to uncertainties in thermodynamic properties has been performed to evaluate their effect on process economy and environmental impact. The sensitivity analysis also provided input to design of experiments for measurements of important uncertain properties. Keywords: solvent-based separation, solvent selection, extractive distillation, CAMD
1. Introduction Increasing the value of a product is an important issue in almost all chemical processes. This is particularly true in naphtha cracking processes where there are opportunities for improvements of a large range of chemical products, which are usually intermediates for a wide range of chemicals-based consumer products. In this way, they enhance the value of the naphtha cracking unit product. Among many options, two commonly employed alternatives to upgrade byproducts is to separate and purify them to high-value (pure) chemicals or to convert them to another higher value chemical through reaction pathway. In this work, the first option of purifying the chemical product is investigated. The design objective for the solvent-based purification process is to not only satisfy the process-product specifications, but also to have a good economic return and reliability of performance. The key to success in this case is not only the process design, but also the effect of solvent selection on the process economy, process operability and the environmental impact. In this work, a systematic methodology integrating the solvent (design) selection issues with the extractive separations issues, the process economy and industrial operational as well as environmental constraints. Various design approaches have been proposed for separation process design and optimization, such as heuristic, insights based approach, graphical or geometric approach and numerical. In this work, the driving force based design, proposed by Gani & Bek-Pedersen [2] for synthesis, design and operation of the separation processes, especially for distillation based separation system is applied. Successful solvent-based
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extraction system design also requires the use of a good (environmentally acceptable) solvent that can increase driving force of interesting key components.
2. Methodology for design of solvent-based extraction processes The systematic methodology integrates the solvent design (selection) issues with the extractive separation issues, the process economy and industrial operational as well as environmental constraints. The CAMD technique [1] is combined with analysis of residue curve maps and separation driving forces to generate feasible solvent-based extractive separation process flow-diagrams. The best process is identified as the one that satisfies all the product-process constraints as well as being economic and environmentally acceptable. Figure 1 shows the main steps of the systematic methodology.
Figure 1: Block diagram of the integrated design of solvent-based separation process sequencing algorithm
The methodology highlighted in Fig 1 employs a number of computer aided methods & tools. For solvent selection, it employs the ProCAMD software [4] that designs/selects solvents for specified solvent target properties. The solvent (entrainer) plus the binary mixtures to be separated forms ternary systems whose distillation boundaries and residue curve maps are analyzed to identify the suitable solvent. ICASPDS is used for this purpose. As the solvent-based ternary systems are non-ideal mixtures, the accuracy of the predicted vapor-liquid phase equilibria are verified, where possible, with available experimental data and compared with more than one property model. In this case, the following software, ICAS®, Aspen Plus®, Aspen Distill®, or DistillDesigner® have been used. For solvent recovery column design, the driving force
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approach of Gani and Bek-Pedersen [2] has been used while for the two-feed extractive distillation column, the method proposed by Petlyuk [3] has been used. For a feasible process configuration, the operational costs as well as the equipment costs are calculated to obtain the final economic analysis. The type of solvent used and its loss with the products provides an account of the environmental impact. In a business (industrial) world, the most important issue is not just operational feasibility but also economic feasibility. Therefore, an economic evaluation is needed before any new process investment can be made. However, before any such investments, any uncertainties in the design need to be quantified. Therefore, a sensitivity analysis of the uncertain parameters to investigate the effects on process economy is performed as the last task of the systematic design methodology. The conclusions of the sensitivity analysis helps the engineers to decide if further experimental work is necessary.
3. Industrial case study This case study involves the recovery of highly valued and high demand ethylbenzene (EB) and mixed-xylenes (comprising of p-xylene (PX), m-xylene (MX) and o-xylene (OX)) from a C8-aromatics mixture (C8A). As point out above, C8A is isomers mixture, so their separation (recovery) is not simple, that why there is only one commercial process of liquid-phase adsorptive separation available for EB recovery from C8A. [8] However, this process requires high investment cost and generates huge volume of waste adsorbent that may become an environmental problem. Therefore, another green process should be considered for the EB purification. The ratio of various properties of the key components (EB and PX) were tested to examine the possibly alternatives. The result showed, by vapor pressure ratio, the solvent-based extractive distillation can be employed for their purification. [7] 3.1. Solvent selection The problem of identifying solvents for the separation of EB from PX by extractive distillation is considered first. The target solvent properties are solubility parameter, the normal boiling point, the normal melting point and selectivity (Sij = γi∞/γj∞). Specifying the above constraints to ProCAMD, a list of feasible solvents were obtained, from which, a selection is listed in Table 1. Table 1 Selected solvent by ProCAMD Result no
1 2 3 4 5 6 7 8 9
Solvent Name
Solubility parameter at 298 K (MPa1/2)
Normal Melting point (K)
Normal Boiling point (K)
Selectivity
Aromatic-Aldehyde-1 (AAD1) Acyclic-Ester-1 (AE1) Cyclic-Ketone-1 (CK1) Acyclic-Ester-2 (AE2) Acyclic-Ketone-1 (AK1) Cyclic-Ketone-2 (CK2) Acyclic-Ketone-2 (AK2) Aromatic-Alcohol-1 (AAL1) Cyclic-Amide-1 (CAD1)
21.44 21.42 17.86 19.84 17.69 19.88 17.88 24.09 23.16
247.15 254.15 265.05 234.15 209.23 244.91 232.4 248.81 249.15
453.51 475.15 488.35 453.95 422.02 419.32 451.08 466.67 475.15
1.23 1.22 1.22 1.20 1.19 1.19 1.18 1.13 1.13
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As result in table 1, the solvent that claimed by Berg’s patent [7] was also presented in the list at the fifth rank. This means successful in solvent selection could be achieved because the better solvents in term of both selectivity and solvent recovery can be acquired. (Berg’s solvent has closed boiling point to OX, so this becomes solvent recovery problem.) Due to its concentration-independent, the selectivity is the primary criterion chosen to be considered for selecting the suitable solvent in stead of the driving force. However, the selection of the best solvent based on only Sij is inadequate because it does not directly relate to the distillation design. The suitable criterion should return to how significant the solvent could alter the driving force between the key components. 3.2. Analysis of the solvents in terms of driving force diagrams The performance of the solvents were checked through solvent-free driving force diagrams for different choices of the property models. Figure 2 shows the solventfree driving forces obtained for the same systems with the original UNIFAC-VLE model and the UNIFAC-Do model [5]. As solvent AE1 (acyclic-ester-1) appears to have desired predicted behavior with both models, it is selected for further studies. One important point of difference is the predicted values of Dy (see Figures 2a-2b). With the UNIFAC-VLE model, it is 0.045 while with UNIFAC-Do, it is 0.145. Therefore, experimental verification is necessary to establish the true value and a sensitivity analysis to determine the solvent property effects on process economy needs to be checked before a decision for pilot plant studies can be made. Diving force curve-UNIFAC-DMD Diving force curve-UNIFAC
0.16
0.06 No-Solvent AAD1 AE1 CK1 AE2 AK2 CAD1 AK1 CK2 AAL1
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No-Solvent AAD1 AE1 CK1 AE2 AK2 CAD1 AK1 CK2 AAL1
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DF
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-0.02
xEB
(a) by UNIFAC
xEB
(b) by UNIFAC-Do
Figure 2: Solvent-free driving force curves plots for selected solvents
Assuming that one of the models is correct, the design calculations can be continued to obtain the process economic analysis. At the same time, the environmental impact can also be investigated. As our selected solvent is an ester, it’s MSDS shows low human effect, which may only act as an irritant to skin, eye and respiratory, and do not have any other environmental effect. So, it can be concluded that solvent is suitable for separation of EB from PX by extractive distillation. 3.3. Process design Solvent-based separation through extractive distillation consists of two distillations. The first is an extraction column with two feed (Aspen Distill® was used designing this column), while the second is a simple distillation column (the driving force concept was used for designing this column). The design was then verified by rigorous simulation using Aspen Plus®. The residue curve map (see Fig. 3) was used
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for the design of the first column to have consistent bottom and top products. The design details for this column for both models are given in Table 2. For the solvent recovery column, fifty theoretical stages were required for total recovery the solvent with degree of purity to level of 99.99%mol. Key components for this column were AE1 and OX. By driving force concept, at Dx = 0.4, the feed location was at 30th stage. The conventional distillation for separating EB to the required purity was also designed to compare with the extractive distillation approach. Since C8 aromatics mixture is an ideal mixture, so the same results were obtained from both property packages [6], which total number of stage was 298 stages, feed location was at 179th stage (Dx = 0.4, Dy = 0.0145), reflux ratio was 20, reboil ratio was 23.3. Separation of EB by a single conventional distillation column is obviously not feasible. However, the data can be used to compare with extractive distillation system in terms of investment cost and operating cost.
AE1
AE1
(a) Feed and products specifications
(b) Complete design
Figure 3 Residue curve maps of EB-PX-AE1 system Table 2 Input data and results from Aspen Distill® for extraction column design
Input Parameter
Value
EB/PX mix. rate EB/PX mix. composition AE1 rate
1.0
AE1 composition Distillate composition
AE1 = 1.0
Bottom product compositon Reflux ratio Operating pressure
EB = 0.6 PX = 0.4 2.5
EB = 0.995 PX = 0.005 AE1 = 1e-6 EB = 0.031 PX = 0.121 AE1 = 0.848 20 1 atm
UNIFAC Output Parameters Number of theoretical stages Feed location
UNIFAC-Do Value 78
Output Parameters Number of theoretical stages Feed location
Value 44
EB/PX mix. stream AE1 stream
33th
0.53
Distillate product rate
0.53
Bottom product rate
0.47
Bottom product rate
0.47
Reboil ratio
2.20
Reboil ratio
2.52
EB/PX mix. Stream AE1 stream
58th
Distillate product rate
7th
(Note: Dy = 0.045)
(Note: Dy = 0.145)
8th
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3.4. Sensitivity analysis A sensitivity analysis was performed to identify the effect of the driving force on the utility cost and the equipment cost. The results are shown in Fig. 4 and they confirm that the driving force is inversely proportional to the ease of separation and therefore the cost. This means that over-prediction of the driving force may lead to infeasible separation while under-prediction of the driving force may lead to waste of resources. The equipment costs were estimated by Aspen ICARUS® and utility pricings were based on general pricings in Thailand. Equipm ent cost sensitivity analysis
Utility cost sensitivity analysis 3,800
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0
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Dr i v i ng f or c e ( D y )
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Figure 4 Sensitivity analysis on uncertainty effect of thermodynamic property prediction
4. Conclusions A systematic methodology where solvent selection and process design have been integrated, has been developed and tested through the solution of an industrial case study involving a difficult separation problem. While the methodology and the corresponding tools were found to be applicable for industrial problems, uncertainties in property model predictions were noted. This pointed out that experimental verification of the model-based results is necessary and the sensitivity analysis provided enough information to plan the experimental effort, as future work for this project. Finally, it can be concluded that the available computer aided methods and tools can significantly reduce the time and effort to solve the class of problems highlighted in this work.
References [1] AT Karunanithi, LEK Achenie, R Gani, 2006, Chemical Engineering Science 61, 1247-1260. [2] R Gani and Bek-Pedersen, 2000, AIChE Journal, 46, 1271-1274 [3] F.B. Petlyuk, 2004, Distillation Theory and Its Application of Optimal Design of Separation units, Cambridge series in chemical engineering [4] R. Gani, 2006, ICAS-Program Package, CAPEC Report, DTU, Lyngby, Denmark (www.capec.kt.dtu.dk) [5] U. Domanska et. al., 2005, Fluid Phase Equilibria 235, 182-190. [6] W.L. Rodrigues, S. Mattedi, J.C.N. Abreu, 2005, Brazilian Journal of Chemical Engineering [7] L. Berg, Sep. of EB form PX by Ex. Dist, US Patent No. 5 425 855 (1995). [8] UOP LLC, 2004, Process Technology and Equipment
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Development of a novel Petri net tool for process design selection based on inherent safety assessment method Fakhteh Moradi, Parisa A. Bahri * School o, Electrical, Energy and Process Engineering, Murdoch University, Murdoch, WA 6150, Australia
Abstract Safety assessment can be implemented using different tools during process design stage. As part of this assessment, the implementation ability and the flexibility of the tools are of great concern. In this paper, a new user-friendly approach using Petri nets as modelling and implementation tool has been presented. Inherent safety methodology is used to assess the safety level of different process options and I2SI indexing system is employed to quantify safety factors. The applicability of this tool is demonstrated through revisiting an aclyric acid production case study taken from literature. Keywords: Petri net, inherent safety, process design.
1. Introduction Due to the importance of safety in process industries various safety and risk assessment methods have been developed to provide the opportunity of considering safety issues in early design stages. Meanwhile several studies have been undertaken to create appropriate implementation tools for developed assessment methodologies (Palaniappan et al., 2002a, Khan and Amyotte, 2004 and 2005). In this paper, inherent safety method and Petri nets modelling have been selected as the safety assessment and implementation tool, respectively. Section 2 briefly describes inherent safety methodology and adapted indexing tool and proposed modifications. Section 3 gives some information about Pteri nets and the related modelling approach undertaken in this research. In section 4 the proposed method is illustrated using a case study. Some discussions are given in section 5 and finally the paper concludes with reviewing the advantages of the proposed method.
2. Inherent safety method Inherently safer design, as one of the assessment techniques used in early design stage, aims at making processes inherently safer by using key principles such as elimination, minimization, substitution, moderation, and simplification (Kletz, 1985, Hendershot and Berger, 2006). Inherent safety methodology applies these principles to a basic process in order to eliminate or reduce the hazards. Using less hazardous materials, minimizing the inventory of hazardous material and changing the form and/or condition of using hazardous materials are some examples of application of these guidewords (Hendershot, 1997, Khan and Amyotte, 2005).
*
Author to whom correspondence should be addressed:
[email protected] 128
F. Moradi and P.A. Bahri
From the financial point of view, considering inherently safer options in process deign will reduce the process lifetime costs. Although conventional systems may have less fixed and operational costs, inherently safer options turn to be the cost-optimal ones given their lower maintenance and safety measure costs. In application of inherent safety concepts, I2SI indexing system is used for quantification of process units and equipment response.
2.1. Indexing system The I2SI indexing system for inherent safety evaluation as developed by Khan and Amyotte (2005) has been adapted in this study. Their final inherent safety index (I2SI) shows the potential applicability of the inherent safety keywords to the process. The index value greater than unity means positive response to inherent safety principles. The larger index indicates better response. A less than unity I2SI indicates that the equipment does not respond to inherent safety guidelines which is a weakness of the process route containing that equipment. In financial analysis two final indices are available: Conventional Safety Cost Index (CSCI) which is the ratio of conventional safety measures of the system over the probable loss cost, and Inherent Safety Cost Index (ISCI) which is the relative amount of the cost of inherent safety measures added to the system to the loss cost (Khan and Amyotte, 2004). Smaller ISCI in comparison to CSCI shows enviable impact of safety features on safety costs. In other words the smaller the ISCI/CSCI fraction the better the response. In this study the total number of non-responding equipment in each route is considered as the first comparison factor named Penalty. It is also proposed that I2SI to be divided by ISCI/CSCI ratio to obtain a unique index called Safety-Cost Ratio which represents a combination of safety and cost factors for each piece of equipment (Equation 1). Since a large I2SI and a small ISCI/CSCI ratio is always desirable, larger values of SafetyCost Ratio will indicate better response to inherent safety principles. In addition the Total Safety-Cost Ratio of each route is calculated as the sum of the individual SafetyCost Ratios of all the equipment existing in that route (Equation 2). These calculations provide decision-makers with a unique index for each route as a judgment base instead of simple assessment of different factors of different equipment in Khan and Amyotte (2005). These modifications will dramatically reduce human intervention into decisionmaking process. Safety-Cost Ratio = I2SI / ( ISCI / CSCI ) Total Safety-Cost Ratio =
¦
n
(1)
(Safety- Cost Ratio)
i 1
i
(2)
n is the total number of equipment Finally, to make decision about the best route, the Penalty factor would be considered in the first step. The route with the smallest Penalty factor is considered as the safest route. At the second level, among the routes with the same and smallest Penalty factors, the best one is the route with the largest Safety-Cost Ratio.
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3. Petri net model The implementation tool has to offer a comparative base to evaluate different process routes and to choose the best possible option. Different factors will come into account to define the efficiency of the tools. Flexibility, complexity and the number of routes that can be evaluated at certain time can be noted as some of these factors. Petri net modelling tool can be considered as a suitable implementation tool for risk assessment due to its flexibility and process simulation ability (Vernez et al., 2004). In addition, different feasible process options can be modelled in a Petri net as a super model, and assessed from safety point of view. A Petri net is a directed bipartite graph including places (drawn as circles) and transitions (drawn as bars). Places contain tokens which are shown as dots. The set of arcs are divided into input and output arcs with an arrowhead on their destinations. A transition is called enabled if all input places have at least the same number of tokens as all its output places. An enabled transition fires by removing tokens from input places to output places. Places, transitions and arcs all can be weighted. Weight is an additional feature that can carry critical attribute of related node through the nets (Gu and Bahri, 2002) In this paper, the first step has been to adapt a type of Petri net to model the process route(s). Initially, the basic route of producing a desired product is chosen. All possible combinations of process units to optimize the production yield and operating conditions of the basic route are considered as new routes. All the possible routes are then put together to create the supernet model of the system. This supernet is divided into various subnets based on the similarities and differences between production alternatives. Similar processing units of different routes build up subnets which are shared between some routes while unlike processing parts may create subnets which are used in one route only. Petri net model is able to automatically create different combinations of these subnets to define all possible process routes. The type of Petri net model used in this research is Place Weighted Petri net. Places represent equipment, transitions show starting and finishing of operations and tokens are raw material, semi-finished and finished products. The weights on places indicate Safety-Cost Ratios for equipment.
4. Case study The selected acrylic acid production process involves catalytic oxidation of propylene in the vapour phase at 190°C and 3 atm pressure. Two side reactions of this one-step process result in production of carbon dioxide and acetic acid with water (Khan and Amyotte, 2005). Three main options from different possible combinations of process units have been previously studied (Khan and Amyotte, 2005, Palaniappan et al., 2002b). The first option is the base case with no additional inherent safety features. The second and third options are revised versions of the first one. Modifications can include some or all of the following: a quench tower to reduce the temperature, change of solvent to lower the severity of the operating conditions, an extraction column, a solvent mixer to optimize the use of solvent and efficiency of acid extraction and the use of solvent recycle. Option 3 (Figure 1) which contains all basic and additional processing units can be described as follows. Acrylic acid is produced by partial oxidation of propylene in a fluidized-bed catalytic reactor. To prevent any side reaction, a cold recycle quench is used immediately after reactor. Deionized water in the off-gas absorber absorbs off-gas from the quench tower, containing acetic acid, acrylic acid, unreacted propylene, and byproducts. In the next step, an acid extractor is used for liquid-liquid extraction to
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separate the acid from water using diisopropyl ether as the solvent. After that diisopropyl ether is recovered and recycled in the solvent tower from the organic phase of extractor products. The bottom stream from this solvent tower is sent to the acid tower to separate and cool the acetic acid and acrylic acid and send them to storage. A waste tower is used to recover and recycle the solvent from acid extractor’s aqueous phase product. The bottom wastewater stream, containing acetic acid and small amount of solvent, is sent to wastewater treatment (Palaniappan et al., 2002b). In order to create the supernet of this process involving all processing units of the three mentioned options, the basic parts of routes are included in the main structure of the supernet. Moreover some groups of one or more units have been created and modelled as subnets. As a result, the following unit groupings/subnets have been considered: x Subnet A: including air compressor (Figure 2a). x Subnet B: including distillation column I, distillation column II, and distillation column III (Figure 2b). x Subnet C: including solvent splitter (Figure 2c). x Subnet D: including acid extraction tower, distillation column I, distillation column II, distillation column III, and solvent mixer (Figure 2d). The Petri net model of the supernet (Figure 2e) is implemented in Visual C++ and the total number of routes generated by Petri net is found to be 8. The results of Total Safety-Cost Ratio and Penalty factor estimations for these routes are presented in Table 1.
5. Discussion The results in Table 1 illustrate that the 8 generated routes have Penalty factors between 2 and 6 and Total Safety-Cost Ratios between 32.25 and 3.6 depending on their added inherent safety feature(s). Routes 3 and 4 with Penalty factor of 2 have the lowest, specifying them as safer options which are the same as options 2 and 3 respectively in Khan and Amyotte (2005). Between these two routes, route 4 has Total Safety-Cost Ratio of 32.25 which is higher than 29.98 for option 3 and the highest among all routes resulting in route 4 to be the best option. Route 5 which is the base case with no added inherent safety feature shows the highest Penalty factor of 6 and the smallest Total Safety-Cost Ratio of 3.6. In comparison with previous methods, the proposed method has significantly reduced human intervention in decision-making process. Route selection can be based on Total Safety-Cost Ratio which is a combination of safety and cost indices of all equipment in each route instead of assessing different factors separately. Moreover this approach has the capability to automatically generate possible process options and carryout safety calculations simultaneously. The automation of route generation which means creating all possible combinations of subnets and the base case is one of the most important advantages of using Petri net model. This minimizes the likelihood of missing any possible combination.
6. Conclusion This paper proposed place weighted Petri nets as a novel tool for selection of process design based on inherent safety technique. Inherent safer design is a methodology to achieve fundamentally safer plants. The impacts of applying inherent safety principals in process design can be quantified using I2SI indexing system.
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The proposed approach provides designer with the opportunity of considering more feasible routes faster through its automatic route generation ability and easier evaluation and comparison of their safety and costs through simultaneous calculation of Total Safety-Cost Ratios. Table 1. Total Safety-Cost Ratio of each route
Penalty factor Total SafetyCost Ratio
Route1
Route2
Route3
Route4
Route5
Route6
Route7
Route8
5
5
2
2
6
6
3
3
8.65
9.57
29.98
32.25
3.6
4.52
24.93
27.20
Figure 1. Aclyric acid production route including all inherent safety features.
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Figure 2. Petri net model of aclyric acid production routes, a: subnet A, b: subnet B, c: subnet C, d: subnet D, e: supernet.
References Gu, T. & A. Bahri, P., 2002, A survey of Petri net applications in batch processes, Computers in Industry, 47, 99-111. Hendershot, D., 1997, Inherently safer chemical process design, Journal on Loss Prevention in the Process Industries, 10, 3, 151-157. Hendershot, D. & Berger, S., 2006, Inherently safer design and chemical plant security and safety, American Institute of Chemical Engineering, Khan, F. & Amyotte, P., 2004, Integrated inherent safety index (I2SI): A tool for inherent safety evaluation, Process Safety Progress, 23, 2, 136-148. Khan, F. & Amyotte, P., 2005, I2SI: A comprehensive quantitative tool for inherently safety and cost evaluation. Loss Prevention, 18, 310-326. Kletz, T. A., 1985, Inherently safer plants, Plant/Operation Progress,4, 3, 164-167. Palaniappan, C., Srinivasan, R. & Tan, R., 2002a, Expert system for the design of inherently safer processes. 1. Route selection stage, Ind. Eng. Chem, 41, 26, 6698-6710. Palaniappan, C., Srinivasan, R. & Tan, R., 2002b, Expert system for the design of inherently safer processes. 2. Flowshhet development stage, Ind. Eng. Chem, 41, 26, 6711-6722. Vernes, D., Buchs, D. R., Pierrehumbert, G. E. & Bersour, A., 2004, MORM-A Petri net based model for assessing Oh&S risks in industrial processes: Modeling qualitative aspects. Risk Analysis, 24, 6, 1719-1735.
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Population balance modeling of influenza virus replication in MDCK cells during vaccine production Thomas Müllera, Josef Schulze-Horselb, Yury Sidorenkob, Udo Reichla,b, Achim Kienlea,b a
Otto von Guericke Universität Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany b Max Planck Institut für Dynamik komplexer technischer Systeme, Sandtorstraße 1, D39106 Magdeburg, Germany
Abstract In this contribution a population balance model of influenza A virus replication during vaccine production in Madin-Darby canine kidney (MDCK) cell cultures is developed. Differentiation on the population level is described by a degree of infection, which is proportional to the amount of intracellular viral proteins. This can be measured directly using flow cytometry. It is shown that the model shows reasonable agreement with experimental data, although not all details of the inner dynamics can be fully reproduced. Keywords: population balance modeling, distributed populations, virus replication, vaccine production, microcarrier cell culture.
1. Introduction In influenza vaccine production the use of permanent mammalian cell lines becomes more and more important. Besides sophisticated cell culture technologies and downstream processing methods, mathematical modeling plays a crucial role in improving production efficiency. Most notably for analysis and optimization of the process, the benefit of combining extensive experiments with mathematical modeling approaches is obvious. Thus, this strategy will contribute to the investigation of dynamic and kinetic phenomena and their link to the measured data. One can distinguish between structured and unstructured models, the latter neglecting intracellular phenomena. On the contrary, structured models account for intracellular processes and states in different compartments of the cell or include explicit kinetics for various intracellular steps of virus replication. Despite the high social relevance of infectious diseases and widespread use of animal cell lines in vaccine production, the application of even unstructured models for quantitative analysis and parameter estimation has not been common practice in bioprocess optimization. So far, research concerning influenza vaccine production in MDCK cell cultures has focused on the characterization of metabolism, growth of different cell lines and virus yields in various production systems [1,2].
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Based on the experimental investigation of the infection status of cells by measuring immunofluorescence of intracellular viral proteins with flow cytometry [3] mathematical models are required, which are able to describe distributed populations of cells with different degrees of infection. For this purpose, in the present paper an internal coordinate is introduced to quantify the degree of infection and the previous approach by Möhler et al. [4] is extended accordingly.
2. Model formulation The population balance model of Möhler et al. [4], which forms the basis for the presented approach, describes the replication of influenza A viruses in MDCK cells growing on microcarriers. It is unstructured and includes three concentrated state variables, which are the number concentrations of uninfected cells Uc, infected cells Ic and free virus particles V. It is assumed that at the time of infection (t0) all microcarriers are completely covered with cells, which corresponds to the maximum cell concentration ( U c , 0 = C max = 1.2 ⋅10 6 ml −1 [4]). Virus seed is added to the microcarrier cell culture and infection takes place. The amount of infectious virus particles added is described via MOI (multiplicity of infection, number of infectious virions per cell at t0 [5]). Virus particles instantly attach to uninfected cells. Consequently, the latter become infected with the infection rate kvi. After a certain time delay (τ = 4.5 h) due to intracellular processes, infected cells start releasing virus particles with the release rate krel and carry on until they die (kcd). Free virions can either attach to still available uninfected cells (kva) or simply degrade (kvd). Attachment to infected cells is neglected. In Möhler et al. [4] it is shown that the simple unstructured model is able to show good agreement between simulated outer dynamics and hemagglutination (HA) assays, which allow to estimate the total number of virus particles in the supernatant. However, the intracellular progress of infection is not considered, and therefore a comparison with flow cytometric fluorescence data characterizing the cell’s status during infection is impossible. To change this situation and to allow differentiation between cells the degree of infection δ is introduced as an infected cell’s property:
I c (t , δ ) = I c ,δ (t ) with δ ∈ N, [1, ∞] The degree of infection specifies the intracellular amount of viral protein and corresponds to the equivalent number of virus particles inside the cell assuming that a complete virus particle comprises 4000 viral proteins M1 and NP (3000 M1/virion +1000 NP/virion [6]). Schulze-Horsel et al. [3] show that the intracellular amount of viral M1 and NP proteins is coupled linearly with the cell's fluorescence caused by immunostaining against influenza A virus M1 and NP. The uptake or production of 4000 viral M1 and NP proteins or 1 virus particle respectively will lead to an increase of δ by 1; the cell’s fluorescence will increase by 2.66 FU/virion (fluorescence units, data not shown). Because not only infected cells but also uninfected cells with no intracellular viral protein show unspecific fluorescence intensity due to unspecific antibody binding, it seems suitable to change the internal coordinate from the degree of infection δ to a more
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general degree of fluorescence ϕ, where every step from one degree to another accounts for a change of the cell’s fluorescence intensity by 2.66 FU. Thereby, also the distributed unspecific fluorescence of uninfected cells can be taken into account: U c (t , ϕ ) = U c ,ϕ (t )
I c (t , ϕ ) = I c ,ϕ (t ) with ϕ ∈ N, [1, ∞ ]
The change of behavior along ϕ is characterized by two processes: virus replication increases fluorescence intensities with the replication rate krep while virus release decreases it respectively with the release rate krel. These two processes describe the inner dynamics of the system. 2.1. Model equations It can be shown that growth and death of the uninfected cells can be neglected due to medium exchange, limited space on microcarriers and fast progression of infection. Therefore, only infection is considered for description of the uninfected cell’s behavior: dU c ,ϕ dt
= −kvi U c ,ϕ V
(1)
As an initial condition, uninfected cells are considered to be normally distributed over the logarithmically scaled fluorescence axis to ensure good agreement with flow cytometric data collected by Schulze-Horsel et al. [3]. Infected cells emanate from uninfected cells, intracellular virus replication starts and the number of infected cells deceases with the specific death rate kcd. As described above convection along ϕ occurs due to virus protein accumulation and release. Every step from one degree of fluorescence to another is associated with the intracellular production or release of one virus particle respectively, so that the actual degree of fluorescence of every infected cell is controlled by these two effects. For brevity only the equation for ϕ > 1 is shown: dI c ,ϕ dt
= k vi U c ,ϕ −1V − kcd I c ,ϕ − k rep (I c ,ϕ − I c ,ϕ −1 ) + k rel (I c ,ϕ +1 − I c ,ϕ )
(2)
Free virions emerge from infected cells with ϕ > 1 by means of virus release. They are able to attach to uninfected cells (kva) or degrade with time (kvd). ∞ ∞ dV = k rel ¦ I c ,ϕ −kvd V − k va ¦ U c ,ϕ V dt ϕ =2 ϕ =1
(3)
Additionally, dead cells are included in the process because intact dead cells show up in the flow cytometric data. For simplicity all dead cells are considered to stay intact and keep the specific ϕ they possessed at time of death.
3. Parameters As the focus of this work is on the further development of the model of Möhler et al. [4], parameter identification was skipped for the time being and the “best-fit” parameter
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set was adopted. It is worth noting that the parameters used here have the same significance as in the undistributed model, except for the replication rate krep which has been introduced for the present model; its value has been derived from the flow cytometric data by means of sum-of-least-squares method (data not shown). Initial conditions are in agreement with the same set of experimental data of Schulze-Horsel et al. [3]. Table 1 summarizes the applied parameters and initial conditions, which differ from the ones published by Möhler et al. [4, Tab. 1, p. 50]. Table 1. Applied parameter set and initial conditions (note, that not every virus particle is infectious and non infectious virions have to be considered) Parameter
Value
Unit
krep
502 3 120 360
h -1 106/ml 106/ml 106/ml
V0 (MOI = 0.025) V0 (MOI = 1.0) V0 (MOI = 3.0)
4. Simulation results All simulations were performed with the dynamic simulator DIVA and visualized with MATLAB. For simplicity the delay behavior between infection and virus release was reproduced by simply shifting the simulation results by tshift = 4.5 h [4]. 4.1. Outer dynamics Figure 1 shows the evolution of virus yields over time for two of the three observed initial conditions. There is no detectable difference between the present structured model and the unstructured approach of Möhler et al. [4]. That is because of the unstructured model being included in the structured model as the zeroth order moment.
Figure 1. Outer dynamics in comparison with model of Möhler et al. [4]: virus yield vs. time post infection for different MOI (circles: experimental results, solid line: unstructured model, dashed line: structured model, tshift = 4.5 h)
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Figure 2. Inner dynamics: number density function qc vs. fluorescence intensity for specific time points post infection. (dots: experimental results, solid line: simulation results, MOI = 3.0, tshift = 4.5 h)
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4.2. Inner dynamics The inner dynamics are determined by the cell distribution over the fluorescence changing with time. For comparability the cell concentrations have to be converted into number density functions, which are obtained by normalization with the overall cell concentration at the specific time point and division by the specific class width in logarithmic scale. All cells (uninfected, infected and dead) contribute to the distribution as they all show fluorescence. Figure 2 shows the comparison between simulation results and the flow cytometric data reported by Schulze-Horsel et al. [3] for MOI = 3.0. The simulation peak lags behind in the beginning and catches up for later time points, but the overall tendency of increasing mean values can be reproduced quite well. However, the present model has a drawback: for an unknown biological reason the experimental distributions fall back to smaller fluorescence intensities at later time points (data not shown). So far, this effect cannot be simulated with the presented model formulation adequately.
5. Conclusion A new deterministic population balance model with distributed cell populations has been presented. The model is based on the unstructured approach of Möhler et al. [4]. Concerning outer dynamics the present model is equivalent to the unstructured model which proved to be sufficient to predict virus yields for different initial conditions [4]. The characteristics of the inner dynamics can be simulated except of the decrease of fluorescence intensity at later time points. The biological reasons for this effect are unclear. Presumably there are more states that have to be considered during virus replication like intercellular communication, extent of apoptosis or specific stage in cell cycle. Future computational and experimental research will aim in this directions and concentrate on structured descriptions of the virus replication in mammalian cell culture.
References [1] J. Tree, C. Richardson, A. Fooks, J. Clegg, D. Looby, 2001. Comparison of large-scale mammalian cell culture systems with egg culture for the production of influenza virus A vaccine strains. Vaccine 19, 3444–3450. [2] Y. Genzel, R. Olmer, B. Schäfer, U. Reichl, 2006. Wave microcarrier cultivation of MDCK cells for influenza virus production in serum containing and serum-free media. Vaccine 24 (35–36), 6074–6084. [3] J. Schulze-Horsel, Y. Genzel, U. Reichl, 2007. Quantification of intracellular accumulation of M1 and NP of influenza A virus – monitoring of infection status of production cells during vaccine production by flow cytometry, Submitted to BioMedCentral Biotechnology. [4] L. Möhler, D. Flockerzi, H. Sann, U. Reichl, Apr. 2005. Mathematical model of influenza A virus production in large-scale microcarrier culture. Biotechnology and Bioengineering 90 (1), 46–58. [5] P. Licari, J. Bailey, 1992. Modeling the population dynamics of baculovirus-infected insect cells: optimizing infection strategies for enhanced recombinant protein yields. Biotechnology and Bioengineering 39 (4), 432–441. [6] D. Knipe, P. Howley, D. Griffin, 2001. Field’s virology, 4th Edition. Lippincott Williams & Wilkins, Philadelphia.
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A population balance model approach for crystallization product engineering via distribution shaping control Zoltan K. Nagy Chemical Engineering Department. Loughborough University, Loughborough, LE11 3TU, United Kingdom
Abstract The paper presents a practical control approach, which can be used to directly design the shape of a crystal size distribution, to robustly achieve desired product properties. The control approach is implemented in a hierarchical structure where on the lower level a model-free crystallization control methodology, the supersaturation control, drives the system in the phase diagram, rather than in the time domain, whereas on the higher level a robust on-line model based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modeled using the population balance equation, which is solved using an efficient implementation of the method of characteristics. Keywords: distribution shaping control, population balance modeling, method of characteristics, optimal control, quadrature method of moments.
1. Introduction Crystallization is one of the key unit operations in pharmaceutical, food and fine chemicals industries. Despite the long history and widespread application of batch crystallization, there remains a disproportionate number of problems associated with its control [1], mainly related the complex nonlinear dynamics with non-ideal mixing, and various disturbances characteristic to these systems. The operating conditions of the crystallization process determine the physical properties of the products which are directly related to the crystal size distribution (CSD), shape or polymorphic form. These properties determine the efficiency of downstream operations, such as filtration, drying, and tablet formation, and the product effectiveness, such as bioavailability and shelflife. With the recent change of industrial procedures from Quality-by-Testing (QbT) to Quality-by-Design (QbD) and the advent of process analytical technology (PAT) initiative, especially in the pharmaceutical industries, approaches which can be used to design desired product properties are of great interest. The classical control objectives expressed in characteristics of the size distribution (e.g. maximize average size, minimize coefficient of variation) can lead to conservative and economically inefficient designs of the crystallization systems [2]. The paper presents an approach which can be used to directly design the shape of a crystal size distribution, to achieve desired product properties. Since dissolution rate depends on the shape of the CSD, when the resulting crystals represent the final product (e.g. drugs for inhalers) controlling the shape of the CSD can provide novel applications in the area of drug delivery, or environmentally friendly dosage of pesticides, where particular multimodal distributions can be designed to achieve desired concentration level of the active compound. The crystallization system is modeled via a population balance equation which is directly used in the
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optimization procedure where the objective function is expressed in terms of the shape of the entire CSD. The population balance model (PBM) is solved using an efficient implementation of the method of characteristics [3] when nucleation and growth are the governing mechanisms, and with the quadrature method of moments (QMOM) when agglomeration and breakage are also considered [4]. It is shown that in special cases when constant supersaturation control is applied analytical solution of the PBM is possible for the case of generic power law growth kinetics. The optimization problem is solved using an efficient multistage approach implemented in the optimization package OptCon. The proposed approach is corroborated in the case of a simulated crystallization system.
2. Population balance modelling of the batch crystallization process 2.1. PBM with growth and nucleation kinetics only Considering a single growth direction with one characteristic length L , and a wellmixed crystallizer with growth and nucleation as the only dominating phenomena the population balance equation (PBE) has the form sfn (L, t ) s{G (S , L; Rg )fn (L, t )} B(S ; Rb )E(L0 , L) , st sL
(1)
where fn (L, t ) is the crystal size distribution expressed in the number density function (number of crystal per unit mass of slurry), t is time, G (S , L; R ) is the rate of crystal growth, B(S ; Rb ) is the nucleation rate, S = (C-Csat) is the supersaturation, C is the solute concentration, Csat = Csat(T) is the saturation concentration, and Rg and Rb are vectors of growth and nucleation kinetic parameters, respectively. Equation (1) can be transformed into a homogeneous hyperbolic equation with boundary condition f (L0 , t ) B(S )/G (S ) and initial condition given by the size distribution of seed, f (L, 0) fseed (L0 ) . The partial differential equation can be reduced to a system of ODEs by applying a combination of the method of characteristics (MoC) and method of moments (MoM). The aim of the MoC is to solve the PDE by finding characteristic curves in the L t plane that reduce the PDE to a system of ODEs. The L t plane is expressed in a parametric form by L L(2 ) and t t(2 ) , where the parameter 2 gives the measure of the distance along the characteristic curve. Therefore fn (L, t ) fn (L(2 ), t(2 )) , and applying the chain rule gives: g
dfn dL sfn dt sfn d 2 d 2 sL d 2 s t
.
(2)
Considering size independent growth and comparing (2) with (1) we find 2 t and the characteristic curve is given by dL G . dt
(3)
Adding (3) to the equations which results by applying the MoM, we can calculate the characteristic curve and boundary conditions f (L0 , t ) by the following ODEs,
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d N0 B dt d Nj G Nj 1 BLj0 , j 1, 2, 3 , (4) dt dL G dt with initial conditions x 0 [N0 (0), N1 (0), N2 (0), N3 (0), 0] where the jth moment Nj is
defined by Nj
¨
d
Lj fn (L, t )dL,
j 0, !, d .
(5)
C (t ) C (0) kv Sc (N3 (t ) N3 (0)) ,
(6)
0
The solute concentration is given by
where Sc is the density of crystals and kv the volumetric shape factor. 2.2. PBM with breakage and agglomeration kinetics The dynamic population balance equation for a closed homogenous system considering a single characteristic size is written,
1/ 3
1/ 3
3 3 3 3 fn M
d sfn L
L2 L C L M , M fn L M
¨ b L, M a M fn M dM ¨ dM 2/3 3 3 L 0 st 2 M
L
birth due to breakage
birth due to agglomeration
(7)
d s G L fn L
E 0, L B0 a L fn L fn L ¨ C L, M fn M dM
0 sL
nucleation death due to breakage growth
death due to agglomeration
where ȕ, a, G, B and b are the aggregation kernel, breakage kernel, growth rate, nucleation rate and the daughter particle size distribution, respectively. The quadrature method of moment (QMOM) is based on the transformation d
Nk
¨
N
fn L Lk dL x wi Lki
(8)
i 1
0
After moment transformation and applying the quadrature rule the model is given by N N N k /3 dNk 1 N wia Li b k, Li wi w j L3i L3j C Li , Lj wia Li Lki dt 2 i 1 j 1 i 1 i 1
birth due to breakage N
N
birth due to agglomeration
N
death due to breakage
(9)
wi Lki w j C Li , Lj k wi Lki 1G Li E 0, k B
i 1 j 1 i 1 nucleation
death due to agglomeration
growth
The breakage and agglomeration kernels depend on mixing conditions. Optimizing the power input to the system which determines the turbulent kinetic energy it is possible to minimize breakage or agglomeration.
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3. Application of the batch NMPC for crystallization product design For the case studies crystallization of paracetamol in water was considered as the model system, for which both the 1D and 2D growth kinetics were determined, by performing D-optimal experimental design. Samples were taken every 10 minutes and the characteristic sizes were determined by using image analysis. Different product design problems were considered, when various objective functions expressed as function of the CSD ( f (CSD; R) ) were optimized, by determining the required temperature profile, seed characteristics (distribution and mass) as well as mixing characteristics (overall turbulent kinetic energy), which can be expressed by the generic robust formulation min{(1 w ) [ f (CSD; R)] wV [ f (CSD; R ]}
T (t ) Seed Mixing
(10)
where (¸) and V (¸) are the mean and variance of the performance index, respectively corresponding to the uncertain model parameter vector R . Equation (10) generally is subject to various operational, productivity and quality constraints. In the first case study the optimization problem is expressed as follows min
T (t ),mseed ,Lseed ,Tseed
{(1 w ) (fn (Lk , t f ; Rˆ) fndesired (Lk , t f ))2 wV [ fn (L, t f ; R ]} (11)
s.t.
k
Tmin b T (t ) b Tmax dT b Rmax dt C (t f ) b C max Rmin b
(12)
mseed ,min b mseed b mseed ,max Lseed ,min b Lseed b Lseed ,max Tseed ,min b Tseed b Tseed ,max
where Rˆ is the nominal parameter vector. The seed distribution is considered to be described by a Gaussian probability distribution function with mean Lseed and standard deviation Tseed . The optimization provided the optimal seed characteristics Lseed 56 Nm , Tseed 12 Nm and amount mseed 2.4 g . The temperature profile is given in Figure 1, together with the linear profile for comparison. For the linear profile the optimal seed characteristics were used as initial conditions. Figure 2 shows the microscopic images of the crystals obtained when the profiles in Figure 1 were implemented at a laboratory scale crystallizer. The entire evolution of the size distribution during the batch is given in Figure 3. It can be seen that the optimal operating policy results in a significant bias of the distribution toward large particle sizes. The schematic representation of the practical implementation of the approach is shown in Figure 5. The proposed control strategy involves two controllers: (i) a tracking controller that follows a reference trajectory in the phase diagram, and (ii) a supervising controller that adapts the reference to changing operating conditions. At near to optimal conditions, the operating curve is usually close to the nucleation curve and even small errors in the tracking can lead to spontaneous nucleation and compromised crystal quality. The feedback controller is designed that takes concentration and temperature
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measurements and adjusts the jacket temperature so that a predefined (using on openloop optimization design case) concentration vs. temperature operating is followed. The initial profile is predefined but it is adapted online using the model based predictive control approach. Concentration measurement is provided in the experimental implementation via ATR-UV/Vis coupled with robust chemometrics. Variations in operating conditions, such as quality and amount of seed, undesired secondary nucleation due to impurities in the system, disturbances in fluid dynamics, etc. require the adaptation of the operating curve both on-line and from batch to batch. The adaptation of the operating curve is especially important for complex organic molecules for which the metastable zone width might not be well defined and/or reproducible. The constrained optimization based nonlinear model predictive control strategy is used to estimate dynamic changes in shape and crystal size distribution. 32
(A)
T (qC)
31
30
(B)
29
28
0
40
80 Time (min)
120
160
0.04
pdf
0.03 0.02 0.01 0 0
80 60
200
40 400
L (Pm)
20 0
time (min)
Fig. 3. Evolution of the pdf along the whole batch for case B.
Probability density function
Fig. 1. The resulted optimal temperature profile Fig. 2. Microscopic images of the crystal products obtained with linear (A) and optimal (continuous line with plusses) and the linear cooling (B), using the optimal seed in both cases. cooling profile (dashed line).
0.6
Initial distribution
0.5 0.4
Optimized final distributon
0.3 0.2
Final distribution
0.1 0 0
200
400 600 L (Pm)
800
1000
Fig. 4. CSD in the case of controlled and uncontrolled agglomeration.
In the second case study the agglomeration is modeled by considering and hydrodynamic agglomeration kernel C (Li Lj )3 . An optimization problem similar to (10) is formulated but using the turbulent kinetic energy as optimization variable.
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Figure 4 illustrate the results of the fluid dynamics optimization. The PBM with the agglomeration kernel is solved using the QMOM with four quadrature points, represented as bars on Figure 4. The distribution is reconstructed from the moments using a modified Gamma distribution with fourth order orthogonal Laguerre polynomials. In both cases bimodal distribution is obtained. The optimized final distribution shows significantly less agglomeration. In this case a perfectly mixed tank is considered with uniform kinetic energy in the volume. Current research considers the use of multi-compartmental model in conjunction with off-line CFD simulation to estimate the distribution of turbulent kinetic energy for optimized mixing conditions.
Fig. 5. Architecture for robust control of crystal habit and shape of CSD for batch cooling crystallization.
4. Conclusions A robust optimization based control algorithm is described, which is able to design crystalline product properties, via optimization of cooling profile, seed properties or hydrodynamics. The approach provides robust performance by taking the parametric uncertainties into account in a distributional multi-objective optimization framework. The crystallization model is solved using a combination of method of characteristics and standard method of moments or quadrature method of moments, leading to a computationally very efficient approach which can be used even in real time. The two level control strategy which includes at the lower level a supersaturation controller and a model based control on the higher level was implemented on a laboratory scale crystallizer. Both the simulation and experimental results illustrate the advantages of the proposed crystallization control approach. Acknowledgements The author would like to acknowledge the financial support from the Engineering and Physical Sciences Research Council (EPSRC) UK, project EP/E022294/1.
References [1] R. D. Braatz, Annual Reviews in Control, 26, (2002) 87. [2] M. Fujiwara, Z. K. Nagy, J. W. Chew, R. D. Braatz, Journal of Process Control, 15, (2005), 493. [3] R. LeVeque, Numerical Methods for Conservation Laws, Birkhauser, 1992. [4] R. McGraw, Aerosol Science and Technology, 27, (1997), 255.
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Uncertainty patterns and sensitivity analysis of an indicator based process design framework Stavros Papadokonstantakisa, Agarwal Siddhartaa, Hirokazu Sugiyamaa, Konrad Hungerbühlera a
Swiss Federal Institute of Zurich, Wolfgang Paulistr. 10, Zurich 8093, Switzerland
ABSTRACT In recent years, many chemical companies have adopted the concept of sustainable development as a core business value. With focus on early phases of process design for continuous processes (Methyl Methacrylate process) this study tests the robustness of an established design framework, which integrates monetary, environmental, health and safety objectives. The framework comprises four stages of process modeling, each one being characterized by the available information for reaction route, yield, reaction time and separation scheme. Since several important factors are available in detail only at later phases of process design, a variety of evaluation indicators is used, which are then aggregated to a total score, realizing a multi-objective assessment. Although this is a popular approach in chemical engineering, especially when the development of rigorous models appears to be problematic or time consuming, the uncertainty issues arising must be clearly identified and analyzed, in order for the decision-maker to be able to evaluate correctly the value and limitations of the framework. The heuristical definition of the evaluation indicators, the experience based and often process specific weighting factors, the unknown nature of interactions between the aforementioned parameters, and the relative ranking based on type of designs taken into account form the ensemble of major uncertainty sources. The present study systematically detects the conditions under which these uncertainties become important and focuses more on those cases that the implementation of such a framework would fail to reach a statistically significant conclusion. A variety of uncertainty patterns and sensitivity analysis methods were applied for each defined stage and the proposed analysis is demonstrated on the design of a Methyl Methacrylate continuous process, considering six different synthesis routes. The crucial limitations identified in the results set the framework boundaries, assisting in this way the decision-maker to evaluate its scope and importance. Keywords: early phase process design, multi-objective assessment, heuristical indicators, uncertainty patterns.
1. INTRODUCTION Among several possible methods for such multi objective decision-making, e.g. spider plots [1] or Principal Component Analysis (PCA) for comparing various Safety, Health and Environmental aspects [2], the present study uses an aggregation approach, i.e.
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Design stages
different indicator results are aggregated into a single evaluation score using weighting factors [3]. Process Chemistry I (PCI)
Process Chemistry II (PCII)
Conceptual Design I (CDI)
Reaction
Reaction
+ Separation + Waste treatment
+ Equipment
Model includes
Stoichiometry, 100% yield (ideal)
Conversion, selectivity, auxiliary, catalyst, solvent, byproduct, heat of reaction
Shortcut process models, simple property data
Rigorous process models, non-ideality, reaction kinetics, detailed property data
Decision structures
No decision forced screen routes with serious problems
Select some reaction routes
Considered aspects
D1 Raw material cost Raw material cost (theoretical minimum) (updated)
Supplemental indicator
Multiobjective evaluation indicators
Economic performance Proxy for gate-to-gate costs /environ. impacts
Conceptual Design II (CDII)
Select process Optimize parameters option(s) &/or route(s) by sensitivity analysis by multiobj. evaluation of all feasible options D2 D3 D4 Production cost
Net present value
Mass Loss Indices (MLI)
Energy Loss Index (ELI)
CED in raw material production (theoretical minimum)
CED in raw material production (updated)
Cradle-to-gate CED
Cradle-to-gate CED (updated)
Hazard in E/H/S
EHS method (substance-level)
EHS method (incl. reaction mass)
EHS method (incl. process mass)
EHS method (updated)
Technical aspects
#Reaction steps; Raw material availability; Patents; Blacklist substances
Technical problems (e.g. long-term catalyst activity)
Process complexity
Equipment specification
Life-cycle environmental impacts
Figure 1: Overview of the framework: definition of design stages and appropriate modeling approaches as well as evaluation indicators for each stage.
This process design framework includes four stages of process modelling and multiobjective decision-making. Focusing on early design phase, Process Chemistry I/II and Conceptual Design I/II, are defined according to the available information as a basis for process modelling and assessment. For each defined stage, appropriate modelling methods and evaluation indicators regarding economy, life-cycle environmental impacts, EHS hazard and technical aspects have been selected. Based on the evaluation results, multi-objective decision-making is performed systematically at each stage (Figure 1). This framework has been previously evaluated in a case study (Methyl Methacrylate, MMA), where it was mimicked step-by-step with 6 synthesis routes as a starting point. By comparing the evaluation profile of these six routes over different stages, several factors were identified that are available in detail only at later stages, and which cause significant updates to the results. An example of the aggregation procedure r
in this framework is depicted in Figure 2. X s ,i is the evaluation indicator of route r at design stage s (i.e. from Process Chemistry II to Conceptual Design II ) in considered category i, (i.e.
Esr , Psr , Lrs , SH sr , HH sr , EH sr ), the different elements being the
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evaluation indicators for economy, proxy for gate-to-gate energy related economic and environmental impacts, life-cycle environmental impacts, and hazards in safety, health and environment, respectively. Before aggregation, the indicator values are normalized by the maximum (i.e. the worst) indicator value of all routes in the respective category i, as follows:
X
r s ,i
=
X sr,i max( X sr,i ) r
Level 1: Normalized scores
X
r PCII ,i
Raw mat. cost: E
Level 2: Mid-point scores
Aggregation step 1
w1,i
M
r PCII , j
Level 3: Total score
Aggregation step 2
r TPCII
w2 , j
x w1,RM-Cost(=0.77)
+
Cost
+
CED
x w2,Cost(=0.50)
x w1,ELI-Cost(=0.23) Proxy by ELI: P
Raw mat. CED: L
Safety hazard: SH
Health hazard: HH Env. hazard: EH
x w1,ELI-CED(=0.23)
x w2,CED(=0.20)
x w1,RM-CED(=0.77)
+
Total score
x w1,S(=0.40)
x w1,H(=0.20)
+
Hazard
x w2,Hazard(=0.30)
x w1,E(=0.40)
Figure 2: Aggregation scheme at Process Chemistry II. Values of weighting factors are those used in the case study.
From the normalized scores at Level 1 three mid-point scores are calculated (Aggregation Step 1 in Figure 2), in cost, overall cumulative energy demand (CED) and hazard (Level 2). In aggregation step 1, weighting factors within cost category are based on industrial statistics about the ratio of raw material and separation cost. The same weighting factors are applied in CED category, for which such empirical values were not available. The adopted values are from commodity industry and in other processes weights can be different, e.g. in fine or specialty chemicals raw material costs are typically higher. Within the hazard category, the indicated weighting factors are chosen according to the respective number of sub-categories, i.e. 4 in safety, 2 in health and 4 in environment. In aggregation step 2 the mid-point scores (Level 2) are aggregated in order to provide the final total score (Level 3). In this second aggregation step the weighting factors reflect company’s culture to rank cost, CED and hazard.
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2. UNCERTAINTY ISSUES AND SENSITIVIY ANALYSIS IN THE FRAMEWORK Despite the promising results after the framework implementation in a complex case study, the assessment of the framework robustness should consider the uncertainties involved in it. These could arise from subjective scaling and weighting of various parameters in the definition of indicators, subjective weighting in the aggregation steps, unknown significance level in differences of the indicator values, as well as limited coverage of the field under consideration for each indicator Among these different sources of uncertainty the present study focuses on the impact of uncertainty in the indicator values and the weights aggregating them, in particular on the identification of those regions where the selection between the best route and the rest becomes statistically insignificant. This problem was approached by examining the ratios of weighting factors which represent the order of relative importance of an indicator or mid-point score over the other. Each defined weight ratio was updated from each original value using a gradient descent method to the direction of minimization of the total scores differences. At each update step of this weight ratio the indicators values were also updated using the same approach, and an uncertainty was incorporated in terms of sampling from a normal distribution. Those regions were identified in which a statistical t-test was indicating that the total score of the best route is not significantly different from the one of its competing route. Following this approach a variety of scenarios was tested, regarding the width of the distribution depicting the uncertainty effect, the combinations of weight ratios and indicator values considered uncertain, the normalization effect based on the worst considered route, and the correlations between the indicators.
3. RESULTS AND ANALYSIS The aforementioned approach for detecting the impact of uncertainties in the regions of specified weight and indicator values was implemented in the MMA case study. The respective MMA data regarding routes chemistry and process information can be found in open literature [4]. Some typical results are presented in Figure 3. For each step of the outer loop of weight ratios update, an inner loop of indicators update is executed a predefined number of times. For each route r the algorithm is updating the indicator X according to the respective first-order partial derivative: X(t) = X(t-1) - Ș ∂ (¨Total Score)/ ∂ X where (¨Total Score) = Total Score route r – Total Score route best.
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Figure 3: The effect of uncertainty in combinations of indicator values with a sequentially forward selection.
At each step of the indicator update, the new value of the indicator is used as the mean of a normal distribution with predefined width, which represents the imposed uncertainty pattern. This results in a distribution of the total score for each route, which is compared with the respective distribution of total score of the best route using a t-test for means. In this way it can be identified which indicator is the “fastest” in affecting the inference based on the total score, “fastest” meaning requiring the minimum percentage change. In this procedure of indicators updating the value of the indicator for the worst route is kept constnat in order not to change the normalization of the system. Since the weight ratios remain constant for all routes, their updating step, which is also calculated on the basis of the first-order partial derivative, is averaged using “sum of digits” method, (i.e. since there are 6 routes considered, the weight ratio update based
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on the second best route receives a weight of 5/15, the third best one 4/15 etc. and finaly the weighted mean of all indicated updating steps determines the weight ratio update). In Figure 3 x-axis represents the number of update steps taken to shift the weight ratios, while y-axis represents the range of percentage change which is required in the indicator values for the decision to become uncertain. The error bars indicate the range of percentage change required for a statistically insignificant decision, while straight horizontal lines refer to indicators whose uncertainty pattern has not influenced the inference at all. For example, an uncertainty in indicator E between 10 and 15% (Figure 3, first graph) can cause a statistically insignificant decision for the selection of the best route. The uncertainty in all other indicators, when taken alone, is not affecting the descision-making. Once such a result has been reached, a sequentially forward selection is performed, i.e couples of E, which is the most sensitive indicator when considered alone, with other indicators are tested and when the most sensitive couple is identified, it forms the base for considering triplets and so on. The results of this procedure are depicted in the rest of the graphs of Figure 3, where it can be seen that the total score is more sensitive to the couple E-HH and the triplet E-HH-L respectively.
4. CONCLUSIONS & OUTLOOK Our analysis has quantified some expected trends but has also revealed some cases for further analysis. The main study result is that the importance of uncertainty in indicators seems to be greater than that of the weights. Therefore, further analysis needs to be carried out to determine and if possible correct the primary source of uncertainty in indicators which arises from their definition and data accuracy used in their calculation, while uncertainty in weights is a matter of design.
REFERENCES [1] J. Gupta, D. Edwards, 2003, A simple graphical method for measuring inherent safety, Journal of Hazardous Materials, 104, 15-30. [2] R. Srinivasan, N. Nhan, 2007, A statistical approach for evaluating inherent benigness of chemical process in early design stages, Process Safety and Environmental Protection Official journal of the European Federation of Chemical Engineering: Part B, Available Online. [3] H. Sugiyama, U. Fischer, M. Hirao, K. Hungerbühler, 2006, A chemical process design framework including different stages of environmental, healt and safety assessment, Computers Aided Chemical Engineering, 21, Part 1, 1021-1026. [4] H. Sugiyama, Decision-making framework for chemical process design, PhD Diss. ETH No. 17186.
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Batch Scheduling With Intermediate Due Dates Using Timed Automata Models Subanatarajan Subbiaha, Thomas Tometzkia, Sebastian Engella a
Process Control Laboratory (BCI-AST), Department of Biochemical and Chemical Engineering, University of Dortmund, 44221 Dortmund, Germany.
Abstract In the process industries, the problem of scheduling multi-product batch plants to satisfy the demand for various end-products within specified due dates occurs frequently. In contrast to the state-of-the art approach of using mathematical model formulations to solve such scheduling problems, an alternative approach is to use reachability analysis for timed automata (TA). In this paper, we discuss an extension of our earlier work on scheduling using TA models where the problem of makespan minimization was addressed. We extend the formulation to the meeting of due dates, modelled as causing additional costs (e.g. penalties for late delivery and storage costs for early production). The proposed solution by reachability analysis of priced timed automata is tested on a case study to demonstrate its successful application. Keywords: Batch plants, scheduling, timed automata, reachability analysis.
1. Introduction Multi-product and multi-purpose batch plants offer the advantage of increased flexibility with respect to range of recipes that can be handled and the production volumes compared to continuous plants. Batch scheduling is particularly difficult due to numerous constraints arising from the process topology, the connection between the pieces of equipments, inventory policies, material transfers, batch sizes, batch processing times, demand patterns, changeover procedures, resource constraints, timing constraints, cost functions and uncertainties. Particularly in batch plants, the problem of satisfying the demands of the various end-products within due dates occurs very often. Most of the solution approaches proposed in the last years solve such problems by modeling them by mathematical programming formulations (MILP or MINLP) and applying commercial solvers. In [8], the authors proposed a slot-based formulation with a continuous time representation which they showed to be suitable for network-based production schemes involving mass balances and product flows. The work presented in [7] proposed a MILP formulation in which the product stocks and mass balance constraints were ignored by fixing the batch sizes to discrete values. The formulation was tested on scheduling a real-life example which resulted in a model with reduced complexity and the results showed increased solution efficiency. The contribution [6] describes an extension of the previous work on continuous time formulations to deal with intermediate due dates with significant improvement in computational efficiency. However, the application of these approaches is hindered by the effort needed to formulate mathematical models and requires experience in algebraic modeling and a deep knowledge of the solver and its internal algorithms. Recently, the approach to solve scheduling problems by reachability analysis for timed automata has gained great attention. The framework of TA has been originally proposed
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by [1] to model timed systems with discrete dynamics. User friendly tools (e.g. Uppaal [3], TAOpt [5]). have been developed to model and to analyze such systems. Previous work on the TA based approach to scheduling problems with makespan minimization on hard job shop benchmarks were reported in [2] and [5]. The particular appeal of this approach comes from the modular and partly graphical modeling which enables inexperienced users to build models. Another advantage is the availability of powerful search algorithms that can be modified and extended for special purposes. The primary objective of this work is to extend the TA based formulation to address the problem of scheduling batch processes with multiple release dates and intermediate due dates with the objective of minimizing tardiness. In the TA based approach the resources, recipes and additional timing constraints are modeled individually as sets of priced timed automata with costs for transitions and cost rates for staying in locations. The sets of individual automata are synchronized through synchronization labels and are composed by parallel composition to form a global automaton. The global automaton has an initial location where no operations have been started and at least one target location where all operations required to produce the demanded quantities of end-products within the specified due dates have been finished. A cost optimal symbolic reachability analysis is performed on the composed automaton to derive schedules with the objective of minimizing the overall cost incurred as the sum of costs due to transitions and the integral costs for staying in locations.
2. Test Problem In order to illustrate the approach, a case study is considered. The case study is a multi-stage multiproduct chemical batch plant demonstrator with a plant topology similar to flexible flow shops. Two recipes to produce the end-products are given. The endproducts blue (B) and green (G) are produced from three raw materials, yellow (Y), red (R) and white (W). Each batch of the product results from two batches of the raw materials. The production process considered is: two batches of material Y and W reacts to produce one batch of Figure 1: P&ID of the multi-product batch plant product B ; similarly two batches of R and W reacts to produce one batch of product G. The plant consists of 3 stages in which the first stage consists of three buffer tanks which are used to store the raw materials Y, R and W (see Fig. 1). The buffer tanks in the first stage may contain at most only two batches of the raw materials. The second stage consists of three reactors that perform the reaction process to produce the end-products. Each reactor can be filled from each raw material buffer tank in the first stage; implying that it is possible to produce either product B or product G in each reactor. After processing the materials, a reactor may contain at most one batch of the product. The third stage consists of two buffer tanks which are used to store the end-products B and G exclusively. Each of the buffer tanks
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has a maximum capacity to store three batches of the respective products. Operations once started should be finished without any interruption (non-preemptive scheduling). The production of one batch of a recipe (B or G) consists of 6 operations and involves timing constraints between individual operations. After the materials are processed by the reactors the end-products must be drained into the buffer tanks in the third stage immediately imposing a zero-wait constraint between the operations. We consider the task to produce 23 orders in total, 12 batches of product B and 11 batches of product G, for which 138 operations have to be scheduled. Each batch of raw material is released at different points of time and for every 3 batches of a product a due date has to be met. The release dates and the due dates are known in advance and a penalty cost is incurred for missing a due date. The objective is to produce the demanded amount of products with minimal penalty cost.
3. Background of Timed Automata Timed Automata (TA) are finite state automata extended by the notion of clocks to model discrete event systems with timed behaviour. A timed automata is defined by a tuple, TA = ( L , C , Ĭ , inv , l0 , F ) in which, L represents the finite set of discrete locations, l0 , F ∈ L , where l0 represents the initial location and F represents the set of final locations. The set of clocks assigned to the TA are represented by C. The relation Ĭ ⊂ L × ϕ × Act × U(C) × L represents the set of transitions between the locations where, ϕ is a set of guards specified as conjunctions of constraints of the form ci ⊗ n or ci - cj ⊗ n , where ci , cj ∈ C, ⊗ ∈ { , = = , , < , >, ≠ } and n ∈ N. The set of actions (e.g. invoking a new event or changing the value of a variable) while taking a transition is denoted by Act. U(C) represent the set of clocks that are reset to zero after taking the transition. inv represent a set of invariants that assign conditions for staying in locations. The invariant conditions must evaluate to true when the corresponding location is active and the automaton is forced to leave the location when the invariant evaluates to false. A transition between a source location l and target location l' with a guard g ∈ ϕ (C), performing an action a ∈ Act and resetting the clocks r ∈ U(C) is denoted by (l, g, a, r, l'). A transition can occur only when the guard conditions are satisfied. An extension of TA with the notion of costs is known as priced TA [4]. A priced TA is equipped with an additional function P : L * Ĭ → R0 which assign cost rates to locations and costs to transitions. The cost of staying in a location with cost rate ƛ for d time units is given by P(L) = ƛ · d . The scheduling problem is modeled using the priced TA framework in a modular fashion. The resources, jobs and timing constraints are modelled as sets of priced TA. The interaction between the automata sets are established by synchronized transitions and shared variables. Two transitions are said to be synchronized when they have the same synchronization labels and the corresponding automata can only change their locations simultaneously. Such sets of automata are composed using parallel composition thereby forming one composed global automaton by considering the synchronization labels. The composed automaton represents the model of the complete system and a cost-optimal reachability analysis can be performed in order to derive schedules. The reachability analysis technique starts from the initial location of the composed automaton that represents the initial state of the system and evaluates the successor states created by a successor relation. This enumerative process is continued until the final target location specified is reached with minimal cost. In the search, branch-and-bound techniques are used in order to explore the solution space quickly.
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4. Priced TA model The idea of modeling the scheduling problem using priced TA is explained using a simple example process. Consider a process that consists of tasks T1 and T2 performed in resources R1 and R2, respectively. Let task T1 be followed by T2 and the time taken to perform T1 be p1 and T2 be p2. The process has a release date ri and a due date di. A storage cost is incurred if the process is finished before the due date and a penalty cost is incurred for missing the due date. The basic principles of modeling the process using a priced timed automata is shown in Fig. 2. The automata on the left hand side model the process and the automata on the right hand side model the required resources. The upper automaton on the left models the release date and the operations, the due date with the penalty cost is modeled by the automaton below. Initially, the process automaton is in the location wait T1 and wait dd representing that the process has not yet started. The release date ri of the process is modeled by the guard ci ri . Once the guard is enabled and the resource R1 is available, the first automaton can take the transition from wait T1 to exec T1 thereby allocating the resource and simultaneously making the resource automaton R1 transit from idle to busy by the synchronization label α1. The clock ci is reset to measure the duration of the task T1 modeled by the invariant ci p1 and the guard ci p1. After p1 time units have elapsed the first part of the process automaton is forced to transit from location exec T1 to wait T2 modeling that task T1 is finished and the process is waiting to perform task T2. At the same time the resource automaton R1 transits back from busy to idle representing that the resource is released by the synchronization labeled by ϕ1. The operation of performing task T2 in R2 is modeled in a similar fashion. Basically the α transitions represent the allocation of a resource and the ϕ transitions represent the release of a resource. The second automaton on the left at the start of the run takes a transition from wait dd to exec dd irrespective of the transitions in the first part of the process automata. At the same time when the transition takes place, the clock cd is reset to measure the due date using the invariant cd di and guard cd di. In the case where the process is finished before the due date, i.e. the second part of the process automaton is still in the state exec dd and the first part is in state exec T2 with the guard ci p2 enabled, the first process automaton transits to the location early and stays there until the due date is reached. The incurred storage cost is calculated using the cost rate at the location early and the time period for which the location is active. Once the due date is reached then the synchronized transition labeled by į is taken thereby representing the termination of the process. On the other hand, for the case where the finishing time of the process is beyond the due date, i.e. the upper process automaton is still in one of the states before early and the second automaton is in state exec dd with the guard cd di enabled; the wait T1
exec T1 α1
ϕ1
wait T2
ci > ri ci > p1 ci := 0 ci < p1
wait dd
exec dd
cd < d i
ci := 0
exec T2
ci < p 2
tardy cd > di
cd := 0
α2
early ϕ2
α1
finish’ δ
ci > p2
idle
Resource R1 α2
finish’’ δ
cd = delay cost
Example Process
busy ϕ1
ci = storage cost
idle
busy ϕ2 Resource R2
Resource Automata
Figure 2: Priced TA model of the simple example process and the corresponding resources
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second automaton transits to the location tardy and stays there waiting for the last operation of the process to finish. The incurred delay cost is calculated using the cost rate at the location tardy and the time period for which the location tardy is active. Once task T2 is finished then the synchronized transition labeled by į is taken thereby representing the end of the process. Apart from the individual clock a global clock is present to model the completion time of the process. Using these principles, the priced TA model for the case study considered can be derived by defining interacting priced TA for the recipes and resources. Each production order (a job) consisting of a release date, due date, recipe number, storage cost and delay cost is modeled as a priced TA with an individual clock. The general structure of each job automaton depends on the corresponding topology of the recipe. Operations that can be performed in alternative resources are modeled using alternative transitions starting from the same location. The parallel operations in a recipe such as pumping the raw materials yellow (red) and white to produce blue (green) is modeled by individual automata with synchronization points established by synchronized transitions. The zero-wait constraint in the process is modeled by imposing the waiting location of the corresponding operation as an urgent location. A reactor which is allocated for preparing the end-product is occupied when the operation of draining the corresponding raw material starts. It is released only after finishing the draining of the end-product to the corresponding buffer tank. This is modeled by synchronizing the transition that represents the start of the draining operation of the raw material in the recipe automata with the transition that represents the allocation of the corresponding (reactor) resource automaton, and the transition that represents the finish of the draining operation of the end-product in the recipe automata is synchronized with the transition that represents the release of the corresponding (reactor) resource automaton.
5. Experimental Results In order to test the proposed modeling and solution approach the prototypic tool TAOpt developed at the Process Control Laboratory is used. It consist of a reachability algorithm for priced TA to perform a symbolic reachability analysis to explore the solution space and to derive production schedules with minimal cost. Various search space reduction techniques introduced in [5] are realized in order to prune parts of the solution space that lead to sub-optimal solutions. Given the process information, priced TA models are created in a modular fashion automatically by TAOpt. The process information consist of the resource data (capacity, equipment purpose), the recipe data (duration of operations, sequence of operations, timing constraints between tasks, materials processed) and the table of production orders (due date, release date, delay cost). Once the individual automata have been created the composed automaton is realized on the fly and the reachability tree is created. The reachability tree consists of nodes and transitions; a node represents a combination of state and clock valuations of all clocks including the global clock. A cost-optimal reachability analysis is performed starting from the initial location where no jobs are started and trying to find a path to the target location where all jobs are finished within the defined due date. The objective is to minimize the penalty cost. The search algorithm used to explore the reachability graph was a combination of maximum depth and minimum cost. The search space reduction techniques weak non-laziness, sleep-set method and passed list inclusions were employed to prune parts of the reachability tree (for detailed explanations see [5]). The number of nodes for all the tests performed with TAOpt was limited to 2.6 million explored nodes. A continuous time based formulation with resource constraints
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Table 1. Tardiness minimization: (Tcpu) computation time in CPU sec., (Tfirst) computation time required to reach the first feasible solution, (Obj.) objective value, (Opt.sol.nodes) total number of nodes explored to reach the optimal solution, (disc.) number of discrete variables, (cont.) number of continuous variables, (eqns.) total number of equations.
Orders
Tcpu
6 12 18 23
53 75 1082 1930
TAOpt 1st sol Tfirst Obj. 0.02 320 0.04 74 0.05 105 0.08 115
Opt.Sol. nodes 330302 335548 1670659 1998302
Tcpu 66 3037 11885 30621
GAMS/CPLEX 1st sol disc. Tfirst Obj. 66 0 1566 3037 0 3132 3629 1 4640 22325 4 6148
cont.
eqns.
3913 6635 9265 11895
16803 36706 60016 87382
presented in [6] was implemented and tested. The TA based solution approach was compared with the MILP-based solution approach for different instances of the test problem. The number of event points considered for the instances with 6, 12, 18 and 23 production orders were 27, 54, 80 and 106, respectively. The objective value of the optimal solution for all the instances was zero. The MILP model was solved with GAMS 22.5 and CPLEX 10.2. For CPLEX the standard configuration with an optimality gap of 0 was chosen. Both approaches were tested on a test environment of a 3.06 GHz Xeon machine with 2 GB memory and Linux O.S. The results obtained for various instances considered are shown in Tab.1. The investigation clearly revealed that both the approaches could reach the optimal solution with zero penalty cost. However TAOpt could compute the first feasible solution and the optimal solution faster compared to the approach proposed in [6]. Except for the first instance for all other instances considered CPLEX took more than 3000 sec to compute the first feasible solution.
6. Conclusions This work presents a successful application of the TA based approach to solve production scheduling with multiple release dates and intermediate due dates and the test results revealed that the TA based approach is competitive compared to state-of-art approaches. Future work will investigate on using decomposition techniques to solve large scale problems and employing the TA based optimization algorithm to solve them. The authors gratefully acknowledge the financial support from the NRW Graduate School of Production Engineering and Logistics at Universität Dortmund.
References 1. 2. 3. 4. 5. 6. 7. 8.
R. Alur and D.L. Dill, 1994, A theory of timed automata. Y. Abdeddaim and O. Maler, 2001, Job-shop scheduling using timed automata. K.G. Larsen, P.Pettersson and W. Yi, 1997, UPPAAL in a nutshell. G. Behrman, A. Fehnker, T.S. Hune, K.G. Larsen, P.Pettersson, J. Romijn and F.W. Vaandrager, 2001, Minimum-cost reachability for linearly priced timed automata. S. Panek, S. Engell, and O. Stursberg, 2006, Efficient synthesis of production schedules by optimization of timed automata. M.G. Ierapetritou, C. Floudas, 1999. Effective Continuous-Time Formulation for ShortTerm scheduling: III. Multiple intermediate due dates. S. Panek, S. Engell, and C. Lessner, 2005, Scheduling of a pipeless multi-product batch plant using mixed-integer programming combined with heuristics, Proc. ESCAPE. J. M. Pinto and I.E. Grosmann, 1994, Optimal cyclic scheduling of multistage continuous multiproduct plants, Comp. and Chem. Eng. 18.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A Decomposition Approach to Short-Term Scheduling of Multi-Purpose Batch Processes Norbert Trautmann,a Rafael Fink,b Hanno Sagebiel,b Christoph Schwindtb a
University of Bern, Schützenmattstrasse 14, 3012 Bern, Switzerland Clausthal University of Technology, Julius-Albert-Straße 2, 38678 ClausthalZellerfeld, Germany
b
Abstract Batch processes are generally executed on production plants consisting of multi-purpose processing units and storage facilities of limited capacity. We deal with the problem of computing a minimum-makespan production schedule for given primary requirements. Our solution approach is based on a decomposition of the problem into two subproblems. The first subproblem consists in computing an appropriate set of batches for each process. We present a novel formulation of this problem as a mixed-integer linear program of moderate size. The second subproblem is to schedule the processing of these batches on the processing units subject to material-availability and storage-capacity constraints. We tackle the latter problem with a new priority-rule based scheduling method. Computational experience with a sample production process presented in Maravelias and Grossmann (2004) shows that with the decomposition method near-optimal production schedules can be computed in a very small amount of CPU time. Keywords: Multi-purpose batch plants, Scheduling, Decomposition, MILP
1. Introduction In the process industries, low volumes of multiple products are typically produced on multi-purpose batch plants. In batch production mode, the total requirements for the final products and the intermediates are split into batches. To process a batch, first the inputs are loaded into a processing unit, then a transformation process is executed, and finally the output is unloaded from the unit. We consider multi-purpose processing units, which can operate different processes. The duration of a process depends on the processing unit used. Between consecutive executions of different processes in a processing unit, a changeover with sequence-dependent duration is necessary. The minimum and maximum filling levels of a processing unit give rise to a lower and an upper bound on the batch size. In general, raw materials, intermediates, and final products can be stored in storage facilities of finite capacity. Some products are perishable and therefore must be consumed immediately after they have been produced. The short-term scheduling of multi-purpose batch plants has been widely discussed in the literature. Recent reviews can be found in Floudas and Lin (2004), Burkard and Hatzl (2005), and Méndez et al. (2006). Roughly speaking, monolithic and decomposition approaches can be distinguished. The major limitation of the former approaches consists in the impractical amount of computation time which is required for solving problem instances of practical size (cf. Maravelias and Grossmann 2004). Decomposition approaches divide the problem into a planning and a scheduling problem. Planning determines the batch size and the number of executions for each process, and scheduling
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allocates the processing units and storage facilities over time to the processing of the corresponding batches (cf. Neumann et al. 2002). In this paper, we present a novel formulation of the planning problem, which allows for considering alternative processing units with unit-specific lower and upper bounds on the batch sizes. In contrast to the nonlinear model presented in Trautmann and Schwindt (2005), the new formulation represents a mixed-integer linear program, which can be solved to optimality using standard mathematical programming software. For approximately solving the resulting scheduling problem, we propose a priority-rule based method. The remainder of this paper is organized as follows. In Section 2, we formulate the planning problem as a mixed-integer linear program. In Section 3, we present our schedule-generation scheme for the scheduling problem. In Section 4, we report the results of an experimental performance analysis that is based on a sample production process presented in Maravelias and Grossmann (2004).
2. Planning Problem 2.1. Problem Statement In the following, we interpret each combination of a transformation process and a processing unit as a task. For example, if two processing units are available for executing a process, then we define two tasks for this process. The planning problem consists in determining the batch size and the number of executions for each task such that the given primary requirements for final products are satisfied, the prescribed intervals for the batch sizes are observed, each perishable product can be consumed immediately after production, and the total bottleneck workload is minimized. 2.2. Formulation as a Mixed-Integer Linear Program In our model formulation, we use the following notation: Sets G set of all groups of processing units P , P p set of all products, set of all perishable products 7 set of all tasks 7S , 7S set of all tasks producing product S , set of all tasks consuming product S 7X set of all tasks that can be processed on unit X UJ set of all processing units in group J Parameters DWS proportion of product S in batch size of task W ( 0 for input products, ! 0 for output products) E , E W lower bound on batch size of task W , upper bound on batch size of task W W
QW upper bound on number of executions of task W US primary requirements of product S V S , TS storage capacity for product S , initial stock of product S Variables EW , EWP batch size of task W , batch size of P -th execution of task W HWP binary; equal to 1, if task W is executed at least P times, and 0, otherwise ZJ workload of group J of processing units
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2.2.1. Constraints The batch sizes must be chosen within the prescribed bounds, i.e.,
E W d EW d E W
( W 7 )
(1)
and such that for each perishable product S P p , the amount consumed by one execution of any task W 7S equals the amount produced by one execution of any task W '7S , i.e.,
DW ' S EW '
( S P p ; W ,W ' 7S u7S )
DWS EW
(2)
The final inventory of product S P must be sufficiently large to satisfy the primary requirements US , but it must not exceed the given storage capacity V S , i.e., QW
US d T S ¦ DWS ¦ EWP d US V S W T
(S P )
(3)
P 1
Eventually, we link the variables EW , EWP , and HWP as follows: 0 d EWP d EW
EW (1 İ IJȝ ) E W d EWP d H WP E W
(W T; P
1, ,Q W )
(4)
It is readily seen (cf. Neumann et al. 2002) that inequalities (4) imply the equivalences HWP 1 EWP ! 0 EWP EW ( W T ; P 1,,Q W ). The linear ordering of the binary variables HWP belonging to the same task W serves to reduce the size of the feasible region significantly without any loss of generality:
H W1 t H W2 t t H WQW
(W T )
(5)
2.2.2. Objective Function Our primary objective is to minimize the total bottleneck workload, which we compute as follows. We divide the processing units into as many groups as possible in such a way that first, each processing unit belongs to exactly one group and second, each transformation process can only be executed on processing units of one and the same group. The set of all these groups is denoted by G . The bottleneck of group J G is the processing unit with the maximum potential workload maxXU J ¦W T pW ¦QPW 1H WP , X where pW denotes the processing time of task W ; we refer to the workload of this bottleneck unit as the workload ZJ of group J G , i.e., QW
ZJ t ¦ pW ¦ H WP W TX
( J G;X U J )
P 1
(6)
Often there are several feasible solutions minimizing the total bottleneck workload. Therefore we additionally try to minimize the workload on the non-bottleneck units (second-order criterion) and the total unneeded inventory (third-order criterion). With G1 and G 2 being sufficiently small constants, we formulate our objective function QW
QW
P P ¦ ZJ G1 ¦ pW ¦ H W G 2 ¦ ¦ DWS ¦ EW
J G
W T
P 1
S P W 7
P 1
(7)
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Optimization Problem In sum, the planning problem reads as follows:
P
Min. (7) ° ®s.t. (1) to (6) ° H WP ^0,1` W 7 , P ¯
1, ,Q W
3. Scheduling Problem 3.1. Problem Statement A solution to planning problem (P) provides us with the set of task executions yielding the required amounts of intermediate and final products. For what follows we refer to a task execution as an operation, and O denotes the set of all operations. The scheduling problem consists in determining a start time S i t 0 for each operation i O in such a way that no two operations are processed simultaneously on the same processing unit, the processing units can be changed over between consecutive operations, sufficient amounts of the input materials are in stock at the start of each operation, there is enough storage space available for stocking the output products at the completion time of each operation, and the completion time of the last operation (i.e., the production makespan) is minimized. The immediate consumption of perishable intermediates is ensured by associating each product S P p with a fictitious storage of capacity zero. 3.2. Scheduling Method The first step of our algorithm consists in generating an operation-on-node network. Each operation i O corresponds to one node of the network. The nodes are connected by arcs representing minimum and maximum time lags between the start times of the operations. If the scheduling problem is solvable, then there always exists an optimal schedule for which all those temporal relationships are satisfied. Assume that we have arranged the operations belonging to the same task in some arbitrary order. Since the task can only be processed on one unit, the operations have to be executed one after another. Accordingly, we define a minimum time lag which is equal to the task’s processing time between any two consecutive operations in the sequence. We may add further arcs by exploiting the input-output relationships between the tasks. If an intermediate is produced by exactly one task, we can identify minimum time lags which are necessary to the timely availability of the input materials. If an intermediate is consumed by exactly one task, we can add arcs to avoid capacity overflows in a similar way. Those arcs correspond to maximum time lags between producing and consuming operations. Next, we determine the strong components of the network, i.e., the -maximal sets of nodes such that the network contains a directed path from each node to each other node of the set. Since any two nodes of a strong component are mutually linked by temporal relationships, all operations belonging to the same strong component are scheduled consecutively in our method. The basic idea of the scheduling method is very simple. In each iteration we schedule one eligible operation, which is selected based on priority values. The operation is started at the earliest point in time at which the minimum and maximum time lags of the network are satisfied, the operation can be executed on the processing unit, and a sufficient amount of input materials is available. The operations of a strong component are eligible to be scheduled if (i), all of those operations' predecessors in the network out-
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side the strong component have already been scheduled, (ii), there is enough input material available to process all operations of the strong component, and (iii), there is no other strong component for which some but not all operations have been scheduled. Thus far we have not taken the limited capacity of the storage facilities into account. The storage-capacity constraints are considered via capacity-driven latest start times. If in some iteration of our method we have generated a capacity overflow in a storage facility at a time t , we temporarily force eligible operations consuming the product stocked in this facility to start no later than time t . Those latest start times are maintained until the capacity overflow has been removed. As a consequence it may happen that an eligible operation can no longer be scheduled because the capacity-driven latest start time is smaller than the earliest feasible start time. If no eligible operation can be selected, we perform an unscheduling step in the following way. At first, we determine the operation i that produced the material which cannot be stocked. Next, we select one of the eligible operations, say, operation j . We then increase the earliest completion time of operation i to the earliest feasible start time t of operation j by introducing a release date of t pi for operation i , where pi denotes the processing time of operation i . If operations i and j belong to the same strong component, we remove all operations of this strong component from the schedule and resume the scheduling method. Otherwise, we remove all operations and restart the scheduling procedure from scratch. The unscheduling step may generate unnecessary idle times, which can easily be removed in a postprocessing step. The algorithm can be implemented as a multi-start procedure by randomly disturbing the priority values of the operations. In our implementation the initial unbiased priority values are based on earliest feasible start times, the sizes of the strong components, and the capacity-driven latest start times of the operations.
4. Performance Analysis 4.1. Implementation and Settings We have tested the performance of our decomposition approach on a set of 28 test instances, which have been generated by varying the primary requirements for the four final products of the Maravelias and Grossmann (2004) sample process. We compare our method to the results obtained with the monolithic time-indexed problem formulation of Kondili et al. (1993). The tests have been performed on an AMD personal computer with 2.08 GHz clock pulse and 1 GB RAM. The mixed-integer linear programs of the planning problem and the monolithic model have been solved with CPLEX 10.2, and the multi-pass priority-rule based scheduling method has been implemented in C++. For the latter method, we have imposed a run time limit of 1 second. 4.2. Results Table 1 shows the optimum makespans computed with the monolithic model and the CPU times in seconds, including the time required to prove the optimality of the solution. The last two columns of the table list the makespans and the CPU times obtained with the decomposition approach. Out of the 28 instances, 17 could be solved to optimality, and the maximum relative optimality gap is less than 7 %. The results obtained for the larger instances indicate that our method scales quite well. The maximum CPU time is less than 3 seconds, versus more than two hours for the monolithic approach. In sum, the analysis shows that the decomposition approach is able to provide good feasible schedules at very modest computational expense. Hence, the method is well-suited
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for the planning and scheduling of real-life processes, where due to various types of uncertainties a frequent rescheduling of the operations is often necessary. Instance MG-01 MG-02 MG-03 MG-04 MG-05 MG-06 MG-07 MG-08 MG-09 MG-10 MG-11 MG-12 MG-13 MG-14 MG-15 MG-16 MG-17 MG-18 MG-19 MG-20 MG-21 MG-22 MG-23 MG-24 MG-25 MG-26 MG-27 MG-28
Primary req. (3,3,7,7) (3,7,7,3) (7,7,3,3) (3,7,3,7) (7,3,7,3) (7,3,3,7) (5,5,5,5) (6,6,14,14) (6,14,14,6) (14,14,6,6) (6,14,6,14) (14,6,14,6) (14,6,6,14) (10,10,10,10) (9,9,21,21) (9,21,9,21) (21,21,9,9) (9,21,9,21) (21,9,21,9) (21,9,9,21) (15,15,15,15) (12,12,28,28) (12,28,28,12) (28,28,12,12) (12,28,12,28) (28,12,28,12) (28,12,12,28) (20,20,20,20)
Kondili et al. (1993) Makespan CPU time 17 19 17 17 17 16 16 29 28 29 26 26 22 25 41 37 41 35 35 28 34 53 47 53 44 44 35 41
1.74 2.11 1.35 1.63 1.79 4.04 7.99 6.41 10.29 0.79 3.68 3.22 33.39 9.58 23.93 31.88 13.98 30.44 17.24 385.18 137.33 190.24 329.47 42.80 221.04 25.43 8804.97 156.93
This paper Makespan CPU time 18 20 17 17 17 17 17 29 29 29 26 26 23 26 41 38 41 35 35 29 35 53 47 53 44 44 37 41
1.34 2.16 1.39 1.57 2.06 1.59 1.27 1.59 1.69 1.75 1.59 1.42 1.80 1.57 1.91 1.54 1.56 1.93 1.70 1.40 1.81 1.70 1.85 2.39 1.94 1.63 2.38 1.40
Table 1: Computational results for the 28 problem instances
References Burkard, R.E., Hatzl, J., 2005. Review, extensions and computational comparison of MILP formulations for scheduling of batch processes. Comp. Chem. Eng. 29(8), 1752–1769. Floudas, C.A., Lin, X., 2004. Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review. Comp. Chem. Eng. 28(11), 2109–2129. Kondili, E., Pantelides, C.C., Sargent, R.W.H., 1993. A general algorithm for short-term scheduling of batch operations: I. MILP formulation. Comp. Chem. Eng. 17(2), 211–227. Maravelias, C.T., Grossmann, I.E., 2004. A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants. Comp. Chem. Eng. 28(10), 1921– 1949. Méndez, C.A., Cerdá, J., Grossmann, I.E., Harjunkoski, I., Fahl, M., 2006. State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comp. Chem. Eng. 30(6-7), 913–946. Neumann, K., Schwindt, C., Trautmann, N., 2002. Advanced production scheduling for batch plants in process industries. OR Spectrum 24(3), 251–279. Trautmann, N., Schwindt, C., 2005. A MINLP/RCPSP decomposition approach for the short-term planning of batch production. In: Puigjaner, L., Espuña, A. (eds.) European Symposium on Computer Aided Process Engineering — 15. Elsevier, Amsterdam, pp. 1309–1314.
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Combined Nitrogen and Phosphorus Removal. Model-Based Process Optimization Noelia Alasino, Miguel C. Mussati, Nicolás Scenna, Pío Aguirre INGAR Instituto de Desarrollo y Diseño (CONICET-UTN), Avellaneda 3657, (S3002GJC) Santa Fe, Argentina.
Abstract An optimization model based on a superstructure embedding several activated sludge process configurations for nutrient removal is formulated and solved. Simultaneous optimization of the process configuration (process synthesis) and operation conditions for given wastewater specifications and influent flow rate in steady state operation are investigated. The performance criteria selected is the total annual operation cost minimization while predicting compliance with the effluent permitted limits. As the piece of equipment is supposed given, investment costs are not considered. The Activated Sludge Model No. 3 extended with the Bio-P module for computing biological phosphorus removal are used to model the reaction compartments, and the Takács model for representing the secondary settler. The resulting mathematical model is a highly non-linear system, formulated as a Non-Linear-Programming Problem, specifically as a DNLP. The model is implemented and solved using GAMS and CONOPT, respectively. The optimal solution computed from the superstructure model provides cost improvements of around 10% with respect to conventional processes. Keywords: Activated superstructure, DNLP.
sludge
process,
ASM3+BioP,
process
optimization,
1. Introduction In previous works, the COST benchmark wastewater treatment plant model (Copp, 2002) to evaluate control strategies for N removal based on the Activated Sludge Model No. 1 had been used as starting point for optimization of the operation conditions as well as for synthesis of activated sludge WWTPs. Based on the ASM3 model (Gujer et al, 1999), the aim was to minimize the total annual operating cost (Alasino et al, 2006a and 2006b) and the total cost (investments and operating costs) (Alasino et al, 2007). Optimization of P removal facilities is nowadays a key issue. Indeed, biological P removal is often persuade in European treatment plants as an alternative to chemical P removal based on P precipitation with salts such as FeCl3 (Gernaey and Jorgensen, 2004). In Gernaey and Jorgensen (2004) a benchmark WWTP for combined N and P removal is developed for evaluating and comparing WWTP control strategies, and a number of scenario evaluations focusing on the selection of DO set points are described to illustrate the simulation benchmark. Here, optimal operation conditions for a superstructure embedding the most widely used configurations for combined nutrient removal aiming at minimizing operating annual costs will be investigated for given wastewater specifications and flow rate. The plant lay-out used as the departing model is that proposed by Gernaey and Jorgensen (2004), which corresponds to the A2/O process. The other configurations embedded are the UCT process (VIP process), the modified UCT process and the Bardenpho process.
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2. Problem Definition The problem addressed is the simultaneous optimization of the process configuration (process synthesis) and the operating conditions (flow rates of aeration, recycles and fresh feed to each reaction compartment and external carbon source dosage) of ASWWTPs for combined biological N and P removal, aiming at minimizing the total annual operating cost. It is assumed: - influent wastewater specifications, - effluent permitted limits, - a process superstructure model, - a cost model computing operation costs, and - process unit sizes.
3. Process Description b) UCT – VIP
a) A2/O process E
D2 ANAE
S
E
RI2 ANAE
RI1
REC PUR
RI
c) Modified UCT process E
RI2 ANAE
ANOX
OX
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D2
S
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ANOX
ANOX
OX RI1
D2
S
REC PUR
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REC PUR
d) Modified Bardenpho process
E ANAE
ANOX
OX
ANOX
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OX
S
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Figure 1. Most widely used ASWWTP configurations for combined nutrient removal
In ASPs, the WW stream is exposed to different environmental conditions (anaerobic, anoxic and aerated zones) to facilitate the different microbiological processes such as the release or uptake of P, nitrification and denitrification. Reduction of carbonaceous matter and nitrification (ammonium is converted to nitrate by autotrophs) are favored by aerobic conditions; while denitrification (nitrate is converted to N gas by heterotrophs) is favored by anoxic ones, if readily biodegradable C is available. Biological P removal relies on P uptake by aerobic heterotrophs (known as phosphate-accumulating organisms PAOs) capable of storing orthophosphate in excess of their biological growth requirements. Under anaerobic conditions, PAOs convert readily available C (e.g., VFAs) to C compounds called polyhydroxyalkanoates PHAs. PAOs use energy generated through the breakdown of polyphosphate molecules to create PHAs. This breakdown results in P release. Under subsequent aerobic or anoxic conditions, PAOs use the stored PHAs as energy to take up the P that was released in the anaerobic zone, as well as any additional phosphate present in the WW. Figure 1 presents the most widely used ASWWTP configurations for combined N and P removal. The A2/O process presents a sequence of anaerobic reactors (to promote the growth of PAOs) followed by a sequence of anoxic to promote denitrification, and finally aerobic reactors. It has one internal and one external recycle stream. The internal recycle stream conducts a fraction of the nitrified liquor from the last aerobic to the 1st anoxic compartment, and the external recycle conducts a fraction of the sludge from the underflow of the sedimentation tank to the 1st compartment. In the UCT process, both recycle streams are feed to the anoxic zone and a second internal recycle stream is present from the anoxic to the anaerobic compartment. The modified UCT process has 2 internal recycles and 1 external one as in the original UCT process but the anoxic zone is divided into 2 zones. The external recycle is directed from the underflow of the decanter to the 1st anoxic zone. The 1st internal recycle stream conducts a fraction of the nitrified liquor from the aerobic to the 2nd anoxic zone. Finally, the second internal recycle stream pumps a fraction of the mixed liquor from the 1st anoxic back to the anaerobic compartment. The Bardenpho process configuration has also an external
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recycle from the sedimentation tank to the anaerobic zone and has an internal recycle from the 1st aerobic zone to the 1st anoxic zone. In general, the addition of external C to the anoxic zone could be detrimental to P removal in a EBPR plant, as the ordinary heterotrophs have competing advantages for nitrate over the denitrifying PAOs, resulting in poor anoxic P uptake. It is recommendable that the external C to be added to the anaerobic zone of an EBPR plant short of COD. The C source is taken up by PAOs to form intracellular C storage compounds, the use of which improves both P and N removal under anoxic conditions.
4. Process Optimization Model The superstructure embeds the four process alternatives described in the preceding section as can be appreciate in Figure 2. As mentioned, the basic plant adopted as starting point for developing the superstructure model is that proposed by Gernaey and Jorgensen (2004), which consists of 7 mixed reaction compartments with a total volume of 6749 m3, and 1 secondary settler of 6000 m3. The 1st and 2nd compartments are anaerobic units; the following 2 are anoxic zones and the last 3 formed the aerated region. This configuration has 1 internal and 1 external recycle stream, and corresponds to the A2/O process. The other process configurations are incorporated into the superstructure by allowing more recycles streams. The superstructure also allowed the distribution of the main process streams. Figure 2. Proposed superstructure Air
uTECSD
Qef
QTfresh M1
kLa1 kLa2 kLa3 kLa4 = 0 d-1 S1 M2 = 0 d-1 S2 M3 = 0 d-1 S3 M4 = 0 d-1 S4 M5 QTr,int,1
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QTr,int,3
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kLa7 S6 M7
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Qwaste
4.1. Reactor model For the aeration tanks, steady state CSTR model is considered. The ASM3 model (Gujer et al, 1999) extended with the Bio-P module (Rieger et al., 2001) is chosen to model the biological processes. The stoichiometric coefficients and kinetic constants are interpolated to 15 oC as proposed by Gujer et al. (1999). The volumes of the reaction compartments are set as follows: 500 m3 for Reactor 1; 750 m3 for Reactors 2, 3 and 4; 1333 m3 for Reactors 5, 6 and 7. The following constraints are considered for the mass transfer coefficient kLai in each compartment i: kLai=0 for Reactors 1, 2, 3 and 4; 0 0.68–4.4. Assuming that syngas is produced using entrained flow reactors with reformers, preliminary economic evaluation revealed that the HQ pipeline should provide syngas in a ratio bandwidth of 0.9–1.1. In case several gasifiers are connected to the network, each may produce syngas of a different quality, as long as their joint product in the pipeline remains within the given
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bandwidth, which provideds leeway to cope with temporary maintenance shutdowns of individual gasifiers. A second pipeline network (LQ, Low Quality) must be developed to allow collection and transport of syngas generated in downstream production processes and to allow for flexibility of syngas quality at end-user point. The LQ pipeline network has a variable syngas quality, which is inadequate for some chemical processes but inconsequential or even beneficial for facilities such as electricity production and DRI [2]. The double bus infrastructure is illustrated in figure 3.
Figure 3. A double bus infrastructure
There are several reasons for building a second pipeline: first, valuable recycle flows can be efficiently transported to downstream users who would not mind the variable ratio and concentration of inert gases. Thereby, in upstream industrial processes the need for recycle equipment ceases to exist. The upstream producers could generate some income by selling their recycle flows. Secondly, in the upstream industrial processes one would not have to re-use flows they normally recycle. As a consequence, the design of such processes can be simplified. A methanol plant, for example, would fit perfectly in such an industrial cluster [3]. Currently, a methanol plant typically consists of a gasification section, a reactor section with a large recycle loop, and a distillation section (see figure 4a). When connected to a double bus syngas infrastructure, a methanol plant would be reduced to a reactor section and a (slightly adapted) distillation section, without the syngas recycle system, as illustrated in figure 4b. The elimination of the recycle equipment would lead to significant cost reductions in the investment and operational cost of the plant. Conversely, 40% of the raw syngas will be relegated to syngas with another ratio and can be sold to the LQ market (see next section).
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a) Conventional methanol process design (after Wesselingh et al., 1990) air furnace
CO2
CH4
CO / H2
Q CH4
reactor
reformer
H 2O
MeOH
condensator
distillation
H 2O b) Methanol process design in syngas infrastructure LQ Pipeline HQ Pipeline
CO / H2 CO / H2
reactor
condensator
MeOH distillation H 2O
Figure 4. Conventional (a) and new (b) methanol process design.
4. Market Design Presently, the institution “syngas market” does not exist. In the double-bus topology there are three dominant aspects in the design of such a market [4-6]: two types of transactions – trading high quality and low quality syngas respectively - and a network fee must be paid for transport services. As outlined in the technical design, in the double bus topology two pipeline networks operate adjacent to each other. Users of the high quality gas are allowed to feed their residue gas into the secondary network. In addition to these recycle flows from industries that use HQ syngas, LQ syngas is directly fed into the secondary network from gasification installations. To coordinate and balance the process of supply and demand over two networks a new organisation must be created, which role resembles the role of balancing organisations in the electricity and gas sectors. This organisation is responsible for balancing both networks through a market based balancing mechanism. Figure 5 presents the structure of the markets and transactions. As outlined in the technical design, the users of high quality syngas can eliminate their recycle stream to act as a supplier for the lower quality network. The HQ users have used the high COcontent syngas and deliver a mixture with a higher hydrogen concentration to the LQ network, and receive a price for their LQ syngas.
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Figure 5. Syngas market design
5. Conclusion An industrial infrastructure based on syngas is a viable answer to the increasing uncertainty in petrochemical and energy feedstock supply. It provides feedstock flexibility through a double-bus network that connects several gasification units. It provides syngas as a multi-functional building block for the downstream chemical and energy industries. The design of these industrial processes may be simplified to a large extent, provided that a syngas market is created similar to the natural gas and electricity markets to allow syngas trade and system load balancing.
Acknowledgements The authors would like to thank Diederik Apotheker, Dirk-Jan van der Elst, Marinda Gaillard, Marlies van den Heuvel, and Wouter van Lelyveld for their creative and hard work in exploring the syngas network topologies and market structures.
References 1. Maier, M.W., Rechting E. (2000), The Art of Systems Architecting, CRC Press, Inc. Boca Raton, FL, USA 2. Herder, P.M., Stikkelman R.M. (2004), Methanol-based Industrial cluster design: a study of the design options and design process, in Ind. Eng. Chem. Res, 43, p3879-3885 3. Energy solution centre (2007), Direct reduction: process description http://www.energysolutionscenter.org/HeatTreat/MetalsAdvisor/iron_and_steel/process_de scriptions/raw_metals_preparation/ironmaking/direct_reduction/ironmaking_direct_reducti on_process_desscription.htm (accessed 24/01/2007) 4. Koppenjan, J. & Groenewegen, J. (2005) ´Institutional design for complex technological systems´, Int. J. Technology, Policy and Management, Vol. 5,No. 3, pp. 240-257. 5. Joskow, P.L. (2003), Electricity sector restructuring and competition: Lessons learned, http://web.mit.edu/ceepr/www/2003-014.pdf (accessed 23/01/2007) 6. Bruin, H.de, Dicke W., (2006) Strategies for Safeguarding public values in liberalized utility sectors, in Public Administration, Vol. 84 No. 3.
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Implementation of a Reactive Dividing Wall Distillation Column in a Pilot Plant Rodrigo Sandoval-Vergaraa, Fabricio Omar Barroso-Muñoza, Héctor Hernández-Escotoa, Juan Gabriel Segovia-Hernándeza, Salvador Hernándeza, Vicente Rico-Ramírezb a
Facultad de Química, Universidad de Guanajuato, Noria Alta, s/n, Guanajuato, Gto., 36050, México b Instituto Tecnológico de Celaya, Depto. De Ingeniería Química, Av. Tecnológico y García Cubas s/n, Celaya, Gto., 38010, México
Abstract Based on the knowledge regarding steady state design, optimization and control obtained by using Aspen Plus and Aspen Dynamics process simulators, we have designed and implemented a reactive dividing wall distillation column (DWDC). The column can be used to carry out the equilibrium reaction between ethanol and acetic acid to produce ethyl acetate and water catalyzed by sulfuric acid. The reactive DWDC contains three packed sections and the middle section is the key part in order to minimize the energy consumption. That section contains a wall that can be moved to three positions to manipulate the split of the vapor stream, whereas the split of the liquid stream is achieved by using a side tank. The reactive DWDC contains a reflux valve used to control either the composition of the distillate or the temperature at some point in the first packed section. Also, a reboiler was implemented in the lower section, and the heat duty supplied to it is used to control either the composition of the bottoms product or the temperature in the reboiler. This design was proposed based on both steady and dynamic simulations. The minimum energy consumption was predicted in the steady state simulation; the dynamic simulations indicated that the minimum energy consumption can be achieved in practice by implementing two control loops of temperature (or composition), as described. Keywords: reactive distillation, thermally coupled distillation, pilot plant, control
1. Introduction Distillation is a unit operation widely used to separate multicomponent mixtures, in spite of its high energy consumption and low thermodynamic efficiency. As a result, engineers and researchers are interested in developing new configurations capable of reducing and improving the use of energy. It has been demonstrated that thermal linking can reduce energy demands between 30 and 50 percent depending on the composition of the mixture to be separated. The three thermally coupled distillation sequences (TCDS) that have been explored more in detail are the TCDS using a side rectifier, the TCDS involving a side stripper and the fully thermally coupled distillation sequence or Petlyuk system. Because of both the reduction in oil reserves and polices of reduction in Carbone Dioxide emissions (Kencse and Miszey, 2007), important research has been focused on design, optimization and control of the TCDS. Regarding the design of TCDS, Cristiansen et al. (1997) reported a design and optimization procedure for the Petlyuk distillation column that involves the search of the interconnecting
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streams of the system. Hernández and Jiménez (1999) presented a design method that minimizes the energy consumption for a given structure of the Petlyuk distillation column. Dunnebier and Pantelides (1999) reported a formal procedure based on mathematical programming for detecting the optimal design of integrated distillation columns. Also, dynamic studies have been reported for the TCDS; for instance, Jiménez et al. (2001) compared the theoretical control properties and closed-loop dynamic responses of conventional and thermally coupled distillation sequences, and they found that the TCDS schemes presented theoretical control properties and dynamic responses better that those of the conventional distillation sequences. In the same context, Serra et al. (2003) compared the controllability of different distillation arrangements and showed that some different operation conditions to those of the optimum energy consumption favored the operation of a dividing wall distillation column (DWDC). The Petlyuk system has been successfully implemented by using a dividing wall inside a distillation column, the resulting configuration is the dividing wall distillation column. Practical implementations of the DWDC have reported savings of up to 40% in both energy and capital costs (Becker et al., 2001; Schultz et al., 2002; Kaibel et al., 2006; Schultz et al., 2006). Because of polices in process intensification, we are interested in carrying out reactions in thermally coupled distillation sequences. Based on our experience regarding steady state design, optimization and control obtained by using simulations, we have designed and implemented a DWDC to carry out the equilibrium reaction between ethanol and acetic acid to produce ethyl acetate and water, using sulfuric acid as catalyst.
2. Base Case: Esterification Process The process used as base case for the design of the DWDC involves a reactor-column where ethanol and acetic acid are introduced to the reboiler, and the chemical reaction proceeds as catalyzed by sulfuric acid according the following reaction at equilibrium. 2 SO 4 ⎯ H⎯ ⎯→ C H 3 C O O H + C 2 H 5 O H ←⎯ ⎯⎯
H 2O + C H 3C O O C 2 H 5
(1)
The distillate is introduced into a decanter tank where two liquid phases are present. The organic phase is fed into the purification column of the reactor-column system to obtain a high purity ethyl acetate compound (99.5% weight at) whereas the separated aqueous phase is fed into a different conventional distillation column to recover the ethanol which is then returned to the reactor-column. It is important to highlight that two inconvenient aspects in the operation can be observed in this process: i) the chemical reaction yield is limited by the thermodynamic chemical equilibrium (presenting a limit to the ethyl acetate produced) and ii) the system shows the formation of two binary homogeneous azeotropes, one ternary homogeneous azeotrope and one heterogeneous binary azeotrope (Figure 1).
3. Steady State and Dynamic Simulation of the Reactive DWDC Previous to our practical implementation, the design and optimization methods reported in Hernández and Jiménez (1999) were implemented in a framework involving the Aspen Plus process simulator. Figure 2 presents the minimization of the energy consumption of the distillation column; notice that the energy consumption depends strongly on the values of the interconnecting streams. Appropriate values of the interconnecting streams are important to obtain the minimum energy consumption in the
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implemented reactive DWDC. Also, dynamic closed loops were designed for the reactive DWDC using the Aspen Dynamics process simulator. Two control loops of temperature were implemented, the first one in the first packed section and the second one in the reboiler. The reflux rate and reboiler heat duty were selected as manipulated variables for the first and second control loop, respectively. Figures 3 and 4 show that the reactive DWDC can achieve positive and negative set point changes in the control loops of temperature. Also, good dynamic closed responses were obtained for load rejection; for instance, changes in the feed composition. These results were considered for the design and implementation of the reactive DWDC.
0.8 0.75
205 185
0.55
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Figure 2 Energy optimization.
Controller Output 0.65 0.7
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Figure 1 Ternary map for the system.
0
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Figure 3. Dynamic responses for a positive change in the set point (1 °F) in the first control loops.
4. Implementation Issues and Operation of the Reactive DWDC Figure 5 depicts the DWDC implemented in a pilot plant using stainless steel 316L. We are interested in the control of the distillate composition, but this task is difficult to implement in industrial practice; hence, we control the temperature at some point in the packed section instead. Both of the control objectives require the manipulation of the
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231.5 229.5
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Process Variable F Set Point F 230.5
Controller Output Btu/hr 1.75e6
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reflux ratio in order to set the composition or temperature in their set points. As a result, a valve was implemented inside the column in order to manipulate the reflux to the distillation column (Figure 5, element 2).
0
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0.8 Time Hours
1
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Figure 4. Dynamic responses for a negative change in the set point (1 °F) in the first control loops.
Several collector and distributor trays were placed in the three packed sections of the DWDC in order to guarantee homogeneous liquid distribution in the packed bed (Figure 5, elements 10 and 11). Special care needs to be taken between the first and second packed sections, because a collector tray (Figure 5, element 11) is needed in the bottom of the first packed bed in order to send the liquid to a side tank. This device plays an important role because during the steady state design and optimization, since it is fundamental to detect the optimal splits of liquid and vapor in the middle section of the DWDC to guarantee the optimal energy consumption in the reboiler. In practice, it is difficult to manipulate the splits of vapor; for that reason, the side tank (Figure 5, element 4) has been implemented to split the liquid to both sides of the wall in the middle section of the distillation column and to extract the water decanted. The DWDC contains three packed sections of Teflon rasching super-rings. In the middle section (Figure 5, elements 6 and 7) of the distillation column, a wall (Figure 5, element 5) was implemented so that it can be moved to three positions to manipulate the split of the vapor stream. This is the key packed section in the energy-performance of the DWDC, because the feed is introduced in one side (equivalent to the prefactionator in the Petlyuk system, Figure 5, element 7) and in the other one (Figure 5, element 6) a liquid side product is obtained (the side product stream in the main column of Petlyuk systems). As it can be seen, this section needs collector and distribution trays in the feed and side stream points. The first and third packed sections are similar to those of a conventional distillation column, and only distributor and support trays are required for the operation of the DWDC. A reboiler (Figure 5, element 9) that can be charged with the reacting mixture in the batch operation fashion was placed at the end of the third packed section. Finally, several thermocouples were implemented in the DWDC to register the temperature
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profiles. The future research work is focused on the experimental study of the hydraulics, steady state and closed-loop dynamics.
1 2 10 3 11 4
13 11
10 5
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6 11
1 2 3 4 5 6 7 8 9 12 13 10 11
Condenser Reflux valve First packed section Side tank splitter Dividing wall Second packed section (side product) Second packed section ( feed) Third packed section Reboiler Side product collector Side tanks for distillate Distributor tray Collector tray
8 9
Figure 5 DWDC implemented in the pilot plant (patent in process).
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5. Conclusions We have designed and implemented a reactive divided wall distillation column for the production of ethyl acetate from acetic acid and ethanol. Important aspects derived from steady state simulation were considered; for instance, a side tank was implemented in order to split the liquid to both sides of the wall and a moving wall inside the column that allows to fix the split of the vapor stream. The dynamic simulations indicate that it is possible to control the composition of the top and bottoms products or two temperatures by manipulating the reflux rate and the heat duty supplied to the reboiler, respectively. The implementation of the reactive divided wall distillation columns takes into account important aspects like process intensification, minimum energy consumption and reduction in Carbon Dioxide emission to the atmosphere.
Acknowledgements We acknowledge the financial support provided by Universidad de Guanajuato, CONACyT and CONCyTEG (México).
References A.C. Christiansen, S. Skogestad, K. Lien, 1997, Complex Distillation Arrangements: Extending the Petlyuk Ideas. Comput. Chem. Engng., 21, S237. G. Dunnebier, C. Pantelides, 1999, Optimal Design of Thermally Coupled Distillation Columns. Ind. Eng. Chem. Res.,38, 162. H. Becker, S. Godorr, H. Kreis, 2001, Partitioned distillation columns –why, when and how, Chem. Eng. 108, 68. S. Hernández, A. Jiménez, 1999, Design of Energy-Efficient Petlyuk Systems. Comput. Chem. Eng., 23, 1005. A. Jiménez, S. Hernández, F. A. Montoy, M. Zavala-García, 2001, Analysis of Control Properties of Conventional and Nonconventional Distillation Sequences. Ind. Eng. Chem. Res., 40, 3757. M.A. Schultz, D.G. Stewart, J.M. Harris, S.P. Rosenblum, M.S. Shakur, D.E. O’Brien, 2002, Reduce costs with dividing-wall columns, Chem. Eng. Prog., 98, 64. B. Kaibel, H. Jansen, E. Zich, Z. Olujic, 2006, Unfixed Dividing Wall Technology for Packed and Tray Distillation Columns, In Distillation and Absorption ‘06, IChemeE Symp. Series No. 15, 252. H. Kencse, P. Mizsey, 2007, Comprehensive Process Investigation Methodology for EnergyIntegrated Distillation, In proceedings of 17th European Symposium on Computer Aided Process Engineering (ESCAPE), Elsevier, 24, 883. M.A. Schultz, D.E. O’Brien, R.K. Hoehn, C.P. Luebke, D.G. Stewart, 2006, Innovative Flowscheme using Dividing Wall Columns, In proceedings of 16th European Symposium on Computer Aided Process Engineering (ESCAPE) and 9th International Symposium on Process Systems Engineering (PSE), Elsevier, 21, 695. M. Serra, A. Espuña, L. Puigjaner, 2003, Controllability of different multicomponent distillation arrangements, Ind. Eng. Chem. Res., 42, 1773.
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Optimisation of a Bio-ethanol Purification Process Using Conceptual Design and Simulation Tools Patricia M. Hoch,a José Espinosa,b a
PLAPIQUI-UNS-CONICET, Camino La Carrindanga km 7-8000, Bahía Blanca, Argentina b INGAR-CONICET-UNL, Avellaneda 3657, S3002 GJC Santa Fe, Argentina
Abstract In this work, we propose an evolutionary optimisation procedure which intensively uses both conceptual and rigorous models for the design and simulation of unit operations involved in a bio-ethanol purification process. While conceptual models are used to determine initial values for design and operating variables of a given operation unit, rigorous simulation departing from initial estimates generated at conceptual design level enables to remove simplifying assumptions, interconnect equipments and calculate operating and investment costs. Once an initial design of the purification plant is obtained, opportunities of improvement are easily recognized and then tested by performing the design and simulation steps until a cost-effective bio-ethanol purification plant is achieved. Keywords: Bio-ethanol Purification Plant, Evolutionary Optimisation, Conceptual Design, Rigorous Simulation.
1. Introduction Optimisation of both design and operation variables of a bio-ethanol purification plant intended to produce fuel grade ethanol is a challenge to make the bio-fuel a realistic alternative in the energy market. Given the plant complexity and the high non-linearity of the corresponding models, we propose an evolutionary optimisation procedure which uses intensively both conceptual and rigorous models for the design and simulation of unit operations. It is quite difficult to obtain an initial estimation of the total number of trays of the main distillation column, placement of feed and side streams, and steam flow rate in the simulation environment, but this task is easily accomplished in the conceptual design environment. In addition, convergence of the rigorous model is enhanced by using initial estimates of internal profiles generated at the conceptual design level despite of the highly non-ideal behaviour of the multicomponent azeotropic mixture. Applying the same philosophy to estimate initial values for design and operating variables of the whole process, optimal values for a cost-effective bio-ethanol purification plant are reported. The methodology is applied to the purification process for a feed leaving the fermentation step of a conventional corn dry-grind processing facility producing 24 million liters/year of ethanol and 19 million kg/year distiller´s dry grains with solubles (DDGS). The feed to the purification plant (22170 kg/h) is mainly composed by ethanol (10.80 % w/w) and water (88.98 % w/w) with traces of methanol (0.0226 %) and fusel (0.2009 %). A simplified flow diagram is shown in Figure 1.
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Figure 1. Simplified flow diagram of a bioethanol purification plant.
2. Initial Design 2.1. Beer Column The vapour stream leaving the stripping column captures nearly all of the ethanol and components in traces produced during the fermentation step. The minimum energy demand of the process (i.e., minimum reboil ratio) is calculated through the lever arm rule by setting the bottom product as high purity water and the composition of the vapour stream as the corresponding to the vapour in equilibrium with hot wine. In other words, a pinch at the top of the stripping column is considered. In order to obtain a feasible design the following steps are performed: i) determine the maximum feasible separation and minimum energy demand (smin) by applying pinch theory. For this task, it is required an equilibrium calculation that can be performed in a conceptual model framework like DISTIL (Hyprotech, 1999); ii) calculate the reboil ratio s = 1.05 smin; iii) set a value for the number of stages N; iv) simulate a stripping column with reboiler first and then replace the reboiler with steam taking into account the reboiler duty and the latent heat of condensation of steam. This task can be done in a simulation framework like Hysys (Hyprotech, 1999). Few simulations were needed to achieve a quasi-optimal column design with 38 equilibrium stages, a column diameter of 0.9 m, a section pressure drop of 34.7 kPa and a steam flow rate of 3600 kg/h. The values obtained for the number of equilibrium stages and steam demand, together with the composition of ethanol in the outlet stream (51.52 % w/w) agree well with results presented in Kwiatkowski et al. (2006). 2.2. Hybrid Column As a multicomponent system formed by ethanol and water with traces of methanol and fusel is to be separated into a single column, a three steps conceptual design and rigorous simulation process is proposed. First, ethanol and methanol are lumped into one pseudo-component in order to obtain a first estimation of steam flow rate, number of stages necessary to separate an ethanol-rich stream from a fusel-rich stream, feed stage and side stream location (DISTIL). After rigorous simulation of the quaternary mixture in Hysys, separation between a methanol-rich stream and an ethanol-rich stream is considered by taking into account the distillation line departing from the composition of the distillate (DISTIL). Finally, both columns are integrated into a single one (Hysys). 2.2.1. Side-Stream Column In order to obtain a feasible design the following steps are performed: i) calculate smin(t) for the separation ethanol/water/1-pentanol (DISTIL), ii) estimate the number of
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equilibrium stages Nstages(t), feed stage Nfeed(t) and side stream location NSide Stream(t) for s(t) > smin(t) (DISTIL), iii) simulate the quaternary system (Hysys) for the design and operating variables obtained in step ii), iv) calculate the steam flow rate Vsteam(q) through the energy balance and simulate the column without reboiler (Hysys), v) simulate the system side-stream column plus decanter and water-rich phase recycle (Hysys). Table 1 presents the results of the conceptual design performed in DISTIL (steps i) and ii)) for the ternary mixture ethanol/water/1-pentanol, with the last component used to approximate the behaviour of a fusel component. Compositions of both ethanol and fusel in the bottom stream were selected taking into account the behaviour of the residue curve (DISTIL) corresponding to the liquid in equilibrium with the vapour feed in the neighbourhood of water vertex. As both for the ternary and quaternary mixture, the residue curve approaches the water vertex with compositions of ethanol above the mole fraction of fusel, the selected bottom composition reflects this behaviour. Figure 2(a) shows the corresponding composition profile in the composition simplex. The figure also shows a distillation boundary departing from the azeotrope ethanol-water and ending at the hetero-azeotrope water-fusel. The side stream is located inside the liquidliquid gap as this stream will be separated in a decanter into a fusel-rich phase (feed to the fusel plant) and a water-rich phase (recycle to column). Table 1. Results for the ternary system ethanol/water/1-pentanol (DISTIL).
Product Compositions, r, s and N Feed (vapor) Distillate Side Stream Bottom Rmin(t) / Smin(t) R(t) / S(t) Nstages(t) [including condenser and reboiler] Nfeed(t)/ NSide Stream(t)
[0.29798, 0.699132, 0.002888] [0.74144, 0.25850, 6.0 E-05] [0.05115, 0.91442, 0.03443] [9.6 E-06, 0.99999, 4.0 E-07] 2.839 / 1.00 2.839 / 1.00 17 [0 + 1-15 + 16] 4/11
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Figure 2. (a) Internal profile in the composition simplex corresponding to the base design with phase separator and water-rich phase recycle (Hysys); (b) Distillation lines corresponding to the distillate composition of the methanol column. System methanol/ethanol/water+1-pentanol at 101.3 kPa (DISTIL).
It is noteworthy that minimum reboil ratio for the given separation does not require an infinite number of stages. This behaviour can be explained in terms of bifurcation of adiabatic profiles and it will be subject of further analysis in a next contribution.
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2.2.2. Methanol Column and Hybrid Column The distillate stream of the side-stream column contains small amounts of methanol that must be separated from ethanol to agree with stringent quality standards (0.1 % V/V methanol in dehydrated ethanol at 20 oC). At a first glance, this separation could be performed in another distillation column. A different alternative would be to integrate this column with the side-stream column. The distillate line (DISTIL) corresponding to the distillate composition of the side-stream column shown in Figure 2(b) resembles the behaviour of the internal profile at total reflux and it can be considered as a good approximation to the actual operation of the methanol rectifying column, as the distillate flow rate of this column is low enough to produce a high reflux ratio. Therefore, it is possible to estimate the optimal number of stages in the rectifying section of the hybrid column as the number of trays necessary to separate the methanol in excess from the ethanol-rich stream. As shown in Figure 2(b), the methanol-rich distillate stream will also contain small amounts of ethanol and water due to the distillation line running from pure methanol to ethanol-water azeotrope. Figure 3 shows the internal profile in the composition tetrahedron after simulation of the hybrid column in Hysys. A loss of about 0.18 % w/w of ethanol in methanol-rich distillate occurs. The side streams are located near the maximum in ethanol (ethanolrich stream, 88.98 % w/w) and fusel (fusel-rich stream, 18.5 % w/w), respectively. The column has 35 equilibrium stages, a column diameter of 1.372 m, a section pressure drop of 11.8 kPa and a steam flow rate of 1800 kg/h. The vapour ethanol-rich stream is diverted to the first effect of the evaporation sector to provide heating while minimizing the steam demand of the plant. The condensed ethanol-rich stream is then fed to the pervaporation sector to remove the excess water. 250
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175 150 125 100 75 50 0.700
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xethanol
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Figure 3. Internal profile in the composition tetrahedron corresponding to the hybrid column with phase separator, fusel plant and pervaporation sector.
Figure 4. Overall investment and operating costs for the two distillation columns and pervaporation sector versus ethanol mole fraction in the distillate of the hybrid column.
2.2.3. Fusel Plant and Pervaporation Sector The fusel-rich stream leaving the decanter is fed to the fusel sector where the stream is washed with water to recover about 96 % of the incoming ethanol. The resulting waterrich stream is recycled to the hybrid column. To do this, an overall amount of 363 kg/h wash-water and seven separation steps are necessary. The conceptual design of a crossflow operation is performed using DISTIL, while process simulation is done in Hysys. A conceptual design of pervaporation (PVA/PAN MOL 1140 membrane by GFT, Germany) following the model proposed by Vier (1995) and Bausa and Marquardt (2000) was implemented in Delphi environment (Borland, 1997) to determine pseudo
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optimal operating values for both maximum temperature (90 oC) and permeate pressure (2.026 kPa). The model was also implemented in Hysys as a user operation extension, which calculates the required membrane area areq as areq =1.25 amin (Bausa and Marquardt, 2000). Both heat and refrigeration duties are calculated in Hysys from the energy balance. Behaviour of trace components is taken into account by using wateralcohol separation factors. Approximate values were taken from D. Van Baelen et al. (2005). High purity bioethanol (99.5 % v/v) is obtained with an actual membrane area of 930 m2, while the water-rich permeate is recycled to the hybrid column. 2.2.4. DDGS Plant The coproduct plant is formed by a decanter centrifuge which separates the bottom stillage from the beer column in a wet cake (35 % solids, 2683 kg/h water) and a thin stillage (18443 kg water/h). Approximately 4626 kg water/h is recycled into the second step of the liquefaction process, while 13817 kg water/h is feed to a three-effect evaporator. The resulting syrup (35 % solids, 1287 kg water/h) is mixed with the wet cake coming from the centrifuge and sent to a rotary drum dryer. While the multiple effect evaporator is simulated in Hysys, only mass and energy balances for the dryer are incorporated in Hysys. The conceptual design of the dryer is performed according to the method presented in Ulrich and Vasudevan (2004) and data from National Corn-To Ethanol Research Center (2005-2007). Table 2 summarizes the investment and operation costs of the DDGS sector. The operation cost of 35.9 $/ton DDGS agrees well with the value reported by Batelle Memorial Institute (2005). Table 2. Operation ($/ton DDGS) and Investment ($) Cost corresponding to DDGS plant. [*] kg natural gas/ kg of water evaporated. [**] Overall operating costs = 34.55 $/ton DDGS Item
Characteristics
Rotary Dryer
D [m]= 1.664 L [m]= 13.31 IJ [min]= 19.6 rpm= 2.869 Qair [kg/h]= 39150 ȘNat. Gas = 0.048 [*] Areaoverall[m2]= 940 Pressure[kPa]= from 10-30 kPa Qsteam [kg/h]= 2700
Evaporator
Decanter Centrifuge
Invest./Op. Cost Ulrich & Vasudevan 1.39 E06/19.74
Invest./Op. Cost [**]; Batelle M. I. [***] 1.57 E06
1.523 E06/16.16
1.47 E06
1.07E06[***]/not calculated
1.07 E06
3. Evolutionary Optimisation Once an initial design is obtained, the following improvement opportunities were tested: i) design of the beer column in the neighbourhood of minimum energy demand (done from the very beginning of design process), ii) heat integration between the hybrid column and evaporation first effect (1270 kg/h of steam are saved), iii) heat recovery from the hot air leaving the dryer (saving 0.014 kg natural gas/kg water evaporated). Finally, a change in distillate composition of the hybrid column is proposed in order to capture the trade-offs between distillation and pervaporation costs. Resorting again to the conceptual design of the hybrid column for a set of distillate compositions, results
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shown in Figure 4 are obtained. The decrease of investment costs for distillate compositions richer in ethanol is related to a decrease in the membrane area needed to obtain dehydrated bioethanol (areq=848 m2). Table 3 shows both investment and operating costs of the quasi-optimal plant. All cases include improvements i), ii) and iii) mentioned above. Investment and operation costs are reduced by 6.64 % with respect to the base case and by 11.48 % with respect to the worst case analyzed. Cost coefficients used to obtain the reported values are Csteam=2.396E-2, Cwater=5.73E-3, Crefr=3.824E-2, Celectr=0.08 all in [$/kWh], Cnat gas=289 $/tn, C memb repl = 400 $/m2. Table 3. Overall costs for a bioethanol plant producing 24 million liters/year. The facility considers both the ethanol and co-product processing plants. DDGS Plant Separation Total
Investment, $ 3.985 E+06 3.768 E+06 7.753 E+06
Operating $/h 96.37 117.96 214.33
Investment, $/h 81.07 76.66 157.73
Total, $/h 177.44 194.62 372.06
4. Conclusions A cost effective design for a bio-ethanol separation plant using conceptual design followed by rigorous simulation is found. The minimum in the operation costs corresponds to a minimum in the steam flow rate of the hybrid column (1600 kg/h). The minimum in steam flow rate can be only explained by the presence of the fusel component, which influences both the energy demand and feasible products of the process. Therefore, designs based on the binary system ethanol-water do not represent the system behaviour in an accurate way.
5. Acknowledgements This work was supported by UNL, UNS, CONICET and ANPCyT from Argentina.
References Batelle Memorial Institute, Pacific Northwest Division, 2005, Quantifying Biomass Resources for Hydrothermal Processing II. Bausa, J. and W. Marquardt, 2000, Shortcut Design Methods for Hybrid Membrane/Distillation Processes for the Separation of Nonideal Multicomponent Mixtures, Ind. Eng. Chem. Res., 39, 1658-1672. Borland International Inc., 1997, Scotts Valley, USA, Delphi 3 User Manual. Hyprotech Ltd., 1999, Calgary, Canada, Hysys & Distil User Manuals. Kwiatowski, J. R; McAloon, A. J.; Taylor, F. and D. B. Johnston, 2006, Modeling the Process and Costs of Fuel Ethanol Production by the Corn Dry-Grind Process, Industrial Crops and Products, 23, 288-296. National Corn-To Ethanol Research Center, 2005-2007, Utilizing the National Corn-to-Ethanol Pilot Plant to Develop a Predictive Model for Distillers Dried Grain for the Fuel Ethanol and Animal Feed Industries. Ulrich, G. D. and P. T. Vasudevan, 2004, Chemical Engineering Process Design and Economics, A practical guide. 2nd ed., Process Publishing, Durham, New Hampshire. Van Baelen, D.; Van der Bruggen, B.; Van den Dungen, K.; Degreve, J. and C. Vandecasteele, 2005, Pervaporation of water-alcohol mixtures and acetic acid-water mixtures. Chemical Engineering Science, 60, 1583-1590. Vier, J.,1995, Pervaporation azeotroper wässriger und rein organischer StoffgemischeVerfahrensentwicklung und –integration, Ph. D. Thesis, Institut für Verfahrenstechnik, RWTH Aachen, Shaker Verlag, Aachen, Germany.
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Improvement of Operating Procedures through the Reconfiguration of a Plant Structure Satoshi Hoshino, Hiroya Seki, Tomoya Sugimoto, Yuji Naka Chemical Resources Laboratory, Process Systems Engineering Division, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku Yokohama 226-8503, Japan
Abstract In this paper, we aim to improve operating procedures through the reconfiguration of an existing chemical plant structure from the viewpoint of process safety and operability. For this purpose, we first structurize, i.e., decompose and modularize, the correspondence relation between the whole plant structure and the operating procedures with the use of a CGU (Control Group Unit) as the unit. Then, we manage information regarding the order relation of the operations among different CGUs by using a proposed CGU coordination. In this way, it is possible to improve the operating procedures by simply assessing and designing an operation or operating procedure within a CGU that needs to be modified. As an industrial example, we examine a startup procedure for an HDS (hydrodesulfurization) plant. Keywords: Process Design; Plant Reconfiguration; Operating Procedure; Improvement.
1. Introduction The structure of a chemical plant and process operating procedures at the plant have to be designed on the basis of careful assessment of the process safety and operability. Similarly, for an existing plant, from the viewpoint of the two criteria mentioned above, the plant structure or operating procedures have to be modified as necessary. To address this issue, we have proposed a plant structurization methodology based on the ANSI/ISA-88 standard (abbreviated as S88) [1] [2]. Furthermore, we have introduced the concept of a CGU (Control Group Unit) as the unit; finally, we have decomposed and modularized the correspondence relation between plant structure and process operating procedures [3] [4]. Here, the CGU is an inventory control unit that is defined as a plant area surrounded by control valves [4]. However, in the event that the process operations spread across different CGUs, to assess the process operating procedures from the viewpoint of safety and operability, we have to manage information regarding the order relation of the process operations as well as the structurization of the correspondence relation. To do so, in this paper, we provide a framework for the remedial design of the plant. As an industrial example, we examine a start-up procedure for an HDS (hydrodesulfurization) plant.
2. Related Studies So far, related studies, which have addressed the process operating procedures in a chemical plant, have mainly focused on the automatic generation of operating procedures. Rivas et al. have proposed a method to generate a procedure for valve operation by composing operation goals hierarchically [5]. Kinoshita et al. have solved the automatic generation of the operating procedures as the state transition problem [6]. Lakshmanan et al. have developed a program to generate the operating procedures with
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the use of a partial planner [7] [8]. Naka et al. have proposed a design methodology that automatically generates the operating procedures by changing the plant topology [9]. However, these related works have not focused on the generation of the process operating procedures in consideration of the correspondence relation with the plant structure. Furthermore, no study has taken into account the order relation among different CGUs. These are the challenges in this paper.
3. Framework for the Improvement of Operating Procedures 3.1. Approach In this paper, we propose and apply the CGU coordination to manage information regarding the order relation of the processes that spread across the different CGUs. By using the CGU coordination, it is possible to assess the process safety and operability in the CGUs. The detailed approach is described as follows: 1. Structurization of the correspondence relation between the plant structure and process operating procedures with the use of the CGU. 2. Careful assessment of each CGU from the viewpoint of process safety and operability. 3. Improvement of a process if necessary as a result of step 2. 4. Management of information regarding the order relation of the process operating procedures among different CGUs. 5. Integration of information and generation of the whole operating procedure. 3.2. CGU Coordination In designing chemical processes on the basis of the procedural control model with the use of the current PFC (Procedural Function Chart defined in the S88), we have to take into account the order relation of the processes among different CGUs. On the other hand, in our design framework, we simply consider the order relation of the operating procedures in each CGU by only using the CGU coordination. That is to say, plant designers are able to assess process safety and operability and design the operating procedures by focusing on a CGU unit only. In order to manage information regarding the order relation of the processes spread across the different CGUs, it is necessary to identify the following information, which is yielded by a conditional transition in a CGU: • end information of the operation in another CGU; and • similar information to the operation in another CGU. For the purpose described above, we have to distinguish the conditional transition from other conditional transitions. Moreover, CGU coordination requires having information. Therefore, in this paper, we contrive several symbols in addition to the conventional PFC. Figure 1(a) shows a symbol of the conditional transition. The operation and conditional transition indicated with the symbol shown in Fig. 1(a) are described in the CGU coordination as shown in Fig. 1(b) and Fig. 1(c). Figure 2 shows an example of the procedural control model, which consists of four CGUs in a continuous process described with the use of the contrived symbols. Thus, it is possible to identify the CGU, in which an operating procedure is executed by painting a color (light blue) on the CGUs that need to be operated. First off, the CGU coordination begins to execute operations from the start symbol; then, the end symbol is executed after all operations are done. As for the conditional transitions indicated by the symbol shown in Fig. 1(a), these conditions depend on the conditions in other CGUs. To manage information, the CGU coordination checks if the conditional transitions, which are depicted by Fig. 1(a), are met.
Improvement of Operating Procedures Through the Reconfiguration of a Plant Structure
(a)
(b)
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(c)
Fig. 1 Further symbols described in the CGU coordination
Fig. 2 An example of a procedural control model and CGU coordination
3.3. Integration of Operation Procedures The integration process of the generated operating procedures for the CGU with the use of the CGU coordination is described as follows: Step 1. Integration of phases that are described with a tag, e.g., TRx, SAMEx, and IFx. Step 2. Checking of conditional transitions shown with an ellipse. Step 3. Indication of the executable phases in each CGU. Step 4. Connection of the indicated phases from the top to the bottom in sequence. Step 5. Execution of the end symbols as a parallel operation at the same time.
4. Case Study 4.1. HDS Plant As an industrial example, we examine a start-up procedure for an HDS (hydrodesulfurization) plant (see the detailed PDF (Process Flow Diagram) in [1] [2]). Figure 3 shows a simplified schematic of the HDS plant divided into four CGUs. Blended diesel oil which flows from the FSD (Feed Surge Drum) is mixed with H2-rich gas and heated by the RCF (Reactor Charge Furnace); after passing through the reactor, the reactor effluent is separated into gas and liquid at the HPS (High-Pressure
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Separator); H2S in the separated gas is absorbed in the amine scrubber, and the remaining H2 is recycled. The liquid is sent to the LPS (Low-Pressure Separator). Figure 4 shows the structurized process operating procedures for the existing operating procedures with the use of the proposed procedural control model. In Fig. 4, ‘Procedure,’ ‘Unit Procedure,’ and ‘Operation’ are shown.
Fig. 3 HDS plant decomposed and modularized by assigning the CGUs
4.2. Assessment of the Existing Operating Procedures For the design of operator-friendly operating procedures, it is necessary to simplify them. Furthermore, an operation should not be controlled in a CGU that is not directly involved. From the assessment result of Fig. 4, we conclude that the operations colored in gray, such as ‘gas circulation,’ ‘catalyst activation,’ and ‘rising temperature,’ present problems, as indicated in the following: • Gas circulation: although this is an operation that aims at the reactor circuit in the CGU 2, it is also included in CGU 4. • Catalyst activation: although this is an operation, which aims at the reactor in the CGU 2, it is also included in CGUs 1, 3, and 4. • Rising temperature: although this operation aims at the RCF in CGU 2, it is also included in CGU 4. 4.3. Improvement of the Operating Procedures For the problems mentioned in 4.2, we improve the operating procedures, i.e., CGUs and operations, as follows in consideration of process safety and operability. • Gas circulation: we remove the operation executed in CGU 4. For this purpose, we also remove the phase, ‘start the air cooler,’ in CGU 4. This phase has to be executed before the heated diesel oil in the RCF flows into CGU 4. • Catalyst activation: we remove the phases in CGU 1, ‘transfer the diesel oil to the reactor’ and ‘add the sulfide,’ the phase in CGU 3, ‘pressurize the LPS,’ and the phases in CGU 4, ‘pressurize the SOrec’ and ‘transfer the product diesel oil to the output tank.’ Moreover, as a new operation, we add the operation, ‘feed the diesel oil
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to the reactor circuit,’ into CGU1. Then, the phase ‘add the sulfide’ in CGU 1 is moved into CGU 2. This modification results in the reconfiguration of a part of the plant structure002E The phases in CGUs 3 and 4, ‘pressurize the LPS’ and ‘pressurize the SOrec,’ are moved into the operation ‘initial charge’ in CGU 2. The operation, ‘catalyst activation,’ in CGU 3 is changed to ‘generation of the on-spec product’ through the LPS. • Rising temperature: we remove all operations executed in CGU 4. These operations are changed to the operation ‘generation of the on-spec product.’ The operation, ‘initial charge,’ in CGUs 3 and 4 is incorporated into the operation, ‘generation of the on-spec product.’ Figure 5 shows the improved operating procedures. Finally, this plant is able to be in a stable state after the operation ‘initial charge’ in CGUs 3 and 4 is executed. The operations shown in color are executed at the same time in each CGU.
Fig. 4 Structured description of the operating procedures of the HDS plant
5. Conclusions and Future Studies In this paper, for an existing chemical plant, we improved the operating procedures in terms of process safety and process operability. We structurized the correspondence relation between the whole plant structure and the operating procedures with the use of the CGU. After that, for the structurized correspondence relation between the plant structure and the operating procedures, we managed information regarding the order relation of the operations among different CGUs by using the proposed CGU coordination. As an industrial example, we examined a start-up procedure for the HDS plant, and, finally, we showed the improved operating procedures by simply assessing and designing an operating procedure within a CGU that needs to be modified.
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Fig. 5. Improved operating procedures (Procedure, Unit Procedure, and Operation)
References 1. 2.
3. 4.
5. 6.
7.
8.
9.
Instrumentation, Systems, and Automation Society, 1996, ANSI/ISA-88.01-1995 Batch Control Part 1: Models and Technology, ISA, Research Triangle Park, USA. Instrumentation, Systems, and Automation Society, 2001, ANSI/ISA-88.02-2001 Batch Control Part 1: Data Structures and Guidelines for Languages, ISA, Research Triangle Park, USA. H. Seki, S. Hoshino, T. Sugimoto, and Y. Naka, 2007, Structured Description of Operating Procedures for Continuous Chemical Processes, (submitted to PSE Asia, China). Y. Naka, H. Seki, S. Hoshino, and K. Kawamura, 2007, Information Model And Technological Information - Infrastructure For Plant Life Cycle Engineering, ICheaP-8 The eight International Conference on Chemical & Process Engineering. J. R. Rivas and D. F. Rudd, 1974, Synthesis of Failure-safe Operations, AIChE Journal, Vol, 20, No. 2, pp. 311-319. A. Kinoshita, T. Umeda, and E. OShima, 1982, An Approach for Determination of Operational Procedure of Chemical Plants, Proceedings of the International Symposium on Process Systems Engineering, pp. 114-120. R. Lakshmanan and G. Stephanopoulos, 1988, Synthesis of Operating Procedures for Complete Chemical Plants - I. Hierarchical, structured modeling for nonlinear planning, Computers and Chemical Engineering Vol. 12, No. 9/10, 985-1002. R. Lakshmanan and G. Stephanopoulos, 1990, Synthesis of Operating Procedures for Complete Chemical Plants - III. Planning in the presence of qualitative mixing constraints, Computers in Chemical Engineering, Vol. 14 No. 3, pp. 301-17. Y. Naka, M.L. Lu, H. Takiyama, 1977, Operational Design for Start-up of Chemical Processes, Computers Chem. Engng, Vol. 21, No. 9, pp. 997-1007.
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Graph-theoretic Approach to Optimal Synthesis of Supply Networks: Distribution of Gasoline from a Refinery Young Kim,a,b L.T. Fan,b Choamun Yun,a Seung Bin Park,a Sunwon Park, a,* Botond Bertok,c Ferenc Friedlerc a
Department of Chemical and Biomolecular Engineering, KAIST, Daejeon 305-701, Korea b Department of Chemical Engineering, Kansas State University, Manhattan, KS 66506, U. S. A. c Department of Computer Science, University of Pannonia, Egyetem u. 10, Veszprem, H-8200, Hungary
Abstract The synthesis of a supply network is profoundly convoluted because of its combinatorial complexity. Global or even near optimal solutions are, more often than not, unobtainable through the heuristic methods. On the other hand, the majority of the algorithmic methods, which mainly resort to mixed integer programming, in theory, can give rise to global optima; however, they are effective only for relatively minute networks. Obviously, it is highly desirable that a novel paradigm be established for optimally synthesizing supply networks; the adoption of the graph-theoretic method based on P-graphs (process graphs) is proposed herein for the synthesis of optimal supply networks. The proposed method is illustrated with examples. Each example has yielded simultaneously the optimal and near optimal structures of the supply network performing a specific task in the ranked order. The example reveals a unique feature of the method. Keywords: Supply network; graph-theoretic; P-graphs; optimal synthesis
1. Introduction The optimal design, i.e, synthesis, of a supply network tends to be profoundly convoluted because of its combinatorial complexities. Thus, excessive time and effort are often required for formulation and computation except for some cases [1]. As a result, a limited number of papers has been published on this subject [2, 3]. Furthermore, the majority, if not all, of the published papers adopts algorithmic methods to carry out the optimization of algebraic models via mixed integer programming (MIP). An approach proposed herein for the optimal synthesis of supply networks resorts to the unique graph-theoretic method based on process graphs (P-graphs) originally developed for process-network synthesis [4-8]. The approach is demonstrated by applying it to the optimal supply-network design for a fuel product, i.e., gasoline, from a refinery.
*
To whom correspondence should be addressed. E-Mail:
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Gasoline produced from crude oil is conveyed through a supply network to markets; obviously, gasoline is a material for which the law of mass conservation is universally valid. This material can be regarded as the raw material entering into the network or the final product exiting from the network. Any actions imposed on or disturbances affecting the material conveyed through the network will induce a change in one or more of its attributes, such as static pressure, flowrate, lot size, and/or locations, thereby transforming the material. Upon reaching the markets or retailers through a series of these transformations, the material can be regarded as the final product exiting from the network. Thus, operating, i.e., functional, units can be unequivocally identified at locations of such actions or disturbances. Naturally, the networks can be represented as P-graphs. One of the two cornerstones of the current graph-theoretic method for process-network synthesis is obviously the representations of the operating units with these P-graphs. The other is a set of 5 axioms of combinatorially feasible process networks [5, 6]. These 5 axioms give rise to 3 highly efficient algorithms for implementing the method. The profound efficacy of the proposed approach is demonstrated with two examples of gasoline manufactured at a refinery and supplied to retailers through distribution networks containing various terminals.
2. Methodology The present methodology comprises the following: (a) representing all the plausible operating units identified in terms of P-graphs; (b) composing the maximal structure from the P-graphs of the operating units via algorithm MSG (maximal structure generation); (c) generating exhaustively the combinatorially feasible network structures as solution-structures from the maximal structure via algorithm SSG (solution-structure generation); and (d) identifying all the feasible network structures among the combinatorially feasible network structures via MIP or, alternatively, determining only a limited number of the optimal and near optimal networks, in the ranked order of the objective function, directly from the maximal structure via algorithm ABB (accelerated branch and bound) [4-6, 9] 2.1. P-graph representations of operating units The structure of a supply network, visualized as a process network, is represented by Pgraphs, which are unique bipartite graphs. Unlike conventional bipartite graphs, or digraphs, the P-graphs are capable of capturing the syntactic and semantic contents of process networks. A P-graph comprises two types of vertices or nodes for representing materials and operating units; the former is symbolized by circles, and the latter, by horizontal bars. Table 1, to be elaborated later, illustrates the conventional as well as Pgraph representations of operating units. 2.2. Implementation of algorithms At the outset, the maximal structure of the gasoline-supply network, playing the role of process network, is composed via algorithm MSG with the P-graphs of all the operating units at its input. This algorithm totally excludes any combinatorially infeasible network structure in light of the five axioms in constituting a supply network. Thus, the maximal structure is the rigorous, minimally complex super-structure containing exclusively and exhaustively the combinatorially feasible network structures. Subsequent to the generation of the maximum structure, the combinatorially feasible network structures are exhaustively recovered as the solution-structures by resorting to algorithm SSG. Each solution-structure signifies a combinatorially feasible network of pathways linking the raw materials to the products. Nevertheless, not all the solutionstructures are necessarily feasible due to the violation of the mass balances in or around
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the network. The feasibility of an individual solution-structure, i.e., combinatorially feasible network structure, is assessed by optimizing the objective function via MIP subject to the mass-balance constraints. Naturally, this also gives rise to the optimality of the individual feasible network structures. In practice, only a limited number of optimal and near optimal structures would be of interest. Such network structures can be determined in the ranked order in terms of the objective function by means of algorithm ABB directly from the maximal structure. The objective function can be, profit, cost, sustainability, speed of supply, or any combination thereof.
3. Illustration The proposed approach is illustrated with a supply network to deliver gasoline from a refinery to one or two terminals through various routes by two means of transportation, i.e., pipelines and tanker-trucks. The optimal and near-optimal networks in the ranked order of cost are obtained for the two examples, one depicted in Figure 1 and the other depicted in Figure 2. Conventional and P-graph representations of an operating unit identified are provided in Table 1 as an example.
Figure 1 Gasoline supply from a refinery to a
Figure 2 Gasoline supply from a refinery to
terminal (Example 1).
two terminals (Example 2).
Table 1. Conventional and P-graph representations of an operating unit: gasoline loading on trucks Operating units No
Designation
Function
Streams
Diagrammatic representation Conventional
P-graph
Notation
S1-2 [G1]
Loading of gasoline on 4
DT1
trucks at distribution terminal 1
Description Gasoline supplied to DT1 Trucks
DT1([G1],[T]) =
S5-2 [T]
supplied to DT1
4
[G T]
Gasoline S4 [G4T]
loaded on trucks
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Y. Kim et al.
3.1. Example 1 Gasoline is transported from one refinery to a single terminal through a pipeline or by tanker-trucks; see Figure 1. The empty tanker-trucks are returned to the refinery to be reloaded for the succeeding delivery. The feasible network structures vary depending on the operating costs and capacity constraints of the pipeline and tanker-trucks. The resultant combinatorially feasible as well as feasible network structures are presented in Tables 2 and 3 for two sets of capacity constraints. Table 2. Combinatorially feasible and feasible networks for Example 1
N1* {1,2,3,6,f1}
Optimal value of objective function ($/month) 29
N2 {1,2,3,4,5,7,f1}
N2* {1,2,3,7,f1}
31
2
N3 {1,4,5,8,f1}
N3* {1,4,5,8,f1}
34
3
Combinatorially feasible networks {operating units} N1 {1,2,3,6,f1}
Feasible networks {operating units}
Rank 1
N4 {1,2,3,4,5,6,7,f1} N5 {1,2,3,4,5,6,8,f1} N6 {1,2,3,4,5,7,8,f1} N7 {1,2,3,4,5,6,7,8,f1} Table 3. Combinatorially feasible and feasible networks for Example 1 (Min. flowrate of S1-1 and S1-2 = 1)
Combinatorially feasible networks {operating units} N1 {1,2,3,6,f1} N2 {1,2,3,4,5,7,f1} N3 {1,4,5,8,f1}
N1* {1,2,3,6,f1}
Optimal value of objective function ($/month) 29
N2* {1,2,3,4,5,7,f1}
34
2
N3* {1,4,5,8,f1}
34
2
N5* {1,2,3,4,5,6,8,f1}
35
4
Feasible networks {operating units}
Rank 1
N4 {1,2,3,4,5,6,7,f1} N5 {1,2,3,4,5,6,8,f1} N6 {1,2,3,4,5,7,8,f1} N7 {1,2,3,4,5,6,7,8,f1} 3.2. Example 2 Unlike Example 1, two terminals are involved in this example; however, gasoline is supplied to the second terminal only by tanker-trucks as depicted in Figures 2 and 3. Empty tanker-trucks from the two terminals are considered to belong to the same materials in the network. They are returned to the refinery to be reloaded for the succeeding delivery; 72 combinatorially feasible network structures have been
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identified for this example, which, in turn, have yielded 4 feasible networks presented in Table 4.
Figure 3 Process flowsheet of Example 2. Table 4. Feasible networks for Example 2
Optimal value of Rank
objective function ($/day)
Feasible networks {operating units}
1
103
N1* {1,2,3,6,11,12,13,16,f1,f2}
2
105
N2* {1,2,3,6,9,10,11,14,f1,f2}
3
110
N3* {1,4,5,8,9,10,11,14,f1,f2}
4
120
N4* {1,4,5,8,11,12,13,16,f1,f2}
4. Discussion The efficacy of adopting the current graph-theoretic method based on P-graphs for systems, which are not traditionally regarded as process networks, such as supply networks, has been amply demonstrated by Halim and Srinivasan [10] in crafting the decision support system for waste minimization. The graph-theoretic method based on P-graphs definitely reveal the structural and operating features of supply networks in unquestionably more details than the conventional algorithmic method based on the MIP. Moreover, the superior computational efficiency of the former over the latter, especially for complex networks, has been unequivocally pointed out [8]. The efficacy of the proposed methodology is demonstrated with the two examples of a gasoline supply network. In Example 1, the combinatorially feasible solutions, i.e., networks, are identified via algorithms MSG and SSG [4~6]. The second columns of Tables 2 and 3 list the feasible networks determined via MIP for all combinatorially feasible networks contained in the first column of each table. Note that not all the combinatorally feasible networks are feasible; moreover, the number of feasible networks identified varies according to the mass constraints imposed as discernable in Tables 2 and 3. Specifically, Table 1 contains the results obtained without any mass flow constraint, and Table 2 contains the results obtained when the minimum mass
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flowrates of streams S1-1 and S1-2 are constrained to be 1. In Example 2, only a limited number of feasible networks satisfying the production requirements are recovered as the optimal or near-optimal networks in the ranked order via algorithms MSG and ABB without resorting to algorithm SSG and MIP [4~6, 9]. It is of utmost importance to simultaneously generate some near-optimal supply networks in the ranked order of the objective-function values along with the optimal one. These near-optimal networks serve as the stand-bys to immediately replace the optimal network in case of interruption arising from man-made catastrophes, e.g., warfare, or natural catastrophes, e.g., wild fires or storms. Such capabilities are totally absent from the MIP-based approaches.
5. Conclusion A highly efficient approach has been proposed for synthesizing, i.e., designing, a supply network for a fuel product. It has been unequivocally demonstrated that such a supply network is a process network, thereby rendering it possible to adopt the graph-theoretic method based on P-graphs (process graphs) for its synthesis. The method yields the optimal as well as near optimal networks simultaneously in the ranked order of a specific objective function, such as profit or cost. The profound efficacy of the proposed approach is amply demonstrated with two examples of supplying gasoline from a single refinery to one terminal in one example and two terminals in the other.
Acknowledgement This work was supported by the Brain Korea 21 project, Korea; and Department of Chemical Engineering and the Institute for Systems Design and Optimization, Kansas State University, U.S.A.
Literature Cited [1] C.H. Timpe and J. Kallrath, Eur. J. Oper. Res., Vol. 126 (2000) 422. [2] M.J. Meixell and V.B. Gargeya, Trans. Res. Part E., Vol. 41 (2005) 531. [3] A.G. Kok and S.C. Graves, Handbooks in operations research and management science, volume 11. Supply chain management: design, cooperation and operation, Elsevier, 2003. [4] F. Friedler, K. Tarjan, Y.W. Huang and L.T. Fan, Chem. Eng. Sci., Vol. 47 (1992a) 1973. [5] F. Friedler, K. Tarjan, Y.W. Huang and L.T. Fan., Comput. Chemeng., Vol. 16 (1992b) S313. [6] F. Friedler, L.T. Fan and B. Imreh, Networks, Vol. 28 (1998) 119. [7] M.S. Peters, K.D. Timmerhaus and R.E. West, Plant Design and Economics for Chemical Engineers, McGraw-Hill, New York, 2003. [8] R. Sargent, Comput. Chemeng., Vol. 29 (2005) 1237. [9] J. Liu, L.T. Fan, P. Seib, F. Friedler and B. Bertok, Ind. Eng. Chem. Res., Vol. 45 (2006) 4200. [10] I. Halim and R. Srinivasan, Ind. Eng. Chem. Res., Vol. 41 (2002) 196.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
253
Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications Mohamed T. Mahmuda, Iqbal M. Mujtabaa, Mansour Emtirb a School of Engineering, Design and Technology, University of Bradford, Bradford, West Yorkshire, BD7 1DP, United Kingdom. bLibyan Petroleum Institute, P.O.Box 6431Tripoli, Libyan Arab Jamahiriya
Abstract Unlike the past work, this work focuses on optimal design and operation of multivessel batch distillation column with fixed product demand and strict product specifications. Both the vapour load and number of stages in each column section are optimised to maximise a profit function. For a ternary mixture, the performance of the multivessel column is also evaluated against that of a conventional batch distillation column. Although the profitability and the annual capitalised cost (investment) of the multivessel column is within 2-3% compared to those of conventional column, the operating cost (an indirect measure of the energy cost and environmental impact) is more than 30% lower for multivessel column. Thus, for a given separation task, multivessel column is more environment friendly. Keywords: Multivessel Batch Distillation, Fixed Product Demand, Product Sequence, Optimisation.
1. Introduction Batch distillation is an important unit operation used in many chemical industries, and in particular in the manufacture of fine and specialty chemicals. While conventional batch distillation had received much attention, the research in multi-vessel batch distillation (MultiVBD) is handful (Furlonge et al., 1999; Low and Sorenson, 2003, 2005). Furlonge et al. (1999) considered the optimal operation problem for a fixed number of stages (total and in between the vessels). The objective was to minimise the mean rate of energy consumption required for producing products of specified purity while optimizing instantaneous heat input to the reboiler subject to product specifications (amount and purity). Various operating polices such as fixed vessel holdup, variable vessel holdup, etc. have been considered. Optimising the initial distribution of the feed among the vessels reduces the energy consumption by almost 15%. Low and Sorenson (2003) presented the optimal design and operation of MultiVBD column. A profit function based on revenue, capital cost and operating cost was maximized while optimising the number of stages in different column sections, reflux ratio, etc. They compared the performance of MultiVBD with that of conventional batch distillation column for a number of different mixtures and claimed that MultiVBD operation is more profitable. However, for all cases considered in their work, the products specifications and amounts were not matched exactly and therefore the
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conclusion is somewhat misleading. Also, reduced batch time in MultiVBD column was leading to additional production of products compared to that produced by the conventional column. Therefore, the additional profit can only be realised if there is a market demand i.e. if all the products which are produced are saleable. Low and Sorenson (2005) considered the optimal configuration, design and operation of batch distillation column based on overall profitability for a given separation duty. Using rigorous model, the mixed integer dynamic optimisation problem was solved using genetic algorithm. Again for a multicomponent separation case, MultiVBD configuration was chosen as optimum from among the conventional and inverted batch distillation columns. However, strict product specification was not maintained and the vapour load hit the upper bound to minimise the batch time and to maximize the profit. This work also led to unlimited production of products which was not sustainable and the profitability calculations were based on the assumption that all products produced are saleable. Contrary to these works, this research is focused on optimal design and operation of a MultiVBD column producing two desired products from a ternary mixture with fixed yearly product demand and strict product specifications. A profit function is maximised while optimising the number of stages in column sections of a MultiVBD and vapour load to the column. The results (profit, design and operation) are compared with those obtained using a conventional column. Simple process models are developed in gPROMS for both configurations and the optimisation problems are solved using the built in facilities within gPROMS.
2. Process Model Figure 1 shows the schematic of a MultiVBD Column. A dynamic model based on constant relative volatility, constant molar liquid holdup on the stages, total condenser and constant pressure is considered here and are shown in Figure 2. Note, the simple model for the conventional column is taken from Mujtaba (2004) and therefore is not presented here.
V, y
L, x j − 2
j −1
Stage j-1
V, yj
Condenser
V
L, x j −1 Stage j
V, y j +1
Vessel
L, x j Stage j+1
Plates
L
Vessel H f x fi L Reboiler
V
L
L
Fig.1 Multivessel Batch Distillation Column with Connection of Trays and Vessels
Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications
255
Condenser Component Balance:
dx1i V = ( y2i − x1i ) dt Hc
Internal plates, j=2 to (N-1); i = 1 to nc Component Balance:
Vapour Liquid Equilibrium:
dx ji dt
(
)
(
L V x j −1,i − x j ,i y j +1,i − y j ,i + Hj Hj
=
)
α i x j ,i
y j ,i =
nc
¦α x
k j ,k
k =1
Vessel Component Balance:
Hf
dx fi dt
(
= L f x ji − x fi
)
Reboiler Component Balance:
HN
dxN ,i dt
(
)
= L x N −1,i − x N ,i − V ( y N − x N ,i
)
The vapour liquid equilibrium relationship is same as in internal plates with j=N
Fig.2 Model Equations of Multivessel Batch Distillation System
3. Product Demands and Specifications A total of 2555 kmol/yr of Product A with 95% purity (molefraction) and 1214 kmol/yr of Product B with 95% purity (molefraction) are to be produced from 9790 kmol/yr of a ternary mixture (A, B, C) with composition molefraction and relative volatility Į =. Due to high purity demand of Product B, an intermediate off-cut is needed to be produced with no more than 60% purity in component A. Component C is not a valuable product. The maximum capacity of the MultiVBD column is 10 kmol and has 4 vessels including the reboiler and condenser holdup tank (3 column sections). Both conventional and the MultiVBD columns are available for a period of 8000 hrs/yr. The set up time for each batch of operation is 30 minutes. The total number of batches will therefore be 979 per year and the individual batch time would be 7.67 hr. For a batch with 10 kmol feed mixture (B0), the product profiles are calculated using steady state mass balance (Miladi and Mujtaba, 2006) as: Product A = 2.61 kmol/batch (D1); Product B = 1.24 kmol/batch (D2); Intermediate Off-Cut = 0.83 kmol/batch (R1) and Bottom Residue (in the reboiler) = 5.32 kmol/batch (Bf). In MultiVBD column, the products will be produced simultaneously while in the conventional column these will be produced sequentially as shown by State Task Network (STN) in Figure 3. Note, there is an extra middle vessel to produce an off-cut between D1 and D2.
4. Objective Function and Optimisation Problem Formulation The objective function (to maximise) is the profit per year and is defined (Mujtaba, 2004) as follows:
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M.T. Mahmud et al.
Product
Feed
D1 T A S K
Bo Initial
R1 D2 Bf
t=0
t = tf
Multivessel Column R1
D1
Bo
Task 1
B1
D2
Task 2
Task 3
B2
Bf
Conventional Column Fig.3 STN for Multivessel and Conventional Column
Profit ($/yr) = P = ( C1 D1 + C2 D2 + C3 D3 − C4 R1 − C5 B0 − OCb ) × Nb − ACC Where, OCb = Operating cost ($/batch) = (K 3 V / A)× (t b − t s ) ACC = Annualised capital cost ($/year), K1 V
0.5
N
0.8
+ K2 V
0.65
(1) (2) (3)
with, K1 = 1,500; K2 = 9,500; K3 = 180; A = 8,000 N b = Number of batches / year = H / (t b + t s ) (4) tb = Batch time (hr); ts = Set-up time = 0.5 hr; H = Production horizon = 8000 h/year C1 = C2 = 20, C3, = C4, = 0 and C5 = 1 are the prices ($/kmol) of the desired products, bottom residue, off-cut, and raw material respectively (taken from Mujtaba, 2004; Mujtaba and Macchietto, 1993). The optimisation problem can be defined as: Given:
Optimise:
Maximise: Subject to:
The column configuration (MultiVBD or Conventional), fixed product demands with strict product specifications (purity), fixed batch time (tb) Number of stages (NS in different column sections for MultiVBD or N in Conventional column), the vapour load (V). In addition, the cut times (ti) and reflux ratio (ri) in each cut of conventional column The total profit (P) Any constraints (model equations, bounds on the variables, etc.)
Mathematically, the problem can be written as:
Max
N S (or N ),V (and ri ,ti )
Subject to:
P
Process Model Equations (Fig. 2) (Equality) Fixed product demands (Equality)
Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications
257
Product specifications (Equality) Bounds on N S (or N ), V , (and ri , ti ) (Inequality) Fixed batch time (Equality) Note, although Furlonge et al. (1999) reported that variable hold-ups in the vessels of MultiVBD reduces energy consumption, in this work, we distributed the feed in different vessels according to the product profiles calculated a priori. Also, for conventional column piecewise constant reflux ratio with two intervals were used for each cut. The above optimisation problem is solved using gPROMS software. Note, for CBD column, two reflux intervals were considered for each cut and the reflux ratio in each interval was assumed to be piecewise constant (Mujtaba, 2004).
5. Results and Discussions The results in terms of optimum number of stages, vapour load, reflux ratio, cut time, etc. are summarised in Table 1 for both columns. The results also show the operating cost per batch, annualised capital cost, profit per batch and per year. For MultiVBD column the total number of stages required is 40% more than that required for the conventional column (CBD). However, the vapour load for the MultiVBD column is about 25% lower compared to CBD and the operating cost (a measure of energy cost) is 30% lower. Finally, the overall profit realised by MultiVBD column is about 3% more that that by CBD column. The product demand and qualities (purities) of each main-cut and off-cut are achieved to the given specifications. Figure 4 shows the product quality at the end of the batch for MultiVBD column in each vessel. Table 1. Summary of the results Configuration
V
Nt
Kmol
OCb
ACC
P
P
$/b
$/yr
$/b
$/yr
CBD
3.0
10
0.55
35795
29.90
29270.8
MultiVBD
2.3
4, 6, 4
0.42
35111
30.72
30080.1
Reflux Ratio Profile for CBD: Main-Cut 1 ( D1) Reflux ratio Switching Time (hr)
Off-Cut ( R1)
Main-Cut 2 ( D2)
0.712
0.819
0.841
0.942
0.660
0.781
0.0-2.10
2.10-3.56
3.56-4.78
4.78-6.21
6.21-6.99
6.99-7.67
6. Conclusions Unlike previous work in MultiVBD column, in this work, the optimal design and operation of MultiVBD column is considered under fixed product demand and strict product quality specifications. Overall product demands, product quality and feed specifications allow calculation of product profiles (amount of each product) of each batch a priori using steady state mass balance calculations. For the given separation task, the MultiVBD column was found to be more profitable than the CBD column. Also the operating cost (an indirect measure of the energy cost
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M.T. Mahmud et al.
and environmental impact) for MultiVBD column was more than 30% lower compared to that by CBD. In all cases, product demand and quality are met on specifications. Reflux drum (main cut-1)
Vessel - 1 (off cut-1) 0.7
Composition (mol fraction)
1
Compostion (mol fraction)
0. 9 0. 8 0. 7
x1
0. 6 0. 5
x3
0. 4 0. 3 0. 2
x2
0. 1
0.6
x1
0.5 0.4
x2 0.3 0.2
x3
0.1 0 0
0 0
1
2
3
4
5
6
7
2
8
4
6
8
10
Time (h)
Time (h)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Reboiler (bottom residue) Composition (mol fraction)
Composition (mol fraction)
Vessel - 2 (main-cut-2)
x2 x3 x1
0
2
4
6
Time (h)
8
10
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
x3
x1 x2 0
2
4
6
8
10
Time (h)
Fig.4 Composition Profiles of Each Vessel of MultiVBD Column
References H. Furlonge, C. Pantelides and E. Sorensen, 1999, Optimal Operation of Multivessel Batch Distillation, AIChE J, 45, 4, 781-801. gPROMS, (2005), Introductory User Guide, Process System Enterprise Ltd (PSE), http://www.psenterprise.com/gproms/ K. Low and E. Sorensen, 2003, Simultaneous Optimal Design and Operation of Multivessel Batch Distillation, AIChE J, 49, 10, 2564-2576. K. Low and E. Sorensen, 2005, Simultaneous Optimal Configuration, Design and Operation of Batch Distillation, AIChE J, 51, 1700-1713. M. Miladi and I.M. Mujtaba, 2006, Optimisation of design and operation parameters for ternary batch distillation with fixed product demand, Engineering Computations: International Journal for Computer-Aided Engineering and Software, 23, 7, 771-793. I.M. Mujtaba, 2004, Batch Distillation: Design and Operation, Imperial College Press, London. I.M. Mujtaba and S. Macchietto, 1993, Optimal operation of multicomponent batch distillationMultiperiod formulation and solution, Computers & Chemical Engineering, 17, 12, 11911207.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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An Integrated Framework for Operational Scheduling of a Real-World Pipeline Network Suelen Neves Boschetto,a Luiz Carlos Felizari,a Lia Yamamoto,a Leandro Magatão,a Sérgio Leandro Stebel,a Flávio Neves-Jr,a Lúcia Valéria Ramos de Arruda,a Ricardo Lüders,a Paulo César Ribas,b Luiz Fernando de Jesus Bernardob a
Federal University of Technology – Paraná (UTFPR/CPGEI), Av. Sete de Setembro, 3165, 80230-901 – Curitiba, PR, Brazil E-mail {suelen, felizari, lia}@cpgei.cefetpr.br {magatao, stebel, neves, lvrarruda, luders}@utfpr.edu.br b Logistic Division-Research and Development Centre, PETROBRAS-CENPES Rio de Janeiro/RJ, Brazil E-mail {paulo.ribas, lfjb}@petrobras.com.br
Abstract This paper addresses the problem of developing an optimisation structure to aid the operational decision-making of scheduling activities in a real-world pipeline network. During the scheduling horizon, many batches are pumped from (or passing through) different nodes (refineries, harbours or distribution terminals). Pipelines are shared resources operated and monitored 365 days a year, 24 hours per day. Scheduling details must be given, including pumping sequence in each node, volume of batches, tankage constraints, timing issues, while respecting a series of operational constraints. The balance between demand requirements and production campaigns, while satisfying inventory management issues and pipeline pumping procedures, is a difficult task. Based on key elements of scheduling, a decomposition approach is proposed using an implementation suitable for model increase. Operational insights have been derived from the obtained solutions, which are given in a reduced computational time for oil industrial-size scenarios. Keywords: Scheduling, Pipeline Network, MILP, Heuristics, Oil Industry. 1. Introduction Scheduling activities related to oil product distribution have received a growing interest in the last years. Distribution and transfer operations of such products can be carried out by road, railroad, vessels, or pipelines. Pipelines are one of the most important transportation modes for oil products in Brazil. Some papers
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have already addressed scheduling decisions for pipeline networks [1,2,3,4]. In this paper, the considered scenario is particularly complex due to the existence of many areas and pipes subject to particular operational constraints. The proposed approach compares to a previously developed work [5] in terms of complexity and computational performance. This paper is organized as follows. Section 2 presents some operational details of the considered pipeline network. The computational framework, including a global view of the optimisation structure, is given on Section 3. Section 4 shows the new implementation used for the optimisation structure, and Section 5 presents the obtained results with conclusions in Section 6. 2. The pipeline network The considered plant (Fig.1) involves 13 areas (nodes), including 4 refineries (nodes N1, N3, N9, and N11) and 2 harbours (N10 and N13), which receive or send products through 7 distribution terminals. In addition, it includes 29 multiproduct pipelines with particular volumes (e.g. pipe 1 has more than 42000 m3). Nodes are “connected” through pipes (e.g. pipes 3, 4, and 5 connect nodes N2 and N3). A product can take many hours to reach its final destination. A batch can remain in a pipe until another one pushes it. Many pipes can have their flow direction inverted due to operational procedures (e.g. pipes 5, 7, and 15). Each product has to be stored in a specific tankfarm within a node. More than 14 oil derivatives can be transported in this network. Adjacent products can share an undesirable interface, e.g. alcohol pumped just after diesel. In this case, it is necessary to pump another product between them (e.g. gasoline). Typical transfer tasks can involve pumping a batch through many areas. For instance, a batch can be pumped from node N3 to N7 through nodes N2, N5, and N8. In that case, the batch uses pipes 4, 8, 12, and 14. 3. The Computational Framework The computational burden to obtain a short-term scheduling for the considered scenario is a relevant issue. Therefore, a decomposition approach is proposed to address such real-world problem (Fig.2). This decomposition is based on the three key elements of scheduling: assignment of resources, sequencing of activities, and determination of resource timing used by these activities [6]. A Resource Allocation block (batch sequencing) takes into account production and consumption functions and typical volume of batches (lot sizes) in order to determine a set of candidate sequences of pumping. For instance, node N3 usually has a planning of diesel that can be (partially) stored within its limited tankage scenario. However, after some refining time, a batch must be sent, otherwise the diesel campaign has to be reduced due to lack of tankage. The Pre-Analysis gathers information provided by the Resource Allocation and calculates a series of temporal and volume parameters (bounds). Such bounds give a preliminary indication about scheduling feasibility. Then, the PreAnalysis pre-processed data are used by a continuous-time MILP model, which
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determines the operational short-term scheduling for the pipeline network. The MILP model considers, for instance, the pumping route (source or pumping origin, pipes, and destination), volume and flow rate for each product from a source. Particular attention is given to the fact that pipes have a considerable volume and they always operate fulfilled. Thus, they can “store” different products during pumping procedures. While a new product is sent from a source, previously “stored” products are pushed according to the new product flow rate. Moreover, stored products should be routed to their original destination. At each area, products arriving from pipes can be pumped to tanks or routed to other pipes. A set of tanks in each area can store different products. Inventory level can increase or decrease according to the volume and flow rate of each product pumping or due to “local” production and consumption. In addition, the MILP model considers the seasonal cost of electric energy and a series of operational requirements. Details of the obtained scheduling can be visualized by a series of graphical user interfaces (e.g. Fig.3).
Pre-Analysis Scenarios of Production, Consumption
MILP Model
Configuration of Routes, Areas Scenarios of Pipelines, Tanks
Data Base
Scheduling of Operational Activities
Operational Data Electric Energy Cost ...
Fig.1 – Pipeline Network
Resource Allocation (batch sequencing)
Fig.2 – Optimisation Structure
4. The Optimisation Structure 4.1. Pre-Analysis In this work, the continuous-time MILP model previously presented [5] was restructured, and a novel computational procedure (Pre-Analysis) is proposed. The Pre-Analysis uses information provided by the Resource Allocation (batch sequencing) unit. Based on the list of demanded batches supplied by this unit, the Pre-Analysis calculates a series of temporal and volume parameters (bounds). The underlying idea here is to provide structured sequences (not necessarily optimal) in a reasonable computation time. As an advantage of this approach, the computational burden to generate the minimum temporal blocks (pumping and receipt times) is removed from the MILP model. Furthermore, the complexity of the temporal constraints may vary from scenario to scenario,
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and the Pre-Analysis unit aids the description of these constraints included in the MILP optimisation model. During the scheduling horizon many batches may remain stopped within a pipeline, which causes different volumes of products to be effectively received and pumped at each operational area. As an output, the Pre-Analysis specifies the precise volumes to be pumped (volbomb,n,n',d) and received (volrecb,n,n',d) in a destination node. In addition, it establishes, for instance, the minimum time that a destination node could start to receive (tmin_irb,n,n',d) and could finish to receive (tmin_frb,n,n',d) a product (e.g. Eq.(1)). In Eq.(1), average flow rates are known (vzbi,n,n',d and vzbkir,n,n',d) as well as volume of pipes (vpd) and the number of necessary products for a batch to achieve a specific (intermediate) node (kir). Since the exact duration of activities involves pipeline stoppages and a series of operational constraints, these conditions should be addressed by the MILP model. kir 1 kir 1
tmin _ irb,n,n ',d
¦ i 1
volbombi ,n,n ',d vzbi ,n,n ',d
vpd
¦ volbom
bi ,n ,n ',d
i 1
(1)
vzbkir ,n,n ',d
4.2. MILP Model The model relies on MILP with a continuous-time approach. Variables were created in order to determine the exact time that a pumping procedure of a batch (b B) is started (ibb,n,n',d) and finished (fbb,n,n',d) from a node (n n' N) through a specific pipe (d D, where d connects n and nƍ). In a similar approach, other continuous variables determine the time that a destination node starts to receive (irb,n,n',d) and finishes to receive (frb,n,n',d) a product. In order to determine the value of these variables, the parameters tmin_irb,n,n',d and tmin_frb,n,n',d, previously calculated in the Pre-Analysis are used. In particular, the Pre-Analysis unit indicates the minimum pumping and receipt times of a batch. The formulation was extensively studied, and binary variables were used to enforce seasonality conditions of electric energy. Specific constraints were created in order to deal with inventory issues. So that, the MILP model tries to manage the operational scheduling in each node in order to minimize violations on time intervals. Each node has particular operational features, and the mathematical model has to address them. For instance, batches can be pumped from N8 by pipes 11, 14, and 20. At this node there exist a limited number of pumps and just one batch is allowed to be sent from N8 at a specific time. Thus, in a hypothetical case that various batches are to be sent from N8, the model must manage pumping start/finish times in order to respect this “local” characteristic. Another issue is that many pipes can have the flow direction reverted, according to operational convenience. A specific set of constraints was created to manage such operational condition. In the pipeline-scheduling literature (e.g. [3]) this has been proved to be a difficult issue. In addition, from node to node, a product typical flow rate can vary. For example, diesel is normally pumped from source N8 to final destination N1. At this case, the
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product “passes” through the intermediate node N4. The operation involves, respectively, pipes 11 and 6. From N8 to N4 by pipe 11 the average flow rate is 450 m3/h; from N4 to N1 by pipe 6 the average flow rate is 330 m3/h. 5. Results The decomposition framework has been extensively tested in typical operational scenarios. At these cases, the Resource Allocation block takes into account the planning of production/consumption of each product in each node during a month. Then, it determines candidate sequences of pumping. The pre-processed data are used by both the Pre-Analysis and the continuous-time MILP model. Typical instances yield large-scale MILPs. Such models have been solved to optimality in few CPU seconds using a commercial package [7]. To previously address the sequencing part has been a fundamental issue to reduce the computational burden. However, the final scheduling is influenced by the predetermined sequencing. Operational insights have been derived from the obtained solutions, and the proposed approach can aid the decision-making process. Fig.3 illustrates a Gantt chart of a real-world scenario involving approximately 70 batches pumped during a month. Information about scheduled batches can be derived from this chart. To determine such information used to be not trivial since the system operation was based on human experience without computational aid. As a consequence, operational losses were common. In particular, each batch has an identifying number, which remains as the batch passes through different pipes. One contribution of Pre-Analysis is highlighted in the Gantt. This module indicates the exact volume that is to be pumped along the product pumping route.
Fig.3 – Gantt Chart
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6. Conclusions A new optimisation structure (Fig.2) for the scheduling of operational activities in a real-world pipeline network (Fig.1) has been addressed in this paper. In addition, a new computational procedure was developed, the Pre-Analysis module. The real scenario could be addressed mostly due to Pre-Analysis scalability. The considered scenario is particularly complex and involves more nodes and pipes, compared to the one discussed in a previous work [5]. In order to address this scenario, a decomposition approach was used. This decomposition relied on a Resource Allocation block, which takes into account production/consumption functions and typical lot sizes to determine a set of candidate sequences of pumping. Furthermore, a Pre-Analysis block uses candidate sequences to determine temporal and volume parameters. These parameters were used in a continuous-time MILP model, which indeed determines the short-term scheduling of each batch in each node of the pipeline network. The implemented structure can be used, for instance, to identify system bottlenecks and to test new operational conditions. Computation time has remained at few CPU seconds. The proposed approach have allowed that a monthly planning of production and consumption be detailed in short-time scheduling operations within the considered pipeline network. Thus, operational insights can be derived from the obtained solutions. As an ongoing research, the Pre-Analysis would be used to determine other parameters for the MILP model. Acknowledgements The authors acknowledge financial support from ANP and FINEP (PRH-ANP / MCT PRH10 UTFPR) and CENPES (Under grant 0050.0017859.05.3). References 1. R. Rejowski Jr. and J.M. Pinto. A novel continuous time representation for the scheduling of pipeline systems with pumping yield rate constraints, Comp. and Chem. Eng. (2007), doi:10.1016/j.compchemeng.2007.06.021. 2. D.C. Cafaro and J. Cerdá. Dynamic scheduling of multiproduct pipelines with multiple delivery due dates, Comp. and Chem. Eng. (2007), doi:10.1016/j.compchemeng. 2007.03.002. 3. L. Magatão, L.V.R. Arruda and F. Neves-Jr. A mixed integer programming approach for scheduling commodities in a pipeline. Comp. and Chem. Eng., v.28 (2004) pp. 171-185. 4. S. Relvas, H.A Matos, APFD Barbosa-Póvoa, J. Fialho and A.S Pinheiro. Pipeline Scheduling and Inventory Management of a Multiproduct Distribution Oil System. Ind. and Eng. Chem. Res., v.45 (2007), pp. 7841-7855. 5. F. Neves-Jr, L. Magatão, S.L. Stebel, S.N. Boschetto, L.C. Felizari, D.I. Czaikowski, R. Rocha and P.C. Ribas. An Efficient Approach to the Operational Scheduling of a RealWord Pipeline Network. Proceedings of 17th European Symposium on Computer Aided Process Engineering, Elsevier Science, 2007. 6. G.V. Reklaitis. Overview of scheduling and planning of batch process operations. Proceedings of the NATO, Antalya, Turkey (1992) pp. 660-675. 7. ILOG OPL Studio 3.6.1 – User’s Manual. ILOG Corporation, France, 2002.
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An optimization framework of multibed pressure swing adsorption systems Dragan Nikolica, Michael C. Georgiadisb, Eustathios S. Kikkinidesa a
University of Western Macedonia, Department of Engineering and Management of Energy Resources, Sialvera & Bakola Str., 50100 Kozani, Greece,
[email protected],
[email protected] b University of Western Macedonia, Department of Engineering Informatics and Telecommunications, Agiou Dimitriou Park, 50100 Kozani, Greece,
[email protected] Abstract Pressure Swing Adsorption (PSA) is an energy-efficient alternative to the traditional gas separation processes. This work presents a systematic optimization framework for complex PSA processes including multibed configurations and multilayered adsorbents. The effects of number of beds, PSA cycle configuration and various operating and design parameters on the separation quality and power requirements have been systematically optimized using recent advances on process optimization. The Unibed principle has been adopted relying on the simulation over time of only one bed while storage buffers have been used to model bed interactions. Two industrial multicomponent gas separations have been used to illustrate the applicability and potential of the proposed approach in terms of power consumption minimization and improvement of the product purity and recovery. Keywords: multibed PSA, dynamic optimization, hydrogen production
1. Introduction Separation of gas mixtures by PSA has become a common industrial practice in the area of small to medium scale air separation, small to large-scale gas drying, small to largescale hydrogen recovery from different petrochemical processes and trace impurity removal from contaminated gases. The theoretical modeling and optimization has accompanied the PSA technological development and few studies have been reported in the literature (Nilchan, and Pantelides, 1998, Jiang et al, 2003 and 2004, Cruz et al, 2003 and 2005). As it has been clearly shown the selection of optimal design and operating parameters is a difficult task due to several reasons: a large number of trade-offs between the key variables, large computational requirements to reach the Cyclic Steady State (CSS), and complicated models (large number of partial differential and algebraic necessary to describe multi-scale transport phenomena in adsorbent column and adsorbent particles). In this work, an optimization framework of multibed PSA systems is presented. A generic modeling framework previously presented by the authors (Nikolic et al, 2007) provides the basis for the development of the overall optimization approach.
2. The optimization framework A systematic optimization procedure, to determine the optimal design and operating conditions of a PSA system requires significant computational effort. In order to
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efficiently perform optimization studies, several changes in the existing modeling framework had to be made. The most important one is related to the reduction of the size of the underlying model as all beds are simultaneously simulated. Based on the work of Jiang et al (2004) the Unibed approach has been adopted. The Unibed approach assumes that all beds undergo identical steps so that only one bed is needed to simulate the multibed cycle. Information about the effluent streams (during pressure equalization steps) are stored in data buffers and linear interpolation is used to obtain information between two time points. To this end a gPROMSTM foreign object, VirtualBed, has been developed which imitates the behavior of the real adsorption column, records and restores pressure, enthalpy and composition of the streams. According to the Unibed approach whenever the real column undergoes the pressure equalization step it interacts with one of the VirtualBeds (depending how many pressure equalization steps exist in the PSA cycle).
3. Systematic analysis of the key optimization variables In this work, three different systems have been investigated: I) hydrogen recovery from steam methane reformer off-gas (SMROG) by using activated carbon, II) hydrogen separation from SMROG by using two layered columns (activated carbon and zeolite 5A), and III) nitrogen separation from air by using RS-10 molecular sieve. Due to the high process complexity, a systematic procedure has been followed to identify the most important process parameters and suitable case-dependent objective functions. The procedure relies on a parameter analysis to establish dependencies of input variables (design and operating) as well as their relative importance. To this end, results and important conclusions from several studies published in the literature (Shin and Knaebel, 1988, Nilchan and Pantelides, 1998, Waldron and Sircar, 2000, Jiang et al, 2003, Cruz et al, 2005 etc) have been used. The parameters studied include the particle size, column length and diameter, step times, feed and purge flowrates, distribution of adsorbents in multilayered adsorption columns, number of beds and PSA cycle design have been investigated. The base case parameters have been selected, only one variable at the time has been varied, and the effects analyzed. 3.1.1. Effect of particle size Particle size has a significant influence on the separation quality according to the well known linear driving force (LDF) equation. The LDF coefficient is inversely proportional to square of particle radius. On the other hand, a decrease in particle size increases pressure drop, which results in an earlier breakthrough and degradation of the performance. To tackle this problem Wankat, 1987 used the method of decreasing the adsorbent particle diameter while at the same time keeping the pressure drop constant (that is ratio Lbed/Rp2 = const since ¨P ~ Lbed/Rp2). Such technique resulted in fat, “pancake” column designs (very short columns with large diameter) which are capable to significantly reduce the dimensions of the column and amount of the adsorbent. In the systems under consideration in case studies I and II, a detailed analysis has shown that in the range of particle radius, bed length and diameter and velocities used, a smaller diameter has been always the preferable choice. However, in case study III, a trade-off has been revealed and particle radius was employed as the optimization decision variable. 3.1.2. Effect of column length and diameter Simulation results indicate that as the length-to-diameter ratio (L/D) increases, the product purity increases while recovery passes through the maximum.
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3.1.3. Effect of feed and purge gas pressures An increase in the feed pressure (for a constant amount of feed) imposes an increase in product purity and recovery due to the type of isotherm - adsorbent capacity increases as the pressure increases. On the other hand, an increase in the feed pressure leads to an increase in power needed for compression. To take advantage of potential opportunities (in terms of improving product purity and recovery) offered by complex cycle designs it is necessary to find the optimal feed pressure which ensures feasible pressure equalization steps and co-current depressurization with purge. In other words, to effectively use void gas in the column, the length of unused bed (LUB) has to be high enough to adsorb strong adsorptive components moving towards the end of column during co-current depressurization(s). This ensures that the product leaving the column is completely pure and can be used to repressurize and purge other columns. High LUB can be achieved by interrupting the adsorption step long before the concentration front reaches the end. This can be practically achieved by: (i) decreasing the feed flowrate (in the case of constant length), or (ii) extending the column length (in the case of constant feed flowrate) or (iii) increasing the adsorbent capacity by increasing the feed pressure. In this work, the adsorbent productivity has been kept constant, and the feed pressure is used to control the LUB (since the feed is available at the high pressures, up to 50bar, as the product of steam methane reforming). 3.1.4. Effect of feed flowrate A higher feed flowrate leads to a decrease in product purity and increase in product recovery. In system I both the product purity and recovery are not significantly affected by the feed flowrate mainly due to the high LUB. 3.1.5. Effect of purgeítoífeed ratio The Purge-to-feed ratio (that is purge gas flowrate) is one of the most important operating variables in PSA whose increase leads to an increase in purity and a significant decrease in recovery. It has been employed as an optimization variable in case studies I and III. 3.1.6. Effect of number of beds and cycle design The number of beds and cycle design are important decision parameters because well designed multibed PSA processes offer significant advantages in terms of continuous production and feed consumption, increased product recovery and energy savings. This can be achieved by using co-current depressurization steps (to repressurize and purge other columns), while simultaneously carrying out a number of certain operating steps. For instance, it is possible to repressurize the column by using high pressure product from the adsorption step thus reducing investments in additional equipment such as storage tanks or compressors. The effect of cycle design and number of beds has been analyzed in case study I due to the scale of the process – hydrogen production is a typical large-scale process where a large number of beds and complex configurations are typically employed. On the other hand, air separation is used for small to medium scale production. 3.1.7. Effect of step times In the range of parameters used in case studies I and II step times have negligible effects on product purity and recovery (due to the high LUB, as it is explained earlier). However, in case study III, the effect on process performance is significant. For instance, as the duration of pressurization (by using feed stream) increases, the purity decreases but recovery increases. This can be justified by the increased amount adsorbed during the prolonged step duration, which lowers the purity. The effect on
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product recovery is rather complicated since decrease in purity also decreases recovery but at the same time the product quantity increases in larger rates and the overall effect is an increase in recovery. In addition, longer pressurization s increases the power requirements. Regarding the duration of the adsorption step, longer adsorption times leads to an increase in purity and decrease in recovery. Purge and blowdown step times have similar effects: as the times increase, product purity increases but recovery decreases (longer time allows more impurities to desorb while at the same time more product is loss during the step). The power requirements slightly increase since larger quantities of feed are needed to repressurize the bed. 3.1.8. Effect of carbon to zeolite ratio The results of the analysis agree well with the literature studies (Park et al, 2000): the product recovery increases as the zeolite fraction increase while purity passes through a maximum. In addition, it is noticed that this effect is more important at lower pressures.
4. Case studies Based on the above analysis, three different case studies have been studied. The focus in case study I is on the effect of number of beds and PSA cycle design, in case study II on the effect of carbon-to-zeolite ratio while in case study III all operating variables and column design have been optimised. The general form of the optimization problems being solved is presented in Figure 1.
Figure 1. – The mathematical definition of the optimization problems
All process parameters (base case column geometry, process and adsorption isotherm parameters) have been adopted from the work of Park et al, 2000 (case studies I and II) and Shin and Knaebel, 1988 (case study III). Six different PSA cycle configurations with one, two, four, five, and eight beds have been selected and analyzed. Configuration C1 includes no pressure equalization steps, C2 and C4 include one, C5a and C5b two, and C8 three pressure equalization steps. Configurations C4 and C5b include one additional co-current depressurization step during which the product gas is used to purge other column (the limiting factor is that impurities are not allowed to breakthrough and contaminate purged column). Configurations C4, C5a, C5b, and C8 are properly designed to continuously produce hydrogen (and consume the feed) and to use the part of the pure product from adsorption step to finally counter-currently repressurize other columns (to the feed pressure). Feasible sequence of all operating steps has been automatically generated according our previous work (Nikolic et al 2006).
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The general optimization problems (presented in Figure 1) have been solved by using gPROMS implementation of reduced sequential quadratic programming algorithm and the orthogonal collocation on finite elements of 3rd order with 20 elements have been used to discretize the spatial domain. The typical size of the NLP problem was about 90,000 variables and the CPU time to reach the optimal solution varied from 13 to 50 hours depending on the complexity of the problem and the initial guesses used. 4.1.Case study I: Hydrogen recovery from SMROG The objective is to maximize product recovery for given minimum requirements in product purity (99.99%) while optimizing purge-to-feed ratio (0.5−2.5)*, feed pressure (15-30bar), L/D ratio (3-20) and gas valve constants (during blowdown and pressure equalization steps). All studies have been carried out keeping the cycle time, column volume, and adsorbent productivity constant. This way it was possible to analyze the separation quality for a given minimum purity and different process designs which process the same amount of feed in the same period of time. A comparison of the results between the base case (L/D ratio=5, purge-to-feed ratio=1, feed pressure=25bar, and base case gas valve constants) and the optimized case is presented in Figure 2.
Figure 2. – Optimization results (Case study I)
The results show that product recovery is improved by 7-38% of comparing to the base case design. An interesting result is that there are no significant differences in the process performance of configuration C4 compared to C5a, and C5b compared to C8. Although they include a lower number of beds and one pressure equalization step less, they employ a co-current depressurization step to purge other columns, which results in a significant effect of the process performance. In addition, the optimal feed pressure in C4 and C5b is higher compared to C5a and C8, respectively, due to the larger amount of gas needed to purge compared to the amount of gas spent in the last pressure equalization. This fact may be the limiting factor if the feed is not available at high enough pressure. However, these two effects are strongly depend on the system under consideration and it might not always possible to exploit them. *
the values in the parenthesis indicate upper and lower bounds in the optimization
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4.2. Case study II: Hydrogen recovery from SMROG (double layer) Two scenarios have been analyzed: a) maximization of product recovery for given minimum purity (99.99%) while optimizing carbon-to-zeolite ratio (0-1), and b) maximization of purity for given minimum recovery (30%) while optimizing carbonto-zeolite ratio (0-1). Two adsorbent layers and the same base case parameters as in the case study I (configuration C1) have been used. In case a) the maximal recovery is 40.38% and carbon-to-zeolite ratio 0.54. In case b) the maximal purity is 99.999%, recovery 41.29% and carbon-to-zeolite ratio 0.39. 4.3. Case study III: Nitrogen production from air The objective is to minimize power consumption for given minimum requirements in product purity and recovery while optimizing the feed pressure (300í600kPa); the feed flowrate (0.001í0.003m3STN); purge-to-feed ratio (0.5í2.0); step times for constant cycle time such blowdown (10í20s), adsorption (10í20s; particle radius (0.2í1.5mm); column length-to-diameter ratio (5í15) for constant column volume. ), It should be noted that purge time is calculated based on the total cycle time. Configuration C1 has been used and pressurization is done co-currently by using the feed stream. The optimization indicate a product purity of 99.99%, recovery of 5.06%, length-todiameter ratio 5, purge-to-feed ratio 0.85, feed pressure 3.5bar, feed flowrate 2.67E2m3STN/s, adsorption time 10.17s, blowdown time 15s and particle size 1.5mm.
5. Conclusions A systematic optimization framework for complex PSA systems has been developed. The results clearly indicate the benefits (in terms of product purity, recovery, and power requirements) that can be achieved by using the proposed approach. Future work will focus on applications in large-scale industrial processes involving complex multicomponent gas separations.
6.Acknowledgments Financial support from PRISM EU RTN (Contract number MRTN-CT-2004-512233) is gratefully acknowledged.
References P.C. Wankat, 1987, Intensification of sorption processes, Ind. Eng. Chem. Res., 26, 8, 1579. H.S. Shin, K.S. Knaebel, 1988, Pressure swing adsorption: An experimental study of diffusioninduced separation, AIChE J., 34, 9, 1409. S. Nilchan, C.C. Pantelides, 1998, On the optimisation of periodic adsorption processes, Adsorption, 4, 113. J.H. Park, J.N. Kim, S.H. Cho, 2000, Performance analysis of four-bed H2 process using layered beds, AIChE J., 46, 4, 790. W.E. Waldron, S. Sircar, 2000, Parametric study of a pressure swing adsorption process, Adsorption, 6, 179. L. Jiang, L.T. Biegler, V.G. Fox, 2003, Simulation and optimization of pressure-swing adsorption systems for air separation, AIChE J., 49, 5, 1140. L. Jiang, L.T. Biegler, V.G. Fox, 2004, Simulation and optimal design of multiple-bed pressure swing adsorption systems, AIChE J., 50, 5, 2904. P. Cruz, F.D. Magalhaes, A. Mendes, 2005, On the optimization of cyclic adsorption separation processes, AIChE J., 51, 5, 1377. D. Nikolic, M.C. Georgiadis, E.S. Kikkinides, 2006, Modelling of multi-bed pressure swing adsorption systems, 17th European symposium on computer aided process engineering, Computer-aided chemical engineering, 24, 159.
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Multi-Objective Design of Multipurpose Batch Facilities Using Economic Assessments Tânia Rute Pintoa, Ana Paula F. D. Barbósa-Póvoab and Augusto Q. Novaisa a b
Dep. de Modelação e Simulação, INETI, Lisboa, Portugal Centro de Estudos de Gestão do IST, IST, Lisboa, Portugal
Abstract This paper deals with the design of multipurpose batch facilities considering economic aspects. Like in almost facilities this type of problem involves the maximization of the total revenue as well as the minimization of the total cost. The best way to deal with these two goals simultaneously is either to combine them into a single criterion (e.g., profit) or to define the efficient frontier which offers the optimal solutions by multiobjective optimization. In this work the latter approach, while more elaborate, was adopted, since the exploration of this frontier enables the decision maker to evaluate different alternative solutions. In this paper the proposed model addresses this problem and presents the identification of a range of optimal plant topologies, facilities design and storage policies that minimize the total cost of the system, while maximizing the production, subject to total product demands and operational restrictions. An example is used to show the methodology application to the design of multipurpose batch facilities. Keywords: Design, Scheduling, Multipurpose, Multi-objective, RTN
1. Introduction In multipurpose batch facilities, a wide variety of products can be produced via different processing recipes by sharing all available resources, such as equipment, raw material, intermediates and utilities. Like most real-world problems, the design multipurpose batch facilities involves multiples objectives and most of the existing literature on the design problem, has been centred on a mono-criterion objective (Barbosa Povoa, 2007). However, some works have been appearing recently addressing such problem. Dedieu et al. (2003) developed a two-stage methodology for multi-objective batch plant design and retrofit, according to multiple criteria. A master problem characterized as a multiobjective genetic algorithm defines the problem design and proposes several plant structures. A sub-problem characterized as a discrete event simulator evaluates the technical feasibility of those configurations. Later on, Dietz et al. (2006) presented a multicriteria cost-environment design of multiproduct batch plants. The approach used consists in coupling a stochastic algorithm, defined as a genetic algorithm, with a discrete event simulator. A multi-objective genetic algorithm was developed with a Pareto optimal ranking method. The same author proposed the problem of the optimal design of batch plants with imprecise demands using fuzzy concepts (2008). The previous work of the same authors on multi-objective using genetic algorithms was extended to take into account simultaneously maximization of the net value and two performance criteria, i.e., the production delay/advance and flexibility. Also, Mosat et al. (2007) presented a novel approach for solving different design problems related to single products in multipurpose batch plant. A new concept of super equipment is used and requires an implicit definition of a superstructure. Essentially the optimization is
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made on the transfers between different equipment units in a design. The Pareto optimal solutions are generated by a Tabu search algorithm. Therefore, the multi-objective optimisation is still a modelling approach that requires further study when applied to the design of batch plants. In this way the resulting models would be able to act as potentially powerful decision making tools where different decisions are accounted for. Through the values of different objectives at the Pareto-optimum surface, decision makers will be able to select any solution depending on how much one objective is worth in relation to the other. In this work, the detailed design of multipurpose batch plants proposed by Pinto et al. (2003), where a RTN representation is used and a single mono-criterion objective was considered, is extended to include more than one economic objective. A multi-objective approach based on the H-constraint is explored. This method presents as an advantage the fact that it can be used for any arbitrary problem with either convex or non convex objective spaces. The final results allows the identification of a range of plant topologies, facilities design and storage policies associated with a scheduling operating mode that minimises the total cost of the system, while maximizing the production, subject to total product demands and operational restrictions. An example is solved to test the model applicability where different situations are evaluated.
2. Design Problem The optimal plant design can be obtained by solving the following problem: Given: x Process description, through a RTN representation; x The maximal amount of each type of resource available, its characteristics and unit cost; x Time horizon of planning; x Demand over the time horizon (production range); x Task and resources operating cost data; x Equipment and connection suitability; Determine: x The amount of each resource used; x The process scheduling; x The optimal plant topology as well as the associated design for all equipment and connectivity required. A non-periodic plant operating mode defined over a given time horizon is considered. Mixed storage policies, shared intermediated states, material recycles and multipurpose batch plant equipment units with continuous sizes, are allowed. Based on the above problem description a model was developed using the RTN representation and considering the discretization of time. N
¦c x
Maximize Z
j
j
j 1
N
s. t.
¦a
ij
x j d bi
i 1, 2,...M ;
j 1
xj t 0
j 1, 2,..., N
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3. Multi-objective optimization Generically the models considered have a clear, quantitative way to compare feasible solutions. That is, they have single objective functions. In many applications single objectives realistically model the true decision process. Decisions become much more confused when the problem arises in a complex engineering design, where more than one objective may be relevant. For such cases, as referred above, a multi-objective optimization model is required to capture all the possible perspectives. This is the case of the design of batch plants where two objectives are under consideration – one that maximizes the revenues (that is, production) and the other that minimizes the cost. The multi-objective optimization can be generically represented as: Maximize f m ( x)
m 1, 2,..., M ;
s. t. g j ( x) d 0 hk ( x) ( L) i
x
j 1, 2,...J ;
0
k
1, 2,..., K ;
(U ) i
i 1, 2,..., n.
d xi d x
where M defines the number of the objective function f(x) = (f1(x), f2(x),…,fm(x))T . Associated with the problem there are J inequalities and K equality constraints. A solution will be given by a vector x of n decision variables: X=(x1, x2 ,…, xn-1 , xn)T However, no solution vector X exists that maximizes all objective functions simultaneously. A feasible vector X is called an optimal solution if there is no other feasible vector that increases one objective function without causing a reduction in at least one of the other objective functions. It is up to the decision maker to select the best compromising solution among a number of optimal solutions in the efficient frontier. There are several methods to define this efficient frontier, but one of the most popular methods is the H-constraint, which is very useful since it overcomes duality gaps in convex sets. Using the H-constraint, the above formulation becomes: Maximize f u ( x) f m ( x) d H m m 1, 2,..., M and m z u
s. t.
g j ( x) d 0 hk ( x) ( L) i
x
where
Hm
j 1, 2,....; k
0
1, 2,..., K ;
(U ) i
d xi d x
represents an upper bound of the value of
f m . This technique suggests
handling one of the objectives and restricting the others within user-specified values. First the upper and lower bounds are determined by the maximization of the total revenue and minimization of the cost, respectively. Next, varying H, the optimization problem (maximization) is implemented with the objective function being the total revenue and the cost being a constraint varying between its lower and upper bounds.
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4. Example The presented method is applied to the design of a multipurpose batch plant that must produce [0; 170] tons of products S5, [0; 166] tons of S9 and S10, [0; 270] tons of products S6 and [0; 143] tons of products S11. Three raw materials, S1, S2 and S7, are used over the horizon of 24 h. The products S5 and S6 are both intermediate and final products. There are six main reactors (R1 to R6) available, and nine dedicated vessels. In terms of equipment suitability, only reactors R1 and R2 may carry out two processing tasks, T1 and T2, while each storage vessel and reactors R3, R4, R5 and R6 are only dedicated to a single state/task. Task T1 may process S1 during 2 hours in R1 or R2; task T2 may processes S2 during 2 hours in R1 or R2; task T3 may process during 4 hours in R3; T4 processes during 2 hours in R4; Task T5 may process S6 during 1 hour to produce the final product 0.3 of S11 and 0.7 of S8 in R5, and finally Task T6 processes during 1 hour S8 in reactor R6 to produce the final products S9 and S10. The connections capacity range from 0 to 200 [m.u./m2] at a fix/variable cost of 0.1/ 0.01 [103c.u.]. The capacity of R1, R2, R5 and R6 range from 0 to 150 [m.u./m2] while the others range from 0 to 200 [m.u./m2] (where m.u. and c.u. are, respectively, mass and currency units). The process resource-task-network representation is visible in figure 1.
Figure 1- The RTN process representation. 1800000 1600000
V2
V2
C
V1
E
B
V1
1400000 R1
Revenues
1200000
R1
R4
R3
V6 R3
1000000
V2
V1
E
V6
R4
D V5 R1
V2
A
D
800000
C
V2
V7
R4 V4
V6 R3
V1
R5
R6
V5
V9 V11 V10
600000
R1
R3 V5
B
V7 R1
400000
R4 R3
V6 V5
200000
R5
R6
V11
V10
V9
A 0 0
200
400
600
800
1000
1200
1400
1600
1800
2000
Costs
Figure 2- Efficient frontier for the optimal design of the multipurpose batch plant.
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The problem described is solved and the efficient frontier obtained shown in figure 2. This forms the boundary of the feasibility region defined by the values of the two objectives. Every efficient point lies along the depicted boundary because no further progress is possible in one objective function without degrading the other. This is an alternative way to plot solutions of multi-objective models. For the case under study the objective value space is represented with axes for the cost and revenue objective functions. In the efficient frontier are visible some optimal plant topologies. The points A, B, C, D and E represent points where there is a topology change caused by the addition of one or more main equipment units to the previous topology. In figure 2 are shown these changes of topology and the respective final products. In table 1 are presented, for each point assigned, the final products and their quantity. In table 2 is presented the optimal design for the main equipment for each assigned point, in terms of capacities. For the point marked E, the optimal scheduling is shown in figure 3. It is visible the multi-task characteristics associated to equipment R1. This equipment performs not only T1 but also T2. All the other processing equipment units are single task dedicated. Table 1 – Quantities produced for each final product. A
B
C
D
E
S5
76.2
-
-
170
170
S6
-
155.5
258.6
270
270
S9
-
-
-
7.6
145.1
S10
-
-
-
7.6
145.1
S11
-
-
-
6.5
124.4
Table 2 – The optimal design for the main equipment. A
B
C
D
E
R1
76.2
93.3
103.4
141.2
120.3
R3
76.2
62.2
103.4
141.2
180.5
R4
-
155.5
129.3
140.5
159.1
R5
-
-
-
21.8
138.2
R6
-
-
-
15.3
96.8
V4
-
-
-
-
120.3
V5
76.2
-
51.72
170
170
V6
-
155.5
258.6
270
270
V9
-
-
-
7.6
145.1
V10
-
-
-
7.6
145.1
V11
-
-
-
6.5
124.4
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T6 T6 T6 R6 96.8 96.8 96.8
T5 T5 T5 R5 138.2138.2138.2
T4 159.1
R4 T3
R3 R1
0
2
4
T2
T2
T2
120.3
120.3
120.3
6
8
10
T4 159.1
T3
180.5 T1
180.5 T1 T1
95.5
12
T4 159.1
14
95.5
16
95.5
18
20
22
24
Figure 3 – The optimal scheduling for the plan topology assigned by E.
5. Conclusions The plant topology, equipment design, scheduling and storage policies of multipurpose batch plants are addressed in this paper, considering production maximization with costs minimization - a multi-objective optimization. The model was developed as a MILP model and the multi-objective method used in this work was the H-constraint. The efficient frontier obtained defined the optimal solutions allowing the identification of a range of plant topologies, facilities design and storage policies that minimize the total cost of the system, while maximizing production, subject to total product demands and operational restrictions. The proposed methodology allows the decision makers to evaluate the relationship between revenue and cost of given batch facilities, thus enabling them to develop an adequate business strategy.
References A.P.F.D. Barbosa-Póvoa, 2007, A Critical review on the design and retrofit of batch plants, Computers and Chemical Engineering, 31,833-855. A. Dietz, A. Aguilar-Lasserre, C. Azzaro-Pantel, L. Pibouleau, S. Domenech, 2008, A fuzzy multiobjective algorithm for multiproduct batch plant: Application to protein production, Comp. Chem, Eng, 32, 292-306. A. Dietz, C. Azzaro-Pantel, L. Pibouleau, S. Domenech, 2006, Multiobjective optimization for multiproduct batch plant design under economic and environmental considertions, Comp. Chem, Eng, 30, 599-613. S. Dedieu, L. Pibouleau, C. Azzaro-Pantel, S. Domenech, 2003, Design and retrofit of multiobjective batch plants via a multicriteria genetic algorithm, Comp. Chem, Eng, 27, 17231740. A. Mosat, L. Cavin, U. Fisher, K. Hungerbühler, 2007, Multiobjective optimization of multipurpose batch plants using superequipment class concept, Comp. Chem, Eng, article in press. T. Pinto, A.P.F.D. Barbosa-Póvoa, A.Q. Novais, 2003, Comparison Between STN, m-STN and RTN for the Design of Multipurpose Batch Plants, Computer Aided Chemical Engineering, Vol. 14, Editores A. Kraslawski e I. Turunen, Elsevier, 257-262.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
277
Oil products pipeline scheduling with tank farm inventory management Susana Relvasa,c, Henrique A. Matosa, Ana Paula F.D. Barbosa-Póvoab, João Fialhoc a
CPQ-IST, DEQB, Av. Rovisco Pais 1049–001 Lisboa, Portugal CEG-IST, DEG, Av. Rovisco Pais 1049–001 Lisboa, Portugal c CLC, EN 366, km 18, 2050 Aveiras de Cima, Portugal b
Abstract The core component of the oil supply chain is the refinery, where the received oil batches are managed to feed the crude distillation units in proportions that give origin to the desired cuts and products. However, the oil supply and the oil products’ distribution have to answer in agreement to their predicted demands. For this reason, there is the need to build decision support tools to manage inventory distribution. This work focuses on the development of a MILP model that describes the oil products distribution through a pipeline that connects one refinery to one tank farm. In order to supply the local market, the model represents the interaction between the pipeline schedule and the internal restrictions at the tank farm. Real world data from CLC (a Portuguese company) validate the model formulation. Keywords: Oil products’ pipeline, inventory management, MILP, continuous time
1. Introduction Pipelines have widely been established as safe and efficient equipments to transport oil and oil products, either in short or long distances and in a cost effective way. However, the benefit will be higher if the relation between pipeline and tank farm is considered as a whole in a decision support tool to the oil products distribution. The works published so far in this area have a large focus on pipeline details and schedule, relying both in discrete (Rejwski and Pinto (2003), Magatão et al. (2004)) and continuous (Cafaro and Cerdá (2004, 2007) and Rejowski and Pinto (2007)) MILP formulations. Nevertheless, the storage availability for products reception at the tank farm, the inventory management issues and the clients’ satisfaction are important tasks that have impact on the optimal pipeline schedule. These issues have been previously addressed in the works by Relvas et al. (2006, 2007). Based on that work, this paper proposed a new MILP model that disaggregates the storage capacity of each product in physical tanks. Two parallel formulations for this problem are introduced and discussed, using as case study the real world scenario of CLC - Companhia Logística de Combustíveis. CLC distributes refinery’s products in the central region of Portugal.
2. Problem description and model representation Figure 1 resumes the operating system that comprises an oil products’ pipeline that pumps from a refinery to a tank farm. This distribution centre is located in a strategic local market. Each tank has a fixed product service and the clients are supplied at the distribution centre with the respective products.
278
Clients
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Pipeline
Tank Farm Refinery
Figure 1 – Problem’s operating system
The main given parameters are: a) the pipeline volume, b) maximum and minimum flowrates, c) the products to be pumped and matrix of possible sequences, d) the tanks’ capacity and product’s service, e) settling period by product; and as scenario data: f) the time horizon extent and number of days, g) the maximum number of batches to be pumped, h) the initial inventory by product and by tank, i) the state of each tank and the initial settling time of each tank (if applicable, otherwise set to zero), j) the daily clients’ demands and k) the planned pipeline stoppages, if any. The problem’s solution will comprise two parts: the pipeline schedule and the tanks’ inventory management. The pipeline schedule includes products’ sequence, pumping flowrates, batches’ volumes, timing issues and pipeline stoppages. The inventory management includes pipeline inputs, settling periods and outputs by product and tank. The problem’s objective is to optimize results under an operational objective function that combines several goals. Each is expressed by one dimensionless and normalized term (to comprise values between 0 and 1) and will be added to the function with a plus (if minimizing) or minus sign (if maximizing) and with a weight. The terms considered minimize the balance between the tank farm inputs and outputs (such that the flowrate is also minimized and imposing that this balance is positive), maximize the pipeline usage and maximize the product whose final inventory has the lowest value. The model formulation is based on the model proposed by Relvas et al. (2006, 2007), modified to account for individual tanks. The main characteristics of the model are: 1. Continuous time and volume scales – The model considers a single event to build the continuous time scale, which corresponds to the time when each batch has finished to be pumped to the pipeline. Additionally, this event is also used to update the batches’ volumetric position inside of the pipeline, referred to an axis with origin in the refinery and end in the tank farm. 2. Daily clients’ demands – The forecast of the demands is provided in a daily basis, which is also implemented in the model formulation. For this purpose, it is built a binary operator that transforms discrete time information in to continuous time. 3. Sequence of products – This is one of the main results of the pipeline schedule. However, it highly influences the model performance. For this reason, it has been approached as fixed or mixed sequences. These basically repeat a cycle unit of products. The main difference is that some products may be concurrent for some positions, which leads to mixed sequences or have fixed positions, fixed sequence.
3. Tanks’ Representation A tank farm is usually constituted by several tanks, which may have a fixed product’s service, i.e., they are always used for the same product, due to product quality conservation and tank’s calibration system, as well as other technical features.
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Additionally, the fact that the product has to settle after discharge from the pipeline and before being available for clients implies that at any moment there is at least one tank receiving product and another one available for clients. This will be part of a rotation scheme between tanks of the same product. The mathematical representation of this operational procedure has a main decision to take: either to represent the tanks in an aggregated manner or include each tank as a model instance and obtain additionally as model result the alternation schemes for all products. For the later, such detail level at the mathematical representation results in higher model size due to a new set, new variables (either continuous and binary, expanding the decision tree size) and higher number of equations. Three key aspects have to be considered when modeling individual tanks: i) the allocation of tanks to products, ii) the tanks’ operational cycle and iii) the initialization data. 3.1. Allocation of tanks to products This work will compare the model proposed by Relvas et al. (2006, 2007), which considers an aggregated tanks’ formulation, with a new formulation for the disaggregated representation. The first will be from now on referred as Aggregated Tanks’ Formulation (ATF), meanwhile the last will be referred as Disaggregated Tanks’ Formulation (DTF). For the DTF strategy a set of tanks (t) is defined such that each tank is referred as the tank t of product p. The variables defined on p are directly disaggregated in t. Therefore, the relation product-tank is implicit in the formulation. 3.2. Tanks’ operational cycle The major challenge in the model formulation is the representation strategy adopted for the tank cycle. Normal operation considers that each tank is filled up completely before settling. After the settling period, the tank is released for clients’ satisfaction, until it is totally empty. These procedures are usually related to the product quality, where it isn’t desired to mix products from several different batches. This implies that they are formulated four states for each tank: i) full, ii) delivering product to clients, iii) empty and iv) being filled up with product from the pipeline. Each one of the states has a corresponding state variable, related to tank inventory (ID), and has to be activated or deactivated whenever a boundary situation occurs (Eq. 1): the maximum (UB) and minimum (LB) capacities of the tank are met. For this purpose, the state variable (y, binary) will have to be activated whenever both inequalities (‘’ and ‘’) hold (Eq. 2):
y 1 o ID UB
(1)
y 1 o ID d UB ID t UB
(2)
These occurrences are formulated using big-M constraints, which require the definition of a tolerance to identify each state (within the given tolerance between the desired value and the variable value, the state variable is activated). Moreover, each variable that occurs in these constraints is now modeled as an integer variable (tank inventory, input and output volumes), enabling the definition of a tolerance lower than 1. The definition of a full or empty tank is applied for specific cases (tank inventory is at its limits). The remaining states are exclusive at any moment, i.e., each tanks is always either in a filling up cycle or in an emptying cycle (idle time intervals may occur in both cycles). Finally, whenever the tank is full and the corresponding state variable is activated, it also controls the settling period accomplishment.
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3.3. Initialization data A new set of data has now to be included in each model instance: the initial inventory of each tank and its current state. The initial state is crucial either in the model performance as well as on the optimal resources allocation. In a real world scenario, this data is provided by the prior time horizon.
4. Results The implementation will consider a real world example taken from CLC – Companhia Logística de Combustíveis, a Portuguese company operating in the distribution of oil products. This company transports six different products from a single refinery located in the south (P1 to P6), and distributes them in the central area of Portugal. The total number of tanks is 29 and they all have specific product service. The time horizon considered will cover 7 days of operation, taking as scenario the data from the first week of April 2006: initial inventories at each tank, initial contents of the pipeline and current state of each tank and, if settling, the current settling time. Additionally, they were considered the real clients’ demands occurred in that period. In order to compare the results obtained through the mathematical model with the real occurrences, it will be used the same sequence of products to pump that was verified within that period. The flowrate will be considered to vary between 450 and 650 vu/h (volumetric units/h). The model was implemented in GAMS 22.4 and solved with CPLEX 10.1, on a Pentium D820 with 2 GHz RAM. The stopping criteria were either the optimal solution or 2 hours of computation. CPLEX’s polishing option was used for 30 seconds. The disaggregated formulation was also run without specifying the initial states for tanks, leaving open their definition (DTFnoinit). Table 1 resumes the model performance for each strategy, as well as the value of the objective function obtained from the real occurrences at CLC. They are also indicated the relaxed solution and the amount of time that was spent to find the optimal solution, but without proving optimality. It can be observed the model size increase between a model with ATF and the corresponding DTF. The number of binary variables increased more than 400% for the same scenario. The model size has a large impact in CPU effort. Table 1 – Model performance for the proposed methodologies Formulation
“CLC”
ATF
DTF
DTFnoinit
# Continuous Variables
-
1736
2907
2994
# Binary Variables
-
414
2098
2156
# Equations
-
2889
6178
6178
# Nodes Explored
-
937
298784
1806494
# Iterations
-
6712
3464991
30364688
CPU time (s)
-
1.359
1096.578
7230.078
Time to find the optimal solution (s)
-
1.359
5.50
6482.00
Objective Function
-1.896985
-2.042726
-1.968652
-2.042726
Relaxed solution
-
-2.043577
-2.043577
-2.043577
Relative Gap (%)
-
0.00
0.00
0.04
Oil Products Pipeline Scheduling w ith Tank Farm Inventory Management
281
Regarding the optimal solutions obtained versus CPU effort, meanwhile in the ATF the optimal solution is found in less then 2 s, the DTF took about 18 min to prove optimality. However, the optimal solution was obtained relatively early in the search tree analysis (§ 5 s of computation), which means that the majority of the CPU effort is used to prove optimality. It should also be pointed out that the relaxed solution is equal between the three strategies, representing a good accuracy between formulations. Table 2 resumes the operational results. All solutions present a lower medium flowrate when compared to CLC’s occurrences. The DTF solution leads to a pipeline stop (without interfaces) and reducing pipeline usage. CLC verified both high flowrate and positive balance in inventory, increasing the final inventory. The results on minimum inventories are similar for all strategies, being P3 the product with lower levels. From the DTFnoinit results they were verified 8 different initial states. The reason why happens a pipeline stop in the DTF is due to P2 having all tanks satisfying clients at the moment when it is necessary to store a new batch. However, the initial state is given by CLC’s real occurrences, which were not provided by an optimization model. Table 2 – Model performance for the proposed methodologies Formulation
“CLC”
ATF
DTF
DTFnoinit
Medium flowrate (vu/h)
521.2
487.34
507.32
487.34
'Inventory (vu)
+5361
+31
+31
+31
Pipeline usage (%)
94.05
94.05
90.34
94.05
Final inventory level (%)
51.16
48.54
48.54
48.54
Minimum final inventory (%, product)
32.67 (P3)
32.53 (P3)
32.53 (P3)
32.53 (P3)
Minimum overall inventory (%, product)
32.67 (P3)
32.53 (P3)
30.54 (P6)
32.53 (P3)
-
-
0
-
# Interfaces during pipeline stops
The major benefit (balanced with the model complexity trade-off) from the DTF is the allocation of arriving batches to available tanks. At any moment it is known the state of a tank, defining precisely the available storage capacity and having impact in the volume and pumping rate of each batch on the pipeline schedule. If the results from the ATF are fed to the DTF, the model may turn infeasible, showing that the detail at the individual tank level is critical to define the pipeline schedule. This would be overcome using an iterative procedure where at each iteration an integer cut would be added to the DTF, eliminating infeasible solutions at the ATF level from the DTF search space. Figure 2 represents the inventory profiles for each product and strategy. It is visible the resemblance between reality and model formulations. The main differences are due to batches volumes transported and pumping rate, because both the sequence of products and outputs are equal between strategies.
5. Conclusions and Future Work This work presented a new model formulation that coordinates pipeline transportation with tank farm inventory management, including individual tanks’ details. The obtained model generates within the solution the rotation scheme for tanks that allows the verification of all required tank farm operations.
282
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P1
ATF
DTF
DTF_noinit
100%
Inventory (%)
40%
DTF_noinit
60% 40% 20%
0%
0% 0
24
48
CLC
P3
72 Time (h)
96
ATF
120
DTF
144
168
DTF_noinit
0
80% Inventory (%)
80%
40%
48
CLC
100%
60%
24
P4
100%
Inventory (%)
DTF
80%
60%
20%
72 Time (h)
96
ATF
120
DTF
144
168
DTF_noinit
60% 40%
20%
20%
0%
0%
0
24
48
CLC
P5
72 Time (h)
96
ATF
120
DTF
144
168
DTF_noinit
0
24
48
CLC
P6
72 Time (h)
96
ATF
120
DTF
144
168
DTF_noinit
100%
100% 80%
80% Inventory (%)
Inventory (%)
ATF
100%
80% Inventory (%)
CLC
P2
60% 40% 20%
60% 40% 20%
0%
0% 0
24
48
72 Time (h)
96
120
144
168
0
24
48
72 Time (h)
96
120
144
168
Figure 2 – Inventory profiles for each strategy and by product
The main achievement of the proposed model is to provide a detailed tank farm inventory management, looking into the sets of tanks of each product (rotation scheme). As future work it is proposed to improve the tanks’ cycle formulation and develop a set of examples to test the behavior of the Disaggregated Tanks Formulation. Additionally, it is proposed to develop a decomposition strategy to link subsequent time horizons.
6. Acknowledgments The authors gratefully acknowledge financial support from CLC and FCT, grant SFRH/BDE/15523/2004.
References R. Rejowski, Jr., J.M. Pinto, 2003, Comp. & Chem. Eng., 27, 1229 L. Magatão, L.V.R. Arruda, F. Neves, Jr, 2004, Comp. & Chem. Eng., 28, 171 D.C. Cafaro, J. Cerdá, 2004, Comp. & Chem. Eng., 28, 2053 S. Relvas, H.A. Matos, A.P.F.D. Barbosa-Póvoa, J. Fialho, A.S. Pinheiro, 2006, Ind. Eng. Chem. Res., 45, 7841 S. Relvas, H.A. Matos, A.P.F.D. Barbosa-Póvoa, J. Fialho, 2007, Ind. Eng. Chem. Res., 46, 5659 D.C. Cafaro, J. Cerdá, 2007, Comp. & Chem. Eng., doi:10.1016/j.compchemeng.2007.03.002 R. Rejowski Jr, J.M. Pinto, 2007, Comp. & Chem. Eng., doi:10.1016/j.compchemeng.2007.06.021
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Methodology of conceptual process synthesis for process intensification Ben-Guang Rong, Eero Kolehmainen, Ilkka Turunen Lappeeranta University of Technology, Fin-53851 Lappeenranta, Finland
Abstract A systematic method based on conceptual process synthesis for process intensification is presented. Starting from the analysis of relevant physical and chemical phenomena, the various possible concepts and principles for the processing tasks are investigated. This includes the introduction of the new concepts and principles through the variations and manipulations of the key process phenomena. The various partial solutions for process and equipment intensification are then generated through phenomena-based reasoning. Next, the feasible conceptual process alternatives are synthesized by combining the generated partial solutions. The example for the intensification of the peracetic acid production process was demonstrated, which particularly illustrated the intensification of the conventional batch process to the on-site microprocess through microreactor technology. Keywords: Methodology, Conceptual process synthesis, Process intensification, Process phenomena, Microstructured devices
1. Introduction Process Intensification (PI) is considered as one of the main current trends in process engineering. It is defined as a strategy for achieving dramatic reductions in the size of a chemical plant at a given production volume (Ramshaw C., 1983). As a consequence, one major approach of Process Intensification is pursuing the multifunctional and microstructured devices for the processing tasks, which are conventionally implemented in the traditional unit operations. Needless to say, to achieve the multifunctional and microstructured devices, we need new concepts and principles other than the traditional unit operations concepts for implementing the processing tasks. On the other hand, process synthesis and conceptual design, i.e. Conceptual Process Synthesis (CPS) has been established as a major discipline in Process Systems Engineering for the optimal design of process systems. Process Synthesis is usually based on the systematic methods for the generation of conceptual process alternatives. Numerous cases in process synthesis have shown that the true efficiency and performance of the manufacturing process are primarily determined by the decisions made at the conceptual design stage on the concepts, principles and mechanisms of the process systems. It is so that the true innovative and inventive designs very often come from the unique understandings and insights to the design problems concerning process concepts, principles and mechanisms. The innovative character of Process Intensification is in nice harmony with the objectives of Process Systems Engineering (Moulijn J.A. et al., 2006). It is so that Process Intensification needs the very front-end creativity for the generation of the novel concepts and principles for the processing tasks. Such novel concepts and principles are also the key elements in process synthesis for the generation of the innovative and inventive designs in terms of systems synthesis and equipment design.
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To this sense, conceptual process synthesis plays a key role and constitutes a major approach for process intensification to achieve the multifunctional and microstructured devices. In this work, a systematic methodology based on conceptual process synthesis for process intensification is presented.
2. The Methodology of conceptual process synthesis for PI The methodology of conceptual process synthesis for process intensification is focused on the generation of the novel concepts and techniques for the processing tasks. The methodology of conceptual process synthesis for process intensification is illustrated in Figure 1.
Process information
Step 1: Selection of main rate-determining and bottleneck processing steps and tasks
Step 2: Identification of the relevant process phenomena in key steps and tasks Step 3: Characterization and analysis of process phenomena Step 4a: Concepts for variation of the analysed process phenomena
Step 4b: Principles for manipulation of process phenomena
Step 5: Multiscale variations and manipulations of the phenomena
Step 6: Partial solutions for process and equipment intensification
Step 7: Combination of the partial solutions for process and equipment synthesis
Step 8a: Phenomena related tasks implemented in Microscale Step 9a: New intensified microstructured devices
Step 8b: Phenomena related tasks implemented in different scales Step 9b: New intensified hybrid devices
Step 8c: Phenomena related tasks implemented in Mesoscale Step 9c: New intensified Mesoscale process units
Step 10: Evaluation of technical feasibility
Figure 1.The methodology of conceptual process synthesis for process intensification
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For a chemical process, it is possible to identify a certain number of process phenomena which represent the key features and characteristics of the process. For example, chemistry and chemical reaction phenomena, materials phases and transport phenomena, phases behaviors and separation phenomena, etc. All these basic process phenomena concerning chemical reaction, mass transfer, heat transfer and fluid hydrodynamics are the fundamental information from which various processing concepts and principles (techniques) are generated for the processing tasks. These processing concepts and principles will principally determine the required process units and equipment for the manufacturing process. However, it must be indicated that for a specific phenomenon, there are very often several possible concepts or principles to deal with it. For example, different separation principles for a mixture separation. The feasible concepts and principles adopted will depend not only on the phenomenon itself, but also on the unique understanding and insights from the process engineers (designers). On the other hand, for a process or equipment intensification and design, it is unlikely that a single phenomenon is dealt with. The interactions and relationship among different phenomena are the real source for the generation of new concepts and principles for novel process and equipment. Moreover, to achieve novel process and equipment, the concepts and principles are concerned with various aspects of the process and equipment, may it be the catalyst or solvent employed, the internals of the equipment, the alternative energy form, the transfer mechanisms, the geometry of the equipment, etc. Therefore, a process phenomenon for process intensification must also consider various aspects of the process and equipment during the generation of the concepts and principles. Figure 2 illustrates the general characterization of a process phenomenon for PI which is concerned with the various aspects of the materials processing and the related elements for process and equipment intensification. Table 1 presents the associated attributes of each category for the characterization of a process phenomenon. Some commonly used principles for manipulation of process phenomena are presented in Table 2.(Rong et al., 2004).
Components and phases
Key variables
Energy sources
A Process Phenomenon for Process Intensification
Surface materials Operating modes
Flow patterns
Geometry
Facility medium
Figure 2. The characterization and related aspects of a process phenomenon for PI It is significant to notice that the concepts and principles to vary and manipulate any aspects of the phenomena will generate the corresponding partial solutions, from which the ultimate intensified process and equipment will be synthesized. Herein, the multiscale approach for variations and manipulations of the phenomena is emphasized. It means that the concepts and principles should be explored at all possible scales for the
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variations and manipulations of the phenomena. As a consequence, the generated partial solutions can be used to synthesize the intensified equipment in different scales. It can be expected that the combination of the partial solutions to synthesize the final process and equipment will not be straightforward; rather, there must be some conflicts and contradictions in the combination of the partial solutions. Therefore, at this stage, one needs some creative methods to remove or eliminate the encountered conflicts or contradictions. During the combination of the partial solutions, a major pivotal decision needs to be made is to determine at what scales to implement the processing tasks related phenomena. It can be microscale, or mesoscale or hybridscale (both microscale and mesoscale). Needless to say, it is the corresponding concepts and principles generated for the variations and manipulations of the processing tasks related phenomena that determine the scales of the intensified process and equipment. As a consequence, microscale, mesoscale or hybridscale devices and units are synthesized by the combination of the partial solutions. Thereby, the intensified microstructured devices, the intensified mesoscale process units, or the intensified hybridscale devices are obtained as the conceptual design alternatives from the conceptual process synthesis. The evaluation of PI results is often self-evident as long as the technical feasibility of the intensification concepts and principles can be verified. Nevertheless, once intensified process alternatives have been identified, the further detailed optimization can be performed. Table 1. The detail characterization to process phenomena for PI Phases+
Changes of variables Temperature Pressure Concentration Velocity Density Viscocity
Energy source
Geometry*
Surface material Metal Ceramic Plastics Chemical surface
L/G Gravity Geometry (1) L/S Centrifugal (Equipment) S/G Microwave Tank L Ultrasound Column G Electromagnetic Channel S Motor Tube S/L/G Heat transfer fluid Geometry (2) L1/L2 Magnetic field (Internals) L1/L2/G Reaction Geometry (3) L1/L2/S (Surfaces) + L-liquid, G-gas, S-solid, L1-Liquid phase 1, L2-Liquid phase 2 *Geometry (2): packings, plates, films, spray, uniform, specific structures, fiber Geometry (3): even, rough, porous, chemically/physically inert/active surface
Facility medium Catalyst Solvent Additive Membrane
Operate mode Static Rotating Moving Swing Spinning
Table 2. General principles for process phenomena manipulation. 1 2
Principles Enhance a favorable phenomenon
3
Attenuate an unfavorable phenomenon Eliminate a phenomenon
4
Combine several process phenomena
5
Separate phenomena
6
Mitigate the effect of a phenomenon by combing it with another Create a new phenomenon
7
Examples Enhance an oxidation reaction by using oxygen instead of air Decrease side-reactions by shortening residence time Eliminate an azeotropic behavior by adding a solvent in a distillation system Combine reaction and distillation into a reactive distillation External catalyst packages in reactive distillation Transfer reaction equilibrium limit by removing desired product immediately Create new phase interface for mass transfer
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3. Case study of peracetic acid process intensification Peracetic acid is the most widely used organic peroxy acid. It is a strong oxidizer, which could be used in disinfection and bleaching agent. Peracetic acid can be synthesized from acetic acid and hydrogen peroxide. The formation of peracetic acid takes place in the equilibrium reaction (1). In order to accelerate the reaction rate, acid catalyst is needed (Swern, D., 1970). Conventionally homogeneous sulphuric acid catalyst is used. The reaction scheme is shown in Eq. (1) CH3COOH + H2O2
H 2SO 4 m o CH3COOOH + H2O
(1)
Conventionally peracetic acid is produced in a tank reactor in the presence of homogeneous acid catalyst. In the process, sulfuric acid catalyst is first charged into the reactor, after which acetic acid and hydrogen peroxide are fed into the reactor. The mixture is heated up and equilibrium reaction (1) takes place. When homogeneous acid catalyst is used, separation of it from equilibrium mixture is carried out in a distillation column. When equilibrium is reached, sub-atmospheric pressure is drawn in the reactor. Vaporization of the reaction mixture begins. In the distillation column acetic acid, hydrogen peroxide and peracetic acid are separated from sulphuric acid catalyst (Swern, D., 1970). The simplified scheme of the conventional process is illustrated in Figure 3.
5
6
7 1 2 3
4
Figure 3. The scheme of the conventional process for producing peracetic acid. 1) Acetic acid, 2) Sulphuric acid, 3) Hydrogen peroxide, 4) Reactor, 5) Distillation column, 6) Distillate receiver, 7) Peracetic acid, acetic acid, hydrogen peroxide and water. In the conventional technology, the temperature range in production is 40 qC-60 qC due to safety reasons. Peracetic acid decomposes to oxygen and acetic acid in higher temperatures. However, higher temperature and higher initial concentrations of raw materials at optimal molar ratios increase the reaction rate and would lead to shortened residence time (Swern, D., 1970). Therefore, the major limits are identified for the conventional process in the reaction step, which is both rate-determining and equilibrium-limit. Moreover, it is also a bottleneck step in terms of inherent safety due to the exothermic reaction, the easier decomposition of peracetic acid and explosion. In order to carry out the reaction in higher temperatures and initial concentrations under controllable conditions, the continuously operated multi-channel reactor is taken into consideration. The continuous process contains a mixing step and a reaction step. Acetic acid and hydrogen peroxide are heated in heat exchangers and mixed in the mixing step. The equilibrium reaction takes place in the parallel reactor system. The scheme of the continuous process is depicted in Figure 4.
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Figure 4. Scheme of the continuous peracetic acid process with microreactors. In the parallel reactor system, the concept of a heterogeneous solid acid catalyst is applied. The phase of the catalyst is changed from liquid to solid. Using of heterogeneous catalyst to accelerate reaction rate enables the elimination of the distillation section described in the conventional process. The small-channel reactor is mechanically strong and it tolerates easily higher pressures than the conventional reactor. Furthermore, increased pressure eliminates the vaporization of the reaction mixture and therefore operation in higher temperatures and concentrations is safer than in conventional reactor. Heat transfer efficiency of the small channel reactor can be orders of magnitude higher than in conventional reactor. Since the reaction can not be considered as extremely fast, mixing step does not necessary require microscale application. However, in order to maximize the contact area between solid acid catalyst and the reacting mixture, microstructures in the catalyst section are beneficial. Variation and manipulation of phenomena result in the changes in phases (L ĺ L/S), process variables (TĹ, cĹ, pĹ) and geometry (tank, column ĺ multichannel, small scale channel, chemically active surface). The concept of the continuous reactor system offers potential to intensify the peracetic acid process.
4. Conclusions Process intensification needs the novel concepts and techniques for the processing tasks in the manufacturing process. At the same time, process intensification aims at the novel process and equipment to be synthesized based on the generated concepts and techniques. In this paper, a methodology of conceptual process synthesis for process intensification is presented. The methodology is focused on the generation of the novel concepts and techniques for the processing tasks by variations and manipulations of the identified key process phenomena. By doing so, various possible partial solutions for process intensification are obtained through varying and manipulating the process phenomena in a multiscale manner. Then, the conceptual process alternatives are synthesized by the combination of the generated partial solutions. A case study for the intensification of the peracetic acid process illustrated that the novel conceptual process alternative is achieved following the procedure in the methodology.
References J.A. Moulijn, A. Stankiewicz, J. Grievink, A. Gorak, 2006, Proceed. of ESCAPE16/PSE9, 29-37. C. Ramshaw, 1983, Chemical Engineer-London, 389, 13-14. B.-G. Rong, E. Kolehmainen, I. Turunen, M. Hurme, 2004, Proceed. of ESCAPE14, 481-486. D. Swern, 1970, Organic Peroxides, vol I, 61-64 and 337-484.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Process plant knowledge based simulation and design a
Jelenka B.Savkovic-Stevanovic, aSnezana B. Krstic, aMilan V.Milivojevic, b Mihailo B.Perunicic a
Department of Chemical Engineering, Faculty of Technology and Metallurgy, The University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia, e-mai:savkovic@ tmf. bg.ac.yu,
[email protected],
[email protected] Faculty of Technology, The University of Novi Sad, Cara Lazara 1, 21000 Novi Sad, Serbia, e-mail:
[email protected] Abstract A many number of modelling and simulation systems have been developed to aid in process and product engineering. In this paper the knowledge based process plant simulation model was developed. On the model development side, the issues of knowledge representation in the form of systematic component composition, ontology, and interconnections were illustrated. As a case study a plant for starch sweet syrup production was used. The system approach permits the evaluation of feasibility and global plant integration, and a predicted behavior of the reaction systems. The obtained results of the this paper have shown the variety quality of syrups simulation for different products. Keywords: Data base integration, Knowledge based operation, Optimizer, Product design.
1. Introduction Chemical and process engineering today is concerned with the understanding and development of systematic procedures for the design and optimal operation of chemical and process systems, ranging from micro-systems to industrial scale continuous and batch processes ( Mah, 1990; Thome, 1993; SavkovicStevanovic, 1995). It many years since process modelling become an advanced tool for design work in most companies. Process plant model objectives include to provide a comprehensive report of materials and energy streams, determine the correlation between process units, study the formation and separation of byproducts and impurities, support preventive maintain by tracking performance of key equipment over time and its relation to the buildup of impurities. In this paper the knowledge based simulation was developed for different products simulation.
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2. Knowledge based simulation The general framework presented here on the model development side, the issues of knowledge representation in the form of systematic composition, ontology, and quantity representaion was involved. On the model analysis side issues involving the automatic evaluation and presentation of simulation results. The plant simulation model should mirror the behaviour of a complex plant subject to constraints in feedstock, products, equipment capacities, operational parameters, and utilities consumptions. The life cycle concept may lead to a reliable and maintainable tool. One of the most widely used forms of simulation is that for operator training. So far operator training simulators have tended to use greatly simplified models in order to ensure real time performance and most effort has been invested in the development of user interface. A further aspect of the extended application of simulation for operator assistance could well be achieved in conjunction with expert systems. 3. Design In design, attention focuses on the main elements of material and heat balances, on equipment investment, and more generally, on process economics. While a deeper systems analysis of the plant would be worthwhile, considering that the basic design could be responsible for more than 80% of the cost of investment and operation, a detailed simulation and constrained, however, by the project schedule and lack of data. 4. Operation In operation, attention centres mainly on product flow rate and specifications, but also plant troubleshooting, controllability, and maintenance. The performance of reactors and separation systems impose the rules of the game. They are independent and time variable to some extent. Only a detailed plant simulation enables an understanding of these interdependencies and their quantitative evaluation. Thus, the exact knowledge of a detailed material and energy balance is by far more important in operations than in design. Even the flow rates of trace impurities are relevant, because they may impact equipment maintenance and environment protection. The material and energy balance as well as the operational characteristics of a plant are highly interconnected, and well suited for a system analysis. 5. Knowledge based process plant model development Using available flowsheeting software, it is possible to produce a computerized tool that will permit us to learn or even mirror the plant behaviour under different operating conditions or with different raw materials and product specifications. Such as tool is called the steady state plant simulation model. The steady state model, which is simpler to build, and has a wide variety of applications in its own right, it can be used directly in revamping and a wide variety of other engineering projects.
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Dynamic simulation is a process engineering tool that predicts how process and its controls respond to various upsets as a function of time. Dynamic simulation model leads benefits during plant start up. Process simulation and modelling techniques are very useful for optimizing design and operation. The outstanding advantage of the knowledge based simulator is its flexibility and semantic network. Developing such as model is a preliminary and necessary stage in achieving real time plant optimization which involves treating data reconciliation and rigorous simulation simultaneously by means of optimization techniques, whose objective is to maximize process profitability (Perunicic et.al.,2007). 6. Model of the sweet syrup production plant As a case study the starch converting plant was used. Summer wheat mills and starch converts into sugars after liquefaction, fermentation and conversion using corresponding enzymes. Partial starch hydrolysis is performed with α-amylase. The second phase deep hydrolysis is occurs at the present sweet enzymes. 6.1Biochemical reaction model
General kinetic model have involved Monod’s model. k1 k2 E + S ⎯⎯→ ES ⎯⎯→ P+E ←⎯ ⎯ k−1
(1)
dc ES = k1 ⋅ c E ⋅ c S − k −1 ⋅ c ES − k 2 ⋅ c ES dt
(2)
and product rate
dc P = k 2 ⋅ c ES dt
υ=
(3)
where E is enzyme, S is substrate, P is product, c is concentration and k is specific rate constant. 6.2 The steady state model
The starch plant for continuous sweet syrup production consists of a container for summer wheat, mill, fermentor, exchangers, bioreactors, and filter as individual process stages, or equipment items as shown in Fig.1(a),(b)and Fig.2. The overall mass balance NM
∑s ∂ F i
i
=0
i
(4)
i =1
Substream mass balance NSS NM
∑∑ s F f i
j =1 i =1
i
ij
=0
(5)
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Component mass balance NC NSS
NM
k =1 j ≠1
i ≠1
∑∑ ∑s F f i
i
ij
zi , j ,k = 0
(6)
and overall energy balance NM
NH
NW
i =1
i =1
i =1
∑ si ∂ i Fi hi + ∑ s j ∂ j H j + ∑ s k ∂ ki wk = RHS
(7)
equation i, where si = ,+1 for inlet streams and -1for outlet streams, ∂ i is stream scale factor, Fi mass flow stream i, fij is mass fraction of substream j in stream i, z ijk is mass fraction of component k in substream j of stream i, NM is number of inlet and outlet material streams, NH is number of inlet and outlet heat streams, NW is number of inlet and outlet work streams, NSS is number of substreams within material streams, NC-number of components specified on the components main or components group forms, hij is enthalpy of stream i, Hj is flow of heat stream j, wk is work of work stream k, RHS is right hand side of the energy balance equation. Additional material relationships can be specified which is very useful for reactive systems, NTi
∑C
ij
Fij = RHS i
(8)
j =1
where Cij coefficient term j in equation i, as determined by stream, substream and term, RGSi right hand side of mole/mass equation i, NTi is number of terms in mole/mass equation i. There are three elementary material balance according to stoichiometric description, and enthalpy balance which were formulated in this case study. The ability to describe the output composition of a reaction system for given reactor operating condition as function of variable input stream is the key feature that needs modelling of the chemical reactor in flowsheeting. 7. Optimization of plant design The input component data base and process parameters data base have developed as a relational data base system which linked with process models by simulation. SWEET SYRUP
GLUCOSABLE SYRUPS P11
P8
P5
P6
P5
P6 P8
Fig.1(a) Three reactors unit process
Fig.1(b) Four reactors unit process
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WHEAT
P1
P2
ENZYMES MIXTURE SWEET ENZYMES
WATER
P3
P5
P6
P8 SWEET SYRUP
P4 P7
P9
P10
P1-cointainer for summer wheat, P2-mill, P3-fermenter, P5-hydrolyser, P6-bioreactor for starch decomposition, P8- bioreactor, P4 and P9–heat exchangers, P7-cooler, P10-filter.
Fig. 2 The starch plant process simulation diagram A reactor simulation with detailed kinetics and a realistic flow model may be executed better with specialized software(Savkovic-Stevanovic.et.al.,2007). In fact, in flowsheeting only need an accurate description of the transformation linking the input the output of the reaction system. Optimization in design specification was achieved. This again highlights the differences between design and operations, in the design mode, the modelling of chemical reactors focuses on the main products rates. In this paper design mode was considered. For the examined starch plant in which starch converts into sugars after liquefaction, fermentation and conversion the main process units are shown in Fig.1(a) and (b). Using min-max principles and global optimization method the engineering economic objectives were provided. 8. Results and Discussion The use modelling for an actual automated equipped involved the continuous steady state nature of the processing units is starting from the crude streams and ending in the product streams as shown in Fig.2. Databases integration with process unit models is shown in Fig.3. Components and parameters data bases have made in Access program. The results are stored in a data base for further use. This is improving information processing.
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The results of starch converts in attending caustic soda and calcium chloride mass of sugar increases. Advantages of the employed technology to the acid hydrolysis are higher dextrin coefficient, less contents salt in the products, and no protein decomposition.
DbC
SIMULATION
DbP
D E S I G N DbC-component data base, DbP-parameters data base
Fig.3 Data bases integration with design structure 9. Conclusion The simulation flow diagram and optimization sequences of the process units for different products were examined. A relational data bases which including input component data base and process parameters data base as well as simulation results data base were developed. In this paper knowledge based process simulation and design of the starch plant were developed. The relational data bases system was linking with simulation models and simulation interface. The obtained results in this paper can be applied in the others domain. Acknowledgement. The authors wishes to express their gratitude to the Fund of Serbia for financial support.
References R.S.H.Mah,1990,Chemical Process Structures and Information Flow, Butterworths, Seyenoaks, U.K.. M..Perunicic, S. Krstic, M.Milivojevic, 2007, Process plant knowledge based simulation for design and manufacturing, Proceedings EUROSIM 2007-The 6th European Congress on Modelling and Simulation, 9-13, Sept., Ljubljana, 2007,pp.394. J.Savkovic-Stevanovic,1995, Process Modelling and Simulation, Faculty of Technology and Metallurgy, Belgrade. J.Savkovic-Stevanovic, T.Mosorinac, S.Krstic, R.Beric, 2007, Computer aided operation and design of the cationic surfactants production- Chapter, Chemical Engineering-24, Escape 17,Eds. V.Plesu and P.S.Agachi, Elsevier Science,p.195200. B.Thome,Ed.,1993, System Engineering-Principles and Practise of Computer Based Systems Engineering, John Wiley, New York.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Study of Arrangements for Distillation of Quaternary Mixtures Using Less Than N-1 Columns Dulce María Méndez-Valenciaa, María Vázquez-Ojedaa, Juan Gabriel SegoviaHernándeza, Héctor Hernándeza, Adrián Bonilla-Petricioletb a
Universidad de Guanajuato, Facultad de Química, Noria Alta s/n, Guanajuato, Gto., 36050, México. b Instituto Tecnológico de Aguascalientes, Departamento de Ingeniería Química, Av. López Mateos 1801,20256, Aguascalientes, Ags. México
Abstract The design and dynamic properties of distillation sequences using side-stream columns with less than N-1 columns for separations of four-component mixtures are studied. Total annual cost and dynamic properties (using singular value decomposition) are used to compare the proposed arrangements with conventional cases. Quaternary feeds containing hydrocarbons were analyzed. For systems with low concentrations of one component in the feed, side-stream cascades often show significantly lower operating and capital costs and better dynamic properties compared to the base cases. Low purity requirements also favor side-stream cascades. Some rules are presented to predict which sequence will have the lowest capital cost and better dynamic properties. Keywords: Complex Distillation, energy consumption, dynamic properties.
1. Introduction Distillation columns consume a large portion of the total industrial heat consumption, so even small improvements which become widely used, can save important amounts of energy. To improve the energy efficiency of separation processes based on distillation, several strategies have been proposed. The optimal design and synthesis of multicomponent distillation systems remain as one of the most challenging problems in process systems engineering. When the number of products is three or four, the design and costing of all possible sequences can best determinate the most economical sequence. Often, however, unless the feed mixture has a wide distribution of component concentrations or a wide variation of relative volatilities may be based on operation factors. In that case, the direct sequence is often the choice. Otherwise, a number of heuristics and mathematical methods that have appeared in literature have proved to be useful for reducing the number of sequences for detailed examination (Seader and Westerberg, 1977; Modi and Westerberg, 1992; Brüggemann and Marquardt, 2003; Kossack et al., 2006). Most of the studies have focused on complete separation of N component mixtures using N-1 distillation columns with a reboiler at the bottom and a condenser at the top of each column. However, cascades that use less than N-1 columns for multicomponent distillation processes have not been extensively studied (Rooks et al, 1996; Kin and Wankat, 2004). In this paper, we present the design and control properties of eleven distillation arrangements with less than N-1 columns (Figure 1) for the separation of quaternary mixtures. The results are compared to five base cases with
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three columns each one (Figure 2). Some rules are presented to predict which sequence will have the lowest energy consumption, capital cost and better dynamic properties.
Figure 1. Schemes using less than N-1 columns for quaternary separations.
2. Design of Schemes In this work, we presented an energy-efficient design procedure for the design of complex arrangements. To overcome the complexity of the simultaneous solution of the tray arrangement and energy consumption within a formal optimization algorithm, we decoupled the design problem in two stages: (1) tray configuration; (2) optimal energy consumption. The first stage of our approach begins with the development of
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preliminary designs for the complex systems from the design aspects on conventional distillation columns. The conventional sequences (Figure 2) show six different tray sections.
Figure 2. Conventional schemes for quaternary separations.
These sections are used as a basis for the arrangement of the tray structure of the coupled schemes through a section analogy procedure. For instance, in the main column of the complex sequence of Figure 1a, the total number of trays is obtained by conceptually moving the stripper section from the third column to the bottom of first column of conventional sequence (Figure 2a). This situation generates an arrangement with less than N-1 columns to base cases with three columns. A similar procedure is applied to obtain the other complex schemes. After the tray arrangement for the arrangement with less than N-1 columns have been obtained, an optimization procedure is used to minimize the heat duty supplied to the reboilers of each complex scheme, taking into account the constraints imposed by the required purity of the four products streams. The optimization strategy can be summarized as: (a) A base design for the
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complex schemes is obtained. (b) Values for each side stream stage and flow were assumed. (c) A rigorous model for the simulation of complex schemes with the proposed tray arrangement is solved. In this work Aspen Plus was used for this purpose. If the product compositions are obtained, then the design is kept; otherwise, proper adjustments must be made. (d) One value of side stream flow is changed, going back to step (c) until a local minimum in energy consumption for the assumed value of side stream stage is detected.(e) The value of side stream stage is modified, going back to step (c) until the energy consumption is minimum. This result implies that an optimum value has been detected for the design of the complex scheme.
3. Control Properties One of the basic and most important tools of modern numerical analysis is the Singular value decomposition (SVD). One important use of the SVD is in the study of the theoretical control properties in chemical process. One definition of SVD is:
G = VΣ W H
(1)
In the case where the SVD is used for the study of the theoretical control properties, two parameters are of interest: the minimum singular value (σ∗), җthe maximum singular value (σ∗), and its ratio known as condition number (γ). The systems with higher minimum singular values and lower condition numbers are expected to show the best dynamic performance under feedback control (Klema and Laub, 1980). Also, it is important to note that a full SVD analysis should cover a wide range of frequencies.
4. Case of Study The case studies were selected to reflect different separation difficulties and different contents of the intermediate component of the quaternary mixtures. The mixtures considered are displayed in Tables 1 - 2. The mole fraction of 0.05 was shown to be a borderline value for use of side-stream columns for ternary separations (Tedder and Rudd, 1978). The total feed flowrate for all cases was 45.5 kmol/h. Since the feed involves a hydrocarbon mixture, the Chao-Seader correlation was used for the prediction of thermodynamic properties. The design pressure for each sequence was chosen such that all condensers could be operated with cooling water. Table 1. Examples with n-heptane.
Table 2. Examples with n-octane. Feed Composition (kmol/hr)
Feed Composition (kmol/hr) Component
M1
M2
M3
M4
M5
n-butane
A
2.56
30
5
5
30
n-pentane
B
25.64
3
45
25
40
n-hexane
C
41.03
55
45
40
25
n-heptane
D
30.77
12
5
30
5
Component
M6
M7
M8
n-butane
A
30
5
3
n-pentane
B
40
25
55
n-hexane
C
25
40
12
n-octane
E
5
30
30
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5. Results From the simulation results for the mixture M1 (Table 3) the system CS–III has the lowest TAC (and energy consumption). The base case shown in CS-IV is next and presents a significantly higher TAC. The purities of all products can be improved by adding more stages for both base cases. Table 3 displays the simulation results for example M1 for saturated liquid side-stream cascades (Figure 1a–1f) and for saturated vapor side-stream cascades (Figures 1g–1k). Since there is little component A in the feed, we expect the saturated liquid side-stream systems to be in general better than saturated vapor side streams. The TAC and energy consumption values confirm this conclusion (Schemes CC – I to CC – V have the lowest values in comparison with configurations CC- VI to CC – X). On the basis of the results, the configurations CC-II and CC-III are the best of the side-stream configurations (they have similar values of TAC and reboiler duty). They require similar heating than the best base cases, and TACs are similar to that of the best conventional sequence. However, the conventional sequences are more flexible if the concentration of A in the feed increases. In this case a more detailed dynamic behavior study would be justified. Similar conclusions can be shown for all mixtures. For this initial analysis of complex configurations, we simply estimated the SVD properties for each separation system at zero frequency. Such analysis give some preliminary indication on the control properties of each system around the nominal operating point. Table 4 gives the results for the SVD test for each sequence (case M1). In the case of conventional sequences, the CS- V has the best values. In the case of the complex sequences, the schemes CC-II and CC-III show the best results, which imply that those sequences are better conditioned to the effect of disturbances than the other complex systems. Those results show that the saturated liquid side-stream systems have better dynamic behavior. This situation is similar to the TAC values for the case M1, since there is little A in the feed. Similar results can be showed for the other mixtures in the case of the control properties. Based on the trends observed, we propose some heuristics for the use of complex sequences (best options in TAC values and dynamic behavior): (a) Use a complex scheme with a liquid side stream above the feed if there is a small amount (approximately 0.05 mole fraction or less) of the most volatile component in the feed. (b) A complex scheme with a vapor side stream below the feed can be used if there is a small amount (approximately 0.05 mole fraction) of the least volatile component in the feed to this column. (C) If a product is required at low purity side-stream configurations that withdraw this product as a side stream are often favored, but heuristic 1 must be satisfied. Table 3. Total annual cost (TAC, $ x 103/yr) of some representative cases of study.
CC - I CC - II CC - III CC - IV CC - V CC - VI CC - VII CC - VIII CC - IX CC - X CC - XI
M1
M2
M3
828 630 603 1879 1983 4191 2429 2497 2812 3521 4523
28905 1926 2394 512 1373 1522 1510 1038 3802 3843 2291
852 866 669 3092 3275 961 543 600 3000 3044 1053
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Table 4. Minimum singular value and condition number for each structure (M1). Sequence
σ*
γ*
CC - I CC - II CC - III CC - IV CC - V CC - VI CC - VII CC - VIII CC - IX CC - X CC - XI
1.4653 E-4 2.3106E-3 5.5807E-3 16101E-3 20189E-4 8.7115E-11 1.3788E-3 1.5073E-3 1.1245E-3 4.5061E-7 8.959E-4
20.714E3 487.7 552.7 95.91E2 121.387E3 43.860E8 42.35E2 64.29E2 18.43E2 14.924E6 59.70E2
6. Conclusions A general energy-efficient design procedure is developed for any type of the sidestreams designs with less than N-1 columns. The method is based on a section analogy procedure with respect to the characteristics of a conventional distillation sequence. The methodology provides a robust tool for the design of multicomponent side-streams designs. Some trends were observed for the use of complex sequences: the best option in TAC values and dynamic properties for complex schemes with a liquid side stream above the feed is when there is a small amount (approximately 0.05 mole fraction or less) of the most volatile component in the feed. In the case of complex scheme with a vapor side stream below the feed is when a small amount (approximately 0.05 mole fraction) of the least volatile component in the feed to this column. In the other cases, the best option is the conventional sequences. The heuristics can be considered useful because they were based on a detailed economic analysis.
7. Acknowledgment The authors acknowledge financial support received from CONCyTEG, CONACyT, Universidad de Guanajuato and Instituto Tecnológico de Aguascalientes, México.
8. References S. Brüggemann and W. Marquardt, 2003, Computer Aided Chemical Engineering, 15, 732. J.K. Kin and P.C. Wankat, 2004, Ind. Eng. Chem. Res., 43, 3838. V.C. Klema and A.J. Laub, 1980, IEEE Transactions on Automatic Control, 25, 164. S. Kossack, K. Kraemer and W. Marquardt, 2006, Ind. Eng. Chem. Res., 45, 8492. A.K. Modi and A.W. Westerberg, 1991, Ind. Eng. Chem. Res., 31, 839. R.E. Rooks, M.F. Malone and M.F. Doherty, 1996, Ind. Eng.Chem. Res., 35, 3653. J.D. Seader and A.W. Westerberg, 1977, AIChE J., 23, 951. D.W. Tedder and D.F. Rudd, 1978, AIChE J., 24, 303.
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A Hybrid Meta-heuristic Method for Logistics Optimization Associated with Production Planning Yoshiaki Shimizua, Yoshihiro Yamazakia, Takeshi Wadab a
Production Systems Engineering, Toyohashi University of Technology, Toyohashi, Aichi, 441-8580, Japan b Industrial Systems Engineering, Osaka Prefectural College of Technology, Neyagawa, Osaka, 572-8572 Japan
Abstract Associated with a strategic optimization of logistics network design to improve the business efficiency, we developed a method termed hybrid tabu search, and have applied it to various real-world problems through imposing proper conditions on the generic model. During a planning horizon for the design, however, there usually occur various changes assumed constant in such a strategic or static consideration. In this study, therefore, we have extended the previous method so that we can make a more reliable and operational decision by taking into account the dynamic circumstances and focusing on the role of inventory management of warehouse over planning horizon. Finally, numerical experiments revealed the significance of multi-term planning and the validity of the proposed method in comparison with the commercial software. Keywords: Multi-term logistics planning, Inventory management, Large-scale combinatorial optimization, Hybrid tabu search.
1. Introduction Logistic optimization has been acknowledged increasingly as a key issue of supply chain management to improve the business efficiency under global competition and agile manufacturing. Though many studies have been made in the operations research field associated with the combinatorial optimization (for example, Campbell, 1994), we need to make more elaborate efforts to cope with complex and complicated real world problems. From such aspect, we concerned various logistic optimization problems for strategic or static decision making. Associate with the production planning, however, it is necessary to notice the various deviations assumed constant in the strategic or static model. Taking into accounts such a dynamic circumstances, we can make a more reliable and operational decision making. In this study, therefore, we have extended our previous approach termed hybrid tabu search so as to deal with multi-term problem, and incorporate an inventory management of warehouse or distribution center (DC) into the logistic network design optimization. After presenting a general formulation and its algorithm, the validity of the proposed method is shown through numerical experiments.
2. Problem Formulation 2.1. Preliminary Statements Many studies in the area of operations research emphasize to develop new algorithms and compete their abilities through simple benchmarking and/or to prove theoretically the facts about how fast, how exactly and how large problem to be solvable. However,
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easy applications following these outcomes often cause a dramatic increase in problem size in real world problems, and accordingly such a difficulty that makes almost impossible to solve the resulting problem by any currently available software. Under such understanding, to cope with the specific problem in complex and complicated situation, we concerned various logistic optimization problems subject to the conditions such like a realistic discount of transportation cost, flexibility against demand deviations, multi-commodity delivery and so on (Shimizu & Wada, 2004; Wada, Shimizu & Yoo, 2005; Shimizu, Matsuda & Wada, 2006; Wada, Yamazaki & Shimizu, 2007). The hybrid tabu search used in those studies decomposes the original problem into upper-level and lower-level sub-problems, and applies a suitable method for each sub-problem. The upper level sub-problem decides the locations of DC by the sophisticated tabu search. Tabu search (TS; Glover, 1989) is a metaheuristic algorithm on a basis of local search technique with a memory structure. The TS repeats the local search iteratively to move from a current solution x to a possible and best solution x' in the neighbor of x. To avoid the cycling of the solution, the TS uses the tabu list that prohibits transition to any solutions for a while even if this will improve the current solution. On the other hand, the lower level sub-problem decides the network routes under the prescribed upper level decision. It refers to a linear program possible to be transformed into a minimum cost flow (MCF) problem. In practice, this transformation is carried out by adding virtual nodes and edges to the physical configuration as illustrated in Fig.1. Then the resulting MCF problem can be solved by the graph algorithm for which especially fast solution algorithm such as CS2 (Goldberg, 1997) is known. Now, by returning to the upper-level, neighbor locations are to be evaluated following the algorithm of the sophisticated tabu search. These procedures will be repeated until a certain convergence criterion has been satisfied. Figure 2 illustrates schematically this solution procedure. Selection probability of the local search operation summarized in Table 1 is decided based on the following ideas. It makes sense that the search types like “Add” and/or “Subtract” might be used often at the earlier stage of search while “Swap” is more suitable at the later stage where the number of open DCs attain almost at the optimum. Letting it be a basis to decide the probability, we further extended an idea to do it more effectively using the long-term memory or a history of so far search processes. That is, the probability of each operation is increased by a certain rate if it has brought about the update of solution. In contrast, these values are reset when the tentative solution is not improved by the prescribed consecutive duration and/or an feasible solution has not been obtained.
Fig.1 Transformation of network to MCF graph
Fig.2 Schematic procedure of hybrid tabu search
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Table 1 Employed neighborhood search operations Search type
Selection probability
Neighborhood operation
Add
padd
Let closed DC open.
Subtract
psubtract
Let open DC close.
Swap
pswap
Let closed DC open and open DC close.
2.2. Multiterm Model over Planning Horizon We have extended the static or single-term development to cope with the multi-term problem in a practical manner. By making use of the available stock of DC to the descendent periods (inventory management), we can expect to bring significant effects to the strategic decision making. After all, we have formulated mathematically the problem as a mixed-integer programming problem stated below. The objective function is composed of the total transportation cost between every facility, the total production cost at plant, and the total operational cost at each facility, the total holding cost at DC over the planning horizon, and the total fixed-charge for the open DCs. On the other hand, the constraints require to meet the demand of every customer every period; capacity constraint at each DC every period. The upper and lower bounds on the production ability of each plant every period, and the material balance at each DC every period. Additionally, non-negative conditions are imposed on the material flows and binary condition on the open/close selection. Finally, the model has the problem size such that: number of integer variables is J, continuous variables T (IJ+J2+JK+IK+J), and constraints T(2I+2J+K) where notation I, J, K and T denote number of plants, DCs, customers and terms, respectively.
3. The Hybrid Tabu Search for Multiterm Transport Under the multi-term condition, the lower level sub-problem of the hybrid tabu search needs to decide the network routes for every period. It refers to a linear program whose coefficient matrix becomes almost block diagonal per each period and expands rapidly with the number of terms as known from the foregoing statement.
(a)
(b) (b)
Fig.3 Transformation procedure to aggregate MCF graph for three-term problem: (a)Add edges for inventory, and (b) Final stage
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Table 2 Labeling on the edge Edge ID
Cost
Capacity
Description
#1
0
tЩTiЩI Pit
source㧙
#2
Cit
Pit - Pit
#3
t
Pi
t
Ci
t
source㧙plant i (period t) 㧙plant i (period t)
#4
Eij
#5
Hj
t
#6
Ejj't
DC j㧙DC j' (period t)
#7
Ejkt
DC j㧙customer k (period t)
#8
Eikt
plant i㧙customer k (period t)
D
Dkt
customer k㧙sink (period t)
stock at DC j (period t)
#9 #10
Kj
t
plant i㧙DC j (period t)
Uj
t
between doubled nodes representing DC
Noticing a special topological structure associated with the minimum cost flow problem, however, we can present a smart procedure to transform the bulk original problem into a compact form as follows: Step 1: Every period, place the nodes that stand for plant, DC (doubled), and customer. Next, virtual nodes termed source, , and sink are placed at the top and the bottom, respectively. Then connect the nodes between source and (#1), source and plant (#2), and plant (#3), up and down DC nodes (#5), and customer and sink (#9). This results in the graph as depicted in Fig.3 (a). Step 2: Letting z be the total amount of customer demand over planning horizon, z=t Щ Tk Щ K Dkt, flow this amount into the source, and flow out from the sink. Step 3: To constrain the amounts of flow, set the capacities on the edges identified by #1, #2, #3, #5 and #9 as each in “Capacity column” in Table 2. Apparently, there never induce any costs on edge #1 and #9 for the connections. Step 4: To allow the stock at DC, add the edges from down-DC node to up-DC node in the next period (#10) as shown in Fig.3 (a). For the labeling, see the “#10” row of the table. Step 5: Connect the edges between plant and DC (#4), DC and DC (#6), DC and customer (#7) and plant and customer (#8) every period. Step 6: Finally, place the appropriate label on each edge. From all of these, we have the final graph as shown in Fig.3 (b) that makes it possible to still apply the graph algorithm like CS2 (Goldberg, 1997). Consequently, we can solve the extensively expanded problem extremely fast compared with the linear programs.
4. Numerical Experiment 4.1. Preliminary Experiments In long term planning, instead of the dynamic model, a strategic or conceptual decision is often made based on the averaged values for the time being. This is equivalent to say that we attempt to obtain only a prospect from the static or single-term problem whose parameters fluctuate in reality over the planning horizon such as demand.
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To verify the advantage of considering the dynamic model that makes use of the stock at DC, first we compared the results between the (averaged) single-term model and the multi-term model using small size benchmark problems. In Table 3, we summarize the results taken place under the conditions of demand deviations. Thereat, we know that the dynamic model can derive the decisions with less total costs (the value of average model is represented as the rate to that of the multi-term model to be one hundred). Particularly, it is remarkable that the average model involve an infeasible solution against the demand deviations while the multi-period model always copes with the situation by virtue of the inventory management. For example, as shown in Fig.4, the appropriate production plan is carried out and the stocks at the DC are utilized to meet the customer demands changed beyond the production ability at plant.
Fig.4 Role of inventory in multi-term planning Table 4 Computation environment for numerical experiments Method
CPU type
Memory
OS
CPLEX
Pentium4 3.0 GHz
512 MB
Windows XP
This work
Pentium4 3.0 GHz
512 MB
Debian 3.0
4.2. Evaluation of the Proposed Algorithm From so far discussions, it is interesting to examine the effectiveness of the proposed method in terms of problem size. Every result of the proposed method is averaged over five trials. In Table 4, we summarize the computation environment for the present numerical experiments. Figure 5 compared the CPU times along the number of planning horizon between the proposed method and CPLEX 9.0 (parameters deciding problem size are set as I=2, J=25 and K=30, and a few problem sizes are shown there.). Thereat, we can observe the CPU time of the proposed method increases almost linearly while exponentially for the CPLEX. As shown in Table 5, the proposed method can derive the same results as the CPLEX (supposed optimal) with much shorter CPU times for every problem within the range where we can compare. For each, the gap between MIP and its LP relaxed problem stays almost at constant, say 8 㨪 10%, but the load (CPU time) rate increased considerably (but not so rapidly) with the term.
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Fig.5 Comparison of CPU time with commercial software
* Objective function value of Hybrid tabu/CPLEX
From these numerical experiments, the proposed method is expected to achieve the high approximation rate of optimality fast even for larger problems, and supposed to be promising for real world applications.
5. Conclusions This paper concerned a multi-term logistic optimization problem by extending a twolevel method termed hybrid tabu search developed by the authors previously. For this purpose, we have invented a systematic procedure to transform the mathematical programming model into a compact graph model manageable for inventory over the planning horizon. This enables us to solve the long-term logistic network optimization problem that any other methods never have dealt with. Numerical experiments revealed that such inventory control could bring about an economical effect and robustness against demand deviations. The validity of the proposed method was also shown in comparison with the commercial software.
References J. F. Campbell (1994). Integer programming formulations of discrete hub location problems, European Journal of Operational Research, 72, pp. 387-405 F. Glover (1989). Tabu search: Part I., ORSA Journal on Computing, 1, pp.190-206 A. V. Goldberg (1997). An Efficient Implementation of a Scaling Minimum-cost Flow Algorithm, J. Algorithm, 22, pp.1-29 Y. Shimizu and T. Wada (2004). Logistic Optimization for Site Location and Route Selection under Capacity Constraints Using Hybrid Tabu Search, Proc. 8th Int. Symp. on ComputerAided Process Systems Engineering, pp.612-617, Kunming, China Y. Shimizu, S. Matsuda and T. Wada (2006). A Flexible Design of Logistic Network against Uncertain Demands through Hybrid Meta-Heuristic Method, Proc. 16th Europe. Symp. on Computer-Aided Process Engineering, pp.2051-2056, Garmisch Partenkirchen, Germany T. Wada, Y. Shimizu, Jae-Kyu Yoo. (2005). Entire Supply Chain Optimization in Terms of Hybrid in Approach, Proc. 15th Europe. Symp. on Computer-Aided Process Engineering, pp.1591-1596, Barcelona, Spain T. Wada, Y. Yamazaki, Y. Shimizu (2007). Logistic Optimization Using Hybrid Meta-heuristic Approach, Transaction of the Japan Society of Mechanical Engineers, C-727, 73, pp.919-926
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Model-based investment planning model for stepwise capacity expansions of chemical plants Andreas Wiesnera, Martin Schlegelb, Jan Oldenburgb, Lynn Würtha, Ralf Hannemanna, Axel Poltb a
AVT-Lehrstuhl für Prozesstechnik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany b Corporate Engineering, BASF Aktiengesellschaft, Carl-Bosch-Str. 38, 67056 Ludwigshafen, Germany
Abstract In this contribution a novel investment planning model for the development of stepwise capacity expansion strategies for chemical plants is proposed. This method is implemented in a decision support tool that can be used during the early stage of plant engineering - a phase which is concerned with the conversion of a chemical process into a highly profitable plant. Based on a previous work by Oldenburg et al. [1], who proposed a method for a quick economic comparison of possible stepwise plant expansion scenarios versus building a full capacity plant, the approach presented in this paper is capable of identifying the optimal process-specific investment strategy on the level of unit operations. A mixed-integer linear programming model dedicated for stepwise capacity expansion strategies for chemical process plants forms the core of the tool. Keywords: Investment planning, Stepwise capacity expansion, Mixed-integer linear programming
1. Introduction One important decision to be taken in the course of investment projects for new chemical productions plants is the production capacity, for which the plant should be designed. In most cases, this decision is based on (often uncertain) marketing forecasts. From an economical point of view, it is paramount to meet the predicted sales amount with the plant capacity rather than having significant over- or under-capacities. Typically, the product demand is expected to grow in the future. However, the wider the time horizon is set for the forecast the less reliable the forecast becomes. In this context, it would be desirable to determine the optimal initial production capacity followed by an optimal sequence of future expansion steps in order to accommodate the product demand without unprofitable overcapacities. Such an approach is certainly more complex and requires taking future measures well into account during the planning phase. Even then, it is by no means certain, whether a stepwise expansion is economically more attractive. Due to those and several other reasons, it is common practice to install the largest possible capacity already at the beginning of the process life cycle, which we will term the “conventional strategy” in the following. To face the aforementioned challenge, Oldenburg et al. [1] proposed a method which enables a quick comparison of possible stepwise plant expansion scenarios versus building a full capacity plant. However, this method is not able to deliver a specific expansion strategy
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in detail, e.g. which piece of equipment has to be installed with which capacity at what time. For this purpose, an investment planning model for the identification of the economically most attractive investment strategy incorporating independent expansions of process units is addressed in this contribution. We propose an optimization approach using an investment planning model. It determines an optimal investment strategy by minimizing the investment costs including depreciation and discounting. The decision variables for the optimization are the dimensions of the installed equipment as well as the time points of installation and/or expansion. Due to the discrete-continuous nature of the problem, a linear mixed-integer formulation (MILP) is used for this purpose. The proposed method may be categorized as a multi-period investment model. The remainder of this paper is organized as follows: Section 2 relates our model to well known approaches based on multi-period investment models proposed in the literature. In Section 3, our investment planning model is introduced while in Section 4 the investment planning strategy of a generic process is presented as a case-study. Section 5 gives a discussion on the results of the case study. Finally, in Section 6 our findings are summarized.
2. Related Multi-Period Investment Models The proposed optimization approach falls into the category of multi-period investment models. Various related approaches can be found in the literature, (e.g. [2], [3]), including MILP optimization for long range investment planning. Some authors also consider stochastic elements to cover the potential uncertainties, which, however, is beyond the scope of this paper. The suggested investment model adopts the multiperiod MILP problem proposed by Sahinidis et al. (1989), which was originally intended to describe large sites consisting of many interconnecting processes producing many chemicals (cf. Fig. 1). For this reason, all process units employed in such a process are assumed to obey identical investment strategies. E
C
A
C
A
C
B A
C
Process 2
Process 1
D
A
A B
B
C
(3) Mixer
Process 3
Fig. 1: Schematic depiction of the multiperiod investment problem as proposed by Sahinidis et al. (1989)
A
A C
(1) Reactor
C
(2) Separation unit
Fig. 2: Schematic depiction of the investment planning model as proposed in this work
Our approach, in turn, can be considered as a process synthesis problem (simplified by linearization) with an additional time dimension, which, to the authors’ knowledge, has not yet been addressed on the level of detail down to unit operations and single pieces of equipment (cf. Fig. 2). Aiming at a stepwise capacity expansion, this is important though, since processes typically consist of a broad range of equipment with different operating ranges and size factors, requiring adapted expansions for different parts of the
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plant. The main issue of this contribution is the specific capacity expansion timing and sizing for each process unit in order to cope with particular investment strategies required for different chemical process units. Therefore, the MILP problem formulation of the investment planning model adds various additional constraints to fulfill the specific requirements as described in the subsequent section.
3. Investment Planning Model First of all, some requirements are stated: the specific problem that is addressed in this paper assumes that a network of process units and a set of chemicals are given. Ideally, this network is based on a stationary process flow diagram and thus all mass fluxes, design temperatures and design pressures are known. Also given are forecasts for the demands of products as well as the investment costs over a finite number of time periods within a long range planning horizon. Furthermore, it is assumed that the availability of raw materials and the demand of products are always fulfilled. In the following the investment planning model is described. The process units are connected by material streams, which include raw materials, intermediates and products. It is assumed that all required units in the process may be represented by one or more of the following three types of model units with respect to the mass balance (cf. Fig. 2): Type (1) represents the function of a reactor. This means that a different set of chemicals may enter and leave the unit due to a physico-chemical conversion. Moreover, it is assumed that material balances for raw materials and by-products can be expressed in terms of linear ratios to the production of the main product. Type (2) describes the function of a separation unit. By means of splitting factors, determined previously in the process simulation, a selective separation is modeled. The same set of incoming and outgoing chemicals is compulsory. Finally, type (3) represents the function of mixing, which is particularly of interest for recycle streams and the union of different partial processes. Again, the set of incoming and outgoing chemicals has to be identical. Either dedicated processes for single product or flexible processes can be modeled, which may operate in either a continuous or batch mode. Process flexibility is realized by a set of alternative production schemes producing different chemicals on identical process units. The process capacity for dedicated processes is determined by the set of process units that are required for a specific production scheme. For flexible processes, the capacity of a process unit has to accommodate for each production scheme. A capacity expansion can be accomplished by either adding parallel equipment or replacement of insufficient equipment. For flexible processes a capacity adaptation due to product change is guaranteed. Technical limitations are fulfilled by means of operating range constraints. Also, technical limits on capacity expansion timing and sizing as well as lead times for the installation can be specified. Generally, it is assumed that the process unit capacity can be expressed linearly depending on the sum of overall material flow leaving the process unit production scheme. Because plant extensions imply temporary shutdowns, constraints are added to guarantee a minimum of downtimes through combined capacity extensions. The objective function minimizes the investment costs over the given horizon and consists of the terms: 1) discounted linearized invest cost of all pieces of equipment, 2) additional costs, e.g. lack of production due to downtimes, and 3) cost savings due to depreciation related tax savings. Linear models are assumed for the mass balances. The cost relation during an early project phase can be nicely captured by a power function that is frequently applied for rough equipment cost estimations:
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C 2 § Q2 =¨ C1 ¨© Q1
· ¸¸ ¹
CEX
(1)
Based on a known cost C1 of an investment of capacity Q1 and so-called capacity exponent CEX, the cost C2 of a new capacity Q2 can be calculated using Eq. (1). Since the cost function is nonlinear, a piecewise linear approximation, e.g. the one proposed by Croxton et al. [4], of the cost function has to be applied leading to an overall linear model. The time horizon is divided into 1 year time periods.
4. Case Study The case study deals with a dedicated process, shown in Fig. 3, to which the investment planning model is applied. The process consists of ten process units including distillation and absorption columns, compressor, pump, heat exchanger and a reactor. Condenser Light ends column Reactant
Product column
Reactor Compressor
Raw material
Product
Vent Gas
By-product
Product Desorber
Heat exchanger
Pump By-product column
Product Absorber
Valuable by-product
Fig. 3: Example process considered for the stepwise capacity expansion
The catalytic reactions take place in the reactor assuming catalyst deactivation. The reaction states that the raw material and a reactant yield the main product. Additionally, a side reaction from raw material to an undesired by-product is considered by conversion of the reactant. Additionally, a second reaction involving the product and the absorbent in the product desorber is assumed to take place, which yields a valuable by-product. Each operation unit capacity is assumed to be designable within an upper and lower boundary to accommodate for any considered production rate. The product demand forecasts are given for a ten year horizon. The costs are represented by power functions which vary in terms of capacity exponents and hence different investment decisions for the process units are expected. The capacity exponents (c.f. Table 1) for the cost functions are taken from Peters and Timmerhaus [5]. For the piecewise linear approximation of the cost function, two time intervals are considered as default. Due to maximum capacity restrictions, the overall capacity of the reactor and the product absorption unit is achieved by an installation of at least three parallel reactors and two parallel absorption units comprising the same capacity. Equipment
Reactor
Column
Heat exchanger
Compressor Pump
Capacity exponent
0.65
0.6
0.44
0.69
0.34
Table 1: Values for capacity exponents for selected pieces of equipment
Due to technical/physical limitations, the range of operation of the compressor and the heat exchanger must be within 60%-100% and 80%-100% of the installed capacity,
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respectively. The capacity expansion can take place either in terms of a parallel installation of identical equipment, or a replacement of equipment accommodating the complete required capacity. In the case study only the compressor is assumed to be of the latter type. Furthermore, a lead time of two years is assumed for each expansion. Expansions of several pieces of equipment are integrated into one simultaneous expansion step. Due to the deactivation of the catalyst, a complete shut down of the process is assumed to take place every two years. The required capacity expansion can be carried out in the period of shut down to minimize the loss of production yield. Hence, any losses of production yields are neglected in this example process.
5. Results & Discussion
1,2
1
1
Fig. 4: Installed capacity sequence according to the conventional investment strategy
Product demand
Condenser
Pump
Compressor
By-product column
Heat exchanger
0
Product column
0,2
Reactor
0,4
L.E. column
0,6
Desorption column
0,8 Absorption column
Product demand
Pump
Condenser
Compressor
Heat exchanger
By-product column
0
L.E. column
0,2
Product column
0,4
Desorption column
0,6
Absorption column
0,8
standardized capacity
1,2
Reactor
standardized capacity
Based on the data mentioned in the previous section, the MILP model has been formulated. Due to the lack of space a thorough discussion of the model equation is impossible. The model has been solved applying the MILP solver SYMPHONY [6]. For the product demand an initial 35% of the total product demand achieved in the tenth year was assumed with a linear progression. This product demand forecast was used for the conventional alternative and the stepwise capacity expansion.
Fig. 5: Installed capacity sequence according to the stepwise capacity investment strategy
Fig. 4 and 5 show the result of the two investment alternatives. The sequence of the installed capacity over the given time horizon for the specific process units are each identified to the left of the diagram and the product demand forecast is located to the right of the respective diagram. Within the diagram one bar represents the investment sequence of one piece of equipment. The differences observed between the two alternatives may be summarized as follows: Equipment with a wide operational range, e.g. a column, is not affected by the stepwise capacity expansions at all, except for the units which were primarily intended on multiple unit installation with restricted capacities. However, for units which have a narrow operating range, the optimal investment strategy is achieved by stepwise capacity expansions. Hence, depending on the characteristics of the product demand a completely different optimal investment strategy for such equipment may arise. The overall discounted investment costs for the alternative are shown in Fig. 6. It demonstrates the significant reduction of investment costs, of about 7 % in total, when applying the stepwise capacity expansions. The major part of the cost reduction is achieved by the postponed installation of the third reactor and the second absorption unit. An experienced engineer may have achieved the obvious cost reduction by splitting the installation of the reactors and the absorption unit as well. However, there still exists a cost reduction due to the rigorous optimal timing and sizing which can be shown exemplarily for the heat exchanger and
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30000
7000
25000
6000
discounted investment cost (in T€)
discounted investment costs (in T€)
condenser capacity expansion. The comparison of cost resulting by either of the investment strategies for the heat exchanger and the condenser is given in Fig. 7. A total cost reduction of about 3.5 % in favor of the stepwise capacity expansion is achieved.
20000 15000 10000 5000
5000 4000 3000 2000 1000 0
0 1
3
5
7
9
total
year of investment conv. investment planning
stepw. investment planning
Fig. 6: Comparison of overall discounted investment costs
1
3
5
7
9
total
year of investment conv. investment planning
stepw. investment planning
Fig. 7: Comparison of heat exchanger and condenser investment cost
6. Conclusions A novel investment planning model for chemical plants has been proposed, which aims at stepwise capacity expansions. It provides the proper timing and sizing of the process units in order to minimize unprofitable overcapacities. That way, economically attractive alternatives compared to conventional investment planning can be offered already at an early stage of planning. Alternatively, it can be proven that the conventional planning, namely installing the full capacity at once, is the most attractive option for the considered case. The method is based on an extension of established multi-period investment models (MILP) and thus provides the minimal discounted investment costs for each process unit in the considered process. For our case study, it has been shown that the investment strategy of operation units with a wide operating range does not significantly vary for the conventional and the stepwise investment planning. However, for units with a narrow operation range, a significant investment cost reduction due to the proper timing and sizing of the unit installation was achieved.
References [1] J. Oldenburg and M. Schlegel and J. Ulrich and T.-L. Hong and B. Krepinsky and G.Grossmann and A. Polt and H. Terhorst and J.-W. Snoeck, A Method for quick evaluation of stepwise plant expansion scenarios in the chemical industry, in: V. Pleasu and P.S. Agachi (eds.) : 17th European Symposium on Computer Aided Process Engineering, Elsevier, 2007 [2] N.V. Sahinidis and I.E. Grossmann and R.E. Fornari and M. Chathrathi, Optimization model for long range planning in the chemical industry, Computers chem. Engng., 13, 9 (1989) 10491063. [3] L.C. Norton and I.E. Grossmann, Strategic planning model for complete process flexibility. IECRED, 33 (1994) 69-76. [4] K.L. Croxton and B. Gendron and T.L. Magnanti, A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems, Management Science, 49, 9 (2003) 1268-1273 [5] M.S. Peters and K.D. Timmerhaus, Plant Design and Economics for Chemical Engineers, McGraw-Hill, 4th Edition, 1991 [6] COIN-OR, SYMPHONY, 2006, online available at http://www.coin-or.org/projects.html, (accessed: 04. Oct. 2006)
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Divided Wall Distillation Column: Dynamic Modeling And Control Alexandru Woinaroschy, Raluca Isopescu UniversityPolitehnica of Bucharest, Polizu Str. 1-5, Bucharest 011061, Romania
Abstract The dynamic modeling of the dividing wall distillation column is used to determine optimal startup policies that minimise the time required to reach the imposed steady state operating values in terms of product compositions and flow rates. The problem is resolved by a convenient transformation of the dynamic model in a system of differential equations, avoiding algebraic calculations generally imposed by equilibrium solving, and by using iterative dynamic programming for the minimization of the startup time. An example referring to the separation of a ternary hydrocarbon mixture is presented. The variables that mostly influence the startup time were found to be the reflux ratio and side-stream flowrate. The optimal policies identified realise a considerable reduction of startup time, up to 70% compared to the startup operation at constant reflux ratio or constant side draw flowrate. Keywords: divided wall distillation column, dynamic modeling, optimal startup control
1. Introduction Despite its high energy consumption, distillation is the widest used separation technique in petrochemical and chemical plants. Thermally coupled distillation columns can lead to a significant energy reduction, up to 40% for the totally thermal integrated structure which is the Petlyuk column. The Petlyuk column built in a single shell is the divided wall distillation column (DWC) and is considered a very attractive solution for energy and capital cost savings in separation processes. Though its efficiency has been proved by numerous theoretical studies such as Triantafillou et al (1992), Sierra et al (2001) and also by some practical industrial applications, among which at least the 40 DWC implemented by BASF should be mentioned, the DWC is not yet a common solution. A reason for this can be a lack of understanding of the design and control of a DWC. Theoretical studies and experimental confrontations are still necessary to prove the big advantages of this solution and to find practical ways for a good design methodology and control strategies. The design and optimization of a divided wall column can be achieved by defining tray sections interconnected by liquid and vapor streams that represent the complex arrangement of a DWC. The structure used in the present paper lumps in four column-sections the trays of the DWC. These column sections represent the top of the DWC (trays above the dividing wall), the prefractionator (left side of the dividing wall) where the feed is located, the right side of divided wall where the side draw is located and the tray section below the dividing wall. The increased number of degrees of freedom (DOF) for a DWC imposes a thorough analysis of control variables to establish a convenient approach in modeling the process and establishing the control policy. Due to the increased number of DOF, both steady state and dynamic modeling of a DWC raises more problems than a simple column with a side draw and needs adequate solving algorithms. Halvorsen and Skogestad (2004) proved that the liquid and vapor splits have a great influence on the thermal efficiency
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of the DWC. More recently, Wang and Wong (2007) demonstrated that outside a given region defined by certain liquid and vapor split values, the composition control can compensate only for variation in feed characteristic, such as feed or composition, but not for internal flow changes. They proposed a temperature-composition cascade scheme to control a DWC. Temperature control strategies proved to be efficient also for complex schemes including heterogeneous azeotropic distillation and a DWC (Wang et al 2008). Startup policies must be considered as well when analysing the efficiency of a DWC. In order to promote the generalisation of DWC in industrial application it is necessary to provide reliable design methodologies and convenient start up strategies of the column. In order to promote the generalisation of DWC in industrial application it is necessary to provide reliable design methodologies, but it is also very important to define strategies for a convenient startup of the column. The present paper proposes a new dynamic model for a DWC and applies it to formulate the startup control.
2. Dynamic Distillation Model (DDM) The DDM proposed by Woinaroschy (1986, 2007) represents a good compromise between the degree of complexity and correctness. The advantage and originality of the selected model consist in the fact that the iterative algebraic equations are avoided. The core of the model consists in the following system of ordinary differential equations (with the usual notations for distillation field): Total mass balance around plate j:
dN j dt
= L j −1 + V j +1 − L j − V j ± FL , j ± FV , j
(1)
Component mass balance around plate j for component i:
d ( N j xi , j ) dt
= L j −1 xi , j −1 + V j +1 y i , j +1 − L j xi , j − V j yi , j ± FL , j x F ,i , j ± FV , j y F ,i , j (2)
Original equation for dynamic calculation of temperature on plate j: m
dT j dt
¦ =−
i =1
γ i , j Pi , j § pj m
¦ i =1
x dγ i , j ¨1 + i , j ¨ γ dx i, j i, j © xi , j γ i , j dPi , j pj
· dx i , j ¸ ¸ dt ¹
(3)
dT j
The state variables are Nj, j=1,2..n; xi,j, i=1,2..m-1, j=1,2..n; and Tj, j=1,2..n. The variation of total pressure during each time integration step is much smaller than the variations of composition and temperature. In order to simplify the procedure, the vapor pressure on each tray is considered constant along the time integration step, but it will be recomputed at the beginning of the new time step. The tray pressure drop is calculated on the base of hydraulic correlations, specific for the plate type. Vapor flow rate Vj is obtained from total energy balance and the vapor composition is calculated according to Murphree efficiency. Liquid flow rate Lj is computed on the base of Francis' correlation for the corresponding plate weir. The equilibrium,
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315
thermodynamic data, and other physical properties correlations are selected in function of the mixture nature. The system of differential equations was numerically integrated by fourth order Runge-Kutta-Gill method, the DDM being coded in FORTRAN.
3. Example A mixture of three components (60% benzene, 30% toluene and 10% ethylbenzene) is separated in a DWC with sieve plates and lateral downcomers. The vapor pressures Pi,j of components were calculated on the basis of Antoine equation, and the trays efficiency was set at value 1 (equilibrium trays). 3.1. Design of the divided wall column. The next column parameters were imposed as follows: feed specification: liquid at bubble point; feed flow rate: 0.0053 kmol s-1; side stream flow rate: 0.001455 kmol s-1; type of condenser: total; condenser pressure: 760 mm Hg; reflux ratio: 3; type of reboiler: total; reboiler heat duty: 417 kW; bottom liquid volume: 0.146 m3; tray surface (for top and bottom sections): 0.451 m2; tray surface (for right and left side of the dividing wall): 0.2255 m2; weir height: 0.025 m; hole diameter: 0.002 m. Using DDM (searching the values at final, stationary state) were established by several iterations the number of trays for the column sections, the location of the feed and side streams and the fraction of liquid flowing in the right hand side of the dividing wall. This iterative search was made in order to obtain the best separation of each component. The corresponding values are: Number of trays: top section: 6; left side: 15; right side: 15; bottom section: 13; Feed stream location: the 2nd from the top of the left side; Side stream location: the 3rd from the top of the right side; Fraction of liquid flowing in the right hand side of the dividing wall: 0.45. In these conditions the components’ mole fractions in the products are: 0.9564 benzene in the top product, 0.970 toluene in the side product and 0.9340 ethylbenzene in the bottom product. 3.2. Optimal startup control. Startup of distillation columns is a very challenging control and simulation problem due to both theoretical and practical aspects. A general sequence of actions which forms the basis for different startup procedures was formulated by Ruiz et al (1988). At the end of several preliminary actions all plates have enough liquid holdup, so that the liquid can start to fall down the downcomers. The downcomers are sealed and no vapor can go up through them. The liquid composition is the same on all plates, being equal with the feed composition. In the frame of present work these conditions define the initial state from which begins the effective startup transient operating regime procedure. Traditionally, the column is operated at constant values of control parameters. Usually, these are the prescribed values for the desired stationary regime. In an optimal transient regime procedure the column will be operated at prescribed time-distributed values of control parameters, in order to minimize the duration of the transient regime. In fact, optimal startup control consist in reaching a desired final state from a set of given initial condition in minimum time by an adequate control policy. That means minimization of the penalty performance index formulated as: ns
si (t f )
i =1
s si
¦ 1− I = tf + ω
ns
(4)
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where tf is the final time, Ȧ > 0 is a penalty coefficient, ssi are the desired final stationary state values, and the final values of state variables si (tf ), i = 1,2,…ns are calculated by integration of equations (1)-(3). Minimization of the penalty performance index is made through control variables ui subject to the bounds:
umini ≤ ui ≤ umaxi
i = 1, 2..., nu
(5)
A set of DDM simulations indicated that the more suitable control parameters for the optimal startup of the divided wall distillation columns are the reflux ratio and the sidestream flowrate. The task of optimal startup control of the DWC was solved using the algorithm proposed by Bojkov and Luus (1994), based on the iterative dynamic procedure given by Bojkov and Luus (1992, 1993) which employs randomly chose candidates for the admissible control. The algorithm was applied for 5 time stages. The grid points number for state-grid was 5, 9 for policy-grid, and 9 for piece time-grid. The region contraction factor was set at 0.8, and the total number of iterative dynamic procedure iterations was 10. The startup time for optimal reflux control is 120 min. and for side-stream flowrate control is 130 min. These results (for each case obtained after 44805 numerical integrations of the system (1)-(3) with 200 differential equations) are remarkable in comparison with operating at constant control parameters where the startup time is 380 min. For all these regimes the final stationary state corresponds to an average value of the normalized derivatives less than 10-6 (maximum integration step is 1 s.). In figures 1 and 2 are presented the optimal reflux control and the optimal side-stream flowrate control (subscript s indicates final, stationary value).
Figure 1. Optimal reflux control
Figure 2. Optimal side-stream flowrate control
The selected control variables (reflux or side-stream flowrate) can be easily manipulated in practical applications. In a DWC the reflux must be high enough to build-up the reflux on both sides of the dividing wall. The value of the reflux ratio strongly modifies the separation on both sides of the diving wall and hence it will affect the concentration profiles along the trays. Not only the distillate and bottom product will be influenced by the variation of reflux ratio, but also the side-stream which is desired to contain the intermediate component at very high concentration. This consideration can lead to the conclusion that a correct reflux policy will bring the DWC in stable operating condition in a reasonable time. The liquid split which is a means of controlling the side draw purity (Mutalib and Smith, 1998) was imposed at the value obtained in steady state as the feed composition did not vary in the present study. The influence of the liquid split
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variation along the startup period had an insignificant influence on the startup time. As regarding the vapor split it was left to adjust naturally according to the temperature distribution along the trays and pressure drop. In figures 3 and 4 are presented the evolutions of components’ mole fractions in the top and bottom products. In figure 3 the evolution of the benzene concentration in the top product at constant control parameters and at optimal side-flowrate control overlaps (for the entire time domain of optimal side-flowrate control, respectively 130 min.). It can be observed that the responses in the bottom concentrations are determinant for the values of startup time, as it was expected.
Figure 3. Evolution of benzene concentration in the top product for startup at constant control parameters and at optimal side-flowrate control ( ʊ ), and at optimal reflux control (---).
Figure 4. Evolution of ethylbenzene concentration in the bottom product for startup at constant control parameters (ʊ ), at optimal reflux control (---) and at optimal side-flowrate control (– · –).
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4. Discussion The selected value for the number of time stages to 5 seems to be too small. A higher value of this number increases drastically the CPU time, without a substantial improving of the performance index (Luus, 1989; Luus and Galli, 1991). In the case of side-stream flowrate control, the increase to 10 of the number of time stages have reduced the startup time only with one minute, but the corresponding control policy is more complicated. The attempt to find the optimal startup control of the divided wall column with other optimization techniques (Luus-Jaakola, Hooke-Jeeves) failed. As in the case of startup optimization of classical distillation columns (Woinaroschy, 2007) it is possible to avoid the undesirable secondary bang-bang effects of the piecewise constant control by replacing it with piecewise linear control.
5. Conclusions The dynamic model proposed proved to represent well the separation in a DWC of a ternary hydrocarbon mixture. The values of internal flows and temperature distributions along the trays reached at steady state were in good agreement with the simulations obtained in the frame of commercial simulators. The use as control variables the reflux ratio or the side-stream flowrate proved to enable a reduction of the startup time with about 70 % compared with classical startup procedures. The complex technique developed can be a useful tool in studying dynamic behavior and startup optimization for complex columns and can be easily extended to various mixtures.
References B. Bojkov, R. Luus, 1992, Use of Random Admissible Values for Control in Iterative Dynamic Programming, Ind. Eng. Chem. Res., vol. 31, p.1308 B. Bojkov, R. Luus, 1993, Evaluation of the Parameters Used in Iterative Dynamic Programming, Can. J. Chem. Eng., vol. 71. p. 451 B. Bojkov, R. Luus, 1994, Time-Optimal Control by Iterative Dynamic Programming, Ind. Eng. Chem. Res., vol. 33, p.1486 I. J. Halvorsen, S. Skogestad, 2004, Shortcut Analisys of Optimal Operation of Petliuk Distillation, Ind. Eng. Chem. Res., vol. 43, p.3994 R. Luus, 1989, Optimal Control by Dynamic Programming Using Accessible Grid Points and Region Reduction, Hung. J. Ind. Chem., vol. 17, p.523 R. Luus, M. Galli, 1991, Multiplicity of Solutions in using Dynamic Programming for Optimal Control, Hung. J. Ind. Chem., vol. 19, p. 55 M. I. A. Mutalib, R. Smith, 1998, Operation and Control of Dividing Wall Distillation Columns, Trans IchemE, vol. 76, part A, p. 318 C. A. Ruiz, I. T. Cameron, R. Gani, 1988, A Generalized Model for Distillation Columns III. Study of Startup Operations, Comput. Chem. Eng., vol. 12, p. 1 M. Serra, M. Perrier, A. Espuna, L. Puigjaner, 2000, Study of the Divided Wall Column Controlabillity: Influence of the Design and Operation, Comput. Chem. Eng., vol. 24, p. 901 C. Tryantafillou, R. Smith, 1992, The Design and Optimisation of Fully Thermally Coupled Distillation Columns, TransIChemE, part A, Chem. Eng. Res. Des., vol. 70(A5), p. 118 S. J. Wang, D. Wong, 2007, Controllability and energy efficiency of high purity divided wall column, Chem. Eng. Sci., vol. 62, p. 1010 S. J. Wang, C. J. Lee, S. S. Jang, S. S. Shien,2008, Plant-wide design and control of acetic acide dehydration system via heterogeneous azeotropic distillation and divided wall distillation, J. Process Control, vol. 18, p. 45 A. Woinaroschy, 1986, A New Model for the Dynamic Simulation of the Rectification Processes. I. Development of the Mathematical Model and Algorithm, Rev. Chim., vol. 37, p. 697 A. Woinaroschy, 2007, Time-Optimal Control of Distillation Columns by Iterative Dynamic Programming, Chem. Eng. Trans., vol. 11, p. 253
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimization of Preventive Maintenance Scheduling in Processing Plants DuyQuang Nguyen and Miguel Bagajewicz The University of Oklahoma, R. T-335 SEC, 100 E. Boyd, Norman, OK 73019, USA
Abstract A new methodology designed to optimize both the planning of preventive maintenance and the amount of resources needed to perform maintenance in a process plant is presented. The methodology is based on the use of a Montecarlo simulation to evaluate the expected cost of maintenance as well as the expected economic loss, an economical indicator for maintenance performance. The Montecarlo simulation describes different failure modes of equipment and uses the prioritization of maintenance supplied, the availability of labour and spare parts. A Genetic algorithm is used for optimisation. The well-known Tennessee Eastman Plant problem is used to illustrate the results. Keywords: Preventive maintenance, Maintenance optimization, Montecarlo simulation
1. Introduction Maintenance can be defined as all actions appropriate for retaining an item/part/equipment in, or restoring it to a given condition (Dhillon, 2002). More specifically, maintenance is used to repair broken equipment, preserve equipment conditions and prevent their failure, which ultimately reduces production loss and downtime as well as the environmental and the associated safety hazards. It is estimated that a typical refinery experiences about 10 days downtime per year due to equipment failures, with an estimated economic lost of $20,000-$30,000 per hour (Tan and Kramer, 1997). In the age of high competition and stringent environmental and safety regulations, the perception for maintenance has been shifted from a “necessary evil” to an effective tool to increase profit, from a supporting part to an integrated part of the production process. Effective and optimum maintenance has been the subject of research both in academy and in industry for a long time. There is a very large literature on maintenance methods, philosophies and strategies. In addition, there is a large number of Computerized Maintenance Management Systems (CMMS) software packages devoted to help managing / organizing the maintenance activities. Despite this abundance, the optimization of decision variables in maintenance planning like preventive maintenance frequency or spare parts inventory policy, is usually not discussed in textbooks nor included as a capability of the software packages. Nonetheless, it has been extensively studied in academic research: Many models were discussed and summarized in the excellent textbook by Wang and Pham (2006)] and various review papers, e.g. Wang (2002). Most of the models are deterministic models obtained by making use of simplified assumptions, which allow the use of mathematical programming techniques to solve. The most common optimization criterion is minimum cost and the constraints are requirements on system reliability measures: availability, average uptime or downtime. More complex maintenance models that consider simultaneously many decision variables like preventive maintenance (PM) time interval,
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labor workforce size, resources allocation are usually solved by Genetic algorithm (e.g. Sum and Gong, 2006; Saranga, 2004). Monte Carlo simulation is usually used to estimate reliability parameters in the model. Tan and Kramer (1997) utilized both Monte Carlo simulation and GA. None of preventive maintenance planning models considers constraints on resources available in process plants, which include labor and materials (spare parts). For example, the maintenance work force, which is usually limited, cannot perform scheduled PM tasks for some equipments at scheduled PM time because of the need to repair other failed equipments. Such dynamic situations can not be handled by deterministic maintenance planning models or are not considered in published maintenance planning models that use Monte Carlo simulation tools. To ameliorate all the aforementioned shortcomings, we developed a new maintenance model based on the use of Monte Carlo simulation. The model incorporates three practical issues that have not been considered in previous work: i) different failure modes of equipment, ii) ranking of equipments according to the consequences of failure, iii) labor resource constraints and material resource constraints. The maintenance model, which was developed by Nguyen et al. (2008) is integrated here with a GA optimization to optimize the PM frequency.
2. Monte Carlo simulation – based maintenance model 2.1. The objective value The objective value is the total maintenance cost plus economic loss (to be minimized). The economic loss is the loss caused by equipment failures that lead to reduced production rate or downtime. It is the economic indicator for maintenance performance, i.e. the better the maintenance plan the smaller the economic loss. Thus by minimizing the maintenance cost plus the economic loss, one simultaneously optimizes the cost and the performance of maintenance. The cost term includes four types of cost: the PM cost and CM cost, which are the costs associated with preventive maintenance and corrective maintenance activities, respectively, the Labor cost (the salary paid to employees) and the inventory cost (the cost associated with storing spare parts of equipments). The economic loss term includes two types of losses: i) economic loss associated with failed equipments that have not been repaired (for example, a fouled heat exchanger can continue operating but at reduced heat transfer rate, ii) economic loss due to unavailability of equipment during repair time. The economic loss is calculated as a loss rate ($ per day) multiplied by the duration of the period within which the loss is realized. To determine economic loss rates, an analysis is carried out on each piece of equipment to determine the economical effects of equipment failure, which include reduced production rate or even shutdown, the deterioration of product quality, etc. 2.2. Input data The following data are needed in the model: i) reliability data for equipment, ii) the time and the associated material cost to perform corrective maintenance (CM) and preventive maintenance, iii) economic data: labor paid rate, inventory cost rate and economic loss rate, iv) other data like the waiting time for an emergently ordered spare part to arrive.
Optimization of Preventive Maintenance Scheduling in Processing Plants
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We assume that the failure distribution is exponential, thus, only one parameter is needed to describe the reliability of equipment: the mean time between failures (MTBF). Other distributions can be used but they require at least two parameters. 2.3. Ranking of repairs The equipments to be repaired are ranked according to the consequences of failures: 1 is emergent and 5 is affordable to go unrepaired. The maintenance of equipments with higher rank (higher priority) takes precedence over the lower ranked ones (Table 1). Table 1: Ranking of equipments for Maintenance purpose (following Tischuk, 2002) Consequence of Failure Probability of subsequent catastrophic Failure
High
Medium
Low
High
1
2
3
Medium
2
3
4
Low
3
4
5
2.4. Failure modes of equipments An equipment may have different failure modes involving different parts of the equipment. It can fail because of deterioration of mechanic parts (possible consequence is complete failure that requires equipment replacement) or electronic parts malfunction (partial failure that can be repaired). Different failure modes need different repair costs and repair times and induce different economic losses. The sampling of different failure modes of equipment is done as follows: i) assign a probability of occurrence for each type of failure mode using information on how common a failure mode is, ii) at the simulated failure time of the equipment, the type of failure mode that actually occurred is sampled in accordance with the failure modes’ probability of occurrence. 2.5. Decision variables Three decision variables are considered in the model: i) the PM time schedule that involves two parameters: the time to perform the first PM (called PM starting time) and the PM time interval, ii) the inventory policy, which is the decision whether to keep inventory for a specific spare part necessary for repairing a specific equipment, iii) the number of maintenance employees. The PM starting time and PM time interval are expressed as a fraction of MTBF (e.g. PM time interval = a*MTBF), the fraction a is to be optimized (for each equipment).
3. Monte Carlo simulation procedure Most of the material in this section is taken from a recent paper (Nguyen et al, 2008) that has explored the use of Monte Carlo simulation for evaluation purposes. 3.1. Maintenance rules - No delay in performing maintenance once the resources are available - If equipment has undergone corrective maintenance a predetermined period of time prior to the scheduled PM (current value = 7 days), the PM is suspended so that resources can be used elsewhere
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-
If, due to unavailability of resources, repair of an equipment has been delayed more than a predetermined threshold value (current value = 21 days), the priority for repair of that equipment is upgraded one level
3.2. Simulation details This technique is based on repeated sampling of the equipment failure and evaluation of the cost of maintenance activities as well as the economic losses associated to the failed states of equipments. The method continues sampling and computing an average until the average converges to a finite value. The sampling procedure is as follows: -
-
-
Failure times of equipments are sampled using reliability function (failure rate) of equipments At failure times of equipment, the type of failure modes that caused equipment failure is sampled in accordance with the probability of occurrence. The cost of corrective maintenance, the repair time and the economic losses are determined corresponding to the type of failure modes identified. Preventive maintenance requests for equipments are generated in accordance with the predetermined preventive maintenance schedule (predetermined PM policy) The planning time horizon is divided into time intervals of weeks. In each week: i) All the CM requests (when equipments failed) and all the scheduled PM requests are identified. ii) CM request and PM requests for equipment with highest priority will be fulfilled. Continuing with CM requests and PM requests for equipments with lower priority until the (labor and materials) resource available is used up. If resources are not available, the requested maintenance action has to be delayed until the resources become available again (e.g. the needed spare part is available through emergent purchasing). When a maintenance action is performed on an equipment at time t, that equipment is assumed to be as good as brand new and failure events for that equipment will be re-sampled (updated) starting from time t.
4. Genetic algorithm We used a standard binary GA whose detail can be found in various textbooks on GA. We describe only the step of coding from true values of decision variables into binary variables in the chromosome as follows: - The PM time frequency is given by a*MTBF (for each equipment). The fraction a, to be optimized by GA, is confined to take one of the following 16 values: [0.025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2] (vector A). The value of a is indicated by the index i (the location) of the elements in vector A, e.g. if i = 2, then a = A[2] = 0.05 - A gene consisting of 4 binary variables klmn is used to represent the index i. - Genes for spare parts inventory and labor are similar (these variables are fixed in this paper). The GA parameters are as follows: population size = 20; fraction of population to keep = 0.5; mutation rate = 0.3; Roulette wheel selection and two point crossover method.
Optimization of Preventive Maintenance Scheduling in Processing Plants
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5. Example The new framework for maintenance analysis and optimization is demonstrated using the well-known Tennessee Eastman (TE) plant. The description and the process flowsheet for the TE process can be found in the literature, e.g. in Ricker and Lee (1995). The list of equipments in the process is given in table 2. Table 2. List of equipment of the TE process Equipments
Quantity
MTBF (days)
Time for CM (hrs)
Time for PM (hrs)
Priority
Valves
11
1000
2-5
2
3
Compressors
1
381
12-18
6
1
Pumps
2
381
4-12
4
4
Heat Exchanger
2
1193
12-14
8
2
x
Flash drum
1
2208
24-72
12
1
x
Stripper
1
2582
48-96
12
1
x
Reactor
1
1660
12-72
12
1
x
PM interferes with production ?
The MTBFs for all equipments are obtained from Center for Chemical Process Safety (1989) and the maintenance time is obtained from Bloch and Geitner (2006) (for pumps, compressors, valves) or estimated if the information is not available (for other equipments). Our example shows the results when the PM time intervals are optimized. Other variables are fixed: ten employees, keeping inventory for all spare parts and reasonable numbers for the PM starting time. The maintenance model and the GA are implemented in Fortran running on a 2.8 GHz CPU, 1028 MB RAM PC. The final results for the fraction a (PM time interval = a*MTBF) are shown in table 3. Table 3. Optimal PM frequency Equipments
11 Valves
2 Compresors
2 Pumps
Flash drum
Fraction a
0.1 (6 valves) & 0.25 (5 valves)
0.1
0.2
1.2
Equipments
Heat Exchangers
Stripper
Reactor
Fraction a
1.2
1.0
1.0
These results are consistent with the results obtained by Nguyen et al.(2008): for the group of equipments whose PM does not interfere with production (e.g. valves & pumps), high PM frequency is obtained: fraction a ranges from 0.1 to 0.25 (Nguyen et al., 2008 obtained 0.1 by inspection). In turn, for group of equipments whose PM interferes with production (e.g. the reactor) such that PM causes economic loss during maintenance time, frequent use of PM is not recommended (fraction a = 1.0, 1.2). The evolution of the current best value of objective function is shown in figure 1, which shows that the objective value converges to a finite value only after 7 iterations. The computation time (after 57 iterations) is 1 hr 24 min.
D.Q. Nguyen and M. Bagajewicz
Obj. value (millions)
324
1.625 1.62 1.615 1.61 1.605 1.6 0
10
20
30
40
50
60
Iteration
Figure 1. Evolution of the current best objective value in GA iterations
6. Conclusions A new maintenance model based on the use of Monte Carlo simulation and integrated with GA optimization is presented in this article. The model incorporates three practical issues not considered in previous work and is capable of analyzing and optimizing complex maintenance operations.
References Bloch H.P and Geitner F.K. (2006). Maximizing Machinery Uptime, Elsevier, MA, USA. Center for Chemical Process Safety, AIChE (1989). Guidelines for Process Equipment Reliability Data with Data Tables, ISBN 0816904227 Dhillon B.S. 2002. Engineering Maintenance, CRC Press, Boca Raton, USA. Nguyen D.Q, C. Brammer and M. Bagajewicz. (2008). A New Tool for the Evaluation of the Scheduling of Preventive Maintenance for Chemical Process Plants. Industrial and Engineering Chemistry Research, To appear. Ricker N.L and Lee J.H. (1995). Nonlinear Modeling and State Estimation for the Tennessee Eastman Challenge Process. Comput. Chem. Eng., 19(9), 983-1005. Shum, Y.S and Gong, D.C. (2006). The Application of Genetic Algorithm in the Development of Preventive Maintenance Analytic Model. The International Journal of Advanced Manufacturing Technology. Vol. 32, pp.169-183. Saranga. H. (2004). Opportunistic Maintenance Using Genetic Algorithms. Journal of Quality in Maintenance Engineering, 10(1), pp. 66-74. Tan J.S. and Kramer M.A. (1997). A General Framework For Preventive Maintenance Optimization In Chemical Process Operations. Computers and Chemical Engineering, 21(12), pp. 1451-1469. Tischuk, John L. (2002). The Application of Risk Based Approaches to Inspection Planning. Tischuk Enterprises (UK). Wang H. and Pham H. (2006). Reliability and Optimal Maintenance, Springer Series in Reliability Engineering, Springer-Verlag, London. Wang H. (2002). A survey of maintenance policies of deteriorating systems. European Journal of Operational Research, 139(3), pp. 469-489.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Predictive Optimal Management Method for the control of polygeneration systems Andr´es Collazos, Fran¸cois Mar´echal ∗
´ Ecole Polytechnique F´ ed´ erale de Lausanne, LENI-STI, Bˆ at. ME A2, Station 9, CH-1015 Lausanne, Switzerland
Abstract A predictive optimal control system for micro-cogeneration in domestic applications has been developed. This system aims at integrating stochastic inhabitant behavior and meteorological conditions as well as modeling imprecisions, while defining operation strategies that maximize the efficiency of the system taking into account the performances, the storage capacities and the electricity market opportunities. Numerical data of an average single family house has been taken as case study. The predictive optimal controller uses mixed integer and linear programming where energy conversion and energy services models are defined as a set of linear constraints. Integer variables model start-up and shut down operations as well as the load dependent efficiency of the cogeneration unit. This control system has been validated using more complex building and technology models to asses model inaccuracies and typical demand profiles for stochastic factors. The system is evaluated in the perspective of its usage in Virtual Power Plants applications. Key words: predictive control, optimal management, polygeneration, microcogeneration
1. Introduction The integration of polygeneration systems in urban areas is seen as one of the promising routes for adressing CO2 mitigation needs. For example, decentralized combined heat and power production is foreseen in virtual power plant concepts [1]. The design of polygeneration systems in urban areas relies on the definition of the system management strategy that decides the operation of the energy conversion equipment (cogeneration ∗ Corresponding author. Email address:
[email protected] (Fran¸cois Mar´ echal). Preprint submitted to Elsevier
January 31, 2008
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and heat pumping) and of the energy storage system in order to provide the energy services required at minimum cost. The design method is typically based on the definition of average days from which the ambient temperature and the demand profiles are taken as reference. One key component of this strategy is the energy storage equipment that is used to create a phase shift between the energy conversion and the demands allowing for equipment size reduction and better profitability. When the management strategy is based on optimization methods such as presented in Weber et al. [2], the design method relies on the definition of typical days during which the performances are computed assuming a perfect knowledge of the temperature profiles and energy demand. This assumption is, however, not acceptable when developing a management strategy for an existing system since these profiles are stochastic and are not perfectly predictable. The goal of this paper is to present a predictive control strategy for the optimal management of polygeneration systems in complex buildings. The method includes a predictive model of the energy demand of the building based on the prediction of the ambient temperature and an Auto Regressive model with eXternal inputs (arx) of the building heat losses, combined with a simplified simulation of the heat distribution system. The optimal management strategy uses a mixed integer linear programming model to decide the start up and shut down times of the equipment and decide the heat storage management. The optimal control system thus developed has been validated by connecting it with a detailed building simulation model that is assumed to represent the real non linear and stochastic behavior of the building in its environment. Finally, access to the electricity market price has been assumed. As targeted in virtual power plants concepts, it has been demonstrated that it is possible to use such systems for exploiting the energy storage systems – including the building structure – to increase the combined heat and power production, thus increasing the benefit of a globalized power production system. 2. Domestic energy system studied The system under study includes one cogeneration unit (a Stirling Engine) and a backup boiler, both fueled by natural gas. The system supplies heat to two heat storage tanks: one for the heating system, the other for the domestic hot water (dhw). The temperature in the heat distribution system (radiator system) is controlled by a 3-way valve and the temperature set point is determined as a function of the ambient and room temperatures using a heat loss model and heat distribution model. On Figure 1, Tdhw and Tsh are the temperatures of the water in the dhw tank and in the heat storage. Tin and Text are the room and outside temperatures of the building respectively. Tcg,out (t) is the temperature of the water exiting the cogeneraton unit, Tb,out (t) is the temperature of the water exiting the back-up boiler, Tdhw,in (t) is the temperature of the hot water going into the dhw tank, Tsh,in (t) is the temperature of the hot water going into the heat storage tank and Tr is the nominal return temperature ˙ b (t) are the mass flows entering the cogeneration unit and of the water. m ˙ cg (t) and m ˙ dhw (t) are the mass flows sent to the heat the back-up boiler respectively. m ˙ sh (t) and m storage and the dhw tank. E˙ cg is the electrical power output of the cogeneration unit, E˙ eg,out is the electrical power delivered by the electricity grid, E˙ eg,in is the power sold to the grid and E˙ h,in is the electrical power consumption in the building.
Predictive Optimal Management Method for the Control of Polygeneration Systems
The independent variables are the load charge of the cogeneration unit ucg (t) = the load charge of the storage heat output ush (t) = ˙
Qsh (t) , Qmax sh
327 ˙ cg (t) Q ˙ max , Q cg
the load charge of the back-up
Qsh (t) Qb (t) boiler ub (t) = Q ˙ b (t) . ˙ max , and the 3-way valve control uvlv (t) = Q ˙ cg (t)+Q b ˙ ˙ Here Qcg (t), Qsh (t) and Qb (t) are the heat outputs at time t of the cogeneration unit, the heat storage tank and the boiler respectively. The superscript max indicates the maximum allowed value for each variable. The sizes of the units in the system are calculated using a the Queuing Multi Objective Optimizer (qmoo) developed at the Energy Systems Laboratory at the EPFL (Leyland [3]) in combination with a linear programming problem as described by in Weber et al. [2]. The sizes of the units considered are shown on Table 1.
Table 1 ˙ ˙ Unit characteristics. Q=maximum heat output, η=efficiency, E=maximum electrical output, ηel =electrical efficiency, ηth =thermal efficiency, V =volume Boiler
Cogeneration Engine
Heat Stroage
dhw tank
˙ Q[kW ]
η[−]
˙ E[kW ]
ηel [−]
˙ Q[kW ]
ηth [−]
V [m3 ]
˙ Q[kW ]
V [m3 ]
2.17
0.8
2.25
0.2-0.25
6.83
0.7-0.75
0.45
10
0.12
The building characteristics correspond to the sia 380/1 target value single family home described by Dorer et al. [4]. The size of the cogeneration unit corresponds to an overall full load operating time of 3962 hours per year. The (variable) efficiencies used are based on the manufacturer’s technical data [5]. 3. The predictive controller The predictive control strategy calculates the optimal values of the controlled variables for t0 ≤ t ≤ t0 + ΔtM H , where t0 is the current instant and ΔtM H is the moving horizon length. The strategy is re-evaluated after every time step Δt. The optimal strategy is calculated by solving a Mixed Integer and Linear Programming (milp) model of the system. The objective of the milp is to minimize the sum of the operating costs as well as a penalty term that measures the total time during which the room temperature is outside the comfort range, for the given time horizon. In order to give a priority to comfort, a significant relative weight is assigned in the objective function to comfort violations. The operating costs are the sum of the gas consumption in the cogeneration unit and back-up boiler, added to the electricity consumption minus the electricity export. The back up boiler is modeled with a constant efficiency. The losses in the storage tanks are modeled using standard heat loss equations. The minimum required temperature for space heating water is calculated using the normalized equation from sia [6] applied to the nominal outlet temperature Text,0 and the nominal heating water supply temperature Tmin,0 [7]. The room temperature of the building is calculated by a second order arx model with the space heat delivered as input ΔTin (t + 2Δts ) + a1 ΔTin (t + Δts ) + a2 ΔTin (t) = b1 Q˙ h,in (t + Δts ) + b2 Q˙ h,in (t)
(1)
where ΔTin (t) = Tin (t) − 18 and Tin (t) is the room temperature. a1 , a2 , b1 and b2 are the coefficients of the model, Q˙ h,in (t) is the heat input and Δts = 14 Δt.
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The control variable for the cogeneration unit is the heat output given by Q˙ cg (t) =ucg (t) · Q˙ max , cg
˙ ˙ max · cgon (t) + cgstart−up (t) · η start−up · Q˙ max . Q˙ min cg · cgon (t) ≤Qcg (t) ≤ Qcg cg,gas cg,th
(2) (3)
The electricity output of the cogeneration unit as a function of the heat output is given by the following piece-wise function start−up min E˙ cg (t) =cgon · E˙ cg + cgstart−up (t) · ηcg,el · Q˙ max cg,gas min min ˙ ˙ ˙ + Ecg + cgpw mel,1 Qcg (t) − Qcg (4) min + (1 − cgpw (t)) mel,2 Q˙ cg (t) − Q˙ cg,pw + mel,1 Q˙ cg,pw − Q˙ cg , The first term of the right hand side of Equation 4 corresponds to the minimal electricity output. cgon ∈ {0, 1} is the integer variable that indicates if the cogeneration unit is on or off. The second term corresponds to the electricity output when the unit is started. The variable cgstart−up (t) indicates whether the cogeneration unit has been started at time t; note that this is not an integer variable, but it can only take the values 0 and 1 because of its definition. The third and fourth terms of Equation 4 correspond to two piecewise linear components modeling the electrical output as a function of the heat output Q˙ cg (t). mel,1 and mel,2 are the linear slopes, cgpw ∈ {0, 1} is an integer variable that indicates which piece is used and Q˙ cg,pw is the breakpoint. A similar equation to Equation 4 is used for modeling the gas input as a function of the heat output. Finally, the cogeneration unit is constrained to stay on for at least nmin cg,on hours. In order to add the knowledge of the periodicity of one day to the next when calculating the strategies, a “cyclic” constraint is included A(t0 + 24 + 1) = A(t0 + 1)
(5)
where A is any state variable such as the room temperature, the energy stored in the heat storage tanks or the controlled variables. t0 is the time at which the strategy is being calculated. The cyclic constraint (Equation 5) is applied at time t0 + 1 in case the state at time t0 is not within the desired temperature range (in case of a large perturbation or a big discrepancy in the predictions). It is assumed that the system can move to a “good” state within an hour. 4. Validation In order to validate this control strategy a numerical model of the installation has been used. This consists of a Simulink model of the building’s thermal behavior adjusted to correspond to the sia 380/1 target value of a single family home [4], of the heat distribution system and a non linear cogeneration engine using the efficiency charts on [5]. The models described in Section 3 for the heat storage and dhw tank were used also for the simulation of these units. Standard and stochastic profiles of outside temperature, solar gains, internal free gains, electricity consumption and dhw consumption were used to simulate the environment and the inhabitants’ behavior. The temperature was predicted by its mean value from the past 30 days as described by [8]. The same approach was used to predict the solar gains, electricity consumption and dhw consumption. The gains from inhabitants and electrical appliances were considered as perturbations since they
Predictive Optimal Management Method for the Control of Polygeneration Systems
329
are not easily measured in a real implementation. The simulation is performed using the real values to validate the behavior of the control system when there are discrepancies between the predicted and real values. A correction is applied when the stored energy or the temperature of the storage tanks are outside the allowed range. This correction consists of adding some energy (positive or negative) in order to keep the allowed range.This extra energy gives an estimation of the reserve needed for the storage tanks. 5. Results
Management Unit
Tb,out
Tcg,out
Tr m cg
Grid Electricity (eg) consumer
Qcg Heat output Qb
Hot water
DHW tank (dhw)
Tdhw,in m dhw
h,in
Back-up boiler (b)
vlv
Tdhw
Tr Heat storage tank (hs)
Tr
Figure 1. Test case system
Tin Ths Thsmin
20 min req temp Resulting strategy Stategy at time 1128 Stategy at time 1139 Stategy at time 1151
18 16 1
ucg >ï@
Stirling engine (cg)
m hs
Eeg,out Ecg Eeg,in E
u b u vlv u sh
22
0.5 0
Text
Internal heat gains
1 ush >ï@
u cg
Electrical power
Tr m b
Tariff info
Temperature [ oC]
The milp optimization was performed using ampl-cplex. The calculation times were below 1 minute per strategy evaluation. The controller was applied during five days in spring. The operating costs for the system with the cogeneration unit are 13% lower than the operating costs when all the heat input to the system is delivered by a boiler and when all the elecricity is bought from the grid, with the same energy storage and distribution strategy. Figure 2 compares the room temperature Tin with its set-point and the temperature predicted by the controller for three non consecutive strategy reevaluation times. This picture shows that the controller reevaluates the strategy and adapts it at every time interval allowing it to compensate for the perturbations and for inaccuracies in the predictions. The Figure also shows that the predicted strategy differs from the final strategy for further times in the horizon (oscillations of ucg around 1160-1170), thus the necessity to re-evaluate the strategy more often than the actual horizon length.
0.5 0 1120
1130
1140 1150 1160 hour of the year [h]
1170
1180
Figure 2. Resulting and predicted strategies
Figure 3 shows the energy management with and without the cyclic constraint (Equation 5). The strategy that uses the cyclic constraint features a better management of the storage tanks, preventing a storage of heat in the tanks for longer periods and therefore reducing the storage losses. The operating costs for this strategy are around 2% lower with no extra penalty in the comfort or in the reserve energy required (Section 4). In the Virtual Power Plants perspective [1], the case where the electricity price is not constant has also been assessed to demonstrate the capabilities of the controller to adapt the strategy to take advantage of a time dependent electricity market price. Figure 4 compares the strategies with a varying electricity price and a constant electricity price. The varying price reduces the cost of energy supply by 5% with no additional comfort violation. The constant electricity price is the average of the varying electricity price over the 5 days considered.
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A. Collazos and F. Maréchal
2 1120
1140
1160 1180 1200 hour of the year [h]
1220
1240
Figure 3. Stored energy with and without the cyclic horizon approach
0.1 0.05 0 3 2 1 0
[kW]
Qdhw [kWh]
4
0 1100
1 0.5 0
electricity price [euro/kWh]
maximum heat storage capacity not cyclic cyclic
6
1 0.5 0
[kW]
0
[-]
ucg ub
5
E eg,out E eg,in
Qsh [kWh]
10
[-]
15
1 0.5 0
constant electricity price variating electricity price 1130
1135 1140 1145 hour of the year [h]
(
1150
Figure 4. Time dependent electricity price
6. Conclusions A model based predictive controller has been developed using a Mixed Linear and Integer Programming model to define the optimal management strategy of micro-cogeneration systems in building applications. The milp model takes into account starting and shutdown of the unit as well as the partial load efficiency using a piecewise formulation. The model includes the balance of the hot water storage tanks as well as the heat accumulation in the building envelope. The controller was validated with a numerical model of the system that is more detailed than the model used for the predictive controller. The predictions of temperature and solar gains as well as the consumption of domestic hot water and electricity are obtained. The cyclic horizon has proved to deliver a better performance than the “open” horizon. In the virtual power plants perspective, this controller shows an ability to adapt the strategy in order to profit from fluctuating price of the electricity. References [1] System-development, build, field installation and european demonstration of a virtual fuel cell power plant, consisting of residential micro-chps. [2] C. Weber, F. Mar´echal, D. Favrat, S. Kraines, Optimization of an SOFC-based decentralized polygeneration system for providing energy services in an office-building in Tokyo, Applied Thermal Engineering 26 (13) (2006) 1409–1419. [3] G. Leyland, Multi-objective optimisation applied to industrial energy problems, Ph.D. thesis, EPFL, Lausanne, Switzerland (2002). [4] V. Dorer, R. Weber, A. Weber, Performance assessment of fuel cell micro-cogeneration systems for residential buildings, Energy and Buildings 37 (2005) 1132–1146. [5] Solo stirling 161 combined power / heat (chp) module (2005). [6] Standard sia 384/2 (1988). [7] M. Zehnder, Efficient air-water heat pumps for high temperature lift residential heating, including ´ oil migration aspects, Ph.D. thesis, Ecole Polytechnique F´ed´ erale de Lausanne (2004). [8] G. Henze, D. Kalz, C. Felsman, G. Knabe, Impact of Forecasting Accuracy on Predictive Optimal Control of Active and Passive Building Thermal Storage Inventory, HVAC & R Research 10 (2) (2004) 153–178.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Comparison of model predictive control strategies for the simulated moving bed Adrian Dietz, Jean-Pierre Corriou Laboratoire des Sciences du Génie Chimique (LSGC), Nancy Université, CNRS, 1, rue Grandville, BP 20451,F- 54001 Nancy Cedex
Abstract This work addresses the study of an efficient chromatographic separation unit operation control, the simulated moving bed (SMB). Linear model predictive control (MPC) is considered in this work. A comparison of two different sets of manipulated inputs is carried out: on one hand, the classical one often presented in the literature, which consists in manipulating directly different flow rates involved in the process and, on the other hand, an approach coming from other counter-current separation processes which consists in manipulating the ratios of flow rates of each SMB zone. The advantages and drawbacks of each control strategy are discussed. In all cases, results show clearly the interest of applying MPC to high complexity systems such as the SMB. Keywords: simulated moving bed, model predictive control.
1. Introduction Chromatographic techniques allow the separation of products with a high purity required in industrial fields such as fine chemistry, pharmaceutics, food. This unit operation is usually operated in batch mode and is well known for its high investment cost due to the adsorbent and large eluent consumption. In order to tackle this drawback, the continuous moving bed technology was first developed as the true moving bed (TMB) where the solid and the liquid flows move in countercurrent way. However, because of the solid flow, this process causes solid attrition, so that the SMB technology was then developed. In a SMB, the solid movement is simulated by simultaneous switching of the inlet and exit ports corresponding to feed, eluent, extract and raffinate, in direction of the fluid flow (Figure 1). Consequently, the continuous system corresponding to the TMB where a steady state can be obtained becomes a hybrid one resulting from a cyclic operation mode. Typical studies in the literature range from the design stage [1-5] to the operation [6], identification [7], parameter and state estimation [8-10], and control [11-16] of the SMB. Many different control techniques are mentioned including linear and non linear model predictive control and non linear geometric control. Several variants of this technology are also developed such as the Varicol process or the power feed operation. In this work, two different model predictive control strategies of a SMB differing by the choice of the manipulated inputs are compared. On one hand, the classical one often presented in the literature consists in directly manipulating different flow rates involved in the process and, on the other hand, the strategy mentioned by Couenne [17] consists in manipulating ratios of flow rates and is used for xylenes separation. The idea of using ratios of flow rates was already used in distillation control [18] where Skogestad consider the two-ratio configuration (L/D,V/B) as the best choice of manipulated inputs in case of dual control. In the same manner, the choice of flow rates ratios seems to be interesting for the SMB control because it reduces the high non-linearity of the process
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A. Dietz and J.-P. Corriou
as the separation phenomena are directly related to flow rate ratios rather than to flow rates themselves. In the flow rate ratio control scheme [17], the two main outputs are the purity and yield of the products, two other outputs are respectively defined to guarantee a stable operation of the process and to optimize it. The manipulated inputs are the ratios of liquid flow rate in zone k divided by the equivalent solid flow rate. In the flow rate control scheme, the controlled outputs are the purities at the extract and raffinate outlets and the manipulated inputs are the eluent (solvent), extract, recycle and equivalent solid flow rates. Zone I Eluent
Raffinate
Zone II
Zone IV
Extract
Port switching direction
Feed
Zone III
Figure 1: Scheme of the Simulated Moving Bed.
A linear model predictive control law is retained in both cases because of its attracting characteristics such as its multivariable aspects and the possibility of taking into account “hard” constraints on inputs and inputs variations as well as “soft” constraints on outputs (constraint violation is authorized during a short period of time). To practise model predictive control, first a linear model of the process must be obtained off-line before applying the optimization strategy to calculate on-line the manipulated inputs. The model of the SMB is described in [8] with its parameters. It is based on the partial differential equation for the mass balance and a mass transfer equation between the liquid and the solid phase, plus an equilibrium law. The PDE equation is discretized as an equivalent system of mixers in series. A typical SMB is divided in four zones, each zone includes two columns and each column is composed of twenty mixers. A nonlinear Langmuir isotherm describes the binary equilibrium for each component between the adsorbent and the liquid phase.
1. Identification of the linear model The linear model for predictive control is based on the step responses of the process with respect to the various manipulated inputs. As mentioned previously, in a SMB, the solid flow is simulated by synchronous valve switching at given intervals. The switching period of the SMB is computed from the equivalent solid flow rate. A variable switching period induces a varying sampling period as the measurements are assumed to be performed only after each commutation and correspond to average concentrations over this switching period. 1.1. Linear model for flow rate control The step responses of the extract and raffinate purities, resp. y1 and y2, (Fig. 2) are obtained for 0.05% steps of respective eluent, recycle, extract and solid flow rates,resp. u1, u2, u3 and u4, used as manipulated inputs. The steps are performed after the process reaches a steady state purity of 95% for both products. Most of the responses are close to first order step responses and present similar time constants, which is suitable for further control. Only the step response of the extract purity with respect to the eluent
Comparison of Model Predictive Control Strategies for the Simulated Moving Bed
333
flow rate (y1/u2) displays an inverse response, however it has a low order of magnitude like two other step responses (y1/u1, y1/u3).
Figure 2: Step response coefficients of the extract and raffinate purities with respect to the flow rates (from top to bottom: eluent, recycle, extract and solid ).
1.2. Linear model for ratio control The step responses for ratio control are obtained by varying successively the ratios uk of the liquid flow rates of the successive zones k over the equivalent solid flow rate (Fig. 3). The results show that several inverse responses are present; moreover different types of response dynamics exist. The liquid flow rates are calculated from the ratios in order to obtain a constant flow rate ratio in each zone of the SMB.
Figure 3: Step response coefficients of the extract and raffinate purities with respect to the flow rates ratios (from top to bottom: ratio in zone 1, zone 2, zone 3, zone 4 ).
The main remark is that the ratio step responses are very different from the simple flow rate step responses of Fig. 2. Second order responses are present (y1/u2, y1/u3), some step responses show low magnitudes (y1/u4, y2/u1, y2/u4). Also, some time constants are relatively different. When ratios are manipulated, several flow rates are simultaneously manipulated which makes the total character complex and unpredictable.
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2. Model predictive control The model predictive control used includes all features of Quadratic Dynamic Matrix Control [19], furthermore it is able to take into account soft output constraints as a non linear optimization. The programs are written in C++ with Fortran libraries. The manipulated inputs (shown in cm3/s) calculated by predictive control are imposed to the full nonlinear model of the SMB. The control simulations were made to study the tracking of both purities and the influence of disturbances of feed flow rate or feed composition. Only partial results are shown. 2.1. Flow rate control
Figure 4: Flow rate control in case of raffinate purity tracking. Left: controlled outputs. Right: manipulated inputs.
Figure 5: Flow rate control in case of feed flow rate disturbance rejection. Left: controlled outputs. Right: manipulated inputs.
Several points must be emphasized before discussing the results obtained. Being given that the sampling period depends on the solid flow rate, the dynamic matrix must be rebuilt at each computing step. In order to maintain the QL (optimization of quadratic criterion with linear constraints) nature of the optimization problem, the switching period for the future inputs is assumed to be identical to the first one calculated. The predicted outputs at different times are obtained by cubic spline interpolation. For a set point change of the raffinate purity from 0.95 to 0.96 and back to 0.95 (Fig. 4), the control of the raffinate purity is well ensured and the manipulated inputs undergo acceptable moves. The control of the extract purity would show similar characteristics. The disturbances of the feed flow rate of +10% and -10% applied at times 13000 and 19000s (Fig. 5) are well rejected and the manipulated flow rates are stabilized after a transient period corresponding to the disturbance effect.
Comparison of Model Predictive Control Strategies for the Simulated Moving Bed
335
2.2. Ratio control As previously mentioned, the manipulated inputs are now the ratios of the liquid flow rates in each zone over the equivalent solid flow rate. However, in the Figures, the operating flow rates are shown. In the case of the SMB, the identification procedure presented some difficulties compared to the more classical flow rate identification and control. The control horizon was set to one for stability reasons, and higher prediction and model horizons were used. Fig. 6 is obtained for the same set point tracking as Fig. 4. The tracking is acceptable, more coupling is present for the extract purity and the manipulated inputs moves are less smooth. These results are slightly less satisfying than for flow rate control.
Figure 6: Ratio control in case of raffinate purity tracking. Left: controlled outputs. Right: operating flow rates.
Figure 7: Ratio control in case of feed concentration disturbance rejection. Left: controlled outputs. Right: operating flow rates.
The unmeasured feed concentration disturbance rejection posed more difficulties (Fig. 7). On the opposite, the measured feed flow rate disturbance is rejected without dynamic effects (Fig. 8) as the manipulated inputs are algebraically and linearly related to the disturbance value. Even if ratio control is globally less efficient that flow rate control, the capacity of ratio control to reject feed flow rate disturbances is attractive in some particular cases such as the pharmaceutical or the fine chemistry where the production is carried out by batches. Thus the set point remains constant because it is associated to the batch recipe resulting in a given final product concentration, and the main disturbance comes from the feed flow rate that can be modified by the pump operation or the operator.
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Figure 8: Ratio control in case of feed flow rate disturbance rejection. Left: controlled outputs. Right: operating flow rates.
4 Conclusions and Perspectives In this work, the influences of two different sets of manipulated inputs have been compared in the case of linear model predictive control of a simulated moving bed. The first one consisting in direct manipulation of flow rates of the SMB showed a very satisfactory behavior for set point tracking and feed disturbance rejection. The second one consists in manipulating the flow rates ratios over each SMB section. At the identification stage, this strategy proved to be more delicate as the step responses displayed important dynamic differences of the responses. However, when the disturbance concerns the feed flow rate, a better behavior is obtained whereas a feed concentration disturbance is more badly rejected. Other control studies, such as robustness and other control strategies, will be carried out in next works. Although the SMB control was carried out in simulation based on a realistic model of the process, the application of these control strategies to a real SMB for validation purposes should be done.
References [1] F. Charton and R.M. Nicoud, J. Chromatogr. A, 702 (1995), 97-112 [2] RM. Nicoud, LC-GC Int., 5 (1992), 43-47 [3] M. Mazzotti, G. Storti and M. Morbidelli, J. Chromatogr. A, 769 (1997), 3-24 [4] O. Ludemann-Hombourger and R.M. Nicoud, Sep. Sci. Technol. 35(12), (2000), 1829-1862 [5] C.B. Ching, K.H. Chu, K. Hidajat and M.S. Uddin, AIChE J., 38(11) (1992), 1744-1750 [6] M. Mazzotti, G. Storti and M. Morbidelli, J. Chhromatogr. A, 827 (1998), 161-173 [7] I.H. Song, S.B. Lee, H.K. Rhee and M. Mazotti, Chem. Eng. Sci., 61 (2006), 1973-1986 [8] M. Alamir, F. Ibrahim and J.P. Corriou, J. Process Cont., 16 (2006), 345-353 [9] E. Kloppenburg and E.D. Gilles, J. Process Cont., 1, (1999), 41-50 [10] M. Alamir, J.P. Corriou, J. Process Cont., 13, (2003), 517-523 [11] M. Alamir, F. Ibrahim and J.P. Corriou, J. Process Cont., 16 (2006), 333-344 [12] G. Erdem, S. Abel, M. Morari, M. Mazotti, M. Morbidelli and J.H. Lee, Ind. Eng. Chem. Res., 43 (2004), 405-421 [13] K.U. Klatt, F. Hanisch, G. Dünnebier, J. Process Cont., 12 (2002), 203-219 [14] M. Ben Thabet, M. Alamir, M. Bailly and J.P. Corriou, AIChE 97, Los Angeles, (1997), 1316-1321 [15] S. Natarajan and J.H. Lee, Comp. Chem. Engng., 24 (2000), 1127-1133 [16] A. Toumi and S. Engeel, Chem. Eng. Sci., 43(14), (2004) 3895-3907 [17] N. Couenne, G. Bornard, J. Chebassier and D. Humeau, in congress SIMO 2002, Toulouse, France, 10 (2002) [18] S. Skogestad, P. Lundstrom and E.W. Jacobsen, AIChE J, 36(5), (1990) 753-764 [19] C.E. Garcia and A.M. Morshedi, Chem. Eng. Comm., 46 (1986), 73-87
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Model Reduction Techniques for Dynamic Optimization of Chemical Plants Operation Bogdan Dorneanua, Costin Sorin Bildeaa,b, Johan Grievinka a b
Delft University of Technology, Julianalaan 136, Delft, 2628BL, The Netherlands Politehnica University of Bucharest, Polizu Street 1, Bucharest, 011061, Romania
Abstract The application of model reduction techniques in the context of dynamic optimization of chemical plants operation is investigated. The focus is on the derivation and use of reduced models for the design and implementation of optimal dynamic operation in large-scale chemical plants. The recommended procedure is to apply the model reduction to individual units or groups of units, followed by the coupling of these reduced models, to obtain the reduced model of the plant. The procedure is flexible and accurate and leads to a major reduction of the simulation time. Keywords: model reduction, dynamic optimization, alkylation
1. Introduction The strong competition in the industrial environment nowadays demands for economical operation of chemical plants. This goal can be achieved in two ways, which do not exclude each other. One approach is to continuously respond to the market conditions through dynamic operation. A second approach is to develop control systems that maintain the steady state or implement the optimal dynamic behaviour. For the first approach, the economical optimality is achieved through dynamic optimization. For the second approach, the development of the plantwide control structures to achieve stable operation is of paramount importance. However, both approaches presented above require dynamic models of the chemical plant. The quality of the model is crucial for achieving the objective: the model must represent the plant behaviour with good accuracy, but the complexity must be limited because both applications require repeated solution during limited time. Another requirement is that the model is easy to be maintained and adapted to future plant changes. The order-reduction of the process model could offer a solution. Several linear [1] and nonlinear techniques [2] have been developed and their application to different case studies reported. Although significant reduction of the number of equations is achieved, the benefit is often partial, because the structure of the problem is destroyed, the physical meaning of the model variables is lost and there is little or no decrease of the solution time [3]. In this contribution, the derivation of the optimal control profiles is realised by using a reduced model obtained through the model reduction with process knowledge approach. The procedure takes into account the inherent structure that exists in a chemical plant in the form of units or groups of units that are connected by material and energy streams. This decomposition mirrors the decentralization of the control problem. The recommended procedure is to apply model reduction to individual units, and then to couple together these reduced models. The technique will be applied to a case study: the iso-butane alkylation plant.
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2. Approaches to dynamic optimization The objective of the dynamic optimization is to determine, for a dynamic system, a set of decision variable time profiles (pressure, temperature, flowrate, heat duty etc.) that optimise a given performance criterion, subject to specified constraints (safety, environmental and operating constraints). The dynamic optimization problem of interest in this contribution can be stated as follows: tf min Obj ( x (t f ), u (t f ), y (t f ), t f , p ) = ∫ obj ( x (t ), u (t ), y (t ), t , p ) dt u (t ),t f 0
(1)
⋅
s.t.
f ( x(t ), x(t ), u (t ), z (t ), p ) = 0
(2)
g ( x (t ), u (t ), z (t ), p ) = 0
(3)
xmin ≤ x (t ) ≤ xmax
(4)
umin ≤ u (t ) ≤ u max
(5)
z min ≤ z (t ) ≤ z max
(6)
x (0) = x0
(7)
In this formulation, x (t ) are state (dependent) variables, u (t ) are control (independent) variables and z (t ) are algebraic variables, while p are time-independent parameters. The dynamic models of chemical processes are represented by differential-algebraic equations (DAEs). Equation (2) and (3) define such a system. Equations (4), (5) and (6) are the path constraints on the state variables, control variables and algebraic variables respectively, while equation (7) represents the initial condition of the state variables. Obj is a scalar objective function at final time, t f . The most common approach to DAE-based optimization problems is the transformation of the infinite-dimensional dynamic problem into a finite-dimensional nonlinear programming problem (NLP) [4]. Two main approaches have been developed in order to make this transformation. The first one is to decompose the dynamical system into the control and the state spaces. In the next step, only the control variables are discretized and remain as degrees of freedom for the NLP solver [5]. The method is called the sequential approach. The DAE system has to be solved at each NLP iteration. The disadvantages of the approach are: problems of handling path constraints on the state variables, since these variables are not included directly in the NLP solver [5]; the time needed to reach a solution can be very high in case the model of the dynamic system is too complex; difficulties may arise while handling unstable systems [4]. In the second approach, both the state and the control variables are discretized. In this way, a large-scale NLP problem is obtained, but the DAE system is solved only once, at
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the optimal point. In this way, the disadvantages of the sequential approach are eliminated, but there is still the issue of handling the problem size [4]. In the recent years, a new approach has been developed for eliminating this disadvantage [5]. This approach is called the quasi-sequential approach and takes the advantages of both the sequential and the simultaneous approaches: since both the control and the state variables are discretized, the path constraints for the state variables can be handled; the DAE system is integrated only once, so the computation becomes more efficient.
3. Model reduction for dynamic optimization As seen in the previous chapter, all the approaches used to solve the dynamic optimization problem integrate, at some point, the dynamical system of the chemical process. In order to obtain more efficiently the values of the optimum profile of the control variable, a suitable model of the system should be developed. That means that the complexity of the model should be limited, but, in the same time, the model should represent the plant behaviour with good accuracy. The best way to obtain such a model is by using the model reduction techniques. However, the use of a classical model reduction approach is not always able to lead to a solution [6]. And very often, the physical structure of the problem is destroyed. Thus, the procedure has to be performed taking into account the process knowledge (units, components, species etc.). In the following chapter, the application of the model reduction with process knowledge for the dynamic optimization will be presented. This will be done by means of a case study: the iso-butane alkylation plant. 3.1. The iso-butane alkylation plant The alkylation of iso-butane is a widely used method for producing high-octane blending component for gasoline. For the purpose of this study, the following reactions capture the overall chemistry: C4 H 8 + i − C4 H 10 → i − C8 H 18
(8)
C4 H 8 + i − C8 H 18 → C12 H 26
(9)
Figure 1. The iso-butane alkylation plant.
The reactions are exothermic and occur in liquid phase. The secondary reaction (9) has large activation energy, therefore high selectivity is favoured by low temperatures. The cooling is achieved in an external heat-exchanger. The second reaction is suppressed by keeping the concentration of butene low. Therefore, a large excess of iso-butane is fed to the reactor. From the reactor effluent, the light impurities, reactants, products and heavy products are separated by distillation and removed or recycled.
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The plantwide control structure (Figure 2) is the same as the one determined to have a stable behaviour in [6]: the flowrate of the fresh butene is specified, while the isobutane is introduced by inventory control. i – C4H10 F3
FB0 F1 LC
FC
FC
FA0 C4H8
F4
LC
Reaction section
Separation section F5
Figure 2. The proposed plantwide control structure for the iso-butane alkylation plant.
Local control is also present: the reactor is operated at constant volume and temperature, while for the distillation columns, the levels, pressure, and top and level compositions are controlled. The objective of the dynamic optimization problem should be stated before the model reduction is performed, in order to choose the right variables to be kept in the reduced model. The objective of the dynamic optimization problem will be stated as follows: Increase the plant production by 20% with minimal energy consumption in the distillation columns. It should be mentioned that this focus on energy may lead to a long transition period. 3.2. Reduced model The full nonlinear model is developed using Aspen Dynamics. For obtaining the reduced model, the same procedure presented in [6] is used. However, in this case the reduced model will be developed using gProms. First of all, the plant flowsheet is split into units / group of units. The splitting it is done in units to which local control is applied: the reactor (plus the heat exchangers around it), the distillation columns, mixing vessels, pumps. Since the mixers and the pumps are considered instantaneous (no dynamics) they are not interesting for the model reduction. Further, the units are individually reduced. Since the reactor has a strong nonlinear behaviour, the model simplification is used. A dynamic model is written using gProms, consisting of five component balances, and considering constant temperature and physical properties. For the distillation columns, linear model-order reduction will be used. The linear model is obtained in Aspen Dynamics. Some modifications to the previous study have been done to the linear models, in order to have the reboiler duty and the reflux ratio as input or output variables of the linear models. This is needed to have access to those variables in the reduced model, for the purpose of the dynamic optimization. A balanced realization of the linear models is performed in Matlab. The obtained balanced models are then reduced. The reduced models of the distillation columns are further implemented in gProms. When all the reduced models of the individual units are available, these models are further connected in order to obtain the full reduced model of the alkylation plant. The outcome of the model reduction procedure is presented in Table 1, together with some performances of the reduced model.
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Model Reduction Techniques for Dynamic Optimization Table 1. The model reduction of the iso-butane alkylation plant Unit
Model reduction technique
Full nonlinear model
Reduced model
CSTR
Model simplification
15 states
5 states
COL1
Model order-reduction
188 states
25 states
COL2
Model order-reduction
194 states
29 states
COL3
Model order-reduction
169 states
17 states
150 seconds
2 seconds
Simulation time
3.3. Dynamic optimization After the reduced model is obtained, the dynamic optimization problem (equations (1) – (7)) is implemented in gProms. The single shooting method is used. The objective function to be minimised is the sum of the reboiler duties in the distillation columns. Two control variables are considered: the flowrate of the fresh feed of butene ( FA0 ) and the flowrate of the first mixer’s outlet stream ( F1 ), which are also the variables on flow control in the plantwide control structure (Figure 2). After the 20% increase in the production is achieved, the optimizer is asked to ensure a new steady state is reached and the production is kept constant for a while. The two control variables are discretized into 25 time intervals. The size of the first 20 intervals is free, while for the last 5 it is fixed. A selectivity constraint is imposed, in order to maintain the formation of the secondary products at a low value. All the constraints are introduced as inequality type constraints. 46
930
43 40 37 34 5
10
15
Time / [hr]
20
870 810 750 Initial profile
a 0
Optimum profile
Optimum profile
F1 / [kmol/hr]
FA0 / [kmol/hr]
Initial profile
b
690 25
0
5
10
15
20
25
Time / [hr]
Figure 3. The optimum control profiles for: a) the component A fresh feed flowrate; b) the recycle flowrate.
The optimum profiles of the control variables (Figure 3) are obtained after several timeconsuming, trial-and-error iterations. The solution was obtained after a number of about 150 manual iterations, not taking into account the iterations performed by the solver. In each manual iteration, the initial profile was modified by the user, while the solver is trying to optimize this profile. The advantage of having a reduced model at this point is obvious. Further, the optimum profiles were implemented into Aspen Dynamics. The agreement between the responses of the nonlinear and reduced model is excellent (Figure 4). The difference between the reduced and the nonlinear model response is less than 2.3% at the end of the time span. However, the transition time is quite long, as expected when the objective was set. From an initial guess of 6 hours, the optimum solution led to a transition time of about 24 hours. To determine the cause of this behaviour, a study of the system’s time constant
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Production rate / [kmol/hr]
should be performed. This should be done before implementing the optimization, in order to get a better initial guess, and reduce the optimization time. 45 40 Full nonlinear model
35 Reduced model
30 25 20 0
5
10
15
20
25
Time / [hr]
Figure 4. Comparisons between the responses of the full and reduced model after the optimum control profiles are implemented.
4. Conclusions This paper proposes and demonstrates the advantage of exploiting the inherent structure that exists in a chemical plant for developing reduced models to be used during the dynamic optimization of chemical plants operation. The recommended procedure is to apply model reduction to individual units of the plant, and then to couple together these reduced models. The procedure is flexible, allowing different reduction techniques to be applied for different individual units, and the units to be chosen considering the future use of the reduced model. The solution time is significantly reduced, which makes the model easier to be applied for the purpose of our study. Another advantage of the procedure is the modularity of the reduced model, which can be very useful in the case of future plant changes, or even for when the reduced model is used for a different application. In these cases, instead of having to obtain a new reduced model of the whole plant, only the reduced model of the new unit would be changed. Acknowledgement: This project is carried out within the framework of MRTN-CT-2004-512233 (PRISMTowards Knowledge-Based Processing Systems). The financial support of the European Commission is gratefully acknowledged.
References 1. Antoulas, A.C., Sorensen, D.C., Approximation of Large-Scale Dynamical Systems: An Overview, Technical report, 2001, (http://www-ece.rice.edu/~aca/mtns00.pdf - last visited 31.10.2007). 2. Marquard, W, Nonlinear Model Reduction for Optimization Based Control of Transient Chemical Processes, Proceedings of the 6th International Conference of Chemical Process Control, AIChe Symp. Ser. 326, Vol. 98 (12), 2002. 3. Van Den Bergh, J., Model Reduction for Dynamic Real-Time Optimization of Chemical Processes, PhD Thesis, Delft University of Technology, The Netherlands, 2005. 4. Biegler, L.T., Grossmann, I.E., Retrospective on Optimization, Computers and Chemical Engineering 28 (1169), 2004. 5. Hong, W., Wang, S., Li, P., Wozny, G., Biegler, L.T., A Quasi-Sequential Approach to Large-Scale Dynamic Optimization Problems, AIChe Journal 52, No. 1 (255), 2006. 6. Dorneanu, B., Bildea, C.S., Grievink, J., On the Application of Model Reduction to Plantwide Control, 17th European Symposium on Computer Aided Process Engineering, Bucharest, Romania, 2007.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A mathematical programming framework for optimal model selection/validation of process data Belmiro P. Duartea,c, Maria J. Mouraa, Filipe J.M. Nevesb, Nuno M.C. Oliveirac a
Department of Chemical Engineering, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199 Coimbra, Portugal,
[email protected]. b CUF – Químicos Industriais, S.A., 3860 Estarreja, Portugal,
[email protected]. c GEPSI – PSE Group, CIEPQPF, Department of Chemical Engineering, University of Coimbra, R. Sílvio Lima – Pólo II, 3030-290 Coimbra, Portugal,
[email protected].
Abstract This work considers the use of information indices for optimal model selection and validation of process data. The approach followed assumes the existence of a set of fundamental process models associated with possible, although distinct, operating regions. A 2-phase mathematical programming algorithm for the assessment of structural changes and optimal fitting of local models in data series is proposed. This approach is used to determine the kinetic parameters of the gelation reaction of chitosan with genipin, employing dynamical elastic modulus data. Keywords: Model selection, Data validation, Information criteria, Mathematical Programming.
1. Introduction and Motivation We address the problem of efficiently using data relative to a chemical process or experiment for a set of activities associated to model validation, process monitoring and knowledge extraction. This problem has become progressively more and more common in the processing industry, with the incremental assembly of large networks of sensors, where extensive amounts of data are continuously produced as a result of a more careful monitoring, to improve the control and reduce the variability of the quality indexes. The approach followed assumes the existence of a set of fundamental process models associated with possible, although distinct, operating regions of the process. These models represent a priori knowledge that can be used to support the plant supervision, either by direct comparison of their predictions with the plant data or by regression of their parameters to particular subsets of the data. A fundamental question is then the determination of regions where some of the available models become applicable, and the selection of “appropriate” data sets for their regression. Related to this problem is also the question of identifying the points where the process changes, commonly referred as transition points. The determination of these transition points and the assessment of structural changes in data sets is traditionally performed by statisticallybased approaches. Two different methodologies can be found in the literature: 1. the use of estimators such as the Maximum Likelihood score [1], and supW [2] to locate iteratively the change points combined with asymptotic estimators or boostraping procedures to assess the confidence level of the original estimator; 2. the use of multivariate adaptive regression splines (MARS) [3], hinging hyperplanes (HH) [4] and adaptive logic networks (ALN) [5]. All these approaches have been considered for data mining purposes, but are not so efficient when a more careful model construction is
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required. Moreover, they often tend to overfit the data, even when cross validation or pruning procedures are employed to avoid that possibility. In this paper, we propose an algorithm based on a mathematical programming approach for the assessment of structural changes and optimal fitting of local models in data series. For simplicity, a system involving only one regressor and several inputs is considered, and maximum likelihood estimation (MLE) is employed in the objective function. This approach aims to reach the global optimal solution while avoiding hard enumeration-based algorithms [6].
2. Mathematical formulation We consider a system with one output Y ∈ ℜ and several inputs X ∈ ℜs . The data set D comprises the sequences {Yi ,1 ≤ i ≤ N } and {X i ,1 ≤ i ≤ N } of observations sampled at instants ti , where N is the total number of observations. We assume that the data is heteroskedastic with constant variance, and that the maximum number of possible underlying local models representing the process is known a priori, and designated by M . We denote by I ≡ {1," , N } the set of points considered, and by J ≡ {1," , M } the set of admissible local models, which are assumed to be linear in the coefficients. Here we consider that C j = ª¬ β 0 j , β1j ," , βsj º¼ characterizes the jth local model, relative to the regressors [1,X ] : T Yˆi = C j [1, X i ] , i ∈ I
(1)
The problem then consists on simultaneously determining the sets of consecutive points
{
S j = i jmin ," , i jmax i
min j
} that can be assigned as the region of validity of the jth model, with
standing for the first point in jth segment and i jmax for the last, and the respective
vectors of coefficients C j that maximize a global maximum-likelihood criteria. It is assumed that structural changes occur at the points where τ = {i : i ∈ S j i + 1 ∈ S j +1} , thus requiring the application of distinct models on each side of the transition points. Consequently, each model is assumed to be only valid in a region which is disjoint from all of the other regions identified in the data set D . Not all of the models in the set J need to be supported by the data used. Possible contamination of the data sets with outliers as well as the presence of points that do not fit any of the given models are also considered. Several related problems have been previously considered in the literature. In addition to the afore mentioned statistical approaches for structural change detection in data sets and their application for linear system identification [7], the joint problem of model structure determination and parameter estimation was addressed by [8-10]. A related approach was used by [11-13] in the context of data reconciliation. Additional aspects of model selection in chemical engineering are covered in [14]. Although the present problem shares common features with the all of the previous applications, it also presents unique characteristics that require a specific formulation. Since each data point needs to be (possibly) assigned to a specific model within J , binary variables wi , j are introduced to express this fact. The algorithm described is
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based on the use of the Bayesian Information Criterion (BIC) for the selection of the optimal model structure. Among other competing information criterion, this specific index was chosen because experience shows that it can provide an equilibrated balance between the discrimination ability towards simple-enough models, and the simplicity of its evaluation. To enlarge the domain of applicability of the present methodology within reasonable solution times, a two-phase approach is proposed. In the first step (problem P1) an approximate solution (number of models and approximate location of the boundaries) is obtained, through the simplification of the objective function considered. In this case a L1 norm is used, which originates a MINLP problem. The first phase of the algorithm can optionally be skipped, when a good initial solution is already available, e.g. through the previous application of one of the iterative strategies such as MARS, HH or ALN. Alternatively, the solution obtained in this step can be used for the identification of outliers in the data set [15-17]; these points are subsequently removed before the final solution phase. This is possible since the L1 norm is closer to the median, producing estimates which are less sensitive to the presence of outliers. In the second solution phase (problem P2) the minimization of the Bayesian Information Criterion (BIC) is directly considered, subject to model constraints, using a recursive estimation of the variance of the data [10]. The optimization problems solved in this case correspond to mixed integer quadratic programs (MIQP). The mathematical formulation of problem P1 can be succinctly expressed as: | ei , j | min ¦ −n j ln(2π ) − n j ln(σ j2 ) − ¦ 2 + p j ln(n j ) (2.a) w ,C ,σ
s.t.
j ∈J
i ∈I
σj
yi = C j [1, X i ] + ri , j , ∀j T
ri , j ≤ ei , j + (1 − wi , j )M max , M
¦w
i ,j
≤ 1, ∀i ,
j =1
wi −1, j ≥ wi , j , i > 1 ∧ j = 1 ,
(2.b)
ri , j ≥ ei , j − (1 − wi , j )M max N
(2.c)
≥ n min, j , ∀j
(2.d)
wi −1, j ≤ wi , j , i > 1 ∧ j = M
(2.e)
¦w
i ,j
i =1
wi −1, j + wi −1, j +1 ≥ w i , j +1 , i > 1 ∧ j < M
(2.f)
w1,1 = 1, w N ,M = 1 , wi , j ∈ {0,1}
(2.g)
Equation (2.a) presents the objective function, equation (2.b) corresponds to the underlying model structure, equations (2.c) formalize the assignment of the points to segments, where M max is a magnitude limit (constant), here set to M max = max (Yi ) + min (Yi ) , n j is the number of points assigned to jth local model, σ j the standard
deviation of the error and p j the number of parameters involved. Furthermore, equation (2.d) assigns each point to a single model, and implements the requirement that each structural model should include at least a pre-assigned minimum number of points. Equations (2.e-g) are employed to reduce the degeneracy of the optimization problem by setting an assignment order of the first points of the data set to the first local models. In many instances this problem can be solved approximately by considering the solution of a sequence of MILP problems that result from fixing both n j and σ j in each iteration; the estimates of these parameters are afterwards updated, and the solution of the MILP problem updated, sequentially. This is especially the case after careful
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initialization of the problem, when N is larger than M , due to the smaller sensitivity of n j and σ j to the exact delimitation of the regions. In the second phase, problem P2 can be formulated as: min
w ,C ,σ
¦ −n j ∈J
j
ln(2π ) − n j ln(σ j2 ) − ¦ i ∈I
ei2, j
σ j2
+ p j ln(n j )
(3.a)
s.t.
equations (2.b-2.g) (3.b) 1 σ j2 = ¦ei2, j (3.c) n i∈I As in the previous case, n j and σ j can often be estimated sequentially, after the solution of a series of MIQP problems. To speed up the solution of problem P2, a significant fraction of the binary variables included in this problem can be fixed to the values previously determined in P1. This is done by considering that possible changes in the assignment of points to different models only occur in the neighborhood of the transition points identified previously. In this case, the binary variables provided to the model are fixed for a set of points designated as S f , j ≡ {i : i ≥ i jmin + Δ ∧ i jmax − Δ} , ∀j with Δ denoting the number of points allowed to change in the vicinity of the structural changes location. The complementary set of S f , j , designated as S f , j contains all the points that are allowed to be reassigned to a different segment in this case. This definition makes the problem P2 much easier to solve, in practice.
3. Application This approach was employed to determine the kinetics of the gelation reaction of chitosan with genipin, employing dynamical elastic modulus data measured with a cone-and-plate rheometer. Chitosan is a biopolymer with large interest in biomedicine and therapeutic applications, due to its properties. Genipin is crosslinking agent employed to modulate the chitosan network properties achieved through the gelation. One of the techniques used to study the kinetics of polymerization reactions is based on monitoring the rheological properties of the mixture, particularly the elastic modulus, designated as rheokinetics [18]. This approach allows to establish a relation of the so called rheological degree of conversion with the fraction of liquid that turns into gel phase. The liquid-solid reactions are described by the Avrami model, here employed to represent the extent of gelation, designated as η (t ) , as a function of the time [19]:
η (t ) = exp ( −kt n )
(4)
where k and n are parameters dependent on the system. This equation can be linearized, defining R (t ) = ln ª¬ − ln (η (t ) ) º¼ = ln (k ) + n ln (t ) . Here
η (t ) =
G ' (t ) − G 0' G ∞' − G 0'
(5)
where G ' (t ) is the elastic modulus at time t , G 0' is its initial value and G ∞0 its maximal value. Several sources refer that the gelation mechanism of biopolymers, such as gelatine, follows a sequence of four phases [20]. The models representing the sol-gel transition are described by linear relations (Equation 5), with different parameters
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holding for different phases. The rheological monitoring of the gelation of the system chitosan-genipin reveals the occurrence of synerysis [21]. Therefore, the third and fourth phases of the gelation reaction are rheologically dominated by mechanical transformations, with the kinetic features extracted from data having no physical meaning. Morever, it was observed that due to the prevalence of the mechanical aspects, the behavior of the gel in phases 3 and 4 is indistinguishable, and three local models can be employed to represent the complete experiment. We used the dynamics of R (t ) resulting from an experiment lasting for about 12 hours (715 min) and the algorithm presented in Section 2 to determine: i. the kinetic parameters of the reaction rate for each of the gelation phases; ii. the points where change transitions occur. It is noteworthy to mention that the kinetic parameters fitted for the last two phases have no chemical significance due to the synerysis phenomenon. Therefore, in this situation, the total number of models could be fixed equal to 3. GAMS/CPLEX was used to solve both MILP and MIQP problems presented, using a relative tolerance of 10−3 . Table 1 presents the preliminary results for the parameters obtained from the solution of problems P1 and P2, with Δ =15, and N =715. We may see that the algorithm captures the dynamic transitions of the rheological behavior, and particularly the synerysis occurrence is located at the same instant by both norms. The transition from phase 1 to phase 2 is located at different instants. The local models determined in pre-processing phase denote a small difference relatively to the models arising from minimization due to the location of the first change point and because of the characteristics of both norms, L1 penalizing large deviations, and L2 penalizing the square of residuals. These features are well demonstrated by Figure 1.
Figure 1 – Experimental data and model fits obtained.
4. Conclusions A mathematical programming formulation for optimal model selection and validation of process data was considered in this paper. One important advantage of this methodology is its capability of reaching an optimal solution, while avoiding enumeration based algorithms. To reduce the total solution time and alleviate problems resulting from the presence of outliers in the data, a two-phase approach is suggested, where an approximated solution is first obtained and later refined by the direct solution of the BIC. While the numerical solution of the optimization problems involved can present
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some difficulties, some of the properties of the problem can be exploited to reduce these problems. The application of the methodology to the basic determination of kinetic parameters was considered and successfully performed in this work. Table 1 – Structural models for each of phases captured by monitoring the behavior. n Phase log(k ) Time interval (min) 1 2.557 -0.458 [0.00; 57.18] Pre-processing step 2 11.316 -2.616 ]57.18; 135.68] ( L1 minimization) 3 -0.686 0.162 ]135.68;714.68] 1 2.309 -0.383 [0.00; 50.18] Final step ( L2 2 10.981 -2.593 ]50.18; 127.18] minimization) 3 -0.292 0.098 ]127.18;714.68]
rheological CPU (s) 49.95
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References 1. 2. 3. 4. 5.
B.E. Hansen, J. Policy Modeling, 14 (1992) 514-533. D.W.K. Andrews, Econometrica, 61 (1993) 821-856. J.H. Friedman, Annals of Statistics, 19 (1991) 1-67. L. Breiman, IEEE Trans. Inf. Theory, 39 (1993) 999-1013. W.W. Armstrong, M.M. Thomas, Handbook of Neural Computation, Oxford University Press (1996). 6. J.A. Khan, S. Van Aelstb, R.H. Zamara, Comp. Stat. & Data Analysis, 52 (2007) 239-248. 7. J. Roll, A. Bemporadi, L. Ljung, Automatica (2004) 37-50. 8. Brink, T. Westerlund, Chemometrics & Intell. Lab. Systems, 29 (1995) 29-36. 9. H.Skrifvars, S. Leyffer, T. Westerlund, Comp. & Chem. Engng., 22 (1998) 18291835. 10. A.Vaia, N.V. Sahinidis, Comp. & Chem. Engng., 27 (2003) 763-779. 11. T.A. Soderstrom, D.M. Himmelblau, T.E. Edgar, Control Eng. Practice, 9 (2001) 869-876. 12. N. Arora, L. Biegler, Comp. & Chem. Engng., 25 (2001) 1585-1599. 13. C.L. Mei, H.Y. Su, J.Chu, J. Zhejiang Univ. Sci. A. 8 (2007) 904-909. 14. P.J.T. Verheijen, In: Dynamic Model Development, Methods, Theory and Applications, Series: Computer-Aided Chemical Engineering, Elsevier, 16 (2003), 85-104. 15. M.A. Fischler, R.C. Bolles, Comm. ACM, 24 (1981) 381-395. 16. S. Pynnonen, Proc. Univ. Vaasa, Discussion Papers 146 (1992). 17. K. Kadota, S.I. Nishimura, H. Bono, S. Nakamura, Y. Hayashizaki, Y. Okazaki, K.Takahashi, Physiol. Genomics 12 (2003) 251-259. 18. A.Y. Malkin, S.G. Kulichikin, Rheokinetics, Huethig & Wepf (1996). 19. M. Avrami. J. Chem. Phys., 7 (1939) 1103-1112. 20. V. Normand, S. Muller, J.-C. Ravey, A. Parker, Macromolecules, 33 (2000) 10631071. 21. G.V. Franks, B. Moss, D. Phelan, J. Biomat. Sci., 17 (2006) 1439-1450.
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Towards on-line model-based design of experiments Federico Galvanin, Massimiliano Barolo and Fabrizio Bezzo* DIPIC – Dipartimento di Principi e Impianti di Ingegneria Chimica Università di Padova, via Marzolo 9, I-35131, Padova, Italy. * E-mail:
[email protected] Abstract Model-based experiment design aims at detecting a set of experimental conditions yielding the most informative process data to be used for the estimation of the process model parameters. In this paper, a novel on-line strategy for the optimal model-based re-design of experiments is presented and discussed. The novel technique allows the dynamic update of the control variable profiles while an experiment is still running, and can embody a dynamic investigation of different directions of information through the adoption of modified design criteria. A case study illustrates the benefits of the new approach when compared to a conventional design. Keywords: model-based experiment design, parameter estimation.
1. Introduction Modern model-based experiment design techniques [1,2] allow the definition of the “best” experimental conditions to adopt in the experimentation in order to increase the informative content about a process being studied. Experimental data from designed experiments are essential in model identification both to assess the validity of a model structure (model discrimination), and to estimate the model parameters that allow the model to match the experimental data in the range of expected utilization. For parameter estimation purposes, a general procedure for the statistical assessment of dynamic process models described by a set of differential and algebraic equations (DAEs) can be defined through the following three steps [1]: 1. the design of a new set of experiments, basing on current knowledge (model structure and parameters, and prior statistics); 2. the execution of the designed experiments to collect new data; 3. the estimation of new model parameters and statistical assessment. The iteration of steps 1 to 3 provides a new information flux coming from planned experiments leading to a progressive reduction of uncertainty region (as demonstrated in several applications [3,4]). However, note that each experiment design step is performed at the initial values of model parameters, and the uncertainty of these values, as reported in the literature [5], can deeply affect the efficiency of the design procedure. In view of above, it would make sense to exploit while the experiment is running the increment of information acquired through the collection of new measurements, so as to perform a dynamic reduction of the uncertainty region of model parameters. In this paper, a new methodology based on the On-line Model-Based Re-design of the Experiment (OMBRE) is proposed and discussed. The basic idea of this novel technique is to update the manipulated input profiles of the running experiment performing one or more intermediate experiment designs (i.e., re-designs) before reaching the end of the experiment. Each re-design is performed adopting the current value of the parameters set, which is the value of estimated model parameters until that moment.
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2. The methodology It is assumed that the generic model is described by a set of DAEs in the form: f (x (t ), x(t ), u(t ), w,θ , t ) = 0 ® yˆ (t ) = g(x(t )) ¯
(1)
where x(t) is the Ns-dimensional vector of time dependent state variables, u(t) and w are, respectively, the model time dependent and time invariant control variables (inputs), θ is the set of Nθ unknown model parameters to be estimated, and t is the time. The symbol ^ is used to indicate the estimate of a variable (or a set of variables): y(t) is the M-dimensional vector of measured values of the outputs, while ǔ(t) is the vector of the corresponding values estimated by the model. Model-based experiment design procedures aim at decreasing the model parameter uncertainty region by acting on the experiment design vector ij: ϕ = [y 0 , u(t ), w , t sp , τ ] , T
(2)
where the vector tsp of sampling times of the y variables is a design variable itself; y0 is the set of initial conditions of the measured variables and IJ is the duration of the single experiment. In order to decrease the size of the inference regions of each of the parameters in a model, some measure ψ of the variance-covariance matrix Vθ of the parameters has to be minimised. This amounts to determining the optimal vector ϕ of experimental conditions required to maximise the expected information content from the measured data generated by one or more experiments. The choice of a proper design criteria (A-, D-, E-optimal [6] or SV-based [7]) deals with the choice of the measure function ψ of Vθ. If we take into account a number Nexp of experiments, the matrix Vθ is the inverse of the Nθ × Nθ dynamic information matrix Hθ (Zullo [8]): −1
ªN ªN M M −1 º −1 º Vș (ș, ϕ ) = « ¦ H *ș k (θ, ϕ k ) + (Ȉ ș ) » = « ¦¦¦ σ ij k QTi k Q j k + (Ȉ ș ) » = 1 = 1 = 1 = 1 k k i j ¬ ¼ ¬ ¼ exp
exp
−1
,
(3)
where H*θ |k is the information matrix of the k-th experiment (superscript * indicates that the information matrix refers to a single experiment), σij is the ij-th element of the inverse of the estimated variance-covariance matrix Σ of measurements errors, Σθ is the Nθ × Nθ prior variance-covariance matrix of model parameters, Qi is the matrix of the sensitivity coefficients the for i-th measured output calculated at each of the nsp sampling points. Prior information on the model parameter uncertainty region in terms of statistical distribution (for instance, a uniform or Gaussian distribution) can be included through the matrix Ȉș. Control vector parameterization techniques [9] allow for the discretisation of the control input profiles. Those profiles are approximated using piecewise constant, piecewise linear or polynomials functions over a pre-defined number of intervals. In the case of piecewise constant parameterization, the variables to be optimized are the switching times tsw (the vector of times at which each control variables change in value) and the switching levels of u (i.e the time invariant values of the control within each of the nsw switching intervals). Equation (3) is sufficiently general to be extended to define an on-line model based redesign of experiments. Through this strategy one seeks to update the current information by executing on-line, after a given “updating time” tup (either assigned or to be optimized), a parameter estimation session followed by a re-design of the remaining part of the experiment (and so adjusting the trajectories of control variables). One or more updates can be attained in the re-design, each one adding a new component (in the form of (2)) to the global ij vector of the experiment, so that it can be rewritten as:
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[
]
ϕ = ϕ1 , ϕ 2 ,..., ϕ j ,..., ϕ nup +1 T
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,
(4)
where nup is the number of control updates and ijj is the design vector after the (j-1)-th update. In a general fashion, each component ijj of ij could have a different dimension in terms of number of discretized control variables and/or sampling points (obviously ij1 will be the only component to enclose the initial values to be optimized). The amount of information gathered after the j-th re-design can be expressed in terms of the dynamic information matrix:
[
]
~ ~ ª j −1 ~ −1 º H ș , j (θ, ϕ ) = «¦ H *ș k (θ, ϕ k ) + H *ș (θ, ϕ j ) + (Ȉ ș ) » = H *ș (θ, ϕ j ) + K , ¬ k =1 ¼
(5)
where the sum of the prior information on model parameters (Ȉș-1) and the information acquired before the j-th re-design can be expressed as a constant term K. The symbol (~) indicates that the information content refers to a single updating interval. The efficiency of a design strategy deals with its capability to provide a satisfactory parameter estimation in terms of accuracy (i.e. closeness to “true” value) and precision (related to the dimension of the uncertainty region). As in practice the “true” values of model parameters are not known a-priori, only the precision is evaluated through two indicators: a global precision (ȍș) and a global t-factor (GTF) defined as: § ȍș = ¨ ¨ ©
−1
· ı ¸ , ¦ ¸ i =1 ¹ Nș
2 și
GTF =
1 Nș
NP
¦t i =1
−1 i
,
(6)
where the ti are the t-values statistics, depending by the diagonal elements of Vș and by the actual parameter estimate. For a reliable parameter estimation, each t-value must be greater than a computed reference value (given by the Student’s t distribution with N×M-Nș degrees of freedom).
3. Case study The OMBRE approach is applied to a biomass fermentation model [1], which, assuming Monod-type kinetics for biomass growth and substrate consumption, is described by the following DAEs set: dx rx șx dx1 = (r − u1 − ș 4 )x1 , 2 = − 1 + u1 (u 2 − x2 ) , r = 1 2 dt dt ș3 ș 2 + x2
,
(7)
where x1 is the biomass concentration (g/L), x2 is the substrate concentration (g/L), u1 is the dilution factor (h-1), and u2 is the substrate concentration in the feed (g/L). The model was demonstrated to be structurally identifiable with respect the parametric set ș. The conditions that characterise an experiment are the initial biomass concentration x10 (range 1-10 g/L), the dilution factor u1 (range 0.05-0.20 h-1), and the substrate concentration in the feed u2 (range 5-35 g/L). The initial substrate concentration x20 is set to 0 g/L and cannot be manipulated for experiment design purposes. The principal aim is to detect a proper design configuration allowing to estimate the parameter set ș in a satisfactory manner through a single experiment where both x1 and x2 are measured. It is assumed that the global experimental budget can be represented by a number of nsp = 24 sampling points and nsw = 12 switches to distribute on a maximum experimental horizon of IJmax = 72 h. The inputs u(t) can be manipulated and are represented as piecewise-constant profiles, and the output sampling times and the control variables switching times can be different. The elapsed time between any two
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sampling points is allowed to be between 0.01 h and IJi (the duration of the updating interval), and the duration of each control interval between 0.1 and 40 h. The model parameters are scaled to unity before performing each design step. A multiple shooting technique was used in order to reduce the possibility of incurring into local minima in the design step. However, note that the re-design strategy allows to split the nijdimensional optimisation problem into (nup+1) smaller optimizations, with great benefit for both robustness and quickness of the computation. Synthetic “experimental” data are obtained by simulation of model (7) with ș = [0.310 0.180 0.550 0.050]T as the “true” parameters set, and by adding normally distributed noise with a mean of zero (the vector of parameter units is [h-1, g/L, -, h-1]T) and ª0.5 0. º Ȉ=« » ¬ 0. 0.8¼
(8)
as the M×M variance-covariance matrix of measurements errors. This matrix assumes that the experimental equipment cannot deliver good quality data and that there is no dependence among different measurements. The initial guesses for the parameters are represented by the set θˆ 0 = [0.527 0.054 0.935 0.015]T, corresponding to a starting point that is quite far from the true value. 3.1. Proposed experiment design configurations and results A standard E-optimal experiment design was compared with the newly introduced OMBRE strategy at a variable number of updates of design variables. The following assumptions are made: 1. nsp/(nup+1) samples are acquired during each updating interval (i.e the time between two updating times), while the number of switches can vary; 2. the i-th re-design starts at the time in which the last optimized sample of each design phase (enclosed in iji-1) is acquired; 3. no delay time occurs between the key activities (design, experiment and parameter estimation phases) of the global design procedure; The following experiment design configurations are implemented: 1. STDE: standard E-optimal experiment design; 2. OMBRE-nup: on-line E-optimal re-design of the experiment with nup=1, 2, 3; 3. OMBRE-SV: on-line re-design with nup=3 including SV design criteria (based on the minimisation of the second maximum eigenvalue of Vθ) in the second updating interval. The results are compared in terms of a-posteriori statistics (Table 1) and global statistics (ȍș and GTF, Figure 1 (a) and (b)) obtained after the final parameter estimation session. Table 1 Comparison of different experiment design configurations. Apex * indicates t-values failing the t-test (the reference value is tref = 1.6802 and ș = [0.310 0.180 0.550 0.050]T ) Design STDE OMBRE-1 OMBRE-2 OMBRE-3 OMBRE-SV
Parameter Estimate șˆ [0.257 0.080 0.022]T [0.309 0.303 0.045]T [0.309 0.294 0.047]T [0.320 0.102 0.059]T [0.310 0.110 0.055]T
0.453 0.518 0.517 0.564 0.560
Conf. Interval (95%) [±0.0890 ±0.2963 ±0.0774 ±0.0882] [±0.0173 ±0.2308, ±0.0697 ±0.0156] [±0.0507 ±0.1009, ±0.0853 ±0.0319] [±0.0292 ±0.0984, ±0.0648 ±0.0276] [±0.0086 ±0.0623, ±0.0238 ±0.0072]
t-values [2.97 0.45* 2.02 0.41*] [11.01 1.32* 7.44 2.87] [6.10 1.12* 6.54 1.68*] [10.27 2.111 8.31 1.50*] [36.01 1.77 23.49 7.62]
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Figure 1 Global precision ȍș (a) and GTF (b) for selected re-design configurations at a variable number of updates (nup = 0 stands for a standard E-optimal experiment design).
30 u2 [g/l]
u2 [g/l]
The precision of the estimate can be assessed through the analysis of confidence intervals (95%) while the t-test allow to assess the accuracy of the designs. The results clearly show the benefits in adopting an OMBRE approach. Although the STDE design does not permit to reach satisfactory θˆ2 and θˆ4 , the insertion of a single update (OMBRE-1) provides a significant improvement in the precision of the estimate (see for instance the statistics for θˆ1 , θˆ3 and θˆ4 ). To improve the precision of θˆ2 the number of updates is increased. Although there is an increase in the global precision ȍș (Figure 1a), the advantages of using two or three updates are not so certain. In fact, the global tfactor exhibits an oscillatory behavior (Figure 1b). Note that OMBRE-2 provides a poor estimation of ș4 , and also θˆ2 is still statistically imprecise (although there is a reduction in interval of confidence with respect to OMBRE-1). An additional update provides a better precision in θˆ2 (see for instance the 95% confidence intervals), but θˆ4 is still inaccurate. It is interesting to note that by increasing the number of updates, one obtains a variation in capability of estimating different parameters, i.e. in the directionality of the design [7]. Therefore, it makes sense to assess the effect of an OMBRE-SV configuration in order to exploit the information related to the smaller eigenvalues of Vș. For the case being investigated, a standard E-optimal design acts mainly on the direction of variability of θˆ2 while a SV-based design tends to improve both θˆ1 and θˆ4 [7]. OMBRE-SV allows to estimate the entire ș set in a satisfactory manner increasing the global performance of OMBRE-3 estimation (see Figures 1a and 1b).
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Figure 2 Dilution factor (u1), substrate concentration in the feed (u2) and distribution of samples (tsp) as planned by OMBRE-3 (a) and OMBRE-SV (b). Black squares show the updating times.
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Figures 2a and 2b underline the differences between OMBRE-3 and OMBRE-SV configurations in terms of manipulated inputs and sampling times distribution. Note that the minimisation of the second largest eigenvalue determines the second redesign to be sensibly different from corresponding one in OMBRE-3. As a consequence, also the third re-designs are different from each other.
4. Final remarks A novel methodology of experiment design based on a on-line model based re-design of experiments (OMBRE) has been proposed and discussed. The new technique allows to embody in a model-based experiment design procedure the information content that is progressively acquired while an experiment is running. Results from an illustrative case study are encouraging and clearly demonstrate how the proper choice of a re-design configuration may guide the estimation to more precise and accurate patterns. It is also shown how OMBRE may incorporate different design techniques (e.g., the SV criterion) and thus take advantage of a more tailored directional approach in exploiting the content of the information matrix. Future work will assess the applicability of the OMBRE technique to larger systems and will develop a systematic procedure for the selection of the optimal re-design configuration.
Acknowledgements This research was carried out in the framework of the Progetto di Ateneo 2005 “Image analysis and advanced modelling techniques for product quality control in the process industry”.
References [1] S.P. Asprey, S. Macchietto, 2000, Statistical Tools for Optimal Dynamic Model Building, Comput. Chem. Engng., 24, 1261-1267. [2] I. Bauer, H.G. Bock, S. Körkel, J.P. Schlöder, 2000, Numerical Methods for Optimum Experimental Design in DAE Systems, J. Comput. Appl. Mathem., 120, 1-25. [3] G. Franceschini, S. Macchietto, 2007, Validation of a model for biodiesel production through model-based experiment design, Ind. Eng. Chem. Res., 46, 220-232. [4] C. Reverte, J.L. Dirion, M. Cabassud, 2007, Kinetic model identification and parameters estimation from TGA experiments, J. Anal. Appl. Pyrolysis, 79, 297-305. [5] S. Körkel, E. Kostina, H. G. Bock, J.P. Schlöder, 2004, Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes, Opt. Methods and Software, 19, 327-338. [6] F. Pukelsheim, 1993, Optimal Design of Experiments, J. Wiley & Sons, New York, U.S.A. [7] F. Galvanin, S. Macchietto, F. Bezzo, 2007, Model-Based Design of Parallel Experiments, Ind. Chem. Res, 46, 871-882. [8] L. Zullo, 1991, Computer Aided Design of Experiments. An Engineering Approach, PhD Thesis, The University of London, U.K. [9] V.S. Vassiliadis, R. W. H. Sargent, C. C. Pantelides, 1994, Solution of a class of multistage dynamic optimizations problems. 1-Problems without path constraints, Ind. Eng. Chem. Res, 33, 2111-2122.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Sensor placement for fault detection and localization Carine Gerkens and Georges Heyen Laboratoire d’Analyse et de Synthèse des Systèmes Chimiques Department of Applied Chemistry, University of Liège Sart-Tilman B6A, B-4000 Liège (Belgium)
Tel: +32 4 366 35 23 Fax: +32 4 366 35 257 Email:
[email protected] Abstract A general approach is proposed for designing the cheapest sensor network able to detect and locate a set of specified faults. The method is based on the sensitivity of process residuals with respect to faults. A genetic algorithm is used to select the sensors and their locations. Results are shown for two water networks. Keywords: sensor network, genetic algorithm, fault detection and isolation.
1. Introduction Nowadays, the interest for chemical process monitoring becomes more and more important. Indeed, environmental and safety rules must be satisfied and the required product quality must be achieved. Moreover, fluid leakages are expensive and must be detected as quickly as possible. Fault detection can only be done if a suitable sensor network is installed in the process. However, all measurements are corrupted by noise and the sensor precision has a great influence on the detectability and isolability of process fault. Therefore the sensor precision must be taken into account when a network is designed. In this study, a general method to design the cheapest sensor network able to detect and locate a list of faults in a given process is proposed. The method is based on the fault detection technique proposed by Ragot and Maquin [4]. Those authors use the notion of fault sensitivity to decide whether a residual is influenced or not by a specified process fault. As the problem is multimodal, not derivable and involves many binary variables, the sensor network optimization is done by means of a genetic algorithm (Goldberg [3]). Indeed, the efficiency of this optimization algorithm has been proved for similar problems, such as the design of efficient sensor networks for data reconciliation (Gerkens [2]). The method is illustrated for two water networks of different complexity. The detected faults are leakage in pipes and storage tanks, but other fault types could also be simulated and detected.
2. Fault detection and isolation The objective of fault detection is to determine whether the measurements remain in a normal range of values, as predicted by a process model for a given operating mode of the plant. If the difference between measurements and estimations is too large, a fault is detected. The fault detection and localization techniques are carried out in two steps: the
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estimation of the residuals and the decision. In order to make sure that all the faults that can occur in a process are detectable, the signature matrix must be analyzed. This matrix is the occurrence matrix of the potential fault variables in the model equations, expressed in residual form. As an example, let us consider the following system, characterized by four residuals and six variables at time t:
r1 ( t ) = f1 ( x1 ( t ) , x2 ( t ) , x5 ( t ) , x6 ( t ) )
r2 ( t ) = f 2 ( x1 ( t ) , x2 ( t ) , x3 ( t ) , x5 ( t ) , x6 ( t ) ) r3 ( t ) = f3 ( x3 ( t ) , x5 ( t ) , x6 ( t ) )
r4 ( t ) = f 4 ( x2 ( t ) , x4 ( t ) , x5 ( t ) ) The corresponding signature matrix has the form:
§X ¨ X Σ=¨ ¨0 ¨ ©0
X 0 0 X X· ¸ X X 0 X X¸ 0 X 0 X X¸ ¸ X 0 X X 0¹
A fault is detectable if the corresponding column in the signature matrix contains at least one non-zero element. A fault can be located if the corresponding column in the signature matrix is different from all other columns of the signature matrix. The fault localization consists of deducing what is the fault from the values of the residuals. For that purpose, fuzzy rules are elaborated from the signature matrix. They are linguistic “if-then” constructions of the general form “if A then B” where A are the premises and B the consequence of the rule. As noise influences the value of the residuals, some random perturbations in the measurements may be large enough to trigger a fault detection even when no fault occurs. Taking into account temporal persistence allows improving the detection procedure. For that purpose, instantaneous measurements are replaced by averages calculated over several time steps. The sensitivities of residuals to a given fault are different so that the magnitude of the residual deviations allows to characterize and isolate a fault. The isolability of faults can then be improved by using this difference of sensitivity. Let y be the measurement of a variable of the process. It is the sum of the true value x, the noise İ and the fault f:
y = x +ε + f
Since the true values satisfy the process model, they do not contribute to the residuals, which reflect two terms: the contribution of the noise rε and the contribution of the fault rf ; thus the effect of a fault can be masked by the effect of the noise according to their relative magnitudes. The noise contribution to the ith residual is defined as follows: n
rε ,i = ¦ mij ε j j =1
where mij are the elements of the matrix of the derivatives of the residuals with respect to the variables. If the errors are replaced by the precision of the sensors e j , one obtains the upper bound of the contribution of the noise on the ith residual:
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n
rε ,i = ¦ mij e j j =1
In the same way, the contribution of a unique fault f j affecting the ith residual is defined as follows:
rf j ,i = mij f j The lowest magnitude of the ith residual that allows distinguishing between the noise and the fault f j is defined by the bound: n
¦m
ij
τ ij =
ej
j =1
mij
So, the ith residual is sensitive to fault f j if the magnitude of that fault is higher than τ ij . Fault f j will be located if for all non-zero elements of the signature matrix, the absolute value of the corresponding residual is larger than the corresponding bound
τ ij
and for each zero element of the signature matrix, the absolute value of the corresponding residual is smaller than a fixed upper bound. For example, if one takes the derivative matrix of the process previously described:
§ 1 −0.5 ¨ 2 −4 Σ=¨ ¨0 0 ¨ 6 ©0
0 0 1 −2.5 · ¸ 2 0 3 1 ¸ 3 0 −2 −1 ¸ ¸ 0 −5 −4 0 ¹ T For the following error vector e = ( 0.5,1, 0.8, 0.4,1, 0.4 ) , the corresponding bounds matrix is given by:
∞ ∞ 3 1.2 · §3 6 ¨ ¸ ∞ 3.3 10 ¸ 5 2.5 5 τ =¨ ¨ ∞ ∞ 1.6 ∞ 2.4 4.8 ¸ ¨ ¸ ∞¹ © ∞ 2 ∞ 2.4 3 So, the third fault will be detected and located if the second residual has an absolute value larger than 5 and the third one an absolute value larger than 1.6.
3. Method description The design procedure allowing configuring the optimal sensor network able to detect and locate all the specified faults is carried out in four steps: - simulation of the process and of the faults that should be detected and located; - specification of the sensor database and the sensor requirements; - verification of the problem feasibility;
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optimization of the sensor network.
3.1. Simulation of the process and of the faults that should be detected and located The process is first simulated for typical operating conditions. Then, for each possible fault one decides the minimal magnitude of the fault that should be detected by the sensor network, for example a leakage of 1% of a stream flow rate. The faults are simulated one by one by increasing progressively the leakage until the minimal fault that should be detected is reached. The values of the variables at the beginning and at the end of each pipe obtained during the k last simulations are kept for each fault. No noise is added to the variables at this step because the noise depends on the precision of the measurement tools. The number of samples used to calculate the moving average of the variables depends on the frequency of the measurements and the speed at which the fault should be detected. If the number of measurement times is higher, the fault detection and location is slower but more reliable. If this number is too small, the noise influences more the magnitude of the residuals and the fault detection is more difficult. In the examples of paragraph 4, a value of 5 has been chosen. 3.2. Specification of the sensor database and the sensor requirements 3.2.1. The sensor database For each sensor type, the database contains the following information: - the name of the sensor; - the annualized cost of the sensor, i.e. the annualized sum of the purchase, installation and operating costs; - the type of variable that can be measured by the sensor; - the domain of validity of the measurement; - the accuracy of the sensor, as defined by the following equation:
σ j = ai + bi X j 3.2.2. The sensor requirements In this file, the sensors that exist and don’t have to be replaced are listed as well as the sensors that can not be placed at a particular location in the process. 3.3. Verification of the problem feasibility The problem feasibility check starts by enumerating all the sensors that can be placed in the plant. A binary gene is created for each sensor; its value is set to 1 when the sensor is selected and 0 otherwise. The set of genes forms a chromosome whose length is equal to the number of possible sensors. It may appear that a variable is measured by more than one sensor so that the precision of the most accurate one is taken into account for the bounds calculation. The residual bounds and the residuals are estimated for the initial sensor network: indeed, a noise bounded by the accuracy of the sensor is added to each variable for each measurement time before the mean of the variables and the residuals are calculated. The noise on the variables and then their values depend thus of the sensor network as well as the residual bounds. To ensure that the design problem accepts a solution, the initial sensor network has to be able to detect all the simulated faults. If it is not the case, new sensor types that are more precise should be added to the data base or the minimal magnitudes of the faults to be detected should be set higher. 3.4. Optimization of the sensor network When the existence of a solution has been verified, it can be optimized. The objective function to be minimized is evaluated this way:
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if all the faults can be detected and located, the objective function is the sum of the costs of all the sensor in the network; - if at least one fault can not be detected or located, the current solution is unfeasible and it is penalized by setting its merit function to a large value (twice the cost of all possible sensors). The goal function being generally multimodal, the problem being not derivable and containing only binary parameters, a genetic algorithm [2] has been used as the optimization method. The algorithm that has been used is based on the one developed by Caroll [1]. In this algorithm, the individuals are selected using tournament selection. A shuffling technique allows choosing randomly pairs for mating. A new population is generated by applying single-point cross-over and the jump mutation mechanisms. Individuals of the first population are chosen randomly, by activating randomly 80% of all each genes. The size of the population is set to 20 individuals. The probability of reproduction is fixed to 50%, the probability of single-point cross-over to 50% and the probability of jump mutation to 1%. The fitness function is evaluated for each individual of the new generation. The best one is then kept and duplicated in the case it would be subject to mutation in the following generation. The calculation is stopped when the objective function of the best individual remains unchanged during a specified number of generations.
4. Cases studies Two water networks have been studied. The first one is composed of five storage tanks and ten connection pipes (figure 1). The fifteen faults that should be detected and located are water leakages in the storage tanks or in the pipes. Each storage tanks can be fitted with a level meter, and the flow rate can be measured at both ends of each pipe, which means 25 possible sensors.
Figure 1
Figure 2
In the sensor database three level meters are available with different accuracies and prices, and 10 flow meters with different accuracies, prices and measurement domains. With this database, it is possible to place 135 sensors. That corresponds to a solution space of 2135 = 4.4*1040 solutions. This measurement system has a total cost of 11950 cost units.
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Obtaining the solution requires 14770 generations (295421 goal function evaluations) for a stop criterion of 6000 generations. The optimal sensor network is obtained after 301 seconds on a 1.6GHz computer. This optimal network costs 1860 units and counts 25 sensors, one for each possible sensor location. It allows detecting and locating all the 15 faults. The initial and most expensive network costs 3100 units (1240 cost units more than the optimal one). The second water network (figure 2) is composed of 14 storage tanks and 31 pipes so that there are 76 possible sensor locations. The sensor database contains three level meters with different accuracies and prices, and 15 flow meters with different accuracies, prices and measurement domains. The initial network counts 392 possible sensors. This corresponds to a solution space of 10118 solutions. This sensor network has a total cost of 34100 units. Obtaining the solution requires 26104 generations (522101 objective function evaluations) for a stop criterion of 6000 generations. The optimal sensor network is obtained after 5667 seconds on a 1.6GHz computer. This solution costs 6200 units and requires 76 sensors: one for each possible sensor location. It allows detecting and locating all the 45 faults. In order to detect and locate all the faults, one sensor is required at each location, but the network cost can be minimized by selecting the cheapest sensor that provides the required precision. The most expensive of those network costs this time 9000 costs units (2800 cost units more than the optimal one).
5. Conclusions The proposed design method allows building a sensor network that is able to detect and locate a specified list of tank and pipe leakages. This network is much cheaper than the initial one. The algorithm provides thus a practical solution, even if global optimality can not be demonstrated when using an evolutionary optimization algorithm. This method could be transposed for other types of faults such as the catalyst deactivation or the loss of efficiency in a compressor.
Acknowledgments The authors are grateful to the Walloon Region and the European Social Funds who cofinanced this research.
References 1. Caroll D.L., 21 August 2001, FORTRAN genetic algorithm driver version 1.7, Download from http://cuaerospace.com/caroll/ga.html, consulted on May 2004. 2. Gerkens C., Heyen G., 2005, Use of parallel computers in rational design of redundant sensor networks, Computers and Chemical Engineering 29, 1379-1387. 3. Goldberg D.E., 1989, Genetic algorithm in search, optimization and machine learning, Reading, MA, Addison-Wesley Publishing Company. 4. Ragot J., 2006, Fault measurement detection in an urban water supply network, Journal of Process Control 16, 887-902.
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Using kriging models for real-time process optimisation Marcos V.C. Gomes,a I. David L.Bogle,b Evaristo C. Biscaia Jr.,c Darci Odloakd a PETROBRAS S.A., Av. Horácio Macedo, 950, Rio de Janeiro RJ,Brazil 21941-915 b Chemical Engineering Department, University College London, London WC1E 7JE,UK c Programa de Engenharia Química – COPPE, Universidade Federal do Rio de Janeiro, P.O. Box 68502, Rio de Janeiro, 21945-970, Brazil d Departamento de Engenharia Química, Universidade de São Paulo, São Paulo 05508900 Brazil
Abstract Kriging models have been used in a number of engineering applications, to approximate rigorous models when those computer codes become too time-consuming to be used directly. In this context, they are called surrogate models or metamodels. The use of kriging models as metamodels for process optimisation was addressed in a previous paper [1] where a methodology for metamodel-based process optimisation was proposed, focusing on real-time applications. In this work, new developments were achieved through the use of new examples, one of which the optimisation of a real crude distillation unit involving 19 decision variables. The performance of the metamodel-based optimisation is compared with results obtained with the optimisation based on a first-principles model, embedded in a sequential-modular process simulator. It is shown that metamodel-based optimisation with adaptation of the metamodels during the optimisation procedure provides results with good accuracy and significant reduction of computational effort. The performance comparison between neural networks and kriging models for chemical processes is another contribution of this work.
Keywords: optimisation, crude distillation, kriging, neural network. 1. Introduction A metamodel is a reduced model that is fitted to approximate a complex model (usually a rigorous, first-principles mathematical model). The data used to fit the metamodel is obtained from several runs of the rigorous model, frequently called computer experiments. By analogy to physical experiments, experimental design techniques are used to define the sites where the data should be generated. Metamodels have been widely used in many fields of engineering, to replace rigorous mathematical models when they become too time-consuming or prone to numerical problems. One of the most typical uses of metamodels has been in optimal design where many design scenarios can be easily analysed by optimisation techniques. One of the most used families of reduced models that have been used as metamodels [2] are the kriging models. 1.1. Kriging models The kriging model structure presented here is the most frequently used in the literature (for more details, refer to [3]). Let the set of functions y(x,u) be a rigorous mathematical description of a process, where x are independent variables and u model parameters. The kriging models that approximate the rigorous one are built from a set of design
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points (X,Y) obtained from runs of the rigorous model for a set of parameters u0. They are composed by a linear regression model and a random function: yˆ i (x ) = ȕiT ⋅ f ( x ) + z i ( x ), i = 1! nY
(1 )
The first term is usually a low-order polynomial. The random functions zi have the following form: z i = riT ( x ) ⋅ R −1 ( Y − Fȕ i )
(2 )
where T
T
ª nX º ª nX º ri ( x) = «∏ ℜij (θij, X kj − x j )» and R im ( X m ) = «∏ ℜij (θij, X kj − X mj )» , ¬« j=1 ¼» ¬« j=1 ¼»
k, m = 1! nP
(3 )
The matrix F is obtained by computing the f(x) values for the design inputs X. ℜ are correlation models [4], usually built as functions of the distance between two sites. Therefore, Rim(Xm) is a matrix that contains the correlations between the design sites, and ri(x) is a vector that contains the correlations among a new site x and the design sites. 1.2. Applications on chemical processes Palmer and Realff [2] proposed the first work based on metamodels applied to chemical process design, using kriging models and polynomials. Later, Gomes et al.[1] proposed the use of metamodels for RTO applications. The alkylation process optimisation problem was used to validate the proposed methodology. Accurate solutions were reported with the metamodel approach with less than 30% of the required runs of the original model when compared to the solution based exclusively on the original model. As an extension of this work, it was attempted [5] to apply this methodology to two other examples, one of them a large real optimisation problem of a crude distillation unit (CDU). It was concluded that the previous proposed procedures should be improved, in order to allow their successful application to a wider class of problems. This improvement was accomplished by the introduction of a SAO algorithm. 1.3. Sequential Approximate Optimisation (SAO) SAO is a procedure used to solve optimisation problems when the model computation is time-consuming. The optimisation problem is decomposed into subproblems, confined to a fraction of the original search space, that are solved sequentially based on a trustregion strategy. The original problem functions are usually replaced by polynomials. The way by which the trust region is changed, the assessment of the model approximations and the termination criteria are important issues of the SAO algorithm. In this work, some aspects of a new methodology based on the use of metamodels for real-time process optimisation are presented. This methodology comprises the metamodel generation and its use along with a new SAO algorithm that contains automatic procedures for adaptation and assessment of metamodels. In this work, the highlights of the proposed methodology are presented, along with the results obtained with the optimisation of a real, industrial-scale crude distillation unit.
2. Example In order to validate the proposed methodologies, a real industrial problem has been addressed: the optimisation of the Crude Distillation Unit (CDU) and the Solvents Units of RECAP, a Brazilian refinery of PETROBRAS.
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2.1. Process description The crude oil is fed to the pre-flash column (N507) of the CDU, from which three streams are obtained. The top product is light naphtha which is sent to the solvents units. An intermediate stream constitutes extra-light diesel (DEL). The bottom stream is sent to the atmospheric column (N506), where it is split into the atmospheric residue (RAT), Kerosene, heavy diesel oil and heavy naphtha. The light and the heavy naphtha streams constitute the Solvents Units feed, where the high-valued products rubber solvent (SBO) and Paint diluent (DTI) are obtained after many separation operations. A third stream containing the heaviest remains of the feed is mixed to DEL, Kerosene and Heavy Diesel streams to generate the diesel oil stream. A recycle stream between column N751 and the solvents units feed tank is used to minimize losses of SBO.
Figure 1 – Scheme of the CDU and the Solvents Units of RECAP/PETROBRAS.
2.2. The process model The process model was built using PETROX, a proprietary sequential-modular process simulator from PETROBRAS. The simulation comprises 53 components and pseudocomponents and 64 unit operation modules, including 7 distillation columns and a recycle stream. All modules are built with rigorous, first-principles models. For optimization applications, PETROX was linked to NPSOL, an SQP optimisation algorithm. 2.3. The optimisation problem The optimisation problem takes the following form: min f [y (x ), x] x
(4 )
s.t. : h[y (x ), x] = 0 ; g[y (x ), x] ≤ 0 The set of functions y(x) in Equation (4) comprises all variables whose values are to be obtained from runs of the process simulator to compute the objective function and equality or inequality constraints. The objective function is the operational cost (ī): Γ=
nprods
¦ i =1
$ iprods ⋅ product i −
nutils
⋅ utility j −$ feed ⋅ feed ¦ $ utils j
(5 )
j=1
Table 1 presents the description of the decision variables and constraints of the problem.The problem inequality constraints (constraints 3-21) are related to product specifications and safety or performance limits. The equality constraints 1 and 2 were included to model the heat integration between the atmospheric column and the feed pre-heating train. Another 18 process variables take part of the objective function, as
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product flow rates or utilities. Table 1 - Decision variables and constraints of the optimisation problem 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Decision variables (x) Crude flow rate Steam flow rate to N507 Steam flow rate to N506 Pumparound flow rate Atmospheric heater outlet temperature Kerosene flow rate Diesel reflux flow rate Heavy naphta molar flow rate DEL flow rate Temp. #2 N507 N701 feed flow rate N701 control temperature N703 control temperature N703 reflux flow rate N752 control temperature N753 reflux flow rate N506 pumparound outlet flow rate N753 top/feed ratio preheating train heat duty to N506
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Constraints (h,g) Equality constraint #1 – heat integration Equality constraint #2 – heat integration Light naphta flow rate Diesel ASTMD86 85% temperature Naphta recycle flow rate DTI– Dry point DTI– Initial boiling point ASTMD86 N703 reboiler steam flow rate SBO– Dry point SBO– Initial boiling point ASTMD86 N753 control temperature N753 reboiler steam flow rate N753 bottom flow rate Temp #2 N506 N506 #10 – molar flow rate N506 #22 – molar flow rate N507 #10 – molar flow rate N701 #17 – molar flow rate N703 #3 – molar flow rate N752 #8 – molar flow rate N753 #14 – molar flow rate
3. Methodology: Metamodeling and SAO The methodology for the use of metamodels in RTO begins with the off-line generation of a base metamodel. All the following steps shall be performed during the optimisation procedure. The use of this metamodel in a real-time environment requires its adaptation to face not only changes in the process behaviour, but eventual mismatches between the metamodel and the rigorous model. A validation procedure is required to allow the assessment of the metamodel throughout the optimisation procedure, as well as a suitable set of termination criteria. A comprehensive description of the proposed methodology is presented in [5]. 3.1. Generation of the base metamodel The main aspects for metamodel generation are: (i) Generation of training data, through an experimental design strategy; (ii) Independent variable selection; (iii) Parameter estimation and (iv) Metamodel validation. The training data is generated based on the Latin Hypercube Design (LHD). A forward stepwise regression procedure is used to select the independent variables to be used by the metamodels of each dependent variable. For kriging models, the structure is defined by the set of independent variables selected – including quadratic terms – and the selection of the correlation model. The parameter estimation is performed by a maximum likelihood procedure. For neural nets, the activation function to be used is defined a priori. The structure is completed by the selection of the number of neurons in the hidden layer. A backpropagation procedure has been used for training. The procedure is presented in Figure 2. It starts with the training data, a set of candidate metamodel structures and a set of sets of initial estimates for the metamodel parameters. The best metamodel will be the one that provides the smaller prediction errors computed with a set of independent validation data. The best metamodel will be the one that provides the smaller prediction errors, computed with a set of independent validation data. 3.2. Sequential Approximate Optimisation (SAO) The SAO algorithm proposed in [6] was used as a basis of the algorithm proposed here (Figure 3). The key features of this algorithm are related to the way by which the base metamodel is adapted and assessed, the trust region updating procedure and the
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termination criteria for the optimisation procedure. CONFIGURATION
Training data Set of model structures {S1,…,Sk,…,SnS} Sets of parameter estimates {θ1,…, θj, …, θnθ}
Rigorous Model Base Metamodel SAO Parameters Problem configuration: Variables, , Limits, Initial estimates
Validationdata
Variable selection
Parameter Estimation
Compute prediction errors no
no
Rigorous Model
Metamodel Adaptation
Keep best metamodel
Optimisation k > nS ? yes
Update Trust Region
Check Termination Criteria
j > nθ? yes
NO
OK?
Best metamodel
YES
Figure 2 – The general procedure for metamodel generation
END
Figure 3 – SAO strategy applied to the metamodel-based optimisation.
4. Results Kriging models and neural nets were generated for each of the 39 dependent variables required for the computation of the objective function and the constraints. Table 2 presents the main characteristics of the metamodels (for more details, refer to [5]). To simulate a real-time operation, a set of case studies (Table 3) were proposed, where changes in the process behaviour were introduced by changing the model parameters. The objective was to verify if the adaptation procedure would be able to change the base metamodels in order to allow acceptable solutions to the optimisation problem. The selected model parameters were the feed composition (I and II), the global heat coefficient of the atmospheric column pumparound (UPPA – III and IV) and the global heat coefficient of the condenser of column N753 (UCOND - V). Table 2 - Main characteristics of the metamodels Size of training data set Size of validation data set Number of initial estimates kriging
186 399 10 Regression model
quadratic Gauss Spline Spherical
Correlation models
Neurons in the hidden layer Neural nets
Activation functions
2-5 Hidden layer
Log-sigmoid
Output layer
Linear
Table 3 – Cases for assessment of the SAO/metamodel procedure Case Base I II III IV V
CDU Feed, °API 33.0 32.5 33.5 33.0 33.0 33.0
UPPA 967 967 967 800 1300 967
UCOND 750 750 750 750 750 900
Two indexes were used to assess the proposed methodology, whose computation is described in Equation (6). The relative benefit shows the fraction of the profit obtained with the rigorous solution that could be attained with the metamodel/SAO procedure. x0
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is the initial state of the decision variables, xRIG is the rigorous solution and xSAO is the approximate solution. The relative effort shows the ratio between the number of simulation runs with the rigorous model required by the metamodel/SAO procedure and the correspondent number of simulations required by the rigorous solution. Benefit(%) = 100 ⋅
( ) ( ) (x ) − F (x )
Fobj x SAO − Fobj x 0 Fobj
RIG
0
Effort (%) = 100 ⋅
obj
NSIMSAO NSIM RIG
(6 )
Table 4 presents the obtained results. In most cases, a relative benefit above 85% was obtained, with a minimum value of 77%. The observed relative computational effort remained below 50% for 9 of the 12 cases studied, showing that good accuracy on the optimisation results was obtained with significant reduction of the computational effort. Table 4 - Attained benefit and relative computational effort with the SAO/metamodel procedure. Case Base I II III IV V
Kriging models Benefit, % Effort, % 94.0 35.8 78.7 42.5 89.0 22.4 85.2 21.1 97.9 87.0 90.2 29.7
Neural nets Benefit, % Effort, % 97.1 43.1 77.1 42.5 89.7 53.1 84.6 12.9 93.9 19.5 94.6 54.7
5. Conclusions A new strategy for Real-Time Optimisation combining metamodels and a Sequential Approximate Optimisation (SAO) procedure has been proposed. This methodology is based on automatic procedures, aiming its use in real-time applications. Kriging models and neural nets were used as metamodels. The methodology was tested with an example involving the optimisation of a crude distillation unit, using the first-principles models of a sequential-modular process simulator. The solution of the corresponding optimisation problem with this rigorous model required considerable computational effort. It is shown that the proposed methodology provides solutions with good accuracy and a significant reduction of computational effort. Another advantage of this approach is that the occurrence of numerical problems during the solution of the rigorous model does not result in the failure of the optimisation procedure. The reported results show that kriging models can be used to model chemical processes involving a large number of independent variables, and that they can perform as good as or better than neural nets.
References [1] M.V.C.Gomes, I.D.L.Bogle, D. Odloak, E.C.Biscaia Jr., An application of metamodels for process optimisation, Proceedings of the 16th European Symposium on Computer Aided Process Engineering, (2006) 1449. [2] K. Palmer, M. Realff, Trans IchemE, 80 (2002) Part A 760. [3] T.J. Santner, B.J. Williams, & W.I. Notz, Springer-Verlag New York, Inc. (eds.) The Design and Analysis of Computer Experiments. New York, 2002. [4] S.N. Lophaven, H.B. Nielsen, J. Sondergaard, DACE - A MATLAB Kriging Toolbox. Technical University of Denmark, Technical Report IMM-TR2002-12, 2002. [5] M.V.C.Gomes, Otimização Seqüencial por Aproximações – Uma aplicação em tempo real para o refino do petróleo, D.Sc. Thesis, (in portuguese), PEQ/COPPE/UFRJ, Rio de Janeiro, Brazil, 2007. [6] A.A.Giunta, M.S.Eldred, Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimisation, Long Beach, USA, AIAA-2000-4935.
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Estimation Of A Class Of Stirred Tank Bioreactors With Discrete-Delayed Measurements Héctor Hernández-Escoto,a Ricardo Aguilar-López,b María Isabel NeriaGonzález,bAlma Rosa Domínguez-Bocanegrab a
Facultad de Química - Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México b Departamento de Biotecnología e Ingeniería, Centro de Investigaciones y Estudios Avanzados – Instituto Politécnico Nacional, Av. 100 m, México D.F., 22222, México
Abstract This work addresses the problem of designing an on-line discrete-delayed measurement processor to estimate the state of a class of stirred tank bioreactors where the growth of sulfate reducing bacteria takes places. On the basis of the Monod-type model of the reactor, a geometric approach is straightforward applied to systematically construct and tune the data processor. The resulting estimator is tested on a continuous and a batch culture process, showing a robust convergence even in the presence of modeling errors. Keywords: discrete estimation, nonlinear estimation, bioreactor monitoring.
1. Introduction Sulfate reducing bacteria are anaerobic microorganisms that have become especially important in biotechnological processes (i.e. water treatment) due to its ability to degrade organic material and remove heavy metals [1]. Many processes of material degradation and heavy metal removal are carried on anaerobic bioreactors, which are large fermentation tanks provided with mechanical mixing, heating, gas collection, sludge addition and withdrawal ports, and supernatant outlets. The anaerobic digestion is affected by many factors including temperature, retention time, pH, and chemical composition of wastewater. In a practical framework, the reactor is operated on the basis of laboratory analysis of samples, usually taken out at periodic sampling times; nevertheless, the obtained information reflects the system status in the past depending on the sampling time interval. In view of the mentioned monitoring scheme, operation improvements imply more-frequent (or continuous) monitoring of the key variables; however, the lack of reliable, sterile and robust sensors obstacles this task [2]. This work focuses on the problem of predicting present-time key variables of a class of stirred tank bioreactors using discrete-delayed (DD) measurements; the class refers to the process of a sulfate-reducing bacterium growth. Related to model-based approaches, it is taken into account that, although the bioreactors can be considered as tank reactors for analysis purposes, their complex phenomena turns the conceptual and mathematical framework for model development large in place; moreover, the existing models are highly nonlinear. Then, a experimentally validated Monod-type kinetics model is considered in order to straightforward apply a state-feedback linearization approach that allows a systematic design of the estimator.
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2. The Bioreactor and its Estimation Problem It was considered a stirred tank reactor where the Desulfovibrio Alaskensis (DA) bacteria growth is carried out. The DA bacterium is a sulfate reducing bacteria used, in this case, to degrade some undesirable sulfate compounds to sulfides. It was previously determined that the Monod’s kinetic equation adequately describes our reactor [2], where its kinetics parameters were determined via standard methodology in a batch culture [3]. From mass balances and the kinetics Monod model, the reactor model is given by, .
X = – D X + μ(S) X := fX(.), . X S = D (SIN – S) – μ(S) Y := fS( .), S/X . X P = – D P + μ(S) Y := fP(.), P/X S μ(S) = μMAX k + S s
X(t0) = X0, S(t0) = S0,
(1a) yS(tk) = S(tk–1),
tD = tk+1 – tk. (1b)
P(t0) = P0,
(1c) (1d)
There are considered three states: substrate (sulfate compound) concentration (S), biomass (or DA) concentration (X), and sulfide concentration (P). The known exogenous inputs are: the dilution rate (D), and the substrate concentration (SIN) in the input flow (D). YS/X and YP/X are the sulfate and sulfide coefficient yields, respectively. μ( .) is the specific growth rate, and μMAX and ks are the maximum specific growth rate and the affinity constant, respectively. With suitable choices of D, the preceding model describes batch (D = 0), semibatch (D S = 0) and continuous (D ≠ 0) operations. In order to monitor the reactor, samples from the culture are taken anaerobically each hour. Sulphate concentration in the medium is measured by a fast and simple turbidimetric method based on the precipitation of barium [4]. Then, this is the only one measurement considered. The substrate concentration (yS) at the instant tk reflects the reactor state at the past instant tk–1; tD is the sampling-delay time period. Resorting to an estimation approach, the monitoring problem is translated to the one of designing an estimator that, on the basis of the bioreactor model, and driven by a sequence of DD-measurements {yS(t0), yS(t1), …, yS(tk)} each sampling time instant (tk) on-line yields estimates of the actual biomass (X(tk)), substrate (S(tk)) and sulfide (P(tk)) concentrations. Besides, X and P measurement could be eliminated, meaning a cost reduction due to additional on-line laboratory analysis.
3. Estimator Design By convenience, the reactor model is rewritten in compact vector notation: .
xS = fXS(xS, u, p), .
xS(t0) = xS0;
yS(tk) = δ xS(tk–1),
tD = tk – tk–1,
P = fP(x, u, p), P(t0) = P0, xS = [X, S,]’, x = [X, S, P]’, u = [D, SIN]’, p = [YS/X, YP/X, μMAX, ks]’, f = [fM, fS]’, f = [fM, fS, fP]’, δ = [0, 1],
(2a) (2b) (2c) (2d)
This form makes the cascade connection between the xS-states and the P-state marked. Also it is important to note that its time-varying solution describes a unique reactor motion x(t) determined by the initial conditions (x0), the inputs (u), and the parameters
Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements 369
(p), because of the continuous differentiability of f(.)(θS and θP are the transition maps of the differential equations 2a and 2b, respectively): P(t) = θP(t, t0, x0, u, p) xS(t) = θS(t, t0, xS0, u, p), θ = [θS, θP]’ or equivalently: x(t) = θ(t, t0, x0, u, p),
(3a) (3b)
On the basis of the reactor model (Eq. 1 or 2), the estimator is designed by a geometric non-linear approach [5]. The approach follows a detectability property evaluation of the reactor motion to underlie the construction, tuning and convergence conditions of the estimator. 3.1. Detectability Property For a moment, it is assumed that the S-measurement is continuous-instantaneous, in the understanding that this unrealistic assumption will be later removed. In a physical sense, the detectabilty property amounts to the solvability of the following differerential estimation problem: reconstruct the reactor motion x(t) provided the data: .
DS = {x0, yE(t), p},
yE = [yS, yS]’,
(4)
To solve this problem, the S-measurement equation (Eq. 2) is recalled in its continuousinstantaneous version (yS(t) = S(t)); later, a one time derivative is taken by replacing the resulting time-derivative of S (in the right-hand side) by the map fS(.); finally, the Pdynamics is recalled to obtain the following differential-algebraic system .
φ(xS, u, p) = yE,
P = fP(x, u, p),
P(t0) = P0;
φ(xS, p) := [S, fS(.)]’
(5)
It must be noticed the cascade interconnection between the algebraic and the differential items. At each time t, the two algebraic equations system admits a unique and robust solution for xS in any motion in which S ≠ 0 (the Jacobian matrix of φ is nonsingular for S ≠ 0). Feeding the solution into the differential equation, the following differential estimator, driven by the output yE, and the input signals u, is obtained: xS = σ(yE, p),
.
P = fP(yE, u, p),
P(t0) = P0,
(6)
On the framework of the detectability motion given in [5], the Jacobian matrix of φ is the observability matrix, and its non-singularity provides the robust partial observability of the reactor motion x(t), with observability index κ = 1; and the differential equation in Eq. 6 is the unobservable dynamics whose unique solution is the unobservable motion (Eq. 3a). 3.2. Estimator Construction Once the possibility of estimator construction was established, as mentioned above, the estimator construction followed a straightforward application of the construction procedure given in [5], but with one tenuous modification: the estimation sequence was delayed in one-step by replacing the discrete-instantaneous output estimation error
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{yS(tk) – S^ (tk)} by the DD one {yS(tk) – S^ (tk–1)} and considering the interval [tk–1, tk], instead of [tk, tk+1] as the work one. Then, the estimator is given by: x^ S(tk) = θS(tk, tk–1, x^ S(tk–1), u, p^ ) + G(x^ S(tk–1), u, p^ , tD, KP) (yS(tk) – δ x^ S(tk–1)) (7a) + H(x^ S(tk–1), u, p^ , tD) xI(tk–1), x^ S(t0) ≈ xS(t0), (7b) xI(tk) = xI(tk–1) + KI (yS(tk) – δ x^ S(tk–1)), xI(t0) = 0, ^ ^ ^ ^ P(tk) = θP(tk, tk–1, x(tk–1), u, p), P(t0) ≈ P(t0), (7c) where GP( .) = (∂Xsφ( .))–1 (Ω(tD))–1 KP, H( .) = (∂Xsφ( .))–1 (Ω(tD))–1 T(tD), tk = tk–1 + tD, P 2 1 0 1 º ª1 tDº, T(tD) = ª /2 tD º, KP = ª« k1 º», KI = kI. Ω(t ∂xsφ( .) = ª¬ . . , D) = ¬ ¬ tD ¼ 0 1¼ ∂XfS( )∂SfS( )¼ ¬ kP2 ¼ and z^ denotes the estimate of the variable z. θS and θP are the transition maps defined in Eq. (3). G(.) is a nonlinear gain constructed on the basis of the observability matrix ∂xsφ, which depends on the state xS, the sampling-delay time tD and the proportional gain KP. The estimator includes a sumatorial correction term (third term of Eq. 7a) to eliminate modeling error problems; xI is an extended state that accounts for the sumatorial output estimate error, and KI is the corresponding sumatorial gain. Ω(tD) is the transition matrix of model reactor in its state-feedback linearized (via the φ map) form; and the matrix T(tD) results from the transformation to original x-coordinates of the observer from its state-feedback linearized form. The estimator can be regarded as formed by two parts: the first (Eqs. 7a, b) is a closedloop observer that yield the estimate sequence {x^ S(tk)} (k = 0, 1, 2, …) convergent to the current sequence {xS(tk)}; and the second (Eq. 7c) is on open-loop observer driven by the xS-estimates that yields the estimate sequence {P^ (tk)} convergent to the current sequence {P(tk)}. 3.3. Estimator Tuning In order to choice the entries of the gain matrices KP and KI, the output estimation error dynamics in its state-feedback linearized form is recalled; this takes the following form: ε(tk+3) + (kP1 – 3) ε(tk+2) + (1/2 tD2 kI + tD k2P – 2 k1P + 3) ε(tk+1) + (1/2 tD2 kI – tD kP2 + k1P – 1) ε(tk) = qy,
ε = yS – δxS
(8)
The linear characteristics can be noticed on the left side of the equation; however in qy the inherent nonlinearities of the estimation error dynamics are enclosed. This means that, by suitable choices of the gains, the left side is stable, but qy is a potentially destabilizing factor of the dynamics. Except for qy, Eq. (8) establishes a clear relationship between the choice of the tuning parameters and the sampling-delay time value in front of the desired kind of estimation error response. Pole assignment into the unit circle was followed to make the linear-part of Eq. (8) stable. It was chosen a pole-pattern from a continuous framework (in the complex splane) as a reference departure point: λ1 = –ω,
λ2,3 = –ω (ξ ± (1 – ξ)1/2)
Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements 371
where ω and ξ corresponds to the characteristic frequency and the damping factor of a stable 3rd order linear dynamics of reference . These eigenvalues were map into the unit circle of the complex z-plane (the discrete framework) according to: γi = exp(λi tD),
i = 1, 2, 3.
Then, the characteristic polynomial of the pole set {γ1, γ2, γ3} was obtained in terms of the tuning parameters (ξ, ω) and the sampling-delay time (tD): (γ – γ1) (γ – γ2) (γ – γ3) = 0
γ3 + c1(tD, ξ, ω) γ2 + c2(tD, ξ, ω) γ + c3(tD, ξ, ω) = 0
Comparing the coefficients set of this characteristic polynomial of reference with those of the output estimation error dynamics (Eq. 8), the gains were obtained in well-defined terms of the sampling-delay time and the tuning parameters (tD, ξ, ω): kP1 = κ1(tD, ξ, ω),
k2P = κ2(tD, ξ, ω),
kI = κ3(tD, ξ, ω),
ω = s ωR.
It was introduced the parameter s, which is regarded as an accelerating factor of the dynamics with a certain time response of reference (ωR). Then, once the tD is defined, usually by practical considerations and ωR and ξ are fixed, s remains as the unique tuning parameter. In order to attain estimation convergence, the stable linear part of the error dynamics must dominate the non-linear one. In [5] it is implied that a value range of s (s ∈ (s*, s*) exists, whose wide directly depends on the magnitude of the modeling error (enclosed in qy) and on the sampling delay time (tD).
4. Simulation Results To show the performance of the estimator, a simulation study was realized. The model parameters for the DA bacteria are (YS/X, YP/X, μMAX, ks) = (0.25, 0.25/0.95, 0.035 h-1, 0.9 g L-1), which are the corresponding for the bioreactor considered as the actual plant. These parameters were obtained from a previous regression fitting over a set of experimental runs. For the estimator, a parametric error was introduced: k^ s = 0.8 instead of 0.9. Attending practical considerations, the sampling-delay time was set at tD = 1 h. 4.1. Continuous Operation For this operation the dilution rate was set at D = 0.025 h-1, and the substrate concentration in the flow input, at SIN = 5 g L-1. The initial conditions were: (i) Bioreactor: (X0, S0, P0) = (0.5, 5, 0), (ii) Estimator: (X^ 0, S^ 0, P^ 0) = (0.3, 6, 0). The tuning parameter were: (ωR, ξ, s) = (1/200, 10, 1). The behavior of the estimator is shown in Fig. 1a. The estimator adequately predicts the key variables at a time equivalent to ¼ of the bioreactor settling time (≈ 200 h); although, for the M and P variables, the presenttime prediction is faster.
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4.2. Batch Operation The initial conditions were: (i) Bioreactor: (X0, S0, P0) = (5, 12, 0), (ii) Estimator: (X^ 0, S^ ^ 0, P0) = (5.1, 11, 0). The tuning parameters were: (ωR, ξ, s) = (1/200, 10, 1). The behavior of the estimator is shown at Fig. 1b. Similar to the continuous operation, the estimator adequately predicts the key variables at a time equivalent to ¼ of the bioreactor settling time (≈ 20 h); but, the estimator must be off at a S-value close to zero, as suggested by the observability property. Biomass
Biomass
0.7
9
0.6
8 X (g/L)
X (g/L)
0.5
7
0.4
6
0.3 0.2 0
50
100
150 t(hr) Substrate
200
250
300
6
5 0
5
10
15 t(hr) Substrate
20
25
30
5
10
15 t(hr) Sulfide
20
25
30
15
5 S (g/L)
S (g/L)
10
4
5
3 2 0
50
100
150 t(hr) Sulfide
200
250
300
3
15 Bioreactor Estimator
10
P (g/L)
P (g/L)
2
1
0 0
0 0
Bioreactor Estimator
5
50
100
150 t(hr)
200
250
300
Fig. 1a. Performance of the estimator in a continuous operation.
0 0
5
10
15 t(hr)
20
25
30
Fig. 1b. Performance of the estimator in a batch operation
5. Conclusions In this work the design of a nonlinear estimator for a class of stirred tank bioreactor driven by discrete-delayed measurements has been presented. Based on a Monod-type kinetics model, the design included a systematic construction and tuning, and a convergence criterion. The design followed a geometric approach, and the tuning was done with a conventional pole-assignment technique. The performance of the estimator was shown in a simulated framework, that motivates the application of the estimator in a practical (laboratory or industrial level) framework.
References [1] [2]
Jorgensen, B. B., 1982, Mineralization of organic matter in a sea bed -the role of sulphate reduction-, Nature, 296, 643-645. Aguilar-López, R., Martínez-Guerra, R., Mendoza-Camargo, J. and M. I. NeriaGonzález, 2006, Monitoring of an industrial wastewater plant employing finite-time convergence observers, J. of Chemical Technology & Biotechnology, 81, 6, 851-857.
Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements 373 [3] [4]
[5]
Bailey, J. E. and D. F. Ollis, 1986, Biochemical engineering fundamentals, Mc GrawHill, Singapore. Kolmert, A., Wikström, P. and K. Hallberg K, 2000, A fast and simple turbidimetric method for the determination of sulfate in sulfate-reducing bacterial cultures. J. Microbiol. Meth., 41, 179-184. Hernández, H. and J. Alvarez, 2003, Robust estimation of continuous nonlinear plants with discrete measurements, J. of Process Control, 13, 1, 69-89.
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Optimal Control of Batch Processes Using Particle Swam Optimisation with Stacked Neural Network Models Fernando Herrera, Jie Zhang School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K.
Abstract An optimal control strategy for batch processes using particle swam optimisation (PSO) and stacked neural networks is presented in this paper. Stacked neural networks are used to improve model generalisation capability, as well as provide model prediction confidence bounds. In order to improve the reliability of the calculated optimal control policy, an additional term is introduced in the optimisation objective function to penalise wide model prediction confidence bounds. PSO can cope with multiple local minima and could generally find the global minimum. Application to a simulated fedbatch process demonstrates that the proposed technique is very effective. Keywords: Batch processes, Neural networks, Particle swam optimisation, Reliability.
1. Introduction Batch or semi-batch processes are suitable for the responsive manufacturing of high value added products [1]. To maximise the profit from batch process manufacturing, optimal control should be applied to batch processes. The performance of optimal control depends on the accuracy of the process model. Developing detailed mechanistic models is usually very time consuming and may not be feasible for agile responsive manufacturing. Data based empirical models, such as neural network models [2] and nonlinear partial least square models [3], and hybrid models [4] have to be utilised. Stacked neural networks have been shown to possess better generalisation capability than single neural networks [5,6] and are used in this paper to model batch processes. An additional feature of stacked neural networks is that they can also provide prediction confidence bounds indicating the reliability of the corresponding model predictions [7]. Due to model-plant mismatches, the “optimal” control policy calculated from a neural network model may not be optimal when applied to the actual process [8]. Thus it is important that the calculated optimal control policy should be reliable. Conventional gradient base optimisation techniques are not effective to deal with objective functions with multiple local minima and can be trapped in local minima. Particle swam optimisation (PSO) is a recently developed optimisation technique that can cope with multiple local minima. This paper proposes using PSO and stacked neural networks to find the optimal control policy for batch processes. A standard PSO algorithm and three new PSO algorithms with local search were developed. In order to enhance the reliability of the obtained optimal control policy, an additional term is added to the optimisation objective function to penalise wide model prediction confidence bounds.
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2. Particle Swarm Optimisation PSO was first proposed by Kennedy and Eberhart [9]. The main principle behind this optimisation method is communication. In PSO there is a group of particles that look for the best solution within the search area. If a particle finds a better value for the objective function, the particle will communicate this result to the rest of the particles. All the particles in the PSO have “memory” and they modify these memorized values as the optimisation routine advances. The recorded values are: velocity (V), position (p), best previous performance (pbest) and best group performance (gbest). The velocity describes how fast a particle should move from its current position which contains the coordinates of the particle. The last two parameters are the recorded best values that have been found during the iterations. A simple PSO algorithm is expressed as [9]: V(k+1)=wV(k)+C1r(pbest(k)-p(k))+C2r(gbest(k)-p(k))
(1)
p(k+1) = p(k) + V(k+1)
(2)
where w is the halt parameter, C1 is the personal parameter, C2 is the group parameter and r is a random number between 0 and 1. The parameters w, C1 and C2 play important roles in PSO. The halt parameter (w) helps the particles to move around the search area. If it is too large the particles may miss the solution and if it is too small they may not reach it. Good values are usually slightly less than 1 [9]. The coefficients C1 and C2 indicate the preference of the particles for personal or communal results. If the value of C1 is larger than C2 then the particles will search for the best value within the best results obtained during its own search; they will not try to reach a communal best point. If vice versa, the particles will not perform individual searches, this will diminish the ability of the particles to perform “adventurous” searches. Kennedy and Eberhart [9] recommended that these values should be 2. This keeps a balance between the personal and communal search. Four PSO algorithms were developed here and they perform different ways to communicate search results within the community. The first one is the simplest code presented in [9], where the particles have the ability to communicate its result to all the members of the community. The other three are based on local searches performed within small groups formed in the community. In the second algorithm, the group is based on a circular community [10]. These small groups will only communicate with members of their own community. The expected result with this formation is that the particles will search more intensively the solution area. In the third algorithm, local search is presented as a cluster community. The difference with the circular community is the fact that only one particle will communicate and compare the results with members of other groups. The fourth algorithm performs a geographical search in that the particles will communicate with the particles that are close to them in the solution area. The expected results are that the local search algorithms explore more intensively the search area. The algorithms were then tested on the following two optimisation problems with multiple local minima or maxima:
max F =
1 2 i
2 § x §x · · 0.1 + ¨¨ ¦ − ∏ cos¨ i ¸ + 1¸¸ © i¹ ¹ © i =1 4000 i =1 2 2 min F = 20 + x1 + x2 − 50(cos 2πx1 + cos 2πx2 ) 2
(3)
(4)
Optimal Control of Batch Processes U sing Particle Swam Optimisation with Stacked Neural Network Models
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All the four PSO algorithms can find the global optimal solutions whereas the gradient based optimisation algorithm from the MATLAB Optimisation Toolbox, fminunc, fails to find the global optimal solutions when the initial values are not close to the global optimal solutions.
3. Modelling of A Fed-Batch Process Using Neural Networks 3.1. A Fed-Batch Process The fed-batch reactor used in this work was taken from [11]. The batch reactor is based on the following reaction system: k1 A + B ⎯⎯→ C k2 B + B ⎯⎯→ D
This reaction is conducted in an isothermal semi-batch reactor. The desired product in this system is C. The objective is to convert as much as possible of reactant A by the controlled addition of reactant B, in a specified time tf = 120 min. It is not appropriate to add all B initially because the second reaction will take place, increasing the concentration of the undesired by-product D. Therefore, to keep a low concentration of product D and at the same time increase the concentration of product C, the reactant B has to be fed in a stream with concentration bfeed = 0.2. A mechanistic model for this process can be found in [11]. 3.2. Modelling the Fed-Batch Process Using Stacked Neural Networks Neural network models for the prediction of the amount of desired product CC(tf)V(tf) and the amount of undesired by-product CD(tf)V(tf) at the final batch time are of the form: (5) y1 = f1(U) (6) y2 = f2(U) where y1 = CC(tf)V(tf), y2 = CD(tf)V(tf), U = [u1 u2 … u10]T is a vector of the reactant feed rates during a batch, f1 and f2 are nonlinear functions represented by neural networks. For the development of neural network models simulated process operation data from 50 batches with different feeding profiles were generated using the mechanistic model of the process. In each batch, the batch duration is divided into 10 equal stages. Within each stage, the feed rate is kept constant. The control policy for a batch consists of the feed rates at these 10 stages. In the stacked neural network models several individual networks are trained using bootstrap re-sampling of the original data. The individual network outputs are combined to give the final model output. For each of the stacked neural network models, a group of thirty individual neural networks were developed. Each neural network contains in the hidden layer three nodes. The number of hidden nodes was selected based on the performance on the testing data. The nodes in the hidden layer use a hyperbolic tangent activation function while that in the output layer uses a linear activation function. The stacked neural network output is taken as the average of the individual network outputs. Fig. 1 and Fig. 2 show, respectively, the performance of individual networks and stacked networks for predicting the amount of desired product CC(tf)V(tf) on the training and unseen validation data sets. Fig. 1 indicates that in some networks the SSE on the training data is small but this is not the case on the unseen validation data. These results show that individual networks are not reliable. It can be seen from Fig. 2 that stacked networks give consistent performance on the training data and on the unseen validation data. The performance gradually improves when more networks are combined and approaches a stable level. This is observed on both the training and unseen validation
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SSE (validation)
SSE (training)
data. This result indicates that the stacked model for predicting the amount of desired product CC(tf)V(tf) is more reliable as the number of individual networks is increased. It does not matter if some networks do not have a good performance, what matters is the communal performance of the group.
Networks
SSE (validation)
SSE (training)
Figure 1. Performance of individual networks for predicting CC(tf)V(tf)
Networks
Figure 2. Performance of stacked networks for predicting CC(tf)V(tf)
4. Optimising Control Using PSO The objective of the optimisation is to maximise the amount of the final product while reducing the amount of the by-product. The optimisation problem solved in this work is:
min J = {α1[ D](t f ) − α 2 [C ](t f )}V (t f ) U
s.t.
0 ≤ ui ≤ 0.01, V (t f ) = 1
(i = 1, 2,", m)
where Į1 and Į2 are weighting parameters which were both set to 0.5 in this study, U is a vector of control actions (reactant feed rates), and V is the reaction volume. Table 1 lists the parameters used in global PSO (PSOG1 to PSOG4) and local PSO (PSOL1 to PSOL4) algorithms. For the local PSO algorithms, the sizes of the internal communities were kept the same in all the cases: 17 particles.
Optimal Control of Batch Processes U sing Particle Swam Optimisation with Stacked Neural Network Models
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Table 1. Parameters used in PSO algorithms PSOG1
PSOG2
PSOG3
PSOG4
PSOL1
PSOL2
PSOL3
PSOL4
Particles
50
70
50
70
20
40
20
40
Halt
0.01
0.01
0.005
0.005
0.01
0.01
0.005
0.005
For the purpose of comparison, optimisation using a single neural network was first carried out. Table 2 shows the obtained results. As can be seen from the table, the values for the difference between the final amounts of product and by-product using the PSO codes were similar to the ones obtained using the MATLAB Optimisation Toolbox function, fmincon, in this fed-batch reactor. However, PSO can cope with multiple local minima in general as shown in Section 2. It can also be appreciated that an increment in the number of particles in the global version of the PSO code does not help the code to find a better solution for the optimization problem. This could indicate that the PSO code only needed a minimum number of particles and the inclusion of more particles will not be helpful. A different behaviour was encountered in the local version of the PSO. When more particles were used for the solution of the problem, then the code required less number of iterations to solve the problem. Changing the value of the halt did not show any improvement in the performance. As can be seen from the table, the results obtained using different halt values are similar. Another difference that could be seen between the two PSO codes is the fact that the local version can find a similar answer to the problem using fewer particles than the global version of the PSO code. Once the optimal feed rates were obtained, they were applied to the actual process (i.e. simulation by the mechanistic model of the process). Table 2 shows the difference between the amounts of the final product and by-product on neural network model and the actual process. It can be seen from Table 2 that the actual amounts of product and by-product under these “optimal” control policies are quite different from the neural network model predictions. This indicates that the single neural network based optimal control policies are only optimal on the neural network model and are not optimal on the real process. Hence, they are not reliable. This is mainly due to the model plant mismatches, which is unavoidable in data based modelling. A method to overcome the impact of model plant mismatch on optimisation performance was previously investigated by Zhang [8] where model prediction confidence bounds are incorporated as a penalty in the objective function. Therefore, the objective function can be modified as
min J = {α1[ D](t f ) − α 2 [C ](t f )}V (t f ) + α 3 ( stderr[C ] + stderr[ D]) U
s.t.
0 ≤ ui ≤ 0.01, V (t f ) = 1
(i = 1, 2,", m)
where stderr[C] and stderr[D] are the standard errors of the stacked models, Į3 is a weighting factor for model prediction confidence and was selected as 0.5 in this work. Table 2 shows the results obtained using the new objective function with stacked neural network models. It can be seen from Table 2 that the modified objective function with stacked neural network models leads to better performance on the actual process. It can be appreciated that the actual performance is very close to the ones calculated using the
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stacked neural network. This demonstrates that control policies obtained using stacked neural networks considering model prediction confidence bounds is much more reliable than those obtained using a single neural network model. Table 2. Values of ([C](tf) - [D](tf))V(tf) on neural network models and actual process Single neural network
Stacked neural network
Neural network
Process
Neural network
Process
fmincon
0.0411
0.0314
0.0304
0.0363
PSOG1
0.0400
0.0344
0.0296
0.0359
PSOG2
0.0405
0.0319
0.0297
0.0370
PSOG3
0.0399
0.0325
0.0302
0.0358
PSOG4
0.0396
0.0347
0.0300
0.0368
PSOL1
0.0377
0.0341
0.0298
0.0338
PSOL2
0.0407
0.0307
0.0298
0.0364
PSOL3
0.0394
0.0364
0.0297
0.0348
PSOL4
0.0397
0.0301
0.0297
0.0363
5. Conclusions The study demonstrates that particle swam optimisation is a powerful optimisation technique, especially when the objective function has several local minima. Conventional optimisation techniques could be trapped in local minima but PSO could in general find the global minimum. Stacked neural networks can not only given better prediction performance but also provide model prediction confidence bounds. In order to improve the reliability of neural network model based optimisation, an additional term is introduced in the optimisation objective to penalize wide model prediction confidence bound. The proposed technique is successfully demonstrated on a simulated fed-batch reactor.
References [1] D. Bonvin, J. Process Control, 8 (1998) 355-368. [2] J. Zhang, Trans. Inst. Meas. Control, 27, (2005) 391-410. [3] S. J. Zhao, J. Zhang, and Y. M. Xu, Ind. Eng. Chem. Res., 45, (2006) 3843-3852. [4] Y. Tian, J. Zhang, and A. J. Morris, Ind. Eng. Chem. Res., 40, (2001) 4525-4535. [5] D. V. Sridhar, R. C. Seagrave, and E. B. Bartlett, AIChE J., 42, (1996) 2529-2539. [6] J. Zhang, E. B. Martin, A. J. Morris, and C. Kiparissides, Comput. Chem. Eng., 21, (1997) s1025-s1030. [7] J. Zhang, Neurocomputing, 25, (1999) 93-113. [8] J. Zhang, Ind. Eng. Chem. Res., 43, (2004) 1030-1038. [9] J. Kennedy and R. Eberhart (1995). Particle Swarm Optimization. In Proceedings of the 1995 IEEE international conference on neural networks, Perth, Australia. Vol VI 1942 – 1948. [10] J. Kennedy and R. Mendes, IEEE Trans. Syst. Man Cybern. Part C-Appl. Rev., 36, (2006) 515-519. [11] P. Terwiesch, D. Ravemark, B. Schenker, and D. W. T. Rippin, Comput. Chem. Eng., 22, (1998) 201-213.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Online LQG stabilization of unstable gas-lifted oil wells Esmaeel Jahanshahi, Karim Salahshoor, Riyaz Kharrat Petroleum University of Technology, South Khosro St., Sattarkhan Ave., Tehran 1453953153, Iran
Abstract The proposed strategies for stabilization of gas-lifted oil wells are offline methods which are unable to track online dynamic changes of the system. However, system parameters such as flow rate of injected gas and also noise characteristic are not constant with respect to time. An adaptive Linear Quadratic Gaussian (LQG) approach is presented in this paper in which the state estimation is performed using an Adaptive Unscented Kalman Filter (AUKF) to deal with unknown time-varying noise statistics. State-feedback gain is adaptively calculated based on Linear Quadratic Regulator (LQR). Finally, the proposed control scheme is evaluated on a simulation case study. Keywords: gas-lift; casing heading; state estimation; AUKF; LQR.
1. Introduction Gas-lift is a method for activation of low pressure oil wells. Figure 1 shows a typical diagram of a gas-lifted oil well [1]. In this method, gas is routed through surface gas injection choke (A) into the annulus (B) and then injected (C) deep into tubing (D) in order to be mixed with the fluid form reservoir (F). This reduces the density of oil column in tubing and lightens it to increase the production (E) rate from the low pressure reservoir. The oil production in the gas-lifted oil wells at their decline stages becomes unstable for low gas lift rates. This study focuses on the instability of gas-lifted wells due to casing heading phenomenon. Figure 2 demonstrates a typical example of the casing heading phenomenon simulated in OLGA®v5.0 [2]. The cyclic operation consists of three main phases [3] as follows: 1. The upstream pressure is smaller than Pti (tubing pressure at injection point), therefore no gas enters the tubing. The annulus pressure builds up until it reaches Pti. Then, injection into the tubing starts. 2. As gas mixes with oil in the tubing, the column lightens and the well starts producing. The gas injection rate does not fulfill the well’s need. Therefore, the pressure in the casing drops and production reaches a maximum. 3. Annulus pressure drops carrying along the injection gas rate wiv and the oil production. Less gas being injected, the oil column gets heavier and Pti exceeds the upstream pressure. Gas injection in the tubing stops. In order to suppress this oscillatory behaviour, the use of the automatic feedback control has been considered [4]. State space model and nonlinear full-state feedback have been used for stabilization of the system [5]. But, some of these state variables are not measurable, therefore, concept of state estimation from well-head measurements has been considered. A nonlinear observer is used for state estimation [6] which has shown satisfactory result in experiment [7]. As noted in [7], estimation is affected by noise. The standard Kalman filter has been used for state estimation and down-hole soft-
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sensing [8]. Advantage of Kalman Filtering (KF) compared to the nonlinear observer [7] is its capability of working in presence of noises [9]. But, the standard Kalman filter could be used only in a single operating point for a locally linearized dynamic of the system. To deal with this problem, extended Kalman Filter (EKF) has been used in [10] for down-hole soft sensing in gas-lifted oil wells.
Fig. 1. A gas lifted oil well
Fig. 2. Casing-heading phenomenon simulated with OLGAv5.0
EKF estimation accuracy may not be satisfactory to use estimated states for feedback control. Because, EKF uses a first-order approximation of nonlinear dynamics [9]. For state estimation of highly nonlinear systems, UKF is recommended [9]. However, for these methods, the measurement noise should be zero-mean Gaussian noise with known statistic characteristics. In this paper, an AUKF estimation approach has been proposed to increase the accuracy of state estimates despite the unknown time-varying statistic characteristics of measurement noise in online real world situations. The organization of this paper is as follows. In Section 2, the mathematical model of system is described. In Section 3, the AUKF algorithm is developed. In Section 4, an optimal control strategy will be introduced to stabilize the system. Simulation results are presented in Section 6. Finally, the results are summarized in Section 7.
2. Mathematical Model The gas-lift oil well operation can be described by the following state-space equations [7]: x1 = wgc − wiv °° ® x2 = wiv − w pc x2 /( x2 + x3 ) ° °¯ x3 = wr − w pc x3 /( x2 + x3 )
(1)
Where the state variables consist of x1 as the mass of gas in the annulus, x2 as the mass of gas in tubing, and x3 as the mass of oil in tubing. For more details, refer to [6, 7].
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3. AUKF State Estimation Algorithm In practice, down-hole measurements relating to tubing and annulus variables are not in general available. x1 can be measured and the remaining two states (x2 and x3) should be estimated. The available measurements are assumed to be y1(t)=x1 and y2(t)=Pt (tubing pressure at well head) [7]. The process dynamics and the measurement equations obey the following non-linear relationships: xk = f ( xk −1 , uk , k ) + wk −1
(2)
yk = h( xk , k ) + vk
(3)
Where f and h are known nonlinear functions. The random variables wk and vk represent the process and measurement noises, respectively. They are assumed to be independent, white noises with normal probability distributions; p(w)~N(0,Q) and p(v)~N(0,R). Julier and Uhlmann [11, 12] developed the UKF algorithm which does not require to linearize the foregoing general nonlinear system dynamics. The UKF algorithm uses a "deterministic sampling" approach to calculate the mean and covariance estimates of Gaussian random state variables (i.e., x) with a minimal set of 2L+1 sample points (L is the state dimension), called as sigma points [12, 13], through the actual nonlinear system dynamics without any linear approximations. Hence, this approach yields more accurate results compared to the KF and EKF. The results are accurate to the third order (Taylor series expansion) for Gaussian inputs for all the nonlinearities. For nonGaussian inputs, the results are accurate to at least the second order [12]. The UKF algorithm is well described in [9] and for sake of limited space we refer readers to this reference. Often, we do not know all parameters of the model or we want to reduce the complexity of modeling. Therefore, in real application, the exact value of R is not known a priori. If the actual process and measurement noises are not zero-mean white noises, the residual in the unscented Kalman filter will also not be a white noise. If this happened, the Kalman filter would diverge or at best converge to a large bound. To prevent the filter from divergence, we use adaptive version of UKF as follows. The innovation sequence is defined as η k = yk − h( xˆk− , k ) . Substituting the measurement model into ηk , gives η k = [h( xk , k ) − h( xˆk− , k )] + vk , with the fact that the difference between xk and xˆk− is a small divination, we could use a linear approximation for the term inside brackets, as η k = H k− [ xk − xˆk− ] + vv , where H k− = [∂h / ∂x]x = x− . Noting that we k
have ek− ≅ xk − xˆk− , Pk− = E[ek− ek−T ] and Rk = E[vk vk T ] . On the basis of assuming that wk and vk are uncorrelated white Gaussian noise sequences and the orthogonallity condition exists between observation error and state estimation error, the innovation covariance can be computed as E[ηkη kT ] = E[( H k− ek− )( H k− ek− )T ] + E[vk vkT ] . Combining the preceding equations, gives E[ηkηkT ] := Sk = H k− Pk− H T + Rk . When the innovation covariance E[ηkη kT ] is available, the covariance of the observation error Rk can be estimated directly from the preceding equation. Calculation of the residual covariance E[ηkηkT ] normally uses a limited number of samples of the innovation sequence:
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1 M
E[ηkη kT ] =
M −1
¦η m =0
η
(4)
− HPk− H T
(5)
T k −m k −m
As a result, Rak =
1 M
M −1
¦η m =0
η
T k −m k − m
In which M=100 represents the estimation window size. However, it is noted that (5) gives a valid result when the innovation sequence is stationary and ergodic over the M sample steps.
4. Adaptive LQR Control State feedback control is commonly used in control systems, due to its simple structure and powerful functions. Data-driven methods such as neural networks are useful only for situations with fully measured state variables. For this system in which state variables are not measurable and measurement function is nonlinear, we are dependant on system model for state estimation. On the other hand, as shown in figure 2, in openloop situations, system has limit cycle behavior and measurements do not give any information of system dynamics. Therefore, we use model-based approach. Parameters and variables that determine the system dynamic changes, such as ambient temperature, flow rate of well-head injected gas are measurable or a priori known as opening of production choke. Therefore, using these values, model can be adapted to the plant. To develop an adaptive controller, it is necessary to solve the related non-adaptive control problem when the parameters of the controlled plant are known. A crucial issue is the existence of an ideal (nominal) controller for a given control objective, which is equivalent to a set of matching conditions [14]. To calculate state feedback gain K[k], discrete linear-quadratic (LQ) regulator is used. The sate feedback law u[k ] = − K [k ]xˆ[k ] minimizes the quadratic cost function [15]: J (u[k ]) =
∞
¦ xˆ[k ]T Qxˆ + u[k ]T Ru[k ] + 2 xˆ[k ]T Nu[k ]
(6)
k =1
Where gain K[k] is calculated using following Riccati Equation: AT S + SA − ( SB + N ) R −1 ( BT S + N T ) + Q = 0
(7)
K[k] is derived from S by K [k ] = R −1 ( B[k ]T S + N T ) . Control scheme tracks values of variables and parameters that determine the operating point of systems and with any change in these parameters, a new linear controller gain is calculated based on the most recent operating point. It should be noted that computation time of every step for the combined state estimation and solving Riccati equation must be less that sampling time of the system.
5. Simulation Results Simulation of the model [6] and the proposed control scheme are implemented in MATLAB® with the nominal values of the case study described in [3]. For the sake of comparison, the same characteristics for process and measurement noises are considered
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in all simulation runs. The initial values assumed for states and estimates have been considered similarly in all simulation runs. A Gaussian noise with constant variance of 0.03 is added to wgc as process noise. Variances of measurement noises for the first hour of simulation are considered to have constant values: 5 for y1(t) and 5000 for y2(t). From t=1 h to the end of simulation run, variances are increased linearly as unknown drifts, so that variances of measurement noises reach up to 50 and 80000 at the end of simulation time. Note that nonlinear observer [6, 7] also needs wpc (flow rate of production choke) as a third measurement that we do not consider any noise for it. First, we simulated the nonlinear observer proposed in previous works [6, 7]. As shown in figure 3, its estimation for the second state variable is very weak in presence of noises.
Fig. 3- The nonlinear observer estimates
Fig. 4- AUKF estimation for open-loop system
Figure 4 shows performance of the proposed AUKF for open-loop system. As described, it’s assumed that the induced drift in sensor noises are not known a priori to the filter and variances of measurement noises are estimated recursively by the adaptive estimation algorithm.
Fig. 5- Control signal and inputs to the system
Fig. 6- Outputs of the closed-loop system
To evaluate the proposed adaptive control performance, opening of production choke and flow rate of injected gas at the well-head are random pulses as command signals, as shown in figure 5. The opening value of the production choke upc also is the manipulated variable of the control strategy. Figure 6 shows noisy measurements and filtering outputs of closed-loop system, where variable variances of measurement noises are apparent. Note that wpc illustrated the stabilized behavior of closed-loop system. The state estimation also has been performed by Particle Filter [9] for comparison purposes. In this case, the algorithm was run with 1000 particle, so that the computation time could be affordable. Also, roughening factor of 0.1 is used. Similarly, the standard UKF algorithm has been simulated. In table 1, root mean square error values and computation times for different simulations are presented. Note that EKF and nonlinear
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observer estimate accuracies are not satisfactory and closing feedback with them can not stabilize the system. Algorithm Observer in [6, 7] EKF Standard UKF AUKF Particle Filter
RMSE Open-loop Close-loop 28.50, 28.43, 7.62 ----------19.13, 5.21, 100.8 ----------1.41, 0.83, 8.77 1.85, 0.52, 6.86 0.84, 0.25, 5.26 0.49, 0.18, 3.72 1.13, 0.42, 42.71 0.84, 0.32, 4.24
Computation time of the open-loop system 20 sec 122 sec 155 sec 188 sec 30400 sec
Table 1- Comparison of root mean square error and computation time of different algorithms.
6. Conclusions An adaptive UKF algorithm is presented to estimate the state variables in the face of unknown changes in characteristics of measurement noise. Accuracy of the proposed AUKF estimator is the best even compared with that of Particle Filter with much less computation time. The proposed LQG control scheme using this adaptive estimator can successfully stabilize the system despite of any system parameter and noise characteristic changes. Implementation of the proposed method in laboratory scale in the same way that is performed in [7] is recommended.
References [1] L. Sinegre, "Etude des instabilités dans les puits activés par gas-lift", in Spécialité “Mathématiques et Automatique”, Phd. thesis, Paris: Ecole des Mines de Paris, 2006. [2] Scandpower, OLGA Software Verion 5 User's Manual: Scandpower, 2006. [3] L. Sinegre, N. Petit, and P. Menegatti, "Predicting instabilities in gas-lifted wells simulation", American Control Conference, ACC, Minneapolis, Minnesota, USA, 2006. [4] B. Jansen, M. Dalsmo, L. Nøkleberg, K. Havre, V. Kristiansen, and P. Lemetayer, "Automatic Control of Unstable Gas Lifted Wells", SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 1999. [5] L. Imsland, B. A. Foss, and G. O. Eikrem, "State Feedback Control of A Class of Positive Systems: Application To Ggas Lift Stabilization," European Control Confrence, Cambridge, UK, 2003. [6] O. M. Aamo, G. O. Eikrem, H. Siahaan, and B. Foss, "Observer Design for Gas Lifted Oil Wells", American Control Conference, ACC, Boston, Massachusetts, USA, 2004. [7] O. M. Aamo, G. O. Eikrem, H. Siahaan, and B. Foss, "Observer design for multiphase flow in vertical pipes with gas-lift - theory and experiments", Journal of Process Control, vol. 15, pp. 247–257, 2005. [8] G. O. Eikrem, L. s. Imsland, and B. Foss, "Stabilization of Gas Lifted Wells Based on State Estimation," Intl. Symp. on Advanced Control of Chem. Processes, Hong Kong, China, 2004. [9] D. Simon, Optimal State Estimation, Kalman, H-inf and Nonlinear Approches. Hoboken, New Jersey: Wiley-Interscience, 2006. [10]H. H. J. Bloemen, S. P. C. Belfroid, and W. L. Sturm, "Soft Sensing for Gas-Lift Wells", SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 2004. [11]S. J. Julier and J. K. Uhlmann, "A New Extension of the Kalman Filter to Non-linear Systems," presented at AeroSense: The 11th Int. Symp. A.D.S.S.C., 1997. [12]S. J. Julier, J. K. Uhlmann, and H. Durrant-Whyte, "A new approach for filtering non-linear systems,", American Control Conference, ACC, Seattle, Washington, USA, 1995. [13]E. A.Wan and R. v. d. Merwe, "he Unscented Kalman Filter for Non-linear Estimatio," presented at IEEE Symposium 2000 (AS-SPCC), Lake Louise, Alberta, Canada, Oct. 2000. [14]G. Tao, Adaptive Control Design and Analysis. New york: Wiley-Interscience, 2003. [15]J. B. Burl, Linear Optimal Control: H-2 and H-inf Methods. Menlo Park, California: Addison Wesley Longman Inc., 1999.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Analysis of the Constraint Characteristics of a Sheet Forming Control Problem Using Interval Operability Concepts Fernando V. Lima a, Christos Georgakis a, Julie F. Smith b, Phillip D. Schnelle b a
Systems Research Institute & Department of Chemical and Biological Engineering, Tufts University, Medford, MA 02155, USA b DuPont Engineering Research and Technology, Brandywine 7304, 1007 Market Street, Wilmington, DE 19898, USA
Abstract An Interval Operability-based approach [1, 2] is applied to calculate operable output constraints for the Sheet Forming Control Problem (SFCP) from DuPont. The SFCP attempts to control the sheet thickness at 15 different points, which represent 15 output variables, using 9 manipulated variables in the presence of 3 disturbances. Thus, this problem represents a computationally complex, high-dimensional non-square system with more outputs than inputs. The SFCP is addressed here under two study cases: 1) a non-square, where all the 15 outputs are controlled independently of each other; 2) a square, where 6 outputs are combined in pairs, or zone variables, and controlled within their corresponding zone. Results show that significant reduction of the constrained region of process operation can be achieved for different output targets specified. Specifically, the hyper-volume ratio of the initial to the designed constrained regions range between 103 – 105. The calculated constraints are validated by running DMCplusTM (AspenTech) simulations for the extreme values of the disturbances. These constraints are intended for use online in model-based controllers (e.g., Model Predictive Control) to calculate the tightness with which each of the outputs can be controlled. Keywords: Operability, Sheet Forming Process, Non-square Systems, Model Predictive Control.
1. Introduction In recent years, chemical process designs have increased in complexity due to material and energy conservation requirements, integration of units, process optimization and stricter environmental regulations. Consequently, tools to systematically assess the capabilities of such designs and its integration with the process control structure have become increasingly important. These tools should identify a design’s ability to achieve the feasible region of operation around a steady-state in the presence of process disturbances. Specifically, it is important to determine the tightest feasible set of output constraints that can be achieved considering the constraint limitations of the input variables, which are design dependent [2]. The improper selection of these output constraints can make the controller infeasible when a disturbance moves the process outside its usual operating region. Hard constraints are enforced whenever feasible and softened whenever it is necessary to retain feasibility [3]. The Operability methodology originally introduced for square systems (Set-Point Operability [4]) and extended for non-square systems (Interval Operability [1, 2, 5, 6]) enables the systematic selection of
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such output constraints, so that they are as tight as possible and do not render the controller infeasible. Using the previously published Interval Operability concepts and algorithms, this paper aims to study the constraint characteristics of a Sheet Forming process from DuPont, which is characterized by a high-dimensional and non-square system. For such system, set-point control is not possible for all the outputs and interval control is necessary. This is done by analyzing two configurations of this problem, a 15 x 9 x 3 (outputs x inputs x disturbances) non-square system and a simplified 9 x 9 x 3 square sub-system. This simplified system is obtained by exploring the distributed characteristics of the SFCP by considering 6 zone variables. The presence of disturbances of high magnitude may preclude set-point control even for square systems. For such cases, the concept of Interval Operability may be equally applicable to calculate the tightest feasible output ranges.
2. Interval Operability Concepts The necessary sets to enable the Interval Operability assessment for an n x m x q (outputs x inputs x disturbances) system are defined in this section [5]. The Available Input Set (AIS) is the set of values that the process input variables can take based on the constraints of the process. The Desired Output Set (DOS) is given by the ranges of the outputs that are desired to be achieved and the Expected Disturbance Set (EDS) represents the expected steady-state values of the disturbances. These sets are mathematically represented by: AIS EDS
^u | u ^d | d
min i min i
` ; 1 d i d q`
d ui d uimax ; 1 d i d m ; DOS d d i d d imax
^y |
`
yimin d yi d yimax ; 1 d i d n ;
The Achievable Output Set for a specific disturbance value, AOS(d), is defined by the ranges of the outputs that can be achieved using the inputs inside the AIS: AOS(d)
^y |
y
Gu G d d ; u AIS, fixed d EDS`
(1)
where the matrices G and Gd represent the linear steady-state process and disturbance gain matrices, respectively. Finally, the Achievable Output Interval Set (AOIS) is defined as the tightest possible feasible set of output constraints that can be achieved, with the available range of the manipulated variables and when the disturbances remain within their expected values. The algorithm developed for the calculation of this important set is presented next.
3. Calculation of AOIS: Linear Programming Approach Two sets of output parameters are considered in the AOIS calculation: the steady-state target point (y0) and the relative output weights (w). The relative output weights represent the relative tightness with which each output will be controlled around its desired target and will affect the aspect ratio of the corresponding sides of the designed AOIS. For example, an aspect ratio of 1:10 between two outputs assures that one will be controlled 10 times more tightly, approximating set-point control. Several examples of AOIS calculations using different weights and output targets have been previously published [1, 2]. The set of points that characterize the vertices of the AOS can be easily calculated by directly mapping the vertices of the AIS and EDS using the linear steady-state process model (eq. 1). The calculation of AOIS in n is performed by
Analysis of the Constraint Characteristics of a Sheet Forming Control Problem
389
formulating the interval operability problem in a Linear Programming (LP) framework, where the AOS and the AOIS polytopes are described as a system of inequalities in the LP formulation. An overview of the algorithm for this calculation, presented in reference [6], is the following: 1) Define the relative weights w1, w2, ... wn that quantify the relative tightness within which each output needs to be controlled; 2) Select one of the extreme disturbance vectors d = di, i = 1, 2, …, k, which corresponds to one of the k = 2q vertices of EDS. Calculate AOS(di) (eq. 1) and the corresponding linear equalities and inequalities that define this set (see details in reference [6]); 3) Define a family of n-dimensional orthogonal parallelepipeds, P(Į), self-similar among them, centered at the target value of the outputs (y0), where the scalar Į affects each of their sizes by the following set of inequalities:
^y | b d y y 0 d b`
P (D )
(2)
where T
b
§ D D D · , ,, ¨ ¸ ; y0 w w w 2 n ¹ © 1
T
y01 , y02 ,, y0n
; and y
T
y1 , y2 ,, yn
4) Calculate the minimum value of Į, Įi, such that P(Įi) and AOS(di) have a single common point vi, by solving the LP problem below: Di
min D x
min f T x, x T
where f
¬ª 0 0 0n 1¼º ; and x
while y
vi P (Di ) AOS (di )
¬ª y1 y2 yn D ¼º
T
T
ª yT D º ; »¼ ¬«
(3)
5) Repeat steps 2 to 4 above for a total of k = 2q times to calculate the set of k points: v1, v2, … vk; 6) The final AOIS is the smallest orthogonal parallelepiped in n that includes all the k vi points from the LP solutions (AOIS = OP(v1, v2, v3, … vk)). This set defines the tightest set of output constraints that makes the process operable for the output target y0 and all the disturbance values inside the EDS.
4. Results: Sheet Forming Control Problem As briefly described above, the objective of the Sheet Forming Control Problem (SFCP) is to control the sheet thickness at 15 different points as uniformly as possible around different targets (y0). Thus, there are 15 controlled variables (CV’s), which correspond to the thicknesses in the cross-direction, with the same relative weight (w). Moreover, this process has 9 manipulated variables (MV’s) and 3 disturbance variables (DV’s). The steady-state gain model, the sets within which the input and output variables are constrained and the relative weights of the output variables are given in the following equations:
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§ G y1 · ¨ ¸ ¨ G y2 ¸ ¨ G y3 ¸ ¨ ¸ ¨ G y4 ¸ ¨G y ¸ ¨ 5 ¸ ¨ G y6 ¸ ¨ ¸ ¨ G y7 ¸ ¨G y ¸ ¨ 8 ¸ ¨ G y9 ¸ ¨G y ¸ ¨ 10 ¸ ¨ G y11 ¸ ¨ ¸ ¨ G y12 ¸ ¨G y ¸ ¨ 13 ¸ ¨ G y14 ¸ ¨G y ¸ ©¨ 15 ¹¸
§ -2 ¨ ¨ -2 ¨ -2 ¨ ¨ -2 ¨ -2 ¨ ¨ -2 ¨ 0 ¨ ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨¨© 0
AIS EDS DOS w y ss u ss y0
0 -1.8
0
0
0 -0.00064
0
0 -1.6
0
0
0 -0.00035
0
0 -1.4 -2
0
0
0
0
0 0
0 -1.8 0 -1.6
0 0
0 0
0 0
-0.00036 -0.00064
0
0
0 -1.6
0
0
-0.00084
-2
0
0
-1.8
0
0
-0.00096
-2
0
0
-2
0
0
-0.001
-2
0
0
-1.8
0
0
-0.00096
-2
0
0
0
0
0
-0.00084
-2 -2
0 0
0 0
0 -1.8 0 -1.8
0 0
-0.00064 -0.00036
-2
0
0
0
-2
0
0
-2
0
0
0 -1.8
0
0
-2
0
0
0
0
0
0
0
0
0
§1.7 · ¨ ¸ ¨1.7 ¸ ¨1.7 ¸ 0 ¨ ¸ u G § · 0 1 ¨1.7 ¸ ¨ ¸ ¨ ¸ G u2 ¸ 1.7 0 ¨ ¨ ¸ 0 ¸ ¨ G u3 ¸ ¨ 0 ¨ ¸ ¨ 0 ¸ Gu 0 ¸¨ 4 ¸ ¨ ¸ ¨ G u5 ¸ ¨ 0 0 ¸ ¨ ¸¨ 0 ¸ ¨ G u6 ¸ ¨ 0 ¸ ¨G u ¸ ¨ 0 0 ¸¨ 7 ¸ ¨ 0 ¸ ¨ G u8 ¸ ¨ 0 ¸ ¨¨ G u ¸¸ ¨ 0 0 ¸© 9 ¹ ¨ 0 ¨ 0 ¸ ¨ 0 -0.00036 ¸¸ ¨ ¨¨© 0 -0.00064 ¸¸¹
0 0 0 0 1.7 1.7 1.7 1.7 1.7 0 0 0 0 0
0 · ¸ 0 ¸ 0 ¸ ¸ 0 ¸ 0 ¸ ¸ 0¸ 0 ¸ § G d1 · ¸¨ ¸ 0 ¸ ¨ G d2 ¸ ¸¨ 0 ¸ © G d3 ¸¹ 0¸ ¸ 1.7 ¸ 1.7 ¸ ¸ 1.7 ¸ 1.7 ¸¸ 1.7 ¸¸¹
(4)
u 9 | 210 d u1 d 230; 210 d u2 d 230; 220 d u3 d 235; ½ ° ° 220 u 235; 220 u 235; 220 u 235; d d d d d d ® ¾ 4 5 6 ° 2000 d u7 d 4000; 2000 d u8 d 4000; 2000 d u9 d 4000° ¯ ¿
^d ^y
3
`
| E d di d E ; for 1 d i d 3; and 0 d E d 12 ; d ss
15
0,
T
0, 0
`
|1.9 d yi d 2.3; for 1 d i d 15
T
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1 T T = 220, 220, 227.5, 227.5, 227.5, 227.5, 3000, 3000, 3000 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1 T
where įy, įu and įd are deviation variables from the steady-state values for the outputs (yss), inputs (uss), and disturbances (dss), respectively. The scalar ȕ represents the magnitude of the disturbances, all three of which move in tandem. The design of the feasible set of output constraints will be performed here by considering the system above with its original dimensionality (section 4.1) and a 9 x 9 x 3 square approximation (4.2). 4.1. System with its Original Dimensionality To demonstrate the effectiveness of the proposed LP-based approach to handle highdimensional non-square systems, the SFCP (eq. 4) is addressed in its full dimensionality (15 x 9 x 3). The calculated minimum (ymin) and maximum (ymax) AOIS ranges for each controlled variable when ȕ = 12 are shown in the first two rows of Table 1. Because sheet-thickness uniformity is desirable, the following conservative set of output constraints, representing the widest thicknesses (y10, y11, y13), should be used: AOIS
^y
15
`
| 2.00 d yi d 2.20; 1 d i d 15
(5)
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Thus, the hyper-volume ratio (HVR) [5] of the original (DOS) to the designed (AOIS) constrained regions is: HVR = (0.4/0.2)15 = 3.28 x 104. Hence, for the assumed disturbance values, this process could be feasibly operated within a constrained region that is significantly tighter than the one initially specified. These designed new limits were validated by running DMCplusTM (AspenTech) simulations for the extreme values of the disturbances, showing that the MPC controller does not violate these limits at the steady-state. Furthermore, the computational time for the AOIS calculation was only 0.18 seconds (Dell PC with a 3.0-GHz Intel Pentium 4 processor). If tighter control of the overall sheet thickness is intended, process modifications should be performed to enlarge the AIS, and thus shrink the AOIS, availing tighter control of y10, y11, and y13, at least. 4.2. Square Approximation Consider now a 9 x 9 x 3 square approximation of the SFCP, where the objective is to control each of the 9 outputs at ranges within the DOS using 9 inputs. In this case, it is assumed that the sheet thicknesses are controlled at specified zones, which are represented by the following set of zone variables (z): z1 z6
y4 y5 y6 y7 y1 y2 ; z2 y3 ; z3 ; z4 ; z5 y8 ; 2 2 2 y9 y10 y14 y15 y11 y12 ; z7 ; z8 y13 ; z9 ; 2 2 2
(6)
where y8 (z5) corresponds to the measurement at the center of the sheet. The zone variables have the same DOS limits, relative weights and the target values of the initial output variables. The solution of this approximated problem also provides an alternative way to calculate the achievable constraints for the output variables using the properties of this distributed process. The AOIS calculation is performed setting again ȕ = 12, which corresponds to its maximum value. The following AOIS ranges are obtained for this case: AOIS
^z
9
| 2.04 d zi d 2.16; 1 d i d 9, E
`
12
(7)
Here as well, the most conservative set of constraints is used, to guarantee feasibility and sheet uniformity, which corresponds to the limits of z5, z6, z7 and z8 (see Table 1). Observe that once again very tight control can be achieved, which is demonstrated by the high value of the ratio between the hyper-volumes of the original constrained region and the designed constrained region (HVR = 5.08 x 104). This implies that for the assumed disturbance values, the process could be operated feasibly within a constrained region 5.08 x 104 tighter than the region initially specified by the DOS. Because different targets for the sheet thickness are intended, the zone target will now be moved from its nominal value of 2.1 units to 2.0 units. For this target, the AOIS ranges for the zone variables obtained when the disturbance range is equal to -12 d1 12 (ȕ = 12) are the following: AOIS
^z
9
| 1.92 d zi d 2.08; 1 d i d 9, E
`
12
(8)
Thus, for the specified conditions, the original constrained region could be again significantly reduced (HVR = 3.81 x 103). As in the previous case, the results for this target of 2.0 units correspond to the conservative set of constraints, representing the widest calculated thicknesses among the zones.
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To conclude the analysis for this process example, the typical computational time for the AOIS calculations of all cases was 0.19 seconds. Here as well, simulations were performed using DMCplus to validate the results for all cases. Finally, observe that the simplification of a non-square system by a square one provides a less realistic calculation of the AOIS (eqs. 5 and 7). In fact, if the results obtained for the zone variables were used for the outputs within the corresponding zone, then infeasibilities would occur for some outputs. Table 1. Feasible output ranges (AOIS) calculated for the SFCP (ȕ = 12). The output variables for the original problem with 15 outputs, 9 inputs and 3 disturbance variables, are represented with y. The zone variables for the simplified square problem are represented with z. yi/zi
i=1
2,3
4
5,7
6
8
9
10,11,13
12
14
15
min
2.05
2.03
2.04
2.08
2.04
2.06
2.08
2.00
2.10
2.05
2.01
ymax
2.15
2.17
2.16
2.12
2.16
2.14
2.12
2.20
2.10
2.15
2.19
min
2.09
2.09
2.10
2.04
2.04
2.04
2.09
max
2.11
2.11
2.10
2.16
2.16
2.16
2.11
y
z z
5. Conclusions Interval Operability concepts were applied to calculate the tightest feasible set of output constraints for the Sheet Forming Control Problem (SFCP). By considering two different configurations of this problem, square and non-square, different sets of constraints were obtained. Results for both scenarios showed that significant constraint reduction can be achieved for the initial set of output constraints without rendering the control problem infeasible in the presence of process disturbances. Although the use of zone variables reduces the complexity of the problem, the results obtained using this configuration are less accurate than the ones calculated by addressing the problem in its full dimensionality. The square nature of the simplified problem provides tighter feasible ranges for the zone variables than the constraints calculated for the individual output variables when the non-square problem is solved. If the calculated ranges of the zone variables were to be used to define the ranges of all 15 measured outputs, in a 15 x 9 MPC (or DMC) controller, infeasibilities would occur. The minimal computational time required for the corresponding calculations enables the online adaptation of the controller constraints depending on the current state of the process.
Acknowledgments The authors gratefully acknowledge the financial support from PRF-ACS through grant # 45400-AC9. We also wish to acknowledge William M. Canney from AspenTech for providing the DMCplus software.
References [1] F. V. Lima and C. Georgakis, In Proceedings of the 2006 IFAC International Symposium on Advanced Control of Chemical Processes (ADCHEM) (2006) 989-994. [2] F. V. Lima and C. Georgakis, In Proceedings of the 2007 IFAC International Symposium on Dynamics and Control of Process Systems (DYCOPS) 3 (2007) 49-54. [3] J. B. Rawlings, IEEE Control Syst. Mag., 20 (2000) 38-52. [4] D. R. Vinson and C. Georgakis, J. Process Contr., 10 (2000) 185-194. [5] F. V. Lima and C. Georgakis, J. Process Contr., doi:10.1016/j.jprocont.2007.09.004 (2007). [6] F. V. Lima and C. Georgakis, Input-Output Operability of Control Systems, Automatica, submitted for publication (2007).
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Real-Time Optimization via Adaptation and Control of the Constraints Alejandro Marchetti, Benoît Chachuat, Dominique Bonvin Laboratoire d’Automatique, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Abstract In the framework of real-time optimization, measurements are used to compensate for effects of uncertainty. The main approach uses measurements to update the parameters of a process model. In contrast, the constraint-adaptation scheme uses the measurements to bias the constraints in the optimization problem. In this paper, an algorithm combining constraint adaptation with a constraint controller is presented. The former detects shifts in the set of active constraints and passes the set points of the active constraints to the latter. In order to avoid constraint violation, the set points are moved gradually during the iterative process. Moreover, the constraint controller manipulates linear combinations of the original input variables. The approach is illustrated for a simple case study. Keywords: Real-time optimization, constraint control, constraint adaptation.
1. Introduction Throughout the petroleum and chemicals industry, the control and optimization of many large-scale systems is organized in a hierarchical structure. At the real-time optimization level (RTO), decisions are made on a time scale of hours to a few days by a so-called real-time optimizer that determines the optimal operating point under changing conditions. The RTO is typically a nonlinear program (NLP) minimizing cost or maximizing economic productivity subject to constraints derived from steady-state mass and energy balances and physical relationships. At a lower level, the process control system implements the RTO results, including product qualities, production rates and active constraints (Marlin and Hrymak, 1997). Because accurate mathematical models are unavailable for most industrial applications, RTO classically proceeds by a two-step approach, namely an identification step followed by an optimization step. Variants of this two-step approach such as ISOPE (Roberts and Williams, 1981; Brdys and Tatjewski, 2005) have also been proposed for improving the synergy between the identification and optimization steps. Parameter identification is complicated by several factors: (i) the complexity of the models and the nonconvexity of the parameter estimation problems, and (ii) the need for the model parameters to be identifiable from the available measurements. Moreover, in the presence of structural plant-model mismatch, parameter identification does not necessarily lead to model improvement. In order to avoid the task of identifying a model on-line, fixed-model methods have been proposed. The idea therein is to utilize both the available measurements and a (possibly inaccurate) steady-state model to drive the process towards a desirable operating point. In constraint-adaptation schemes (Forbes and Marlin, 1994; Chachuat et al., 2007), for instance, the measurements are used to correct the constraint functions in the RTO problem, whereas a process model is used to
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estimate the gradients of the cost and constraint functions. This way, the iterates are guaranteed to reach a feasible, yet suboptimal, operating point upon convergence. Two types of transients can be distinguished in RTO systems: at the lower level, the dynamic response of the controlled plant between successive steady-state operating points generated by RTO; at the upper level, the transient produced by the iterates of the RTO algorithm. Most RTO algorithms do not ensure feasibility during these transient periods, thus resulting in conservative implementations with significant constraint backoffs and limited changes in operating point between successive RTO periods. Constraint violations during both types of transients can be avoided by controlling the active constraints that define optimal operation (Brdys and Tatjewski, 2005). The implementation of constraint control can significantly decrease the constraint backoffs required in the RTO optimization problem, resulting in increased cost. The set of active constraints might change due to process disturbances and changing operating conditions, thus resulting in different constraint-control schemes (Maarleveld and Rijnsdorp, 1970; Garcia and Morari, 1984). In this work, a constraint-adaptation scheme is combined with a constraint controller. Special emphasis is placed on selecting the set points and the manipulated variables used in the constraint controller at each RTO period. The effect of the constraint controller on the feasibility of intermediate operating points is studied, under the assumption of an ideal constraint controller. The paper is organized as follows. Section 2 formulates the optimization problem. The RTO scheme combining constraint adaptation and constraint control is presented in Section 3. The behavior of the proposed scheme, with and without the constraint controller, is illustrated for a simple quadratic programming (QP) problem in Section 4. Finally, Section 5 concludes the paper.
2. Problem Formulation The optimization problem for the plant can be formulated as follows:
min (u) := (u, y(u))
(1)
u
s.t. G(u) := g(u, y(u)) G max ,
(2) ny
where u denotes the vector of decision (or input) variables, and y is the n n vector of controlled (or output) variables; : u y is the scalar cost function ny nu to be minimized; and g i : , i = 1,..., ng , is the set of operating constraints. Throughout the paper, the notation ( . ) is used for the variables that are associated with the plant and (.) for those of the process model. The steady-state mapping of the plant, y(u), is assumed to be unknown, and only an n approximate model F(u, y, ) = 0 is available for it, where is the set of model parameters. Assuming that the model outputs y can be expressed explicitly as functions of u and , the cost function and the operating constraints predicted by the model can be written as (u, ) := (u, y(u, )) and G(u, ) := g(u, y(u, )), respectively. nu
3. Real-Time Optimization Scheme 3.1. Constraint Adaptation In the presence of uncertainty, the constraint values predicted by the model do not quite match those of the plant. The idea behind constraint adaptation is to modify the optimization problem by adding a correction term to the constraint functions. At each RTO iteration, a model-based optimization problem of the following form is solved:
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min (u k , ) uk
s.t. G(u k , ) + k G max ,
(3)
ng
where k denotes the vector of constraint correction factors. Under the assumption that measurements are available for every constrained quantity at the end of each RTO period, the correction factors can be updated recursively as:
k +1 = (I B) k + B[G(u k ) G(u k , )] ,
(4)
ng ng
where B is a diagonal gain matrix with diagonal elements in the interval (0,1] . An important property of the constraint-adaptation algorithm is that the iterates are guaranteed to reach a feasible, yet suboptimal, operating point upon convergence (Forbes and Marlin, 1994). However, the constraints can be violated during the iterations, which calls for using constraint backoffs and limiting operating point changes between successive RTO periods. Constraint adaptation (3-4) represents the “classical” constraint-adaptation scheme (Forbes and Marlin, 1994; Chachuat et al., 2007). In this paper, a novel way of adapting the constraints is proposed:
min (u k , )
(5)
s.t. G(u k , ) + k G max,k ,
(6)
uk
where the correction term k := G(u k 1 ) G(u k 1 , ) stands for the difference between the measured and predicted values at the previous RTO period. The maximum values G max,k for the constraints are calculated as:
G max,k = G(u k 1 ) + B[G max G(u k 1 )] .
(7)
For the combination with constraint control, constraint adaptation (6-7) is preferred because it gives the ability to vary the set points G max,k passed to the constraint controller. Upon convergence of this algorithm, the set points reach the original constraint bounds G max . Let u0 denote the optimal solution for the process model with = 0 in (3). It can be shown that the constraint-adaptation schemes (3-4) and (6-7) produce the same iterates when initialized with 0 and u0 , respectively, and the same diagonal gain matrix B is used, provided the set of active constraints does not change. At each RTO period, a set of optimal inputs, uk , and corresponding Lagrange na multipliers, k , are obtained from the numerical solution of (5-6). Let G ak k denote the vector of active constraints at u k . It is assumed that the Jacobian matrix of the na n a R k u , has full row rank at uk , i.e. the constraints satisfy a active constraints, G u,k regularity condition. It follows that the input space can be split into the nka -dimensional subspace of constraint-seeking directions and the (nu nka ) -dimensional subspace of sensitivity-seeking directions. These subspaces are spanned by the columns of the orthogonal matrices Vkc and Vks , respectively, as obtained from singular-value a decomposition (SVD) of G u,k : a = [U ck U sk ][ ck 0][Vkc Vks ]T . G u,k (8) 3.2. Combination with Constraint Control At the constraint-control level, the variables are considered as time-dependent signals. In this work, the constraint controller is designed so as to track the iteratively-updated active constraints by varying the process inputs along the constraint-seeking directions.
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More precisely, the manipulated variables (MVs) in the constraint controller correspond na to the corrections uck (t) k along the directions Vkc , from the model optimum uk . Observe that the MVs may change from RTO period to RTO period, e.g. when the active set of (5-6) changes. At each time instant, the inputs u k (t) are then reconstructed from the values of uck (t) , based on the knowledge of uk and Vkc , as:
(
)
u k (t) = U uk ,Vkc , uck (t) := uk + Vkc uck (t) .
(9)
The set points in the constraint controller correspond to the active constraints, na a G max,k k , determined at the RTO level. Finally, the controlled variables (CVs) are the active constraints G ak (t) := g a u k (t), y k (t) for the plant. At the initial time tk 1 of the k-th RTO period, the constraint controller is started from uck (tk 1 ) = VkcT u k 1 uk . At the terminal time tk of that period, the constraint controller yields a new steady-state operation, which corresponds to the set points a G max,k . The corresponding steady-state inputs u k are obtained from (9) as u k = U uk ,Vkc , uck (tk ) .
(
(
(
)
)
)
Figure 1. Scheme combining constraint adaptation and constraint control.
The overall optimization and control scheme is illustrated in Fig. 1, and the procedure can be summarized as follows: 1. Set k = 0. Initialize B. Start from a feasible (conservative) operating point u0 (without the constraint controller). 2. At steady state, measure G (u k ) and compute G max, k +1 from (7). Set k := k + 1 . 3. Calculate the solution uk of (5-6). 4. Determine the constraint-seeking directions Vkc from SVD of the Jacobian a matrix G u,k of active constraints at uk . 5. Formulate a square constraint-control problem where the MVs are the values of uck (t) , the CVs are the active constraints G ak (t) , and the set points are the a values G max,k of the active constraints identified in Step 3. 6. Apply the constraint controller to the plant and get the inputs u k corresponding to the new steady-state operation. Go to Step 2.
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3.3. Implementation Aspects The approach assumes that all the constrained variables can be measured or estimated on-line at a sampling period much smaller than the time constant of the controlled plant. Notice that the decision variables u in the RTO problem may very well be set points of feedback controllers acting directly on the plant manipulated variables. In this case, the constraint controller can be viewed as a primary controller in a cascade control configuration that corrects the set points produced at the RTO level. The constraint-control problem is a multivariable square control problem, and various controllers can be used, such as a discrete integral controller or a model predictive controller. In order to avoid overshoots, the set-point corrections can be implemented by ramps rather than steps. Also, small overshoots can usually be accommodated during the first a few iterations, i.e. when the set points G max,k are conservative with respect to the actual bounds G max .
4. Illustrative Example Consider the following QP problem:
min (u, ) := (u1 1)2 + (u2 1)2
s.t. G1 := 1 + 2 u1 u2 0,
(10)
G2 := 3 + 4 u1 + u2 0,
(11)
with two decision variables u = [u1 u2 ] , four model parameters = [1 ,..., 4 ] , and two uncertain constraints G1 and G2 . The parameter values for the model and the simulated reality are reported in Table 1. Note that the operating point determined from the model, without constraint adaptation, leads to constraint violation. T
T
Table 1. Values of the parameters for the model and the simulated reality.
1 2
3
4
Reality 0.4 0.8 -1.8 1.9 Model 0.9 0.4 -2.0 1.4
In this simple QP problem, an ideal constraint controller is assumed, i.e. the controller a determines uck (tk ) such that G a U uk ,Vkc , uck (tk ) = G max,k . The objective here is to illustrate the effect of constraint control on the feasibility of the steady-state intermediates. Both constraints are active at the optimum either for the reality or for the model. The constraint-adaptation algorithm is applied with and without constraint control, starting from u 0 = [0 1.4]T and with a diagonal gain matrix B = b I 22 with b (0,1] . The results obtained with b = 0.7 are shown in Fig. 2. It can be seen that, without constraint control, the iterates converge by following an infeasible path (left plot). In fact, the iterates can be shown to follow an infeasible path for any value of b (0,1] ; the constraint violation is reduced by decreasing the value of b, but this is at the expense of a slower convergence. With constraint control, on the other hand, the iterates converge without violating the constraints (right plot), irrespectively of the value of b. Both constraints are found to be active at the solution point of the optimization problem (5-6) for all iterations. Since the number of active constraints is equal to the number of decision variables, the constraint-seeking directions span the whole input space here.
(
)
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Figure 2. Illustration of the proposed algorithm for Problem (10-11). Left plot: Without constraint control; Right plot: With constraint control; Thick solid lines: constraint bounds for the simulated reality; Thick dash-dotted lines: constraint bounds predicted by the model without adaptation; Dotted lines: contours of the cost function; Light solid lines: iterates; Point R: optimum for the simulated reality; Point M: optimum for the model without adaptation.
5. Conclusions An optimization scheme combining constraint adaptation with constraint control has been proposed. This scheme presents two important features: (i) the constraint controller tracks the active constraint determined at the RTO level by adapting the inputs in the subspace of constraint-seeking directions, and (ii) the set points for the active constraints in the constraint controller are updated at each iteration and reach the actual constraint bounds upon convergence. In future work, this combined scheme will be compared to other existing approaches (e.g. Ying and Joseph, 1999). The combination of more involved RTO schemes with constraint control (e.g. Gao and Engell, 2005) will also be considered.
References M. A. Brdys and P. Tatjewski, 2005, Iterative algorithms for multilayer optimizing control. Imperial College Press, London, UK. B. Chachuat, A. Marchetti, and D. Bonvin, 2007, Process optimization via constraint adaptation, J. Process Contr., In press. J. F. Forbes and T. E. Marlin, 1994, Model accuracy for economic optimizing controllers: The bias update case, Ind. Eng. Chem. Res., 33, 1919-1929. W. Gao and S. Engell, 2005, Iterative set-point optimization of batch chromatography, Comp. Chem. Eng., 29, 1401-1409. C. E. Garcia and M. Morari, 1984, Optimal operation of integrated processing systems. Part II: Closed-loop on-line optimizing control, AIChE J., 30, 2, 226-234. A. Maarleveld and J. E. Rijnsdorp, 1970, Constraint control on distillation columns, Automatica, 6, 51-58. T. E. Marlin and A. N. Hrymak, 1997, Real-time operations optimization of continuous processes, AIChE Symp. Ser., 93, 156-164. P. D. Roberts and T. W. C. Williams, 1981, On an algorithm for combined system optimization and parameter estimation, Automatica, 17, 1, 199-209. C.-M. Ying and B. Joseph, 1999, Performance and stability analysis of LP-MPC and QP-MPC Cascade Control Systems, AIChE J., 45, 7, 1521-1534.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Integration of Engineering Process Control and Statistical Control in Pulp and Paper Industry Ana S. Matos, José G. Requeijo, Zulema L. Pereira Dept. Mec & Ind Eng and UNIDEMI, Faculty of Science and Tecnology, New University of Lisbon, 2829-516 Caparica, Portugal
Abstract The main goal of this article is to present a methodology and a framework that is able to bring together two important concepts: Engineering Process Control (EPC), which was developed by process engineers to achieve short time control, and Statistical Process Control (SPC), conceived and implemented by statisticians and quality managers for attaining medium and long term control. The integration of both concepts can represent a breakthrough in the final product performance, by creating the necessary conditions to decrease the variability of quality characteristics both in the short and long term. The integrated methodology was designed for the pulp and paper industry and was established in several phases. First, a mathematical model was developed to represent as much as possible the process dynamic behaviour. The transfer function obtained was then used to implement two components of the above mentioned concepts, namely controllers, based on the minimum variance criterion, and statistical control charts. At last, the two components were integrated into the process, which was submitted to several disturbances to ascertain the control achieved with the integration. The methodology was tested in a real industrial process of one of the most important pulp producers in the world and considered several scenarios. To illustrate the methodology, we present one of the scenarios that shows the benefits of EPC/SPC integration. Through the application of the developed methodology to real data, process engineers at the company are now able to use a valuable decision making tool when the production process is affected by certain disruptions, with obvious consequences on product quality, productivity and competitiveness. Keywords: Engineering Process Control, Statistical Process Control, Process Modelling.
1. Introduction Continuous improvement of any process requires reduction in the variability around the target value of its parameters. Traditionally, two different approaches have been used to accomplish this goal: Engineering Process Control (EPC) developed and employed by process and control engineers and Statistical Process Control (SPC), used by statisticians and quality engineers. Until recently, the main reason for keeping these two concepts separate was the different view each of them had about an industrial process. While SPC monitoring procedures seek to reduce the output variability by detecting and eliminating assignable causes of variation, EPC is usually applied to minimize the output variability by making online adjustments of one or more process inputs on a regular basis. The first attempts to integrate EPC and SPC appeared long ago, with the work of Barnard (1959). Using the machine-tool case study, the author demonstrated that automatic control and statistical control can be used in parallel.
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The first approach of integration presented to the statistical community was developed by MacGregor (1988), who suggested the use of control charts for monitoring the behaviour of a process under EPC. Inspired by the work of MacGregor (1988), several other authors became notorious in the field, leading to different approaches that reveal two great concerns associated with this type of integration: • Identification of the variables that must be monitored: if only output variables (quality characteristics), input variables (adjustable variables) or both of them; • Decision on whether to use automatic or manual controllers, the latter being or not constrained by statistical control; such decision would depend on adjustment costs and type of adjustment. The first approach that explicitly combines SPC with EPC was proposed by Vander Wiel et al. (1992) under the name of Algorithmic Statistical Process Control (ASPC). Following the same philosophy of ASPC, other reference studies emerged, such as Montgomery et al. (2000) and Huang and Lin (2002), among many others. An innovation introduced to the ASPC approach was the use of control charts applied to adjustable variables; the joint monitoring of input and output variables (using different control charts) was presented by Messina et al. (1996) and was followed by Tsung and Tsui (2003). Within a slightly different context, a third approach appears which considered the existence of adjustment costs. The implementation of control charts acting as a “supervisor” of the control actions was the way found by several authors to minimize adjustment costs (e.g. Box and Luceño, 1997 and Ruhhal et al., 2000). Recent years have witnessed the appearance of several research studies in this field. However, there have been scarce publications using real production data and demonstrating the practical application of the integration. This article tries to fill this gap, as it gives an example of integrated EPC/SPC applied to a real and complex continuous process. This new development was carried out in cooperation with a large paper and pulp production plant in Portugal, which is one of the most important producers in the world.
2. Development of an EPC/SPC Integration Methodology This article summarises an integrated EPC/SPC methodology developed by Matos (2006) as a doctoral research project. The main goal was the development of a methodology that could be tested and applied to a real case study. Additionally, it should also be adjustable to other industrial processes with similar technical requirements. Once the pulp production process is well understood, the first step is to characterize the methodological “hardware” and “software” elements that will be part of the integrated EPC/SPC. Within this work, the term hardware is used to describe the more physical elements, such as the mathematical model, the controllers and the control charts. On the other hand, the software is related to the rather intangible elements, namely the intervention criteria, the type of disturbances (for testing purposes) and the performance measures. The intervention criteria will constrain the rule to be applied by the controller and the control chart, as well as the way they interact in the integration. Altogether, the software elements allow the evaluation and comparison of different integration scenarios. As Figure 1 shows, the main stages of the proposed methodology are the preliminary data analysis, the identification of all process variables (outputs, inputs and disturbance variables), the transfer function model (i.e. the mathematical model that describes the
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process behaviour), the controllers (based on the minimum variance criterion) and, finally, the univariate and multivariate control charts (designed to be applied to autocorrelated data).
Figure 1 – The main stages of the integrated EPC/SPC methodology
2.1. Case Study – Pulp and Paper Industry The case study presented here deals with a pulp and paper production process. The plant produces Bleached Eucalyptus Kraft Pulp, using the ECF process (Elemental Chlorine Free). The Kraft pulping process is performed in two different phases, which influence the final pulp quality: the cooking process of wood chips (eucalyptus globules) followed by the pulp bleaching. The cooking process is the phase that most contributes to the preservation of the main pulp characteristics, which, in turn, will ensure high quality paper. The viscosity of the bleached pulp, among other quality characteristics, constitutes one of the most important control parameters; the viscosity value depends, to a great extent, on the cooking process carried out in two continuous digesters working in parallel. After understanding the MO (modus operandis) of the bleached pulp process, the main input variables (which are measured in the digesters) were identified (Table 1). Table 1 – Input variables and symbols
Temperature Variables
Symbol
Concentration Variables Symbol Active-alkali AA Temperature in C4 zone TemC4 Sulphur index SI Temperature in C5 zone TemC5 Top black liquor TBL Temperature in C6 zone TemC6 White liquor C4 WLC4 Temperature in C8 zone TemC8 White liquor C8 WLC8 The present study considered four production periods with stabilized operational conditions (3 temporal data windows for estimation and 1 for validation). The samples were collected every 4 hours for both input (Table 1) and output (viscosity) variables. 2.2. Model Fitting After the preliminary data analysis, a satisfactory Box-Jenkins transfer function model was developed to describe, as much as possible, the dynamic behaviour of the bleached
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pulp process. The methodology used to obtain the transfer function model was carried out in three phases, as follows:
•
1st phase: fitting of several single-input single-output (SISO) transfer function models to identify possible relationships between input - output variables.
•
2nd phase: merging of the three data windows with the goal of obtaining a better profile of the bleached pulp process; the 1st phase was then repeated.
•
3rd phase: development of a multiple-input single-output (MISO) transfer function model using the results of the 2nd phase. The obtained model, which was developed using the Toolbox System Identification from MATLAB® software, explained 42% of the total data variation within the observation period: yt =
( −2,86 − 7, 46B ) WLC 8tD−12 + 5,90SI tD−12 − 4, 01WLC 4tD−22 − 5, 23TemC 4tD−21 − (1+0,99B )
− 2,90TemC 5tD−21 + 1, 66 AAtD− 22 +
1 ε (1 − 0,56B ) t
(1)
In the previous equation, yt is the deviation of viscosity from target at time t, εt is the white noise sequence and B defines the backshift operator. WLC8, SI, WLC4, TemC4, TemC5 and AA represent the variables of Table 1 in digester 1 (D1) and digester 2 (D2). The fitted model was successfully validated utilizing the data of the 4th window established for that purpose. Such mathematical model is the first “hardware” element and is the foundation of the complete methodology developed in the research. 2.3. Engineering Process Control and Statistical Process Control According to Figure 1, once the mathematical model has been defined, the study carries on with the definition of the other hardware components: controllers and control charts. The integrated control strategy used manual controllers constrained by the control chart decisions. The Ridge controller (del Castillo, 2002) based on a minimum variance criterion was found to have good characteristics to be adapted to the transfer function defined in (1). This controller has a tuning parameter that balances the variances of the output with the inputs. The development of an appropriate monitoring scheme through control charts leads to several questions, such as: which characteristics are to be monitored, where to apply the charts and which control charts are appropriate. To monitor the viscosity, three control charts were considered as good candidates, namely the EWMA with residuals, the CUSCORE chart and the EWMAST chart, since they revealed to be more effective in detecting changes of small magnitude than some other charts. It was considered equally important to apply multivariate control charts to monitor the input variables of the digesters. The multivariate study was performed using two control charts of the same type, but applied with different goals. The first one was applied directly to the digesters input variables, whereas the second one was applied to the difference between each input variable (real value) and the theoretical value shown by the controller. Given the large amount of variables and the auto-correlated structure exhibited by the data, the control charts were based on projection methods, namely the dynamic principal components analysis (DPCA), proposed by Ku et al. (1995). In both cases, i.e. controllers and control charts, the tuning parameters were obtained through simulation models developed on a MATLAB® platform.
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3. Results and Discussion of Integration Outputs After the definition of the three “hardware” elements previously described, one has to establish the “software” elements: intervention criterion, performance measures, type of disturbances and simulation conditions. The approach used in the research is somehow in between the second and the third approaches mentioned in the Introduction; on one hand, the integrated EPC/SPC focuses on control charts to monitor both the input and the output variables and, on the other, it uses a constrained manual controller. Therefore, the intervention criterion was established as a constrained action of the controllers by both control charts. The Asymptotic Mean Square Deviation (AMSD) was used as the performance measure to compare different scenarios, since it incorporates the deviations from the target and the variability (particularly useful when a process is submitted to a disturbance). Besides the use of AMSD, the Average Run Length (ARL) was applied to evaluate the performance of each control chart. Given the main characteristics of the pulp process, it was possible to list seven different types of disturbance that can affect the dynamic behaviour of the process: the input and output variables, the autoregressive parameter and the residuals of the model (φ, Nt). As regards the simulation conditions, the running of 10 000 cycles, with 248 observations each, was considered sufficiently credible. Since the proposed EPC/SPC was designed to be applied in sequential stages, the construction of the different scenarios starts with an open-loop process, followed by the incorporation of the control charts and then the manual controller. The scenarios are: 1)– open loop (system operating freely), 2)– entry of univariate control chart, 3)– entry of controllers (manual regime), 4)– entry of multivariate control chart applied to controllers, and 5)– entry of multivariate charts to control the input variables. Figure 2 compares the five scenarios when two disturbances were applied to the process. In the figure, δ is the size of the shift in the mean, measured in terms of the standard deviation (new mean = μ+δσ). Disturbance in noise component (N t(N ) t) Disturbance in noise component 3200
0
3100
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2
Disturbance Alcali-Active (AA Disturbance in in Alcali-Active (AA ) ) 3200 2.5 3100
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Scenario 2
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0
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0.5
1
1.5 2 2.5 shift δ
Scenario 4
3
3.5
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Scenario 5
Figure 2 – AMSD for the five scenarios with implementation of EWMAST chart
As can be seen in Figure 2, the scenarios present a different behaviour when the same control chart (EWMAST) was used. It is visible that the proposed methodology increased the process performance (scenarios 4 and 5), when compared with scenario 1 (no control) or with the tradicional approaches (scenarios 2 and 3).
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4. Conclusions The success inherent to an integrated methodology of this nature is closely associated with the ability of creating different scenarios and the skill in comparing them. Other requirements equally important are the quality of the mathematical model and the selection of both the controllers and the control charts. Although this study has used real production data to create the model, the employment of computational simulation revealed to be an essential tool in accomplishing the aim of the research. The developed simulation models were used for studying the sensitivity and robustness of controllers and control charts. Additionally, the simulation exercise is the only way of testing different scenarios when the process is submitted to several types of disturbance. As far as the literature review revealed, the pulp and paper industry has not applied integrated methodologies based on “black boxes”. According with the findings of present research, and once the best integrated scenario is obtained and appropriate interface software is developed, the process engineers can use the methodology as a decision making tool when the production process is affected by certain disruptions, with valuable consequences on quality, productivity and competitiveness. Consequently, one expects that the company where the research took place will, in the near future, benefit from the implementation of the proposed appoach. At last, it is also important to highlight the flexibility and adaptability of the methodology to any other type of production system when the production staff can use the available data to build a mathematical transfer function that models the dynamic behaviour of the process.
References Barnard, G. A., 1959, Control Charts and Stochastic Processes, Journal of the Royal Statistical Society B, 21(2), 239-271. Box, G. and Luceño, A., 1997, Statistical Control by Monitoring and Feedback Adjustment, John Wiley & Sons, NY. del Castillo, E., 2002, Statistical Process Adjustment for Quality Control, John Wiley & Sons, NY. Huang, B. and Lin, Y. L., 2002, Decision Rule of Assignable Causes Removal under an SPC-EPC Integration System, International Journal of Systems Science, 33(10), 855-867. Ku, W., Storer, R. H. and Georgakis, C., 1995, Disturbance Detection and Isolation by Dynamic Principal Component Analysis. Chemometrics and Intelligent Laboratory Systems, 30, 179-196. MacGregor, F., 1988, On-Line Statistical Process Control, Chemical Engineering Process, Oct: 21-31. Matos, A. S., 2006, Engenharia de Controlo do Processo e Controlo Estatístico da Qualidade: Metodologia de Integração Aplicada na Indústria da Pasta de Papel, PhD thesis, FCT/UNL, Lisboa, Portugal. Messina, W. S., Montgomery, D. C. and Keats, J. B., 1996, Strategies for Statistical Monitoring of Integral Control for the Continuous Process Industries, Statistical Applications in Process Control, New York, Marcel Dekker, 47, 193-214. Montgomery, D. C., Yatskievitch, M. and Messina, W. S., 2000, Integrating Statistical Process Monitoring with Feedforward Control, Quality and Reliability Engineering International, 16(6), 515-525. Ruhhal, N. H., Runger, G. C. and Dumitrescu, M., 2000, Control Charts and Feedback Adjustments for a Jump Disturbance Model. Journal of Quality Technology, 32(4), 379-394. Tsung, F. and Tsui, K. L., 2003, A Mean-Shift Pattern Study on Integration of SPC and APC for Process Monitoring, IIE Transactions, 35, 231-242. Vander Wiel, S. A., Tucker, W. T., Faltin, F. W. and Doganaksoy, N., 1992, Algorithmic Statistical Process Control: Concepts and an Application, Technometrics, 34(3), 286-297.
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A combined Balanced Truncation and MultiParametric Programming approach for Linear Model Predictive Control Diogo Narcisoa, Efstratios Pistikopoulosa a
Imperial College London, South Kensington Campus, Department of Chemical Engineering, SW7 2AZ, London, United Kingdom
Abstract We present a novel approach to Model Predictive Control problems, which combines a model reduction scheme coupled with parametric programming. Balanced Truncation is used to first reduce the size of the original Model Predictive Control formulation, while multi-parametric programming is employed to derive the parametric control laws offline. The theoretical developments are presented with an example problem. Keywords: MPC, Multi-Parametric Programming, Balanced Truncation.
1. Introduction Multi-parametric programming [1] has recently received a lot of attention in the open literature, especially because of its important applications in Model Predictive Control (MPC) [2]. In this context, a new class of controllers, the so-called parametric controllers has been invented [3] which allow for the off-line derivation, hardware implementation and installation of Model Predictive Control [4]. While the advantages of parametric controllers are well established, a key challenge for their wider applicability is the ability to derive parametric controllers from arbitrary large scale and complex mathematical models. In this context, Model Order Reduction [5] can be a useful tool, since it could lead to an approximate model of reduced size, and complexity and of sufficient accuracy. In this paper we present a Model Reduction technique incorporated with multiparametric programming and control, namely Balanced Truncation (BT). The use of Balanced Truncation eliminates a number of states of dynamic linear systems, while a bound on the maximum error obtained for the output vector can be established. This then allows for the derivation of (approximate) linear parametric controllers, which can be tested and validated (against the original high-fidelity model) off-line. These theoretical developments are presented next.
2. Balanced Truncation in Multi-parametric programming and control Balanced truncation is one model reduction technique, which is particularly suitable in the context of state-space dynamic models, linear Model Predictive Control and Multiparametric controller design, as discussed in the following. In Eq. (1) we present the mathematical formulation of the MPC problem we aim to solve. Given Eq. (1), we first seek to use balanced truncation to reduce the size of the model, and then solve the reduced control problem via our multi-parametric programming and control methodologies. The derived parametric controller can then be validated against the original, full space model.
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2.1. Balanced truncation in Multi-parametric programming and control We consider the following formulation in discrete time and linear form, already recast as a mp-QP problem (See [6]):
(1) Where the initial state x(t) corresponds to the vector of parameters in the multiparametric programming framework. Balanced truncation is then applied to Eq. (1). We work with the dynamic system (xt+k+1|t = Axt+k|t + But+k; yt+k|t = Cxt+k|t) and seek to find a transformation T such that the transformed system is balanced. Following the procedure as described in [5], we describe the dynamic system in an equivalent balanced form:
(2) -1
b
b
-1
b
For convenience, we write TAT as A , TB as T and CT as C . We incorporate (2) in (1) and hence convert into the transformed state x : for matrices K, P, Q and V in Eq. (1) we substitute x for T-1 x resulting in matrices Kb = KT-1, Pb = (T
−1 T
) PT-1, Qb =
(T −1 ) T QT-1 and Vb = T-1V, respectively (where superscript b denotes balanced realization of the corresponding matrices obtained after this step). For simplification, we rewrite Eq. (1) as follows:
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(3) Note that in Eq. (3) the parameter space has also been transformed. In the next step, we partition the vector x such that x = [ x1T , x 2T ]T, where x1 comprises the first p (the order of the reduced model) components of x . The matrices in Eq. (3) are also partitioned according to the partition of the state vector. The reduced order problem can then result from the deletion of the last n-p states, x 2 , and the corresponding matrix blocks, as follows:
(4) Note that Eq. (4) is not exactly equivalent to either Eq. (1) or Eq. (3): information on the dynamics is lost during the balanced truncation step. There is an “inherent” error in the calculation of the output vector y: even though a feasible solution may be obtained from the reduced problem, this may actually lead to constraint violations of the original problem. We consider here two ways to deal with this problem: (i) neglect the output bounds and keep only the input bounds; (ii) update the output bounds in order to ensure feasibility of all output solutions. These are presented next.
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2.1.1. Recasting option I: neglect output constraints Neglecting the output constraints will lead to a controller which is driven only by states stabilisation. In this case we keep only the constraints on the inputs as they are the same of the original problem. This type of control can be used whenever we do not have hard constraints. The main drawback of this is the loss of one of the most important features of MPC: the ability to deal with all types of constraints. 2.1.2. Recasting option II: update the output bound The second approach we consider here consists of updating accordingly the bounds of the outputs in order to ensure feasibility as follows. Given bounds on the output, ymin ≤ y ≤ ymax, these bounds are updated based on the output error according to the magnitude of the control input as follows [5]:
(5) Where σk corresponds to the singular values of the neglected states. Through Eq. (5) one can compute the maximum error, δ, on output y, as:
(6) We can then update the bounds on the outputs by further restricting the bounds on y as follows: (7) Eq. (7) will ensure that feasibility of the outputs is obtained regardless of the error on the outputs. 2.2. mp-QP formulation Using the state model (xt+k+1|t = Axt+k|t + But+k) we can proceed to convert Eq. (4) by updating the bounds on y (using either Eq. 7 or neglecting the output constraints), thereby recasting the MPC framework in a way that all future states are eliminated, as follows:
(8) T
ut+N_u-1T]T
Note that only inputs vector U = [ut , …, contain the optimisation variables where x1 provides the initial conditions for the states, which are the parameters in the multi-parametric programming framework. Finally, using the transformation of variables z = U + H-1FT x1 (t), Eq. (8) is converted into the mp-QP problem, as follows:
(9)
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The solution of Eq. (9) results in a set of parametric control laws valid in convex critical regions (the so called critical regions). An algorithm for the solution of Eq. (9) can be found in [1] or [7]. The algorithm has been implemented in MATLAB. A full example is presented next to simply illustrate its key steps and features. Detailed computational results and other examples are given elsewhere [8].
3. Example A random state-space system was generated in MATLAB. It consists of n = 10 states, m = 3 inputs and o = 3 outputs. We choose a small model for which the parametric controller can be derived for the original model; based on this solution we can then validate the solution of the controllers obtained from the reduced problems. Matrix A will not, in general represent a continuous stable system. Matrix A is stabilized and the model is then discretized, through the use of a time step (Δt = 1). In general, this step has to be as small as necessary to guarantee an accurate description. We perform a second discretization with Δt = 0.01 for simulation purposes, which we will use to test the performance of the obtained controllers. For the present control problem we considered the following bounds: (-2,-2,-2)T ≤ u ≤ (2,2,2)T; (-10,-10,-10)T ≤ y ≤ (10,10,10)T. We defined the parameter space so that: (-2, -2, …, -2) T ≤ x ≤ (2, 2, …, 2)T. The methodology was applied for p=10 (original size), p=6 and p=3. The first recasting option for the output bounds - deletion of the output constraints is presented here. We selected a time and control horizon with three steps. The parametric solutions, including both the set of critical regions and the associated parametric laws were obtained for each case. In order to test the performance of each controller, we simulated the behaviour of the system using the full descritized model with Δt = 0.01, starting from an initial perturbed state x = [1,1,… ,1]T. The aim of the controller is to drive the states to the origin. We simulated each of the controllers and the open loop responses for a total of 30 time steps. Fig. 1(A) shows the open loop response. 1.5
1.5
1
1
B 0.5
0
0
x
x
A 0.5
−0.5
−0.5
−1
−1
−1.5
−1.5
0
5
10
15 t
20
25
30
1.5
0
5
10
15 t
20
25
30
10
12
8
6
1
4 0.5
x
x
2 0
0 −0.5 −2
C −1
−1.5
D
−4
0
5
10
15 t
20
25
30
−6
0
2
4
6 t
8
Figure 1: Dynamic responses of the model used (A – open loop; B – controlled with p=10; C – controlled with p=6; D – controlled with p=3)
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In Fig. 1(B) one can observe that the parametric controller of order p = 10 improves the response when compared with the open loop response, as expected for this class of fullscale parametric controllers. For order p = 6 (Fig. 1(C)), there is an initial strong response from the controller which makes its performance of inferior quality by comparison to cases A and B. Nevertheless, it stabilizes the states. However, controller p=3 (Fig. 1(D)) shows a poor performance as a consequent of significant model reduction. While a controller based on reduced model of order p = 6 captures the significant dynamic information and enables stabilization of the perturbed state, in the case of reduced model of order p=3, important information is lost and the controller is not capable of stabilizing the states. Hence, the controller based on p=3 is rejected.
4. Concluding remarks We have presented a systematic procedure to derive parametric controllers based on (i) reduction of the original MPC model by the use of Balanced Truncation, and (ii) application of our multi-parametric programming and control toolbox [7]. Critical issues, which we have attempted to address in this paper and are subject of further developments at Imperial College include: • Controlling the error in the output constraints • Guarantee feasibility of all constraints for all parameter realization • Establishing equivalence between original and transformed problem • Identify the most suitable model reduction scheme for a wider class of models and applications
Acknowledgements Financial support from Marie Curie European Project PROMATCH (MRTN-CT-2004512441) is gratefully acknowledged.
References [1]. [2]. [3]. [4]. [5]. [6]. [7]. [8].
Pistikopoulos, E.N. et al., V., Multi-Parametric Programming, Wiley, Weinheim, 2007 Pistikopoulos, E.N. et al., Multi-Parametric Model-Based Control, Wiley, Weinheim, 2007 European Patent 1399784, ParOS, 2007 Dua, P. et al., Computers and Chemical Engineering, In Press (Available online 19 March 2007) Antoulas, A.C., Approximation of Large-Scale Dynamical Systems, SIAM, Philadelphia, 2005 Bemporad et al., Automatica 38, 2002 Dua, V. et al. , Computers and Chemical Engineering 26, 2002 Narciso, D. A. C. et al., Internal Report, CPSE – Imperial College, 2007
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Fault detection and isolation based on the modelbased approach : Application on chemical processes Nelly Olivier-Mageta, Gilles Hétreuxa, Jean-Marc Le Lanna, Marie-Véronique Le Lannb,c a
Laboratoire de Génie Chimique (CNRS - UMR 5503), INPT-ENSIACET 118, route de Narbonne F-31077 Toulouse Cedex 04, France b CNRS ; LAAS, 7, avenue du Colonel Roche, F-31077 Toulouse France c Université de Toulouse ; INSA ; LAAS ; 135, avenue de Rangueil ; F-31 077 Toulouse, France
Abstract In this paper, we present a method for the fault detection and isolation based on the residual generation. The main idea is to reconstruct the outputs of the system from the measurement using the extended Kalman filter. The estimations are compared to the values of the reference model and so, deviations are interpreted as possible faults. The reference model is simulated by the dynamic hybrid simulator, PrODHyS. The use of this method is illustrated through an application in the field of chemical process.
Keywords: Fault Detection and Isolation, Extended Kalman Filter, Dynamic Hybrid Simulation, Object Differential Petri nets, Distance.
1. Introduction In a very competitive economic context, the reliability of the production systems can be a decisive advantage. This is why, the fault detection and diagnosis are the purpose of a particular attention in the scientific and industrial community. The major idea is that the defect must not be undergone but must be controlled. Nowadays, these functions remain a large research field. The literature quotes as many fault detection and diagnosis methods as many domains of application (Venkatasubramanian, et al., 2003). A notable number of works has been devoted to fault detection and isolation, and the techniques are generally classified as: • Methods without models such as quantitative process history based methods (neural networks (Venkatasubramanian, et al., 2003), statistical classifiers (Anderson, 1984)), or qualitative process history based methods (expert systems (Venkatasubramanian, et al., 2003)), • And model-based methods which are composed of quantitative model-based methods (such as analytical redundancy (Chow and Willsky, 1984), parity space (Gertler and Singer, 1990), state estimation (Willsky, 1976), or fault detection filter (Franck, 1990)) and qualitative model-based methods (such as causal methods: digraphs (Shih and Lee, 1995), or fault tree (Venkatasubramanian, et al., 2003)). In this paper, the proposed approach to fault detection and isolation is a model-based approach. The first part of this communication focuses on the main fundamental concepts of the simulation library PrODHyS, which allows the simulation of the system reference model of a typical process example. Then, the proposed detection approach is presented. This exploits the extended Kalman Filter, in order to generate a fault indicator. In the last part, this approach is exploited through the simulation of the monitoring of a didactic example.
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2. PrODHyS environment The research works performed for several years within the PSE research department (LGC) on process modelling and simulation have led to the development of PrODHyS. This environment provides a library of classes dedicated to the dynamic hybrid simulation of processes. Based on object concepts, PrODHyS offers extensible and reusable software components allowing a rigorous and systematic modelling of processes. The primal contribution of these works consisted in determining and designing the foundation buildings classes. The last important evolution of PrODHyS is the integration of a dynamic hybrid simulation kernel (Perret et al., 2004 ; Olivier et al., 2006, 2007). Indeed, the nature of the studied phenomena involves a rigorous description of the continuous and discrete dynamic. The use of Differential and Algebraic Equations (DAE) systems seems obvious for the description of continuous aspects. Moreover the high sequential aspect of the considered systems justifies the use of Petri nets model. This is why the Object Differential Petri Nets (ODPN) formalism is used to describe the simulation model associated with each component. It combines in the same structure a set of DAE systems and high level Petri nets (defining the legal sequences of commutation between states) and has the ability to detect state and time events. More details about the formalism ODPN can be found in previous papers (Perret et al., 2004).
3. The supervision module Nowadays, for reasons of safety and performance, monitoring and supervision have an important role in process control. The complexity and the size of industrial systems induce an increasing number of process variables and make difficult the work of operators. In this context, a computer aided decision-making tool seems to be wise. Nevertheless the implementation of fault detection and diagnosis for stochastic system remains a challenging task. Various methods have been proposed in different industrial contexts (Venkatasubramanian et al., 2003). 3.1. Architecture Reference Model
– Residual Extended Kalman filter
Process
Signature
+
+
Rebuilt Incidence – Matrix
Generation of Fault Indicator
Decision : occurency of fault(s)
ON LINE OFF LINE
Adjustment of the Extended Kalman filter Process and/or Faulty simulated system Reference Model
+ –
Residual
Incidence matrix: Theoretical fault signatures
Experience return
Figure 1. Supervision Architecture For this purpose, the simulation model of PrODHyS is used as a reference model to implement the functions of detection and diagnosis. The supervision module must be able to detect the faults of the physical systems (leak, energy loss, etc.) and the faults of the control/command devices (actuators, sensors, etc.). As defined in (De Kleer et al.,
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1984), our approach is based on the hypothesis that the reference model is presumed to be correct. The global principle of this system is shown in Figure 1, where the sequence of the different operations is underlined. Moreover, a distinction between the on-line and off-line operations is made. Our approach is composed of three parts: the generation of the residuals, the generation of the signatures and the generation of the fault indicators. 3.2. The generation of the residuals The first part concerns the generation of the residuals (waved pattern in the Figure 1). In order to obtain an observer of the physical system, a real-time simulation is done in parallel. So, a complete state of the system will be available at any time. Thus, it is based on the comparison between the predicted behavior obtained thanks to the simulation of the reference model (values of state variables) and the real observed behavior (measurements from the process correlated thanks to the Extended Kalman Filter). The main idea is to reconstruct the outputs of the system from the measurement and to use the residuals for fault detection (Mehra and Peschon, 1971, Welch and Bishop, 1995, Simani and Fantuzzi, 2006). A description of the extended Kalman filter can be found in (Olivier-Maget et al., 2007). Besides the residual is defined according to the following equation: ˆ (t ) − X (t ) X i rir (t ) = i avec i ∈ {1, n} (Eqn. 1.) X i (t )
ˆ is the estimated state variable with the extended where Xi is the state variable, X i Kalman Filter and n is the number of state variables. Note that the generated residual rir (t ) is relative. As a matter of fact, this allows the comparison of a residual of a variable with a residual of an other one, since the residual become independent of the physical size of the variable. 3.3. The generation of the signatures The second part is the generation of the signatures (doted pattern in the Figure 1). This is the detection stage. It determinates the presence or not of a default. This is made by a simple threshold, ε i (t ) . The generated structure S rN i (t ) is denoted by the following equation: S rN i (t ) =
[ (r (t ) − ε' (t )); 0 ] ∑ Max [ (r (t ) − ε' (t )) ; 0 ] Max
n
k =1
r i
i
r k
avec i ∈ {1, n}
(Eqn. 2.)
k
ε (t ) , where ε i is the detection threshold. The value of ε i is chosen with ε' i (t ) = i X i (t ) according to the model error covariance matrix of the Extended Kalman Filter. 3.4. The generation of the fault indicators The last part deals with the diagnosis of the fault (hatched pattern in the Figure 1). The signature obtained in the previous part is compared with the theoretical fault signatures by means of distance. A theoretical signature T•,j of a particular default j is obtained by experience or in our case, by simulations of the process with different occurency dates of this fault. Then, a fault indicator is generated. For this, we define two distances: the
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relative Manhattan distance and the improved Manhattan distance. The first distance is denoted by the following expression: n
∑ SirN (t ) − Tij
i =1 D Mr j (t ) =
(Eqn. 3.) n The second distance, which allows the diagnosis of many simultaneous faults, is denoted by the following expression: n
∑ SirN (t ) × m ′ − Tij × n ′ ⋅Tij
i =1 D Ma j (t ) =
(Eqn. 4.)
n′
where n ′ is the number of non-zero elements of the theoretical default signature T•,j and m ′ is the number of non-zero elements of the default signature S rN (t ) .
4. Application: the adding-evaporation unit operation 4.1. Description FB
Treactor
Ulmax
Ulmin A+B
xB
Reactor
Material Feed
T (K)
298,15
298,15
P (atm)
1
1
xA=eau
0,6
0,01
xB=méthanol
0,4
0,99
Ul (mol)
300
-
Flow rate (mol/min)
-
5
Figure 2. The studied process Table 1. The operating conditions The process of adding-evaporation is generally used to change solvents. Its recipe describes a succession of evaporations and adding of the new solvent. This process is studied here (Figure 2). The operation conditions are listed in the Table 1. The values of the minimum and maximum holdups are respectively 200 and 800 moles. Before each adding of solvent, the reactor is cooled up to the temperature of 300,15K. The pressure is supposed to be constant during this operation. The goal of this process is to have a molar composition of methanol in the reactor at 0,95. 4.2. Results The behavior of this process is governed by thermal phenomena. A default of the reactor thermal system can damage the success of this operation. That is why, it is important to detect it as soon as possible. 4.2.1. Detection results We remind that the thresholds for the detection correspond to the model uncertainties obtained by the adjustment of the Extended Kalman filter. A default of the reactor heating energy feed is introduced at t = 20 min. This energy feed provides a heat quantity lower than the nominal one. Figure 3 shows the detection stage. It illustrates the evolution of the residuals linked to the liquid composition of water and methanol. From t = 80 min, the values of the both residuals underline the abnormal behavior of the process. The diagnosis is launched at t = 95 min.
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Residual xeau résidu xeau 0,06 0,04
Residual xméthanol résidu xméthanol
Max threshold
Min threshold
The detection date of the default
The occurency date of the default
Residual
0,02 0 0
20
40
60
80
100
120
140
-0,02 -0,04 -0,06 Time (min)
Figure 3. The evolutions of the composition residuals during the evaporation stage s1
0,0044098
s2
0,49367559
s3
0,50191462
s4
0
s5
0
s6
0
s7
0
Table 2. The instantaneous fault signature
4.2.2. Diagnosis results The residual is then estimated and we obtain the corresponding instantaneous default signature (Table 2). Notice that the exploited signature in this approach is non binary, in order to quantify the deviation due to the default. The construction of the theoretical fault signatures is based on numerous simulations, in which one of the defaults exposed in the Table 3 is generated. We compare the instantaneous fault signature (Table 2) with the theoretical fault signatures, by calculating the relative and improved Manhattan distances (Eqn. 3. and 4.). Then, the fault indicators are generated (Table 3). They correspond to the complement to 1 of these distances. Manhattan relative indicator
Manhattan improved indicator
Default 1
The up holdup sensor detects a value higher than the nominal value.
0,71428571
0,605
Default 2
The up holdup sensor detects a value lower than the nominal value.
0,71554566
0,7254961
Default 3
The temperature sensor detects a value higher than the nominal value.
0,71428571
0,64
Default 4
The temperature sensor detects a value lower than the nominal value.
0,71554566
0,7104961
Default 5
The material feed provides material with a degraded flow rate.
0,71714286
0,645
Default 6
The heating energy feed of the reactor has a temperature lower than the nominal one.
0,71428571
0,645
Default 7
The heating energy feed provides a heat quantity lower than the nominal value.
0,99819303
0,75330735
Default 8
The energy feed used for the cooling of the reactor has a temperature higher than the nominal one.
0,71554566
0,7104961
Default 9
The energy feed used to the cooling of the reactor provides a heat quantity lower than the nominal value.
0,71428571
0,585
Table 3. The default indicators of the example
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The relative Manhattan indicator detects the presence of the fault 7 with a probability of 99,8%. Nevertheless, any default is discriminated, since their indicators are higher than 0,68. 0,69 is the fixed criterion, which corresponds to the probability at the standard deviation according to the normal distribution. In the opposite, with the improved Manhattan indicator, the defaults 1, 3, 5,6 and 9 are eliminated, since their indicators are lower than 0,68. The four possibilities are these defaults 2, 4, 7 and 8. This example underlines the importance to the use of the both indicators to be able to conclude. So, by combining the results of the both indicators, we can rule on the presence of the default 7, since their indicators are the maximums. For this reason, this default is the most probable. So, the default is located on the energy feed of the reactor. Furthermore, it has been identified: the heating energy feed of the reactor provides a heat quantity lower than the nominal value.
5. Conclusion In this research work, the feasibility of using the simulation as a tool for fault detection and diagnosis is demonstrated. The method developed in this PhD rests on the hybrid dynamic simulator PrODHyS. This simulator is based on an object oriented approach. The fault detection and diagnosis approach, developed here, is a general method for the detection and isolation of the occurency of a fault. Besides, this approach allows the detection of numerous types of fault and has the ability to underline the simultaneous occurency of many faults. The works in progress aim at integrating this simulation model within a model-based supervision system. The goal is to define a recovery solution following the diagnosis of a default. For this, we exploit the results of signatures in order to generate qualitative information. For example, with these results, we have the ability to distinguish a simple degradation and a failure. Next, we combine our diagnosis approach with an other method, such as classification or case-based reasoning.
References Anderson T.W. (1984). An introduction to multivariate statistical analysis, New York: Wiley Chow E.Y. and A.S. Willsky (1984). IEEE Transactions on Automatic Control, Vol. 29 (7), pp. 603-614 De Kleer J. and B.C. Williams (1987). Artificial Intelligence, Vol. 32, pp. 97-130 Frank P.M. (1990). Automatica, Vol.26, pp. 459-474 Gertler J. and D. Singer (1990). Automatica, Vol. 26, pp.381-388 Mehra R.K. and J. Peschon (1971). Automatica, Vol.5, pp. 637-640 Olivier N., G. Hétreux and J.M. LeLann (2007). Fault detection using a hybrid dynamic simulator: Application to a hydraulic system CMS’07; Buenos Aires, Argentina Olivier N., G. Hétreux, J.M. LeLann and M.V. LeLann (2006). Use of an Object Oriented Dynamic Hybrid Simulator for the Monitoring of Industrial Processes, ADHS’06, Alghero, Italia Perret J., G. Hétreux and J.M. LeLann (2004). Control Engineering Practice, Vol. 12/10, pp. 1211-1223 Simani S. and C. Fantuzzi (2006). Mechatronics, Vol.16, pp. 341-363 Shih R. and L. Lee (1995). Industrial and Engineering Chemistry Research, Vol. 34 (5), pp. 16881717 Venkatasubramanian V., R. Rengaswamy, K. Yin and S. N. Kavuri (2003). Computers & Chemical Engineering, Vol. 27, pp. 293-346 Welch G. and G. Bishop (1995). An introduction to the Kalman filter, Technical Report TR 95041, University of North Carolina Willsky A.S. (1976). Automatica, Vol. 12, pp. 601 – 611
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Computer Aided Operation of Pipeless Plants Sabine Piana and Sebastian Engell Process Dynamics and Operations Group, Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, 44221 Dortmund, Germany
Abstract Pipeless plants are a new production concept in which automated guided vehicles transport the substances in mobile vessels between processing stations. Since several batches are produced in parallel, decisions have to be made on the scheduling of the production, on the assignment of the equipment and on the routing of the vessels. This paper describes the combination of an evolutionary scheduling algorithm with a simulation-based schedule builder. The new algorithm yields up to 16 % better solutions than an as-soon-as-possible scheduling heuristic. Keywords: Pipeless plant, evolutionary algorithms, simulation, scheduling.
1. Pipeless Plants Pipeless plants are an alternative to traditional multiproduct plants with fixed piping. Their distinctive feature is that the processing steps are performed at fixed stations and the substances are moved around in mobile vessels by automated guided vehicles (AGVs). The recipes determine the order in which a vessel must visit the different stations. The cleaning of the vessels is carried out in separate cleaning stations and the stations are cleaned in place. Pipeless plants offer a high degree of flexibility, e. g. by enabling a change of the priorities of the orders or the bypassing of a blocked station. The reduction of fixed piping results in up to 20 % less time for cleaning and sterilizing when a product changeover occurs compared to conventional batch plants [1]. Under the simplifying assumption of fixed and known processing times for the steps of the recipes, the optimal scheduling of a pipeless plant can in principle be determined by mixed-integer linear programming. However, due to the presence of the spatial dimension of the problem (the movement of the vessels in the plant, collision avoidance of the AGVs, parking of vessels in different locations that lead to different travel times), an exact solution is currently infeasible for realistic problem sizes. The option which we pursue in this paper is to combine a detailed simulation with embedded heuristics and routing algorithms of a pipeless plant with an optimization algorithm that determines the optimal sequence of processing steps. As evolutionary algorithms (EAs) can embed simulations as black-box computations of cost function values, we use an EA for the optimization. The EA only handles a subset of the degrees of freedom (the sequencing decisions), and the simulation algorithm takes the role of a schedule builder that generates a full schedule using additional information and heuristics. The paper is structured as follows. The next section describes the inter-dependent decision variables that have to be determined during the operation of a pipeless plant. Section 3 motivates and describes the use of an EA for the scheduling of the steps of the recipes. Special attention is paid to the handling of infeasibilities by repair algorithms
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and the evaluation of the individuals by the schedule builder in Sections 4 and 5, respectively. The results of the algorithm for three example problems are described in Section 6 and the paper concludes with an outlook to further research.
2. Problem Statement and Previous Work The increased flexibility of a pipeless plant comes at the expense of a higher degree of complexity. Knowing the product demand, the number and size of the batches, the recipes and the plant layout, our objective is to find a schedule with minimum makespan that is feasible with respect to a set of constraints. 1. A schedule must guarantee that the steps are executed according to the sequence prescribed by the recipes. 2. Each recipe step must be assigned to a vessel, an AGV and a station. The chosen equipment must be available at the desired time and has to be able to perform the required operations, i.e. to possess the necessary technical functions. 3. After the assignment, the selected AGV must pick up the vessel and transport it to the selected station. The AGVs must not collide with each other during transports. The time that a recipe step needs for its execution at a station may depend on the initial state of the material in the vessel. The mass and the temperature of the content of a vessel are therefore included as state variables in the simulation model. The scheduling of the recipe steps is the most important decision. It has mostly been tackled by mixed-integer linear or nonlinear programming. These methods have been combined with other techniques, for example with a discrete event simulator [2], with a queuing approach [3], or with constraint programming [4], to find optimal schedules. The operation of a pipeless plant can be modeled using different degrees of accuracy. In [4] it is assumed that the vessels possess their own transportation device. Then the assignment of a vessel to an AGV is not necessary. Also fixed travel times and fixed paths of the AGVs are assumed. Furthermore, the durations of the processing steps are assumed to be deterministic. In contrast to [4], in [1] a modeling and simulation software that represents the pipeless plant and the chemical processes in a detailed fashion is described where the problems mentioned above are solved simultaneously by heuristic algorithms. Shortest paths for the AGVs are calculated using the A* algorithm, path conflicts are resolved by a first-come-first-serve (FCFS) scheme and a production schedule is determined by an as-soon-as-possible (ASAP) heuristic. In this paper, we continue the detailed model in [1] with an evolutionary optimization algorithm.
3. Evolutionary Scheduling Algorithm An EA works with a set of candidate solutions to the optimization problem. A solution is referred to as an individual and a set of μ solutions is called the population. Each individual has a fitness value which shows how good the solution is with respect to the objective function. Ȝ new individuals are added to the population by recombination and mutation of existing individuals. The idea is that the new individuals inherit good characteristics from the existing individuals. The Ȝ worst solutions are removed from the population. After several iterations, which are called generations, the algorithm provides a population that comprises good solutions. In our case, the EA generates individuals which represent a fully ordered sequence of the recipe steps of all batches. To evaluate the fitness of the candidate solutions, the assignment of the equipment, the routing of the AGVs and a calculation of the durations of the recipe steps are carried out by the simulation algorithm of [1]. The recipe steps are identified by their batch IDs to maintain precedence relations in the recipes when
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steps are exchanged during recombination and mutation. Fig. 1 shows the idea by means of a small example. The order of the sequence indicates the priority of the recipe steps. Each entry directs the simulator to schedule the first unscheduled step of the corresponding batch as soon as possible without delaying higher-priority steps. Schedule Encoded By Batch IDs
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Fig. 1: Representation of an Individual
Since each batch ID must occur a certain number of times (as often as the number of recipe steps of the batch), a recombination operator that preserves permutations is applied. The two best individuals out of a set of randomly chosen individuals are selected from the population. Then a random segment is copied from the first individual into a new individual. The missing elements are filled with the entries of the second individual. The newly generated individual is then subject to mutation with a probability p. By mutation, two randomly chosen entries are exchanged.
4. Handling of Infeasibility There are several reasons for infeasibility of new individuals. Precedence violation in a recipe is avoided by the chosen representation of an individual. However, it is possible that a recipe step cannot be scheduled at its position in the sequence because no suitable station or empty vessel are available. We could deal with this infeasibility inside the simulator by postponing the currently infeasible recipe step and continuing with the next recipe step in the sequence. Alternatively, the infeasibility can be removed before passing the individual to the simulator. This is done by a repair algorithm that employs problem-specific knowledge on recipes, vessels and stations. We chose the second option since the repair algorithm can be designed to maintain the priorities of the recipe steps to a larger degree than by postponing infeasible assignments. The repair algorithm for occupied stations is explained by the example individual in Fig. 2. Suppose that there are only two charging stations in the plant. After the fourth recipe step (charging batch 3) both charging stations are occupied by batch 2 and batch 3. Therefore it is impossible to execute the next step (charging batch 4). A charging station must be freed first. The first recipe step in the sequence that frees such a station is the seventh entry (heating batch 3). By inserting this step before the currently infeasible step, batch 3 is moved from the charging station to the heating station and batch 4 can be processed. It must, however, be checked that a heating station is available at this point. If not, another repair is needed. It may also happen that there is no free vessel available to start a new batch. The repair algorithm moves all recipe steps of the batch which can currently not be started to a position after a batch has been finished and thereby frees a vessel. Note, that entries of the batch which occur behind this position, are not moved forward as this would violate the specified order of the priorities.
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2 charging stations available
insert
n := number of occupied charging stations charge 1
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Fig. 2: Repair Algorithm for Occupied Stations
5. Evaluation of Individuals The software PPSiM (Pipeless Plant Simulation [1]) provides an environment to model a pipeless plant in a fast and intuitive manner and to perform simulation studies to compare design alternatives. The routing of the mobile vessels as well as variable durations of the processing steps are taken into account during the simulation. The program generates a production schedule according to a simple ASAP heuristic in which the recipe steps are scheduled in a chronological order according to their earliest possible start times. The solutions can be visualized as Gantt charts. The EA is embedded into PPSiM to perform an optimization of the decision variables. It interacts with the simulator in two ways. First, the simulator computes the ASAP solution. The initial population of the EA consists of multiple copies of this solution and other random solutions. Secondly, the simulator maps the sequence of recipe steps proposed by the EA into a feasible schedule and evaluates its fitness. The framework is shown in Fig. 3 where it can be seen which tasks are accomplished by the graphical interface, the simulator and the optimizer.
Problem Definition
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Fig. 3: Simulation Optimization with an Evolutionary Scheduling Algorithm
6. Experimental Results This section reports on the experimental results that were obtained with the proposed approach on three case studies: a small problem, an industrial problem and a problem from the literature. In the small problem, two batches of a first product and two batches of a second product have to be produced. There are two AGVs, three vessels and one station for each of the technical functions required by the recipes. The problem is simple
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since neither timing constraints such as different starting times or deadlines nor much potential for routing conflicts are present. The second case study is an industrial problem. The plant under consideration produces a set of consumer care products. 7 batches of the same product and of the same sizes have to be produced. All batches can start at the same time. The underlying process is a mixing process in which various substances are charged and the material is mixed, heated and cooled. The production recipe defines 12 steps and has a linear structure. After the production process, all products have to be stored to determine the product quality by a laboratory analysis. Then the content is discharged (packed) and the vessel is cleaned. The plant area is divided into a production area, an intermediate storage and parking area, a discharging area, and a cleaning area. The production stations are arranged in a clockwise order to minimize the probability of collisions during the execution of the recipes. Finally a plant with a herringbone layout taken from [4] is treated. The authors of [4] assume that the recipe steps have fixed processing durations and that the AGVs move on specified paths with fixed transfer times. Thus, a detailed simulation of the processing steps and the routing of the AGVs are unnecessary. A difference to our simulation model is that the authors assign buffers to the stations at which AGVs can wait. It is possible to use these buffers as parking positions for empty and for clean vessels. We modeled the example without these buffers and instead defined parking positions at the side of the plant layout. To be able to compare the results, we subtract the time needed for these additional transfers from the makespan. This corresponds to 18 minutes per batch. Table 1 shows the relative improvement obtained by the proposed EA on the initial ASAP solution. The parameters of the EA were set to ȝ=10 and Ȝ=2. The probability of a mutation was 80 %. The results are reported for a set of five runs with a time limit of 60 seconds. It can be seen that the improvement for the simple problem is larger than for the industrial problem. The best solutions for the simple problem do not run many batches simultaneously. It is a weakness of the ASAP solution to start too many batches at once. Thereby vessels are blocking each other and stations can be occupied only later in time. For the industrial problem, however, it seems that the ASAP solution is already a good schedule so that the EA cannot improve it much. We suppose that this is due to the plant layout which minimizes the probability of collisions. Table 1. Improvement obtained by the Scheduling EA within 60 seconds Best run
Worst run
Median run
Simple
-16.3 %
-15.4 %
-16.1 %
Industrial
-2.4 %
-0.0 %
-1.0 %
Herringbone
-4.8 %
-3.9 %
-4.5 %
For the third example, our algorithm is compared to the results of the authors of [4] who solve the scheduling and sequencing problem by constraint programming (CP). It can be seen in Table 2 that it takes slightly more time to compute the heuristic ASAP solution than to find the first feasible solution by CP, but that the ASAP solution has a significantly smaller makespan. The EA improves the initial solution in less than half a minute to a solution which is very close to the optimum.
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1: Pentium 4, 3 GHz, 512 MB RAM
2: P3500 MHz
7. Conclusion and Outlook Pipeless plants are an interesting alternative to standard multiproduct plants due to their flexibility and the potential to decrease the makespan of a production plan significantly. The optimization of a pipeless plant is treated in a hierarchical way. An EA schedules the production steps and a simulator with heuristics for the assignment of the equipment and for the routing of the AGVs is used as the schedule builder. In examples, the new scheduling procedure decreased the makespan by up to 16 % compared to a heuristic solution. For a problem from the literature we found a good first solution and the EA quickly returned a solution that is very close to the optimum. Our approach is therefore suitable for online applications where the fast computation of a good feasible solution is of prime concern. The simulation of the transfers is the most time consuming step in our approach. Many AGV paths have to be generated and eventually to be modified. In the future we plan to work with approximations to decrease the calculation time and to steer the algorithm more efficiently to good solutions. This can be done by evaluating the individuals exactly only after several generations of the algorithm. This may, however, result in infeasible individuals whose fitness is overestimated. An approach that circumvents this problem was proposed by [5] where the authors advise to evaluate the individuals first by an approximated simulation. Only promising individuals are then evaluated by the exact simulation. Individuals that are estimated to be of low quality are directly eliminated. Both schemes cause an uncertainty in the cost function of the EA. The tradeoff between the precision of the evaluation of the cost function and the computation times will be investigated in future work. In addition, it will be investigated whether the assignment of the equipment to the steps of the recipe can also be improved with reasonable computing times by using a second embedded EA for this task.
References 1. A. Liefeldt, 2008. Logistic Simulation of Pipeless Plants. In: S. Engell (Edt.), Logistics of Chemical Production Processes, 1st edn, Wiley VCH Verlag GmbH. 2. R. Gonzalez and M. Realff, 1998. Operation of pipeless batch plants – I. MILP schedules. Computers & Chemical Engineering 22 (7-8), 841 – 855. 3. D. Yoo, I.B. Lee and J. Jung, 2005. Design of Pipeless Chemical Batch Plants with Queueing Networks. Industrial & Engineering Chemistry Research 44, 5630 – 5644. 4. W. Huang and P. Chung, 2005. Integrating routing and scheduling for pipeless plants in different layouts. Computers & Chemical Engineering 29, 1069 – 1081. 5. J. April, F. Glover and M. Laguna, 2003. Practical Introduction to Simulation Optimization. Proceedings of the 2003 Winter Simulation Conference.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Off-line design of PAT* systems for on-line applications Ravendra Singha, Krist V. Gernaeyb, Rafiqul Gani †a a
CAPEC, bBioEng, Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
Abstract In the manufacturing industry, for example, the pharmaceutical industry, a thorough understanding of the process is necessary in addition to a properly designed monitoring and analysis system (PAT system) to consistently obtain the desired end-product properties. A model-based computer-aided framework including the methods and tools through which the design of monitoring and analysis systems for product quality control can be generated, analyzed and/or validated, has been developed. Two important supporting tools within the framework are a knowledge base and a model library. The knowledge base provides the necessary information/data during the design of the PAT system and the model library generates additional or missing data needed for design. Optimization of the PAT system design can be achieved in terms of product data analysis time and/or cost of monitoring equipment subject to the maintenance of the desired product quality. Keywords: monitoring, quality control, process analytical technology, modelling
1. Introduction Today a significant opportunity exists to improve the product quality and to optimize the production process through the implementation of innovative system solutions for on-line monitoring, analysis and system control. Application of PAT systems (FDA/CDER, 2005) in manufacturing paves the way for continuous process and product improvements through improved process supervision based on knowledgebased data analysis, ‘Quality by design’ concepts, and through feedback control (Gnoth et al., 2007). Currently, one of the main difficulties in implementing PAT systems on a manufacturing process is the unavailability of methods and tools through which a PAT system can be designed in a systematic way. In this manuscript a model-based computer-aided framework is presented, including the methods and tools through which the design of monitoring and analysis systems (i.e., the PAT systems) for product quality monitoring and control can be generated, analyzed and/or validated.
2. Design Framework The design of a process monitoring and analysis system (note, from here on we will use the term ‘PAT system’ to refer to such a system) is a step-wise procedure involving the selection of critical process variables, followed by the selection and placement of suitable monitoring and analysis equipments, and finally, the coupling of the monitoring and analysis tools to a control system to ensure that the selected critical process * PAT: Process Analytical Technology † Corresponding author (
[email protected])
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variables can be controlled. As shown in fig. 1, the starting point for the design methodology is the problem definition in terms of process specifications and product quality specifications that can be provided either by the manufacturer or the PAT system designer. A model library and a knowledge base have been developed, and act as the supporting tools for the design of a PAT system. The ICAS-MoT modeling tool (Sales-Cruz, 2006) is used for simulation of process operational models and the systematic procedure proposed by Gani (Gani et al., 2006) is used for model analysis. As shown in fig.1, the developed design algorithm relates the available product and process specifications to the available supporting tools, and subsequently generates the PAT system. If the obtained PAT system satisfies the requirements then it is selected as the designed PAT system. The validation of the obtained PAT system is achieved by comparing the simulated process performance with known process specifications. If the process performance does not comply with the process specifications then the corresponding design steps are repeated until a satisfactory design is obtained.
Figure 1. Framework overview 2.1. Supporting Tools 2.1.1. Knowledge base The knowledge base contains useful information needed for design of PAT systems. It has been built through an extensive literature and industrial survey. It covers a wide range of industrial processes such as fermentation, crystallization and tablet manufacturing. It contains information for typical unit processes in terms of the type of operation they perform, the process variables involved, the corresponding manipulating variables (actuators), the equipments typically used for on-line measurement of data (type of equipment, accuracy, precision, operating range, response time, resolution, drift, cost etc.). 2.1.2. Model library The model library contains a set of mathematical models for different types of unit processes, sensors and controllers. Similar to the knowledge base, it covers a wide range of industrial processes (fermentation, crystallization, tablet manufacturing). These models support process analysis and help to generate additional or missing data needed to obtain the design of a PAT system. For example, the models can be applied for the prediction of process variables which are not measurable but required for the final design. Simulations with the models can also be used for performing a sensitivity analysis through which the effect of process variables on the final product properties can be analyzed and critical process variables can be identified. The simulation models
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fermentation. Analyzing the effect of process variables on the fermentation operation shows that the pH violates the lower and upper limit of the optimal pH range in open loop (see fig. 4), indicating thereby that it needs to be controlled throughout the fermentation process. Repeating this procedure for all process variables yields the following critical variables: temperature, pH, DO, dissolved CO2, homogeneity in the fermentor and temperature in sterilizer and homogeneity in the mixing tank. 0.16
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Figure 3. Profile of operational objective
Figure 4. Critical process variable (pH)
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3.5. Interdependency analysis Interdependency analysis is performed for each critical process variable to select the actuator. For example, the dependency of the DO concentration (response variable) on the air flow rate & stirrer speed (sensitivity parameters) is shown in fig 5. The air flow rate is more sensitive compared to the Interdependency analysis 12 stirrer speed and thus the air flow rate is Air flow rate selected as an actuator for DO control. 10 Stirrer speed Repeating the procedure for all critical 8 control variables yields actuators as M ore sensitive 6 follows: coolant flow rate for temperature, Less 4 ammonia flow rate for pH, air flow rate sensitive for DO and dissolved CO2, stirrer speed 2 for homogeneity control in the fermentor, 0 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 steam flow rate for heat sterilization Parameter (% change) temperature control and stirring duration Figure 5. A ctuator selection for D O for homogeneity in the mixing tank. 3.6. Performance analysis of monitoring tools The performance of available monitoring tools (obtained from the knowledge base) for each measured variable is compared and monitoring tools are selected as follows: Thermocouple for temperature, electrochemical sensor for pH, optical sensor for DO and dissolved CO2, and NIR for homogeneity. 3.7. Proposed process monitoring and analysis system A feasible alternative of the process monitoring and analysis system is shown in fig. 6. Within the fermentor, the DO concentration, pH, temperature and homogeneity need to be monitored and controlled. Temperature in the heat sterilizer and homogeneity in mixing tank also need monitoring and control. The aeration intensity used for DO control also influenced the dissolved CO2 concentration so it is not needed to control this variable explicitly. The critical process variables, corresponding monitoring tools and actuators are shown in fig. 6. The response time of the selected monitoring tools is
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selected control variable. In this analysis the effect of process parameters on the individual selected critical process variable is compared. A special feature (Sales-Cruz and Gani, 2006) of ICAS-MoT can be used for this analysis. First, the response variable and the sensitivity parameters are selected. Then these parameters are perturbed and the effect of each parameter on the response variable is analyzed. The process parameter which has the most significant effect on the considered critical process variable (response variable) is selected as the actuator for that variable. At the moment only SISO control is considered in the design methodology. The possibility to also select more advanced multivariable control systems in the PAT system design will be included in the future. 2.2.4. Performance analysis of monitoring tools The performance analysis of the process monitoring tools is performed to select the appropriate monitoring tools for each measurable critical process variable. The measurement equipment for each measured critical process variable is selected from the knowledge base, where one is able to list all the available sensors included in the knowledge base for that variable. The performance of different types of measurement equipment can be compared. The monitoring tool is then selected on the basis of one or more of the following performance criteria: accuracy, precision and resolution, sensor drift, response time and cost and operating range. The type of performance criterion selected is application specific.
3. Case study: Fermentation process - Design of PAT system The process flow sheet is adopted from the literature (Petrides et al., 1995) (see fig. 6). 3.1. Product property specifications The desired product from the fermentation process is E. coli cells. At the end of the fermentation process, the assumed E. coli cell concentration is 30 g/liter (dry cell weight) in which the protein content is assumed to be 20% of the dry cell mass. The composition (mass basis) of the outlet stream from the fermentor comprises 2.95% biomass, 4.00% glucose, 0.58% salts, and 92.46% water. 3.2. Process specifications The basic raw materials required include: starting culture (E. coli cells), nutrients (glucose and salts), tryptophan, water, ammonia and air. The process equipment includes: fermentor, mixing tank, continuous heat sterilizer, centrifugal compressor, air filter and storage tank. 3.3. Process analysis The process analysis provides the following list of process variables: temperature in the fermentor, pH in fermentor, dissolved oxygen (DO) in the fermentor, dissolved CO2 in the fermentor, coolant flow rate, coolant temperature, ammonia flow rate, stirrer speed in the fermentor, stirrer speed and stirring duration in the mixing tank, air flow rate to the fermentor, heat sterilization temperature, steam flow rate in sterilizer, stirrer speed in the mixing tank and stirring duration, cell growth rate, heat of reaction, substrate concentration, biomass concentration in the fermentor, homogeneity in the fermentor, homogeneity in the mixing tank 3.4. Sensitivity analysis The operational objective for the fermentation step is to maximise the specific cell growth rate. Open loop simulations (fig. 3) show that the value of the specific growth rate is considerably lower than the maximum specific growth rate throughout the batch
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fermentation. Analyzing the effect of process variables on the fermentation operation shows that the pH violates the lower and upper limit of the optimal pH range in open loop (see fig. 4), indicating thereby that it needs to be controlled throughout the fermentation process. Repeating this procedure for all process variables yields the following critical variables: temperature, pH, DO, dissolved CO2, homogeneity in the fermentor and temperature in sterilizer and homogeneity in the mixing tank. 0.16
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Figure 4. Critical process variable (pH)
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3.5. Interdependency analysis Interdependency analysis is performed for each critical process variable to select the actuator. For example, the dependency of the DO concentration (response variable) on the air flow rate & stirrer speed (sensitivity parameters) is shown in fig 5. The air flow rate is more sensitive compared to the Interdependency analysis 12 stirrer speed and thus the air flow rate is Air flow rate selected as an actuator for DO control. 10 Stirrer speed Repeating the procedure for all critical 8 control variables yields actuators as M ore sensitive 6 follows: coolant flow rate for temperature, Less 4 ammonia flow rate for pH, air flow rate sensitive for DO and dissolved CO2, stirrer speed 2 for homogeneity control in the fermentor, 0 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 steam flow rate for heat sterilization Parameter (% change) temperature control and stirring duration Figure 5. A ctuator selection for D O for homogeneity in the mixing tank. 3.6. Performance analysis of monitoring tools The performance of available monitoring tools (obtained from the knowledge base) for each measured variable is compared and monitoring tools are selected as follows: Thermocouple for temperature, electrochemical sensor for pH, optical sensor for DO and dissolved CO2, and NIR for homogeneity. 3.7. Proposed process monitoring and analysis system A feasible alternative of the process monitoring and analysis system is shown in fig. 6. Within the fermentor, the DO concentration, pH, temperature and homogeneity need to be monitored and controlled. Temperature in the heat sterilizer and homogeneity in mixing tank also need monitoring and control. The aeration intensity used for DO control also influenced the dissolved CO2 concentration so it is not needed to control this variable explicitly. The critical process variables, corresponding monitoring tools and actuators are shown in fig. 6. The response time of the selected monitoring tools is
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also shown in the figure, which shows that the selected monitoring tools are robust enough to allow for successful implementation of the control system.
Figure 6. Fermentation process flow sheet with designed PAT system. c: controller, R: response time, T90: time for 90% response, NIR: near infrared, [ ]: indicates the reference number in the knowledge base‡
4. Conclusions A well-designed PAT system is essential to obtain the desired product quality consistently. In this work we proposed a model-based computer aided framework including the methods and tools for systematic design of PAT systems. The application of the developed framework and methodology was demonstrated through a fermentation process case study. The developed framework and methodology are generic: the proposed systematic approach to the design of a PAT system is complimentary to traditional process design, and should thus have a broad application range in chemical and biological processes.
References FDA/CDER, 2005, PAT, Process Analytical Technology (PAT) Initiative, U.S. Food and Drug Administration, Center for Drug Evaluation and Research, http://www.fda.gov/Cder/OPS/PAT.htm Gani, R., Muro-Suñé, N., Sales-Cruz, M., Leibovici, C., & Connell, J. P. O. (2006). Fluid Phase Equilibria, 250, 1-32. Gnoth, S., Jenzsch, M., Simutis, R., & Lübbert, A. (2007). Journal of Biotechnology, 132 (2), 180-186. Petrides, D., Sapidou, E., & Calandranis, J. (1995). Biotechnology and Bioengineering, 48 (5), 529-541. Sales-Cruz, M. (2006). Development of a Computer Aided Modelling System for Bio and Chemical Process and Product Design. PhD. Thesis, CAPEC, Department of Chemical Engineering, Technical University of Denmark. Sales-Cruz, M., & Gani, R. (2006). ChERD, 84 (A7), 583-594. ‡
[9]http://www.rmprocesscontrol.co.uk/Electrochemical-sensors/pHPLUS-Electrodes.htm [50] http://www.in-situ.com/In-Situ/Products/TROLL9500/TROLL9500_RDO.html [60] http://195.173.150.81/Process_16_2.pdf, [107] http://www.smartsensors.com/spectherm.pdf
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
New Method for Sensor Network Design and Upgrade for Optimal Process Monitoring Miguel J. Bagajewicz, DuyQuang Nguyen and Sanjay Kumar Sugumar School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, OK 73069
Abstract Previous methods on nonlinear sensor network design minimize cost subject to a variety of constraints linked to the network performance: precision, residual precision, error detectability and resilience. In recent work, the use of accuracy as an attribute of a network that can replace precision, error detectability and resilience more effectively has been considered. In this paper, we propose a sensor network design methodology based on accuracy thresholds. Keywords: Software Accuracy, Sensor Networks, Instrumentation Network Design.
1. Introduction In contrast with the use of objective functions such as observability or reliability that had been used, Bagajewicz (1997, 2000) formulated a mixed integer nonlinear programming to obtain sensor networks satisfying the constraints of residual precision, resilience, error detectability at minimal cost. A tree enumeration was proposed where at each node the optimization problem of the different characteristics are solved. To reduce the computational time Gala and Bagajewicz (2006a), proposed the tree enumeration approach based on branch and bounding, using cutsets. To make the computation more effective, especially for large scale problems, Bagajewicz and Gala (2000b), proposed a decomposition procedure where the process flow diagrams are decomposed to reduce the number of cutsets used for the enumeration. Non linear networks have been discussed by Nguyen and Bagajewicz (2007), where they resort to an equation based approach using bipartite graph as opposed to regular directed graphs and show that the concept of cutsets needs further modification. They explore the use of variable enumeration in an inverted order that is removing sensors from a fully instrumented network, as opposed to adding sensors to a sensor-empty network. This strategy proved efficient for networks with stringent requirements of precision, error detectability and resilience. All the above work focused on minimizing network cost using precision, residual precision, error detectability and resilience constraints. In this work we also minimize network cost, but we use software accuracy (as defined by Bagajewicz, 2005), which replaces all the above network attributes, as a constraint. We first review accuracy and we then discuss issues of the methodology involved to calculate accuracy at each node. We finish with an example.
2. Software Accuracy Accuracy has been conventionally defined as the sum of absolute value of the systematic error and the standard deviation of the meter (Miller, 1996). Since in the absence of hardware or software redundancy the systematic errors cannot be detected, this conventional definition is not practical. Bagajewicz, (2005) defined accuracy with
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respect to the gross error detection scheme used to identify gross errors, thus differentiating software accuracy from hardware accuracy. Specifically, Bagajewicz (2005) considered that the presence of gross systematic errors δ induces biases in all streams through the use of data reconciliation. These induced biases are given by
δˆ = [I − SW ]δ
(1)
where, W = A T (ASA T )−1 A , matrix A is the incidence matrix and matrix S is the variance-covariance matrix of measurements. The case considered is the linear case. He then defines accuracy as the sum of precision and the maximum undetected aforementioned induced bias.
aˆ i = σˆ i + δ i∗ where aˆ i
δ i∗
(2)
and σˆ i are the accuracy, the maximum undetected induced bias and the
precision (square root of variance , Sˆ ii ) of the estimator, respectively. Next, he proposed to calculate the maximum undetected induced bias under the assumption that the maximum power test would be used in a serial elimination procedure. Thus, the maximum induced bias that will be undetected is given by (Bagajewicz, 2005):
( p) ( p) δˆi( p ,1) = Max δˆcrit ,i , s = Z crit Max ∀s
[(I − SW )is ]
∀s
(3)
Wss
In the presence of nT gross errors in positions given by a set T, the corresponding induced bias in variable i is ( p) ]i = δ crit( p),i − ¦ (SW ) is δ crit( p),s δˆi( p ) = [[I − SW ]δ crit
(4)
s∈T
where
( p) is the vector containing a critical value of the gross error size in the selected δ crit
positions corresponding to the set T at the confidence level p. In order to find the maximum possible undetected induced bias, one has to explore all possible values of gross errors in the set. Thus for each set ‘T,’ he proposed to define a binary vector ‘qT’ to indicate the location of gross errors and obtain the maximum induced and undetected bias by solving the following problem: ½½ δˆi( p ) (T ) = Max ®δ crit ,i qT ,i − ¦ ( SW )is δ crit , s qT , s ¾° ∀s ¯ ¿° ° s.t (5) ° ¾ Wks ( p) ° ∀k δ crit , s qT , s ≤ Z crit ¦ ° W ∀s kk ° ° ∀k qT ,k δ crit ,k ≥ 0 ¿
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The absolute value constraint can be replaced by two inequalities, one for the negative sign and one for the positive one. The problem becomes a linear one. Thus for nT=2, the feasible region has a form of a rhombus, as in Figure 1. The rhombus is composed of positive and negative constraints of the problem that arise from the absolute value. We recognize that the solution lies in one of the four corners, which depends on how the two gross errors in question contribute to the induced bias
Both θ1 & θ2 are detected
θ2
Only θ2 is detected δ2
−δ1 = −
ξ
Both θ1 & θ2 are detected
ξ Wi 2i 2
ξ
Z2 = ξ
W 'i1i1
Wi1i1
No gross error - δ1
δ1
is detected
Only θ1 is detected
Z1 = ξ - δ2
Both θ1 & θ2 are detected
−δ 2 =
−ξ
Only θ2 is detected
W "i 2i 2
θ1 Only θ1 is detected Both θ1 & θ2 are detected
Figure 1. Different regions when two gross errors are present in the system (From Nguyen et al, 2006) Worth noticing, in some cases the above set of equations can be linearly dependant. This happens when the set of gross errors proposed in an equivalent set (Jiang and Bagajewicz, 1998). We illustrate this for the system of Figure 2. S2
S1
S3 Figure 2. Equivalency of gross errors Assume that one wants to compute the induced bias in stream S1 by considering two biases in S2 and S3. This leads to two parallel lines, as it is illustrated in Figure 3. θ2
Undetected region θ1
Figure 3. Graphical consequence of biases equivalency
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It can be inferred from figure 2 and clearly shown in figure 3 that if the bias in stream S2 and bias in stream S3 are equal but in opposite side (such that the balance S1 = S2 + S3 is still valid), then those biases cannot be detected no matter how big they are.
3. Calculation of Software Accuracy at each node of the search tree In this work, we use the tree enumeration method using list of fundamental units, which can be variables (Bagajewicz, 1997) or cutsets (Gala and Bagajewicz, 2006a, b) or equations (Nguyen and Bagajewicz, 2007). At each node, software accuracy needs to be evaluated based on two inputs: 1. 2.
The positions of the sensors (given by a binary vector q). We assume there are n sensors. The maximum number of gross errors (nT) the user is willing to consider in the definition of accuracy.
Thus, if nT >n, the maximum number of gross errors is assumed to be n, that is nT=n. When n=nT , only one system of equations needs to be solved, and if nT 0 , 0 < z < H (t ) k C ° 2 ∂z ρ1e c p1 ∂z ρ1e c p1 ρ1e c p1 d sw ° ∂t ° 2 ° ∂T2 = α ∂ T2 , t > 0 , H (t ) < z < L 2 ° ∂t ∂z 2 ® 1 ° dH ° dt = − ρ − ρ N w , t > 0 , z = H (t ) 2 1 ° ° ∂Csw = − k d Csw t > 0 , 0 < z < H (t ) ° ¯ ∂t
(1)
Optimal Operation of Sublimation Time of the Freeze Drying Process by Predictive Control: Application of the MPC@CB Software
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Where T1 is the dried layer temperature, T2 is the frozen layer temperature, Nw is the mass transfer flux of the water vapour, Csw is the bound water and H is the sublimation interface. The different parameters of the model are presented in [12]. In this work, we use a simplified equation to describe the dynamic of the mass flux based on the diffusion equations of Evans. The equation is given by the following expression:
Nw =
−Mwk1 ( pH − p0 ), t > 0 RigT1H
(2)
Where p0 and pH is the partial pressures of water vapor at z=0 and z=H(t) respectively. The pressure boundary condition at the top surface of the material being dried is defined as a constant pressure inside the drying chamber, and the vapor pressure at the sublimation interface is defined as an equilibrium vapor pressure according to the temperature of the interface. The initial conditions for the equation (1) are given by:
T1(z, t) = T2 (z, t) = T o °° + ®H(t) = 0 ° 0 °¯Csw (z, t) =Csw
for 0 ≤ z ≤ L , t = 0 for t = 0
(3)
for 0 ≤ z ≤ L , t = 0
The boundary conditions for the equations (1) are as follows: ∂ T1 ° − k1e ∂ z = q1 , t > 0, z = 0 ° °° ρ 2 c p 2T2 − ρ1c p1T1 ∂ T1 ∂ T2 § = − k2 + ¨ −Δ H s + ® − k1e ¨ ∂z ∂z ρ 2 − ρ1 ° © ° ° − k 2 ∂ T2 = q 2 t > 0, z = L , ∂z ¯°
· ¸¸ N w , ¹
t > 0, z = H ( t )
(4)
Where Tlp(t), Tup(t) are respectively the temperatures of the lower and upper heating plates. For general freeze dryers, the temperature of the upper and lower heating plates are the same, i.e. Tlp(t)=Tup(t). The important objective of the on-line control is to decrease the drying time under constraints, while maintaining the quality of the product. Furthermore, an important constraint for primary drying is that one must never allow the product temperature to exceed its glass transition temperature. This constraint can be expressed by:
T2 ( z , t ) ≤ Tg ,
H (t ) < z < L , ∀t > 0
(5)
The output variable of the process considered in our control problem corresponds to the measured temperature at the bottom of the vial. In the sequel, it is assumed that only the process output is constrained to satisfy the inequality (5). The second constraints during the primary drying stage of the freeze drying process dealing with the heat flux at the top and bottom surfaces and respectively. Their magnitudes depend respectively on the value of the temperature of the heating plate at the upper surface of the vials, and the temperature of the heating plate at the bottom surface of the vials. These temperatures are assumed to be the same and the manipulated variable u(t) is subjected to the constraints in the following form:
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Tmin ≤ u (t ) = Tlp (t ) = Tup (t ) ≤ Tmax , ∀t > 0
(6)
3. Simulation results In this study, we are interested to find the optimal on-line tuning of the manipulated variable for the constrained optimization of the sublimation time. To realize the MPC under constraints of the freeze drying process, we used the MPC@CB software 1 developed with Matlab. Control Software: main features of MPC@CB The codes of the MPC@CB software have been written to run with Matlab. It allows realizing the MPC under constraints of the specified continuous process. The originality of these codes is first the easy use for any continuous SISO process (Single Input Single Output), through the user files (where model equations have to be specified), synchronized by few main standards files (where the user has to make few (or no) changes. The original feature of the software is the straightforward resolution of various model based control problems through different choices: 1. Open or closed loop control. 2. MPC for a trajectory tracking problem, with or without the output constraint. 3. MPC to solve an operating time minimization problem, with or without the output constraint. The other originality is the method used to develop the codes : it is very easy to introduce new parts in the code, such as : 1. MPC with an user defined control problem. 2. Handle SIMO, MISO or MIMO model . 3. Introduce a software sensor (observer). 4. Apply the software for a real time application [11]. For more the details about the MPC@CB software and the operations conditions, the reader can refer to [12]. The optimal minimization of the drying time under constraints may be equivalent to define the performance index as the maximization of the velocity of the sublimation interface. Since MPC@CB solves a minimization problem, the objective function is: min u J (u ) =
1
¦ ϑ + V ( j)
Np
2
∀j ∈ J1
j
(7)
accounting for the magnitude constraints for the manipulated variable and the output process. The velocity V is given by V=dH/dt and ϑ >0 is a small positive parameter, introduced to avoid the division by zero in (7). In Figure 1, the dynamics of the moving sublimation ice front H(t) and its velocity are presented. The optimization procedure based on the MPC@CB software is iterated until the position H(t) reaches the length L, which means the end of the primary drying stage.
1
© University Claude Bernard Lyon 1 - EZUS. In order to use MPC@CB, please contact the author :
[email protected] Optimal Operation of Sublimation Time of the Freeze Drying Process by Predictive Control: Application of the MPC@CB Software
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The profile of the bottom surface temperature of the materiel being dried, the heating plate temperature, as well as the glass transition temperature are presented in Figure 2. In order to satisfy the output constraint, the temperature is then kept near this constraint value for the rest of the time of the primary drying stage by reducing iteratively the heat flux input. The efficiency of the IMC-MPC strategy over open loop control can be seen: The drying time obtained for the primary drying stage using the MPC@CB software is equal 18 hours, while the required time for the sublimation step is about 24.11 hours in open loop.
4. Conclusion This study tackled the model based predictive control of the primary stage of the freeze drying process. Using the mathematical model of Liapis et al., in which the dynamic of the mass flux was simplified, the model based predictive control of the freeze drying is studied. Taking into account of the non linear partial differential equation model of the process, the idea was to combine the IMC structure and the MPC framework. The resulting IMC-MPC chart corrected the modelling errors introduced in the model based on line optimizer. Constraints on the manipulated variable and controlled variables are handled. This framework was used to optimize the drying time during the primary drying stage of the freeze drying process. The simulations results of the minimization problem were established using the MPC@CB code developed in Matlab. The difficulty related to this problem was the choice of the trajectory given by u0 . Since the measured temperature is at the bottom surface of the vial, one may design an observer that estimates the temperatures at different z.
References [1] A.I. Liapis, M.J. Pikal, R. Bruttini 1996 Research and development needs and opportunities in freeze drying. Drying Technology, 14, 1265-1300. [2] A.I. Liapis, R. Bruttini 1994 A theory for the primary and secondary drying stages of the freeze drying of pharmaceutical crystalline and amorphous solutes ; comparison between experimental data and theory, Separation Technology, 4, 144155. [3] A.I. Liapis, R.J. Litcheld 1979 Optimal control of a freeze dryer-I: theoretical development and quasi-steady state analysis Chemical Engineering Science, 34, 975-981. [4] CJ. King CJ 1971 Freeze drying Foods CRC Press, Cleveland, OH, 1-54. [5] R.J. Litcheld, A.I. Liapis 1979 An adsorption-sublimation model for a freeze dryer. Chemical Engineering Science, 34:1085. [6] A.I. Liapis, L.J. Litcheld 1979 Numerical solution of moving boundary transport problems in finite media by orthogonal collocation. Computers and Chemical Engineering, 3: 615-621. [7] Ferguson, RW. Lewis, L. Tomosy 1993 A finite element analysis of freeze-drying of a coffee sample Computers Methods Applications Mechanical Engineering 1993, 108: 341-352. [8] H. Sadikoglu, A.I. Liapis 1997 Mathematical Modelling of the Primary and Secondary Drying Stages of Bulk Solution Freeze-Drying in Trays: Parameter stimation and Model Discrimination by Comparison of Theoretical Results with Experimental Data, Drying Technology, 15: 791-810
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[9] P. Dufour P, F. Couenne, Y. Touré 2003 Model predictive control of a catalytic reverse flow reactor. Control of industrial spatially distributed parameter processes, Special issue of IEEE Transactions on Control System Technology, 11(5) : 705-714. [10] N. Daraoui, P. Dufour, H. Hammouri 2007 Model predictive control of the primary drying stage of a freeze drying of solutions in vials : a application of the MPC@CB software (part 1). The 5th Asia-Pacific Drying Conference, Hong Kong, China, 2 : 883-888. [11] K. Abid, P. Dufour, I. Bombard, P. Laurent 2007 Model predictive control of a powder coating process : an application of the MPC@CB software. IEEE Chinese Control Conference, Zhangjiajie, China, 2 : 630-634. [12] N. Daraoui, P. Dufour, H. Hammouri, A. Hottot 2007 On line constrained optimization of the primary drying stage of lyophilization, American Institute of Chemical Engineers (AIChE) Journal, submitted, ref. AIChE-07-10884.
FIG. 1: Optimization of drying time : time variation of the moving interface H(t)(bottom) and its velocity (top) during the primary drying stage
FIG. 2: Optimization of drying time : time variation of the bottom surface and heating plate temperatures during the primary drying stage
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Improving Steady-State Identification Galo A. C. Le Roux,a Bruno Faccini Santoro,a Francisco F. Sotelo,a Mathieu Teissier,b Xavier Joulia,b a
LSCP, Departamento de Engenharia Química, Escola Politécnica da USP, Av. Prof. Luciano Gualberto 580, Tr3, São Paulo, SP zip code 05508-900, Brazil bEcole Nationale Supérieure des Ingénieurs en Arts Chimiques et Technologiques 118 Route de Narbonne 31077 TOULOUSE Cedex 04, France
Abstract The use of online data together with steady-state models, as in Real Time Optimization applications, requires the identification of steady-state regimes in a process and the detection of the presence of gross errors. In this paper a method is proposed which makes use of polynomial interpolation on time windows. The method is simple because the parameters in which it is based are easy to tune as they are rather intuitive. In order to assess the performance of the method, a comparison based on Monte-Carlo simulations was performed, comparing the proposed method to three methods extracted from literature, for different noise to signal ratios and autocorrelations. The comparison was extended to real data corresponding to 197 variables of the atmospheric distillation unit of an important Brazilian refinery. A hierarchical approach was applied in order to manage the dimension of the problem. The studies showed that the method proposed is robust and that its performance is better than others. Keywords: Steady-State, Savitzky-Golay, Simulation, Non-Parametric Tests, Refining
1.
Introduction
Petroleum shortage is an important issue. Improving the efficiency of refineries by optimising their operation is one of the measures that must be implemented. In order to do so using computational tools available, like Real Time Optimization (RTO), it is mandatory to use data obtained in steady-state operation. This justifies the need for steady-state detection procedures, because the adaptation of process models to data obtained exclusively in steady state operation leads to better solutions (Bhat & Saraf, 2004). The analysis of real data is non-trivial because they include a stochastic component and statistical methods must be employed in order to perform the task. In this work an original usage of Savitzky-Golay filter is proposed. An estimate for the local derivative is obtained from the interpolation process, which is used in a test that allows the discrimination of steady-states. In this contribution, first, a short review of the steady-state identification methods most used is presented. Then, a comparison of the behavior of these methods based on benchmark data is performed in order to develop and calibrate the methodologies that are further applied to a case study based on real data from a crude distillation unit.
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G.A.C. Le Roux et al.
Steady-State Identification
Steady-State identification is the first step for data processing in RTO (Bhat and Saraf, 2004) that also includes gross error detection and data reconciliation. In this work we present a review of the techniques used for steady-state identification. But, as literature reports experiences exclusively with parametric methods, we propose the study of some non-parametric techniques. 2.1. Modified F Test Cao & Rhinehart (1995) proposed an F-like test applied to the ratio (R) of two different estimates of the variance of the system noise. Each of these estimates is calculated using an exponential moving-average filter. The data are also filtered using a moving-average filter. One parameter, varying from 0 to 1, must be chosen for each of the filters (λ1, λ2 and λ3). The values of these parameters are set based on the relevance of the actual values in comparison to the past ones, and could be interpreted as forgetting factors and express something analog to a window size. If the statistic R, which is evaluated at each time step, is close to one, then the data can be considered in steady state. The maximum acceptable variability is defined by means of a critical value Rcrit. Cao & Rhinehart (1995) proposed that the parameters of the method be tuned empirically and present some guidelines for the procedure. 2.2. Reverse Arrangements Test (RAT) A non-parametric test is the Reverse Arrangements Test, in which a statistic, called A, is calculated in order to assess the trend of a time series. The exact procedure of calculation as well as tables containing confidence intervals is described in Bendat & Piersol (2000). If A is too big or too small compared to these standard values could mean there is a significant trend in the data, therefore the process should not be considered in steady state. The test is applied sequentially to data windows of a given size. 2.3. Rank von Neumann Test The rank modification of von Neumann testing for data independence as described in Madansky (1988) and Bartels (1982) is applied. Although steady-state identification is not the original goal of this technique, it indicates if a time series has no time correlation and can thus be used to infer that there is only random noise added to a stationary behavior. In this test a ratio v is calculated from the time series, whose distribution is expected to be normal with known mean and standard deviation, in order to confirm the stationarity of a specific set of points. 2.4. Polynomial Interpolation Test (PIT) Savitzky & Golay (1964) developed the algorithm for a filter to treat data measured in noisy processes, as spectroscopy. An experimental measurement series is filtered first by choosing a window size, n (which must be an odd number). Each window is interpolated using a polynomial of degree p, with p < n. Information obtained from the interpolated polynomial is less noisy. Thus, the first derivative of each polynomial at the central points is calculated and the value is used as a statistic for assessing the stationarity of the point. The parameters of the filter are the window size, n, and the polynomial degree, p.
Improving Steady-State Identification
3.
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Benchmark Data
To analyze the advantages and drawbacks of each test comparatively, two sets of calibration functions were created. The first one is derived from four functions, representing different levels of stationarity. In each of these cases, three levels of random white noise are added with different amplitudes corresponding to 1, 5 and 10% standard deviations, of the original data. This set of functions is presented in Fig. 1.
Figure 1. Set of calibration functions: (A) original and (B) with first level of noise
The second one is based on two intervals: a ramp and a constant segment. For the ramp segment, three different slopes are tested: 1, 0.5, and 0.1. As previously, random noise with different amplitudes was added. A Monte-Carlo study was carried out in order to estimate the performance of each test. The methodology for assessing the performance is as follows: random noise is generated and each test for stationarity is applied to the central point of the positive slope segment and also at the central point of the constant piece. The number of times where the test succeeds or fails are recorded and a new random noise is generated. After some iterations (typically 1000) it is possible to find an approximate distribution for the probability of success and also for the type I (the process is considered nonstationary while it is in fact) and II errors. This procedure is applied for each test and for different parameters, thus portraying the sensitivity of the probability distribution as a function of the parameter values. Even for non-parametric tests, such sensitivity can be studied with respect to the size of the window, for instance.
4.
Results and Discussion
4.1. Benchmark Set 4.1.1. Polynomial Interpolation Test The degree of the polynomials is kept constant and equal to 2. This choice is justified by the fact that results depend more on the window size than on the degree of the polynomial.
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When applied to the first set of functions, the estimations of the first derivative are quite close to the intuitive expected values. In order to quantify its efficiency, the second set of functions is used in the Monte-Carlo study described above. For a given noise level, the average accuracy is calculated as the mean of accuracies for the 3 different slopes. The major difficulty in tuning this test is not that of choosing n but that of finding which should be the threshold for the derivative for a process is considered as stationary. This is the most important parameter and must be chosen according to the expected tolerance to variations. In Fig. 2, the dependence of the quality of the results on this treshold value is apparent.
Figure 2. Performance of Polynomial Interpolation Test for window size=51 and first level of noise
The existence of a region where fractions of errors type I and II are simultaneously small indicates that for some data series this test is able to clearly identify a stationary from a non-stationary point. However, for the case with several simultaneous variables that is analyzed later this is not necessarily true. 4.1.2. Modified F Test For the first set, it was possible to observe that this test works adequately (there is a significant trend in the analyzed data) and the values of R obtained were much larger than Rcrit. However, as noise level increases, the test does not perform properly and all the functions are considered stationary. It is possible to verify this fact from the Monte Carlo analysis results (Table 1) and to notice that its efficiency is similar to PIT for the first level of noise, which is the closer to real data. It is found that Ȝi parameters have little influence over the final result. 4.1.3. Reverse Arrangements Test Standard values of A are only tabulated for a few data sizes. As a consequence it is more difficult to choose a length for the window that would be neither too small nor too large.
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One reasonable choice was to consider 30 data points. But, for this, only the means of 3 successive points could be analyzed because the resulting time series has to be only 10 values long, which is the smallest value presented in tables. Unfortunately, averaging reduces the influence of noise. As for the other tests, this test behaves adequately for the first data set. From Monte Carlo analysis it was observed that the results are worst than for the Polynomial Interpolation Test but better than the techniques described in literature. 4.1.4. Rank von Neumann Test 30-points data windows were analyzed in order to make the comparison with the previous tests similar. The performance is adequate for the first data set, but type I errors get too large if the noise is too intense. The same behavior arises when testing the second set (Table 1). Table 1. Results of Steady-State identification on benchmark set (MF = Modified F test, RAT = Reverse Arrangements test, RVN = Rank von Neumann test) Noise Level
1
2
3
RAT
RVN
MF
RAT
RVN
MFa
RAT
RVN
Correct Answers 78,52
87,58
84,75
50,77
72,42
63,92
50,52
59,67
53,45
Type I Error
41,88
13,17
26,40
97,46
44,50
68,13
97,92
69,75
89,13
Type II Error
1,08
11,67
4,10
1,0
10,67
4,03
1,04
10,92
3,97
Test
a
a
MF
a
Ȝ1 = 0.2, Ȝ2 = 0.1, Ȝ3 = 0.1
4.2. Case study: crude oil atmospheric distillation unit Data from a Brazilian Refinery corresponding to the units comprehended from the desalinization to the separation into LPG, naphtha, kerosene, diesel and gasoil were analyzed. 197 relevant variables were retained and data measurements concerning 5 months of operation (one measurement every ten minutes) were available. Among the variables, 27 were considered to be key to the process, based on engineering considerations. The stationarity test is applied only to this smaller set. The whole system is considered to be at steady state if and only if all these 27 variables are stationary. As RAT appeared to be the most reliable test among the non-parametric ones, it was used to designate some steady-state windows from the huge database. According to RAT there are not many of these windows. Even so, one can choose some of them and verify the agreement between any other given test and RAT. If the accuracy of both parametric tests was not so different in the benchmark set, the situation changes dramatically towards PIT performance. This might be explained by, what can be termed “lack of noise” in the real data. In fact, for a time series to be considered stationary by the F-like test, it must have some level of noise. Cao & Rhinehart (1995) recommend the introduction of a white noise before analyzing data,
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but this procedure could lead to inconsistent results, for enough noise makes any time series “stationary “.
Figure 3. Steady-state identification for real data and for its first derivative (window size=51 and limit of derivative =0.1)
In Fig. 3 an example of the steady-state identification using PIT for real temperature data (left side) is presented. For illustrative purposes only five variables were used. The analysis of the first derivative (right side) is an auxiliary tool in order to analyze the behavior of the system.
5.
Conclusions
It was shown that for simulated data PIT performs better than the other tests studied. In addition, this test is the one that agrees better with RAT in the real case study. Its most important parameter, the window size, can be adjusted in order to deal with situations where the process could be more sensitive to small changes. PIT is very simple and intuitive: for its implementation, a plot of the derivatives can be used in order to help in the selection of the steady states.
References Savitzky, M. Golay, 1964, Smoothing and Differentiation of Data by Simplified Least Squares Procedures, Anal. Chem., Vol 36, pp. 1627-163 S. Cao, R. Russell, 1995, An efficient method for on-line identification of steady state, J. Proc. Cont. Vol 5, No. 6, pp. 363-374 S.A. Bhat, D.N. Saraf, 2004, Steady-state identification, gross error detection, and data reconciliation for industrial process units, Ind. Eng. Chem. Res. Vol 43, pp. 4323-4336 J. Bendat, A. Piersol, 2000, Random data : analysis and measurements procedures, John Wiley & Sons Madansky, J. 1988, Prescriptions for working statisticians, Springer - Verlag New York R. Bartels, 1982, The Rank Version of von Neumann’s Ratio Test for Randomness, Journal of the American Statistical Association, Vol. 77, No. 377, pp. 40-46
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Application of adaptive neurofuzzy control using soft sensors to continuous distillation Javier Fernandez de Canete, Pablo del Saz-Orozco, Salvador Gonzalez-Perez System Engineering Dpt. , Plaza El Ejido s/n, Malaga, 29013, SPAIN
Abstract Recent years have seen a rapidly growing number of hybrid neurofuzzy based applications in the process engineering field, covering estimation, modeling and control among others. In fact, proper operation of a distillation column requires knowledge of products compositions during the entire duration of the operation. The use of inferential composition estimators (soft sensors) has long been suggested to assist the monitoring and control of continuous distillation columns. In this paper we describe the application of an adaptive network based fuzzy inference system (ANFIS) predictor to the estimation of the product compositions in a binary methanol-water continuous distillation column from available on-line temperature measurements. This soft sensor is then applied to the composition dual control of the distillation column. Genetic algorithms are used to automatically selection of the optimum control signal based on an ANFIS model of the plant. The performance of the developed ANFIS estimator is further tested by observing the performance of the dual control system for both set point tracking and disturbance rejection cases. Keywords: distillation control, neurofuzzy networks, soft sensors, genetic algorithms
1. Introduction Neural and fuzzy applications have been successfully applied to the chemical engineering processes [1], and several control strategies have been reported in literature for the distillation plant modeling and control tasks [2]. Recent years have seen a rapidly growing number of neurofuzzy control applications [3]. Beside this, several software products are currently available to help with neurofuzzy problems. Basically, a fuzzy controller is composed of a rule base containing fuzzy if-then rules. A database with membership functions of the fuzzy sets, an inference engine and two fuzzification and defuzzification interfaces to convert crisp inputs into degrees of match with linguistic values and vice versa. An ANFIS system (Adaptive Neuro Fuzzy Inference System) [4] is a kind of adaptive network in which each node performs a particular function of the incoming signals, with parameters updated according to given training data and a gradient-descent learning procedure. This hybrid architecture has been applied mostly to the control of nonlinear single input single output (SISO) nonlinear systems [5], while application to general multiple inputs multiple outputs (MIMO) control problems rely both on decoupling control to produce a set of SISO controllers or else designing a direct multivariable controller . Proper operation of a distillation column requires knowledge of products compositions during the entire duration of the operation. Although product composition can be
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measured on-line, it is well known that on-line analyzers are complex pieces of equipment that are expensive and difficult to maintain. They also entail significant measurement delays, which can be detrimental from the control point of view [6]. Therefore, to circumvent these disadvantages, it is possible to estimate the product composition on-line, rather than measuring it. The use of such inferential composition estimators (or soft sensors) has long been suggested to assist the monitoring and control of continuous distillation columns [7]. Genetic algorithms (GA) are model machine learning methodologies, which derive their behaviour from a metaphor of the processes of evolution in nature and are able to overcome complex non-linear optimization tasks like non-convex problems, noncontinuous objective functions, etc. [8]. They are based on an initial random population of solutions and an iterative procedure, which improves the characteristics of the population and produces solutions that are closer to the global optimum. This is achieved by applying a number of genetic operators to the population, in order to produce the next generation of solutions. GAs have been used successfully in combinations with neural and fuzzy systems. Particularly in neurofuzzy control, GAs have been utilized extensively to tune the neurofuzzy controller parameters and acquire the fuzzy rules [9]. In this paper we describe the application of an adaptive network based fuzzy inference system (ANFIS) predictor to the estimation of the product compositions in a binary methanol-water continuous distillation column from available on-line temperature measurements. This soft sensor is then applied to train an ANFIS model so that a GA performs the searching for the optimal dual control law applied to the distillation column. The performance of the developed ANFIS estimator is further tested by observing the performance of the ANFIS based control system for both set point tracking and disturbance rejection cases.
2. Process Description The distillation column used in this study is designed to separate a binary mixture of methanol and water, which enters as a feed stream with flow rate Fvol and composition XF between the rectifying and the stripping section, obtaining both a distillate product stream Dvol with composition XD and a bottom product stream Bvol with composition XB. The column consists of 40 bubble cap trays. The overhead vapor is totally condensed in a water cooled condenser (tray 41) which is open at atmospheric pressure. The process inputs that are available for control purposes are the heat input to the boiler Q and the reflux flow rate Lvol. Liquid heights in the column bottom and the receiver drum (tray 1) dynamics are not considered for control since flow dynamics are significantly faster than composition dynamics and pressure control is not necessary since the condenser is opened to atmospheric pressure. The model of the distillation column used throughout the paper is developed by [10], composed by the mass, component mass and enthalpy balance equations used as basis to implement a SIMULINK model (figure 1) which describes the nonlinear column dynamics as a 2 inputs (Q , Lvol ) and 2 output (XD , XB ). Implementations details for the overall column dynamics are given in [11].
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Figure 1. Schematic of the SIMULINK model of the distillation
3. ANFIS Estimator An ANFIS system is a kind of adaptive network in which each node performs a particular function of the incoming signals, with parameters updated according to given training data and a gradient-descent learning procedure. This hybrid architecture has been applied to the modeling and control of multiple-input single-output (MISO) systems [4].
Figure 2. Architecture of the ANFIS structure
The architecture of the ANFIS is constituted by several layers (fig. 2). If we consider for simplicity two inputs x and y and two outputs f1 and f2 for a first-order Sugeno fuzzy model, with Ai and Bj being the linguistic label associated with x and y respectively, every node in layer 1 represents a bell-shaped membership function μ Ai (x) or μ B ( y ) i with variable membership parameters. Usually we choose the bell-shaped functions. Nodes of layer 2 output the firing strength defined as the product ω ji = μ A ( x) × μ B ( y ) , i i where the set of nodes in this layer are grouped for each output j. A normalization process is computed in layer 3 giving the normalized ω ji , and the Sugeno-type consequent of each rule with variable parameters pi, qi and ri is implemented in layer 4 yielding fj as the output of the single summation node f i = ω ji ( pi x + qi y + ri ) and finally the single node of layer 5 computes de overall outputi as a summation of all incoming signals.
¦
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The learning procedure consists of two stages. In the forward pass training input data go forward the ANFIS architecture, and in the backward pass the error rates propagate backward, being the both the consequent and the membership parameters updated by gradient descent.
4. ANFIS-GA Controller The complete ANFIS based estimation and control system is described below (figure 3). yˆ[ k ]
T [k ] ANFIS ESTIMATOR
~ y [k ]
TDL ANFIS MODEL
+ -
u[k ] e[k ]
GA CONTROLLER DISTILLATION COLUMN
y d [ k + 1] TDL : Tapped Delay Line Figure 3.Estimation and Control ANFIS based structure
4.1. ANFIS estimator of the composition (ANFIS ESTIMATOR block) In order to infer the composition from temperature an ANFIS net is used. Previously, a sensitivity study is performed in order to choose the correct set of temperatures to infer top and bottom compositions (figure 4). The sensitivity index proposed is defined as the partial derivative of each available primary variable (product composition) with respect to changes in each secondary variable (tray temperature). dependency 41 36 31 tray
26 21 16 11 6 1 0
0,01
0,02
0,03
0,04
0,05
0,06
normalized derivate
Figure 4.Composition-temperature dependencies.
A three temperature vector T[k] = [T41[k],T21[k],T1[k]] is selected as input to the ANFIS predictor which output the predicted values of composition vector
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yˆ[k ] = [ Xˆ D [k ], Xˆ B [k ]] . After a trial-error process we have selected 5 membership
functions per input as a compromise solution between computation time and precision. Normally, in a plant operation, both real values are measured off-line in the laboratory. In this study, the ANFIS parameter update is made accepting the simulation results as same with the actual plant data. Training set is generated by selecting 1200 temperature data points obtained by during column open loop operation with range for LVol (0-5E-06 m3/h) and heat flow Q (0-2000 J/s) for fixed feed rate conditions FVol = 1 E-06 m3/h, XF = 0.3. An additional temperature data set consisting of 150 data points was used to test the ANFIS predictor afterwards. The error in the training phase is under 0.00025% and 0.0015% in the validation phase. For training pattern generation we assume an initial steady state for the column after a start-up process. 4.2. ANFIS modeling of the distillation column (ANFIS MODEL block) Prior to the design of the controller, an ANFIS network has been used as an identification model of the distillation column dynamics. To obtain representative training data, varying feed flows, initial liquid composition values both in the column, boiler and condenser along with input values for the control actions were imposed on the model. The identification model has been carried out using an ANFIS network given by ~ y[k ] = f ( yˆ[k ], yˆ[k − 1], yˆ[k − 2], u[k ]) after selecting the best structure among possible ones, with u[k] = [LVol[k],Q[k]] and yˆ[k ] regularly spaced covering the same range as defined in section 4.2. As the model’s dynamic will be modified with unknown perturbations, this ANFIS model will be updated with the real plant response. 4.3. Genetic Algorithm Controller (GA CONTROLLER block ) As the estimation of the composition vector ~ y[k ] in the next simulation step according the present and previous states of yˆ[k ] and the input to the system u[k] can be achieved using the ANFIS model net, the control problem can be implemented as an optimization problem in which the function to minimize is the difference between the desired output yd [k ] and the estimated one ~y[k ] in the next step. As a result, the optimum control law u[k] is elicited for the distillation control problem. This control approach enables the searching of an optimum control signal for each point in the operating range of the nonlinear distillation plant. In order to search for the optimum for the highly non-linear function a genetic algorithm is used with 75 members fixed population, 75 generations and random mutation. If an error under 0.01% is achieved, the algorithm is stopped in order to accelerate the simulations.
5. Results The aim in the design of the composition ANFIS estimator is to use together with ANFIS-GA for dual composition control of the distillation column. Therefore, the composition estimator is tested by using the SIMULINK model before it is used for control. The performance of the control structure is checked for set-point and disturbance rejections, as is shown in figure 5.
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Figure 5. Performance of the ANFIS-GA for a pulse change in top (bottom) product purity from 96% to 98% (4% to 2%) in t = 2000 s and change in XF from 40% to 30% in t = 4450 s.
6. Conclusions and Future Works We have proposed a hybrid neurofuzzy design methodology to dual composition control in a MIMO binary distillation column. An ANFIS structure has been employed both for prediction of composition profiles from temperatures and design of optimum control law using a GA search technique, by using an ANFIS model based fitness function. The results obtained point to the potential use of this control strategy in areas of design related to operability and control in process engineering. Future works are directed towards the application of the proposed methodology to a real small scale pilot plant.
References [1] A. Bulsari. Neural networks for chemical engineers. Elsevier, Amsterdam, 1995. [2] M.A. Hussain, M. A. “Review of the applications of neural networks in chemical process control. Simulation and on-line implementations”, Artificial Int. in Eng, Vol. 13 (1999) pp. 55-68. [3] J. Engin, J. Kuvulmaz and E. Omurlu. “Fuzzy control of an ANFIS model representing a nonlinear liquid level system”. Neural Computing and Appl., Vol. 13, n. 3 (2004) pp. 202-210. [4] R. Jang and C. Sun. Neuro-fuzzy modeling and control. Proceedings of the IEEE 1995, Vol. 83 n. 3 (1995) pp. 378-405. [5] M. Denai, F. Palis and A. Zeghbib. “ANFIS based modeling and control of nonlinear systems: A tutorial”, Proceedings of the IEEE Conference on SMC (2004), pp. 3433-3438. [6] H. Leegwater. Industrial experience with double quality control. In W. L. Luyben (Ed.), Practical distillation control. New York, USA: Van Nostrand Reinhold, 1992. [7] S. Park and C. Han. “ A non-linear soft sensor based on multivariate smoothing procedure for quality estimation in distillation columns”, Comp. and Chem. Eng. Vol. 24 (2000), pp. 871-877. [8] Z. Michalewitz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin, Germany, 1992. [9] P. Fleming and R. Purshouse – Evolutionary algorithms in control systems engineering: a survey. Control Engineering Practice, Vol. 10 (2002) pp. 1223–1241. [10] M. Diehl, I. Uslun and R. Findeisen.”Real-time optimization for large scale processes: Nonlinear predictive control of a high purity distillation column”, On Line Optimization of Large Scale System: State of the Art, Springer-Verlag, 2001. [11] J. Fernandez de Canete, S. Gonzalez-Perez and P. del Saz Orozco. “A development of tools for monitoring and control of multivariable neurocontrolled systems with application to distillation columns”, Proc. EANN 2007 Int. Conf., Thesaloniki, Greece, (2007), pp. 296-305.
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Correlation-Based Just-In-Time Modeling for SoftSensor Design Koichi Fujiwara, Manabu Kano, Shinji Hasebe Kyoto University, Nishikyo-ku, Kyoto, 615-8510, Japan
Abstract Soft-sensors are widely used for estimating product quality or other key variables when on-line analyzers are not available. However their estimation performance deteriorates when the process characteristics change. To cope with such changes and update the model, recursive methods such as recursive PLS and Just-In-Time (JIT) modeling have been developed. When process characteristics change abruptly, however, they do not always function well. In the present work, a new method for constructing soft-sensors based on a JIT modeling technique is proposed. In the proposed method, referred to as correlation-based JIT modeling, the samples used for local modeling are selected on the basis of the correlation among variables instead of or together with distance. The proposed method can adapt a model to changes in process characteristics and also cope with process nonlinearity. The superiority of the proposed method over the conventional methods is demonstrated through a case study of a CSTR process in which catalyst deactivation and recovery are considered as changes in process characteristics. Keywords: soft-sensor, Just-In-Time modeling, recursive partial least squares regression, principal component analysis, estimation
1. Introduction A soft-sensor, or a virtual sensor, is a key technology for estimating product quality or other important variables when online analyzers are not available (Kano and Nakagawa, 2008). In chemical industry, partial least squares (PLS) regression has been widely used for developing soft-sensors (Mejdell and Skogestad, 1991; Kano et al., 2000; Kamohara et al., 2004). However, their estimation performance deteriorates when process characteristics change. For example, equipment characteristics are changed by catalyst deactivation or scale adhesion. Such a situation may bring to decline product quality. Therefore, soft-sensors should be updated as the process characteristics change. To cope with such changes and update statistical models, recursive methods such as recursive PLS were developed (Qin, 1998). However, when a process is operated within a narrow range for a certain period of time, the model will adapt excessively and will not function within a sufficiently wide range of operation. On the other hand, Just-In-Time (JIT) modeling, which was proposed to cope with the changes in process characteristics and the process nonlinearity (Bontempi et al., 1999), generates a local model from past data around a query point only when an estimated value is requested. JIT modeling is useful when global modeling does not function well. However, its estimation performance is not always high because the samples used for local modeling are selected on the basis of the distance from the query point and the correlation among variables is not taken into account. In the present work, a new method for soft-sensor design is proposed. In the proposed method, referred to as correlation-based JIT (C-JIT) modeling, the samples used for local modeling are selected on the basis of the correlation instead of or together
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with the distance. The C-JIT modeling can cope with abrupt changes of process characteristics that conventional method cannot. The usefulness of the proposed method is demonstrated through a case study of a CSTR process in which catalyst deactivation and recovery are investigated as the changes in process characteristics.
2. Conventional methods In this section, conventional soft-sensor design methods are briefly explained. 2.1. Dynamic PLS PLS has been widely used for building a soft-sensor because it can cope with a colinearity problem. Here X ∈ ℜ N × M and Y ∈ ℜ N × L are matrices whose ith rows are the ith measurements of inputs xi and outputs yi, respectively. The columns of these matrices are mean-centered and scaled appropriately. In PLS, X and Y are decomposed as follows: X =TP T + E , Y = TQ T + F (1) where T ∈ ℜ N × R is the latent variable matrix, P ∈ ℜ M × R and Q ∈ ℜ L× R are the loading matrices of X and Y , respectively. R denotes the number of latent variables. E and F are the error matrices. The estimation performance of soft-sensors can be improved by taking into account process dynamics. For this purpose, the past information is used as inputs in addition to the present information. This method is referred to as Dynamic PLS (Ricker, 1993; Kano et al., 2000). 2.2. Recursive PLS The estimation performance of a statistical model will deteriorate when process characteristics change. Therefore, soft-sensors should be updated as process characteristics change. However, redesign of them is very laborious and it is difficult to determine when they should be updated. To cope with these problems, recursive PLS was proposed (Qin, 1998). Whenever both new input and output variables, x new and y new , are measured, the recursive PLS updates the model by using ª βP T º ª βQ T º X new = « T » Ynew = « T » , 0 < β ≤ 1 ¬ x new ¼ ¬ y new ¼ where β is the forgetting factor.
(2)
2.3. Just-In-Time modeling In general, a global linear model cannot function well when a process has strong nonlinearity in its operation range, and it is difficult to construct a nonlinear model that is applicable to a wide operation range since a huge amount of samples are required. Therefore, methods that divide a process operation region into small multiple regions and build a local model in each small region have been proposed. An example is a piecewise affine (PWA) model (Ferrari-Trecate et al., 2003). However, in the PWA model, the optimal division of the operation region is not always clear and the interpolation between the local models is complicated. Another method for developing local models is JIT modeling, which has the following features: • When new input and output data are available, they are stored into a database. • Only when estimation is required, a local model is constructed from samples located in a neighbor region around the query point and output variables are estimated. • The constructed local model is discarded after its use for estimation.
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In JIT modeling, samples for local modeling should be selected appropriately and online computational load becomes large.
3. Correlation based Just-In-Time modeling Conventional JIT modeling uses a distance to define a neighbor region around the query point regardless of the correlation among variables. In the present work, a new JIT modeling method that takes account of the correlation is proposed. In the proposed C-JIT modeling method, the data set that has the correlation best fit to the query sample is selected for local modeling. 3.1. Evaluation of correlation similarity Although several indices of similarity between data sets have been proposed (Kano et al., 2001; Kano et al, 2002), the Q statistic is used in C-JIT modeling. The Q statistic is derived from principal component analysis (PCA), which is a tool for data compression and information extraction (Jackson and Mudholkar, 1979). P
¦ (x
Q=
p
− xˆ p ) 2
(3)
p =1
where xˆ p is the prediction of the pth input variable by PCA. The Q statistic is a
distance between the sample and the subspace spanned by principal components. That is, the Q statistic is a measure of dissimilarity between the sample and the modeling data from the viewpoint of the correlation among variables. In addition, to avoid extrapolation, Hotelling's T 2 statistic can be used. R t r2 T2 = (4) 2
¦σ r =1
tr
where σ t2 denotes the variance of the rth score t r . r
The T 2 statistic expresses
normalized distance from the origin in the subspace spanned by principal components. To improve the model reliability, Q and T 2 can be integrated into a single index for the data set selection as proposed by Raich and Cinar (1994) for a different purpose: J = λT 2 + (1 − λ )Q, 0 ≤ λ ≤ 1 (5) 3.2. Correlation-based Just-In-Time modeling In the proposed C-JIT modeling, samples stored in the database are divided into several data sets. Although the method of generating data sets is arbitrary, each data set is generated so that it consists of successive samples included in a certain period of time in this work, because the correlation among variables in such a data set is expected to be very similar. To build a local model, the index J in Eq. (5) is calculated for each data set, and the data set that minimizes J is selected as the modeling data set. Figure 1 shows the difference of sample selection for local modeling between JIT modeling and C-JIT modeling. The samples consist of two groups that have different correlation. In conventional JIT modeling, samples are selected regardless of the correlation, since a neighbor region around the query point is defined by distance. On the other hand, C-JIT modeling can select samples whose correlation is similar to that of the query point by using the Q statistic. Assume that S samples are stored in the database and z i = [ x iT , y iT ]T . To cope with process dynamics, measurements at different sampling points can be included in z i . The procedure of C-JIT modeling is as follows:
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1. Newly measured input and output measurements z S +1 are stored in the database. 2. The index J is calculated from z S +1 and a data set z {S } that was used for building the previous local model f {S } . J I = J . 3. If J I ≤ J I , then f {S +1} = f {S } and Z {S +1} = Z {S } . f {S +1} is used for estimation until the next input and output measurements z S + 2 are available. When z S + 2 is available, return to step 1. If J I > J I , go to the next step. Here J I is the threshold. 4. k = 1 . 5. The kth data set Z k = [ z k , " , z k +W −1 ]T ∈ ℜ ( M + L )×W is extracted from the database, where W is the window size. 6. The index J of the kth data set, J k , is calculated from Z k and z S +1 . 7. k = k + d . If k ≤ S − W + 1 , then return to step 5. If k > S − W + 1 , then go to the next step. Here d is the window moving width. 8. The data set Z k that minimizes J k is selected, and it is defined as Z {S +1} . 9. A new local model f {S +1} whose input is X {S +1} = [ x K , ! x K +W −1 ]T and output is Y {S +1} = [ y K , ! , y K +W −1 ]T is built.
10. The updated model f {S +1} is used for estimation until the next input and output measurements z S + 2 are available. When z S + 2 is available, return to step 1. Principal component regression (PCR) is used in the proposed C-JIT modeling because scores are calculated in step 6. In addition, steps 2 and 3 control the model update frequency.
Fig. 1: Sample selection for local modeling in JIT modeling (left) and C-JIT modeling (right).
4. Case Study In this section, the estimation performance of the proposed C-JIT modeling is compared with that of recursive PLS and conventional JIT modeling through their applications to product composition estimation for a CSTR process. 4.1. Problem Settings A schematic diagram of the CSTR process is shown in Fig. 2 (Johannesmeyer and Seborg, 1999). In this process, an irreversible reaction A → B takes place. The set point of reactor temperature is changed between ± 2K every ten days. Measurements of five variables, reactor temperature T, reactor level h, reactor exit flow rate Q, coolant flow rate QC, and reactor feed flow rate QF, are used for the analysis and their sampling interval is one minute. In addition, reactant concentration CA is measured in a
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laboratory once a day. A soft-sensor that can estimate CA accurately in real time needs to be developed. In this case study, to consider catalyst deactivation as the changes in process characteristics, the frequency factor k0 is assumed to decrease with time. In addition, the catalyst is recovered every half year (180 days). Figure 3 shows the deterioration and recovery of the frequency factor. The operation data for the past 540 days were stored in the database. While newly measured data are stored, the soft-sensor is updated in the next 180 days. 4.2. Estimation by Recursive PLS and Just-In-Time modeling Soft-sensors are constructed by using recursive PLS with the forgetting factor β = 0.97 and JIT modeling. In recursive PLS, the model is updated every 24 hours when CA is measured. To take into account process dynamics, the inputs consist of the samples at present and one minute before. The number of latent variables is four, which is determined by trial and error. On the other hand, in JIT modeling, linear local models are built by using Euclid distance as the measure of selecting samples used for local modeling. Matlab Lazy Learning Toolbox was used (http://iridia.ulb.ac.be/~lazy). The estimation results are shown in Table 1. In this table, r denotes the correlation coefficient between measurements and estimates, and RMSE is the root mean square error. The results show that neither recursive PLS nor JIT modeling functions well. In general, recursive PLS is suitable only for slow changes in process characteristics. On the other hand, the reason for the poor performance of JIT modeling seems that JIT modeling does not take account of correlation among variables when a local model is built.
Fig2: Schematic diagram of CSTR.
Fig. 3: Change of a frequency factor.
Table 1: Estimation performance of recursive PLS, JIT modeling, and C-JIT modeling
r RMSE
recursive PLS 0.88 2.07
JIT modeling 0.82 2.43
C-JIT modeling 0.99 0.54
Fig. 4: Estimation result of CA by C-JIT modeling with λ = 0.01 (Window Size: 10 day).
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4.3. Estimation by Correlation-based Just-In-Time modeling The criterion for selecting a data set is to minimize the index J in Eq. (5) with λ = 0.01 . The local model is updated every 24 hours when CA is measured, W=10, and d=1, which are determined by trial and error. The estimation results are shown in Fig. 4 and Table 1. The left figure shows the estimation result for 180 days. The right figure shows the enlarged result for two months before and after the catalyst recovery. In this figure, PCs is the number of principal components. The results show that the estimation performance of C-JIT modeling is significantly higher than that of the conventional methods. With the proposed C-JIT modeling, RMSE is improved by about 78% and 74% in comparison with recursive PLS and JIT modeling, respectively.
5. Conclusion In the present work, to develop a soft-sensor that can cope with the changes in process characteristics, a new correlation-based JIT modeling method is proposed. The superiority of the proposed C-JIT modeling over the conventional methods is demonstrated through a case study of a CSTR process in which catalyst deactivation and recovery are investigated. In recursive PLS and conventional JIT modeling, it is difficult to adapt models when the process characteristics change abruptly. On the other hand, the C-JIT modeling can cope with the abrupt changes in process characteristics.
References G. Bontempi, M. Birattari and H. Bersini, 1999, Lazy Learing for Local Modelling and Control Design, Int. J. Cont., Vol. 72, No. 7/8, 643 G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari, 2003, A Clustring Technique for the Identification of Piecewise Affine System, Automatica, Vol. 39, Issue 2, 205 J. E. Jackson, and G. S. Mudholkar, 1979, Control Procedures for Residuals Associated with Principal Component Analysis, Technometrics, Vol. 21, Issue 3, 341 M. Johannesmeyer and D. E. Sebog, 1995, Abnormal Situation Anaylsis Using Pattern Recognition Techniques and Histrical Data, AIChE Annual meeting, Dallas, Oct.31-Nov. 5 H. Kamohara, A. Takinami, M. Takeda, M. Kano, S. Hasebe and I. Hashimoto, 2004, Product Quality Estimation and Operating Condition Monitoring for Industrial Ethylene Fractionator, J. Chem. Eng. Japan, Vol.. 37, No.3, 422 M. Kano, S. Hasebe, I. Hashimoto and H. Ohno, 2002, Statistical Process Monitoring Based on Dissimilarity of Process Data, AIChE J., Vol. 48, No.6, 1231 M. Kano and Y. Nakagawa ,2008, Data-Based Process Monitoring, Process Control, and Quality Improvement: Recent Developments and Applications in Steel Industry, Comput. Chem. Engng., Vol. 32, 12 M. Kano, H. Ohno, S. Hasebe, and I. Hashimoto, 2001, A New Multivariate Statistical Process Monitoring Method Using Principal Component Analysis, Comput. Chem. Engng., Vol. 25, No.7-8, 1103 M. Kasper and W. H. Ray, 1993, Partial Least Squares Modeling as Successive Singular Value Decomposition, Comput. Chem. Engng., Vol. 17, Issue 10, 985 T. Mejdell and S. Skogestad, 1991, Estimation of Distillation Compositions from Multiple Temperature Measurements Using Partial-Least-Squares Regression, Ind. Eng. Chem. Res., Vol. 30, Issue 12, 2543 S. J. Qin, 1998, Recursive PLS Algorithms for Adaptive Data Modeling, Comput. Chem. Engng., Vol. 22, No. 4/5, 503 A. Raich and A. Cinar, 1994, Statistical Process Monitoring and Disturbance Diagnosis in Multivariable Continuous Processes, AIChE J., Vol. 42, Issue 1,995 N. L. Ricker, 1988, Use of Biased Least-Squares Estimators for Parameters in Discrete-Time Pulse Response Models, Ind. Eng. Chem. Res., Vol. 27, Issue 2, 343
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Integrating strategic, tactical and operational supply chain decision levels in a model predictive control framework José Miguel Laínez, Georgios M. Kopanos, Mariana Badell, Antonio Espuña, Luis Puigjaner Universitat Politècnica de Catalunya, Av. Diagonal 647, E-08028, Barcelona, Spain
Abstract In this work an MILP model which achieves the integration of all three Supply Chain (SC) decision levels is developed. Then, the stochastic version of this integrated model is applied as the predictive model in a Model Predictive Control (MPC) framework in order to incorporate and tackle unforeseen events in the SC planning problem in chemical process industries. Afterwards, the validation of the proposed approach is justified and the resulting potential benefits are highlighted through a case study. The results obtained of this particular case study are analyzed and criticized towards future work. Keywords: supply chain optimization, decision levels, MILP, model predictive control.
1. Introduction Although the Process Systems Engineering community (PSE) faces an increasing number of challenging problems, enterprise and SC remain subjects of major interest offering multiple opportunities. It is believed that further progress in this area will mean a unique opportunity demonstrating the PSE potential to enhance company’s “value preservation”. One of the key components in supply chain management (SCM) and enterprise wide optimization (EWO) is the decision making coordination and integration at all levels. Recent work offers models to separately tackle problems arising in the three standard SC hierarchical decision levels: strategic (long-term: network design), tactical (medium-term: aggregated planning) and operational (short- term: scheduling). These models, because of their nature and purpose, have very different timescales. It becomes evident the challenge of solving large size multi-scale optimization problems when considering the integration of decision levels. Since scheduling is also a basic building block in the more general area of EWO1, it is indispensable its incorporation into the already existed design-planning models. Furthermore, it is noteworthy that SC planning is not a one time event, but a dynamic activity. Firms are in the need of a closed-loop planning approach in order to preserve competitiveness. This approach should be capable of revising planned activities, updating uncertain parameters (e.g., lead times, market demand and interest rates) and considering the effects of incidences; so that future plans are adapted to enhance SC performance under the current highly dynamic business environment. A MPC framework can be used as an appropriate approach to continuously improve the SC planning. The MPC framework attempts to optimize a performance criterion that is a function of the future control variables. By solving the optimization problem all
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elements of the control signal are defined. However, only a portion of the control signal is applied to the SC system. Next, as new control input information and disturbance forecasts are collected, the whole procedure is repeated, which produces a feed-forward effect and enables the SC system to follow-up the dynamic business environment.
2. Problem statement A novel stochastic multi-period design/planning/scheduling MILP model of a multiechelon SC with financial considerations is used as a predictive model in this work. The model assumes that different technological equipment is available to be installed in potential sites and assists in their selection. Furthermore, the model allows the expansion of plant equipment capacities, not only in the first planning period. Regarding the financial area, the mathematical program endeavors to evaluate the shareholder value.
3. Control Strategy In Fig.1, a general schematic of the proposed MPC framework for SCM is shown. It follows a brief description of the control strategy. When the SC process is disturbed, data required to describe the current SC state are captured and sent to the controller. Next, scenarios are calculated by the forecasting module. As it is indicated there, the control signal that is implemented in the SC processes only comprises the first stage variables resulting from the stochastic optimization problem. In fact, first stage variables are associated to next period decisions that are made prior to uncertainty realization. Disturbances (i.e. demand, prices, interest rates)
SC Planners & executives
Control variables: capacity increases, facilities production and distribution rates
Supply chain processes
1st Stage control signal
Process output
Control algorithm Integrated SC model Strategic (Design) Tactical (Planning)
Forecasting module
Finances
Time series analysis: Mean and forecast error caracterization
Operational (Scheduling)
SC design/planning model Stochastic MILP
1st stage Here and now variables (Frozen stage)
Sampling tool
Recourse stages Wait and see variables (Flexible stage)
Output: Parameters estimation, Scenarios
Optimizer
Predictive and optimal controller
Figure 1. Control strategy
Sensors (data collecters)
Control input: current demand, capacity and materials availability, stocks, capacity pitfalls …
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3.1. The control algorithm The predictive model within the control algorithm consists in a multistage stochastic MILP. A scenario based approach is applied. Refer to Puigjaner and Laínez 2 for scenario tree description and stochastic formulation indices details (l; ~l). 3.1.1. Process operations formulation Design-Planning formulation. The stochastic design-planning approach presented in this work is inspired from the STN formulation3. The presented approach relies on the flexible echelons concept. The connectivity between echelons is not imposed; consequently, a facility may play the role of either a processing or a distribution site. Material flows among facilities are allowed. Moreover, the proposed design-planning formulation simplifies the representation of batch and/or continuous process into the same framework, which facilitates its integration with scheduling models. The basic equations are next presented. Eq.(1) is the mass balance equation for each echelon f and material s. The design decisions are modeled through Eqns.(2)-(3). Eq.(4) forces the production to be within installed capacity and a minimum utilization factor. Eqs.(5)-(6) force materials flow from suppliers and to markets to be lower than an upper bound given by their capacity limitations. l Ssft~ = l
XX f0
X
l ®sij Pijf 0 f t~ ¡ l
f0
i2Ts j2(Ji \Jf 0 ) l¤ +Ssf t¡1~l¤
XX
X
i2T¹s j2(Ji \Jf )
l ® ¹sij Pijf f 0 t~l
(1)
8s; f; ~l ; t 2 Tl ; l¤ 2 L¤t¡1 ; ~l¤ 2 AH l¤ ~l
¤
l l l Fjft~ = Fjf t¡1~l¤ ¡1 + F Ejf t~l¡1 l¡1
8f; j 2 Jf ; l; ~l¡1 ; t 2 Tl ; l¤ 2 L¤t¡1 ; ~l¤ ¡1 2 AH l¤ ¡1;~l¡1 l L l l U Vjf t~l¡1 F Ejf t · F SEjft~l¡1 · Vjf t~l¡1 F Ejf t l ¯jf Fjf t~l¡1 ·
XX
8f; j 2 Jf ; l; ~l¡1 ; t 2 Tl
(2) (3)
l l ijff 0 Pijf f 0 t~l · Fjf t~l¡1
f 0 i2Ij
(4)
8f; j 2 Jf ; l; ~l ; t 2 Tl ; ~l¡1 2 AH l¡1;~l
X X X f0
l l Pijf 0 f t~ · Demsft~ l l
8s 2 f p; f 2 m; l; ~l ; t 2 Tl
(5)
i2ITs j2Ji
X X X
l Pijf f 0 t~l · Asft
8f 2 e; s 2 rmf ; l; ~l ; t 2 Tl
(6)
f 0 i2ITs j2Ji
Scheduling formulation. The scheduling formulation is an extension of STN representation 2 permitting scheduling in multiple facilities. Eqns.(7)-(8) are used for mass balances and assignment decisions, respectively. 0
¡pti +1 X ts =tsX i2Ji
t0s =ts
Wijf t0s · 1 8f; j 2 (Jbatch \ Jf ); ts
(7)
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Sschedsfts ¡ Sschedsf ts ¡1 = XX
XX
®sij Bijf ts ¡pti ¡
i2Ts j2Ji
® ¹ sij Bijfts + RMsf ts
8s; f; ts
(8)
i2T¹s j2Ji
Integration of decision levels. The integration between the models for design-planning and scheduling is carried out through Eqns.(9)-(11). Eq.(9) states that production allocated in equipment j is identical in both models. In Eq.(10) the availability of raw material is computed from received materials according to the planning formulation. Raw material availability is then included in the scheduling mass balance of Eq.(8). Scheduling equations may be applied in more than one planning period. The appropriate equations for incorporating scheduling in first planning period (t = 1) are next presented. l Pijff t~l =
X
Bijf ts
8f; j 2 (Jbatch \ Jf ); i 2 Ij ; t = 1; l 2 Lt ; ~l
(9)
ts
RMsf ts =
X XX f 0 6=f i2T¹s j2Ji
l ® ¹ sij Pijf 0 f t~ l
8s; f; ts = 1; t = 1; l 2 Lt ; ~l
(10)
Eq.(11) is included to rectify capacity availability in the planning model. This correction is done based on the scheduling model task assignment (Wijts). Eq.(11) should be merely applied to those equipments which are production bottlenecks. Additionally, it is worth to mention that it must be checked that market demand is not actually the bottleneck process in the planning period, where scheduling is performed. X
l ijf f Pijff t~l ·
XX
Wijfts pti
8f; j 2 (Jbottle \ Jf ); t > 1; l 2 Lt ; ~l
i2Ij ts
i2Ij
(11)
As it can be noticed, Eqs.(7)-(11) can be easily unplugged from the whole model in case the decision maker decides not to consider scheduling issues. 3.1.2. Financial formulation and objective function The financial side of the problem is tackled through the inclusion of a set of constraints that characterize economical issues, such as payments to providers, short and long term borrowing, pledging decisions, buying/selling of securities, fixed assets acquisition. Furthermore, the expected corporate value (E[CV]), which is calculated using the discounted-free-cash-flow method (DFCF) as described by Eqns.(12)-(13), is the objective function used in this work. The complete set of financial constraints as well as the equations that permit the integration between finances and process operations models can be found in the work of Puigjaner and Laínez 2.
E[CV ] =
X ~L
L
P~
L
³
L
L
DF CF~ ¡ N etDebtT ~ L
L
´ (12)
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Integrating SC Decision Levels in a MPC Framework
L
DF CFT ~
L
0 XX =@ t
X
¡
l2Lt ~l 2ADl~
L
+
l F CFt~ l l 1 + W ACCt~ l
SV~LL L
(1 + W ACCT ~ )
1 ¢t A
(13) 8~L
T
L
4. Illustrative example The special characteristics of the proposed approach are highlighted by solving the design-planning of a SC comprising three potential facility locations that can act as distribution and/or processing sites. A set of potential equipment technologies are assumed to be available for the processing sites. Five products (P1-P5) can be manufactured into seven different equipments types (TA to TG); final products can be transferred to three markets (M1-M3) even without passing through distribution centers. Batch products P4 and P5, which are produced in batch equipments TD-TG, follow the STN example presented in Kondili et al2. A time horizon of five years is considered. It is composed of twelve planning periods with a length of one month each. In this example, market demand, prices of final products and interest rates are regarded as uncertain factors which unfold every year. A scenario tree which contains 32 leaf nodes (scenarios) is considered. It takes 27,970 CPU seconds to reach a solution for the design problem with a 5% integrality gap on an Intel Core Duo 2 computer using the MIP solver of CPLEX. 1 0.9 0.8
Financial Risk (Ω)
0.7 0.6 0.5 0.4 0.3 0.2
Stochastic Integrated Approach Deterministic Sequential Approach
0.1 0 0.5
1
1.5
2
CV (m.u.)
2.5
3 8
x 10
Figure 2. Financial risk curve of Corporate Value
The two stage shrinking horizon approximation presented in the work of Balasubramanian and Grossmann4 was used to solve the multistage stochastic problem. In the first step of the control strategy, a design problem is solved. For the first month the scheduling model is taken into consideration. The problem has been also solved using a sequential manner (bi-level optimization) in order to compare it with the proposed approach. In this sequential manner the scheduling is not included when dealing with the design of the SC network. As shown in Fig. 2, the E[CV] and financial risk for the traditional approach seem to yield to better values. It should be noted that differences may arise when executing detailed scheduling in the sequential approach. Obviously, this fact occurs because of the aggregated capacity overestimation.
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Recalling this fact, the MPC algorithm has been repeated during 10 planning month periods. Here, the uncertainty is assumed to unveil every month. The results are shown in Fig. 3. It can be noticed that the proposed integrated approach gives higher accumulated free cash flows (which are a key element in corporate value calculation) than the sequential one after the implementation of scheduling. An improvement of 12.33% is achieved. 6
Accumulated value
15
x 10
Proposed approach Sequential approach
10
5
0
−5
1
2
3
4 5 6 7 Periods (month)
8
9
10
Figure 3. Accumulated value for both approaches
5. Final considerations and future work A means of integrating the three standard SC decision levels is presented. Moreover, a novel SC design-planning model that permits a simple integration with scheduling models is proposed. The results show that significant improvements can be gained when all of these decision levels are incorporated into a single model. Moreover, the absence of scheduling can lead to apparently better corporate value which does not correspond to real scenario; resulting in myopic decision making. A drawback of the proposed approach is the computational burden that is required to solve the stochastic integrated monolithic model. Future work will be focused on applying decomposition strategies for tackling the aforementioned problem.
Acknowledgments Financial support received from the "Generalitat de Catalunya" (FI grants) and Ministerio de Educación y Ciencia (FPU grants). European Community (projects PRISM-MRTN-CT-2004-512233) is fully appreciated. Besides, financial support from Xartap (I0898) and ToleranT (DPI2006-05673) projects is gratefully acknowledged.
References 1. I.E. Grossmann, 2005, Enterprise-wide optimization: A new frontier in process systems engineering. AICHE J., 28, 260-275 2. L. Puigjaner, J.M. Laínez, 2007, Capturing dynamics in integrated supply chain management, Comput. Chem. Eng. ,doi:10.1016/j.compchemeng.2007.10.003. 3. E. Kondili, C. Pantelides, R. Sargent, 1993, A general algorithm for short-term scheduling of batch operations-I: MILP formulation, Comput. Chem. Eng., 17, 211-227. 4. J. Balasubramanian, I.E. Grossmann, 2004, Approximation to multistage stochastic optimization in multiperiod batch plant scheduling under demand uncertainty. Ind. Eng. Chem. Res., 43, 3695-3713.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Hybrid strategy for real time optimization with feasibility driven for a large scale three-phase catalytic slurry reactor Delba N.C. Meloa, Adriano P. Marianoa, Eduardo C. Vasco de Toledob, Caliane B. B. Costaa and Rubens Maciel Filhoa a
Laboratory of Optimization, Design and Advanced Control (LOPCA).Faculty of Chemical Engineering; State University of Campinas (Unicamp). P.O. Box 6066 13081-970, Campinas, SP, Brazil.
[email protected] b Petrobras SA, Paulínia Refinery (REPLAN),Rodovia SP 332 - KM 132, P.O. Box 1, CP: 13140-000. Paulínia, SP- Brazil.
Abstract In this work it is proposed a suitable hybrid optimization algorithm built up with the association of global and local optimization methods. The adopted computer assisted approach is driven by the need for a global optimization method characterized by efficiency in terms of reduced computational time and efforts whereas being robust. The basic idea is to join the fast convergence properties of gradient-based optimization methods with the wide exploration ability of population-based ones, which makes the developed algorithm a useful tool in real-time applications. Since unavoidable disturbances are present during process operation, efficient optimization algorithms must be available to deal in an on-line fashion with high dimensional and non-linear processes. In the developed code, a Genetic Algorithm (GA) is designed to provide an estimate of the global optimum. Then, a local method of search (the Sequential Quadratic Programming, SQP) is used to improve this candidate solution. As case study, the optimization of a three-phase catalytic slurry hydrogenation reactor is considered. The optimization algorithm determines, in real time, the optimal operating condition, defined in terms of maximization of profit. This condition should then be used in an advanced control layer. The results of the hybrid approach are compared with those obtained only considering the micro-GA. The latter approach was able to, alone, solve the optimization problem, but using a large number of generations and, consequently, with higher computational time. The advantage of the hybrid algorithm are that fewer number of generations is employed prior to the SQP utilization. Thus, the new GA-SQP code was able to determine the final solution considerably faster than the isolated GA, reducing the number of functions evaluations for solutions when compared to the number required for the GA to stop the evolution. The hybrid algorithm drives to feasible solution translated into higher profits at reasonable computational costs, being identified as a robust optimization code, useful in real time optimization applications. Keywords: Real-time Optimization, Genetic Algorithm, Sequential Quadratic Programming, Hybrid Algorithms, Hydrogenation Reactors.
1. Introduction On-line optimization must cope with the variability of the process conditions, originated by disturbances that significantly affect the process economy.
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The present work introduces a hybrid optimization algorithm, GA-SQP, which joins an initial genetic search to a deterministic optimization algorithm (Sequential Quadratic Programming, SQP). This sort of hybrid algorithm is demanded for efficient online optimization of high dimensional and non-linear processes, in which purely deterministic optimization algorithms normally fail to drive the process to the global optimum. In order to illustrate the application of the developed hybrid algorithm, the optimization of a three-phase hydrogenation catalytic slurry reactor is considered. The study aims to determine the optimal operating conditions that lead to maximization of profit. Some researchers have combined various optimization algorithms to improve the search efficiency and computational effort, including evolutionary algorithms (EA), simulated annealing (SA), particle swarm optimization (PSO), ant colony optimization (ACO), hybrid PSO-SQP, hybrid GA-ACO. Nevertheless, the combination of the GA and SQP algorithms is reported only in a few works [1,2].
2. Case Study- Three-phase hydrogenation catalytic slurry reactor In order to show the efficiency and applicability of the hybrid optimization algorithm, the three-phase catalytic reactor, in which the hydrogenation of o-cresol to 2-methylcyclohexanol takes place, is considered. This process was modeled by Mariano et al. [3]. The resistances to mass and heat transfers at the gas–liquid and liquid–solid interfaces, the heat exchange with the coolant fluid and the consideration of the physicochemical properties variation, which impacts on the mass and heat-transfer coefficients, were considered. The rigorous model also included a multi-component flash to consider the effect of the phase change of the reacting medium on the reactor dynamic behavior, as well as an appropriate procedure of correction of the global heattransfer coefficient to represent the phase change of the refrigerant fluid. The model developed by Mariano et al. [3] is therefore here used as internal process model for the optimization routine, which seeks the optimal process conditions that drive the reactor to maximization of profit.
3. Proposed Hybrid Optimization The proposed hybrid optimization algorithm is built up with the association of global and local optimization methods. The basic idea is to join the fast convergence properties of gradient-based optimization methods with the well-known ability of populationbased ones, which makes the developed algorithm a useful tool in real-time applications. In the developed code, a Genetic Algorithm (GA) is designed to provide an estimate of the global optimum. Then, a local method of search (Sequential Quadratic Programming, SQP) is used to improve this candidate solution. Figure 1 illustrates the basic idea of the hybrid algorithm. The hybrid optimization starts with the GA, which executes all subroutines until the specified number generations; the algorithm then shifts to the SQP, which is a faster method.
Hybrid Strategy for Real Time Optimization with Feasibility Driven for a Large Scale Three-Phase Catalytic Slurry Reactor
485
Figure 1. Flowchart of the GA-SQP Hybrid Optimization Algorithm.
4. Optimization Problem Applied to the Case Study 4.1. Selection of the decision variables The decision variables used for the optimization of the reactor must be selected among the operating ones. After considering industry requirements, the effect of each of the operating variables on the objective function and the easiness of how these variables can be changed in the plant, the feed flow rate of hydrogen (FAo) and the reactor feed temperature (Tfo) were chosen as the decision ones. Thus the optimization routine searches for the values of FAo and Tfo that, with the current value of o-cresol flow rate, lead to maximal reactor profit. 4.2. Selection of objective function The optimization of any industrial process aims the profit maximization. Thus, the profit function is a natural choice as an objective function. The profit function, as outlined by Xiong and Jutan [4] and Sequeira et al. [5], can be calculated based on the selling price of the products and on the costs of raw materials, operation and energy. Then, in this work, the objective function, adapted to the multiphase reactor, is as follows: Profit = a*(FC) – b*(FAo-FA) – c*(FBo-FB)
(1)
where a is the selling price of the reaction product and b and c are the costs of raw materials; FA, FB and FC are the molar stationary flow rates of hydrogen, o-cresol and 2-methyl-cyclohexanol at the reactor exit, respectively and FAo and FBo are the flow rate of hydrogen and o-cresol in the feed. In Eq. (1), it is considered that there is a recycle of unreacted hydrogen and o-cresol. Since the remaining operating costs are fixed (salaries and others) and the energy cost related to the utilities can be considered negligible (the excess heat generated by the chemical reaction can be removed without significant cost [6]), the terms related to operating and energy costs do not appear in Eq. (1). It is important to stress that this work considers just the reactor itself in the hydrogenation plant and, therefore, the higher the o-cresol conversion, the greater the profit is expected to be. In this way, separation costs are not considered and, consequently, the profit here maximized is referred only to the reactor operation. Obviously, upstream and downstream operations have their own costs, which would decrease the calculated profits of Section 5.
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4.3. Optimization Problem The optimization problem considered is expressed by Eq. (2). Maximize Eq.(1) (FAo, Tfo) subject to model equations
(2)
In order to search for the optimum, the relations between variables must be given to an optimization algorithm. This is here provided by the model equations developed by Mariano et al. [3]. The model calculates all mass and heat transfers, besides the hydrogenation reaction rate. Since there are three phases (the catalysts is solid, the hydrogen is a gas and the o-cresol is liquid), both reactants must come to the solid pores, where the reaction takes place, and the unreacted reactants and the reaction product must then leave the catalyst particle. All these phenomena are accounted for by partial differential equations for mass and energy balances for each component in each phase. Since the feed flow rate of hydrogen and the reactants temperature are searched for, the upper and lower bounds stipulated for these variables in the optimization algorithms were selected according to the hydrogenation reaction stoichiometry and practical possible temperatures. For the optimizations here accomplished, the o-cresol feed rate was considered to be 1.29 kmol/h. In this way, Table 1 shows the lower and upper bounds of the considered decision variables. Table 1. Lower and upper bounds of the decision variables Variable
Lower bound 1.07 450.0
FAo (kmol/h) Tfo (K)
Upper bound 6.44 650.0
5. Results and Discussion 5.1. Optimization by Genetic Algorithm (GA) A binary micro genetic algorithm (GA) code was run for 50 generations with 5 individuals, totalizing 250 evaluations of the objective function. A maximum number of generations were used as stopping criterion in the genetic programming. The values for the crossover, the jump mutation and creep mutation probabilities (the genetic algorithm parameters) were previously optimized and the best ones were 0.5, 0.02 and 0.02, respectively. These values were the ones used in all optimization trials using the GA in this work. Table 2 brings the characteristics of the optimal operating point found solely by a micro-GA for the 50 generations, as well as the computational time demanded for the search (on a 2.8 GHz 768 Mb RAM AMD Athlon processor). Table 2. Optimal response found by micro-GA Optimal point and run characteristic
Profit (US$/h) o-cresol conversion (%) FAo (kmol/h) Tfo (K) Computational time (min)
Value 467.02 94.37 1.16 649.2 184
Hybrid Strategy for Real Time Optimization with Feasibility Driven for a Large Scale Three-Phase Catalytic Slurry Reactor
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Figure 2 shows the profit evolution for the best individual in each generation. This Figure shows how the solutions evolve in the 50 generations. Clearly the profit increases rapidly in the beginning of the search, but, after some generations, the rate of improvement gradually ceases, until almost no gain in the objective function is achieved in the last generations.
Figure 2. Evolution of the profit for each generation in a solely micro-GA optimization run
5.2. Hybrid optimization As it was observed in item 5.1, the GA was able to solve the problem after a large number of generations, consuming around 3h of CPU time, although it was also observed that the best fitness value does not change after a number of generations. In this way, a hybrid approach has been used, which couples GA with SQP. The GA procedure is used in the first stage to find a solution (i.e. an individual) within the attraction domain of the supposed global optimum. This solution is then used as initial guess for the SQP algorithm. The GA-SQP hybrid algorithm was built in order to run a micro-GA with the same code parameters as in section 5.1, except by the maximal number of generations, which was stipulated to 5. Afterwards, a SQP algorithm is used to improve the best individual found by the GA. Table 3 brings the optimal characteristics found by the hybrid algorithm, as well as the computational time the code demanded for the search. Table 3. Optimal response found by GA-SQP Optimal point and run characteristic
Profit (US$/h) o-cresol conversion (%) FAo (kmol/h) Tfo (K) Computational time (min)
Value 467.90 94.54 1.07 650.0 13
The hybrid structure was proved to be of high efficiency. First of all, it is easy to see, from Tables 2 and 3 that the profit and conversion are slightly greater for the optimal point found by the GA-SQP algorithm. Secondly, and very importantly, the computational time was significant lower for the hybrid algorithm, with scales compatible with real time applications for a supervisory control.
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The time demanded for an optimization algorithm to solve the problem is a consequence of the number of function evaluations it uses to come to the response. The micro-GA (section 5.1) evaluated the profit 250 times, each one for each individual of each generation. The GA-SQP, however, demanded just 31 function evaluations and, even so, achieved a better objective function value than the isolated micro-GA. The evolution of both algorithms (isolated GA and GA-SQP) during the search, as a function of objective function evaluations, is shown in Figure 3.
Figure 3. Trajectory of GA and GA-SQP methods towards the optimum point
6. Conclusions A hybrid optimization algorithm was developed joining a genetic search (GA) to the Sequential Quadratic Programming (SQP) algorithm. The developed code had its efficacy tested in the maximization of a hydrogenation reactor profit. Although no proof of convergence is available for GA-based codes in literature, the hybrid algorithm was able to solve the optimization problem, achieving a better optimal point within only 7% of the time demanded by a rigorous GA search. The computational time the GA-SQP algorithm solves the problem makes it a useful tool for real-time applications in a supervisory control structure.
Acknowledgements The authors acknowledge FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for the financial support given to this work.
References [1] B. Mansoornejad, N. Mostoufi and F. Jalali-Farahani, Chem. Eng., in Press (2007). [2] R. Faber, H. Arellano-Garcia and G. Wozny, 2007. A Hybrid Optimization Approach to parameter Estimation. In: V. Plesu and P. S. Agachi (Eds.), Proceedings of the 17th European Symposium on Computer Aided Process Engineering (ESCAPE 17), Bucharest, Romania. [3] A. P. Mariano, E. C.Vasco de Toledo, J. M. F. Silva, M. R. Wolf-Maciel and R. Maciel Filho, Comp. Chem. Eng., 29 (2005), 1369. [4] Q. Xiong, A. Jutan, Chem. Eng. Sci., 58 (2003), 3817. [5] S. E. Sequeira, M. Herrera, M. Graells and L. Puigjaner, Comp. Chem. Eng., 28 (2004), 661. [6] J. F. Forbes, T. E. Marlin and J. F. MacGregor, Comp. Chem. Eng., 18(6) (1994), 497.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Adaptive Control of the Simultaneous Saccharification - Fermentation Process from Starch to Ethanol Silvia Ochoaa, Velislava Lyubenovab, Jens-Uwe Repkea, Maya Ignatovab and Günter Woznya. a
Department of Process Dynamics and Operation, Technical University of Berlin, Sekr. KWT 9, Strasse 17. Juni 135, Berlin 10623, Germany. b Institute of Control and System Research, Bulgarian Academy of Sciences, Sofia, Bulgaria.
Abstract In this paper, a new adaptive control strategy for the fed-batch Simultaneous Saccharification - Fermentation Process from Starch to Ethanol (SSFSE) process is proposed in order to maintain the glucose concentration at a quasi-equilibrium state by feeding starch into the process only when the glucose production rate is lower than its consumption rate. By maintaining the equilibrium state for the glucose, it is possible to reach higher values for the ethanol production rate for a longer time; and therefore to increase the ethanol concentration along the process. As the adaptive controller requires online information about the glucose production and consumption rates, software sensors for them are developed. The difference between the estimated values for the consumption and production rates is considered as a control marker, which is used for determining the feeding profile of starch into the fermentor. Keywords: Adaptive Control, Soft sensors, Ethanol, Fed batch process.
1. Introduction During the past years, the demand for the production of bio-fuels has increased rapidly, especially in the bioethanol case, which currently is produced mostly from sugar cane and starch - containing raw materials. Traditionally, ethanol production from starchy materials is done in a sequential two-step process which includes two main stages: i) the enzymatic hydrolysis of starch to glucose (by means of the enzymes α- amylase and glucoamylase) and ii) the fermentation of glucose to ethanol (mostly by the action of yeast). A crucial drawback of the sequential (two-step) process is the slow hydrolysis rate (usually hours) due to the reduction of the enzymatic activity caused by an inhibitory effect when high sugar concentrations are present. A challenging perspective to overcome this problem and at the same time to increase the yield of the ethanol production process is to conduct the process in a one-step mode doing the simultaneous saccharification and fermentation of starch to ethanol (SSFSE) by means of recombinant strains (Altintas et al., 2002.). In this way, the ethanol production process from starch is more efficient not only in terms of saving overall production time but also in terms of reducing equipment costs. Due to these reasons, the SSFSE process seems to be a suitable alternative for bio-ethanol production at an industrial level. It is important to notice that as have been stated by Nakamura et al. (1997), by means of a fed-batch
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SSFSE process, the ethanol production can be enhanced when compared to a batch process. For all these reasons, in this work a novel adaptive control scheme for a fedbatch SSFSE process is proposed, which due to its simplicity is suitable for industrial applications.
2. Soft Sensors Development 2.1. Model for Control According to the well known General Dynamical Model Approach by Bastin and Dochain (1990), a model for the control of the process can be derived on the basis of a process reaction scheme. For the bio-ethanol production from starch by Saccharomyces cerevisiae, the reaction scheme can be assumed as shown in Figure 1. ϕ1 S ⎯⎯→ G
ϕ2 G ⎯⎯→ X + Enz
ϕ3 G ⎯⎯→ E
Figure 1. Reaction scheme for the bio-ethanol process.
The model for control for the fed batch process is given by (Lyubenova et al; 2007): dS F = −ϕ1 + [S − Sin ] V dt
(1)
dG F = k1ϕ1 − k2ϕ 2 − k3ϕ 3 − G V dt
(2)
dX F = ϕ2 − X V dt
(3)
dE F = ϕ3 − E V dt
(4)
dEnz F = k4ϕ 2 − Enz V dt
(5)
dV =F dt
(6)
Where S, G, X, E and Enz are respectively the starch, glucose, cells, ethanol and enzyme concentrations inside the reactor, Sin is the starch concentration on the feed, F is the feed flow rate, V is the volume of liquid in the fermentor and ϕ1, ϕ2, ϕ3 represent the reaction rates for starch degradation, cells growth and ethanol production, respectively. The unstructured model presented in (Ochoa et al., 2007) is used here as the “real” plant. The ki (for i=1 to 4) kinetic parameters of the model for control were identified by an optimization procedure given in Mazouni et al. (2004), using as error index the mean square error between the state variables of the unstructured model and the model for control. 2.2. Soft Sensors of Glucose Production and Consumption rates: As the main purpose of this paper is to implement an adaptive control strategy for controlling the SSFSE process by means of starch feeding only when the glucose consumption rate is higher than its production rate; it is necessary to follow these two rates on line. Unfortunately, such kind of sensors are not available and therefore, soft
Adaptive Control of the SSFSE Process
491
sensors must be developed. For that purpose, in the following it is assumed that on-line starch and glucose concentrations measurements are available. 2.2.1. Soft sensor of glucose production rate The software sensor for ϕ1 is an observer-based estimator with the following structure:
(
dSˆ F F = −ϕˆ1 − S m + Sin + C1 Sm − Sˆ V V dt
(
dϕˆ1 = C2 S m − Sˆ dt
)
(7)
)
(8)
where C1 and C2 are tuning parameters and Sm is the measurement value for the starch considering white noise (ε). Glucose production rate θ1 is estimated using the first term of the right hand side of equation (2), that is: ∧
∧
θ1 = k1 ϕ1
(9)
2.2.2. Soft sensor of glucose consumption rate By observing equation (2), it can be seen that glucose consumption rate θ2 is given by: (10)
θ 2 = k2ϕ2 + k3ϕ3
Where an estimator of θ2 can be obtained by:
(
dGˆ ∧ ∧ F = θ1 − θ 2 − Gm + C3 Gm − Gˆ V dt ∧
(
d θ2 = C4 Gm − Gˆ dt
)
(11)
)
(12)
where C3 and C4 are tuning parameters and Gm is the measurement value for the glucose considering white noise. The four tuning parameters are found using the procedure described in Ignatova et al. (2007). For the present case, the expressions shown in Figure 2 are applied. C1 = 2ξ
C3 = 2ξ
2
m11s 2m21s
C2 =
C1 4ξ 2
m11g
C4 =
C3 4ξ 2
2m21g
2
Figure 2. Tuning Parameters for the Estimators (Ignatova et al. 2007) ∧
∧
where m11s and m21s are the upper bounds of d ϕ1/ dt and d θ 2 / dt ; m21s and m21g are the upper bounds of additive noise for starch and glucose measurements respectively, and ξ is a damping coefficient taken as an usual value of 0.99 (Bastin and Dochain, 1990). The white noise signals, ε , simulate measurement noises at standard deviation of 5% of the mean of S and G concentrations. The optimal values for the tuning parameters Ci are C1=1.23, C2=0.386, C3=4.427, C4=5; using m11s=0.35, m21s=1.3, m11g=0.45, and m21g=0.1. In Figure 3, the glucose consumption and production rates soft sensors are compared to the values obtained in the real plant (unstructured model); it can be seen that the observers track adequately the behavior of the true values.
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Glucose Production /Comsumption Rates (g/lh)
0.5 Production (Real) Production (Soft Sensor) Consumption (Soft Sensor) Consuption (Real)
0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5
0
50
100 Time (h)
150
200
Figure 3. Soft Sensors Vs Real Plant (Unstructured Model)
3. Adaptive Controller Usually it is claimed that a fed-batch process (when compared to a batch) offers the main advantage of having a dilution ratio that is used as a degree of freedom for control purposes. However, it is not straightforward to calculate a suitable dilution rate (or a feeding profile), because when this is too high, the concentration of the metabolite of interest can be decreased due to the dilution effect. Additionally, when the dilution rate is too low, it is possible that the substrate fed into the process be not enough to fulfill the requirements for cell growth, cells maintenance and product formation. Therefore, in this paper, it is proposed to calculate the dilution rate as a function of the glucose production and consumption rates; in order to keep a balance between them. Besides, we propose to feed starch into the process only when the process really needs it, that is, when the glucose production rate is lower than its consumption rate. For that purpose, in this work a marker is used as a switch to decide between batch (without feeding) or fed batch operation. The marker, used in the adaptive control scheme proposed in Figure 4, is defined as follows: ∧
∧
Δ = θ1− θ 2
(13)
The marker is the difference between the glucose production and consumption rates, ∧
∧
where θ1 ,θ 2 are the corresponding values predicted by the software sensors presented in section 2. As mentioned by Kapadi and Gudi (2004), usually it is considered that the feeding stream to the process contains not only starch but also glucose (∼15% of the starch concentration), due to the previous autoclaving of the starch. Therefore, the mass balance for the glucose should consider this term as follows: d (GV ) = g input + g produced − g depleted dt
(14)
dG F (Gin − G ) = +Δ dt V
(15)
Where g represent the glucose mass flow rates (fed into the process, produced or consumed) and Gin is the glucose concentration on the feed stream. Assuming that after an initial batch period, the glucose concentration in the fermentor reaches an equilibrium state, we have:
Adaptive Control of the SSFSE Process
F =−
493
Δ ⋅V Gin − G
(16)
Furthermore, after the initial batch period Gin>>G; therefore, the control law for calculating the feeding rate of starch into the fermentor is given by: F ≈−
Δ ⋅V = − KVΔ Gin
(17)
Equation 17 shows the control law that should be applied for maintaining the glucose concentration in an equilibrium state reaching a balance between the glucose production and consumption rates. By analyzing equation 17, it is possible to see that the dilution rate will be calculated by means of a proportional feedback controller in which the feedback error is taken as the deviation between both rates. Of course, control law (17) will present offset due to the fact that an integral action is not taken into account as part of the control calculations, but as the idea of this paper is to present a simple and easy way to implement the control law, we decided to allow the offset error. In Figure 4 it is shown the adaptive control scheme proposed in this work for controlling the SSFSE process. S F
Control Algorithm Adaptive Controller
Δ
Process (unstructured model)
-θ2
θ1
Estimators
+ε +ε
G
Sm Gm
Figure 4. Adaptive control scheme of the SSFSE process
It is important to remark that the control scheme proposed in Figure 4 is catalogued as adaptive (according to the definition by Bastin and Dochain (1990)), because it has the potential to adapt itself (due to the online estimations given by the soft sensors) to variations in the kinetics of the process.
4. Example: Adaptive Control of the SSFSE process The control scheme shown in Figure 4 was applied to the SSFSE process using the fed batch version of the unstructured model proposed in Ochoa et al. (2007) as the object for control. Simulations of starch and glucose concentrations are corrupted by additive noise ε. These white noise signals, simulate measurement noises at 5% of the standard deviation for the mean values of both S and G concentrations. As stated before, the control law (17) will be applied only when the marker is negative; therefore, the control algorithm block is expressed as follows: if Δ ≥ 0 0 F =® ¯− KVΔ if Δ < 0
(18)
In Figure 5 are shown the simulation results for the ethanol concentration and the ethanol growth rate for the fed batch SSFSE process using a starch input concentration of 50g/l (containing 7.5g/l of glucose available due to autoclaving), applying the adaptive control scheme (Figure 4). Besides, the fed batch results are compared to those for the batch process, which was open loop simulated using the model given in Ochoa et al. (2007). It can be seen that the ethanol concentration (and therefore the productivity) for the controlled fed batch process is higher than the ethanol concentration reached
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under batch operation. Furthermore, it is important to remark that the ethanol production rate in the fed batch process can be kept at higher values than for the batch, assuring a more productive process. 18
0.4
16
0.35
Ethanol Production Rate (g/lh)
14
Ethanol (g/l)
12
Fed Batch Batch
0.3
0.25
10 8
0.2
0.15
6 Fed Batch Batch
4
0
0.1
0.05
2
0
50
100
150 Time (h)
200
250
0
0
50
100
150
200
250
Time (h)
Figure 5. Ethanol concentration (left side) and ethanol production rate (right side): controlled Fed batch vs. Batch.
5. Conclusions In this paper, an adaptive control strategy for the fed-batch SSFSE process was proposed, convergence and stability will be analyzed in a future work. The process is monitored by means of software sensors for glucose consumption and production rates. The difference between the estimated values for the consumption and production rates is considered as a control marker, which is used for i) switching from the batch to the fed-batch phase automatically, and ii) for determining the magnitude of the input flow required to maintain the desired value for the glucose. By maintaining that quasiequilibrium state, it was possible to avoid a fast decrease in the ethanol production rate, and therefore to continue producing ethanol for a longer time, improving the productivity of the process.
References M. Altintas, B. Kirdar, Z. I. Önsan and K. Ülgen. 2002, Cybernetic Modelling of growth and ethanol production in a recombinant Saccharomyces cerevisiae strain secreting a bifunctional fusion protein, Process Biochem., 37, 1439-1445. G. Bastin and D. Dochain. 1990. On-line estimation and adaptive control of bioreactors. M. Ignatova, V. Lyubenova, M.R. García and C. Vilas. 2007, Indirect adaptive linearizing control of a class of bioprocesses – Estimator tuning procedure, Journal of Process Control, In Press. M Kapadi and R Gudi. 2004. Optimal Control of Fed-batch Fermentation Involving Multiple Feeds using Differential Evolution. Process Biochemistry 39, 1709-1721. V. Lyubenova, S. Ochoa, J-U. Repke, M. Ignatova and G. Wozny. 2007, Control of one Stage Bio Ethanol Production by Recombinant Strain, Biotechnol. & Biotechnol. Eq. D. Mazouni, M. Ignatova, and J. Harmand. 2004, A simple mass balance model for biological sequencing batch reactors used for carbon and nitrogen removal, Proceedings of the International IFAC Workshop Decom-TT’2004 Automatic Systems for Building the Infrastructure in Developing Countries Regional and Global Aspects, 283–288. Y. Nakamura, F. Kobayashi, M. Ohnaga and T. Sawada. 1997. Alcohol Fermentation of Starch by a Genetic Recombinant Yeast Having Glucoamylase Activity. Biotechnology and Bioengineering, 53, 21–25. S. Ochoa, A. Yoo, J-U. Repke, G. Wozny and D.R. Yang. 2007, Modeling and Parameter Identification of the Simultaneous Saccharification-Fermentation Process for Ethanol Production, Biotechnol. Prog., 23, 1454-1462.
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Advanced Control Monitoring in Petrobras’ Refineries: Quantifying Economic Gains on a RealTime Basis Rafael Pinotti,a Antonio Carlos Zanin,a Lincoln Fernando Lautenschlager Moroa a
Petrobras, Refining Technology, Optimization,Av. República do Chile, 65, Sala 2102, Centro, Rio de Janeiro - 20031-912 - Brazil Abstract In this paper we describe how Petrobras’ engineers have been using information from real-time databases in order to continuously monitor the performance of advanced control applications, including the calculation of economic gains. The monitoring uses formulas that take into account feed flow rates, targets calculated by the optimization layer of multivariable control, controlled variables upper and lower limits and other parameters. The economic benefits are based on the degrees of freedom and the active constraints at the steady state predicted by the linear model embedded in the controller. In order to improve the current monitoring, parameters dealing with process variability will be incorporated in the formulas. By doing this, it will be also possible to quantify external disturbances that affect the performance of the advanced control systems and identify regulatory control problems.
Keywords: advanced control monitoring, industrial automation, refining industry, online optimization
1. Introduction The Advanced Control Monitoring in Petrobras’ refineries serves a twofold objective: to evaluate the efficiency of the installed applications, and to manage the engineering staff aiming at the improvement of this efficiency, which can be translated through adequate formulas into economic gains. The fact that Solomon’s 2006 Worldwide Refining APC/ Automation Performance Analysis placed Petrobras in the second quartile, and one particular refinery in the first quartile, shows us not only that we have managed well the applications and the several systems that support them, such as DCS and data banks, but also that there is still room for improvement. Advanced Control applications are part of the broader context of Industrial Automation, a multidisciplinary activity which has evolved for more than twenty years in our refineries, so it seems fit to start with a brief history of Industrial Automation in the Downstream area of the company. This is dealt with in section 2. Section 3 explores the details of the monitoring process and the plans to develop a more comprehensive approach by adding measures of
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process variability. Section 4 shows the results obtained by the management of advanced control applications, and section 5 summarizes the main conclusions. 2. Industrial Automation in Downstream Nowadays every Brazilian oil refinery has at least one operating advanced control application. This is the result of many years of investment in hardware, software and the development of human resources. Additionally, real time optimization systems are being successfully implemented in many units. Industrial Automation history in the Petrobras’ Downstream area can be traced back to 1986, when the company decided to replace old analog instrumentation by digital control systems (DCS), which, given the sheer size of the refining park, with 10 oil refineries, demanded a considerable investment. A second stage was initiated in 1989, with the issue of a general plan, focusing on the rate of return of investments in industrial automation. It was acknowledged then that this return would only be fully realized through the implementation of systems aiming the real time optimization of process units. This situation prompted a significant investment in: • An array of technical training to the technical staff, ranging from specialization to doctoral work, in order to provide the company with high level human resources; • Development of Multivariable Predictive Control (MPC) algorithms [1] and inferences, through a gradual absorption of technology; • Widespread installation of automation systems, including advanced control, real time optimization, blending, etc. A third stage has been initiated around the year 2000, focusing on the effectiveness of the installed applications. In order to guarantee such effectiveness a series of actions has been planned and executed: • Development of a benefits evaluation methodology for each kind of optimization application [2]; • Rigorous monitoring of the actual results; • Technical assistance to solve problems that negatively impact the applications performance; • Continuous improvement of the technology and software; • High level training to improve the technical skills of users and developers; • An extensive optimization program, involving the mathematical modeling of all process units and the use of these models to define the operating targets. 3. Advanced Control Monitoring The main benefits that can be obtained from advanced control are:
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• • • • • •
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Improvement in product quality; Increased yields of the most valuable products; Increase in unit feed flow rate; Energy savings; Improved operational stability; Increased unit operational factor by protecting the process from violating operational constraints.
It is usually assumed that an advanced control application will reduce the standard deviation of controlled variables by at least 50%. This allows the controller to move the controlled variables closer to the constraints, without increasing the probability of off-spec production, as illustrated in figure 1. Cutler and Perry [3] state that available benefits for on-line optimization plus advanced control can amount to 6-10% of the added value of a given process. The basis for the monitoring methodology is the fact that the economic benefits from the advanced control are directly associated with the activation of process constraints within the operating region, that is, a good control system pushes as many as possible controlled variables to their limits, although it is not always true due to the nonlinearities involved. Thus, each control application calculates an index, defined as:
PCAT =
Nactcontr × 100 Nman
Figure 1 – Illustration of Advanced Control Benefits
Where PCAT stands for Percent of Active Controlled Variables, while Nactcontr is the number of active controlled variables and Nman is the total number of manipulated variables. However, this formula has to be corrected with a factor PCATopt (Optimum PCAT) due to the fact that not every manipulated variable
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corresponds to a degree of freedom and that disturbances in the unit prevent the controller from operating continuously at constraints. So, the economic benefits from the application are calculated as follows:
$CAV = $ Benefit ×
PCAT PCATopt
Where $CAV is the economic benefit obtained and $Benefit is the standard benefit for the unit, drawn from literature or from process data before and after advanced control implementation. Both have units of dollars per unit feed flow rate. The Optimum PCAT is defined as:
PCATopt =
fd × PNactcontr × 100 Nman
Where fd is a factor (smaller than 1) used to compensate for unit disturbances, and PNactcontr is the potential number of active controlled variables, which is defined according to the optimization objectives and the controller potential for effective action upon these variables. 4. Results The Advanced Control Performance Index for each application is defined by the fraction PCAT/PCATopt [2], where PCATopt is defined caseby-case. The Performance Index for a whole refinery is calculated as a weighted average of the application indexes, with each weight corresponding to the application economic benefit. Although the Performance Index has oscillated substantially for some refineries, the general average has been fairly stable above 80%, with a slight tendency for increase. This methodology can pinpoint applications that demand technical assistance, but a thorough performance assessment requires a more detailed analysis. More specifically, the current methodology has the following disadvantages: it offers only a macroscopic analysis of the applications; it does not give a statistical distribution of the active variables, which is of great value for the improvement of the operating systems; it does not assess the operational stability of the process. So, a computational solution has been developed to provide valuable information on the statistical distribution of active variables, both controlled and manipulated. It consists, as shown in figure 2, of a Visual Basic tool, which gets data from the process historian and from the MPC configuration database. The tool can generate reports in Excel format. Figure 3 shows a a general view of the controlled (CV) and manipulated (MV) variables. Figure 4
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shows a VB display for the end point of gasoline, a very important product quality parameter and an advanced control controlled variable as well. As for the operational stability of the process, Petrobras has recently developed another VB tool, which also generates excel reports. The mathematical basis for the measurement of operational stability is focused on the standard deviation of process variables related to product quality (mainly product draw temperatures from fractionators). Petrobras joined the group of oil companies that participated in Solomon’s 2006 Worldwide Refining APC/ Automation Performance Analysis, and the final report ranked Petrobras, in the second quartile, with one particular refinery in the first quartile.
Figure 2 – Computational Tools for Advanced Control Monitoring
Figure 3 – VB display of a general view of the variables
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5. Conclusions The advanced control applications installed in Petrobras’ refineries are part of an Industrial Automation effort that goes back more than twenty years. The recent focus on the monitoring of these applications in order to guarantee the realization of their full economic benefit has prompted the development of a useful methodology, which shows that we are now reaping more than 80% of the potential benefits, on average. However, this methodology has a macroscopic nature.
Figure 4 – VB display of the gasoline ASTM end point New tools have been recently developed allowing a thorough analysis of each application in terms of statistical distribution of active variables and of process variability. The last Solomon APC Study has evidenced the fact that the company has a good position among the leading oil companies with respect of advanced process control and automation performance in general. References 1. L. F. L. Moro, D. Odloak, 1995, “Constrained multivariable control of fluid catalytic cracking converters”. Journal of Process Control, v.5, n.1, p.29-39. 2. A. C. Zanin, L. F. L. Moro, 2004, “Gestão da Automação Industrial no Refino”. Rio Oil & Gas Expo and Conference. 3. C. R. Cutler, R. T. Perry, 1983, “Real time optimization with multivariable control is required to maximize profits”. Computers and Chemical Engineering, v.7, n.5, p.663-667.
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Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation Diego Martinez Prata, José Carlos Pinto, Enrique Luis Lima Programa de Engenharia Química/COPPE/UFRJ, Cidade Universitária, Rio de Janeiro - CP 68502, CEP 21945-970, Brasil.
Abstract This paper presents a comparative performance analysis of various robust estimators used for nonlinear dynamic data reconciliation process subject to gross errors. Robust estimators based on cost functions derived from robust probability theory reduce the effect of gross errors on the reconciled data, avoiding the traditional iterative requirement procedures. The following robust probability functions were compared in this paper: Cauchy, Fair, Hampel, Logistic, Lorentzian, Normal Contaminated and Welsch. As a benchmark for this study it was adopted a nonlinear CSTR frequently reported in the process data reconciliation literature. The comparative analysis was based on the ability of the reconciliation approaches for reducing gross errors effect. Although the presence of constant biases has represented a problem for all the analyzed estimators, Welsch and Lorentzian cost functions, in this order, have shown better global performance. Keywords: Nonlinear dynamic data reconciliation, robust estimation and gross error.
1. Introduction Nowadays, data reconciliation (DR) represents an important step for many engineering activities in chemical processes as for example real time optimization and control implementations. It adjusts the measurement data, usually assumed associated to normally distributed random errors, to satisfy process constraints. However, to obtain satisfactory estimates, the negative influence of less frequently gross errors should be eliminated. This class of errors can be considered measurements that do not follow the statistical distribution of the bulk of the data. Gross errors can be divided in two classes: outliers and bias. The first class may be considered to include some abnormal behavior of measurement values as for example process leaks or malfunctioning instruments. The second class refers to the situation in which the measurement values are systematically too high or too low. A number of approaches have been proposed to deal with gross errors, mainly related to their detection and elimination. The traditional methods include serial elimination, compensation, and combinatorial ones, however these approaches are based on the assumption that the measurements are normally (Gaussian) distributed in which case Corresponding author:
[email protected] 502
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Weighted Least Squares (WLS) is the maximum likelihood estimator. As gross errors do not satisfy this ideal assumption an iterative sequential procedure is necessary for gross error detection and elimination, increasing computational effort. Tjoa and Biegler (1991) proved that using the Contaminated Normal estimator instead of the WLS one, any outlier present in the measurements could be replaced with reconciled values, without requiring iterative detection and elimination procedures. Johnston and Kramer (1995) reported the feasibility and better performance of robust estimators when used to cope with DR problems in the presence of gross errors. Subsequently, different types of robust estimators and their performance on DR were reported (Table 1). These studies have shown the potential of robust statistics to perform DR in the presence of gross errors, resulting in robust estimators that are insensitive to deviations from ideal assumptions, tending to look at the bulk of the measured data and ignoring atypical values. Table 1 Examples of Robust Estimators used for Data Reconciliation
Author (Year) Tjoa and Biegler (1991) Johnston and Kramer (1995) Zhang et al. (1995)R Albuquerque and Biegler (1996) D Chen et al. (1998)R Bourouis et al. (1998) R Arora and Biegler (2001) D Özyurt and Pike (2004) R Wongrat et al. (2005) Zhou et al. (2006) R
Estimator Applied Normal Contaminated Normal Contaminated and Lorenzian Normal Contaminated Normal Contaminated and Fair Fair and Lorenzian Normal Contaminated Hampel Normal Contaminated, Cauchy, Fair, Logistic, Lorenzian and Hampel Hampel Huber
Works applied on real plant data (steady state conditions).
D
Works applied in NDDR.
In our knowledge robust estimators have not been applied in nonlinear dynamic real plant data yet. The first comparative study among some robust estimators in DR has been presented by Özyurt and Pike (2004). They conclude that the estimators based on Cauchy and Hampel distributions give promising results, however did not consider dynamic systems. Other earlier studied has been accomplished by Basu and Paliwal (1989) in autoregressive parameter robust estimation issues, showing that for their case the Welsch estimator produced the best results. This work presents a comparative performance analysis among some robust estimators (all estimators reported by Özyurt and Pike, 2004, and Welsch estimator) for nonlinear dynamic data reconciliation (NDDR in the presence of gross errors.
Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation 503
2. Problem formulation The most important robust estimators for data reconciliation belong to the class of M-estimators, which are generalizations of the maximum likelihood estimator. Assuming uncorrelated measurement data their covariance matrix becomes diagonal and the generalized DR problem has the form, § z yi min ¦ U ¨ i i © Vi s. t. ª dy t º , y t » f« ¬ dt ¼
b ¬ª y t ¼º
· ¸ min ¦ U ([i ) i ¹
(01)
0 (02)
0
g ª¬ y t º¼ t 0 where ȡ is any reasonable monotone function used for DR formulation, ıi and ȟi are, respectively, the standard deviation and the standard error of the discrete measured variable zi, y is the vector of estimated functions yi (reconciled measurements, model parameters and non-measured variables), f is a vector of dynamic constraints, h and g are, respectively, vectors of equality and inequality algebraic constraints. As an example, using the generalized formulation the ȡ functions for the weighted least squares and Welsh estimators take the following forms, WLS
UWLS ([ )
1 2 [i 2
Welsch
UW ([ , cW )
cW2 2
° ª § [ · 2 º ½° « ¨ i ¸ » ¾ 1 exp ® «¬ © cW ¹ »¼ ¿° °¯
(03)
(04)
where cW is a tuning parameter related to asymptotic efficiency (Rey,1988). Methods used to measure the robustness of an estimator involve an influence function (IF) that can be summarized by the effect of an observation on the estimates obtained (Arora and Biegler, 2001). The Welsch M-estimator introduced by Dennis and Welsch (1976) is a soft redescending estimator that, as the Cauchy estimator, presents an IF asymptotically approaching zero for large |ȟ|. The 95% asymptotic efficiency on the standard normal distribution is obtained with the tuning constant cW = 2.9846. Figures 1 and 2 show, respectively, the effect of the standard error on the standardized ȡ functions and influence functions for the WLS and Welsch
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estimators. It can be observed in both figures that the robust estimator is much less influenced by large errors. 50
4
40 Influence Functions
ȡ functions
3 30
20
2
1 10
0 -10
0 -5
0
5
Standard Error
Fig. 1. ȡ: WLS (---) and Welsch (ņ).
10
0
5
10
15
20
Standard Error
Fig. 2. IF: WLS (---) and Welsch (ņ).
Several strategies have been proposed to solve constrained nonlinear dynamic programming problems (Biegler and Grossman, 2004). In this work a sequential strategy is applied to a time moving window (size = 5). For every sample time the differential equations of the dynamic constraints and the nonlinear programming optimization problem are solved sequentially using the measured data over the window until convergence is reached. The optimization problem is solved using the Gauss-Newton based solver ESTIMA (Noronha et al., 1993). 3. Illustration example
The performance of the robust estimators has been tested on the same CSTR used by Liebman et al. (1992) where the four variables in the system were assumed to be measured. The two input variables are the feed concentration and temperature while the two state variables are the output concentration and temperature. Measurements for both state and input variables were simulated at time steps of 1 (scaled time value corresponding to 2.5 s) adding Gaussian noise with a standard deviation of 5% of the reference values (see Liebman et al., 1992) to the “true” values obtained from the numerical integration of the reactor dynamic model. Same outliers and a bias were added to the simulated measurements. The simulation was initialized at a scaled steady state operation point (feed concentration = 6.5, feed temperature = 3.5, output concentration = 0.1531 and output temperature = 4.6091). At time step 30 the feed concentration was stepped to 7.5. Due to space limitations, only results of output concentration and temperature for the WLS and Welsch estimators are presented in Figures 3, 4, 5 and 6. The symbols (ņ), (ż) and (Ɣ) represent the “true”, simulated and reconciled data, respectively. The output temperatures plotted have been magnified to emphasize the effect of the bias on their estimates.
Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation 505
5.20
0.17
Output Temperature (scaled)
Output Concentration (scaled)
0.19
Bias
0.15 0.13 0.11 0.09 0.07 Outlier
0.05 0.03
5.10 5.00 4.90 4.80 4.70 4.60 4.50 4.40
0
20
40 60 Sampling Instant (scaled)
80
100
70
80 85 90 Sampling Instant (sacled)
95
100
Fig. 4. WLS: Output Temperature.
Fig. 3. WLS: Output Concentration. 5.20
0.19 0.17
Output temperature (Scaled)
Output Concentration (scaled)
75
Bias
0.15 0.13 0.11 0.09 0.07 Outlier
0.05
5.10 5.00 4.90 4.80 4.70 4.60 4.50 4.40
0.03 0
20
40 60 Sampling Instant (scaled)
80
Fig. 5. Welsch: Output Concentration.
100
70
75
80 85 90 Sampling Instant (scaled)
95
100
Fig. 6. Welsch: Output Temperature.
Comparing Figures 3 and 5 it can be seen that in the presence of an outlier in sampling time 25 the reconciled output concentrations using the robust Welsch estimator are better that the ones using the WLS estimator, which presents smearing values around this sampling time. However, even a robust estimator can result in biased estimates in the presence of a bias as can be seen around sampling times 80-82. In this work the time varying window always corresponds to measured values. However if the time varying window is built with the measured values at the current sample time and the already reconciled values at past sample times the effect of a bias will be minimized. Figures 4 and 6 show the effect of bias measurements in the reconciled values of the output temperature, and again the WLS estimator results in worst estimates. Looking for a fair comparison among the estimators it was used the TER (Total Error Reduction) criteria proposed by Serth et al. (1987) that can be applicable when the “true” values are known. Table 2 summarizes the results obtained and shows best results for the Welsch and Lorentzian estimators. Table 2. TER analysis results for the estimators studied.
Estimator Applied WLS Normal Contaminated Cauchy Fair Hampel Logistic Lorentzian Welsch
Output Concentration 0.2040 0.2885 0.3667 0.4072 0.3953 0.3633 0.4290 0.4724
Output Temperature 0.9501 0.9635 0.9631 0.9632 0.9622 0.9628 0.9655 0.9657
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4. Conclusions
In this work a comparative analysis of the capacity of robust estimators to reduce the negative effect of gross errors on nonlinear dynamic data reconciliation was accomplished. The results obtained have shown that among the studied cases the Welsch and Lorentzian robust estimators produced better reconciled values, but they also have shown that, although the robust estimators were more efficient in reducing the effect of biases, this problem still deserves more investigation. References Albuquerque, J. S., Biegler, L. T., 1996. Data Reconciliation and Gross-Error Detection for Dynamic Systems. AIChE J. 42, 2841. Arora, N., Biegler, L. T., 2001. Redescending estimators for Data Reconciliation and Parameter Estimation. Comput. Chem. Eng. 25, 1585. Basu, A., Paliwal, K. K., 1989. Robust M-Estimates and Generalized M-estimates for Autoregressive Parameter Estimation. TENCON 89, 4th IEEE region 10 Int. conf., Bombay. Biegler, L. T., Grossmann, I. E., 2004. Retrospective on optimization. Comput. Chem. Eng., 28, 1169. Bourouis, M., Pibouleau, L., Floquet, P., et al., 1998. Simulation and data validation in multistage flash desalination plants. Desalination. 115, 1. Chen, X., Pike, R. W., Hertwing, T. A., Hopper, J. R., 1998. Optimal Implementation of On-Line Optimization. Comput. Chem. Eng. 22, S435. Dennis, J. E., Welsch, R. E., 1976. Techniques for Nonlinear Least Squares and Robust Regression. Proc. Amer. Statist. Ass. 83-87. Johnson, L. P. M., Kramer, M. A., 1995. Maximum Likelihood Data Rectification: Steady-State Systems. AIChE J. 41, 2415. Liebman, M. J., Edgar, T. F., Lasdon, L. S., 1992. Efficient Data Reconciliation and Estimation for Dynamic Processes Using Nonlinear Programming Techniques. Comput. Chem. Eng. 16, 963. Noronha, F.B., Pinto, J.C., Monteiro, J.L., et al.. 1993. Um Pacote Computacional para Estimação de Parâmetros e Projeto de Experimentos, Technical Report, PEQ/COPPE/UFRJ. Özyurt, D. B., Pike, R. W., 2004. Theory and practice of simultaneous data reconciliation and gross error detection for chemical process. Comput. Chem. Eng. 28, 381. Rey, W. J. J., 1983. Introduction to Robust and Quasi-Robust Statistical Methods. SpringerVerlang, Berlin/ new York. Serth, R. W., Valero, C. M., Heenan, W. A., 1987. Detection of gross errors in nonlinearly constrained data: a case study. Chem. Eng. Commun. 51, 89. Tjoa, I. B., Biegler, L. T., 1991. Simultaneous Strategy for Data Reconciliation and Gross Error Detection of Nonlinear Systems. Comput. Chem. Eng. 15, 679. Wongrat, M., Srinophakun, T. Srinophakun, P., 2005. Modified genetic algorithm for nonlinear data reconciliation. Comput. Chem. Eng. 29, 1059. Zhang, Z., Pike, R.W., Herting, T., 1995. Source reduction from chemical plants using on-line optimization. Waste Management. 15, 183. Zhou, L., Su, H., Chu, J., 2006. A new method to solve robust data reconciliation in nonlinear process. Chinese J. Chem. Eng. 14, 357.
Acknowledgements The authors would like to thank CNPq and CAPES for financial support.
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State estimation for dynamic prediction of hydrate formation in oil and gas production systems J. Rodriguez Perez, C.S. Adjiman, C.D. Immanuel Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K.
Abstract Since oil and gas production is moving to deeper waters, subsea pipelines are being subjected to higher pressures and lower temperatures. Under such conditions, the formation of hydrates is promoted. Hydrates are solid, non-flowing compounds of gas and water whose formation can cause line blockages, with the consequent economical losses and safety risks. The increasing hydrate formation propensity suggests the necessity to predict the possibility of hydrate formation in on-line operation so as to take preventive control actions and thereby provide flow assurance. Although a detailed dynamic model will enable the prediction of the possibility of hydrate formation, model inaccuracies and process disturbances will make this prediction less accurate. The usage of key available measurements will enable to address these disadvantages. The aim of this paper is to develop a combined state and parameter estimator for this process, by combining a dynamic model with available measurements. Keywords: hydrate formation, state estimation, moving horizon, particle filtering.
1. Introduction As the readily accessible oil and gas reserves are becoming exhausted, it is necessary to be able to consider oil fields prone to more severe conditions and from more remote locations. This includes oil fields previously considered to be uneconomical, like those in deep ocean environments, which are subjected to high pressures and low temperatures. Such extreme conditions promote the formation of a solid nonstoichiometric compound of gas and water – the so-called clathrate of natural gas, or more commonly known as gas hydrates [1]. When hydrates form, they block transmission lines, causing important economic losses due to the production stoppage. It would be ideal to operate the pipeline outside the hydrate formation envelop. However, as mentioned above, the high pressures and low temperatures associated to less accessible reserves leave the pipelines within the hydrate formation region [2]. Therefore, the ability to predict formation of hydrates in the field will play a vital role in exploiting these reserves. The aim of this study is to develop a combined state and parameter estimator for this process as a means for the prediction of hydrate formation towards preventive feedforward control. The present focus is on the gas-liquid flow riser. The model used is a complex nonlinear infinite-dimensional system accounting for momentum, mass and energy balances [3], and the measurements available include temperature and pressure at different locations along the riser. Since the problem being tackled is of distributed parameter nature, location where such measurements are taken, along with its type, is crucial for estimator performance. Moving horizon estimation (MHE) is well suited as it facilitates the sensor structure selection (both in a dynamic and static sense). MHE is proven to outperform
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the Kalman classic approach with greater robustness to both bad initial state guess and poor tuning parameters [4, 5]. Besides, MHE framework naturally handles most of the challenges of state estimation as applied to real systems, such as constraints and nonlinearities [4, 5]. However, solving the optimisation that underlies the MHE formulation at each sampling interval becomes too expensive in such a complex system, making it necessary to reduce the computational requirements. Particle filtering (PF) is a fairly new and promising class of state estimator that provides a recursive Bayesian approach to dynamic estimation in nonlinear systems, based on sequential Monte Carlo techniques. Although very fast and easy to implement, their ability to converge under poor priors (initially-specified regime of the uncertain states and parameters) is unproven. Thus, it becomes advantageous to combine the robustness of MHE with regard to good initial guesses and a convenient sensor structure on the one hand, and the speed of PF on the other hand to solve the combined state and parameter estimation problem [6, 7]. The MHE and PF frameworks will be demonstrated separately for a simpler problem involving the Van der Vusse reactor, before tackling the hydrate formation problem in the complete oil and gas production system. Future work will consider the individual and the hybrid frameworks for the hydrate prediction problem.
2. Methodology The state estimation problem is to determine an estimate of the state x(T) given the chosen model structure and a sequence of observations (measurements) of the system Y(T) = { y(0),…, y(T)}. 2.1. Moving horizon estimation Moving horizon estimation is a practical strategy for designing state estimators by means of online optimization, which allows one to include constraints and nonlinearities in the state estimation [8]. In order to improve the estimation procedure, imperfect models can be augmented with other physical information, such as constraints on states variables, process disturbances or model parameters. Many process uncertainties are bounded, as well as state variables, which are also almost always positive. Unlike the process uncertainties, constraints on state variables are implicitly enforced by the model of the process, but it is not rare to face approximate models where this implicit enforcement may fail. Then, the inclusion of constraints is needed also on the state variables so as to reconcile the approximate model with the process measurements. The online solution of this constrained estimation problem, known as full information estimator because we consider all the available measurements, is formulated as an optimization problem – typically posed as a least squares mathematical programsubject to the model constraints and inequality constraints that represents bounds on variables or equations. Although online optimization allows constraints on estimates as part of the problem formulation, formulating a state estimation problem with inequality constraints prevents recursive solutions as Kalman filter, and therefore, the estimation problem grows with time as more measurements become available. The computational complexity scales at least linearly with time, and consequently, the online solution is impractical due to the
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increasing computational load, necessitating bounds on the size of the mathematical program. To make the problem tractable, the strategy adopted is to reformulate the problem using a moving, fixed-size estimation window by breaking the time interval into two pieces. Thus, in moving horizon estimation we account explicitly only for the second part of the time interval, while the remaining process measurements are compactly summarized using a function named arrival cost, responsible for transforming the unbounded mathematical problem into an equivalent fixed-dimension mathematical program [8, 9]. Assuming the discrete model is readily available, the following is a simple mathematical formulation of the problem T −1
min
xT
− N
,{ w
k
} Tk
−1 =T − n
¦
Lk (w
k
,vk ) + Z
k =T − N
T − N
(z)
s.t.
x k + 1 = f ( x k , u k ) + Gw
k
yk = h(xk ) + vk Where xk are state variables, wk and vk are the model and process disturbances, respectively, Lk is a stage cost function and ZT-N (z) is the arrival cost function. A discrete-time model is adopted in the above formulation for illustrative purposes. A continuous-time model can also be used. 2.2. Particle Filtering From a Bayesian interpretation, MHE and the extended Kalman filter assume normal or uniform distributions for the prior and the likelihood. Unfortunately, these assumptions are easily violated by nonlinear dynamic systems in which the conditional density is generally asymmetric, potentially multimodal and can vary significantly with time. Unlike other nonlinear estimation methods, particle filtering (PF) allows to solve the online estimation problems without any assumption about the dynamics and shape of the conditional density. Bayes’ rule provides the theoretical background to integrate the past information or prior, with the current information or likelihood. The core idea is to represent the required conditional density of the states as a set of random samples (particles), rather than as a function over state space. The algorithm starts with a randomly generated set of samples at the first point, and propagates these samples to produce future distributions. Samples representing the prior are generated as the prediction of the state passing samples from the posterior at the previous step through the state equation. Hence, this prediction step utilises information about process dynamics and model accuracy without making any assumption about any characteristics of the distributions. Alike, once the measurement is available, the posterior is obtained as the correction of the state using the updated prior and the measurement (likelihood) itself. Therefore, this correction step utilises the measurement model and information about the measurement error, again without requiring any assumptions about the distributions. At this stage, solving the estimation problem is simply a matter of
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selecting a representative sample such as a mean, mode or median from the samples representing the posterior [6, 7]. 2.3. Combination of MHE and PF Solving the optimisation that underlies the MHE formulation at each sampling interval becomes too expensive in a complex system, making it necessary to reduce the computational requirements. Particle filtering (PF) is a fairly new and promising class of state estimator that provides a recursive Bayesian solution to estimation in nonlinear systems based on sequential Monte Carlo techniques. Although very fast and easy to implement, PF is more sensitive to poor initial guesses, because it means that there is little overlap between the particles representing the initial prior and the likelihood obtained from the measurements. Due to the limited number of particles, the posterior distribution is often less accurate than that obtained by methods that rely on an approximate but continuous prior distribution. Thus, it becomes advantageous to combine the robustness of MHE with regard to good initial guesses and a convenient sensor structure on the one hand, and the speed of PF on the other hand to solve the combined state and parameter estimation problem. This promising combined strategy will be explored in the future [7].
3. Case study The MHE and PF frameworks will be demonstrated separately for a simpler problem involving the well studied nonlinear benchmark problem of the Van der Vusse scheme [10]: a feed stream of feedstock A enters a reactor and reacts to form the desired product, B. The model assumes a first order reaction for the conversion of A into B, with two competing reactions BĺC and 2AĺD. Temperature-dependent Arrhenius reaction rates are assumed. The model has four states: concentration of A, concentration of B, reactor temperature, and cooling jacket temperature. 3.1. Moving horizon estimation For this case of study, it is supposed that the four states are directly measurable. The estimation problem is posed as a least squares objective function subject to the model nonlinear differential equations as constraints, restricting the mathematical program to the size of the moving window, and therefore ignoring the data outside such window. A model-process mismatch is introduced by using a E/R value in the Arrhenius Law of the first order (A ĺ B) reaction of -9658.3 K instead of the nominal value (-9758.3 K). The initial state is x0 =[2.14; 1.09; 387.15; 385.15] and the estimator is implemented with a window length of 50 samples (measurements are taken every 10 seconds) and the prior guess x =[2.34; 1.29; 392.15; 390.15]. Noise is added to the measurements with mean zero and variance 0.5 for the temperatures and 0.01 for the concentrations. Figure 1 shows the model prediction, the actual values (measurements) and the MHE prediction for the four states. 3.2. Particle filtering The particle filter is implemented with 100 particles at the same conditions used for the MHE. Figure 2 shows the model prediction, the actual values (measurements) and the PF prediction for the four states.
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#ONCENTRATION"MOL,
#ONCENTRATION!MOL,
As can be seen from the two figures, the moving horizon estimator recovers much faster than the particle filter from the bad prior guess. The price of this higher robustness is the greater computational expense required to solve the MHE optimisation.
-(% -EASUREMENTS -ODELPREDICTION
-(% -EASUREMENTS -ODELPREDICTION
-(% -EASUREMENTS -ODELPREDICTION
4IMESEC 4EMPERATURE#OOLANT+
4EMPERATURE2EACTOR+
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Figure 1. Moving horizon estimation
-ODEL0REDICTION -EASUREMENTS &ILTER%STIMATION
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4IMESEC
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Figure 2. Particle filter state estimation
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4. Conclusion and future research State estimation has been proposed as a way to improve our ability to predict hydrate formation in subsea pipelines. PF and MHE, state-of-the-art state estimation methods, have been reviewed and tested with a simple example case study with satisfactory results. Strategies based on both MHE and PF are being tested at present. The ultimate aim is to develop an efficient observer by relying on the robustness and the optimisation-based approach of MHE to provide initial guesses on the one hand, and the speed of PF on the other hand to solve the state and parameter estimation problem.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
E.D. Sloan, Nature (Invited Review), 426 (2003) 353. E.D. Sloan, Marcel Dekker, New York, 1998. E. Luna-Ortiz et al., AIChE Conference Salt-Lake City, Utah, USA (2007). E. L. Haseltine and J. B. Rawlings, Ind. Eng. Chem. Res., 44 (2005) 2451. J. D. Hedengren et al., CPC-VII, Meeting in Lake Louise, Alberta, Canada, 2006. N. J. Gordon et al., IEE Proc. F-Radar and Signal Processing, vol. 140, no.2 (1993) 107. J. B. Rawlings and B. R. Bakshi, Comput. Chem. Eng. vol. 30, no. 10, (2006) 1529. F. Allgower et al., Advances in Control: Highlight of ECC’99, London (1999) 391. C.V. Rao et al., Automatica, 37 (2001) 1619. Chen et al., Proc. Of the European Control Conf.. Rome, Italy, 3247.
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RCS for process control: Is there anything new under the sun? Manuel Rodríguez, Ricardo Sanz ASLab-UPM, José Gutiérrez Abascal, Madrid 28006, Spain
Abstract The purpose of this paper is to explore the potential use in process control of cognitive architectures used in other domains. A well-known cognitive architecture, used to control complex systems of different areas has been selected. It has been compared with the current control strategy used in process plants. Conclusions on its applicability, its strengths and weaknesses are also presented in the paper. Keywords: complex control, cognitive architecture, process control.
1. Introduction The process industry is quite mature in many aspects. One of these is process control. Although decentralized control based on PID controllers still is extensively used, significant advances (and research) have been made: multivariable predictive control, use of simulation models, real-time optimization, change in communication protocols (hybrid or digital). Even the implementation of the control architecture may change (and flatten) in the future if standard protocols like Industrial Ethernet apply to all the levels of the plant [1]. But still the classic hierarchical organization in four levels remains. Nowadays many fields look into other domains to see if the ideas developed for the original domains can be successfully applied to their domains. In this paper a cognitive architecture successfully applied to implement complex controllers in different areas is considered and its possible application to the process industry studied. The paper is organised as follows: next section presents the RCS cognitive architecture, its components and organization, section three describes how process control is currently implemented in most industrial plants, section four compares both approaches and finally section five draws some conclusions out of the presented ideas.
2. RCS: the cognitive architecture RCS (Real-time Control System) [2-4] is a cognitive architecture designed to enable any level of intelligent behavior. Initially based on a theoretical model of the cerebellum, it has been evolving over the last three decades. Today it is a real-time cognitive control architecture with different applications. It has been used for intelligent machine tools[5], factory automation systems[6] and intelligent autonomous systems[7] among others. RCS is a multilayered multiresolutional hierarchy of computational agents or nodes. RCS nodes have vertical (hierarchical) as well as horizontal relationships. Each node follows a common design pattern, being composed of the following elements: sensory processing (SP), World Modeling (WM), value judgment (VJ), behavioral generation (BG) and knowledge database (KD).
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Figure 1 shows the basic control node with its elements and relationships.
Fig 1. RCS Computational (control) node.
A brief description of the different elements of each of the control agents follows. Sensory Processing: This element gets sensory input and compares these observations with expectations generated by an internal world model. World Model: It is the system’s best estimate of the state of the world. The world model includes a database of knowledge (KD) about the world. It also contains a simulation capability which generates expectations and predictions. It can provide answers to requests for information about the past, present and probable future states of the world (What if and What is queries). This information goes to the task decomposition element (in the BG) and to the sensory processing element. Value Judgment: It determines what is good and bad. It evaluates the observed and predicted state of the world. It computes costs, risks and benefits of observed situations and of planned activities. Behavior Generation: Behavior is generated in a task decomposition element that plans and executes tasks by decomposing them into subtasks, and y sequencing these subtasks so as to achieve goals. Goals are selected and plans generated by a looping interaction between task decomposition (hypothesize plans), world modeling (predict results) and value judgment (evaluate the results). Behavior generation is typically done via Finite State Machines or rules governing costs for nodes and edges in a graph-search method. This node contains three subelements: the Job Asigner, the Planner and the
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Executor. RCS systems are built following the RCS methodology that has several steps. The first one is to gather domain knowledge with experts, and to generate (with the help of the experts) the hierarchical task decomposition. Knowledge Database: It stores information about space, time, entities, events, states of the system environment and about the system itself, parameters of the algorithms, models for simulation, etc.
3. The process control hierarchy The process industry comprises mainly continuous but batch processes also. The industries involved are chemical, petrochemical, pharmaceuticals, refineries, etc. These are usually very large and complex facilities. The main goal of any process plant is to get the maximum benefit (which means the demanded amount with the specified quality using the less resources) assuring safety and stability of the plant. In order to achieve this goal, control strategies have been applied and evolved over the years as new capabilities were available. From the initial manual control to the current digital distributed control system (DCS). To handle the complexity of the plant and to still achieve the overall goal, a control hierarchy has been developed and used for many years. This architecture gets the company policy (several weeks time resolution) and refines it to the current action to be applied on any actuator of the plant (ms-sec resolution time). The procedure is to observe the state of the plant through thousands of sensors and evaluate the next action for any resolution time. Implicit, explicit, heuristic and first principles models are used in order to generate the adequate action. The common process control architecture has four control levels. The lower level of the architecture is the basic regulatory control, this control is achieved by single decentralized loops. Most of these loops are controlled by standard PID controllers. The actuating horizon at this level is just one. The second level is the advanced and predictive control. These are two different control schemes that work at the same level. Information is transmitted horizontally and vertically in this (and upper) level. More elaborated control strategies as selective control, ratio control, feedforward control are implemented. In this second level implicit as well as explicit (heuristic and first principles based) models are used to generate the action. The action is the set point (goal) to achieve at the lowest level. Prediction horizon is (in the case of model predictive control) of tens of movements. Upper levels of control deals with optimization, scheduling and planning. Unit optimization can be made on-line with continuous information flow from and to the lower levels. Site optimization, scheduling and planning are done off-line. Very different types of models are used in these levels. As commented, information flows vertically and horizontally through the architecture and each upper level is of lower time resolution.
4. RCS vs DCS Many similarities exist between the two architectures, as can be observed in figure 2. Of course in the process control system there is no a common identified computational agent with so well defined elements as in the RCS architecture, but at any level a good
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matching can be established, as it is shown in the following comparison between the process control and the RCS elements
Fig 2. DCS vs. RCS architecture
Regulatory control node. This is the simplest node. It implements the simplest RCS node, one in which the behavior is purely reactive. It has a World model (the PID algorithm is a model, an empirical or heuristic model, but a model of the system under control), but this model does not predict the behavior. It only reacts to the current values of the plant and decides an action to be performed (there is no plan, it is just an action for the next time). It can be considered to have a KD where the model parameters are stored. Very simple preprocessing is performed (but some it is done as signal failure,...) Model predictive control node. MPC has several components. It has a model (usually an identified linear) of the world. It has a KD where past values of the manipulated variables (MVs) and controlled variables (CVs) are stored. In this KD other information is stored as MVs and CVs limitations, weighting factors, etc. The model uses the inputs to predict the future. This state is used in Behavior Generation module. In this module an optimization is performed to select the best action plan. This plan (a set of movements for the MVs along with CVs values) is set and sent to the regulatory level. Some preprocessing is implemented as well. The MPC module implements also a feedback loop to correct model errors (due to model mismatch with the actual plant). Real Time Optimization. This module receives the values of the variables of the plant, performs reconciliation on these values. This node has a steady state (mathematical, physically based) model of the plant. An optimization is made using that model every hour or so. The optimization results are sent to the lower level, the supervisory control. These results are the new set points of the controlled variables. The best operating point of the plant (which means a set of set points values) is calculated in each optimization. The optimization takes into account constraints on the variables (limited change in manipulated variables, safety, quality, etc. constraints in controlled variables). The node uses as well a historian module with past data of the plant.
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Planning and scheduling. This module corresponds with the business part of the control hierarchy. It has a business model and based on plant data (current and past values), on external data (market data, external plant info, etc.) and using the company business goals derives a production plan for the plant. It gives capacity production values as well as quality values to the lower, optimization, level. The resolution time at this level is days or weeks.
Fig 3. Process control levels as RCS agents
The control levels introduced above are presented in the figure 3. following the structure of a RCS node. It can be observed that the node in any level complies with the RCS node. As a preliminary conclusion it can be said that the conventional control structure is RCS compliant, or can be considered as an implementation of it. So is there anything new under the sun?, what's the benefit of using RCS (or other type of cognitive architecture) for process control? The answer is that it depends on the application and on the point of view. In spite of this and knowing that DCS is RCS compliant some differences or capabilities must be stressed:
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• Model update. In the RCS architecture the World Model update is made continuously and in an automatic way. In the process control architecture (PCA) it usually is made by hand. • Task decomposition. In the PCA the task decomposition is unique, i.e., there are no different explicit tasks to evaluate in order to select the best one. In the case of normal operation of the plant this is perfectly right but the RCS allows in the presence of faults (detected by the SPs and WM) to select new different tasks. • Adaptivity. Although not explicitly said in the literature, RCS seems well suited to be dynamically (or almost) changed in size or in configuration. PCA is less flexible and more conditioned by the initial design. • Behavior generation. RCS way of generating behavior seems best for discrete or semi-continuous systems (usually implements finite state automata). There is no documented application of RCS for large continuous processes. Some adaptation on how to exploit the knowledge should be done (for process systems, knowledge is strongly based in laws and equations so numerical techniques to deal with them should be available). • Querying. In the process industry it is very important to be able to answer structural (What is) questions as well as functional (What if). RCS integrate this capability in its structure while in the PCA it is generally done using external tools. • Heterogeneity. The ability of having different views and different models for the same part of a system seems to be easier to implement using RCS than using PCA.
5. Conclusions In this paper the use of cognitive architectures for process control has been explored. Specifically, the real-time control system architecture which has been applied to implement different complex control systems. A comparison between the current process control architecture and the proposed one has been established showing that the existing architecture is very similar to the RCS and can be considered compliant to it. Even so, there are some features of the cognitive architectures that seem appealing for the process control. These have been identified in the present paper. Their implementation is subject of future research along with the study of the benefits of providing a new capability to the process control (as it is in the cognitive architecture): world and self awareness.
•
References
[1] P. Neumann, “Communication in industrial automation—What is going on?”, Control Engineering Practice, Volume 15, (2007), pp. 1332. [2] J.S. Albus, “Outline for a Theory of Intelligence,”, IEEE Transactions on Systems, Man and Cybernetics, Vol. 21, (1991) pp. 473. [3] J.S. Albus, “The NIST Real-time Control System (RCS): An approach to Intelligent Systems Research,” Journal of Experimental and Theoretical Artificial Intelligence, 9, (1997) pp. 157 [4] Albus, J. and Meystel, A. Engineering of Mind: An Introduction to the Science of Intelligent Systems, John Wiley & Sons, N.Y., 2001 [5] F.M. Proctor, B. Damazo, C. Yang and S. Frechette , “Open Architectures for Machine Control,” NISTIR 5307, National Institute of Standards and Technology,1993, Gaithersburg, MD, [6] H.A. Scott, K. Strouse, “Workstation Control in a Computer Integrated Manufacturing System,” Autofact VI, 1984, Anehiem, CA. [7]M. Herman and J.S. Albus, “Overview of the Multiple Autonomous Underwater Vehicles Project,” IEEE International Conference on Robotics and Automation, Philadelphia, PA, 1988
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Data Treatment and Analysis for On-Line Dynamic Process Optimization Nina Paula G. Salau*, Giovani Tonel, Jorge O. Trierweiler, Argimiro R. Secchi Chemical Engineering Department – FederalUniversity of Rio Grande do Sul Rua Sarmento Leite288/24, CEP: 90050-170, Porto Alegre – RS – Brazil E-mail: *
[email protected],
[email protected],
[email protected],
[email protected] Abstract The filters tuning is a crucial issue due the need to quantify the accuracy of the model in terms of the process noise covariance matrix for process characterized by structural uncertainties which are time-varying. Thus, approaches to time-varying covariances were studied and included to a traditional EKF and an optimization-based state estimators constrained EKF (CEKF) formulations. The results for these approaches have shown a significant improvement in filters performance. Furthermore, the performance of these estimators as a transient data reconciliation technique has been appraised and the results have shown the CEKF suitability for this proposes. Keywords: Data Reconciliation, State Estimation, Covariance Estimation.
1. Introduction Due to the improvements in computational speed and the development of effective solvers for nonlinear optimization problems, optimization-based state estimators, such as the Moving Horizon Estimator (MHE) and CEKF, simpler and computationally less demanding, has become an interesting alternative to common approaches such as the EKF. The benefits of them arise due to the possibility to consider states physical constraints into an optimization problem [1, 2]. An important issue in applying state estimators is the appropriate choice of the process and measurement noise covariances. While the measurement noise covariance can be directly derived form the accuracy of the measurement device, the choice of Q is much less straightforward. Some process, such as continuous process with grade transitions and batch or semi-batch process, for instance, are characterized by structural uncertainties which are time-varying. In [3, 4], two systematic approaches are used to calculate Q from the parametric model uncertainties and the accuracy of this techniques are compared favorably with the traditional methods of trial-and-error tuning of EKF. Moreover, the NMPC algorithm proposed by [5] takes parameter uncertainty in account in the state estimation through these systematic approaches. Furthermore, the use of data preprocessing and dynamic data reconciliation techniques can considerably reduce the inaccuracy of process data due to measurement errors, improving the overall performance of the MPC when the data is first reconciled prior to being fed to the controller [6]. Moreover, poor measurements can lead to estimates that violate the conservation laws used to model the system. In their paper, [7] have considered the EKF and MHE formulations, as a dynamic data reconciliation technique to the problem of detecting the location and magnitude of a leak in a wastewater treatment process. While the constrained estimators provide a good estimate of the total losses when there is a leak, MHE and Kalman filter provide poor estimates when there are no leaks. The problem stems from an incorrect
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model of the process (the true model process has no leaks while the model assumes leaks) and, for solving this problem; they have just suggested a proper strategy where this problem is formulated as a constrained signal-detection problem. However, they had not implemented this proposal strategy. In order to assess the proposed techniques for state estimators tuning and transient data reconciliation of this work, the filters are applied in a case-study: the Sextuple TankProcess, which presents a high non-linearity degree and a RHP transmission zero, with multivariable gain inversion.
2. Case Study The proposed unit [8], depicted in Figure 1, consists of six interacting spherical tanks with different diameters Di. The objective consists in controlling the levels of the lower tanks (h1 and h2), using as manipulated variables the flow rates (F1 and F2) and the valve distribution flow factors of these flow rates (0x11, 0x21) that distribute the total feed among the tanks 3, 4, 5 and 6. The complemental flow rates feed the intermediary tank on the respective opposite side. The levels of the tanks 3 and 4 are controlled by means of SISO PI controllers around the set-points given by h3s and h4s. The manipulated variable in each loop is the discharge coefficients Ri of the respective valve. Under these assumptions, the system can be described by equations and parameters showed in Table 1 and 2, respectively. Table 1. Model Equations
Tanks Levels
Control Actions dI3 1 (h 3s − h 3 ) = dt TI3
dh A 5(h 5) 5 = x1F1 − R 5 h 5 dt dh 3 A 3(h 3) = R 5 h 5 + (1 − x 2 )F2 − R 3 h 3 dt dh A1(h1) 1 = R 3 h 3 − R1 h1 dt dh 6 A 6 (h 6 ) = x 2 F2 − R 6 h 6 dt dh A 4(h 4) 4 = (1 − x1 )F1 + R 6 h 6 − R 4 h 4 dt dh 2 A 2(h 2) = R4 h4 − R 2 h2 dt
dI 4 1 (h 4s − h 4 ) = dt TI 4
Supporting Equations R 3 = R 3s + K P 3 (h 3s − h 3 ) + K P 3 I3
R 4 = R 4s + K P 4 (h 4s − h 4 ) + K P 4I4 R 3s = R 4s =
x1s F1s + (1 − x 2s )F2s h 3s
x 2s F2s + (1 − x1s )F1s h 4s
A i (h i ) = ʌ(Di h i − h i2) i = 1, 2, 3 , 4, 5, 6
Table 2. Model Parameters Value 3
F1s, F2s
7500 cm min-1
D1, D2
25 cm
h3s, h4s
15.0 cm
x1s
0.6
D3, D4
30 cm
h1 (t0)
9.41 cm
x2s
0.7
D5, D6
35 cm
h2 (t0)
10.9 cm
R1
2200 cm min
-1
Kp3
-136.36
h3 (t0)
15.0 cm
R2
2500 cm2.5min-1
Kp4
-112.08
h4 (t0)
15.0 cm
Ti3
0.0742
h5 (t0)
5.06 cm
Ti4
0.0696
h6 (t0)
6.89 cm
R3s, R4s R5, R6
2.5
2.5
2875.7 cm min 2.5
2000 cm min
-1
-1
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3. State Estimation 3.1. Extended Kalman Filter Estimation Consider the dynamic systems whose mathematical modeling often yields nonlinear differential-algebraic equations as shown below: x (t ) = f [x (t ), u (t ), t, p(t )] + w(t)
(1)
z(t ) = h[x (t ), u (t ), t ] + v(t)
where x denotes the states, u the deterministic inputs, p the model parameters and z the vector of measured variables. The process-noise vector, w(t), and the measurement error, are assumed to be a white Gaussian random process with zero mean and covariance Q(t) and R(t), respectively. In the continuous-discrete Extended KalmanBucy Filter [9], the prediction stage of the states and the state covariance matrix is achieved by integrating the above nonlinear model equations in the time interval [tk-1, tk], according to the Equations 2 and 3, respectively: k
xˆ -k = xˆ k+ −1 +
³ f (xˆ, u, IJ) dIJ
(2)
k −1
³ [F(IJ)P(IJ ) + P(IJ )F k
Pk− = Pk+−1 +
T
(IJ ) + Q(IJ )] dIJ
(3)
k −1
The Kalman gain is then computed in the Equation 4. The measurement update equations are then used to estimate the state and the covariance updates, according to the Equations 5 and 6, respectively:
(
K k = Pk− H TK H k Pk− H Tk + R k
[
(
xˆ k+ = xˆ k− + K k z k − h xˆ −k , k
)
−1
)]
Pk+ = [I n − K k H k ] Pk− [I n − K k H k ] + K k R k K Tk
(4) (5) (6)
In the preceding equations, the superscripts (-) and (+) indicate the values before and after the measurement update has occurred, respectively. F and H are the Jacobian matrices of the functions f and h relative to xˆ −k . 3.2. Constrained Extended Kalman Filter Estimation CEKF is an alternative state estimator based on optimization, originated from MHE, introduced by [10], for a horizon length equals to zero [1]. The basic equations of CEKF can be divided, like in the EKF, in prediction and updating stages [2]. However, the integration of state covariance matrix is not carried through into the prediction stage. Furthermore, instead of a simple algebraic calculation of a gain (Kalman gain) as in the EKF, a resolution of a quadratic optimization problem is performed and the system constrains directly appears in the optimization problem in the updating stage. min
ˆ w
k −1
Ȍ
k
ˆ k -1 T Pk -1 -1 w ˆ k −1 + vˆ k T R k -1 vˆ k =w
(7)
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subject to the equality and inequality constraints:
(
)
ˆ k −1 , z k = h xˆ k+ , k + vˆ k xˆ +k = xˆ −k + w
(8)
ˆ min ≤ w ˆ k −1 ≤ w ˆ max , vˆ min ≤ vˆ k ≤ vˆ max xˆ min ≤ xˆ +k ≤ xˆ max , w
(9)
If the measurement equation is linear, the resulting problem is a quadratic program which can be solved with small computational effort. The measurement updating equations are then used to estimate the state and the state covariance matrix updates, according to Equations 5 and 6, respectively:
[
Pk = Qk + ϕk Pk -1ϕk T − ϕk Pk -1H k T H k Pk -1H k T + R k H k
]
−1
H k Pk -1ϕk T
(10)
where ϕ k is the discrete states transition, carried through the Jacobian matrix F.
4. Systematic Tuning Approach The two methods proposed in [3, 4] differ in the way the w(t) statistics of Equation 1 are calculated from the known statistics of the plant parameters p. w (t ) = f [x (t ), u (t ), t , p] − f [x nom (t ), u (t ), t , p nom ]
(12)
where xnom and pnom are the nominal state and nominal parameters vectors, respectively. 4.1. Linearized Approach Performing a first-order Taylor’s series expanson of the righthand side of Equation 12 around xnom and pnom, and computing the covariance of the resulting w(t), Q(t) is given by Q(t ) = J p, nom (t ) C p J Tp, nom (t )
where Cp ∈ℜ
n p ×n p
(13)
is the parameter covariance matrix and J p, nom (t ) is the Jacobian
computed using the nominal parameters and estimated states. 4.2. Monte Carlo Approach For the kth Monte Carlo simulation, the process noise is given by
[
]
w k (t ) = f xˆ (t ), u (t ), t , p k − f [xˆ (t ), u (t ), t , p nom ]
(14)
and the process noise deviation from the noise process mean w k (t ) is defined as ~ k (t ) = w k (t ) − w (t ) w
(15)
Q is obtained as the covariance of these process noise deviation values assuming a normally distributed data set. The process noise mean is utilized in the prediction step xˆ -k +1 = xˆ +k +
k +1
³ f (xˆ, u, IJ ) dIJ + w
k
(t )* Ts
k
where Ts is the filter sample time.
(16)
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5. Results and Discussions Both formulations EKF and CEKF were implemented in MatLab 7.3.0.267 (R2006b) and applied in the process dynamic model, previously presented. The system initial condition is an operating point that presents a minimum-phase behavior (1<x1+x25019 l), while M3, M5, M9, M10 and M12 can take the place of R2 for a total of 5 systems. Overall, 578 processing tasks are required. The set of valid equipment systems for task k of chemical i is given by Xk,i.
4. New decomposition approach Instead of solving the full mixed-integer linear program (MILP), we derive the periodic schedule one chemical at a time, following sequence A-E (see Figure 3). A total of |I| MILPs are solved, each featuring on each calculation stage the same set of variables and constraints as the full MILP. However, their domain is now much smaller. Dynamic sets were employed for this purpose. The chemical under consideration (i’’’) is the only element of set FiP. The algorithm starts with the first product of the sequence (1ŁA), the only one tackled in the first stage. The dynamic sets are then updated accordingly, FiP=AcP={A} and AcPi={}. The last two hold the active products and those that on a particular unit can be executed after i, respectively. In the first block of variable bounds, it is important to note that only i’’’ will be produced over the cycle. The actual amount must be greater than the production goal, pgoal, corrected by the yield of all chemicals i>i’’’. Attribute .lo defines the lower bound of variable ǻi’’’. The upper bound (.up), ensures that only the final material state of i’’’ is allowed. In model constraints given next, ȍ is a wrap-around operator (Shat et al., 1993), IJk,i holds the duration of tasks in number of time intervals (į=8 h) and set Ki gives the tasks belonging to chemical i. The objective function minimizes the total cost of the schedule in relative money units (r.m.u.). Eq 2 ensures that the volume handled by the task does not exceed the capacity of the vessel Vm. Eq 3 ensures that material production only occurs if the corresponding task is executed. The periodic schedule features exactly one batch of each chemical (eq 4). Eqs 5-6 are the excess resource balances. Eq 7 ensures that the start-up procedure does not require more units than those available.
min dcost⋅ | T | ⋅δ / 24 +
¦ setup ⋅ vcostm ⋅Cm0 + ¦ ¦ vcostm ⋅ δ / 24 ⋅ (Cm0 − ¦ Ci,m,t ) (1)
m∈M
m∈M t∈T
¦ ¦ ¦ ξ i,k , x,t / ρ k ,i, x,m ≤ Vm ∀m ∈ M , t ∈ T
i∈I
(2)
i∈AcP k∈K i x∈X k ,i
ξ i ,k , x ,t ≤ 1000 ⋅ N i ,k , x ,t ∀i ∈ AcP , k ∈ K i , x ∈ X k ,i , t ∈ T
¦ ¦ N i,k , x,t = 1 ∀i ∈ AcP, k ∈ K i
(3) (4)
x∈X k ,i t∈T
C i , m,t = C i , m,Ω (t −1) +
¦ ¦
3
τ k ,i
¦ ¦ ¦ μ k ,i, x,m,θ N i,k , x,Ω(t −θ ) +
k∈K i x∈ X k , i θ = 0
¦ μ i '.i '',i,θ N i ',i '',m,Ω(t −θ ) ∀m, i ∈ AcP, t
i '∈I i ''∈ AcPi ' θ = 0
(5)
MILP-Based Decomposition Method for the Optimal Scheduling
561
Figure 3. Algorithm of proposed decomposition approach
S i , k ,t = S i , k ,Ω (t −1) − Δ i
t =1∧ i∈FiP ∧ k =| K i |
¦ ¦ ¦ υ k ',i ',k ,i ξ i ',k ', x,t
+
τ k ', i
¦ ¦ ¦ν k ',i,k ,θ ξ i,k ', x,Ω(t −θ ) +
k '∈K i x∈ X k ', i θ = 0
∀i ∈ AcP, k ∈ K i , t ∈ T
(6)
i '∈ AcP k '∈K i ' x∈ X k ', i '
τ k ,i
¦ C i,m,|T | = C m0 + ¦ ¦ ¦ ¦ ¦ μ k ,i, x,m,θ N i ,k , x,t −θ
i∈ AcP
i∈ AcP k∈K i x∈ X k , i t∈T θ = 0 3
¦ ¦ ¦ ¦ ¦ μ i '.i '',i,θ N i ',i '',m,t −θ
i∈ AcP i '∈ AcP i ''∈ AcPi ' t∈T θ = 0
+
(7) ∀m ∈ M
Following the solution of the MILP, other variables are updated. Binary variables linked to processing and changeover tasks are fixed (.fx) to their values (.l). Selected equipment units get their binaries ( C m0 ) fixed and both the excess amount of all material states of i’’’ and ǻi’’’.up are set to 0. The complete schedule is found after all products have been tackled. In order to illustrate the second step, note that for i’’’=2, FiP={B}, AcP={A,B}, AcPA={B} and AcPB={A} so only changeovers tasks A-B and B-A are considered (in the first step there are no changeover tasks since there is only A).
5. Results In discrete-time periodic scheduling formulations the cycle time is fixed by both į and |T|. Thus, finding the optimal cycle time implies a search procedure over |T|. The equipment costs, vcostm are given in Figure 2, while the operating cost dcost=22.5 r.m.u./day and the initial setup=10 days. While the production goal cannot be disclosed we can say that a total of 20 batches are required. The algorithm was implemented in GAMS 22.5 and the resulting MILPs were solved to optimality (relative tolerance=1E6) by CPLEX 10.2 on a Pentium-4 3.4 GHz PC running Windows XP Professional. The results are given in Table 1. Columns 2 and 7 refer to the largest MILP solved. When compared to the full MILP, we get a 45% reduction in binary variables. The
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integrality gap is also tighter and for some instances it is even 0. The five subproblems are very easy to solve and so the computational effort is significantly lower. For |T|>14 the proposed method is about one order of magnitude faster. The overall search time is 86 instead of 1078 CPUs. The drawback of the decomposition approach is that the lowest cost equipment for a particular function is always selected on each step, which may not always be the best choice. Nevertheless, the optimality gap is very low. The global optimal solution corresponds to a cycle time of 11, 8-hour shifts. The lowest makespan (|T|=9) is equal to 236 shifts, has a total cost of 250.7 r.m.u. and involves the selection of 19 units. The cost can be reduced by 3% (|T|=11) for a makespan of 274 shifts (16% higher) due to selection of 16 units. Another interesting solution (|T|=15) involves the selection of just 13 units for a makespan of 350 shifts (48% higher). Table 1. Computational statistics |T|
RMIP
TCost (r.m.u.)
Gap (%)
Total CPUs
|T|
RMIP
TCost (r.m.u.)
Gap (%)
Total CPUs
9
251.1
251.1
0.16
4.9
15
249.5
249.5
0.81
6.9
10
252.3
258.6
0.15
5.0
16
250.0
256.4
0.08
7.6
11
236.9
243.3
0.04
5.2
17
260.2
266.6
1.18
8.0
12
267.2
267.2
0.11
6.1
18
260.8
267.3
0.87
8.8
13
261.0
261.0
0.08
5.9
19
269.3
275.8
0.91
10.9
14
269.0
269.0
0.34
6.5
20
276.0
282.8
2.20
10.2
6. Conclusions This paper has addressed the optimal periodic scheduling of an industrial batch plant from a new perspective. The aim has been to select a convenient number of equipment units so as to minimize the total equipment allocation cost and hence achieve a trade-off between a low makespan and high free capacity. A decomposition method based on a Resource-Task Network discrete-time formulation has been proposed that, when compared to the solution of the full problem, was able to reduce the total computational effort by one order of magnitude without severely compromising optimality. The proposed approach can in theory be applied to more complex cases and we are currently working on a problem that involves just two chemicals but with a 3:2 proportion in the number of batches. This means that more than a single instance of every production task will need to be executed, which will be translated into a longer cycle time and a higher number of time intervals. Preliminary results have shown that such problem is significantly harder to solve. And this is just for a single API. Ideally, one would have liked to consider more products simultaneously to better illustrate why better schedules in terms of flexibility are desirable.
References I. Grossmann, 2005, AIChE Journal, 51, 1846 S. Janak, C. Floudas, J. Kallrath, N.Vormbrock, 2006, Ind. Eng. Chem. Res., 45, 8234. C. Méndez, J. Cerdá, I. Grossmann, I. Harjunkoski, M. Fahl, 2006, Comput. Chem. Eng., 30, 913. C. Pantelides, 1994, Proceedings 2nd FOCAPO, Cache Publications, New York, pp 253. J. Röslof, I. Harjunkoski, J. Björqvist, S. Karlsson, T. Westerlund, 2001, Comput. Chem. Eng., 25, 821. N. Shah, C. Pantelides, R. Sargent, 1993, Annals Operations Research, 42, 193.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Design of constrained nonlinear model predictive control based on global optimisation Michal ýižniar,a,b Miroslav Fikar,b M.A.Latifi a a
Laboratoire des Sciences du Génie Chimique, CNRS – ENSIC, B.P. 20451, 1 rue Grandville, 54001, Nancy Cedex, France b Department of Information Engineering and Process Control FCFT, Slovak University of Technology in Bratislava Radlinskeho 9, 812 37, Bratislava, Slovakia Abstract In this paper a constrained nonlinear model predictive control (CNMPC) based on deterministic global optimisation is designed. The approach adopted consists in the transformation of the dynamic optimisation problem into a nonlinear programming (NLP) problem using the method of orthogonal collocation on finite elements. Rigorous convex underestimators of the nonconvex NLP problem are then derived within a spatial branch-and-bound method and solved to global optimality. The resulting control is compared to the CNMPC based on local optimisation in the control of a single-input single-output (SISO) continuous stirred tank reactor where a set of consecutive and parallel reactions take place. Keywords: orthogonal collocation, finite elements, dynamic optimisation, global optimisation, CNMPC 1.Introduction The interest of global dynamic optimisation is constantly growing mainly in security analysis of processes, state observation, parameter estimation and model based predictive control. Despite the increasing interest, deterministic global methods have not been extensively investigated. Very few academic research contributions including experimental studies and numerical simulations have been recently published in the open literature. This is mainly due to the lack of methods that allow the construction of rigorous convex underestimators for nonlinear differential constraints. One class of approaches that can be applied to solve dynamic optimisation problems to global optimality consists in the discretisation of variables in order to transform the problem into a nonlinear programming (NLP) problem. This means that in the process dynamic models, described by systems of ordinary differential-algebraic equations (DAEs), both the state and control variables are discretised (known as complete discretisation). The well-established global static optimisation algorithms, mainly deterministic methods, can then be used. The approach proposed in this paper belongs to this class and uses the orthogonal collocation method on finite elements [1, 2, 3] to convert the DAEs
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into a set of algebraic constraints. The objective here is the design of constrained nonlinear model predictive control (CNMPC) based on global optimisation. The case study is a single-input single-output (SISO) continuous stirred tank reactor involving a set of consecutive and parallel reactions. 1.1.Open-loop optimal control problem Consider a deterministic optimal control problem in Bolza form on a fixed horizon t [t 0 , t f ] with tf
G ( x ( t f )) ³ F ( x (t), u (t))d t
min J u (t )
s.t.
t0
x
f ( x , u ),
x (0)
h(x ( t ) , u ( t ) )
0,
x L d x (t ) d x U ,
x0
(1)
g(x ( t ) , u ( t ) ) d 0 , u L d u (t ) d u U
where J represents the objective function (this comprises G , the component of the objective function evaluated at final conditions, and F , the component of the objective function evaluated over a period of time. In the case of tracking problems the functional F under the integral may be given by an appropriate norm of the difference between the reference trajectory and the output trajectory, such as a weighted Euclidean norm with the particular weighting Q : || x || Q2 ), f is a vector valued function, x(t ) R n x the state variables with n constant initial conditions x 0 , u(t ) R u the sequence of control variables, h g and represent some equality and inequality constraints imposed to the process. 1.2.NLP Formulation-Collocation Based Approach One class of approaches that can be applied to solve dynamic optimisation problems such as problem (1) is total discretisation (TD) or total parametrisation (TP) method [2, 3]. It transforms the original optimisation problem (1) into a NLP by parameterising both input and state variables over finite elements using polynomials (e.g., Lagrange polynomials) or any suitable basis functions. The coefficients of these polynomials and the length of the finite elements then become the decision variables in the resulting NLP problem. Following the procedure in [4] for a given approach the complete formulation can be written as min J ( z ) z
s.t. h(z) 0, g(z) d 0,
zL
dzd
(2)
zU
where z is a vector of decision variables, h and g represent the equality and inequality constraints (both linear and nonlinear) resulting from the discretisation approach. Problem (2) can be solved using any standard nonlinear programming solver.
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565
It is important to notice that the NLP problem (2) exhibits multiple local optima mainly due to the nonlinearity of equations h and g . Methods for determination of the global optimum are therefore needed. 1.3.Global Solution Here only deterministic methods for global optimisation are considered. They are based on the generation of convex relaxations of the original non-convex problem (2). Numerous methods have been proposed for constructing such relaxations [5–9]. In this work, the branch-and-bound method [5, 6, 10, 11] is exploited to guarantee the global optimality within İ-tolerance to the solution of the non-convex NLP problem (2). The branch-and-bound algorithm begins by constructing a relaxation of the original non-convex problem (2). This relaxation is then solved to generate a lower bound on the performance index. An upper bound is generated by the value of the non-convex objective function at any feasible point (e.g., a local minimum found by standard NLP algorithm, or a problem (2) evaluation at the solution of the relaxed problem). If these bounds are not within some İtolerance a branching heuristic is used to partition the current interval into two new sub-problems (e.g., bisect on one of the variables). Relaxations can be constructed on these two smaller sets, and lower and upper bound can be computed for these partitions. If the lower bound on a partition is greater than the current best upper bound, a global solution cannot exist in that partition and it is excluded from further consideration (fathoming). This process of branching, bounding and fathoming continues until the lower bound on all active partitions is within İ-tolerance of the current best upper bound.
2.Case Study 2.1.Problem Formulation In this work we consider a benchmark control problem of the isothermal operation of a continuous stirred tank reactor (CSTR) where the Van de Vusse reactions take place [12, 13] (i.e. A o B o C and 2A o D ). The performance index is defined as the weighted sum of squares of errors between the setpoint c Bset and the estimated model output cˆB predicted for the k th time step in the future with w(t k ) 0.01 for all k z H p and w(t k ) 10,000 for k H p . The control problem is then formulated as H p 30
min
cA , c B , F / V
s.t.
J
dc A dt dc B dt
¦ w(t k )(c Bset (t k ) cˆ B (t k )) 2
k 1
( F / V )(c A0 c A ) k1c A k 3 c A2
(3)
k1 c A k 2 c B ( F / V ) c B
where F is the feed flow rate of A into the reactor, V is the constant reactor volume, c A and cB are the reactant concentrations in the reactor, and k i are the -1 reaction rate constants for the three reactions. In this work, k1 50 h ,
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k 2 100 h -1 , k 3 10 l mol -1 h -1 . We assume that the volume of the reactor is constant, that the feed consists of pure component A , and that the nominal -1 concentration of A in the feed is c A0 10 mol l . An upper bound on the input -1 (F/V) is assumed to be set at 200 h . The objective of NMPC is to regulate the concentration of the product B in the isothermal operation of the CSTR by manipulating the control variable (F/V) in the presence of disturbance d which will be simulated through changes in c A0 . The objective function is minimised over the future time horizon H p (equal to 30 sampling times) with a sampling mes time of 0.002 h (7.2s). At each sampling time t k , measurements c B are taken from the perturbed plant and output disturbance is estimated as d (t k ) c Bmes (t k ) c B (t k )
(4) c ( t ) where B k is the model output at time t k . The updated disturbance is then assumed to be constant in dynamic optimisation over the whole prediction horizon. Therefore, the estimation of c B (t ) in the performance index is calculated as cˆ B (t ) c B (t ) d (t k ), t t t k
(5)
Once the solution of the dynamic optimisation problem is found (with 8 collocation points for state variables, and considering the control variable as piecewise constant within 1 element with a length of 0.06 h which is the prediction horizon), the computed optimal input within the first sampling period is applied both to the actual plant and to the model. The whole procedure is repeated with the moving horizon strategy in each sampling instant. 2.2.Closed- loop results The results obtained in the closed-loop control are summarised in Fig. 1 where five time varying curves are presented. The first one is the controlled variable (c B ) , the second is the input or control variable ( F / V ) , the third is the feed concentration change (c A0 ) , the fourth is the performance index (or objective function) and the last one is the computational time required to get the solution. It should be noted that it happens to the system under consideration to exhibit a steady-state input multiplicity and thus several solutions. This point is well discussed in [12].
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567
Figure 1: Closed-loop results obtained with local and global optimisation
In order to demonstrate the benefits of the global optimisation method over the local optimisation, setpoint transitions to track and disturbance loads to reject are generated as follows. The setpoint transitions are obtained by stepping the -1 1 set concentration c B from 1.1 to 1 mol l at time 0.05 h and then to 0.8 mol l at time 0.5 h (first curve in Fig. 1). In the same way the disturbance loads are 1 simulated by changing the feed concentration c A0 from 10 to 9 mol l at time 0.2 h and to 7 mol l 1 at time 0.35 h (third curve in Fig. 1). The global optimisation method leads to two significant improvements in setpoint tracking visible at setpoint changing times 0.05 h and 0.5 h . In the first change, at time 0.05 h , the global algorithm chooses to use an offset free -1 position corresponding to an input value of F / V 25 h (second curve in Fig. 1). The local technique is helpless as it finds the problem to be locally infeasible, forcing the relaxation to the hard terminal constraint and chooses to 1 move in an improving direction and ends on the constraint F / V 200 h . In this case the global method leads to significantly lower performance index than the local one (fourth curve in Fig. 1). In the second change, at time 0.5 h , the locally tuned controller is able to track -1 the setpoint offset free without issue using an input value of F / V 29.9 h .
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On other hand, the globally tuned controller finds a better solution choosing the -1 opposite steady state input value of F / V 185 h (second curve in Fig. 1). This gives a better setpoint tracking behaviour. Concerning the time required to compute a solution (fifth curve in Fig. 1), in most cases the global solver is able to guarantee the global optimality within the sampling period of 7.2 s . However, it should be mentioned, that at time of 0.35 h the solver can no longer achieve the desired setpoint due to a large disturbance. At this point, guaranteeing the global solution takes much more time than in previous cases and the solution is returned too late to be used for real-time purposes (within 7.2 s ). In this time instant, the best local solution is implemented and thus the guarantee on global optimality is lost. For the global optimisation method used to design the CNMPC the increase of the computation capacities or the decrease of the global optimum accuracy would probably guarantee the global optimality of the computed control.
3.Conclusions A globally optimal NMPC algorithm has been proposed. A deterministic approach is used to find the guaranteed global optimum to the nonconvex NLP problem resulting from the simultaneous optimisation method. The algorithm has shown its capabilities to eliminate the poor performance in a simple CSTR example resulting from the suboptimal input trajectories obtained by local optimisation techniques. It has been shown, that with growing computational capabilities, the global CNMPC may be used also in real-time applications. Reference: [1] J.E. Cuthrell and L.T. Biegler, AIChE Journal, 33 (1987) 1257 [2] J.E. Cuthrell and L.T. Biegler, Comput. Chem. Eng., 13 (1989) 49 [3] J.S. Logsdon and L.T. Biegler, Chem. Eng. Sci., 28 (1989) 1628 [4] W.R. Esposito and C.A. Floudas, Ind. Eng. Chem. Res., 39 (2000) 1291 [5] C.S. Adjiman and S Dallwing and C.A. Floudas and A. Neumaier, Comput. Chem. Eng.. 22 (1998) 1137 [6] C.S. Adjiman and I.P. Androulakis and C.A. Floudas, Comput. Chem. Eng., 22 (1998) 1159 [7] B. Chachuat and M.A. Latifi, “User’s guide for Fortran global optimization code NLPGLOB”, 2002 [8] J.E. Falk and R.M. Soland, Manage. Sci., 15 (1969) 550 [9] G.P. McCormick, Math. Program., 10 (1976) 147 [10] W.R. Esposito and C.A. Floudas, J. Global Optim., 17 (2000) 97 [11] W.R. Esposito and C.A. Floudas, J. Global Optim., 22 (2002) 59 [12] C.E. Long and P.K. Polisetty and E.P. Gatzke, J. Proc. Cont., 16 (2006) 635 [13] P.B. Sistu and B.W. Bequette, Chem. Eng. Sci., 50 (1995) 921
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Biclustering of data matrices in systems biology via optimal re-ordering Peter A. DiMaggio Jr.,a Scott R. McAllister,a Christodoulos A. Floudas,a XiaoJiang Feng,b Joshua D. Rabinowitz,b Herschel A. Rabitz,b a
Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544 USA b Department of Chemistry, Princeton University, Princeton, NJ, 08544 USA
Abstract In this work we present an optimal method for the biclustering data matrices in systems biology. Our approach is based on the iterative optimal re-ordering of submatrices to generate biclusters. A network flow model is presented for performing the row and column permutations for a specified objective function, which is general enough to accommodate many different metrics. The proposed biclustering approach is applied to a set of metabolite concentration data and we demonstrate that our methods arranges the metabolites in an order which more closely reflects their known metabolic functions and has the ability to classify related objects into groups. Keywords: rearrangement clustering; biclustering; network flow; Mixed-integer linear programming (MILP).
1. Introduction Problems of data organization and clustering are important and utilized in a variety of applications. The overall purpose of data clustering, regardless of the content of the data set being analyzed, is to organize the data in such a way that objects which exhibit “similar” attributes are grouped together. The definition of similarity is dependent on the types of trends that one hopes to extract from a given data set. The most common methods available for the clustering of large-scale data sets are hierarchical [1] and partitioning [2] clustering. These formulations are often solved using heuristics and result in suboptimal clusters because comparisons are only evaluated locally. The problem of rearrangement clustering has emerged as an effective technique for re-ordering data based on minimizing the sum of the pair-wise distances between rearranged rows and columns. The bond energy algorithm (BEA) was originally proposed for finding “good” solutions to this problem [3] and it was later discovered that it could be cast as a traveling salesman problem (TSP) [4,5]. The concept of biclustering has emerged in the context of microarray experiments since a gene can be involved in more than one biological process or could be co-expressed with other genes for only a subset of the conditions. Several existing approaches use heuristic methods, discretize the expression level, and/or solve a simplified model to address this NP-hard problem [6]. An excellent review of several biclustering methods can be found in [7]. In this work, we present a method for biclustering data matrices which is based on iteratively computing the optimal ordering for the rows and columns of a data matrix.
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We present a general form of the objective function for quantifying the similarity between rows or columns that are adjacent in the final ordering. A network flow model is used to perform the actual permutations of the rows and columns. Our method is applied to a set of metabolite concentration data [8] and compared with other clustering techniques. We show that the proposed approach provides a denser grouping of related metabolites (i.e., rows of the data matrix) than does hierarchical clustering, which suggests that optimal ordering has distinct advantages over local ordering. It is also demonstrated that this global method also reconstructs underlying fundamental patterns in the data as it perfectly separates the nitrogen and carbon starvation conditions (i.e., the columns) into different halfs of the data matrix.
2. Biclustering algorithm In this section we present the mathematical framework used for biclustering dense data matrices. We begin by defining the problem representation, which is based on nearest neighbor assignments in the final ordering. Given the proposed variable representation, we present a generalized objective function for assessing the quality of a reordering. A network flow model is then used to perform the actual permuations of the rows and columns of the data matrix according to the selected objective function. For the sake of brevity, we present the terminology and mathematical model only for the rows of the data matrix, but an analogous representation follows for the columns. 2.1. Variable Definitions We define the index pair (i,j) to correspond to a specific row i and column j of a matrix and the value asscoiated with this pair is denoted as ai,j. The cardinality (or in this case, the dimension) of the rows and columns of the matrix will be represented as |I| and |J|, respectively. The problem respresentation adopted in this article is based on defining whether or not two rows i and i' are adjacent in the final rearrangement of the matrix, where row i' is directly below row i. We accomplish this by defining the following binary {0-1} variables. yi,i’ = 1 if row i is adjacent and above row i’ in the final arragnement, 0 otherwise For instance, if the binary variable y8,3 is equal to one then row 8 is immediately above row 3 in the final arrangement of the matrix. The assignment of y8,3 = 0 implies that row 8 is not immediately above row 3 in the final arrangement, but does not provide any additional information regarding the final positions of rows 8 and 3 in the matrix. 2.2. Objective Function The proposed method optimally rearranges the rows and columns of a data matrix according to a metric of similarity, which is left to the user to specify. Given the problem representation of assigning neighboring elements in the final ordering using the binary variables yi,i', we present a generic similarity measure for determining the associated cost of placing rows i and i’ adjacent in the final ordering in Eq. (1). i i' j yi,i' ·ij(ai,j, ai’,j)
(1)
In Eq. (1), ij(ai,j, ai’,j) represents any pairwise similarity measure between the elements of two rows. For instance, one might want to penalize large pairwise differences between adjacent elements in the final rearrangement. For this purpose, one could evaluate the squared difference between two rows as shown in Eq. (2).
Biclustering of Data Matrices in Systems Biology via Optimal Re-ordering
i i' j yi,i' ·(ai,j-ai’,j)2
571
(2)
It should be noted that the form of the objective function presented in Eq. (2) is not limited to this Euclidean metric and can accommodate almost any pairwise similarity measure. 2.3. Network Flow Model Network flow models [9] have been extensively studied in the field of optimization and mathematical programming. The final ordering of the row permutations can be represented as a directed acyclic graph, where the rows correspond to nodes and an edge connects two nodes (rows) if they are adjacent in the final ordering. As defined in the previous section, the binary variables yi,i' represent the assignment of a neighboring row i' directly below row i in the final arrangement. Thus, this binary variable yi,i' represents the physical existence of an edge between the rows i and i'. We introduce another set of binary variables, ysource,i and ysink,i, to indicate which rows are assigned at the top and bottom of the final rearranged matrix, respectively. ysource,i = 1 if row i is the top-most row in the final ordering, 0 otherwise ysink,i = 1 if row i is the bottom-most row in the final ordering, 0 otherwise
A set of continous variables, fi,i', are denoted as the flows of the network. For this problem representation, we define the flow entering a node (row), fi,i’, to denotes its final position in the re-ordered matrix. Note that there is a one-to-one correspondence between the existence of an edge, yi,i', and the flow assigned to that edge, fi,i'. These flows start from a fictitious source row and end at a fictitious sink row. fi,i' = the flow from row i to row i' fsource,i = the flow entering the source row i fsink,i = the flow leaving the sink row i To ensure that each row has unique neighbors, we define constraints that assign exactly one row above and one row below each row i in the final ordering, as shown in Eqs. (3) and (4), respectively. i'i yi’,i + ysource,i =1
(i)
(3)
i'i yi,i' + ysink,i = 1
(i)
(4)
These constraints enforce that each row, i, has only one neighboring row above it (or is the top-most row) and only one neighboring row below it (or is the bottom-most row) in the final arrangement, respectively. We also need to enforce is that only one row is the top-most row (i.e., source) row and only one bottom-most (i.e., sink) row in the final arrangement. i ysource,i = 1
(5)
i ysink,i = 1
(6)
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The set of constraints defined by Eqs. (3) through (6) are sufficient for assigning a unique ordering of the rows. However, cyclic arrangements of the rows can also satisfy these constraints (i.e., it is possible to have yi,i' = yi,i'’ = yi’’,i = 1, which corrsponds to the cyclic ordering of i, i', i'', i, ... etc.). To remove cyclic arrangements in the final ordering, unique flow values, fi,i', are assigned to each edge, yi,i' which denote their final positions in the ordering. We intialize the positions to begin at the source row (or topmost row) by setting it equal to the total number of rows (|I|). fsource,i = |I|·ysource,i
(i)
(7)
Starting from this source row, each subsequent row in the final arrangement will have an entering flow value of |I|-1, |I|-2, and so on. This cascading property of the flow values will ensure that the flows corresponding to the final orderings are unique. A flow conservation equation is used to model this cascading of the flows by requiring that the flow entering a row is exactly one unit greater than the flow leaving that row. i' (fi’,i - fi,i') + fsource,i – fsink,i = 1
(i)
(8)
Since we have defined the convention that fsource,i starts at |I|, then fsink,i has a flow value of zero and thus can be eliminated from the model. Lastly, we can assign general upper and lower bounds for all flow values since a flow connecting two rows i and i' (i.e., yi,i' =1) can never be greater than |I|-1 nor less than 1. yi,i' fi,i' (|I| - 1) ·yi,i'
(i,i’)
(9)
These constraint equations also ensure that if rows i and i' are not connected by an edge (i.e., yi,i' = 0), then no flow is assigned (i.e., fi,i' = 0). The set of constraint in Eqs. (3)-(9) comprise the entire mathematical model necessary for performing the row and column permutations, which are guided by any of the aforementioned objective functions. This is a mixed-integer linear programming (MILP) model and can be solved to global optimality using existing methods such as CPLEX [10]. 2.4. Iterative Approach We utilize the mathematical model for optimal re-ordering in an iterative framework to bicluster data matrices. First, a single dimension of the data matrix is optimally reordered and we refer to this dimension as the columns of the data matrix. For example, in gene expression data the columns would correspond to the conditions over which the expression levels are measured. Given the optimal re-ordering of the columns, the median value of the objective function for every pair of adjacent columns in the final arrangement is computed. Cluster boundaries are defined to lie between those columns which have the largest median objective function value and these boundaries are used to partition the original matrix into several submatrices. The rows of each submatrix are then optimally re-ordered over their corresponding subset of columns and the clusters in this dimension are defined based on the largest median objective funciton values between adjacent rows in the final ordering.
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3. Computational Studies 3.1. Metabolite Concentration Data The proposed biclustering approach, denoted as OREO, was applied to a data set comprised of concentration profiles for 68 metabolites recorded dynamically over the conditions of nitrogen and carbon starvation for the organisms E. coli and S. cerevisiae [8]. The columns of the data matrix (i.e, the starvation conditions) were re-ordered using the objective function in Eq. (2). The network flow formulation for the column re-ordering problem was solved by CPLEX [10] in 168 seconds on an Intel 3.0 GHz Pentium 4 processor and the results are presented in Fig. 1. It is interesting to note in the column re-orderings that the nitrogen and carbon starvation conditions are perfectly separated into different halfs of the matrix. This suggests that the algorithm has the ability to reconstruct underlying fundamental patterns. The top four cluster boundaries partition the original matrix into the five submatrices A, B, C, D and E, as shown in Fig. 1.
Figure 1: Optimally re-ordered columns of metabolite concentration data result in submatrices A, B, C, D and E. The enlarged regions show the concentration profiles for the optimally re-ordered metabolites in submatrices A and E.
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For the sake of brevity, we only present the optimal ordering over the metabolites for the submatrices A and E using the objective function in Eq. (2), which were optimally re-ordered in 4085 and 4587 CPU seconds using CPLEX, respectively, and the results are shown in the enlarged regions in Fig.1. It is important to note that the re-orderings over different submatrices result in better groupings of different metabolites. For instance, the optimally re-ordered metabolites in region A produce a strong grouping of the biosynthetic intermediate metabolites carbamoyl-aspartate, ornithine, dihydrooroate, N-acetyl-ornithine, IMP, cystathionine, and orotic acid. This clustering supports the observation that most biosynthetic intermediates decrease in concentration over all starvation conditions based on the hypothesis that the cells turn off de novo biosynthesis as an early, strong, and consistent response to nutrient deprivation [8]. In contrast, the re-orderings of the metabolites in region E results in an excellent grouping of 16 amino acid metabolites into a single cluster and 8 of these metabolites are ordered consectively: serine, glycine, valine, glutamate, tryptophan, alanine, threonine, and methionine. This richness of amino acid metabolites is consistent with the observation that amino acids tend to accumulate during carbon starvation [8]. One should note the almost monotonic behavior of the re-ordered concentration profiles in regions A and E, which groups the decreasing concentrations at the top and the increasing concentrations at the bottom of the matrix As a basis for comparison with traditional clustering techniques, we examined the results for hierarchical clustering applied to the metabolite concentration data [8]. Overall, when compared to hierarchical clustering, OREO arranges the metabolites in an order which more closely reflects their known metabolic functions. We also applied the biclustering methods ISA, Cheng and Church, BiMax, and Samba to the metabolite concentration data but all these methods were unable to produce any biologically meaningful biclusters.
References 1. M.S. Eisen, P.T. Spellman, P.O. Brown, and D. Botstein, 1998, Cluster analysis and display of genome-wide expression patterns, Proc. Natl. Acad. Sci., 95(25), 14863-14868. 2. J.A. Hartigan and M.A. Wong, 1979, Algorithm AS 136: a K-means clustering algorithm. Applied Statistics, 28, 100-108. 3. W.T. McCormick Jr, P.J. Schweitzer, and T.W. White, 1972, Problem decomposition and data reorganization by a clustering technique. Operations Research, 20(5), 993-1009. 4. J.K. Lenstra, 1974, Clustering a data array and the traveling-salesman problem. Operations Research, 22(2), 413-414. 5. J.K. Lenstra and A.H.G. Rinnooy Kan, 1975, Some simple applications of the traveling salesman problem. Operations Research Quarterly, 26(4), 717-733. 6. Y. Cheng and G.M. Church, 2000, Biclustering of expression data, Proc. ISMB 2000, 93103. 7. S.C. Madeira and A.L. Oliveira, 2004, Biclustering algorithms for biological data analysis: A survey. IEE-ACM Trans. Comp. Bio., 1(1), 24-45. 8. M. J. Brauer, J. Yuan, B. Bennett, W. Lu, E. Kimball, D. Bostein, and J.D. Rabinowitz, 2007, Conservation of the metabolomic response to starvation across two divergent microbes. Proc. Natl. Acad. Sci., 103,19302-19307. 9. Ford L, Fulkerson D, 1962, Flows in Networks, Princeton University Press. 10. CPLEX, 2005, ILOG CPLEX 9.0 User's Manual.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimum Experimental Design for Key Performance Indicators Stefan Körkela, Harvey Arellano-Garciab, Jan Schönebergerb, Günter Woznyb a
Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany (corresponding author) b Institut für Prozess- und Verfahrenstechnik, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany
Abstract In this paper the methods of experimental design are used to minimize the uncertainty of the prediction of specific process output quantities, the so called key performance indicators. This is achieved by experimental design for constrained parameter estimation problems. We formulate these problems and apply our methods to an example from chemical reaction kinetics. Keywords: dynamic process models, constrained parameter estimation, optimum experimental design.
1. Introduction Optimal experimental design for parameter estimation is a powerful method used for model validation. It drastically reduces the experimental cost to obtain significant estimates of the unknown model parameters. Numerical methods and application examples are discussed in [1,2]. The paper [3] addresses a sequential approach for parameter estimation and experimental design. A robust modification considering the parameter dependency in nonlinear models is introduced in [4]. In this paper, we want to use the method of experimental design to minimize not only the statistical uncertainty of the model parameters but also of some quantities of interest – the key performance indicators – which are given implicitly as functions of the model state variables. To this end we consider experimental design for constrained parameter estimation problems. We give an analysis for this class of problems and apply our approach to an example from chemical reaction kinetics.
2. Modeling and Simulation of Nonlinear Processes Modeling of chemical engineering processes by physical and chemical principles, as e.g. mass action kinetics, conservation laws, thermodynamics or phase transitions, typically yields systems of differential equations, e.g. differential algebraic equations (DAE):
y = f(t, y, z, p, q) 0 = g(t, y, z, p, q) with state variables ( y, z ) , unknown model parameters p and process controls q . Typically in chemical engineering, these equations are nonlinear and stiff.
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We assume that for given parameters p , controls q and initial values, the solution of the model equations exists and is unique. For DAE this e.g. is the case if the functions f and g are continuously differentiable with bounded derivatives and if the DAE is of index 1, i.e. ∂g / ∂z is regular. The solution of the model equations can be computed by use of suited numerical methods. This procedure is called simulation of the process. We will write x(t ; p, q ) for the simulation results of the states as functions of parameters and controls.
3. Key Performance Indicators Often the engineer is interested in specific outputs of the process, for example the yield of a certain substance or the ratio of main product and byproducts. We want to call these target quantities key performance indicators s . Usually they can be defined as functions of states, controls and parameters and may be given explicitly
si = ri (~ ti , x(~ ti ; p, q ), p, q ) , i = 1,! , K or implicitly
~ ~ ~ ~ r ( t1 , x( t1 ; p, q ),!, tK , x( tK ; p, q), p, q, s ) = 0 . In the following sections the approach of optimum experimental design will be used to give precise predictions for the values of the key performance indicators.
4. Constrained Parameter Estimation Problems To estimate the unknown parameters, the model has to be fitted to experimental data. For given measurement values
ηi
measured with variances
σ i2 / wi
at measurement
times t i , i = 1, ! , M this yields – under assumption of normal distribution of the measurement errors – the least squares parameter fit problem M
min ¦ wi p ,s
i=1
(Și − hi (ti , x(ti ; p, q), p,q))2 ı i2
s.t. ~ ~ ~ ~ r ( t1 , x( t1 ; p, q ),!, tK , x( tK ; p, q), p, q, s ) = 0 In this formulation, the equations defining the key performance indicators s become constraints of the parameter estimation problem and the s become additional variables besides the parameters p . Thus the values of the key performance indicators are also estimated from the experimental data. The quantities wi are 1 for every given measurement point. Later in experimental design they can be used to select the actual measurements out of all possible measurements by choosing wi ∈ {0,1} . For the solution, tailored methods for constrained optimization of least squares problems have to be applied. In general, data not only from one experiment but from a
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series of experiments is available. In this case it is useful to apply special multiexperiment formulations. For details on the numerical methods see e.g. [5] and [6]. In the next section we will calculate the variance-covariance matrix as a measure of the uncertainty of the parameter estimation.
5. Statistical Analysis and Nonlinear Experimental Design Because the input of the parameter estimation problem – the experimental data – is random, so is the solution – the estimate of the parameters and key performance indicators. We apply a first order analysis by linearizing the parameter estimation ˆ , sˆ) : problem in the solution point ( p 2
§ Δp · min F1 + J 1 ¨¨ ¸¸ Δp , Δs © Δs ¹
2
§ Δp · s.t. F2 + J 2 ¨¨ ¸¸ = 0 © Δs ¹
where
Și − hi (t i , x(ti ; pˆ , q), pˆ ,q) ıi ~ ~ F2 i = ri ( t1 , x( t1 ; pˆ , q ),!, ~ tK , x ( ~ tK ; pˆ , q), pˆ , q, sˆ) , F1i = wi
(
and J 1 = J 1
J 1p i , j = − J 2p i , j =
p
)
(
J 1s , J 2 = J 2p
)
J 2s consist of the Jacobian w.r.t. p
· wi § ∂hi ∂h ∂x ¨ (ti , x(ti ; pˆ , q), pˆ , q) (t i ; pˆ , q) + i (ti , x(t i ; pˆ , q), pˆ , q ) ¸ ¸ ∂p j ∂p j σ i ¨© ∂x ¹
∂ri ∂X ∂ri ~ ˆ , q ),!, x(~ with X = ( x ( t1 ; p tK ; pˆ , q )) + ∂X ∂p j ∂p j
and the Jacobian w.r.t. s : J 1 i , j = 0 ,
J 2s i , j =
s
∂ri . ∂s j
§ Δp ·
+
§ F1 ·
¸¸ = − J ¨¨ ¸¸ The solution of this linearized parameter estimation problem is ¨¨ © Δs ¹ © F2 ¹ where J
+
is the generalized inverse J
+
= (I
§JTJ 0 )¨¨ 1 1 © J2
J 2T · ¸ 0 ¸¹
−1
§ J 1T ¨ ¨ 0 ©
0· ¸. I ¸¹
The variance-covariance matrix
§ I 0 · +T ¸¸ J C = J + ¨¨ ©0 0¹ describes the statistical uncertainty of the distribution of the model parameters and the key performance indicators.
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The variance-covariance matrix depends on the process controls q and the measurement selection weights w . Optimum experimental design aims at computing controls q and weights w in order to maximize the statistical reliability of the parameter estimation by minimizing a functional (e.g. trace, determinant or maximal eigenvalue) on the variance-covariance matrix:
min φ (C ) q,w
subject to constraints on feasibility, operability and costs of the experiments. The design may consist of a single or several parallel new experiments and may sequentially take into account the information from several previous old experiments. Numerical methods for the solution of this nonstandard optimization problem are discussed e.g. in [2].
6. Example As an example process we consider the Diels-Alder reaction [7], see Fig. 1. It is a chemical reaction with a catalytic and a non-catalytic reaction channel. Modeling of the reaction as a batch-process in a homogenous stirrer tank yields a system of ordinary differential equations. The activation energies and steric factors of the reaction velocities of the two reaction channels and the deactivation rate of the catalyst are the five unknown model parameters. Details of the model can be found in [2].
Figure 1: Reaction mechanism of the DielsAlder reaction. There is a catalyzed and a non-catalyzed reaction channel.
Figure 2: The production scenario experiment. The plot shows the temperature profile and the molar numbers of the educts and the reaction product.
A first experiment is run in the “production conditions” scenario. In this experiment, no measurements are taken and the experimental settings are fixed. The quantity of interest is the yield of the reaction product at the end of the experiment, see Fig. 2. Hence the molar number of the reaction product is defined as the key performance indicator (KPI). Four additional parallel “laboratory conditions” experiments are now planned by experimental design taking into account the first experiment, i.e. we consider the variance-covariance matrix for a constrained parameter estimation problem consisting of five experiments. Experimental design variables are the initial molar numbers of the educts, the molar number of the solvent, the concentration of the catalyst and the
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temperature profile as well as the placement of six HPLC measurements of the mass concentration of the reaction product for each experiment. Optimization yields the experimental settings shown in Table 1 and Fig. 3. Experimental design variables
Exp. 1 (fixed)
Exp. 2 (optimized)
Exp. 3 (optimized)
Exp 4 (optimized)
Exp. 5 (optimized)
Initial molar number of first educt
1.0
1.84
2.09
2.24
2.30
Initial molar number of second educt
1.0
2.22
2.14
2.26
2.36
Molar number of solvent
4.0
0.85
0.90
0.96
1.00
Catalyst concentration
1.0
0
0.05
1.11
1.72
Initial temperature
20.0
29.6
84.4
46.8
20.0
Final temperature
80.0
27.0
60.8
44.9
45.7
Measurements at
-
5, 6, 7, 8, 9, 10
0.3, 0.6, 1, 1.3, 1.6, 2
0.33, 0.66, 1, 8, 9, 10
1, 1.3, 1.6, 8, 9, 10
Table 1: Results of the optimization: design of five parallel experiments with the first experiment fixed.
Figure 3: The four optimized experiments. The plots show the temperature profiles and the placement of measurements, indicated by the bars on the curve of the measurable quantity.
Table 2 shows the improvement of the standard deviations of the parameters and the key performance indicator by experimental design optimization. The standard deviation of
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the key performance indicator is reduced by a factor 10. The overall statistical quality is improved by an average factor 7. In comparison, to achieve this gain without optimization by just repetition of experiments would require a 49 times higher experimental effort. Parameter
Standard deviations in % before optimization
Standard deviations in % after optimization
Steric factor uncatalyzed
22
3.3
activation energy uncatalyzed
20
1.2
Steric factor catalyzed
11
4.3
activation energy catalyzed
11
4.0
catalyst deactivation rate
21
7.5
key performance indicator
10
1.0
Table 2: Standard deviations of the parameters and the key performance indicator before and after experimental design optimization.
The numerical computations have been run with our software package VPLAN [2].
7. Conclusion We have extended the approach of minimizing the statistical reliability of parameter estimates to user defined quantities of interest, the key performance indicators. To cope with this task, the treatment of experimental design for constrained parameter estimation is necessary. In an ongoing project together with partners from industry, we will apply this method to industrial processes.
Acknowledgement The idea of applying experimental design to key performance indicators has arisen from discussions with Johannes Schlöder, University of Heidelberg, and Hergen Schultze, BASF AG Ludwigshafen.
References [1] I. Bauer; H. G. Bock, S. Körkel, J. P. Schlöder, Numerical methods for optimum experimental design in DAE systems, Journal of Computational and Applied Mathematics, 2000, 120, 1-25 [2] S. Körkel, Numerische Methoden für Optimale Versuchsplanungsprobleme bei nichtlinearen DAE-Modellen, Dissertation, Universität Heidelberg, 2002 [3] S. Körkel, I. Bauer; H. G. Bock, J. P. Schlöder, A sequential approach for nonlinear optimum experimental design in DAE systems, In Keil, F.; Mackens, W.; Voss, H. & Werther, J. (eds.), Scientific Computing in Chemical Engineering II, Springer-Verlag, 1999, 2, 338-345 [4] S. Körkel; E. Kostina, H.G. Bock, J. P. Schlöder, Numerical Methods for Optimal Control Problems in Design of Robust Optimal Experiments for Nonlinear Dynamic Processes, Optimization Methods and Software (OMS) Journal, 2004, 19, 327-338 [5] H. G. Bock, Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen, Bonner Mathematische Schriften 183, 1987 [6] J. P. Schlöder, Numerische Methoden zur Behandlung hochdimensionaler Aufgaben der Parameteridentifizierung, Dissertation, Hohe Mathematisch-Naturwissenschaftliche Fakultät der Rheinischen Friedrich-Wilhelms-Universität zu Bonn, 1987 [7] R. T. Morrison, R. N. Boyd, Organic Chemistry, Allyn and Bacon, Inc., 1983
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Inductive Data Mining: Automatic Generation of Decision Trees from Data for QSAR Modelling and Process Historical Data Analysis Chao Y Ma, Frances V Buontempo and Xue Z Wang* Institute of Particle Science and Engineering, School of Process, Environmental and Materials Engineering, University of Leeds, Leeds LS2 9JT, UK
Abstract A new inductive data mining method for automatic generation of decision trees from data (GPTree) is presented. Compared with other decision tree induction techniques that are based upon recursive partitioning employing greedy searches to choose the best splitting attribute and value at each node therefore will necessarily miss regions of the search space, GPTree can overcome the problem. In addition, the approach is extended to a new method (YAdapt) that models the original continuous endpoint by adaptively finding suitable ranges to describe the endpoints during the tree induction process, removing the need for discretization prior to tree induction and allowing the ordinal nature of the endpoint to be taken into account in the models built. A strategy for further improving the predictive performance for previously unseen data is investigated that uses multiple decisions trees, i.e. a decision forest, and a majority voting strategy to give a prediction (GPForest). The methods were applied to QSAR (quantitative structure – activity relationships) modeling for eco-toxicity prediction of chemicals and to the analysis of a historical database for a wastewater treatment plant. Keywords: inductive data mining, decision trees, genetic programming, QSAR, process historical data analysis
1. Introduction Collecting data and storing it in databases has now become a routine operation in industry. The data clearly represents a useful ‘mine’ from which valuable information and knowledge could be extracted. Discovering information and knowledge from data is particularly useful when first-principle models and knowledge are not available or not applicable due to uncertainties and noise in real world applications. Knowledge extracted from data has statistical basis and the $WWULEXWHV 2XWSXW advantage of being P objective compared to the P knowledge and 5RZV !6 6 Q experience of human experts. One of the most attractive knowledge discovery techniques is 5DQGRPO\FKRRVLQJDVORWZLWKWKHYDOXHV inductive data mining (IDM) which refers to a Fig. 1 GPTree generates binary decision trees from the training data by class of techniques that initially growing trees with randomly selected attribute and value pairs from randomly selected rows in the training data to form each splitting node. can generate transparent
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and causal models, give both qualitative and quantitative predictions and can incorporate human experts’ knowledge, giving advantages over other techniques employed in data mining. When properly trained, IDM models could match the accuracy of more opaque methods such as neural networks. IDM techniques proposed in literature are mainly based upon recursive partitioning employing greedy searches to choose the best Parents Child splitting attribute and value at each node therefore will + necessarily miss regions of the search space. In this paper a genetic programming Fig. 2 Two parent trees forming a new child by splitting at a random place, based approach for decision tree indicated by the dotted lines, and crossing-over to generate a new individual that contains part of the solution encoded in each parent. generation is introduced which can overcome the limitations of greedy search based methods. Case studies will be presented in applying the approach for building QSAR (quantitative structure activity relationships) for toxicity prediction of chemicals, and for process historical data analysis for a wastewater treatment plant.
2. Genetic Programming for Induction of Decision Trees (GPTree) 2.1 The Algorithm GPTree generates trees from data that is arranged in a tabular form with the columns representing the attributes (i.e. variables), and the rows being the data cases. The data is firstly divided into training and test sets. GPTree then generates binary decision trees from the training data by initially growing trees with randomly selected attribute and value pairs from randomly selected rows in the training data to form each splitting node (Fig. 1). For example randomly picking attribute m with corresponding value s for the randomly selected training row n would form the decision node If attribute m value s
(1)
Any training data for which this is true is partitioned to the left child node, while the remaining data is partitioned to the right child node. If less than 5% of the training data will be partitioned to one child node, a new row and
Cl attached to C2 (sp3) İ 1 Yes Highest eigenvalue of Burden matrix weighted by atomic mass İ 2.15 Yes
No Self-returning walk count of order 8 İ4.048 Yes
No
Class 3 (8/8)
Class 1 (12/12)
No Class 4 (7/7)
Lowest eigenvalue of Burden matrix weighted by van der Waals vol İ 3.304 No Yes Class 4 Distance Degree (5/6) Index İ 15.124 Yes
No
Summed atomic weights of angular scattering function İ 1.164
Class 4 (5/6)
Class 2 No (5/6) R autocorrelation of lag 7 Weighted by atomic mass İ 3.713 Yes No Yes
Class 2 (7/8)
Class 3 (6/7)
Fig. 3 Decision tree produced by generic programming GPTree for a bacteria data set in generation 37, which has higher accuracies for both training and test data in comparison with See5 generated tree. 7/8 means 7 were correctly classified, and 1 misclassified
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attribute is chosen at random. This percentage is user configurable. The child nodes are grown as follows. When less than 10% (or double the pre-specified minimum percentage coverage required at a node) of the training data are partitioned to a branch of the tree, so that any further splits will cover less than 10% of the data, or all the data at that branch are pure (in the same class), a terminal or leaf node is formed. This predicts the class of the data partitioned there as the majority class of the training partitioned to that node. This process continues until all nodes have child nodes or are themselves leaf nodes. Once the first generation is fully populated, new trees are grown by crossover, splitting the selected parents at a random node and recombining the parts to form new trees (Fig. 2). In order to select the parent trees that will take part in crossover, tournament selection is employed. The number of trees taking part in the tournament is configurable. The fittest tree from the tournament forms the first parent. This process is then repeated to find a second parent. The fitness function uses the accuracy of the trees in the competition since it is enforced that a node must contain a certain number of rows during the tree growth process: i n ( Rows at node i with Class m ,i ) Fitness (Tree) ¦ (2) Rows i 1 where n is the leaf nodes and Classm,i is the majority class at node i . If the number of leaf nodes was included in the fitness function, the population tended to converge to a relatively small set of trees, decreasing the parts of the search space explored, thereby leading to a slower overall increase in accuracy and often seeming to get stuck in regions containing less accurate trees of the same size as those produced without using the leaf node count in the fitness function. The tree taking part in the tournament maximizing the equation (2) is selected as a parent. Thirdly, the child trees may possibly be mutated before being added to the next generation. The pre-defined numbers of trees are mutated, with random choice of mutation operators. (i) Change of split value (i.e. choosing a different row’s value for the current attribute). (ii) Choose a new attribute whilst keeping the same row. (iii) Choose a new attribute and new row. (iv) Re-grow part of the tree from any randomly selected node (apart from leaf nodes). If either crossover or mutation gives rise to a node previously classed as a leaf node which is no longer pure or can now usefully be split further, that part of the tree is regrown. If a node becomes a leaf node during either operation, its previous children will not be copied to the new tree. Steps (ii) and (iii) are repeated until the required number of trees has been grown for the new generation, and generations are grown up to the requested number. 2.2 GPTree for QSAR Model Development Quantitative structure – activity relationships (QSAR) correlates molecular structural, biological and physicochemical descriptors to toxicity end-points have been considered as the most promising technique for minimising toxicity assay test using animals. Various techniques have been studied in literature such as, expert systems, neural networks and linear regression and there are also commercial tools available such as TOPKAT, DEREK, Oncologic, and MultiCase. One of the challenges is the lack of knowledge on what molecular descriptors are important to the toxicity prediction and what are not so should not be included in a QSAR model. Inductive data mining based decision tree construction clearly has the potential to address this issue since during construction of a decision tree, the less important variables are excluded from the tree
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model. Fig. 3 shows a decision tree built using GPTree for predicting toxicity using data obtained from literature(Zhao, et al., 1998). The data comprises Vibrio fischeri data for 75 compounds. The endpoint is the effect on the bioluminescence of the bacterium Vibrio fischeri measured over 15 min in a single laboratory using a standard protocol. This is scaled as log(1/EC50), ranging from 0.90 to 6.32. Values for the octanol/water partition coefficient, log P, and McGowan characteristic volume, Vx, were taken from the original paper and 1093 further topological, fragment and physical property descriptors with non-zero variation were calculated by DRAGON (a software system that has been widely used for calculating molecular descriptors), after optimisation using HyperChem (Hypercube Inc., Waterloo, Canada). The compounds are diverse mixture of chlorobenzenes, nitrobenzenes, anilines and phenols. Fig. 3 shows the decision tree built by GPTree. The toxicity endpoint log(1/EC50) was partitioned into four equal frequency groups, d3.68, d4.05, d4.50 and > 4.50. In Fig. 3, only a few variables were selected by the decision tree out of all the over a thousand descriptors. A second data set from literature which was tested using algae(Cronin, et al., 2004) was also studied and details can be found in (Buontempo, et al., 2005). See5 (Quinlan, 1993,Quinlan, 1996), probably the most widely used inductive data mining algorithm was also applied to the same two data sets. It was found that for both data sets, GPTree always performed better than See5 in terms of prediction accuracies for the test data.
3. Adaptive Discretization of Real-valued Output GPTree and other inductive data mining techniques require that data with a continuous endpoint be transformed prior to tree induction, so that the real-valued endpoint is split into classes. Taking advantage of the inherent properties of genetic programming, GPTree has been further developed to a new algorithm, YAdapt, which can adaptively partition the output values to classes. YAdapt uses a different fitness function and introduces new mutation operators. The new fitness function uses the sum of squared differences in rank (SSDR), based on Spearman’s rank correlation coefficient in order to utilise the ordinal nature of the data and to compensate for the differences in accuracy between different numbers of classes. SSDR is calculated as follows: i. Prior to tree induction the data is sorted on the endpoint, from least to greatest. ii. For each y range, find the middle row. For the sorted data, this is midway between the last and first rows covered by that range. This is used as the range’s rank, and as the actual rank for data with an endpoint in that range. iii. At a leaf node, calculate the sum of the squared differences, d2, between the ranks of the range each data item covered actually belongs to and the majority range’s rank. iv. Calculate the sum of each leaf node’s sum squared differences in rank to find a measure of fitness for the tree. The lower this value, the better the performance of the tree. An SSDR of zero means the tree is 100% accurate. The SSDR was used in the fitness function instead of the accuracy: i
n
Fitness(Tree)= i
1
¦
i
¦
(SSDR), for all n training rows
n
= ((leastact,i+(greatestact,i-leastact,i)/2) –(leastpred,I +(greatestpred,i - leastpred,i)/2)2) (5) where the ith training data's endpoint belongs to the range (leastact,i, greatestact,i) and the leaf node to which it is designated covers training rows with majority endpoint range (leastpred,i, greatestpred,i). Details of YAdapt can be found in Wang et al. (Wang, et al., 2006). Fig. 4 shows a decision tree that was generated for the same bacteria data as described above by adaptively adjusting the splitting of the end point. i
1
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Polar surface area 40.368 Yes H autocorrelation lag 0 weighted by Sanderson electro-negativities 2.111 No
Yes Class 1 (16/16)
Class 1 (13/13)
Class Class Class Class
1: 2: 3: 4:
3D MoRSE signal 15 weighted 18 weighted by Sanderson electronegativites -0.644 Yes
Geary autocorrelation lag 4 weighted by atomic mass 0.007 Yes
No
No Class 2 (9/9)
No
Class 2 (5/7)
H autocorrelation lag 0 weighted by Sanderson electro-negativities 2.394
Yes
No
Class 3 (7/9)
Log(1/EC50) 4.08 4.08 < Log(1/EC50) 4.51 4.51 < Log(1/EC50) 4.99 otherwise
Class 4 (6/6)
29 cases 16 cases 9 cases 6 cases
Fig. 4 A decision tree generated in generation 46 for the bacteria data, found four classes from the continuous endpoint adaptively during induction.
4. Decision Forest - GPForest Much research on decision trees has been devoted to improving the prediction accuracy in particular for unseen data that was not used in building the tree models. One of the most promising methods is decision forest that uses ensembles of trees. Decision forest combines the results of multiple distinct but comparable decision tree models to reach a consensus prediction. The idea assumes that a single decision tree could not fully represent the relationships between input variables and the output variable or a single tree model is optimum for a specific region of the solution space, while a decision forest captures relationships of different regions using different tree models. The genetic programming method described here, the GPTree, has great advantages in decision forest application because it is designed to generate multiple trees from generation to generation. In addition, by slightly varying the parameter values, more groups of trees can be produced. The GPForest method has the following steps. Firstly, GPTree is run for a given number of times (called experiments), each time with slight variations in parameter values and a given number of generations. Then trees were selected from all the generated trees in all experiments based on some defined criteria such as accuracy for test data, complexity (details are not listed here due to space limitation). In applying the decision forest for prediction, each tree in the decision forest gives an output. The final prediction is determined based on a majority voting strategy. The GPForest method has been applied to the analysis of data collected from a wastewater treatment plant. A total of 527 sets of data were collected which correspond to 527 days of operation. Each dataset has 38 variables, of which 29 correspond to measurements taken at different points of the plant, remaining 9 are calculated performance measures for the plant. In the study, decision forests were developed for four variables: suspended solids in effluent (SS-S), biological oxygen demand in effluent DBO-S, conductivity in effluent COND-S, and chemical oxygen demand in effluent DQO-S. The numbers of decisions trees selected into the four decision forests for predicting SS-S, DBO-S,
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DQO-S and COND-S are 24, 25, 23 and 24. Fig.5 shows one of the decision trees selected into the decision forest for predicting SS-S. It was found that the decision forest always gave better prediction accuracy for test data, than GPTree and See5 (Table 1). Global performance input suspend solids RD-SS-G 79.6 Input suspended solids to plant SS-E 188
Input suspended solids to plant SS-E 186
H (14/14)
Global performance input suspend solids RD-SS-G 95.1
Global performance input suspend solids RD-SS-G 92
Input suspended solids to plant SS-E 264
N Input pH to primary Input sediments to (218/218) settler PH-P 8.2 secondary settler N SED-D 0.3 Global performance (2/2) Input suspended solids N input suspend solids to plant SS-E 166 (9/9) N L RD-SS-G 79.6 (4/4) (3/3) N Input suspended solids N H (87/88) to plant SS-E 146 (3/3) (14/14) L (4/4)
N (26/27)
N (7/7)
Fig. 5 A decision tree selected into the decision forest which was generated in generation 69 of experiment 14 for predicting suspended solids in effluents SS-S. The training and test accuracies by this tree are 99% and 94% respectively.
5. Conclusions
Table 1 Comparison between GPForest, GPTree and See 5 in predicting the four outputsa Results GPForest See5 GPTree Training 99.5 % 96.7 % 99.5% SS-S Test 99.3 % 98.5 % 98.5% Training 99.5 % 99.2 % 99.0% DBO-S Test 99.3 % 95.5 % 99.3% Training 99.7 % 99.2 % 99.7% DQO-S Test 97.8 % 96.3 % 97.8% Training 100.0 % 99.0 % 100.0% COND-S Test 98.5% 96.3 % 97.8%
The applications on developing QSAR models for chemical toxicity prediction and for analysis of the data collected from a wastewater treatment plant proved that GPTree has great advanatges in comparison with algorthms that employ a greedy search strategy. a SS-S: suspended solids in effluents; DBO-S: effluent The extension of it, the YAdapt, biological oxygen demand; DQO-S: effluent chemical allows adaptive partitioning of the oxygen demand; COND-S: effluent conductivity. output values into classes during the decision tree building process, which was not possible with previous methods. In addition, GPTree provides a natural way for developing decision forest (GPForest) that proved to be an effective strategy for improving the prediction performance for previously unseen data.
References F.V. Buontempo, X.Z. Wang, M. Mwense, N. Horan, A. Young, D. Osborn, 2005, J Chem Inf Model, 45, 904-912. M.T.D. Cronin, T.I. Netzeva, J.C. Dearden, R. Edwards, D.P. Worgan, 2004, Chem Res Toxic, 17, 545 - 554. J.R. Quinlan, 1993, (Morgan Kaufmann Publishers Inc., 302. J.R. Quinlan, 1996, J Artif Intell Res, 4, 77-90. X.Z. Wang, F.V. Buontempo, A. Young, D. Osborn, 2006, SAR QSAR Env Res, 17, 451-471. Y.H. Zhao, M.T.D. Cronin, J.C. Dearden, 1998, QSAR, 17, 131-138.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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The solution of very large non-linear algebraic systems Davide Manca and Guido Buzzi-Ferraris CMIC Department, Politecnico di Milano, P.zza Leonardo da Vinci, 32 20133 MILANO – ITALY
[email protected] Abstract The manuscript describes how to simulate the formation of macro and micropollutants in complex combustion devices. This is not possible by simply introducing a detailed kinetic scheme into a fluid dynamics (CFD) code. Actually, the resulting problem would reach a so huge dimension that is still orders of magnitude larger than the feasible one (by means of modern computing devices). To overcome this obstacle it is possible to implement a separate and dedicated kinetic post-processor (KPP) that, starting from the CFD output data, allows simulating the combustion in a burner by means of a detailed kinetic scheme. The resulting numerical problem consists of the solution of a very large algebraic non-linear system comprising a few millions of variables. The manuscript describes the KPP organization and structure as well as the numerical challenges and difficulties that must be overcome to get the final numerical solution. Keywords: Applied numerical calculus, Very large non-linear algebraic systems, Mixed CFD and detailed kinetics
1. Introduction Modern programs on computational fluid dynamics (CFD) are capable of working with a reduced number of chemical species when simulating complex combustion devices such as burners, furnaces, and kilns. A reduced number of species means that only a rather simplified kinetics can be accounted for. Conversely, if one wants to quantify the formation of macro and micropollutants (such as CO, NOx, SOx, PAH, and soot) in a combustion chamber, then a detailed kinetic scheme is required. By working with a detailed kinetics, it is possible to optimize the burner geometry while assessing both its impact on the environment and its thermodynamic efficiency. Unfortunately, a detailed kinetic scheme usually comprises hundreds of chemical species (molecular and radical species) and thousands of elementary direct and inverse reactions. Consequently, the straight interaction of a CFD program with a detailed kinetic scheme is still unfeasible within any program and any available computing device being either a personal computer or a workstation. This is due to the overall dimensions of the resulting numerical problem and as a consequence to the CPU time required. It is quite simple to get an idea of the overall dimensions of the numerical problem since they are proportional to the product between the number of finite elements, which discretize the equipment, and the number of chemical species along with a few physical variables (e.g. temperature, pressure, momentum). It would be common to have some tens of millions of variables describing the coupled CFD and kinetic problem. Nowadays, commercial CFD codes cannot solve such large problems. To overcome this obstacle the manuscript describes a kinetic post-processor (KPP) that,
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starting with the CFD output data produced by a well known commercial program, simulates the combustion in a burner by means of a detailed kinetic scheme. The numerical case-study is based on the combustion of syngas, which is a mixture of hydrogen and carbon monoxide that can be obtained from natural gas, coal, petroleum, biomass and organic waste. Methanol synthesis and Fischer-Tropsch synthesis remain the largest use of syngas. Recently, syngas has become also a significant source of environmentally clean fuels and this is why an accurate study of the structure of syngas flames with a special attention to pollutant formation is of paramount interest. The design of syngas-fuelled combustion systems can utilize CFD to optimize the energetic efficiency. However, combustion systems have to respect increasingly stringent pollutant emission limits. Therefore, pollutant formation is one of the focuses of new burner designs. This explains the increasing demand for computational tools capable of characterizing the combustion systems also in terms of pollutant species.
2. The KPP structure As reported in Cuoci et al. (2007), the CFD simulation of the syngas burner is done by a commercial CFD code that integrates the Navier-Stokes equations with a very simplified kinetic model, which allows keeping rather low the overall number of unknowns. Actually, even with new generation computers, the direct coupling of detailed kinetics and complex CFD remains a very difficult and expensive task, especially when considering the usual number of grid points used in industrial applications. When referring to 105-106 grid cells (finite elements) and 100-200 reacting species, the dimensions of the overall system of mass balance equations become higher than 107-108. The general concept of “reactor network analysis” has already been employed by various authors to post-process CFD results and evaluate the formation of pollutants, using detailed kinetic mechanisms for various applications by utilizing a different level of description and various numerical methodologies (Falcitelli et al., 2002a, 2002b; Skjøth-Rasmussen et al., 2004; Novosselov et al., 2006).
Figure 1: Predicted CO and NOx emissions from the burner as a function of the number of lumping reactors.
The KPP uses as input data the temperature and flow fields predicted by the CFD code and solves the overall system of mass balance equations in a complex reaction network with detailed kinetic schemes. Two major simplifications characterize the KPP and
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make the numerical model feasible and advantageous over the direct coupling of a detailed kinetic scheme with the CFD code. The first feature is the transformation of the original computational grid into a reactor network. Knowledge of the thermo fluid dynamic field, as evaluated by the CFD code, allows several adjacent and very similar cells to be lumped into single equivalent reactors. A second way of making the numerical computations more stable and viable is defining an average and fixed temperature inside the different reactors. The solution of the CFD code provides the detailed flow, composition and temperature fields, and this information allows identifying both critical and non-critical zones in the overall reacting system. The description detail can be reduced in several regions without affecting significantly the results. The grouping or clustering of several kinetically similar cells into a single lumped reactor reduces the dimensions of the overall system (see also Figure 1). The fixed temperature inside these reactors reduces the extreme non-linearity of the algebraic system, which is mainly related to the reaction rates and to the coupling between mass and energy balances. The temperature, composition, and fluid dynamic fields obtained through the CFD code allow identifying the critical zones in the combustion chamber, i.e. the specific regions where large temperature and/or composition gradients are present. It is convenient to retain the original detail of the CFD grid in these zones. However, large volumes of the system are less critical from a kinetic point of view, e.g. cold and/or non-reactive zones. This fact suggests that the detail of the grid can be locally reduced by clustering and combining several cells into a single equivalent reactor. Of course, the lumped cell volume is simply the sum of the volumes of the grouped cells. The original grid size is thus transformed into a network of several reactors where the links between the different reactors simply combine and reflect the original flow field as evaluated by the CFD code. This allows reducing the total number of equivalent reactors and it makes feasible handling the mass balance equations by using detailed kinetic schemes with a large number of species. The original 105-106 cells can be conveniently grouped into 103-104 equivalent reactors thus maintaining a more than reasonable description of the flame structure and the reacting system. A mesh-coarsening algorithm was designed so to prevent possible dangerous situations such as the creation of geometrical irregularities and/or non-smooth transition between zones with very different volumes. The interlinking flows are evaluated according to the convective rates exchanged between the cells belonging to the different reactors. The mass diffusion coefficients for the coarse mesh are calculated in agreement with the original diffusive flow rates. Temperature and initial compositions in the equivalent reactors are the volume-averaged values of the combined cells. Different clustering levels are sequentially adopted and calculations are iteratively performed by increasing the number of cells up to the final convergence, i.e. up to the point where a further increase in the reactor network dimensions does not change significantly the predicted profiles.
3. The numerical solution of large algebraic non-linear systems The burner model (Cuoci et al., 2007) simulates the steady state behaviour of the equipment. Moreover, each cell either lumped or not is assumed to be perfectly mixed. These assumptions drive to the solution of a system of non-linear algebraic equations. CFD results are used to define the overall system by describing the mass balance equations of all the chemical species involved in the detailed kinetic scheme as well as providing the initial composition guess. For all the equivalent reactors, the steady-state
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mass balance of each species ( Xi ) accounts for convection, diffusion and chemical reaction terms (Frassoldati et al., 2007). As already mentioned, the dimension of the overall system, which is conveniently reduced using the cells lumping procedure, becomes: nVariables = nLumpedCells × nSpecies . Figure 2 shows a typical Boolean structure of the whole matrix system for a simple structured 2D grid as well as the structure of a single block.
Figure 2: Top left: Boolean structure of the Jacobian matrix of the non-linear system for a simple structured 2D computational mesh. Top right: zoom of the diagonal region. Bottom center: zoom of the single block structure (square in Top right panel) describing the chemical species presence.
The global Newton or modified Newton methods are not robust enough to solve the system using the CFD results as a first-guess. Therefore, it is convenient to approach a better estimate of the solution by iteratively solving the sequence of individual reactors with successive substitutions (helped by suitable acceleration techniques), which have the advantage of being inexpensive in terms of CPU time and take the whole system closer to the solution. Each reactor is solved by using a local Newton method (i.e. a conventional Newton method applied to the single reactor) with the possible integration of a “false transient” by means of an ordinary differential equation (ODE) system to improve the initial guess while approaching the solution. Only when the residuals of all the equations reach sufficiently low values, can a modified global Newton method be
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applied to the whole system (see also Buzzi-Ferraris and Manca, 2006). Otherwise, the previous procedure is iterated to further improve the residuals. At a very basic level, the Newton method involves the solution of a linear system of the Jacobian coefficient matrix. In order to increase the computational efficiency, special attention is devoted to the evaluation of the sparse Jacobian coefficients. The derivatives of rate equations are evaluated analytically rather than numerically. The bottleneck of this very large system consists of both memory allocation and CPU time when a Gauss factorization method is applied to the whole system. Thus, Gauss factorization is used only for the main diagonal square blocks, while an iterative method is applied to the off-diagonal terms (Manca et al., 1995). This approach saves on the memory allocation and makes the solution of the overall system viable. Also in this case, if the global Newton method does not converge, a “false transient” method is applied to ensure a better approach to the solution of the whole system. The global Newton method not only increases efficiency but also ensures the complete convergence to the solution. In fact, it is necessary to speed up the convergence procedure, which is very slow in case of direct substitutions. Moreover, high attention is required in the convergence check. In fact, in case of direct substitutions, convergence is generally controlled by the typical normalized error sum of squares: 2 nVariables (n ) X Xi(n 1) ¬ err = i (1) Xi(n ) ® i =1 where Xi are the mass fractions and suffix n refers to the iteration number. The request for err to be less than a user-defined precision F1 is a necessary but not sufficient condition. Actually, when working with direct substitutions, a small err value may just be the result of convergence failure rather than the approach to the numerical solution. Conversely, when a Newton method is adopted, if err < F1 then the method is converging to the solution within the required precision (see also BuzziFerraris and Manca, 2006). Our numerical procedure checks also for the residuals of all the equations of the global non-linear system to be less than a user-defined precision F2 . By doing so, the effective convergence to the solution of the non-linear system is extensively and consistently controlled. The KPP numerical framework is shown schematically in Figure 3. The KPP takes about 20 hours of CPU time on a Pentium IV @ 2.8 GHz with 2 GB of RAM to solve the overall problem that at the maximum extension (depending on the adaptive cells lumping procedure) reaches the significant dimension of 34,632 reactors with a detailed scheme of 106 species and 1,536 elementary reactions. Therefore, a maximum number of 3,670,992 algebraic non-linear equations are solved by the aforementioned procedure. The KPP is written in C++ and uses the object-oriented classes of the BzzMath library (Manca and Buzzi-Ferraris, 2005). The KPP output results are extensively discussed in Frassoldati et al. (2005) and in Cuoci et al. (2007).
References Buzzi Ferraris G., D. Manca, “Large Scale Algebraic Systems”, in Computer Aided Process and Product Engineering, Wiley-Vch, Weinheim, 1, 15-34, (2006) Cuoci A., A. Frassoldati, G. Buzzi Ferraris, T. Faravelli, E. Ranzi, “The ignition, combustion and flame structure of carbon monoxide/hydrogen mixtures. Note 2: Fluid dynamics and kinetic aspects of syngas combustion”, Int. J. of Hydrogen Energy 32, 3486 – 3500, 2007.
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Falcitelli M., S. Pasini, and L. Tognotti, “An algorithm for extracting chemical reactor network models from CFD simulation of industrial combustion systems”, Combustion Science and Technology, 174, 22, 2002a. Falcitelli M., S. Pasini, N. Rossi, and L. Tognotti, “CFD+reactor network analysis: an integrated methodology for the modelling and optimisation of industrial systems for energy saving and pollution reduction”, Applied Thermal Engineering, 22, 971, 2002b. Frassoldati A., G. Buzzi-Ferraris, T. Faravelli, and E. Ranzi, “Post-Processing of CFD simulations with detailed kinetics”, 28th Meeting of Italian Section of The Combustion Institute, Naples, Italy, 2005. Frassoldati A., T. Faravelli, E. Ranzi, “Ignition, Combustion and Flame Structure of Carbon Monoxide/Hydrogen. Mixtures. Note 1: Detailed Kinetic Modeling of Syngas Combustion also in Presence of Nitrogen Compounds”, Int. J. of Hydrogen Energy, 32, 3471-3485, 2007. Manca D., T. Faravelli, G. Pennati, G. Buzzi Ferraris, E. Ranzi, “Numerical Integration of Large Kinetic Systems”, ICheaP-2, ERIS, Milan, 115-121, 1995 Manca D., G. Buzzi Ferraris, “Bzzmath: an Object Oriented Library for Applied Numerical Analysis”, ACS, Reed Business Information, Milan, 7, 209-218, 2005 Novosselov I.V., P. C. Malte, S. Yuan, R. Srinivasan, and J. C. Y. Lee, “Chemical reactor network application to emissions prediction for industrial DLE Gas Turbine”, Proceedings of GT2006 ASME Turbo Expo 2006, Barcelona, Spain, 2006. Skjøth-Rasmussen M.S., O. Holm-Christensen, M. Østberg, T.S. Christensen, T. Johannessen, A. Jensen, and P. Glarborg, “Post-processing of detailed chemical kinetic mechanism onto CFD simulations”, Computers and Chemical Engineering, 28, 2351-2361, 2004.
CFD results Adaptive cells lumping criteria
Partial first guess solution + T, P, v profiles
Local solution in each reactor of the network Newton’s method
OK
Time stepping Æ ODE solver NO YES
NO
Low residuals for every reactor?
YES
Global solution for all the reactors Newton’s method
OK
Time stepping Æ ODE solver NO YES
NO
Low residuals in all the equations?
YES
FINAL SOLUTION
Figure 3: Schematic representation of the numerical procedure for the solution of large NLS.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Multi-Operations Time-Slots Model for Crude-Oil Operations Scheduling Sylvain Moureta, Ignacio E. Grossmanna, Pierre Pestiauxb a
Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA Centre de Recherche de Gonfréville, Total France, 76700 Le Havre, France
b
Abstract This paper addresses the crude-oil short-term scheduling problem, which is the first stage of the crude-oil refining process. The problem involves crude-oil unloading from marine vessels to storage tanks, transfers and mixings in charging tanks, and a charging schedule for each crude-oil mixture to the crude distillation units. Previous work on this problem includes discrete-time and continuous-time formulations. In this paper, we present a new continuous-time model that is based on the idea of postulating a potential number of tasks, which simplifies both the formulation and the application to crude-oil scheduling problems. The proposed formulation results in a non-convex mixed-integer nonlinear programming model (MINLP) which is solved using a two stage decomposition procedure. The algorithm converges quickly within a small ( TSj. 3.4. Inventory level constraint For each time-slot i, only one of the variables Viv is non-zero. This can be expressed using the upper bound constraint 0 Viv M· Ziv. We can then write the inventory level constraints for each time-slot i < n: (6)
L(i +1)t = Lit −
¦Viv +
v∈OUT (t )
¦Viv
v∈IN (t )
Inventory capacity limitations are expressed by setting the bounds of variable Lit to the minimum and maximum capacity of tank t. 3.5. Composition constraint For each crude-oil c, variables Vivc and Litc are defined as well as corresponding inventory level constraints. The composition constraint states that for each time-slot i and operation v, the composition of the stream is the same as the composition of the tank of origin. This can be expressed by the following nonlinear (bilinear) constraint
Multi-Operations Time-Slots Model for Crude-Oil Operations Scheduling
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Vivc Litc = ⇔ Vivc ⋅ Lit = Litc ⋅ Viv Viv Lit
(8)
v ∈ OUT (t )
where t is the origin tank. This leads to an MINLP model. It has been shown that when both mixing and splitting occur in a chemical process, the problem cannot be linearized and gives rise to nonconvexities [9]. Mixing occurs before a distillation when the charging tank has been filled up by two or more transfers. Splitting occurs when a distillation does not completely empty the charging tank. Instead of solving directly this nonlinear model, the following linear relaxation (MILP), corresponding to mass balances in streams and tanks, is used:
Viv = ¦ Vivc ° c ® = L Litc ¦ ° it ¯ c
(9)
It can be noted that this linearization is a correct representation of the problem studied if distillations are constrained to totally empty the charging tank, as then there is no splitting. This explains why the MILP solution is very close to the actual MINLP solution for the problems presented in section 4. 3.6. Decomposition scheme Due to the linear approximation, the solution returned by the MILP solver may violate the nonlinear composition constraints. To circumvent this problem, a nonlinear programming (NLP) model is designed to adjust the MILP solution in a two step procedure. This NLP model contains the same constraints as in the MILP solution plus the nonlinear constraints (8). The binary variables Ziv are fixed to their values in the MILP solution. The resulting solution may not be optimal for the overall MINLP model but the optimality gap can be estimated from the lower bound given by the MILP solution and the upper bound given by the NLP solution.
4. Computational results The model has been tested on several case-studies from [4] whose sizes are given in Table 1. Note that problem 4 is representative of a real industrial application. The computations were run using GAMS 22.5 with Xpress-MP 17.10 (MILP) and CONOPT 3 (NLP). For different problems and different numbers of postulated time-slots, Table 2 presents the root LP relaxation, MILP solution with CPU time and number of nodes explored, NLP solution, and the optimality gap (between MILP and NLP solutions). With less than 8 time-slots, problem 1 is proved to be infeasible. A minimum of 9 timeslots is necessary in order to find a feasible schedule that meets the demand for each mixed-oil and the arrival time of vessels. The MILP solution violates some of the nonlinear composition constraints, so the NLP solver returns a different solution. Adding another time-slot allows getting the optimal solution directly from the MILP relaxation. Solving with a larger number of time-slots returns the exact same solution as unused time-slots have a transferred volume of 0. The larger problems have been solved in less than 2 minutes within a small optimality gap (90%); CS1 is faster. In the case of CS1, the ratio between solver calls and expression evaluations is approximately 1.9; in CS2, the ratio is 5.7. One would not expect the unit cost of expression evaluations to be different between these two runs; however, the cost of solver calls per step for CS2 is 2.1 times more expensive than that of CS1. The unit cost of the IKR integration scheme is approximately one order of magnitude more expensive than that of BDF integration (0.19 vs 0.022 respectively). Interestingly, the number of steps taken by the IRK method is much smaller than that of the BDF method (23 vs 122, respectively); however, this less than an one-fold reduction is not enough to compensate for the increased unit cost. Table 1. Computational statistics
System 1
EE FS
SV
OH
TRE TJE NRE NJE TPP TSV NSA NSF NCI NCF SYS CPU ESF ISF
System 2
CS1
CS2
CS3
CS4
CS1
CS2
CS3
CS4
0.844 0.047 324 15 0.000 2.000 122 0 324 2 0.266 3.156 1.6e0 3.4e-4
0.531 0.109 70 23 0.000 3.703 23 0 233 0 0.031 4.375 1.1e0 2.4e-4
1.875 0.031 601 23 0.000 3.875 215 1 601 6 0.656 6.438 7.8e-1 1.6e-4
0.016 0.000 6 2 0.000 1.750 5 0 6 0 0.047 1.813 2.8e0 5.9e-4
2.703 0.563 2396 337 1.047 5.250 1128 17 2396 52 2.625 12.188 4.0e2 2.1e-1
3.109 0.609 1034 272 1.407 11.453 302 22 3374 4 0.641 17.219 3.5e2 1.8e-1
0.375 0.109 365 33 0.187 1.281 233 0 365 12 0.500 2.453 2.4e3 1.3e0
0.250 0.094 83 33 0.109 0.875 36 0 282 3 0.063 1.391 4.3e3 2.2e0
Time and number of on residual and Jacobian evaluations (TRE, NRE, TJE, NJE), time of physical-property package calculations (TPP), time of solver calls (TSV), number of steps attempted (NSA), number of step failures (NSF), number of corrector iterations (NCI), number of corrector failures (NCF), total system time (overheads) (SYS), total execution time (CPU); extensive- and intensive-speed factor (ESF, ISF), time units in seconds.
CS1 vs CS3: the model under consideration is a distributed parameter system given by a set of IPDAEs; these equations are discretised by the gPROMS kernel according to a user-defined approximation scheme that gives rise to the low-level model representation upon which the solution engine actually operates. Loosely speaking, these case studies have the same problem definition but different "solver configurations". In both cases
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expression evaluations and solver calls account for approximately 89% of the overall computational cost. CS3 is approximately 2.0 times slower than CS1; while CS3's costs on expression evaluations are 2.1 times more expensive than CS1, its solver calls are 1.9 times more expensive. The ratio between integration steps taken for CS3 and CS1 is 1.8, while the ratio of corrector iterations is 1.9 (hence, the number of corrector iterations per step is approximately constant for both runs). This explains the increased computational cost of expression evaluations, since one additional function evaluation is needed per corrector iteration. The increased cost of solver calls can be explained as a combination of the cost of factorisations (a ratio of 1.5 in Jacobian evaluations and one additional, more expensive factorisation in the case of RADAU-IIA IKR methods) and the cost of back-substitutions (1.9) at the level of the LA of the corrector computation, plus unaccounted overheads. CS1 vs CS4: these two simulation studies represent a “plant” at two very distinct operating regimes) and, not surprisingly, they give rise to very different computational loads. This example shows that a “model” does not have an intrinsic computational cost associated to it but only a model/problem ensemble does and, therefore, the trajectories of forcing inputs and values of initial conditions are paramount to a realistic characterisation of computational cost/load. 4.2. System 2 CS1 vs CS2: the cost of expression evaluations, foreign services (PPs) and solver calls only are approximately 34%, 55% & 11% and 23%, 68% & 9% respectively. Overall, this indicates that efficient PP calculations case consume approximately 25% of modelserver call costs and 10% of the overall computation load. Note that the number of error test failures increased by one fold in the IRK scheme, which indicates good scope for fine-tuning the step-adaption heuristics. CS3 vs CS4: the cost of solver calls is marginally larger for IRK methods compared with BDF methods (0.81sec vs 0.78sec), but IRK methods benefit from a reduced number of expression evaluations resulting more computationally attractive in this case. CS1 vs CS3 and CS2 vs CS4: this couple of simulation studies represent different operating conditions and use BDF/IKR integrators. The cost decrease of BDF-type integration is 6.2 while the cost decrease of IKR-type integration is approximately 12. It follows that the choice of most efficient integration scheme greatly depends on the operating regime; IRK integration seems more favourable for more nonlinear processes.
5. Summary and Future Work This work is the first step towards the development and validation of a comprehensive framework for evaluation of computational speed of state-of-the-art CAPE tools. The framework aims at shedding some light into the issue of computational load and how choices at the level of engineering/mathematical modelling and numerical solution algorithms can substantially change the computational speed of an application, providing a basis to tackle the analysis and reduction of computational load in a systematic and quantitative way. This contribution is the first of a series of publications addressing the topic of computational cost of model-based activities (including optimisation-based problems) and the impact of process modelling technologies.
6. Acknowledgments PA Rolandi acknowledges the funding of the Marie Curie Research Training Network under the programme PROMATCH, contract number MRTN-CT-2004-512441.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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An Implementation of Parallel Computing for Hierarchical Logistic Network Design Optimization Using PSO Yoshiaki Shimizua, Hiroshi Kawamotoa a
Production Systems Engineering, Toyohashi University of Technology, Toyohashi, Aichi, 441-8580, Japan
Abstract Recently, we have concerned the strategic optimization on logistic network design and developed an efficient two-level solution method. To cope with extremely large-scale problems, in this paper, we propose a novel algorithm for parallel computing. Thereat, noticing the analogy between the two-level algorithms and the master-slave configuration of PC cluster on one hand, and the suitability of the population-based algorithm like particle swarm optimization (PSO) on the other hand, we have developed a parallel procedure that can make overhead and idle time extremely small, and bring about high performance finally. Keywords: Logistic network optimization, PSO, Parallel computing algorithm, Masterslave PC cluster.
1. Introduction Noticing growing importance of supply chain management in manufacturing, we have concerned a logistic optimization that refers to mixed-integer programming problem. And we developed a two-level solution method termed hybrid tabu search and showed its effectiveness through various applications (Wada, Shimizu & Yoo, 2005; Shimizu, Matsuda & Wada, 2006; Shimizu, Wada & Yamazaki, 2007). To cope with extremely large-scale and complicated problems encountered in realworld applications, this study proposes a novel algorithm for the parallel computing aiming at time reduction and improvement of solution quality at the same time. For this purpose, we employed particle swarm optimization (PSO) for solving the upper level sub-problem instead of tabu search used in the previous studies. Population-based algorithm of the PSO seems particularly suitable for the parallel computing in accordance with the present goal and circumstance. After showing a modified algorithm of PSO to deal with the binary variables standing for open or close of the sites, we will outline the algorithm and discuss its properties. DC Finally, we provide a few numerical Plant experiments to validate the effectiveness of the proposed method.
2. Parallel Computing Optimization
for
Logistic
2.1. Strategic Logistics Network Model Let us take a logistic network composed of plant, distribution center (DC), and customer as shown in Fig.1. Then consider an optimization problem formulated as the following mixedinteger programming problem.
Customer
Fig.1 Logistic networks concerned here
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Minᇫᇫ ¦¦ (T1ij + Ci ) ⋅ eij + i∈ I j ∈ J
¦f
¦ ¦ (T 2
jk
j ∈ J k ∈K
+ H j ) ⋅ f jk + ¦ F j ⋅ x j j∈ J
= Dk ᇫ∀k ∈ K
(1)
=
(2)
jk
j∈ J
¦e
ij
i∈I
subject to
¦f
jk
ᇫ∀i ∈ I
k ∈K
¦e
ij
≤ S i ᇫ∀i ∈ I
(3)
j∈J
¦f
jk
≤ U j ⋅ x j ᇫ∀j ∈ J
(4)
k ∈K
x j ∈ {0,1}ᇫ∀j ∈ J
eij , f jk ∈ {Non negative real number}, ∀i ∈ I , ∀j ∈ J , ∀k ∈ K
where notations denote as follows: Ci: production cost per unit amount at plant i Dk: demand of customer k eij: shipped amount from plant i to DC j Fj: fixed-charge cost for opening DC j fjk: shipped amount from DC j to customer k Hj: holding cost per unit amount at DC j Si: upper bound for production at plant i T1ij: transport cost from plant i to DC j per unit amount T2jk: transport cost from DC j to customer k per unit amount. Uj: upper bound of holding capacity at DC j xj: take 1 if DC j is open, otherwise 0 I, J, K: index set of plants, DCs and customers, respectively The objective function is the total cost composed of transportation costs, production costs at plant, operational costs at DC, and fixed-charge costs for opening the DC. On the other hand, we impose the constraints on demand satisfaction of every customer Eq.(1), input-output balance at each DC Eq.(2), available amount of product from each plant Eq.(3), and holding capacity bound at each DC Eq.(4). In addition, binary decision variables are introduced for the selection of open DC while non-negative real variables for transport amount. To solve this kind of problem, we applied successfully the hybrid tabu search. Its development relies on the fact that metaheuristic method is amenable for solving the upper-level sub-problem that refers to a combinatorial optimization. On the other hand, the lower-level problem reduces favorably to the linear program after the binary variables are fixed. Additionally, it can be further transformed into the minimum cost flow problem that is solvable by the graph algorithm much faster than any other mathematical programming method. Furthermore, noticing the analogy between such two-level algorithms and the masterslave configuration of the PC cluster, we can realize an appropriate framework for the parallel computing. Thereat, the master PC engages in the decision of DC locations that corresponds to the upper-level sub-problem while each slave tries to optimize the route selection in the lower-level sub-problem under the DC sites allocated by the master. Moreover, we employ the PSO for solving the location sub-problem after giving a modified algorithm mentioned below to deal with the binary decision variables. Its population-based algorithm can help reach the global optimum more efficiently than a local search-based algorithm like the tabu search.
An Implementation of Parallel Computing for Hierarchical Logistic Network Design Optimization Using PSO
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2.2. Modified PSO for 0-1 Programming Problem The PSO is a metaheuristic optimization technique developed recently (Kennedy and Eberhart, 1995, 1997) after the behavior of bird flocking or fish schooling (swarm), and known as a powerful global optimization method with respect to real valued-variables. Members of swarm communicate with each other and adjust their own positions and velocities based on the information regarding the good positions both of their own and swarm. In practice, the position and the velocity are updated through the following formulas, respectively. xi (t + 1) = xi (t ) + vi (t + 1),
(5)
vi (t + 1) = w ⋅ vi (t ) + r1b( pi − xi (t )) + r2 c( y n − xi (t ))
(6) ᇫᇫᇫᇫ (i = 1,2, !, N p ), where t is generation, Np a swarm size, w an inertial constant, b and c are constants emphasizing how to guide each member to a good position. Moreover, r1 and r2 are random values in the range [0,1], pi is the best position seen by the boid i (personal best), and yn the global best position seen by the swarm (net best). The algorithm is simple enough as outlined below. Step 1: Set t=1. Initialize xi(t) and vi(t) randomly within the admissible range of these values, each pi to the current position, and yn to the position having the best fitness among the swarm. Step 2: For each member, do the following: obtain xi(t+1) and vi(t+1) according to Eqs.(5) and (6), respectively, and evaluate the new position. If it outperforms pi, update pi, and if it outperforms yn, update yn. Step 3: If the stopping condition is satisfied, stop. Otherwise let t:=t+1, and go back to Fig.2 Coding and four different bit patterns Step 2. Now, to cope with the 0-1 programming problem, we modified the original method (discrete PSO). First, let us give a binary code of decision vector describing whether the site is open (1) or close (0). Figure 2 exemplifies such coding for yn, pi and vi(t), respectively. Then viewing that the calculation by Eqs.(5) and (6) is a sort of real-value relaxation of Boolean algebra, we attempt to update the velocity and position as follows: In bit-wise, apply the majority rule among the elements vi(t), pi, yn, and decide vi(t+1) based on the vote with the different probabilities ra, rb, rc and rd depending on the occurrence among them (There occur four different cases as shown in Fig.2.). Here ra is a probability when vi(t)=pi=yn (Case 1), rb when vi(t)=piҁyn (Case 2), rc when vi(t)=ynҁpi (Case 3), rd when vi(t)ҁ(yn=pi) (Case 4). In tuning of these parameters, therefore, the following relations should be held: 1>ra>rb>rc>rd>0. Likewise, if xi(t)=vi(t+1), then let xi(t+1) be xi(t) with probability re. Otherwise let it be vi(t+1) with rf. Here set the probability rate so that 1>re>rf>0. Moreover, magnitude of the velocity is considered by the number of locus where the bit operation mentioned above is undertaken. It should be decreased linearly or nonlinearly along with the generation. 2.3. Algorithm for Parallel Computing by Discrete PSO In what follows, we outline the tasks assigned to master and slave PCs, respectively. Master PC
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Step 1: Notify the number of DC location that is different per each slave PC. Step 2: Enter “at call” mode Step 3: If contact from the slave is a request for notification of the latest net best, inform it to the slave. Then, go to Step 4. If the contact is the report of new finding, compare it with the current net best. Then update the current best if it outperforms the current one. Otherwise return the current net best to the slave. Step 4: If a certain convergence condition is satisfied, let every slave stop, and the net best be the final solution. Otherwise go back to Step 2. Slave PC Step 1: According to the notified DC number, allocate the initial location. Step 2: Solve the route selection problem. If the current search finds the personal best, update it. In addition, if it outperforms the net best on hand, report it to the master PC. Otherwise, contract with the master without doing anything. Step 3: Ask the master to inform the latest net best. Step 4: Re-locate the DC sites based on the PSO algorithm mentioned already and go back to Step 2. 2.4. Evaluation of the Parallel Computing There are popularly known several factors that will affect on the performance of the parallel computing, i.e., loads imbalance between master and slave, granularity and frequency of information exchange, and overhead for the parallelism. Regarding these factors, our algorithm has nice properties. First, it can provide a wonderful timing chart that enables us to avoid almost completely the idle time due to the load imbalance. Regarding the communication between the master and slave, not only its amount is small (only a binary code standing for DC location and the objective value) but also N: Notify & Inquire update B: Inform objective function value & DC location
x1 (t + 1) x1 (t + 2 )
x1 (t )
ڎ
=
=
PC㧝
n k +1
nk x 2 (t + 1)
…
n k +1
nk
n k −1
N ω
N ω
PCN B ω
Master
χ B
N ω
N ω
B ω
χ B
=
= (net best)
=
ڎ
=
PC2
x 2 (t + 2 )
n k +1
nk
ع: Personal best (Found) ڎ: (Outperformed net best)
Real time t Fig.3 Timing chart of communication between master and slave PCs
frequency is low due to the multi-walk implementation (The search starting from different point is leaved totally to each slave PC). Moreover, synchronization regarding information exchange between every PC is unnecessary as known from Fig.3. That can produce an additional effect on the performance of metaheuristic. Since each member is to be controlled by the different net best (See Eq.(6)), by the virtue of asynchronization, we can increase the manifoldness essential for the metaheuristic algorithm without paying any particular attentions. Due to these effects, we can make the overhead for the parallelism very small, and realize the high performance algorithm. To evaluate the total performance of the parallel computing, the following two indices are commonly used. When it takes T(P) CPU time using P number of PCs, speedup rate
An Implementation of Parallel Computing for Hierarchical Logistic Network Design Optimization Using PSO
609
S(P) is defined by S(P) = T(1)/T(P), and the efficiency ǯ by ǯ=S(P)/P. Hence, ideally these values become S(P)=P and ǯ=1, respectively.
3. Numerical Experiments Using up to 9 PCs, one of which works as the master while the others as slaves, we performed the numerical experiments under the environment on a cluster of Athlon 500 MHz processor and 100 Mbps network speed, running under Debian Linux and using the library of MPICH (Pacheco, 1997).
We prepared totally six benchmark problems with 3 different problem sizes two each. Table 1 summarizes the results (averaged over five trials) in comparison with another method that was developed based on the multi-start tabu search with information sharing and exchange (M-Tabu in Table 1 & Fig.4). Though the M-Tabu method could outperform the conventional sequential algorithm in some numerical experiments, it was implemented sophisticatedly based on the minute preliminary investigations (Ohbora, 2005). Hence, another advantage of the proposed approach is said to be its simplicity and plainness tuning the algorithm compared with the M-Tabu method. From Table 1, we know the proposed method achieves nearly the same Fig.4 Convergence trend along generation Table 2 Numerical results of the parallelism performance
perf P Obj. value CPU time Speedup S(P) Efficiency ǯ orma nce 1 33433.5 15209.9 with 2+master PC 33519.3 7448.2 2.04 0.68 less +master PC 33526.2 3658.4 4.16 0.83 4 com putat 8+master PC 33492.5 1892.8 8.04 0.89 ion time. In addition, convergence property is known better than the conventional result as shown in Fig.4 (stopping condition is the prescribed generation).
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Finally, the speedup rate and the efficiency in Table 2 also validate the effectiveness of the proposed method. Thereupon the parallelism effect along the increase in the number of PC is known to be splendid nevertheless the effect is discounted by the idle master PC. To increase the efficiency in the further development, just an extra shared memory or blackboard is enough in instead of the master PC. From these facts, we can expect to utilize the proposed method to solve much larger scale problem efficiently using larger cluster.
4. Conclusions To solve the strategic optimization problem for large scale logistic network design, we have developed a practical and efficient method for the parallel computing and implemented it as a master-slave configuration. Thereupon, we are interested in the PSO and applied it after giving its modified algorithm to handle the binary variables. In our knowledge, this is the first and novel approach of PSO for realizing information sharing and exchange and multi-walk in parallel computing. Additionally, due to the analogy between the two-level solution algorithms and the master-slave configuration of PC cluster, the developed procedure can provide very nice properties regarding the reduction of the overhead and the idle time in the parallel computing. Through numerical experiments, effectiveness of the proposed procedure is confirmed. Relying on these results, the proposed approach is shown promising for large-scale and complicated real world applications targeting at global logistics of chemical industries.
References J. Kennedy and R. C. Eberhart, 1995, Particle Swarm Optimization, Proceedings of IEEE International Conference on Neural Networks, Piscataway, NJ.pp. 1942-1948 J. Kennedy and R. C. Eberhart, 1997, A Discrete Binary Version of the Particle Swarm Algorithm, Proceedings of World Multiconference on Systemics,Cybernetics and Information, Piscataway, NJ.pp. 4104-4109 T. Ohbora, 2005, Bacheor Thesis of Toyohashi University of Technology. P. S. Pacheco, 1997, Parallel Programming with MPI, Morgan Kaufmann Publisher Y. Shimizu, S. Matsuda and T. Wada, 2006, A Flexible Design of Logistic Network against Uncertain Demands through Hybrid Meta-Heuristic Method, Proc. 16th Europe. Symp. on Computer-Aided Process Eng., Garmisch Partenkirchen, Germany, pp. 2051-2056 Y. Shimizu, T. Wada, Y. Yamazaki, 2007, Logistics Optimization Using Hybrid Meta-heuristic Approach under Very Realistic Conditions, Proc. 17th Europe. Symp. on Computer-Aided Process Eng., Bucharest, Romania T. Wada, Y. Shimizu and J.K. Yoo, 2005, Entire Supply Chain Optimization in Terms of Hybrid in Approach, Proc. 15th Europe. Symp. on Computer-Aided Process Eng., Barcelona, Spain, pp. 1591-1596
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Service-Oriented CAPE: A New Direction for Software Applications Iain D. Stalkera, Eric S. Fragab, Aidong Yangc, Nikolay D. Mehandjieva a
Manchester Business School, The University of Manchester, Manchester M15 6PB, UK Centre for Process Systems Engineering, Department of Chemical Engineering, University College London WC1E 7JE, UK c Department of Chemical and Process Engineering, University of Surrey, Guildford GU2 7HX, UK b
Abstract We introduce our vision of Service Oriented Computer-Aided Process Engineering. We consider this an exciting new direction for software applications, which promises increased flexibility and provides a way to leverage the resources of the Grid and the potential of current developments in the Web. We suggest that it is a natural, next step. Keywords: Service Orientation, CAPE-OPEN, Architecture, Ontology Agents.
1. Introduction Initiatives such as CAPE-OPEN (www.colan.org) have done much to promote the interoperability of heterogeneous software components for Computer-Aided Process Engineering (CAPE). Enthusiastic support of the resulting (interface) specifications by software vendors facilitates a plug-and-play paradigm in which an engineer can take the true “best-in-class” for each component, free of proprietary constraints, to create a (process) simulation which more closely captures his intentions. The EC-funded COGents Project (Braunschweig et al 2004) added an intelligent, semantic layer, using an agent-based software system to assist an engineer in identifying, locating, downloading and integrating those software components required for a specific CAPE application. So, what next for (software applications in) CAPE? We believe that a shift towards pure service-orientation is the next step for CAPE. Service-orientation abstracts to a level at which a service—think of as a remotely accessible software component—becomes the building block for (distributed) applications. It offers an opportunity to build upon the success of the initiatives above and promises many exciting returns, especially within the vision of “Software as a Service” where software is discovered, assembled and delivered on demand, typically at the point of need, and then “discarded”. We report on preliminary studies which convince of the achievability of such an approach. Our primary aim here is to clarify the SO-CAPE vision. We also present an initial model which combines CAPE-OPEN specifications, ontological structures and architectural descriptions inside of a multi-agent framework.
2. Preliminaries We introduce the main ideas underpinning our SO-CAPE vision. We aim to provide an intuitive feel for these elements and to establish a vocabulary for use in the sequel. 2.1. CAPE-OPEN and COGents The CAPE-OPEN initiatives (see www.colan.org) developed sets of interface standards to promote interoperability of heterogeneous process modelling software components.
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This provided a good solution to structural (in)compatibility problems. However, much was left to the (human) user. This motivated the COGents Project (Braunschweig et al 2004): a semantic layer was added in the form of a FIPA compliant (see www.fipa.org) agent-based framework to assist a user in such tasks as locating and integrating the “best” software component for a specific application. The (distributed) agents include design agents, monitoring agents, catalogues and wrappers for CAPE-OPEN software. 2.2. Service Orientation and Software as a Service Service-orientation (in software applications) is “an emerging computing paradigm that utilizes services as the constructs to support the development of rapid, low-cost composition of distributed applications. Services are self-contained modules— deployed over standard middleware platforms—that can be described, published, located, orchestrated, and programmed using [typically] XML-based technologies over a network” (Papazoglou 2008). Current service-oriented approaches usually bundle services together as a “package solution. This reflects the influence of the application service providers (ASPs) offering complete solutions which combine software and infrastructure elements with business and professional services. Typically, the level of descriptions supported is not sufficiently detailed for domains such as CAPE. Yet, that essentially any piece of software can be appropriately “wrapped and packaged” as a service has motivated interest in exploring services at finer granularities to leverage the billions of services which could emerge in the wake of Web 2.0, cf. www.soa4all.eu. A corollary to this is the desirability of intermediaries, so-called (service) brokers, which maintain networks of providers of (fine-grained) services to be composed ad hoc to fulfil a specific consumer request, cf. Gold et al (2004). Traditionally, software is designed, developed, marketed, distributed and owned as a product. In contrast, “Software as a Service” (SaaS) encourages a pure service-based software platform to procure the necessary software at the instant that it is needed (Papazoglou 2008, Gold et al 2004). Resources are invoked as services under licence and “discarded” after use. 2.3. Architecture, Styles and Views The term “(software) architecture” has many interpretations. Our working definition is the highest-level views of a software system, capturing the significant structures, components, interrelationships and the externally visible properties of these, cf. Barr et al (2003). As the size or distribution of software systems increases, the locus of design decisions moves to “higher” levels: for example, the choice of algorithms and data structures no longer comprises the major design problem (Garlan and Shaw 1994). Successful architectural models and solutions are “written up” for the purposes of re-use as architectural styles. Garlan and Shaw (1994) define an architectural style to be “a family of … systems [alike] in terms of a pattern of structural organization. More specifically, an architectural style determines the vocabulary of components and connectors that can be used in instances of that style, together with a set of constraints on architectural descriptions”. The appeal of architectural styles is that each encapsulates a compact description which answers such questions as “What is the structural pattern—the components, connectors, and constraints? What is the underlying computational model? What are the essential invariants of the style? What are some common examples of its use? What are the advantages and disadvantages of using that style? What are some of the common specializations?” (Garlan and Shaw 1994). Kruchten (1995) recognised multiple views of an architecture, including: a logical view (we prefer the more descriptive functional view) exposing functionality, a process view exposing control flow, a physical view which maps software onto hardware and reflects its distribution, and a development view describing the static
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organisation of the software in its development environment. These four views are brought together and illustrated using a representative set of scenarios. Other views are possible, e.g., a security view: it is the notion that acts as an informing principle.
3. The SO-CAPE Vision To “set the scene” we take an example from the COGents project, viz.: modelling a leacher unit in the Polyamide-6 production process, where water is used in counterflow to leach caprolactam from Polyamide-6 (in pellets), see, for example, Eggersmann et al (2002) for details of the process. An appropriate software component (for this) must compute flow-rates and compositions of the departing streams and be compatible with its simulation environment. In COGents (Braunschweig et al 2004), such requirements are expressed as an instance of the OntoCAPE concept “modeling task specification” (MTS): the user is typically facilitated in the development of this by appropriate intelligent software. The instantiated MTS is sent to a matchmaking software agent which consults with known libraries and catalogues and returns a suitable component. In the actual test case, see Yang et al (2007), the matchmaking agent was unable to locate a suitable component; only an incomplete software component, namely, a partial differential equation set object. The description of this was returned to the calling application. Subsequently, an additional instance of an MTS was created to obtain a necessary (CO-compliant) numerical solver to complete the functionality required.
Figure 1 “Psuedo-Leacher”
Effectively, the local platform created a blueprint of the required component, and located appropriate components to implement it: once integrated, the two items comprise a “Pseudo-Leacher” Model; cf. Figure 1. This anticipates precisely the current trends in web computing, especially the service orientation and the fine granularity of services encouraged by SaaS. The SO-CAPE vision enlarges and formalises this. In a nutshell, the SO-CAPE vision combines a pure service-orientation, in the mould of SaaS, with architectural views and styles, and applies this to the CAPE domain. Software components are viewed as “composite services” which are “rented” rather than being bought. Such composite services can be composed ad hoc by brokers. 3.1. The Model Suppose that we are seeking a CAPE-OPEN compliant unit operation. Currently, an engineer would (directly or indirectly) approach software vendors. If the unit does not exist, then he needs to use his expertise to create a blueprint and locate and assemble the appropriate pieces. Instead, in the SO-CAPE vision, we (would) view the CAPE-OPEN
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specification for a unit operation—indeed, each CAPE-OPEN specification—as an architectural description, with two views of the architecture: • Structural View: the interface is an external structural view (strictly, part of the development view of Kruchten (1995)). The relevant architectural style is Encapsulation: a separation of properties (what) and implementation (how). • Process View: CAPE-OPEN calling patterns in the Thermodynamics and Physical Properties packages, or the state-charts for Unit Operations, prescribe a (partial) order of steps. This is a process view of the internal architecture of the component, in the style of Pipeline (or Pipe-and-Filter) (Garlan and Shaw, 1994). Each actual class of unit operation, e.g. reactor, leacher, etc. adds the functional view. Moreover, an engineer can enlarge on or augment these views to include performance requirements, operating ranges, etc.; cf. Physical View of Kruchten (1995). In the absence of the required unit operation, an engineer—or appropriate matchmaking agent if using a COGents-like platform—approaches a broker with these architectural descriptions requesting a composite service. The broker convenes an appropriate supply network of (potential) providers, cf. Gold et al (2004); for the “Pseudo-Leacher”, the broker assembles a network of providers of equation object models and numerical solvers. The broker uses the architectural descriptions received to create appropriate requests for services from (potential) providers. For example, we most likely want to build the equation model before we try to solve this, which suggests a Pipeline process, thus, the broker would arrange for the solver provider to contract to receive information from the equation model when the solution procedure is invoked; conversely, the equation model provider would contract to provide the information to solver provider. The broker and the engineer agree terms of use, price, duration, etc. and our engineer has a purpose-specific unit operation based on his architectural descriptions. From this example, we can enumerate the essential ingredients of the SO-CAPE vision: • A (predefined, agreed upon) set of architectural styles and views. • A communication language and an appropriate ontology reflecting inter alia a shared ontological commitment to a set of components, architectural styles and views, etc. • An implementation mechanism, which includes appropriate transport protocols, etc.; cf. the “Web services technology stack”, see, for example, (Papazoglou 2008). • Service-orientation, including brokers and ideally a commitment to SaaS. 3.2. Initial Explorations We created an initial model and a first, rudimentary implementation that we summarise here. Our initial explorations were to confirm that the necessary elements are currently available or fast emerging, thus we concentrated on establishing communication among agents, using a CAPE ontology enriched with additional (conceptual) structures (for services and architectural descriptions), modelled on the COGents platform (plus software broker). Our initial model comprises: CAPE-OPEN specifications to provide us with the bases for our architectural styles; COGents framework augmented with a broker to provide a communication language and implementation mechanism; and a simplified set of concepts from OntoCAPE augmented with concepts for architectural descriptions and service descriptions, borrowed from WSDL (Web Services Description Language), to provide our ontology. The additional class of agents, Brokers, was (is) a natural fit to the COGents model: a broker can register with appropriate libraries (and of course the directory facilitator) to make its services available within the platform(s); cf. Braunschweig et al (1994). The augmented COGents framework and accommodation of service concepts ensures the desired service-orientation. We (re-)implemented the augmented COGents framework in skeletal form using the JADE agent-based platform
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(http://jade.tilab.com/). We simplified relevant OntoCAPE concepts and devised new concepts for service descriptions enriched with architectural concepts. We created Protégé (http://protege.stanford.edu/) class structures for these and exported these for use by our agents, via the JADE Ontology Bean Generator, a plug-in for Protégé (http://hcs.science.uva.nl/usr/aart/beangenerator/index25.html). The broker agents were equipped with logic-based reasoning capabilities (implemented using tuProlog, see http://www.alice.unibo.it/tuProlog/) to allow decomposition of service requests and formulation of appropriate requests for subservices to be made to a “list of acquaintances” possessed by each broker. 3.3. Next Steps Our preliminary implementations resulted in a framework synthesising the different pieces to “prove” the achievability of the approach. That the individual pieces are proven elsewhere—for example, COGents (Braunschweig et al 2004), CAPE-OPEN (www.colan.org), etc.—allowed us to focus on this framework rather than fully recreating the individual aspects. Yet, it is only through a complete implementation, that addresses a number of case studies, that we can fully assess the potential of a serviceoriented approach for CAPE. Indeed, this is our primary motivation for calling this “a vision”. Thus, the next steps are to create such an implementation and for this some groundwork is first needed, including a particular initial focus on establishing a stable set of concepts for enriching CAPE terminology with architectural styles and views.
4. Discussion and Concluding Remarks CAPE is an exciting area in which to apply service-orientation as many of the “nutsand-bolts” are available, in particular, there is a well-established vocabulary and the CAPE-OPEN standards provide the ready-made architectural descriptions and views. Service orientation offers a number of exciting benefits including flexibility, agility, increased choice, potentially an exponential growth in available resources and the removal of software maintenance and evolution concerns which come as a natural consequence (Gold et al 2004). The SO-CAPE vision (potentially) augments “try before you buy” with “use as you need” and allows for completely one-off ad hoc units, etc. In theory, a complete process could be designed and packaged as a unit operation. The realisation of the SO-CAPE vision depends significantly implementation issues and those pertaining to anticipated end users are key. A service oriented architecture (SOA) must address a number of usability issues if it is to be accepted. Engineers are conservative in the tools they use and will only accept new means of working if these are not intrusive. Perhaps, the most important user requirement, therefore, is one of transparency or immersion. Whether an application is provided as a service or resides locally should not be apparent to the user unless he wishes to know. When a user initiates a task, the software or service required should simply run. This requirement has impact on a number of tightly-related aspects, specifically: • Efficiency. When objects, still the best means of encapsulating distributed tools and services (Coatta, 2007), are distributed, “latency”, the delay between initiation and delivery, becomes a problem. The technologies for information transfer, such as the Grid, CORBA/COM, COGents and ontologies (O'Hara, 2007), provide the means for distribution. However, they do not and cannot address latency directly. Caching and data aggregation are well known approaches for tackling latency in SOA, but “SOA is no more a silver bullet than the approaches which preceded it” (Coatta, 2007). The key is ensuring that the cache and data aggregation techniques used are targeted dynamically (see below). One solution is the use of knowledge-based agent systems
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that can, over time, learn to predict what the users are likely to require and thus cache expected sets of services locally to counter latency problems. • Flexibility. It is impossible to predict exactly how any user may wish to use the system provided. The language for describing requests must be flexible, extensible and generic enough to cater for the unexpected, perhaps, sufficiently “self-aware” in the sense of being able to identify when it is unable to describe what is required. • Shared learning. A key aspect of most personal user agents, i.e., agents which learn to interact with a given user, is that they target a particular user. For SO-CAPE to be successful, such learning should be shared across the community, improving (over time) the experience of novice users. However, this sharing of knowledge must not overwhelm novice users so a balance will be required. Secondary implementation issues include security, payment and access when not connected to the Internet. The latter can be addressed by long term caching of objects subject to the satisfactory resolution of the efficiency (see above). Other issues are the target of research in SOA and networking communities and are not specific to CAPE. In summary, the key is knowledge acquisition and management, not just of the domain (CAPE) but of the users, how they work and what they expect. We have introduced our vision of service-orientation in CAPE. We have indicated how service-orientation can both enrich and complement traditional approaches; and further that a pure service-oriented model, in the mould of SaaS, is both realisable and desirable. To us, these studies provide a starting point and we invite further work.
References L Barr, P Clements, R Kazmann, 2003, Software Architecture in Practice, Addison-Wesley. B Braunschweig, E Fraga, Z Guessoum, W Marquardt, O Nadjemi, D Paen, D Pinol, P Roux, S Sama, M Serra, I Stalker, A Yang, 2004, “CAPE Web Services: The COGents way”, In A P Barbosa-Póvoa & H Matos (Eds.), European Symposium on Computer Aided Process Engineering 14 (ESCAPE-14), Elsevier, 1021-1026. T Coatta, 2007, “From here to there, the SOA way”, ACM Queue, 5(6). M Eggersmann, J Hackenberg, W Marquardt, and I Cameron, 2002, “Applications of modeling a case study from process design”, In B Braunschweig and R Gani (Editors) Software Architectures and Tools for Computer Aided Process Engineering, 335–372, Elsevier. E Gamma, R Helm, R Johnson, J Vlissides, 1995, Design Patterns: Elements of Reusable ObjectOriented Software, Addison-Wesley. D Garlan, M Shaw, 1994, “An Introduction to Software Architecture,” In Ambriola, V. and Tortora, G. (Eds.), Advances in Software Engineering and Knowledge Engineering, Series on Software Engineering and Knowledge Engineering, Vol 2, World Scientific Publishing Company, Singapore, pp. 1-39, 1993. Also available as: Carnegie Mellon University Technical Report CMU-CS-94-166, January 1994. N E Gold, C Knight, A Mohan, M Munro, 2004, “Understanding Service-Oriented Software”, IEEE Software, 71-77. J O'Hara, 2007, “Toward a commodity enterprise middleware”, ACM Queue, 5(4), 48-55. P Kruchten, 1995, “The 4+1 view model of architecture”, IEEE Software, 12 (6), 42-50. M P Papazoglou, 2008, Web Services: Principles and Technology, Pearson Education Ltd. I D Stalker, E S Fraga, 2007, “Enhancing Automated Process Design with Cognitive Agents, Distributed Software Components and Web Repositories”, Engineering Optimization, 39(5), 615-630. A Yang, B L Braunschweig, E S Fraga, Z Guessoum, W Marquardt, O Nadjemi, D Paen, D Pinol, P Roux, S Sama, M Serra, and I D Stalker, 2007, “A multi-agent system to facilitate component-based process modeling and design”, Computers and Chemical Engineering, In Press.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Using Grid Computing to Solve Hard Planning and Scheduling Problems Michael C. Ferrisa, Christos T. Maraveliasb, Arul Sundaramoorthyb a Department of Computer Sciences, University of Wisconsin - Madison, WI 53706, USA b Department of Chemical and Biological Engineering, University of Wisconsin Madison, WI 53506, USA
Abstract Production planning and scheduling problems routinely arise in process industries. In spite of extensive research work to develop efficient scheduling methods, existing approaches are inefficient in solving industrial-scale problems in reasonable time. In this paper we develop a dynamic decomposition scheme that exploits the structure of the problem and facilitates grid computing. We consider the problem of simultaneous batching and scheduling of multi-stage batch processes. The proposed method can be used to solve hard problems on a grid computer to optimality in reasonable time. Keywords: mixed-integer programming; grid computing; decomposition algorithm.
1. Introduction In a process facility, scheduling decisions are made on a daily or weekly basis. Rescheduling is common because of new order arrivals, delays in raw material deliveries, processing delays and other disruptions. Thus, an efficient solution method is required to solve the real-life problems in reasonable time frame. In this paper we consider multi-product multi-stage batch processes, where a set of orders has to be processed sequentially in multiple stages and each stage consists of parallel units (Méndez et al. 2006). In most existing methods each order is divided into a set of batches (batching problem) and then these batches are used as input to a scheduling method. This sequential approach, however, often leads to suboptimal decisions due to the trade-offs between batching and scheduling decisions. Recently, Prasad and Maravelias (2007) proposed a mixed-integer programming (MIP) model to address the simultaneous batching and scheduling of multi-stage batch processes. The proposed model can potentially lead to better solutions, but it is computationally expensive. The goal of this paper is the development of a solution method that enables us to solve real-world batching and scheduling problems simultaneously in reasonable time. The proposed method is based on a dynamic decomposition algorithm that is well suited to grid computing using the Condor resource management system.
2. Batching and Scheduling of Multi-stage Batch Processes 2.1. Problem Statement Given are a set of orders (iI) with demand qi and release/due time ri,/di; a set of processing units (jJ) with minimum/maximum batch sizes bjmin/bjmax, processing time Wij and processing cost cij; a set of stages (kK) with parallel processing units (jJk; J = J1J2 …J|K|) at each stage k; a set of forbidden units FJi for order i and a set of
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forbidden production paths (j,jƍ)FP for all orders. The goal is to determine the number and size of batches for each order (batching), the assignment of batches to processing units at each stage, and the sequencing of assigned batches in each processing unit (scheduling), so as to minimize the makespan. We assume that all orders go through all stages, unlimited storage is available for intermediates between stages, and changeover times are negligible. 2.2. MIP Formulation min max To account for the batching decisions, we have to calculate the minimum li = ªqi/ bˆi º max max and maximum li = ªqi/ bi º possible number of batches that order iI can be divided max max to, where bˆi = minkK (maxjJAik bj ) is the maximum feasible batch size for order i, max max bi = minkK (minjJAik bj ) is the largest batch size for order i that can be processed on all allowed units, and JAik = Jk\FJi is the set of units that can be used for the processing of order i in stage k. The set of potential batches for order iI is Li = {1, 2, …limax}. More details can be found in Prasad and Maravelias (2007). 2.2.1. Batch Selection and Assignment We introduce binary variables Zil, Xilj and continuous variable Bil to denote the selection, assignment, and size respectively of batch (i,l). Eq. (1) enforces that a batch is assigned to a processing unit at each stage if it is selected. If assigned, then the size of batch (i,l) has to be within the processing limits, as in eq. (2). Eq. (3) ensures that the demand for each order is met.
¦
X ilj
i , l L i , k
Z il
(1)
jJA ik
¦
¦
min
b j X ilj d Bil d
jJAik
max
b j X ilj
(2)
i , l L i , k
jJA ik
¦B
il
t qi
i
(3)
l L i
2.2.2. Batch Sequencing and Timing We introduce binary Yili’l’k that is equal to 1 if batch (i,l) precedes (i’,l’) in stage k. The sequencing and timing of batches in the same stage is accomplished via eqs. (4) and (5): X ilj X i ' l ' j 1 d Yili ' l ' k Yi ' l ' ilk i , l , i ' l ' IL : i d i ', k , j JA ik JA ick
¦
Ti ' l ' k t Tilk
IJ i'j X i ' l ' j M 1 Yili ' l ' k
i , l , i ' l ' IL, k
(4) (5)
jJA ick
where Tilk denotes the finish time of batch (i,l) in stage k. The timing of a batch between two consecutive stages is enforced by eq. (6), while release and due time constraints are enforced by eq. (7), where IL ^i , i ' I , l L i , l ' L ic : i z i ' i i ' l z l ' ` is the set of all combinations of batches that can be sequenced on a unit:
Ti ,l , k t Tilk 1
¦IJ
ij
X ilj
i , l Li , k
(6)
jJAik
ri Z il
¦¦ k ' d k jJA ik c
IJ ij X ilj d Tilk d d i Z il
¦¦ k ' ! k j JA ik c
IJ ij X ilj
i , l Li , k
(7)
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2.2.3. Additional Constraints We introduce eq. (8) to exclude infeasible assignments. Eq. (9) takes care of forbidden paths, while eqs. (10) and (11) are used to avoid symmetric solutions:
¦ ¦W
ij
X ijl d MS min iIA j
iIA j l Li
X ilj X ilj ' d Z il
Z il 1 d Z i ,l Bil 1 d Bi ,l
^¦ k '! k
` ^
`
min( IJ ij' ) min ri ¦ min( IJ ij ' ) j 'J k c
iIA j
k ' k
j 'J k c
k , j J k
(8)
i I , l L i , ( j , j ') FP
(9)
i , l L i
(10)
i I , l L i
(11)
Integrality and non-negativity constraints are expressed by eq. (12). Z il , X ilj , Yili ' l ' k ^0,1`
Bil , Tilk t 0
(12)
where IAj=I\FIj is the set of orders that can be assigned to unit j. min
We also fix all variables for lLi to zero. Finally, we fix binaries Zil to 1 for l li . 2.2.4. Objective The objective is to minimize the makespan MS, which is greater than the finish time of all batches at the last stage. min MS (13)
MS t Til |K |
i I, l Li
(14)
The MIP model P consists of eqs. (1) – (14). Note that the model has an inherent hierarchy of decisions: a selected batch is assigned to a single unit in each stage via eq. (1), and a sequencing binary is activated if two batches are assigned to the same unit via eq. (4).
3. Grid Computing Grid Computing utilizes a pool of computers as a common resource in an opportunistic manner. It does not require dedicated computers, but it simply uses distributively owned computational resources and facilitates better utilization of CPU power. We use the Condor resource manager (Epema et al., 1996) that manages a large collection of Linux-based machines at University of Wisconsin Madison. However, Condor can be used on other machine architectures and operating systems (Windows, Solaris) as well. We implement the proposed solution approach for this problem using GAMS/Grid options (Bussieck et al., 2007). We adopt the master-worker paradigm as a model of computation, where model P is decomposed into a number of subproblems (tasks). The master processor generates and spawns all the subproblems, and also collects the results of each subproblem (see Figure 1). A separate task directory is created for each subproblem by the master processor. Condor submits the subproblems to worker processors for execution. Condor does not require a shared file system between the master and the workers. Instead, it simply ships the subproblem directory to a “sandbox” on the worker machine, which in turn executes the subproblem within the sandbox. Once the subproblem is completed, a file “finished” is created in the subproblem directory of the master processor along with the requisite solution files. The
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appearance of the “finished” file and the solution loading process are carried out in GAMS using the “handlecollect” primitive. Communication between the master and worker processors is implemented via the Condor_chirp utility. When a new incumbent is found, the utility updates the master processor by creating a “trigger file” in the task directory. Further, it uses the current best incumbent from the master processor to prune/continue the subproblem in other worker processors. Examples of the GAMS syntax used for grid submission, and the methods that deal with different grid engines are discussed in Bussieck et al. (2007). “handlecollect” repeatedly checks for “finished” files Separate directory for each subproblem
“finished” file upon completion of subproblem
Master …
Co
“trigger” file is created if new incumbent is found
or nd
Worker 1
Worker 2
Sandbox
Sandbox
…
Worker N Sandbox
condor_chirp utility Fetch: copies trigger file Remove: removes trigger file after copying Put: places new incumbent in master directory
Figure 1. Architecture for Optimization on the GAMS/Grid using Master-worker Paradigm.
4. Dynamic Decomposition Algorithm 4.1. Strong Branching Our goal is to dynamically decompose original model P into smaller subproblems that can be solved using Grid computing. Unlike static decomposition, where subproblems are generated a priori, dynamic decomposition generates subproblems over the time as and when required. We first used strong branching with the goal of generating subproblems that are easier than problem P. Based on the size of the grid engine, problem P is partitioned using strong branching into a number of subproblems (open nodes), which are submitted to worker processors. Subproblems that remain unsolved after a resource limit, are re-partitioned using strong branching. The process is repeated dynamically as necessary until, in principle, all subproblems are easy to solve (Figure 2a). Nevertheless, our preliminary results indicated that strong branching does not always lead to easier subproblems. Specifically, some of the open nodes correspond to problems that are almost as hard as the original problem P. This motivated us to develop a domain-specific decomposition method. 4.2. Proposed Decomposition Our solution method exploits the inherent structure of the problem to sequentially decompose original model P into subproblems of different levels of complexity (Figure 2b). Subproblems are generated by fixing batch selection Zil and batch-unit assignment Xilj binary variables. 4.2.1. Fixing Selection of Batches The 1st-level subproblems are generated by fixing the number of batches for each order iI. If li denotes the number of batches that are fixed for order iI, then each subproblem is generated by setting li = limin = limax, iI in eqs. (1) – (14) of model P. Note that we consider all possible combinations of li between limin and limax for a given set of orders.
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4.2.2. Fixing Batch-unit Assignments If any of these 1st-level subproblems remains unsolved within a resource limit (typically 1 hr), then it is decomposed into a set of 2nd-level subproblems by fixing batch-unit assignment decisions at one stage kF (typically the bottleneck stage). If any of these 2ndlevel subproblems remains unsolved, then it is further decomposed into 3rd-level subproblems by fixing batch-unit assignment decisions at another stage. This process can be repeated multiple times, or it can be followed by the dynamic decomposition based on strong branching (section 4.1). P
Master
P 1st-level subproblems by fixing Zil Worker 2
Worker 1 Promising Worker 3
Non-promising
Worker 4
Promising Non-promising
a) Strong-branching-based decomposition
2nd-level subproblems by fixing Xilj in one stage 3rd-level subproblems by fixing Xilj in another stage
b) Domain-specific decomposition
Figure 2. Dynamic decomposition based on a) strong branching and b) problem structure (grey nodes denote hard subproblems that need to be decomposed further).
The number of different batch-unit assignments is very large even for medium size problems. Some of these assignments lead to promising subproblems(i.e. subproblems that are likely to yield a good solution), while others lead to non-promising ones. Although non-promising subproblems are easy to prune, the resources required for their generation, submission and solution are substantial. To avoid generating a large number of such tasks, we identify a subset of assignments that are likely to lead to good solutions and solve each one of them separately, while subsets of non-promising assignments are lumped into larger subproblems that are easier to prune. To this end, we use the idea of balanced batch-unit assignments: a min makespan schedule is likely to have the load in the bottleneck stage distributed almost equally among units. Thus, subproblems that correspond to balanced assignments are generated by fixing all variables Xilj at stage kF: X ilj
1,
j J k F , (i , l ) D j
(15)
where set Dj is the set of batches that are assigned to unit j in the current subproblem. Non-promising subproblems are generated by adding either of the following constraints for each unit in stage kF:
¦X
d NJ
MIN
ilj
1
(16)
t NJ
MAX
ilj
1
(17)
i ,l
¦X i ,l
where NJMIN (NJMAX) is an estimate of the number of batches that if assigned to a single unit makes it highly (lightly) loaded. In this paper we use NJMIN = ¬0.9M/|J(kF)|¼ and
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NJMAX = ª1.1M/|J(kF)|º, where M is the total number of batches in the current subproblem and |J(kF)| is the number of units in stage kF. Note that promising subproblems have all batch-unit variables fixed in stage kF from eqs. (1) and (15) but are hard to solve due to their poor lower bounds. On the other hand, non-promising subproblems are less tightly constrained by eq. (16) or (17) but are pruned easily because they encompass many but unbalanced assignments, thus have high lower bounds. Finally, we developed a pre-processing procedure in order to identify infeasible batchunit assignments. First, we remove subproblems with the forbidden batch-unit assignments. Then, we check the capacities of units to ensure that the demands of orders are met. Finally, when variables Xilj are fixed in more than one stage, we remove the subproblems with forbidden paths. The proposed procedure improves the performance of our algorithm by screening infeasible subproblems a priori, thus reducing the time required to generate, spawn and solve a number of subproblems.
5. Results We present results for a process that consists of three stages with two units per stage and 10 orders. We consider two instances of this problem: instance 1 results in a problem with 10-11 batches, while instance 2 with 12-15 batches. The problem data are available from the authors. We analyzed the effect of both the automatic decomposition scheme based solely on strong branching (scheme 1) and the domain-specific decomposition (scheme 2). Instance 1 was solved to optimality in almost 2 hr of wall clock time and 2,905,742 nodes using scheme 1. In scheme 2, we carried out the 1st-level domain-specific decomposition and then followed with decomposition based on strong branching. Instance 1 was solved in only 7.5 min of wall clock time and 9,601 nodes. For instance 2, scheme 1 failed to solve the problem due to the generation of innumerable subproblems. On the other hand, scheme 2 solved the problem to optimality in 9 hr of wall clock time exploring 222,065,793 nodes. In this case, we carried out the 1st, 2nd and 3rd level domain-specific decompositions followed by strong branching. In this paper we proposed a solution method to solve the problem of simultaneous batching and scheduling in multi-stage multi-product processes. Our method uses GAMS/Grid options and grid computation facilitated by the Condor management system. It couples problem-specific knowledge with strong branching to dynamically decompose hard problems into a set of subproblems. Our computational studies showed that the proposed method can be used to solve hard problems to optimality with reasonable time. Finally, we note that the proposed methodology can be applied to a wide range of production planning and scheduling problems.
References Bussieck, M., Ferris, M. C., Meeraus, A., 2007. Grid Enabled Optimization with GAMS. Technical Report, Computer Sciences Department, University of Wisconsin. Epema, D. H. J., Linvy, M., van Dantzig, R., Evers, X., Pruyne, J. 1996. A Worldwide Flock of Condors: Load Sharing among Workstation Clusters. Future Generation Computer Systems 12, 53-65. Méndez, C.A., Cerda, J., Grossmann, I.E., Harjunkoski, I., Fahl, M., 2006. State-of-the-art Review of Optimization Methods for Short-term Scheduling of Batch Processes. Comput. Chem. Eng. 30, 913-946. Prasad, P., Maravelias, C.T., 2008. Batch Selection, Assignment and Sequencing Multi-stage Multi-product Processes. Comput. Chem. Eng., (doi:10.1016/j.compchemeng.2007.06.012).
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Benchmarking numerical and agent-based models of an oil refinery supply chain Koen H. van Dama, 1, Arief Adhityab, Rajagopalan Srinivasanb, c , Zofia Lukszoa a
Delft University of Technology, Technology, Policy and Management, the Netherlands Institute of Chemical and Engineering Sciences, Singapore c National University of Singapore, Dept of Chemical and Biomolecular Eng, Singapore 1 Corresponding author. E-mail:
[email protected] b
Abstract Today’s integrated refinery supply chains embrace two distinct types of complexities – (i) a complex production processes that can operate in various regimes, handling different raw materials and producing a variety of products, and (ii) a complex network of intelligent plan-source-move type elements that synchronize among the far-flung supply chain entities to ensure smooth, efficient, and profitable operation. Modelling such socio-technical systems poses a significant challenge. Traditionally numerical modelling has been the preferred choice, especially in process systems engineering; but recently agent-based modelling, which take an actor-centric perspective, has begun to be considered as an alternative. In this paper, we critically evaluate the choice of modelling paradigms for an integrated oil refinery supply chain. Initial experiments confirm that the behaviour of the two models is the same – thus validating the conjecture that a problem can be adequately described in both paradigms. The equationbased model appears to be better suited for describing complex physical and chemical phenomena; the agent-based model allows efficient ways to describe actions and behaviours of human and decision-making elements where cooperation and negotiation between intelligent entities come to the fore. Keywords: Agent-based model, numerical model, benchmarking, oil refinery, supply chain
1. Introduction Contemporary problems in Process Systems Engineering often require a model of the process, product, or system for their solution. There are many ways to model a system depending on the purpose of modelling, functional specifications, available information, etc. In contrast to traditional process systems where artefacts and physical loads are the key constituents, supply chains (SCs) are best thought of as socio-technical systems where complex production technologies interact with distributed intelligent entities – each with their own dynamics, goals and desires. There is significant challenges in modelling such systems that function in dynamic, stochastic, socio-economic environments with intra- and inter-organizational complexity. Numerical modelling, traditionally the paradigm of choice in process systems engineering, could be adopted to represent such complex socio-technical systems. An alternative with complementary strengths is offered by agent-based models, which take an actor-centric perspective instead of the activity-based one. The actions of each agent and the interactions between them are explicitly represented in such models, and in consequence the behaviour of the entire system emerges.
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In this paper, we critically evaluate the choice of modelling paradigms for an integrated oil refinery SC. The two different modelling approaches will be compared with a view to identifying their relative strengths and weaknesses. Benchmarking is performed to identify the role best suited for each. The rest of this paper is structured as follows. Section 2 describes the benchmarking process and the performance indicators, followed by the refinery case study in Section 3. Section 4 discusses the numerical and agentbased models, which are used to conduct a comparative experiment in Section 5. Section 6 concludes with lessons learnt from the benchmarking exercise.
2. Benchmarking process Benchmarking is about making comparisons and through these, learning generalisable lessons. It is not possible to compare modelling paradigms based only on the conceptual model specifications; rather a well-defined benchmarking process is required. In order to assess the performance of the two modelling paradigms, the following scheme is suggested (Monch, 2007): 1. Definition of the objectives for the study 2. Determination of what is to be benchmarked (the object of the study) 3. Determination and specification of performance measures 4. Description of scenarios (well-structured experiments) that should be simulated 5. Simulation and discussion of the results with recommendations The objective of the study, as said in the Introduction, is the comparison of the two modelling paradigms. The objects of the study are two models of a refinery SC. To determine the performance measure for both ways of modelling it is essential, besides comparison of the outcomes, to also reflect on the modelling exercise as a whole. For instance, it is now widely accepted that the ease of developing the model and maintaining it over the lifespan of the application is an important (sometimes critical) determinant in successful industrial acceptance. Therefore, in addition to comparing the numerical simulation results from the two models, we also look at other qualitative key performance indicators. Cavalieri (2007) describes a benchmarking service for different users of control systems (e.g., researchers, vendors as well as practitioners from the industry). There performance is evaluated in terms of efficiency, robustness and flexibility. We use the same indicators here. Considering efficiency, we will look at the ease of expressing the problem in each modelling paradigm. For robustness, the possibility of extending the models can be compared and for flexibility their re-usability. Inspired by the work of Cavalieri, an additional performance indicator is formulated: the ease of explaining the model and its applicability.
3. Case study: Integrated refinery supply chain A typical refinery SC comprises crude oil suppliers, 3rd party logistics providers (3PL), shippers, jetty operators, the refinery and customers. The refinery occupies a pivotal position in the SC with its functional departments initiating and controlling the interactions with the external entities for the various SC activities. Crude procurement is managed by the procurement department, which interacts with the sales department to get demand forecasts, the operations department to confirm crude suitability, and the logistics department to arrange crude transport before ordering from a supplier. Crude is typically transported in a very large crude carrier (VLCC). The storage department manages the crude unloading from VLCC to crude tanks via pipeline or jetty.
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The operations department is responsible for supervising the transformation of crudes into various products through the refining operations such as distillation, reforming, cracking, isomerisation and product blending. The operations department decides the throughput and production mode and requests the release of crudes from storage. Each production mode maximizes the yield of a specific product and has an associated recipe, (i.e. the ratios of the various crudes). The sales department provides actual demand information to the storage department to release the products for delivery. A maze of complex interactions between the different entities and resulting decisions ensure the orderly and efficient functioning of the supply chain as described in detail by Julka et al. (2002). There combined performance determines the economics via crude costs, product prices, operation costs, transportation, etc.
4. Integrated refinery supply chain modelling Two dynamic models of the supply chain have been developed: a numerical model and an agent-based one. Despite the differing paradigms, the models share the same assumptions and model boundaries. Both models explicitly consider the various SC activities mentioned above. Both models use the same values for parameters such as production recipes and yields, capacities of storage and throughput, mean demands, crude prices, variation percentages, etc. 4.1. Numerical model The SC entities and operations described in Section 3 have been modelled as a blockbased simulation (Pitty et al., 2007) and implemented in Matlab/Simulink (MathWorks, 1996). Four types of entities are incorporated in the model: external SC entities (e.g. suppliers), refinery functional departments (e.g. procurement), refinery units (e.g. crude distillation), and refinery economics. Some of these entities, such as the refinery units, operate continuously while others embody discrete events such as arrival of a VLCC. Both are considered using a unified discrete-time representation. The model explicitly captures the various SC activities such as crude oil supply and transportation, along with intra-refinery SC activities such as procurement planning, scheduling, and operations management. Stochastic variations in transportation, yields, prices, and operational problems are considered. The model allows the user the flexibility to modify not only parameters, but also replace different policies and decision-making algorithms in a plug-and-play manner through ‘m’ files. 4.2. Agent-based model The agent-based (AB) model is based on a generic ontology for socio-technical systems (van Dam and Lukszo, 2006) and Java building blocks that have previously been used in other infrastructure case studies, such as intermodal freight transport (Sirikijpanichkul et al., 2007), CO2 emission trading (Chappin et al., 2007), and industrial clusters (Nikolic et al., 2007). All the instances of the model components, including the agents and all technical components (e.g., refinery units, jetty, etc) and their links (e.g., pipeline between the jetty and the crude storage tank) have been stored in a Protégé knowledge base, which can be changed without having to adjust the model source code, which works independently. For physical components possible in and out flows are defined, along with certain other properties. Furthermore, the ontology contains concepts such as 'transport contract' and 'physical flow' which are instantiated during the model run. The agents in the model all act autonomously according to their own goals. A schedule is made so that some processes (e.g., procurement) only occur at certain intervals while others (e.g., production) happen each time step of the model. Events such as the arrival
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#RUDE3TOCKKBBL
#RUDE #RUDE
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Figure 1. Base case for crude inventory and production profiles from the numerical model
of a VLCC at the jetty are continuously monitored. Agent negotiation about trade and transport is formalized in contracts, providing a natural representation of the problem. This agent-based model is implemented in Java using the Repast agent simulation toolkit (North et. al, 2006).
5. Experiments To assess the validity and similarity of the two modelling paradigms for the current case study, the model predictions for a base-case scenario are first compared. Other scenarios have also been identified but are not elaborated here due to space constraints. The basecase considered the operation of the integrated refinery supply chain over a period of 120 days. Both models reflect the specification data and parameters reported in Pitty et al. (2007). The model predictions show that both modelling paradigms result in very similar behaviour of procuring and processing crudes. One visible indication of this is from the evolution of the various crude inventory levels (compare Figures 1 and 2). Given the numerous stochastic effects in the models, it is natural that the two profiles do not coincide exactly. For instance, the underlying random number generators in Matlab and Java do not result in the same sequence of random numbers. These platform-dependent quirks will however be overcome though our ongoing work and enable more precise comparisons of the model outcomes. However, overall the experiment confirms that the behaviour of the two models is the same, validating the conjecture that the supply chain can be adequately described in both paradigms.
6. Evaluation and conclusions Our preliminary results from model development and base case scenario are reported next. More scenarios are being currently studied to draw further insights about the
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relative advantages of the two paradigms, but some initial conclusions can already be drawn. Here the four performance indicators from Section 2 are revisited: 1. Ease of expressing the problem in each modelling paradigm. Any supply chain contains two distinct types of elements – production processes (technological system) with complex physical and chemical phenomena, and decision-making / business processes involving inter-entity collaboration (social system). The behaviour of the former is best described through equations and the latter through rules. The numerical model caters well to the equation-oriented aspects. The agent-based model has lesser expressive breadth for these, but offers instead a rich vocabulary for describing business processes and rules. For example, limitations to transfer of crudes from the jetty to the storage tank or including hold-ups in the pipes was easily addressed in the numerical model but more complicated in the AB model. On the other hand, the role of the 3PL and the negotiations between various shippers are easily represented in the agent-based model. 2. Ease of extending the models. From our current studies, the two paradigms appear comparable in this aspect. For example to incorporate a new procurement strategy in the numerical model, a new equation to calculate crude procurement amount was needed. In the AB model, this can be addressed by changing the behavioural rules of the procurement department to include a request to the storage department to provide up to date data on stocks. This additional term was then added to the equation to determine the new amount. 3. Ease of re-use. The AB paradigm provides a hierarchical framework to describe the model constituents. In this work, a key part of the model – the ontology – was derived from earlier modelling efforts in other domains. The use of a generic ontology makes re-use easier and also allows connections to other models, for example one of an industrial cluster incorporating other chemical industries where other agents could become consumers of the refinery. The numerical model does not enforce any such structure, hence reusability is in general difficult especially across different modellers.
Figure 2. Base case for crude inventory and production profiles from the AB model
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4. Ease of explaining the model. As stated by Van der Zee (2006), “a fundamental challenge in simulation modelling of manufacturing systems is to produce models that can be understood by the problem owner”. The explicit hierarchical structure in the agent-based model also enables a natural representation for behaviours, both in terms of organization and visualization; mostly, this is harder with a set of equations. It is important to stress that the current study is an initial part of a larger, more comprehensive effort to map the relative merits of the two modelling paradigms. The agent-based and numerical approaches have complementary strengths because they can be used for different operational schemes with minimal customization. In our on-going and future work, we will include further refining the two models to address more detailed issues to evaluate how they capture various aspects of the problem. Furthermore, we are working on addressing the important issues of quantifying efficiency, robustness and flexibility by involving an expert panel to evaluate the modelling paradigms. Our future work will also concentrate on approaches to re-use model components and modelling results across applications. This would eliminate modelling expertise on the part of the user and enable a new breed of applications where the developer does not have to be a rate-limiting conduit between decision makers and models.
References S. Cavalieri, M. Macchi, P.Valckenaers, 2003, Benchmarking the performance of manufacturing control systems: design principles for a web-based simulated testbed, Journal of Intelligent Manufacturing, 14(1), pp. 43–58 E. Chappin, G. Dijkema, K.H. van Dam, Z. Lukszo, 2007, Modeling strategic and operational decision-making – an agent-based model of electricity producers, The European Simulation and Modelling Conference 2007 K.H. van Dam, Z. Lukszo, 2006, Modelling Energy and Transport Infrastructures as a MultiAgent System using a Generic Ontology, 2006 IEEE SMC, Taipei, Taiwan N. Julka, I. Karimi, R. Srinivasan, 2002, Agent-based supply chain management – 2: a refinery application, Computers and Chemical Engineering, 26(12), pp. 1771-1781 MathWorks, 1996, Using Simulink: Version 2 L. Monch, 2007, Simulation-based benchmarking of production control schemes for complex manufacturing systems, Control Engineering Practice, 15, ,pp. 1381–1393 I. Nikolic, G.P.J. Dijkema, K.H. van Dam, 2007, Understanding and shaping the evolution of sustainable large-scale socio-technical systems towards a framework for action oriented industrial ecology. In: M. Ruth and B. Davidsdottir (Eds.) The Dynamics of Regions and Networks in Industrial Ecosystems, Edward Elgar (In Press) M.J. North, N.T. Collier, J.R. Vos, 2006, Experiences Creating Three Implementations of the Repast Agent Modeling Toolkit, ACM Transactions on Modeling and Computer Simulation, 16(1), ACM, New York, USA, pp. 1-25 S. S. Pitty, W. Li, A. Adhitya, R. Srinivasan, I. A. Karimi, 2007, Decision Support for Integrated Refinery Supply Chains. 1. Dynamic Simulation, Computers and Chemical Engineering (In Press) A. Sirikijpanichkul, K.H. van Dam, L. Ferreira, Z. Lukszo, 2007, Optimizing the Location of Intermodal Freight Hubs: An Overview of the Agent Based Modelling Approach, J. of Transportation Systems Engineering & Information Technology, 7(4), pp 71-81 D.J. Van der Zee, 2006, Modeling decision making and control in manufacturing simulation. International Journal of Production Economics, 100(1), pp. 155–167.
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Large-Scale Nonlinear Programming Strategies for the Operation of LDPE Tubular Reactors Victor M. Zavala and Lorenz T. Biegler Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avnue, Pittsburgh PA 15213, USA
Abstract There is substantial economic interest to optimize the operations of low-density polyethylene (LDPE) tubular reactors. Due to the high complexity of these units, systematic optimization techniques need to be used for this. One of the main limitations associated to this is the high dimensionality and complexity of the multi-zone tubular reactor model. In this work, we demonstrate that a simultaneous full-discretization approach coupled to a full-space nonlinear programming (NLP) solver results in an efficient strategy to cope with these limitations. We exploit these advantages in the analysis of different scenarios arising in the operation of LDPE reactors. In particular, we propose a multivariable optimization strategy able to compensate for time-varying disturbances in order to keep the reactor temperature profile and final properties of the polymer at targets. Finally, we show that the optimizer can easily be extended to incorporate economic decisions in the objective and we illustrate the potential benefits and bottlenecks of this approach. Keywords: LDPE, tubular reactor, large-scale optimization, operations, economics.
1. Introduction Low-density polyethylene (LDPE) is often produced in tubular reactors through freeradical polymerization of ethylene at high pressures (1500-3000 atm) and in the presence of peroxide initiators. In addition, a chain-transfer agent (CTAs) is incorporated in order to control the polymer melt index. While LDPE processes are often highly profitable, there exist multiple factors limiting their performance. The high exothermicity of the reactions and the high pressures force the design of long multizone tubular reactors (1-3 km) with thick walls, small inside diameters (6-10 cm) and sophisticated jacket cooling systems. A schematic representation of a typical LDPE reactor is presented in Figure 1. These designs involve multiple peroxide, monomer and CTA side streams distributed along the reactor zones. This gives rise to strong multivariable interactions between different phenomena occurring downstream of the reactor and leads to complex operating procedures. In addition, the selected operating conditions might also promote continuous polymer deposition on the reactor walls (fouling) that further limit the reactor productivity (Buchelli et.al, 2005). During the last years, several steady-state rigorous models for LDPE tubular reactors have been proposed (Kiparissides et.al, 2005). These models usually comprise several hundred highly nonlinear differential and algebraic equations (DAE) that describe the evolution of the reacting mixture along the reactor. In addition, in most reactor arrangements, the zone jackets are operated countercurrently, giving rise to multi-point boundary conditions. The resulting model complexity has limited the use optimization techniques, especially in on-line applications where fast solutions are required
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(Asteuasin and Brandolin, 2007). In this work, we propose a full-discretization formulation of LDPE tubular reactor models. The strategy is able to handle multi-point boundary conditions along the reactor zones. In addition, it allows the use of efficient NLP solvers able to solve highly nonlinear problems with many degrees of freedom quickly and efficiently. These benefits are exploited in the design of a multivariable optimizer for LDPE reactors that can be used for different operating scenarios of industrial interest.
Figure 1. Schematic representation of multi-zone LPDE tubular reactor.
2. Mathematical Model 2.1. Model Structure In this work, we consider the rigorous model presented in (Zavala and Biegler, 2006). The model describes the steady-state evolution of the reacting mixture and of the cooling agent along each one of the reactor zones. The material balance equations have the generic form,
1 dFk , j Ak dz
rk , j ( z k )
k 1,..., N , j 1,..., NS
Fk , j 0 M kM Fk 1, j z kL1 , Fkss, j F1, j 0 F j fs
k
(1)
2,..., N , j 1,..., NS
j 1,..., NS
Where Fk , j denotes the molar flow rate of component j at zone
k and rk , j denotes the
corresponding net reaction rate varying along the axial position z k at each zone. The components present in the mixture are the multiple peroxides contained in the initiator feed streams, monomer, comonomer, solvent, chain-transfer agent(s), moments of live polymer chains, moments of dead polymer chains, long-chaing branching and shortchain branching. Symbols N and NS denote the number of reactor zones and species in the mixture, respectively. Fkss, j denotes the side stream flowrate of a particular component to a particular zone while F j fs denotes the feed stream flowrate of a particular component. Finally, Ak is the internal cross-sectional area of a given zone,
z kL is the corresponding total length. Symbol M kM denotes material balances at the feed points which implicitly determine the initial conditions of the zones. The model incorporates energy balances for the reacting mixture along the zones,
U kR z k Q kR z k C pR,k z k
dTkR dz
rp
4U k R Tk z k TkJ z k dk
k
1,..., N
Large-Scale NLP Strategies for the Operation of LDPE Tubular Reactors
TkR 0 M kR Fk 1, j z kL1 , TkR1 z kL , F jss, k , Tkin
k
2,..., N
631
(2)
T1R 0 T1in
Where U kR ,Q kR and C pR,k are the density, velocity and heat capacity of the reacting mixture, respectively, which vary along the axial position. Symbol d k denotes the zone diameter. Functions M kR denote energy balances at the feed points. For the cooling agent flowing along the jackets we have the energy balances,
U kJ z k Q kJ z k C pJ, k z k J k
T
z L k
where
in k
T
dTkJ dz
S d kU k AkJ
T z T z J k
k
R k
k
k 1,..., N
(3)
k 1,..., N
U ,Q and C pJ ,k are the density, velocity and heat capacity, respectively, of the J k
J k
cooling agent which vary along the axial position. From (3) notice the presence of boundary conditions that dictate the inlet temperature of the cooling agent at the end of the reactor zone. The reactor model includes a large number of algebraic equations for the calculation of the thermodynamic, physical, and transport properties of the reacting mixture and of the polymer molecular properties (molecular weights, branching, melt index and polymer density). The reactor model used in this work contains around 130 ordinary differential equations and 500 algebraic equations; these are fully described in Zavala and Biegler (2006). 2.2. Model Uncertainty There exists a high degree of uncertainty in the model associated to the heat transfer coefficients (HTCs) of the zones, which originates from the time-varying fouling layer inside the reactor encountered in industrial operations. It has been so far impractical to incorporate mechanistic models to predict this fouling onset (Buchelli, et.al, 2005). A typical strategy to get around this limitation consists in parameterizing the HTCs and estimating them on-line. The HTCs are estimated to match the reactor temperature profile and the jacket temperatures. In a previous study (Zavala and Biegler, 2006), we proposed an on-line estimation strategy able to match the temperature profile accurately. The strategy follows a simultaneous all-at-once approach to match the entire reactor and jacket temperatures. In Figure 2 we illustrate the resulting match of the reactor temperature profile at a particular point in time.
3. NLP Formulation and Solution After embedding the rigorous reactor model to a general objective function and inequalities, we obtain a DAE-constrained optimization problem. In this work, the optimizer is allowed to manipulate some of the reactor inputs (initiator flows, jacket flowrates, CTA flowrates and side feed temperatures) all at once. The novelty of the approach lies on the multivariable all-at-once nature of the strategy which accounts for downstream interactions along the reactor. This is in sharp contrast with the current industrial practice where individual loops are used to control locally the reactor zones peak, inlet and outlet temperatures which complicate the control of the polymer properties at the reactor exit. The proposed strategy is expected to decouple these control loops and thus obtain better performance.
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Figure 2. Reactor model match of temperature profile after estimation of HTC and initiator efficiencies. We propose a simultaneous full-discretization approach to solve the DAE-constrained problem. A Radau collocation scheme is used in order to incorporate, directly, the multi-point boundary conditions. After discretization, we obtain an NLP with around 13,000 constraints and 71 degrees of freedom. The resulting NLP is very sparse and this structure can be exploited using the full-space interior point solver IPOPT. The NLP is implemented on the modeling platform AMPL which provides exact first and second order derivative information. This information is important in order to handle highly nonlinear NLPs. On average, the NLPs converge in around 10-12 iterations and 15-20 CPUs on a Pentium IV, 3.0 GHz PC.
4. Case Studies 4.1. Tracking Objective Function In the first case study, we evaluate the performance of the optimizer for a given decaying sequence of the HTC in the reaction zones. This scenario arises during normal operation where the HTC drops from its original value after the defouling or cleaning stage (Buchelli, et.al, 2005). The simulated decreasing HTC sequence for the reaction zones is illustrated in Figure 3. The HTC is ramped linearly from its nominal value (value of 1) to less than 40% of its nominal value. The nominal point is obtained by matching the reactor model to industrial plant data. The optimizer objective is to react to the changing HTCs by manipulating the full set of input variables in order to keep the reactor peak temperatures within the protection zones (see Figure2) and the polymer properties on target. For confidentiality reasons, all the variables have been scaled using their nominal values. The plant response is obtained by perturbation of the heat transfer coefficients in the simulation model. The resulting input profiles of the optimizer are presented in Figure 4. It is clear that, as the HTC decays (i.e., the reactor fouls) the controller can only keep the reactor under the desired peak temperature limits by dropping production (-12% in the most fouled case). This is normally done by decreasing the initiator flows in the zones independently. However, it is interesting to observe that the optimizer decides to move only the initiator of the first (Z1) and second (Z2) reaction zones while the flows for Z3 and Z4 are kept at their nominal values. In Z3 and Z4 the optimizer decides that it is more efficient to attenuate the decreasing cooling capacity by decreasing the feed temperatures at the mixing points. Also, the optimizer is able to keep the melt index and
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polymer density always on target despite of the decreased conversion. For this, the optimizer drops the CTA side flowrates at the same rate in all zones. From the temperature profile, it is possible to observe that the fouling onset is most notable in the first reaction zone where the outlet temperature tends to rise; the optimizer manipulates the feed temperature to the second reaction zone to keep the inlet temperature of this zone at target.
Figure 3. Decaying sequence for heat transfer coefficients along all reaction zones.
Figure 4. Response of optimizer to decaying sequence of HTCs in reaction zones. Case 2.2. Tracking Objective Function + Economic Objective In this case, we incorporate an additional term in the objective function to maximize production. From Figure 5, it is clear that the incorporation of the economic term in the objective forces the optimizer to manipulate the inputs in order to attenuate the decreased production. In this case, the optimizer only needs to drop production by 7% in the most fouled case (saving 5% compared to first case study). Furthermore, for the highest value of the HTC, the optimizer is able to increase production by 3%. Interestingly, the optimizer keeps the same trends of the initiator flowrates as in the previous case study. In this case, the optimizer overcomes the lost production due to
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fouling by decreasing the feed temperatures. This increases the temperature difference between the inlet and the peak temperatures, thus increasing production. Finally, the melt index and density are always kept at target. For this, the CTA flowrate profiles need to be distributed in a different way compared to the previous case study. It is important to emphasize that, even if the multivariable optimizer can attenuate the lost production by distributing the inputs more efficiently, it is not able to overcome the lost production completely. As expected, this implies that production losses are dominated by the fouling effect.
Figure 5. Response of optimizer to decaying sequence of HTCs in reaction zones. Economics included in objective function.
5. Conclusions and Future Work In this work, we propose an all-at-once discretization strategy to optimize the operations of LDPE processes using first-principles tubular reactor models. It is demonstrated that the multivariable strategy can cope rigorously with downstream interactions along the reactor and attenuate disturbances in order to follow objectives of industrial interest. As part of future work, we will incorporate rigorous dynamic models that will allow for a higher fidelity in the analysis.
References A. Buchelli et.al., 2005, Modeling Fouling Effects in LDPE Tubular Polymerization Reactors. 1. Fouling Thickness Determination, I&ECR, 44(5), 1474-1479. C. Kiparissides et.al., 2005, Mathematical Modeling of Free-Radical Ethylene Copolymerization in High-Pressure Tubular Reactors, I&ECR, 44(8), 2592-2605. M. Asteuasin and A. Brandolin, 2007, Modeling and Optimization of a High-Pressure Ethylene Polymerization Reactor Using gPROMS, C&CE, In Press. V. Zavala and L.T. Biegler, 2006, Large-Scale Parameter Estimation in Low-Density Polyethylene Tubular Reactors, I&ECR, 44(23), 7867-7881.
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Simulis® Thermodynamics: an open framework for users and developers Olivier BAUDOUINa, Stéphane DECHELOTTEa, Philippe GUITTARDa, Alain VACHERa a
ProSim, Stratège Bâtiment A, BP 27210, 31672 LABEGE Cedex, FRANCE
Abstract Simulis® is the name of ProSim’s new software suite. The component-oriented approach of its architecture is based on the Microsoft®’s COM/DCOM middleware. Simulis® Thermodynamics, one of the first components, is a thermophysical calculation server that generates highly accurate pure component and mixture properties (thermodynamic, transport, compressibility…) and fluid phase equilibria (liquid-vapor, liquid-liquid and vapor-liquid-liquid). One main benefit of Simulis® Thermodynamics is its CAPE-OPEN compliance through its CAPE-OPEN thermodynamic plug and socket facilities. Another powerfull feature is the capability to use legacy codes either as a DLL (Dynamic Link Library) following a standard syntax, either as VBScript (Visual Basic Script) directly written from the Simulis® Thermodynamics’ environment. The standard version of Simulis® Thermodynamics is provided as an add-in in Microsoft® Excel and as a toolbox in MATLAB® and enables the user to run complete thermodynamic calculations in these applications, but it can also be plugged in any legacy code using the SDK (Software Development Kit). This paper will introduce all these different features. Keywords: Thermodynamic, CAPE-OPEN, Simulis, Microsoft Excel, Modeling.
1. Introduction Throughout their history, process simulation tools had to adapt to the evolutionary nature of hardware and software technologies and to an ever more and more demanding market. Usage is again disturbed today by computer networks and co-operative work. In addition to the performance and user-friendliness criteria, the various tools must enable substitution one to another and exchange of services: they must be interoperable and integrable. New technologies based on software components developed with objectoriented languages are available to meet this new market requirement. Considering this situation, ProSim decided to change the architecture of its tools to answer not only its own customers' expectations, but also the whole simulation process software user community. Simulis® project fulfills that goal. The software component Simulis® Thermodynamics is presented in this paper to demonstrate the advantages of this approach for both thermodynamic experts and end-users.
2. Simulis® Thermodynamics Simulis® Thermodynamics is a thermodynamic properties and phase equilibria calculation server for pure substances and mixtures (up to 200 compounds). It is based on ProSim traditional thermodynamic calculation library which has been validated through many years of intensive industrial use. A pure substance property database, containing more than 1900 compounds (based on AIChE’s DIPPR® database), is
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provided with the standard version. Using Simulis® Thermodynamics, the user can calculate the following properties: • • • • •
Transport properties (Cp, μ, λ…); Thermodynamic properties (H, S, U…); Compressibility properties (Z, Cp/Cv…); Non-ideality properties (γ, φ…); Critical properties (Tc, Pc, Vc, Zc).
Derivatives of these properties can also be accessed. The following phase equilibrium calculations can be performed: • • • •
Vapor-Liquid flashes (TP, HP, SP, ωT, ωP, UV…) ; Vapor-Liquid phase envelope ; Liquid-Liquid flashes (TP); Vapor-Liquid-Liquid flashes (TP, HP, ωP).
Its model library includes the most important ones such as: • • • • • • • • • • • • • • • • • •
Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), Lee-Kesler-Plöcker (LKP), Benedict-Webb-Rubin modified Starling (BWRS), PPR78, Wilson, NRTL, Margules, UNIQUAC, UNIFAC original, UNIFAC modified Dortmund, UNIFAC modified Larsen, PSRK, Engels, Chao-Seader, Sour water, MHV2, ULPDHS…
3. Simulis® Thermodynamics and CAPE-OPEN 3.1. CAPE-OPEN CAPE-OPEN is an industry standard on interfaces between software commonly used in process engineering modeling and simulation activities. CAPE-OPEN standard is supported, enhanced and maintained by the CAPE-OPEN Laboratories Network (COLaN), a non-for-profit organization created in 2001. CAPE-OPEN technology widens the application range of any CAPE software and a number of CAPE software providers, such as ProSim, have already brought their software to CAPE-OPEN compliance.
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CAPE-OPEN facilitates plug and play in CAPE tools, meaning that the same software component (unit operation module, thermodynamic property package…) can be used in a number of process modeling environments without having to write any single line of code. Development costs for specialized CAPE tools are consequently reduced while the market for each software component is immediately expanded. This facility motivates software developers to migrate their product to CAPE-OPEN compliance in order to retain and achieve market competitiveness. On the usage side, CAPE-OPEN compliant software tools are providing end-users with an increased capability to choose and use the best tools available for the process engineering objective they have to meet. 3.2. CAPE-OPEN Thermodynamic Plug and Socket Even if Simulis® Thermodynamics architecture is not based, in native, on CAPE-OPEN standard (mainly in order to re-use existing codes), Simulis® Thermodynamics offers a complete interoperability with other software implementing the CAPE-OPEN standardized interfaces. On one hand, throughout its “socket” facility, Simulis® Thermodynamics allows a client application to calculate properties and phase equilibria using an external “CAPEOPEN Thermodynamic Property Package” coming, for example, from Aspen Properties (AspenTech), PPDS (TUV-NEL), Multiflash (Infochem)... On the other hand, with Simulis® Thermodynamics, a end-user is able to create a “CAPE-OPEN Thermodynamic Property Package” which can be used inside software from other providers: this is the CAPE-OPEN thermodynamic “plug” facility. Thanks to existing Simulis® Thermodynamics features, a thermodynamic expert can easily build, record and deploy a Property Package to his colleagues. Then, the Property Package can be safety used in all CAPE-OPEN compliant modeling tools of a company. This functionality has been successfully tested in Aspen Plus® and Aspen Hysys® (AspenTech), PRO/II (SimSci-Esscor), gPROMS® (PSE), INDISS (RSI) or Xchanger Suite 4.0 (HTRI). Any application integrating Simulis® Thermodynamics automatically inherits this CAPE-OPEN thermodynamic compliance, both as a plug and as a socket.
4. “Integrability” capability of Simulis® Thermodynamics Another important capability of Simulis® Thermodynamics is what we call "integrability". Benefiting of the architecture based on a component approach, any application supporting the COM/DCOM technology can be linked with Simulis® Thermodynamics. So, the standard commercial packaging of Simulis® Thermodynamics contains a Microsoft® Excel add-in and a MATLAB® toolbox and allows to use it in these different environments. A complete SDK (Software Development Kit) is also provided and it can be easily programmed by using languages such as Visual Basic, C++, Delphi, FORTRAN…
5. Expert Mode Recently, at the opposite of the “integrability” capability seen previously, Simulis® Thermodynamics “Expert Mode” has been implemented. It is dedicated to users (or developers) willing to integrate existing codes or to develop their own new thermodynamic models in view to using these developments in other applications
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(commercial software, Microsoft® Excel, MATLAB®, legacy codes…). Two possibilities are offered: • VBScript (Visual Basic Script); • External DLL (Dynamic Link Library). 5.1. VBScript When the Expert Mode is enabled, a specific tabsheet (Figure 1) is available to enter new models using VBScript. Then, the code can be directly entered after doubleclicking on the required function, creating automatically a skeleton of the method. The function syntax (parameters, units…) is displayed at the bottom of the screen. A feature allowing to test, in place, the implemented function brings also more efficiency to the developer to include his own code with more safety.
Figure 1: VBScript in Simulis® Thermodynamics
VBScript is an interpreted language and is not very efficient. This way to include external models must be considered as a first step, a step of prototypes showing the feasibility of a model. External DLL use might be the next step. 5.2. External DLL Like for VBScript, the Expert Mode being activated, a specific tabsheet (Figure 2) is available to connect an external DLL to Simulis® Thermodynamics. The user must select the required library implementing his own functions. These functions are marked using a bold font within the global list of all possible ones. Like for VBScript approach, the syntax (parameters, units…) of the different functions (entry points from the DLL) is displayed at the bottom of the screen and an integrated tool also allows testing the
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function from the window. User parameters, used in some models, are supported and can be entered thanks to a specific dialog.
Figure 2: External DLL in Simulis® Thermodynamics
It is important to note that the external DLL can be built using any languages (FORTRAN, C++, Delphi…), the unique constraint is to respect the syntax of the different functions and the calling convention (stdcall by reference) that have been specified. Following this methodology, existing codes can be easily re-used and wrapped in such libraries. To conclude on external DLL, this way can be very efficient, definitively more than VBScript, and could be applied in applications requiring performances in computing time. 5.3. General considerations With the Expert Mode, it is not necessary to implement all properties and equilibrium calculations. In fact, VBScript, external DLL and native models can be mixed, each one computing a different property or equilibrium. However, the user must define priorities between the 3 sources of models when different implementations are available to calculate a property or an equilibrium (native models will be used when neither VBScript models nor DLL model are found). This point appears as a great advantage compared with a CAPE-OPEN Thermodynamic Wizard approach where all the capacities of the final CAPE-OPEN Thermodynamic Property Package require to be written. To complete the comparison, the Expert Mode allows an easy configuration in term of pure compounds and in term of thermodynamic profile which has been selected. Even switched to Expert Mode, the user can continue to take advantage of Simulis® Thermodynamics environment, graphical editors and all other graphical services. Globally, the Expert Mode offers a more general and flexible approach than previously proposed systems.
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5.4. REFPROP: an application case The Expert Mode in Simulis® Thermodynamics introduces an interesting way to embed external codes. To demonstrate the power of this approach, it has been recently selected for instance to develop a link with REFPROP calculation library developed by the NIST (US Department of Commerce) for fluid properties. The wrapping has been done in a reduced time and now the user can access REFPROP, throughout Simulis® Thermodynamics’ framework, in different client applications: Microsoft Excel, MATLAB, CAPE-OPEN Process Modeling Environments… Furthermore, the Expert Mode manages directly the interface with REFPROP calculation kernel and will fix all conflicts between the current release and next ones.
6. Conclusion More generally, the Expert Mode allows the user (developer) to focus his work on his know-how related to some specific models and to inherit automatically all features from Simulis® Thermodynamics without any more efforts, Simulis® Thermodynamics offering a real development environment for thermodynamic users and developers.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
647
Modeling and simulation of the particle size distribution for emulsion polymerization in a tubular reactor Ala Eldin Bouaswaig,a Wolfgang Mauntz,a Sebastian Engella, a
Process Control Laboratory, Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, 44221 Dortmund, Germany, Email:
[email protected] Abstract In this paper, a model for the multiphase process of emulsion polymerization in a tubular reactor is presented. Besides well investigated properties like e.g. conversion., the model predicts the particle size distribution of the polymer particles using a population balance equation. The model consists of a two-dimensional partial differential equation for the particle size distribution and dynamic balance equations for the components that are present in the reactor. It also includes a set of algebraic equations that e.g. describe the monomer distribution among the coexisting phases in the reactor. Numerically, the use of flux limiters is considered for the growth term in the PBE to obtain at least second order accuracy and oscillation-free solutions. Experimental results reported in literature are used to validate the model. Keywords: Emulsion polymerization, tubular reactor, particle size distribution, modeling
1. Introduction Emulsion polymers are usually produced in semi-batch reactors, single continuously stirred tank reactors (CSTR), multiple CSTRs connected in series or, less frequently, in batch reactors. In all these cases, the production rate is limited by the cooling capacity of the reactors, as the heat generated by the polymerization has to be removed to achieve safe operation. Tubular reactors have an excellent heat removal capacity due to their large surface area to volume ratio. Moreover, they are capable of producing large amounts of product with uniform product quality. However, despite the potential benefits, only few works have been published in the open literature on the use of tubular reactors for emulsion polymerization. Paquet and Ray [1] developed a model for emulsion polymerization in a tubular reactor and validated it with their experimental data [1,2]. In the work of Sayer and Guidici [3], a dynamic model for styrene emulsion polymerization in a pulsed tubular reactor was developed. Two different modeling approaches were considered, the tanks-in-series model and the axial dispersion model. In another work, Sayer et. al. [4] used a very similar dynamic model to that of Sayer and Guidici [3] for simulating the emulsion polymerization of vinyl acetate in a pulsed sieved plate column. The developed model was also used to investigate different start up procedures. Recently, Marin et. al. [5] developed a model for the emulsion polymerization of styrene in a tubular reactor with internal-inclined angular baffles. All these models assume the particles to be monodisperse and they are here referred to as lumped models. Taking into account the polydispersity of the particles can be done by modeling the particle size
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A.E. Bouaswaig et al.
distribution (PSD) by a population balance equation (PBE). As far as the authors are aware, only Abad et. al. [6] have made use of a PBE with axial dispersion terms to simulate PSD in a closed loop reactor and no work has been done so far on modeling the PSD in an open loop tubular reactor which is the aim of the current contribution. In section 2 of this paper, a lumped axial dispersion model for emulsion polymerization in a tubular reactor is extended with a PBE to predict the PSD of the produced latex. The partial differential equations that arise from balancing the quantities in the reactor are discretized using suitable numerical methods that take into account the highly convective nature of the flow and the hyperbolic nature of the PBE and this is described in section 3. In section 4, the model predictions with respect to conversion and PSD are compared with experimental data reported in literature, and finally, section 5 is devoted to drawing conclusions and highlighting future research directions.
2. The emulsion polymerization model The work of Paquet and Ray [1], Sayer et al. [4] and Abad et al. [7] form the basis of the model. Several assumptions are made: • The reactor is perfectly mixed in the radial direction. Dispersion is only considered in axial direction. • Particles of the same size have the same number of radicals per particle (i.e. the PSD is modeled by a pseudo-bulk model). • The fluid density and viscosity are constant. • Particles are colloidally stable (i.e. the coagulation term is neglected in the PBE). Based on these assumptions, the PBE for a tubular reactor reads:
∂F (v, z , t ) ∂ ∂F (v, z , t ) ∂ 2 F ( v, z , t ) = − (v(v, z , t ) F (v, z , t ) ) − u z + Dax ∂t ∂v ∂z ∂z 2 + δ (v − v nuc )ℜ nuc .
(1)
F (v, z , t ) is the population density function, v(v, z , t ) represents the growth rate of the particles with respect to the internal coordinate (v) and ℜ nuc is the rate of particle generation by nucleation. Following [1], only micellar nucleation is considered, thus:
ℜ nuc
Vw = 4πr k mm N A N m [ R] . VR 2 m
w
(2)
The coexisting phases in the reactor are assumed to be in thermodynamic equilibrium. This enables the usage of so-called partition coefficients to determine the monomer concentration in the droplet phase, water phases and particle phase. In addition, to determine the overall monomer concentration in the reactor the following monomer balance is required: v
max ∂[ M ] ∂[ M ] ∂ 2 [M ] P = −u z + Dax − k [ M ] p ³ F (v, z, t )n (v, z, t )dv. ∂t ∂z ∂z 2 vmin
(3)
The emulsifier is an inert in the reactor and it can be adsorbed on polymer particles, adsorbed on monomer droplets or be present in the form of micelles. The typical diameter of the final polymer particle is in the range of 100 nm while the diameters of
Modeling and Simulation of the Particle Size Distribution for Emulsion Polymerization in a Tubular Reactor
649
the monomer droplets are in the order of 10 ȝm. Because monomer droplets possess a significantly larger diameter, and hence lower specific area, the amount of emulsifier required to stabilize the monomer droplets is considered negligible. Thus, micelles will only be present in the reactor if the emulsifier concentration is above the critical micelle concentration (Ecmc) plus the amount of emulsifier necessary to stabilize the formed polymer particles. Mathematically this can be written in the following form:
°a ° em N m = ® 4πrm2 ° ° ¯0,
§P a ¨ ¨ EVR ¨ Vw ¨ ©
b
· vmax § · ¸¸ 4πVR 2 ¨ F (v, z , t )rp dv ¸ , a > b - E cmc + w ³ . ¨ ¸¸ a V ep vmin © ¹¸ ¹ otherwise
(4)
Usually a water soluble initiator is used. Assuming that it undergoes a first order decomposition, the material balance of the initiator is given by:
∂[ I ] ∂[ I ] ∂ 2[I ] = −u z + Dax − fk I [ I ]. ∂t ∂z ∂z 2
(5)
Since a pseudo-bulk model is used for the PSD, an expression for the average number of radicals per particle ( n ) is required in Eq. (3). n depends on the rate of radical generation, concentration of polymer particles, rate of radical entry into particles, rate of radical desorption from particles and rate of radical termination. These phenomena are modeled by the Smith-Ewart recursion formula, and the partial fraction expansion proposed by Ugelstad et.al. [10] is used in this work to calculate n . For the calculation of n , the concentration of radicals in the water phase is required. Their balance takes into account initiator decomposition, desorption from particles, entry into particles, water phase termination and entry into micelles:
∂ 2 [ R] w ∂[ R ] w ∂[ R ] w + Dax + 2 fk I [ I ] + = −u z ∂z ∂t ∂z 2 vmax
³ F (v, z, t )k d (v, z, t )n (v, z, t )dv −
vmin
vmax
³ F (v, z, t )k ap (v, z, t )dv −
vmin
(
VR [ R] w × Vw
VR k T [ R] w Vw
)
2
− 4πrm2 k mm N A N m [ R] w
(6)
Vw . VR
3. Numerical solution To simulate the set of PDAEs it is transformed to a set of DAEs by discretization. 3.1. Discretizing the spatial derivatives As reported by Paquet and Ray [1], the Pe numbers that are encountered in emulsion polymerization tubular reactors are large and this implies that the flow is convection dominated. The Pe number poses a restriction on the minimum number of discretization nodes that is required to avoid numerical oscillations [11]. As suggested by Vande Wouwer et al. [12], upwind finite differencing is considered in this work to avoid
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oscillations. A fourth-order (five-point) biased-upwind finite difference method is used to approximate the first order spatial derivatives, while all second order derivatives are approximated by a fourth-order (five-point) centered finite difference method. 3.2. Discretizing the growth term in the PBE Upon discretizing the spatial derivatives in Eq. (1) the following semi-discrete equation results: Ψi ( v ,t ) · ∂Fi (v, t ) ∂ §¨ = − ¨ vi (v, t ) Fi (v, t ) ¸¸ + Γi (v, t ) ∂t ∂v ¨ ¸ © ¹
(7)
where (i) represents the index of the discretization node in the spatial direction. Γi(v,t) includes the nucleation term at node (i) plus the terms that arise from discretizing the spatial derivatives in Eq. (1) and Ψi(v,t) is the flux of the population density function. Eq. (7) is a hyperbolic partial differential equation with a source term. Solving this equation numerically is challenging because low order discretization schemes cause smearing near discontinuities and steep fronts and high order discretization schemes can be unstable and produce numerical oscillation in the vicinity of steep fronts. Furthermore, numerical stability problems may cause convergence to wrong solutions [13]. The approach used in this work to overcome these difficulties is to describe the flux (Ψi) by a high order scheme wherever possible and only switch to an oscillationfree low-order scheme when it is inevitable [13]. This can be achieved by using flux limiters which are auxiliary functions that operate when steep fronts are encountered in the solution in order to switch to the low-order scheme [13]. Thus, Eq. (7) is discretized with respect to the internal coordinate (v) as follows:
∂Fi , j
· 1 § ¨ Ψ 1 − Ψ 1 ¸ + Γi , j ¨ i, j− ¸ Δv © i , j + 2 2 ¹
(8)
Ψ
§ · = ψ low1 + ξ ( si , j )¨¨ψ high1 − ψ low1 ¸¸ i, j+ i, j+ 2 2 ¹ © i, j+ 2
(9)
Ψ
· § = ψ low1 + ξ ( si , j −1 )¨¨ψ high1 − ψ low1 ¸¸ i, j− i, j− 2 2 ¹ © i, j−2
(10)
∂t
1 i, j+ 2
1 i, j− 2
=−
where, si,j is a smoothness indicator and it is calculated from the ratios of the consecutive gradients with respect to the internal coordinate (v):
si , j =
Fi , j − Fi , j −1 Fi , j +1 − Fi , j
.
(11)
are the fluxes of the In Eq. (9,10) ξ is the flux limiter function and ψ ,ψ population density function approximated by a low order and a high order scheme respectively. For the problem at hand, the low order flux is approximated by the first order upwind finite difference scheme and the high order flux is approximated by the low
high
Modeling and Simulation of the Particle Size Distribution for Emulsion Polymerization in a Tubular Reactor
651
second order Lax Wendroff scheme [13]. The monotonized central flux limiter function is chosen for ξ [14]. 3.3. Time discretization After discretizing the spatial derivatives in all balance equations and the growth term in the PBE the model reduces to a set of DAEs. To simulate the discretized model an explicit fourth-order Runge Kutta method is used to march through time to the steady state solution. The time steps are chosen sufficiently small to guarantee stability.
4. Results and discussion Paquet and Ray [1,2] reported experimental data for emulsion polymerization of methyl methacrylate in a tubular reactor. Their experiments are used to validate the model in this work. All model parameters are taken from literature. Fig.1 compares the conversion predicted by the model with the experimental data reported by Paquet and Ray [1]. As can be seen, model prediction of conversion is good. Figures 2-4 depict the comparison between the experimental PSD and the model prediction for three different residence times, namely 20, 30 and 40 minutes respectively. The PSD predicted by the model is narrower than that reported experimentally. Immanuel et. al. [15] reported similar findings for semi-batch operation and attributed the mismatch to the nucleation model and to the assumption of the particles being colloidally stable. Adjusting the rate constant for radical entry into micelles (kmm) in Eq. (2) and taking into account homogeneous nucleation could improve model prediction. Part of the available emulsifier would then be used to stabilize the formed polymer particles and this amount would not be available for micellar nucleation at the reactor inlet. The formation of larger particles by collision would release part of the emulsifier and allow for further micellar nucleation at later stages. The interaction of this improved nucleation model with the coagulation model would make the PSD prediction broader and more comparable to experimental data.
5. Conclusion and future work By extending the emulsion polymerization model with a Population Balance Equation (PBE), the Particle Size Distribution (PSD) of the produced latex can be predicted. However, modeling the PSD necessitates the use of an internal coordinate and this significantly increases the size of the discretized model.
Conversion [-]
0.8 0.7 0.6 0.5 0.4
Exp (Pe=253) Exp (Pe=325) Exp (Pe=370) Sim (Pe=370) Sim (Pe=325) Sim (Pe=253)
Normalized frequency [%/nm]
1 0.9
0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Normalized reactor length [-]
Figure 1. Steady state conversion: Model prediction compared with experimental data from [1]
1
12 11 10 9 8 7 6 5 4 3 2 1 0 0
Sim. Exp.
15 30 45 60 75 90 105 120 135 150 Particle diameter [nm]
Figure 2. Steady state PSD (Pe=253): Model prediction compared with experimental data from [2]
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A.E. Bouaswaig et al. 9
9 8
Sim. Exp.
7 6 5 4 3 2 1 0 0 15 30 45 60 75 90 105 120 135 150 165 Particle diameter [nm]
Figure 3. Steady state PSD (Pe=325): Model prediction compared with experimental data from [2]
Normalized frequency [%/nm]
Normalized frequency [%/nm]
10
8 7
Sim. Exp.
6 5 4 3 2 1 0 0
15 30 45 60 75 90 105 120 135 150 Particle diameter [nm]
Figure 4. Steady state PSD (Pe=370): Model prediction compared with experimental data from [2]
To handle the highly convective flow in emulsion polymerization tubular reactors a forth order biased upwind differencing method is proposed to discretize the convective terms. For the growth term in the PBE flux limiters are used to combine an oscillation free upwind difference method with a higher order method. The developed model predicts the steady state conversion well; however, additional phenomena have to be considered to improve the PSD prediction. Neglecting the homogeneous nucleation and particle coagulation is questionable. Furthermore, since the particle nucleation is included in the model, the dependence of the monomer concentration in small particles on the particle size might be significant. This will influence the growth rate of the particles and the final shape of the PSD. Finally, the flow profile in the reactor will have an impact on the PSD predictions. The significance of this influence is currently being studied by our group through the use of a hybrid decoupled CFD-polymerization model that investigates the effect of the polymerization process on the flow profile in the tubular reactor and vice versa. Future work will focus on improving the presented model by reconsidering the assumptions made in this work.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
D.A. Paquet and W.H.Ray, AICHE J, 40 (1994) 88. D.A. Paquet and W.H.Ray, AICHE J, 40 (1994) 73. C. Sayer and R.Giudici, Braz. J. Chem. Eng., 19(2002) 89. C. Sayer, M. Palma and R.Giudici, Ind. Eng. Chem. Res., 41(2002) 1733. F. L. M. Marin, L. M. F. Lona, M. R. W. Maciel and R. M. Filho, J. Appl. Pol. Sci., 100(2006) 2572. C. Abad, J. C. de la Cal and J. M. Asua, Macromol. Symp., 92(1995) 195. C. Abad, J. C. de la Cal and J. M. Asua, Chem. Eng. Sci., 49(1994) 5025. H. M. Vale and T. F. McKenna, Prog. Polym. Sci., 30(2005) 1019. S. Omi, K. Kushibiki, M. Negishi and M. Iso, Zairyou Gijutsu, 3(1985) 426. J. Ugelstad, P. C. Mörk, and J. O. Aasen, J. Pol. Sci.: Part A: Pol. Chem., 5(1967) 2281. B. A. Finlayson, Nonlinear analysis in chemical engineering, McGraw Hill, New York, 1980. A. Vande Wouwer, P. Saucez, and W. E. Schiesser, Ind. Eng. Chem. Res., 43(2004) 3469. R. J. Le Veque, Numerical methods for conservation laws. Birkhäuser Verlag, Basel, Switzerland, (1992). H. Smaoui and B. Radi, Environ. Fluid Mech., 1(2001) 361. C. D. Immanuel, C. F. Cordeiro, S. Sundaram, E. S. Meadows, T. J. Crowley, and F. J. Doyle III, Comp. Chem. Eng., 26(2002) 1133.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
653
Composite zeolite membranes characterization by using a transient state experimental technique and a parameter estimation procedure Lucile Courthial,a Arnaud Baudot,a Mélaz Tayakout-Fayolle,a Christian Jallutb a
IFP-Lyon, BP 3, 69390 Vernaison, France Université de Lyon, Université Lyon 1, Laboratoire d’Automatique et de Génie des Procédés-UMR CNRS 5007,ESCPE, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne, France
b
Abstract We describe a non-destructive transient state method for the determination of thermodynamic and transport properties of zeolite composite membranes. The properties under consideration are included as parameters of a linear dynamic model of the membrane. The parameters values are obtained thanks to an estimation procedure based on the comparison between simulated and measurements realized in the linear domain. A step-by-step experimental procedure is derived from a structural identifiability analysis of a simplified linear model of the membrane. A more detailed linear model is then used for the estimation procedure. Due to its transient nature, this technique allows the zeolite selective layer effective thickness determination as well as that of thermodynamic and transport properties of sorbing hydrocarbons. Some examples of results are given to illustrate the capabilities of the technique. Keywords: membrane, identifiability
dynamic
modelling,
parameter
estimation,
structural
1. Description of the system A scheme of the composite membranes to be characterized is represented in the figure 1. These membranes are composed of a very thin and dense zeolite layer deposited on the inner side of a α-alumina porous support. The length of this tubular support is 150 mm, its internal diameter 6 mm and its external diameter 10 mm. Enameled sections and connections tubes Macroporous support
L2 0
Zeolite layer
L4
LZ
L3 z2
z1
z
Figure 1: the composite membrane
The support global porosity is 0,48 but it is made of three layers having respectively the three following mean pore diameters: 10 μm, 20 μm and 1700 μm. The zeolite active layer is obtained by using an in situ crystallisation process (Chau et al., 2003) at the surface and within the inner layer of the support having a mean pore diameter of 10 μm. As a consequence, the only way to characterize this active layer with a non-destructive
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L. Courthial et al.
macroscopic method is to perform experiments by using the membrane as it is represented in the figure 1. In this paper, we describe the way transient experiments similar to the transient version of the well-known Wicke-Kallenbach diffusion cell can be done according to the principle that is represented in figure 2 (Bakker et al., 1996; Sun et al., 1996; Tayakout-Fayolle et al., 1997; Courthial et al., 2006; Courthial, 2007). zeolite layer inner compartment outer compartment macroporous support
Figure 2: principle of the transient experiments
A fixed composition gaseous mixture flows through the outer and inner compartments of the membrane. The initial conditions are established when the thermodynamic equilibrium is reached. The inlet composition of the inner compartment feed gas is then suddenly modified and the time evolution of the two outlet compositions is measured. We use a concentration pulse injection and we verify that its intensity is sufficiently low so that experiments are performed in the linear domain of the system. The abovedescribed experiments can be performed with pure components or mixtures. Furthermore, one can vary the concentrations of the gases at the initial equilibrium state in order to study the evolution of the parameters with the zeolite active layer loading and composition according to the approach that is used in inverse chromatography (Tondeur et al., 1996; Jolimaitre et al., 2001). We use the capabilities of a gas phase chromatograph and an infrared analyzer to perform the experiments (see Courthial, 2007 for more details about the experimental set-up).
2. Structural identifiability study for pure component experiments The estimation procedure is based on a linear state model of the system. One has to check for the structural identifiability of its parameters. It has been previously shown that when linear or non linear state models are derived for chromatographic columns (Tayakout-Fayolle et al., 2000; Couenne et al., 2005), the solid phase composition should not be represented by the ordinary concentration q but by the concentration of a *
gas phase C that would be at equilibrium with the solid phase at each point and at each time. A simple examination of a state model written according to the classical choice of state coordinate q cannot lead to the conclusion that it is overparametrized and to propose an adapted experimental estimation strategy. In order to check for the pertinence of the proposed change of state coordinate in the case of the composite membrane, a simplified version of the model is used in order to apply the transfer function technique (Walter and Pronzato, 1997). Since the result is based on the way the adsorbent composition in the zeolite is represented, we assume that the main conclusion of the structural identifiability study will be valid for the more realistic model that is used to perform the parameter estimation. 2.1. A simplified linear model of the system In this model, we have neglected the axial dispersion in the gas flows as well as the zeolite layer curvature. Furthermore, the macro-porous support is not taken into
Composite Zeolite Membranes Characterization by Using a Transient State Experimental Technique and a Parameter Estimation Procedure
655
consideration and we take into account only the part of the membrane situated between z1 and z2 (see figure 1). The equilibrium condition between the zeolite layer and the gas phase is represented by the Henry law q(r,t ) = κ A C (r,t ) with C (r,t ) the adsorbate concentration of a gas phase that would be at equilibrium with the zeolite. Once the r − Ri z − z1 dimensionless coordinates are defined – ie – ξ = and η = where Lz is the Lz ez zeolite active layer length, ez its thickness and Ri its internal radius, the dimensionless adsorbate balance equations for the inner and outer gas phases as well as for the zeolite are as follows: *
∂C i 1 =− L °° τi ® ∂t 1 ∂C o ° °¯ ∂t = − τ oL
∂C i ∂ξ ∂C o
z
z
∂ξ
∂C (η = 0, t )
*
*
+ a i Bz
(
∂η
Boundary conditions :
C i (ξ = 0,t ) = C i0 (t ) ® ¯C o (ξ = 0,t ) = 0
)
− a o ko C o − C (η = 1, t ) *
(1)
Boundary conditions :
∂C ∂t
2 *
*
=
1 ∂ C
τ z ∂η 2
C * (η = 0, t ) = C i (ξ ,t ) ° * ® ∂C ko * °¯ ∂η (η = 1, t ) = B C o − C (η = 1, t ) z
)
(
C i and C o are the inner and outer compartments gas phase concentrations, Bz =
(2)
κ A Dz
ez is a mass transfer resistance included in the boundary condition of the zeolite layer inner 2 ez is the diffusion time constant. a i and a o are the specific surface areas surface. τ z = Dz of the active layer and k o a mass transfer coefficient between the outer gas flow and the active layer surface. As far as the inner surface of the active layer is concerned, it is assumed to be at equilibrium with the gas phase (see figure 1).
2.2. Transfer function analysis The derivation of the transfer function is very long and we only give the result for the transfer function between the inlet concentration of the inner compartment and the outlet concentration of the outer compartment (see figure 2) as an example (see the appendix): G (s) =
L Cˆ o (s) Cˆ o (ξ = 1,s) D(s) r ( s) r (s) = = e −e 0 Cˆ i (s) Cˆ i (ξ = 0,s) r1 (s) − r2 (s) z
(
1
2
)
(3)
These expressions show that the same macroparameters including the initial microparameters (Walter and Pronzato, 1197) appear in the state model and in the corresponding transfer functions. As a consequence, the state model is correctly
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parametrized. As far as the active layer is concerned, only τ z =
ez
Dz
and Bz =
κ A Dz ez
are structurally identifiable. 2.3. A step-by-step experimental procedure In order to get the Henry constant κ A , the zeolite layer thickness ez and the diffusion coefficient Dz , we propose to first use a tracer that is not adsorbed in the zeolite. In this case, κ A ≈ 1 and the layer effective thickness can be determined as well as the tracer diffusion coefficient in the zeolite. The latter can be used to check for the results. Once ez is known, κ A and Dz can be obtained for a given adsorbate from the estimations of 2
τz =
ez
Dz
and Bz =
κ A Dz
.
ez
3. Examples of results for a pure adsorbate We present here some results concerning membranes that has been obtained at IFP from an aqueous solution containing the following species: SiO2/tetrapropyle ammonium hydroxyde/H2O (Chau et al., 2003). 3.1. The linear model of the system for the parameter estimation We use a more realistic model than the one used for the identifiablity study for the membrane as it is represented in the figure 1. The main features of this model are the followings: • the diffusion within the macroporous support is taken into account; • the curvature of the crystal layer is taken into account; • axial dispersion is included in the gas flows model; • the tubes connected to the system are included in the model. They are represented by CSTR’s or plug flow- axial dispersion models. The parameters of the flow models have been estimated from experiments where the membrane was replaced by a stainless steel tube. We don’t present this part of the study here (see Courthial, 2007). The volume of the connection tubes is about 9 % of the total volume of the system and we have checked for the consistency of the estimated axial dispersion coefficients with respect to literature. 3.2. Estimation of the active layer effective thickness by using hydrogen as tracer One can see in the figure 3a an example of time domain fitting that is obtained in this case. In the figure 3b is shown the stability of the effective thickness estimation according to different operating conditions (gas flow rates and temperature). From the results represented in the figure 3b, the effective thickness of the active layer of the membrane under consideration is ez = 26 ± 4 μm . This result is consistent with previous knowledge about this membrane. 3.3. Properties of the membranes with respect to pure n-butane In the figure 4a is shown an example of time domain fitting that is obtained for the nbutane at 200 °C. One can see in the figure 4b the evolution of the n-butane diffusion coefficient through the zeolite layer as a function of the gas phase concentration of n-
Composite Zeolite Membranes Characterization by Using a Transient State Experimental Technique and a Parameter Estimation Procedure
657
butane at the initial equilibrium state. The mean confidence interval that is obtained for these estimations is 10 %. 4.5E-5 4.0E-5
0.5
3.5E-5
Estimation: 0.4 0.3
D z = 6.12x10
-9
m 2 .s -1
3.0E-5
e z = 2.55x10
-5
m 2.s -1
2.5E-5
k k
0.2
s o
-1
= 0.963 m.s = 2.70x10
-2
ez (m)
Concentration (mol.m -3)ZZZZ
0.6
m.s
-1
2.0E-5 1.5E-5 1.0E-5
0.1
5.0E-6 0.0E+0
0.0 0
2
4
6
8
0
10
Time (s)
1
2
Volumetric flow rate (cm
(a)
3
4 3
.s-1 )
(b)
Figure 3: estimation procedure for the zeolite layer thickness 1.0E-8
Estimation:
0.25 0.20
D z = 3.69x10
-10
e z = 2.58x10
-5
m
k s = 0.700 m.s
-1
k o = 7.09x10
-3
m 2.s -1
m.s
0.15 0.10
-1
9.0E-9
Dz (m2.s -1 )zzzz
Concentration (mol.m-3)zzzzz
0.30
8.0E-9 7.0E-9 6.0E-9 5.0E-9 4.0E-9 3.0E-9
0.05
2.0E-9
0.00
0.0E+0
1.0E-9 0
5 10 15 Volumetric flow rate (s)
(a)
20
0
5
10
15
20
CI = C E (mol.m -3)
(b)
Figure 4: properties of the membrane with respect to n-butane at 200 °C
The method turns to be sensitive since we find that the diffusion coefficient of the nbutane increases with the zeolite loading as it is well known in this domain (Jolimaitre et al., 2001).
4. Conclusion In this paper, we have shown how to derive a transient state technique for the characterization of zeolite composite membranes from a structural identifiability study. Since the three parameters of interest are included into two macroparameters that are structurally identifiable, we have designed a step-by-step procedure. The first step is the determination of the zeolite active layer by using an inert tracer. Then, the equilibrium and the diffusion coefficients can be obtained by performing transient experiments with sorbing hydrocarbons. We have shown some results that have been obtained for a pure adsorbate to illustrate the capabilities of the technique.
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Appendix The quantities present in the transfer function Eq. 3 are as follows:
lo =
Bz ko
τ z s , r1 (s) =
(
)
− A (s) + C (s) + Δ (s) 2
§ A(s) = τ iL ¨¨ s + 2ai Bz (1+ lo )e © z
)
and
2
(1+ lo )e
τs z
τ zs
z
z
− (1− lo )e−
(
τ s z
)
§ § e τ s − e− τ s ¨ ¨ C (s) = ¨ s + ao k o ¨1− ¨ (1+ lo )e τ s − (1− lo )e− ¨ © © lo D(s) = 2τ oL ao ko . τs (1+ lo )e − (1− lo )e− τ s
τ oL
(
− A (s) + C (s) − Δ (s)
· ¸ τ s − (1− lo )e− τ s ¸¹ τ zs
z
B(s) = 2τ iL ai Bz
, r2 (s) =
z
z
z
z
·· ¸¸ τ s ¸¸ ¸¸ ¹¹ z
z
z
z
References W. J. W. Bakker, F. Kapteijn, J. Poppe, J. A. Moulijn, 1996, Permeation characteristics of a metal-supported silicalite-1 zeolite membrane, Journal of Membrane Science, 117, 57-78 F. Couenne, C. Jallut, M. Tayakout-Fayolle, 2005, On minimal representation of heterogeneous mass transfer for simulation and parameter estimation: application to breakthrough curves exploitation, Computers and Chemical Engineering, 30, 42-53 L. Courthial, 2007, Caractérisation des propriétés physico-chimiques et morphologiques des membranes zéolithes par mesure de perméation en régime transitoire, PhD Thesis, Lyon I University L. Courthial, A. Baudot, E. Jolimaitre, M. Tayakout-Fayolle, C. Jallut, 2006, Moments method applied to the in-situ characterisation of normal butane mass transfer in MFI zeolite membranes, Desalination, 193, 215-223 C. Chau, I. Prevost, J. A. Dalmon, S. Miachon, 2003, Process for preparing supported zeolitic membranes by temperature-controlled crystallisation. US Patent, 6582495 B2 E. Jolimaitre, M. Tayakout-Fayolle, C. Jallut, K. Ragil, 2001, Determination of mass transfer and thermodynamic properties of branched paraffins in silicalite by inverse chromatography technique, IEC Res., 40, 914-926 M. S. Sun, O. Talu, D. B. Shah, 1996, Diffusion measurements through embedded zeolite cristal. AIChE Journal, 42, 3001-3007 M. Tayakout-Fayolle, C. Jallut, F. Lefèvre, J. A. Dalmon, 1997, Application of transient methods to measurements of mass transfer parameters in zeolitic membranes, ECCE1, First European Congress on Chemical Engineering, Florence, Italy, May 4-7-1997, 2, 1209-1212 M. Tayakout-Fayolle, E. Jolimaitre, C. Jallut, 2000, Consequence of structural identifiability properties on state-model formulation for linear inverse chromatography, Chemical Engineering Science, 55, 2945-2956 D. Tondeur, H. Kabir, L. A. Luo, J. Granger, 1996, Multicomponent adsorption equilibria from impulse response chromatography, Chemical Engineering Science, 51, 3781-3799 E. Walter, L. Pronzato, 1997, Identification of parametric models from experimental data. Springer
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
659
MPC@CB Software: A Solution For Model Predictive Control Bruno da Silva, Pascal Dufour,* Nida Othman, Sami Othman, Université de Lyon, F-69000, Lyon, France ; Université Lyon 1, F-69622, Lyon, France ; CNRS, UMR 5007, LAGEP (Laboratoire d’Automatique et Génie des Procédés), 43 bd du 11 novembre, F- 69622 Villeurbanne, France.
Abstract This paper deals with a reusable user friendly simulation computer code (MPC@CB†). The original program was developed under Matlab for single input single output (SISO) model predictive control (MPC) for constrained optimization problems (trajectory tracking, processing time minimization…). The control structure is an adaptation of MPC with internal model control (IMC) structure. The original algorithm was applied and validated for different processes. In this work, it was adapted for multiple input multiple output (MIMO) constrained systems and validated on a polymerization process. Keywords: model predictive control, control software, polymerization processes.
1. Introduction Model predictive control (MPC) is employed in a wide variety of real-time control applications, including chemical engineering. MPC refers to a class of control algorithms in which an explicit model is used to predict the process dynamics. At each sample time, with the update of new process measurements, an open-loop optimization over a finite prediction horizon aims to find the sequence of manipulated variable [1]. But few MPC studies are devoted to processes involving complexity of chemical properties and equations which describe such systems. This MPC@CB software has already been used in its SISO version to control a simulated drying process of pharmaceutical vials [2], an experimental laboratory implementation of Powder Coating Curing Process [3] and to control a pasta dryer. The main objective of this work is to continue the development of the MPC@CB software for MIMO systems described by nonlinear ordinary differential equations (ODE) or/and nonlinear partial differential equations (PDE). Various user defined process models may be controlled by this software. Emulsion polymerization process control is considered in this work [4]. The study of a finite dimensional model is tackled, with the monomer flow rate and the jacket temperature as manipulated variables. The heat production and the concentration of monomer in the polymer particles are the process outputs. The process constraints, due to physical limitations such as the bath capacity of heating and cooling or the maximum possible monomer flow rate, are taken into account. In the first part of this paper, the process control strategy is presented. Secondly, the developed control *
Corresponding author:
[email protected] © University Claude Bernard Lyon 1 – EZUS. In order to use MPC@CB, please contact the author:
[email protected] †
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software is detailed. The polymerization model and the simulation results are finally discussed.
2. Process control strategy Model predictive control is an approach in which the control action is obtained by solving on-line, at each time, an optimisation problem [5]. More information about the predictive control algorithm used in the present paper may be found in [6]. Briefly, the control structure is an adaptation of MPC with internal model control (IMC) structure. In order to explicitly take into account magnitude and velocity constraints by the optimization argument u, a transformation method is used to get a new unconstrained argument p. For the output constraints handling, the exterior penalty method is adopted [7]. Consequently, the penalized problem can be solved by any unconstrained optimization algorithm: the well-known and robust Levenberg-Marquardt's algorithm is used. Nonlinear algebraic differential equations are solved off-line (S0) and the time varying linearized system (STVL) is used on-line to decrease the time calculation during the control optimization. Given small input variations ǻu, small state variations ǻx and small output variations ǻym about S0 can be represented through the STVL. The final unconstrained penalized optimal control objective is formulated as a cost function J, considering the variation ǻu of the manipulated variable u about a chosen trajectory u0. The control problem is a general optimization problem over a receding horizon Np where the cost function Jtot to be minimized reflects any control problem J (trajectory tracking, processing time minimization, energy consumption minimization, …), and nc constraints ci on measured (or estimated) outputs may be explicitly specified by Jext. k (resp. j) is the actual (resp. future) discrete time index, yref describes the specified constrained behaviour for the process measure yp and ym is the continuous model output. Since the problem is solved numerically, a mathematical discrete time formulation is:
min J tot ( p ) = J ( p ) + J ext ( p ) k+Np
J ( p) =
¦ g( y
( j ), y p (k ), ym ( j ), u ( p ( j )))
ref j = k +1 j = k + N p i = nc
J ext ( p ) =
(1)
¦ ¦ max [0, c ( j )] 2
i
j = k +1
i =1
3. Control software : Main features of MPC@CB Based on the process control strategy described above, the codes of the MPC@CB software have been written in Matlab. The program allows realizing the MPC of a process under constraints. The codes were adapted to make them easy to implement to any SISO or MIMO process, through the user files (where the model equations have to be specified), synchronized by few main standards files (where the user has to make few (or no) changes). The model has to be given under the form:
MPC@CB Software: A Solution for Model Predictive Control
661
dx ° = f ( x, u ) ® dt °¯ y = g ( x)
(2)
In the newly developed program, the number of states in the SISO or MIMO model is not limited. The model may be linear or nonlinear, time variant or time invariant, based on ordinary differential equations (ODE) and/or on partial differential equations (PDE). Another originality of the software is the simplicity for the user to solve control problems by various choices: • MPC for a custom cost function (trajectory tracking, processing time minimization…), with or without output constraints. The user may specify any reference trajectory. • SISO, MISO, SIMO or MIMO model (a new feature introduced by this work). • In order to study the robustness of the control law, it is easy to introduce, for any model parameter, different values in the model (used in the controller) and in the simulated process. It is assumed that the simulated process and the model are described by the same equations. • Closed loop control with PID in order to compare control performances with the MPC. • Possibility to introduce a cascaded process (which input of the cascaded process is the output controlled by the software) • Possibility to specify any condition to stop the run before the final time. • A software sensor (observer) can be introduced. • Open or closed loop control. The software has been already used for a real time application. The development of this software is still in progress and it is very easy to introduce new parts in the current code.
4. Application example 4.1. Process model A simplified model of emulsion polymerization process is described by the following equations (for more details see [4]):
dNT ° dt = Qm ° dN = Qm − R p ° ° dt ® dT 1 = ΔH R p + UA(Tj − T ) + Qm C p _ feed (T feed − T ) ° ρ dt C V m p ° ° dV MWm ° dt = ρ m ¯
[
]
(3)
Where NT (mole) is the total number of moles of monomer introduced to the reactor. Qm (mole/s) is the monomer input flow rate. N (mole) is the number of moles of residual
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B. da Silva et al.
monomer. Rp (mol/s) is the reaction rate. T, Tfeed, Tj (K) are the reactor, feed and jacket temperatures respectively. ρm and ȡp (kg/dm3) are the monomer and polymer densities respectively. Cp and Cp_feed (J/kg/K) are the heat capacities of the reaction medium and the feed. V (dm3) is the total volume of the reaction. ΔH (J/mole) is the reaction enthalpy. A (dm2) is the heat transfer area between the jacket and the reactor. U (W/K/dm2) is the heat transfer coefficient of the reactor wall. MWm (kg/mol) is the monomer molecular weight. With
Rp = μ k p0 e
− EA [M ] p ( N , N T ) RT
(4)
Where μ (mole/dm3) is the number of moles of radicals in the polymer particle. kp0 (dm3/mol/s) is the pre-exponential factor of the propagation rate coefficient. EA (J/mole) is the activation energy of the propagation rate coefficient. [M]p (mol/dm3) is the concentration of monomer in the polymer particles. Usually, when polymer particles are saturated with monomer, only the jacket temperature can be used to control the reaction rate. The reaction rate is insensitive to the monomer flow rate during this interval. This reduced the controller to a SISO system. In this work, we will be interested in showing the interest of controlling MIMO systems. Therefore, we consider the interval where polymer particles are not saturated with monomer. In this case both control variables: the monomer flow rate and the jacket temperature affect the reaction rate and can be used in the MISO controller. During this interval [M]p is given by:
[M ] p ( N T , N ) =
N §N −N N · ¸ + MWm ¨ ¨ ρ ρ m ¸¹ p © T
(5)
The heat production QR is given by:
QR = ΔH R p
(6)
4.2. Process measurements The nonlinear state given by equations (3) is x = (NT ; N ; T ; V) . The state x is assumed to be completely measurable each 10s by calorimetry. ȝ is also a state of the system which is not modelled and not measured but can be estimated online from the other measurements. In the presented simulations, this state is assumed to be constant, but variations of ȝ can be taken into account in the software scheme. 4.3. Control objective Due to physical limitations, the jacket temperature was constrained in the admissible range 50-90°C with a small variation rate (1°C/min). The maximal admissible flow rate is 0.001 mol/s. The control objective is to maximize the reaction rate, which implies to attain as fast as possible the allowable reaction heat. The maximum allowable heat should be calculated from the capacity of the jacket to evacuate the heat in order to ensure the process safety. It is obvious that maximizing the heat production and therefore the reaction rate leads to the reduction of the process time. Optimizing the heat
MPC@CB Software: A Solution for Model Predictive Control
663
production leads therefore to optimize the process productivity. In order not to exceed the saturation concentration of the polymer particles, a constraint is considered on [M]p which is considered by the controller as a constraint on the state N. 4.4. Simulation results The parameters of styrene polymerization were used in the simulation. The objective of the first simulation was to maintain the heat production QR at its maximum admissible value fixed arbitrarily at 60W using the SISO MPC controller by manipulating the monomer flow rate (Figure 1). It can be seen that the desired heat production was reached rapidly by manipulating the monomer flow rate that was not saturated at any moment. This is due to the long horizon length used in the simulations. In the second simulation (Figure 2), the MISO control strategy was applied to obtain the desired heat. The adapted MPC@CB software for a multi-variable case was used with the four dimensional ODE’s system of the emulsion polymerization process. In this case the monomer flow rate and the jacket temperature were both manipulated in order to reach the desired heat. It can be seen that no saturation in their values was reached and the desired heat production can be attained more rapidly with the MIMO strategy than with the mono-variable SISO controller.
5. Conclusion and future works In this paper, the existing MPC@CB software was extended for a multi-variable use. From a practical point of view, the drawback of MPC is the computational time aspect. MPC@CB algorithm allows decreasing the computational burden during on-line control. The predictive control strategy used in this software is robust and is defined by few adjustable parameters. MPC@CB software offers a turnkey solution for a constrained nonlinear multi-variable predictive control. Simulation results have shown that the MIMO strategy improves the control performances. Possibilities to control the particle size distribution of a styrene emulsion polymerization with this multi-variable strategy and this software are under study. Nonlinear PDE such as the particle size distribution can easily be discretized using numerical methods, like the finite differences and can therefore be used by the software.
References [1] S.J. Qin and T.A. Badgwell, A survey of industrial model predictive control technology, Control Engineering Practice, No 11 (2003) 733. [2] N. Daraoui, P. Dufour, H. Hammouri, Model Predictive Control of the Primary Drying Stage of the Drying of Solutions in Vials: an Application of the MPC@CB Software (Part 1), Proceedings of the 5th Asia-Pacific Drying Conference 2007, vol. 2, pp. 883-888, Hong Kong, China, August, 13-15 2007. [3] K. Abid, P. Dufour, I. Bombard, P. Laurent, " Model Predictive Control of a Powder Coating Curing Process: an Application of the MPC@CB© Software ", Proceedings of the 26th IEEE Chinese Control Conference (CCC) 2007, Zhangjiajie, China, vol. 2, pp. 630-634, July 27-29 2007. [4] Mazen Alamir, Nida Sheibat-Othman, Sami Othman, Constrained nonlinear receding horizon control for maximizing production in polymerization processes, IEEE Transaction on Control Systems Technology, 2006. [5] D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. Scokaert, Constrained model predictive control: Stability and optimality, Automatica, No 36 (2000) 789.
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[6] P. Dufour, Y. Touré, D. Blanc and P. Laurent, On nonlinear distributed parameter model predictive control strategy: On-line calculation time reduction and application to an experimental drying process, Computers and Chemical Engineering, Vol. 27, No. 11, 15331542, 2003. [7] R. Fletcher. Pratical Methods of Optimization. John Wiley and Sons, 1987.
Figure 1: Optimization by SISO MPC of the dynamic of the output heat production.
Figure 2: Optimization by MISO MPC of the dynamic of the output heat production.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
665
Detection of multiple structural changes in linear processes through Change Point Analysis and bootstraping Belmiro P.M. Duartea,b, P.M. Saraivab a
Department of Chemical Engineering, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199 Coimbra, Portugal,
[email protected]. b GEPSI – PSE Group, CIEPQPF, Department of Chemical Engineering, University of Coimbra, Pólo II, Pinhal de Marrocos, 3030-290 Coimbra, Portugal,
[email protected].
Abstract This paper presents an approach for detecting structural change of processes described by linear relations from restrospective data. The algorithm proposed comprises two steps: i. location of the change point at which the structural change did occur; ii. assessment of the confidence level of the change point detected. The location step is carried out by fitting linear models using Ordinary Least Squares (OLS) in the partitions generated from considering each data point as a pottential boundary. Subsequently, the supremum of Wald statistic is employed to estimate the change point. The confidence level is computed using a bootstraping with replacement algorithm. The approach is applied to a benchmark problem to assess its performance, and to a set of data sampled from an industrial process devoted to the production of precipitated calcium carbonate, comprising four input variables and a quality variable as output. Keywords: Change point, structural change, bootstraping, process monitoring.
1. Introduction and Motivation The need of industrial plants to operate within optimal regions and implement adequate global control strategies is nowadays well recognized and accepted. Within such a context, the development of control approaches focused on quality control and process monitoring techniques based upon data mining, analysis and the associated knowledge extraction, has become more and more relevant. One of the most commonly found problems in this regard corresponds to the proper identification of structural process changes, designated as change points, since they are associated with signals of malfunctions and/or process shifts [1]. Change point detection procedures fall under two main categories: retrospective (or a posteriori) tests, and on-line (or a priori) tests [2]. Here we consider a process described by a linear model, comprising multiple input variables and one output variable, which also includes a white noise term, subject to multiple structural changes quantified by variations on the parameters involved in the underlying plant model. The aim is to detect structural changes of the model based on retrospective data to improve the process knowledge and indentify the causes that lead to those changes. This kind of problem is quite common in econometry to identify process shifts [2]. In this paper we propose a combination of techniques already applied in the analysis of econometric time series to identify process changes in the operation of chemical processes. It is assumed that the output variable is related with inputs through linear relations, but the process analysis in larger time horizons may reveal near nonlinear behaviors in result of different piecewise sequential linear models. The purpose of
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B.P.M. Duarte and P.M. Saraiva
the approach is particularly focused on the detection of the points where one piecewise linear relation is replaced by another, thus indicating the occurrence of important shifts on the process.
2. Structural change detection algorithm Here we consider that the retrospective data, termed D = [X ,Y ] , was discretely sampled from a process, with D ∈ ℜs +1 , X ∈ ℜs representing the input vector, and Y ∈ ℜ the output. The sequences {Yi ,1 ≤ i ≤ N } , and {X i ,1 ≤ i ≤ N } are observations sampled at instants t 0 + i Δt , where t 0 is the initial absolute reference time, Δt is the sampling time, and N is the number of observations. The process follows a linear regression model :
Yi = X iT βi + ε i
(1)
with ε ∈ ℜ standing for the random error, ε ≈ N (0, σ 2 ) and β ∈ ℜs for the vector of parameters. One assumes that no structural change occurs during the first m records of the data sample, a common assumption in structural change identification designated by non-contamination condition, represented by the relation βi = β 0 , 1 ≤ i ≤ m [3]. The purpose is to test the model structural stability, designated as null hypothesis H 0 vs. the occurrence of model structural changes at point k , with 1 ≤ m ≤ k ≤ N , denoted as hypothesis H 1 . Several test procedures can be employed for such a purpose. Among them are all tests belonging to the generalized fluctuation test framework [4], the tests based on Maximum Likelihood scores [5], and the tests derived from the F statistic [6]. Recently Zeileis demonstrated that all three families of tests can be unified into a framework designated as generalization of M-fluctuation tests [7]. The family of tests based on F statistics, such as the Wald statistic and likelihood ratio were developed for testing the occurrence of a single structural change at an unknown time instant [8]. We address a similar problem, thus choosing the sup W test [6], belonging to the F statisticbased tests, for the purpose of testing the null hypothesis. It must be stressed that one assumes that the underlying process has an unknown number of structural changes, which are determined one at a time by iteratively partitioning and testing the original data set. The model estimation algorithm employed is OLS, and the methodology is described as follows. For each k partition comprising the observations (1," ,k ) the associated leastsquares estimates of β , termed as β (k ) , are obtained through the minimization of
¦
k i =1
(y − X i
observations
T i
β (k )
)
2
. The complementar set of the partition k , denoted as k , includes
(k + 1," , N ) ,
and the associated least squares estimates of β k are ( )
computed by the minimization of
¦
N i =k +1
(y − X β( ) ) . The sum of square residuals 2
i
T i
k
for each of the pottential k partitions considered under the H 1 hypothesis depends on the break point k , and is given as:
Detection of Multiple Structural Changes in Linear Processes Through Change Point Analysis and Bootstraping k
(
S (k ) = ¦ yi − X iT β (k ) i =1
)
2
+
¦( N
i =k +1
yi − X iT β (k )
)
667
2
(2)
The Wald statistic can now be constructed, assuming that the covariance matrix of the residuals is heteroskedastic [9] : W (k ) =
S (N ) − S (k ) S (k ) /(N − s )
(3)
where S (N ) is the sum of square residuals of the model fitted under the null hypothesis. The change point, τˆ , is therefore estimated as :
τˆ = sup [W (k ) ] , k ∈ [γ N , (1 − γ )N ]
(4)
with γ =0.15, the fraction of points considered to define a non-contamination condition [6]. Next to the assessment of the change point one has to validate it deriving confidence intervals for its occurrence. In the literature two basic strategies are employed for such a purpose: i. the deveolpment of proper analytical assymptotic estimators for the statistic τˆ ; ii. the use of bootstraping algorithms. The bootstraping technique was firstly proposed by Effron and Tibshirani to build an approximation of the distribution of a test statistic [10]. The idea behind its application is to create a new sample by drawing the error terms from the empirical distribution produced by the null hypothesis model, where no break exists. Each bootstrap sample serves to compute a test statistic τˆ* in the same fashion as τˆ . Here we employ a parametric bootstrap technique standing on a data-generating process described by a parametric distribution of ε i arising from fitting the model yi = X iT β (N ) + ε i with the complete set of data. An uniform distribution that assigns probability 1/ N is used to sample with replacement the values of ε i and build a new distribution of the error, ε i* , subsequently employed to build a new distribution of the output, denoted as yi* [11]: yi* = X iT β (N ) + ε i*
(5)
and a new data sample D * = ª¬X ,Y * º¼ is then used to determine the bootstrap change point τˆ* . The degree of confidence of τˆ is therefore given by: p (τˆ ) =
1 B ¦ I τˆ ≥ τˆ* B i =1
(
)
(6)
where I ( • ) is an indicator function whose value is 1 if its argument is true and 0 if not, and B is the number of bootstrap samples. In case p (τˆ ) ≥ 1 − α a structural change
occurred at the point τˆ and both partitions (1," ,τˆ ) and (τˆ + 1," , N ) are subsequently
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B.P.M. Duarte and P.M. Saraiva
tested (one at a time) regarding the occurrence of structural changes, with α standing for the Type I error assumed. This procedure is carried out iteratively until no more change points found achieve probabilities higher than 1 − α .
3. Application The algorithm described in Section 2 was tested with two data samples. The process has a structural change at the point τˆ = 50 , which is captured with 100% of confidence, and no more change points are identified. The values of B and α employed were 399 and 0.01, respectively, in both cases handled. The number of bootstraps was chosen taking into account the empirical rule of Davidson and MacKinnon, who proposed that α (B + 1) should be an integer in order to achieve an exact test [12]. The power of the test increases as B increases, however the computational effort also augments proportionally, thus requiring an appropriate trade-off between those two factors. The first data set represents a benchmark problem with a single input and a single output, with the data generated according to the relation :
{
1 ≤ i ≤ 50 yi = 5.0 − 0.1x i + z i −5.0 + 0.1x i + z i 51 ≤ i ≤ 100 xi = i , i ∈ {1," ,100}
(7)
and z ≈ N (0, 0.2) standing for normal noise, and i is an integer counter. Figure 1 reveals the accuracy of the algorithm, and Table 1 presents the stuctural form of the local models identified. The change point is located at observation 50 due to noise of the output variable, as can be seen from Figure 1. Moreover, the local models identified are in close agreement with the data, thus proving the accuracy of the algorithm. Table 1 – Structural models for each of the regions. Region
Interval
β
1
[1;49]
[4.8852
-0.0970]T
2
[50;100]
[-5.6084
0.1010]T
The second case used for testing the methodology is about an industrial unit devoted to the production of precipitated calcium carbonate (PCC). The process dynamics are monitored measuring an output variable which is simultaneously a quality variable, and four input variables which affect the former. The data set used for analyzing the occurrence of structural changes is formed by 93 records respecting to almost 3 months of operation. One may see from Figure 2.a that 2 structural changes were identified, with the order representing the sequence of change points detected. The visual analysis of the output variable does not reveal different trends, but the structural changes correspond to different linear models (Table 2). The quality variable exhibits an almost random behavior due to the changes of the input variables. Additionally, the magnitude of inputs becomes larger for t > 30 days, thus leading to an increase of the model residuals (Figure 2.b). However, our approach is able to capture changes in regression coefficients. Although with a different variation, due to model structural and input
Detection of Multiple Structural Changes in Linear Processes Through Change Point Analysis and Bootstraping
669
changes, one can see from Figure 2 that no underlying structure seems to be present in the zero centered residuals, apparently confirming that linear input-output relationships do convey a good approximation about this plant´s behaviour. The statistical analysis of the residuals produced by three local model stucture revealed its independency on the inputs and normality
Figure 1 – Results for Case 1 (CPi identifies ith change point and α for the Type I error probability). Table 2 – Structural models for each of the regions. Region
Interval
β
1
[1;33]
[10.9877 -0.0101 -0.4398 -2.6186 -1.7795]T
2
[34;62]
[39.1254 0.1533 26.3165 36.3046 -91.9578]T
3
[62;93]
[63.1440 -0.2038 -88.8527 -34.4503 178.7011]T
4. Conclusion In this paper a methodology often used in the analysis of econometric time series (Change Point Analysis) is employed to detect structural changes of the process model of production units based on retrospective data series. The process model is linear and OLS is used to fit the data. The detection of a single change point estimator at an unknown instant is performed employing the sup W test, a tool included in the group of F statistics tests. The construction of confidence level intervals for such an estimator is carried out through a bootstrap technique based on sampling with replacement of the error terms of the model associated to the null hypothesis. The detection of change points and validation through the computation of its confidence level is performed sequentially by partitioning the original data into smaller regions, where no change point is found. The approach was successfully applied to a benchmark process model an to an industrial set of data representing the dynamics of a process unit during a certain time horizon.
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Figure 2 – Results for Case 2 - Plot a. Behaviour of the quality variable and change points where CPi identifies ith change point and α stands for the Type I error probability; Plot b. L ocal model residuals .
References 1. F. Li, G.C. Runger, E. Tuv, Inter. J. Prod. Res., 44 (2006) 2853-2868. 2. M. Basseville, I.V. Nikorov, Detection of abrupt changes – theory and applications, Prentice Hall (1993). 3. C.-S. J. Chu, M. Stinchcombe, H. White, Econometrica, 64 (1996) 1045-1065. 4. L. Horváth, M. Husková, P. Kokoszka, J. Steinbach, J. Stat. Planning and Inference, 126 (2004) 225-251. 5. B.E. Hansen, J. Policy Modeling, 14 (1992) 514-533. 6. D.W.K. Andrews, Econometrica, 61 (1993) 821-856. 7. A. Zeileis, Econometric Reviews, 24 (2005) 445-466. 8. J. Bai, P. Perron, Econometrica, 66 (1998) 47-78. 9. J. Bai, Econometric Theory, 13 (1997) 315-352. 10. B. Efron, R.J. Tibshirani, An introduction to the bootstrap, Chapman & Hall (1994). 11. J. Jouini, M. Boutahar, Working paper, http://www.edgepage.net/jamb2003/Jamboree-Greqam-Jouini.pdf (2003). 12. R. Davidson, J. MacKinnon, Econometric Reviews, 19 (2000) 55-68.
81hEuropean Symposium on Computer Aided Process Engineering - ESCAPE18 Bertrand Braunschweig and Xavier Joulia (Editors) 2008 Elsevier B.V.All rights reserved.
Applications of grey programming to process design Edelmira D. G i l v e ~ "Luis ~ ~ , A.
ist tern as^.^, Pamela S. patiiiob, Kathy L.
Ossandonb "UniversidadCatdlica del Norte, Antofagasta, Chile b~niversidad de Antofagasta, Antofagasta, Chile 'Centro de Investigacidn CientSficay Tecnoldgicapara la Mineria, Antofagasta, Chile
Abstract One of the methodologies utilized for process design consists on the application of optimization techniques, e.g. mathematical programming, to identify the best design inside a set of alternatives. In spite of the efforts and advances, this approach faces the problem that it is not broadly utilized in the industrial practice. One reason, among other, is that their implementation requires complex mathematical developments and therefore a good knowledge of the mathematical programming techniques. Therefore, it important to develop procedures that can consider real situations, but on the other hand does not require complex mathematical methods. this work the potential application of grey programming (GP) and grey system to process design is analyzed. GP is a simple technique to consider uncertainty. The design of flexible heat-exchange network is used as an example. Complete methodologies is developed, which include the grey composite curve, the determination of the grey minimum utility consumption, and the determination of grey number of interchangers units. The utilized techniques consider grey linear programming (GLP) and grey mixedinteger linear programming (GMILP). Keywords: grey system, grey programming, process synthesis, heat exchange networks
Introduction In chemical and metallurgical process synthesis, designers must balance and integrate many disparate factors prior to settling upon a final decision. To facilitate this process, several methods have been developed. These methods can be classified as: the methods that are knowledge based and employ heuristics; the methods that employ optimization techniques and use superstructures to represents the alternatives; and, the hybrid methods combining different approaches that blends physical insights with mathematical techniques. The methods that employ optimization techniques are based on mathematical programming techniques and have been used in numerous applications to successfully facilitate the synthesis of process. However, most of these methods have been based upon deterministic techniques and, therefore they have not incorporate process uncertainties and flexibility into their solution, or complex techniques as stochastic programming has been used to represent the uncertainty. real practices, however, at least three factors must be considered. First, any process synthesized by modeling techniques would usually not be operationalized without supplementary information input from additional expert oversight so that the design can satisfy all disagreeing dimensions. Second, the quality of the information on the uncertain parameters can be poor, for example with unknown distribution. Finally, a
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E.D. Gklvez et al.
complex technique as stochastic programming requires efficient numerical solvers and a good knowledge of the techniques which can be an important restriction. Grey theory (GT) [I] can mitigate the above troubles because 1) GT will not conduct to more complicated models, and thus will be more easy to understand and use and will have lower computational requirements compared with other techniques, 2) GT will not require distribution information for the uncertain parameters and therefore it will be more easy for designers to define the uncertainty, 3) GT will provide feasible ranges for the decision variables simplifying the decision maker. In this work, GT is applied to process synthesis, specifically to the synthesis of heat exchange network (HEN).
2. Background In this section, we first introduce some useful information on GS and GP, and then provide some basic information on HEN. 2.1. Grey Systems Each GS is described with grey numbers, grey equations, grey matrices, etc. A grey number is such a number whose exact value is unknown but a range within that the value lies is known, this is a grey number x* is defined as un interval with known upper and lower bounds but unknown distribution information for x,
Where x- and x+ are the lower and upper bounds of x* respectively, when x'=x+, x* turn into a deterministic number. For grey numbers x* and y*, we have x* * y* = [min(x * y), max(x * y)] ,
(2)
Where x- 5 x < x+ , y- I y < y' and * E {+,-,x,+) is a binary operation on grey numbers [I] The whitened value of a grey number, x*, is a deterministic number with its value remaining between the upper and lower bounds of 2.A grey integer number is a grey number with integer upper and lower bounds, and all its whitened values are integers. A grey mixed-integer linear programming (GMILP) model is formulated by introducing concepts of GS into a mixed integer linear programming modeling framework as follows[2] max f* =C*X* S.I.
A* X* IB* Where is a vector of grey continuous and grey integer variables, A* EJI?]""", EJR*]~~',(where R* stand for a set of grey numbers) andf is a grey objective function. GMILP provides feasible ranges for the decision variables which are useful for decision makers to validate the generated alternatives. The solution of the grey binary variables have four possible presentation ([0,0], [1,1], [0,1], and [1,0]). They can be interpreted as grey decisions alternatives, reflecting potential system condition variations caused by the uncertainties. 2.2. Heat Exchange Network Grey systems and grey programming are easy to apply, and therefore it can be applied to many problems, for example heat exchange network (HEN). The synthesis of HEN is
Applications of Grey Programming to Process Design
673
one of the extensively studied problems in chemical engineering, where the objective is the generation of a network of heat exchangers either with minimum total utility consumption, minimum number of heat-transfer units, or minimum total cost. The methods for the synthesis of HEN can be classified as heuristic-algorithmicevolutionary and mathematical-programming [3]. Usually in these methods nominal parameters values are used, e.g. constant values for source-heat-capacity-flowrates and temperatures. The problem of including uncertainties in these parameters in the synthesis of HEN'S has started to receive attention over the last years. Several works have been published on flexible HEN including MILP transshipment model with the active set strategy to guarantee the desired HEN flexibility [4,5]. A simple way to synthesize HEN is the transshipment model, which solve the problem using sequential optimization. In this strategy the minimum utility consumption is determined first by means of a LP model, and based on these results the minimum number of matches is determined using a MILP model [6].
3. Grey heat integration 3.I . Grey heat Exchanger Network Pinch analysis is a methodology that allows the calculation of minimum hot and cold utilities consumptions in a process from the knowledge of some data of the hot and cold streams. This methodology is well known in the literature and it based in the calculation of cascade composite hot and cold heat flows [6] based on initial and final temperatures stream and its mean heat capacity flowrate. Let denote Ch 4 (T,Q) I Q = FCp(Tn- T ) , T, 5 T 5 T,,}as the HohmannILockhart curve for a hot stream h, then the hot composite curve can be defined as CCH= R Chwhere Q represents the composition of one curve heH
based on the set of Ch, and H denotes the set of hot streams. A similar definition is possible for the cold streams, this is C, 4 ( T ,Q ) 1 Q = FCp(T - T,,), T,, I T I T,, } and CCc = =$CC where C denotes the set of cold streams. Then the grey hot HohmannILockhart curve can be defined as C: = [ c ~ , c A ] where
c,I T * I T : } , i.e. C;.(
C,'=( (T*,Q*)IQ*=Fc;(?:-T*),
T:,
, IT -
1 Q+= FCp+(Ti- T + ) , I T i } and C;14 (T+,Q+)
(T-,Q-)IQ-=FC;(T;-T-),
TiII T+< T i } . Based in these
definitions the grey hot composite curve is GCCH= h s C ; = = [*S&
c;,h$ c;].
C;
In the same way, the grey cold Hohmannlhckhart curve is where
C;=[C;,C:]
[GCC;,GCC;~]
c ~ ~ ( T * , Q ~ ) ~ Q * = F c , ' ( T * - ~ ~ ) , ~ ~i.e. IT*~~~~},
4 (T-,Q-) I Q- = FCL(T- -Ti), q: I T - I T,;,} and C i 4 (T',Q') I Q' = FC;(T+ -Ti), , I T + , I ~ ~ Subsequently ~}. the grey cold composite curve is GCC - Rec* = - c.c
]
[GCC;, GCC; =
[gc;, 2C:] .
Also, it is possible to calculate the grey grand
composite curve, which can be very useful to analyze the heat integration problem under uncertain parameters. As an example, for process streams presented in table 1, we can calculate the GCCHand GCCc as it is shown in Fig. 1. This problem is a modification of the example 16.1 presented in [6], with steam available at 500°C, cooling water 20-30°C, and minimum grey recovery approach temperature of [10,10] OC. This mean that the approach
674
E.D. Gcilvez et al.
temperature, for this example, is a deterministic number. For the calculation of grey minimum hot and cold utilities consumptions (Qiand Qi ) we need to integrate the GCC; withGCC; to determine Q; and Qi, and integrate GCC; with GCC; to determine Q,'and Q; . Also to determine the grey possible heat integration, Qf , we need to integrate the GCCA withGCCb to determine Q: , and GCC;, with GCC; to determine Q; . Table 1. Process data adapted from example 16.1 presented in [6] Stream H1
FC;
(MW I C)
[0.97,1.03]
T: (c)
c,(c)
[388.0,412.0]
[116.4,123.6]
- - - -Grey Hot Composite Curve + Grey Hot Composite Curve Grey Cold Composite Curve - - - - Grey Cold Composite Curve -
Cascade Heat, kW Figure 1. Grey hot and cold composite curves
3.2. Grey transshipment model for HEN The transshipment model for the calculation of the minimum utility consumption and the minimum number of units can be applied using GP to consider the uncertainty in the temperatures and the heat capacity flowrate. For example, the heat contents of the hot and cold processing stream can be calculated considering grey temperature intervals, which are based on the inlet and outlet temperatures and in the grey approach temperature. Table 2 shows the grey heat contents (MW) for our example. In this work the transshipment model proposed by Papoulias and Grossmann[7] is used. The mathematical models are the same models proposed in [7], but grey numbers are used in heat contents in each interval. For example the GLP transshipment model for minimum utility consumption is:
675
Applications of Grey Programming to Process Design
The grey mathematical programming problem is solved in two steps, first GCCA with GCC; are used to determine Q; and Qi , and then GCC;; with GCC; to determine Q,' and Q; . Also, it is possible to calculate the grey heat integration in two steps, first GCC; with GCC; are used to determine Q; , and then GCC;; with GCC; to determine Q; . All problems are LP, and therefore easy to calculate. After the calculation of grey minimum hot and cold utilities consumptions (Q; andQ; ) we can calculate the grey fewest number of units in the network using the MILP transshipment model proposed by Papoulias and Grossmann [7], but with GS which transforms the problem into a GMILP transshipment model. To define the subnetworks, a grey pinch point can be identified if a grey residual, Rf has the lower bound equal to cero. Table 2. Grey temperature intervals and grey heat contents (MW) Interval
Hot 1
Grey Heat Contents (MW)
Grey Temperature Intervals
Cold
H1
[398.0,422.0 ] [388.0,412.0 ] [9.7,10.30 ]
H2
C1
C2
[0.0,52.53 ]
Table 3 contains the computational results obtained through the GLP and GMILP models. It is point out that solution for the objective function values and decision variables are grey numbers. The GLP model gives grey numbers for the hot and cold utilities, with a grey pinch in interval 2 ( R : = [0,4.4]). The GMILP model, for the minimum number of matches, gives a grey optima function equal to [5, 61. Note that if the solution of grey binary number are [0,0] or [1,1] then the grey binary number is a deterministic number, meaning that the match cannot or can be adopted with certainty. This is the case for matches H1.Cl (above and below pinch), H2.C1, H2.C2 and H2.CW below pinch. On the other hand, the [0,1] and [1,0] solutions represent grey decisions and can provide decision alternatives according with the desired flexibility of the network. This is the case for matches ST.Cl above pinch, H1 .C2 and H1 .CW below pinch. Thus, decision alternatives can be generated by adjustinglshifting the grey number solutions within their solution intervals according to the operational conditions.
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E.D. Gcilvez et al.
Table 3. Results to example of table 1 Grey minimum hot and cold utilities
Grey Matches
Above pinch
Y ~ , C= I [1,11
Y:T,CI
= [1,01
Below pinch
Y ~ I , C=Z[1,01
Y;Z,C,
= [1,11
y;,.cw
= [OJI
y;,,c1 = [1,11
Y;Z,CW
= [1,11
y;,,o = [1,11
4. Conclusions Grey systems and grey programming methods have been applied to the synthesis of heat exchange network. It improves upon other existing deterministic methods by allowing uncertain information to be directly considered into the synthesis/optimization process, and improves upon other no-deterministic methods by simplifying the mathematical problem. The results indicate that reasonable solutions have been generated for both continuous and binary variables. The grey system can be easy applied to other problems like mass exchange networks.
Acknowledgments The authors wish to thank CONICYT for support through Fondecyt Project 1060342.
References [I] S. Liu and Y. Lin, Grey Information, Springer, USA, 2006 [2] G.H. Huang, B.W. Beatz, G.G. Patry, 1995, Grey integer programming: An application to waste management planning under uncertainty, European Journal of operational Research, 83, 594-620. [3]A.E. Konukrnan, M.C. Camurdan, U. Akman, 2002, Simultaneous flexibility targeting and synthesis of minimum-utility heat-exchanger networks with superstructure-based MILP formulation, Chemical Engineering and Processing, 41,501 -518. [4] C.A. Floudas, I.E. Grossmann, 1986, automatic synthesis of optimum heat exchanger network configurations,AIChE J., 32,276. [5] C.L. Chen, P.S. Hung, 2007, Synthesis of flexible heat exchange networks and mass exchange networks, Computers and Chemical Engineering, 3 1, 1619-1632. [6] L.T. Biegler, I.E. Grossmann, A.W. Westerberg, 1997, systematic methods of chemical process design, Prentice Hall. [7] S.A. Papoulias, I.E. Grossmann, 1983, A structural optimization approach to process synthesis-11. Heat recovery networks. Computer and Chemical Engineering, 8,707.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
677
Flexible and configurable MILP-Models for Meltshop Scheduling Optimization Iiro Harjunkoski*, Guido Sand ABB Corporate Research, Wallstadter Str. 59, 68526 Ladenburg, Germany
Abstract This paper discusses MILP-models for meltshop scheduling optimization that can be flexibly adapted to different plant structures. Moreover, the flexibility allows for modeling individual characteristics of parallel equipment, particular processing and changeover times, scarce resources and maintenance requests. A small example illustrates the size and solution time of a typical model instance. Keywords: Meltshop, steel plant, scheduling, MILP
1. Introduction Steel production scheduling is a challenging task that has been actively studied in the recent years. The last processing step, continuous casting, has alone given rise to numerous research results, not the least because of its crucial role in the overall steel production planning. Another research focus has been in how to combine the continuous caster with the next production step: The operations at rolling mills (Tang et al., 2001). This work limits itself to the melt shop, starting from the Electric Arc Furnaces and ending with the Continuous Caster. This area has not received as much attention and the planning task has mainly been tackled through expert systems and heuristics or evolutionary algorithm-based solutions (Dorn et al., 1996; Pacciarelli and Pranzo, 2004). Here, we actually focus on an MILP-based decomposition approach and followup on the basic research work in Harjunkoski and Grossmann (2001), where meltshop scheduling and heat grouping models were presented as a part of an integrated solution algorithm. In that work, a fixed plant structure was assumed. This paper deals with two aspects of the further development towards a commercial meltshop scheduling tool, namely the flexibility of the models and their configurability. This makes the melt shop scheduling tool generally applicable to different steel plants and enables easier ways to express add-on features. A generalization can be expected to cause some performance losses, and the efficiency of the new model is compared to the original one. Here, the main mathematical constraints are shown and explained and finally, a numerical example is used to illustrate the size and the typical solution time of the revised model.
2. Model flexibility The meltshop scheduling problem in Harjunkoski and Grossmann (2001), is solved in four steps to reach close-to-optimal solutions in a limited solution time. The steps are: 1. Grouping of individual heats into casting sequences 2. Scheduling each casting sequence separately 3. Aggregation of the already scheduled sequences 4. Finalization to further tighten the aggregated schedule
I. Harjunkoski and G. Sand
678
The generalization discussed in this paper affects mainly the scheduling model (step 2), and therefore the main focus is on the scheduling part. 2.1. Plant layout The mathematical model should be fully configurable in terms of the plant layout. Figure 1 shows a “superstructure” of different plant layouts which should be covered by the flexible model. In order to be able to model some relations correctly, it is also necessary to provide the production stages, types of equipment, equipment routing, equipment connectivity and focus on specific properties of these. In this paper, parallel equipment may have individual characteristics.
($)
$2'
/)
&&
($)
$2'
/)
&&
opt
Figure 1. Stainless steel plant layout superstructure
2.2. Production Stages In the following model, we assume that for each heat to be produced a number of stages s=1,…,S is executed in a given sequence. However, the heats only need to go through those defined in their respective production recipes. The equipment m=1,…,M must be mapped to the stages. A stage-equipment matrix looks like S1 S2 S3
M1
M2
1
1
M3
M4
1
1
M5
1
2.3. Processing and changeover times In a similar manner, data is needed for the production times and here three processing times are considered: minimum/standard/maximum time for a heat in an equipment. By providing a range, the optimization can flexibly select the best timing for each heat at each equipment and, if wished, penalize for deviations from the targeted standard time. Changeover times may depend on the equipment or a heat, e.g. after a heat the equipment needs a certain maintenance time, cleaning and other setup-actions that need to be always done. The changeover times may also be dependent on the product sequence, which means that the setup time depends on the optimization result. Other specific issues that need to be handled by the optimization are for instance restrictions on the number of simultaneously operating parallel equipment (e.g. EAFs due to electricity requirement), heat routing and equipment connections. 2.4. Maintenance Maintenance requests are a common and very important part of metals processing. The main idea here is to couple the maintenance scheduling with the production scheduling, instead of keeping these two tasks apart. The most important information needed are: which equipment to maintain, maintenance duration and the earliest and latest start-time of the maintenance (time window)
Flexible and Configurable MILP-Models for Meltshop Scheduling Optimization
679
With these, the maintenance requests can be treated as a job with fixed equipment assignment and strictly limited time-window.
3. Flexible mathematical model for the scheduling Major changes in the scheduling model come from the introduction of a stage-index onto which the processing times are coupled. In this way, there is only one active time variable per stage and building the scheduling constraints is more straightforward. This also allows flexibility through easy equipment changes and modifications. 3.1. Sets and indices Sets are written with capital letters and corresponding indices are noted in lowercase. P = set of heats M = set of equipment S = set of production stages U = set of restricted units (parallel processing limitations) MNT = set of maintenance jobs SM sm = equipment m that belong to the stage s SPsp = stages s that should be executed on heat p HR pm = heat routing, defines which equipment m are allowed for heat p BADmm ' = connections between equipment m, m′ that are not allowed SU su = stage of restricted unit MEQmnt , m = which equipment m to maintain in mnt
These sets allow a flexible re-modeling of a plants. If one of the indices is used more than once in an equation, this will be shown with a ´ and ´´ notation, e.g. m, m´, m´´. 3.2. Parameters and Variables The necessary parameters here are partly covered by the sets above, where already some connections between two sets are defined, such as stage-equipment relationship. The basic parameters are always numeric data and here some of them are simply listed: Standard, minimum and maximum production times for each heat on each equipment, setup and clean-up times of each equipment, resource-intensive time if there are parallel processing restrictions, sequence-dependent change-over times, for each job-pairs on each equipment, minimum and maximum allowed transfer times between the stages (maximum hold time) and maintenance duration and earliest/latest start-time. The variables are: t pm = start time of heat p on equipment m t ps = start time of stage s of heat p
τ pm = processing time of heat p on equipment m x pm = 1, if heat p is processed on equipment m, else = 0 (assignment variable) y spp ' = 1, if stage s of heat p is processed after heat p' (sequencing variable) t TR ps = transfer time of heat p between stage s and the following stage xu pu = assign heat p to a restricted unit u
I. Harjunkoski and G. Sand
680
M y mnt , p = 1, if maintenance job mnt is done before heat p (sequencing variable) M t mnt = start time of maintenance job mnt
t MS = make span
All variables are positive and the x and y variables are binary variables (0, 1). 3.3. Problem Constraints The objective function is defined to minimize total production time (make span) and inprocess times of individual heats. The latter is done such that the start time of the first stage of each heat should be as late as possible, thereby reducing the hold and in-process times. Coefficient c1 should be small in order not to affect the make span.
min t MS − c1 ⋅
¦t
(1)
p, s p∈P , s = min{ SPsp }
The assignment constraint states that only one equipment per valid stage is selected.
¦x
m∈SM sm
pm
= 1 ∀p ∈ P, s ∈ S, {s, p}∈ SPsp
(2)
The following equation ensures a correct stage-sequence
(
t ps ' ≥ t ps + τ pm + t TR ps − Μ ⋅ 1 − x pm
)
∀p ∈ P, m ∈ M ,
s, s '∈ S , s < S , {s, p}∈ SPsp , {s′, p}∈ SPs′p , s ' > s, {s, m} ∈ SM sm
(3)
Here, s’ is one of the following valid stages for the heat. Some hold-times between two processing steps may have to be restricted. Therefore, the same equation is repeated to enforce an upper bound to allow both flexible processing- and transfer times.
(
t ps ' ≤ t ps + τ pm + t TR ps + Μ ⋅ 1 − x pm
{
)
∀p ∈ P, m ∈ M , s ∈ S , s < S , {s, p}∈ SPsp ,
{s, m} ∈ SM sm , s ′ = min s ′′ {s ′′, p}∈ SPs′′p , s ′′ > s s′′∈S
}
(4)
The start time of a stage must be connected to the corresponding equipment time. This is done by the two following constraints.
(
)
(
)
t pm ≤ t ps + Μ ⋅ 1 − x pm ∀p ∈ P, m ∈ M , s ∈ S , {s, p}∈ SPsp ,{s, m} ∈ SM sm , {p, m}∈ HR pm (5) t pm ≥ t ps − Μ ⋅ 1 − x pm ∀p ∈ P, m ∈ M , s ∈ S , {s, p}∈ SPsp ,{s, m} ∈ SM sm , {p, m}∈ HR pm (6)
We need two types of sequencing constraints as the casting must be continuous. First the general case.
(
t pm ≥ t p′m + τ p′m + Tms + Tmcl + Tm, p′, p − Μ ⋅ 3 − ysp ' p − x pm − x p′m ∀p, p′ ∈ P, p ≠ p′, s ∈ S , s < S , m ∈ M , {s, m}∈ SM sm ,
) (7)
{p, m}∈ HR pm , {p′, m}∈ HR p 'm
The constraint (7) applies to all stages except casting. To enforce continuous operation on the caster, we need a pair of inequalities. These constraints are simpler, as the casting sequence is fixed and all heats within a sequence must be assigned to the same caster.
Flexible and Configurable MILP-Models for Meltshop Scheduling Optimization
(
)
(
)
t p+1,m ≥ t pm + τ pm + Tm, p , p +1 + Μ ⋅ 1 − x p +1,m
(8)
∀p ∈ P, p < P , m ∈ M , {s = S , m}∈ SM sm , {p, m}∈ HR pm
t p+1,m ≤ t pm + τ pm + Tm, p , p +1 + Μ ⋅ 1 − x p +1,m
681
(9)
∀p ∈ P, p < P , m ∈ M , {s = S , m}∈ SM sm , {p, m}∈ HR pm
Only one sequence is possible per stage.
y spp′ + ysp′p = 1 ∀p, p′ ∈ P, p < p′, s ∈ S , {s, p}∈ SPsp , {s, p′}∈ SPsp '
(10)
The definition of makespan must be valid for all alternative casters, which means that the focus must be on the entire stage. Here, the cardinality of the set of stages refers to the last stage (casting). t MS ≥ t pm + τ pm
∀p = P , s = S , {m, s}∈ SM sm
(11)
As mentioned above, it must be ensured that all heats of one casting sequence are cast in the same caster. Thus, the assignment variables must be coupled. x pm = x p′m
∀p, p′ ∈ P, p < P , p = p′ + 1, s = S , m ∈ M , {m, s}∈ SM sm
(12)
If there are forbidden equipment combinations defined, these can be implemented also through the assignment constraints by hindering a heat to be assigned on both equipment, as follows: x pm + x pm′ ≤ 1 ∀p ∈ P, m, m′ ∈ M , {m, m′}∈ BADmm′
(13)
The earlier parallel unit restriction from the Electric Arc Furnace (EAF) has been generalized. Here, we map stages to restricted units to hinder more parallel activities than available units. One can either specify a fixed overlapping time or assume that a new parallel equipment should not start the processing before the other one has finished.
(
)
(
)
(
t ps ≥ t p′s + TsFIX if TsFIX > 0 + τ p′m if TsFIX = 0 − Μ ⋅ 3 − y sp′p − xu pu − xu p′u
)
∀p, p ′ ∈ P, p ≠ p ′,
s ∈ S , u ∈ U , {s, u}∈ SU su , m ∈ M , {p, m}∈ HR pm , {p ′, m}∈ HR p 'm , {m, s}∈ SM sm
(14)
Here, for instance the electricity consumption may restrict parallel operation of EAFunits or only two of three casters operated simultaneously. For the restricted units, also only one assignment should be allowed. This is enforced by:
¦ xu
pu ′ u ′∈U ,{s ,u ′}∈SU su′
= 1 ∀p ∈ P, s ∈ S , {p, s}∈ SPsp , s ∈ ∪ SU su u∈U
(15)
Smaller maintenance jobs can be integrated to the scheduling, since this allows the best planning of the equipment-downtimes. This is done by the following two constraints.
(
M DUR M t pm ≥ t mnt + Tmnt − Μ ⋅ 2 − y mnt , p − x pm
)
∀p ∈ P, mnt ∈ MNT , m ∈ M , {mnt , m}∈ MEQmnt ,m
(
M t pm + τ pm + Tms + Tmcl ≤ t mnt + Μ ⋅ 2 − y Mp ,mnt − x pm
)
∀p ∈ P, mnt ∈ MNT , m ∈ M , {mnt , m}∈ MEQmnt ,m
(16)
(17)
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Finally, the times for equipment that are not used should be put to zero, in order to allow the flexible unit sequencing in Eq. (14). Simultanously, this means that the lower limit for the production time must be defined as a constraint. These are shown below.
τ pm ≤ Μ ⋅ x pm ∀p ∈ P, m ∈ M , {p, m}∈ HRpm
(18)
LOW τ pm ≥ τ pm ⋅ x pm ∀p ∈ P, m ∈ M , {p, m}∈ HR pm
(19)
The derived generalized model is very flexible but has several binary variables. The performance issue has to be checked with a realistic problem and further reductions/simplifications need to be added accordingly. Naturally, the optimization should be efficient for steel plants with a simpler structure.
4. Example In this small example we compare a problem instance of 15 heats. The solution times (CPU, wallclock) using the fixed model and new model are shown. As it is difficult to compare the entire models, we will just show the model size for the scheduling part. The example shows that the flexible model requires less binary variables while the number of continuous variables and constraints is higher. However, the solution times are not significantly different. Table 1. A comparison (constraints and variables only for the discussed model) Method
CPU-s
Wallclock time
Constraints
Variables (bin/cont)
Harjunkoski et al. (2001)
4.27
14
173
103 / 68
Flexible model
3.96
9
307
87 / 110
5. Conclusions The presented flexible model is easily configurable e.g. through an ISA-95 interface (B2MML) or any other approach that contains the necessary information. Even if a minor performance loss can be expected, it is very important for practical cases to have easily configurable models. The model takes a step towards a product, as the example case can fully be formulated outside the model.
References Jürgen Dorn, Mario Girsch, Günther Skele and Wolfgang Slany (1996). Comparison of iterative improvement techniques for schedule optimization. European Journal of Operational Research, Volume 94, Issue 2, pp. 349-361 Iiro Harjunkoski and Ignacio E. Grossmann (2001). A decomposition approach for the scheduling of a steel plant production. Computers & Chemical Engineering, Volume 25, Issues 11-12, pp. 1647-1660 Dario Pacciarelli and Marco Pranzo (2004). Production scheduling in a steelmaking-continuous casting plant. Computers & Chemical Engineering, Volume 28, Issue 12, pp. 2823-2835 Lixin Tang, Jiyin Liu, Aiying Rong and Zihou Yang (2001). A review of planning and scheduling systems and methods for integrated steel production. European Journal of Operational Research, Volume 133, Issue 1, pp. 1-20
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Functional Data Analysis for the Development of a Calibration Model for Near-infrared Data Cheng Jiang, Elaine B. Martin School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne NE1 7RU, UK
Abstract The calibration performance of two functional data analysis approaches is investigated in this paper. The performance of the method is considered for different basis functions, the penalized B-spline with equally spaced knots and the B-spline with unequally spaced knots and wavelets. The various approaches are compared with respect to the prediction of the mole fractions of different components from the spectrum of mixture samples. The different approaches are benchmarked against the more traditional calibration modelling approach of PLS. Keywords: Functional Data Analysis, Calibration Model, Near-infrared Data
1. Introduction The implementation of spectroscopic techniques is expanding partially as a consequence of the recent Federal Drug Agency’s Process Analytical Technology (PAT) initiative. Of the different spectroscopic techniques, near infrared (NIR) spectroscopy is one of the more popular in terms of application. The NIR spectral region corresponds mainly to overtones and combinations of the active molecular fundamental oscillating frequencies with interfering peaks, together with various optical effects resulting in a complex spectral matrix. However to attain the greatest benefit from the data, there is a need for calibration procedures that extract the maximum information content. Based on Beer’s law, a calibration model between the specific properties and spectra can be assumed to be approximately linear. Multiple linear regression (MLR) is the simplest approach for the creation of a calibration model but it is not suitable for the modelling of NIR data where the number of samples is less than that of wavelengths recorded since linear dependency among the columns of the data matrix X, called collinearity, results, and the matrix XT X will be singular. The application of subspace projection techniques is one approach to addressing the collinearity issue with Partial Least Squares (PLS) being one of the more popular techniques. PLS first projects the input variables, or predictors, onto several independent latent variables that are a linear combination of the original predictor variables, and the response y is then regressed on the space spanned by the latent variables, i.e. the subspace of the column space of X. In an increasing number of fields, observations can be characterised by curves. NIR is one exemplar. This form of data is termed ‘functional data’ since curves are examples of functions. Ramsay and Dalzell (1991) proposed the concept of functional data analysis for analyzing such data. In contrast to multivariate data analysis, functional data analysis considers the observations as a function as opposed to a sequence of numerical values. Consequently a function lies behind each sample. A number of
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applications of FDA have been reported including in the areas of economics, medicine, biology and chemometrics. As NIR spectra can be considered as functional data, it is hypothesised that functional data analysis can capture the inherent structure of NIR spectra and hence FDA may provide an alternative approach to constructing a calibration model. Two functional linear regression approaches are discussed in this paper and are benchmarked against the more traditional approach of PLS. The arrangement of this paper is as follows. Section 2 introduces the different FDA approaches with details of the data set used in the study described in section 3. The results and a discussion of them is presented in section 4 with overarching conclusions provided in the final section.
2. Functional Linear Regression Approaches Functional data analysis is a new way of thinking. The underlying philosophy behind it is that the item (sample) on which the functional data analysis is performed is considered as a function as opposed to a series of discrete data points. Based on this definition, with respect to the calibration analysis of NIR data, the NIR spectrum is considered as a function with the response being a specific property of an analyte. The goal of calibration is to build a model between a functional predictor and a scalar ~ response. Consequently there exists a linear operator L between R ∞ and R 1 such that it maps a function lying in R ∞ to a scalar lying in R1 : ~ L : R ∞ 6 R1
(1)
Thus the relationship between the NIR spectrum and the specific property is represented ~ ~ by the linear operator L . Two approaches for estimating the operator L are discussed in this paper. One approach is fitting the NIR spectra with mathematical basis functions and then developing regression model between the response variables and the fitting coefficients. The second approach represents the regression coefficients by basis functions as opposed to the original spectra. Both approaches utilize the functional properties of NIR spectra. The first approach assumes the shape information contained within NIR spectra can be captured by the basis functions and the second hypothesis that the curve information of the NIR spectra can be reflected by that of the regression coefficients. A mathematical framework for these approaches is now presented. 2.1. Indirect Approach Although the individual spectrum is a point in the R ∞ space, the dimension of variation between the N samples is always finite. Thus it can be assumed that the N spectra samples lie in the space spanned by a set of finite mathematical basis functions. Let the functional format of the whole spectrum be x(λ ) , where λ denotes the wavelength. φ1 (λ ),φ2 (λ ),",φk (λ ) indicates the set of basis functions and x(λ ) is represented by a linear combination in terms of the k basis functions k
x(λ ) = ¦ ciφi (λ ) + ε (λ ) i =1
(2)
Here ε (λ ) represents noise and c1,!, ck are the fitting coefficients. Since φ1 (λ ),φ2 (λ ),",φk (λ ) are mathematically independent, c1 , c2 ," ck are unique. Consequently according to the property of linear operators:
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~ ~ ~ ~ y = L x(λ ) = c1 L φ1 (λ ) + c 2 L φ 2 (λ ) + " c k L φ k (λ ) (3) ~ Therefore, L x(λ ) can be calculated from Eq. (3) as a linear combination of ~ ~ ~ L φ1 (λ ),!, L φ k (λ ) , as opposed to estimating the operator L directly. Eqs. (2) and (3) can be expressed in matrix notation as:
X = Cĭ + E X
(4)
where the elements of ĭ are the basis functions φ1 (λ ),φ2 (λ ),", φk (λ ) , C is the fitting coefficient matrix and E X is that part of X unexplained by basis functions. y = CL Φ + e
(5) ~ ~ where the elements of L Φ are L φ1 (λ ), ! , L φ k (λ ) and e is a noise term. Typically, the number of samples (spectra) is less than the number of fitting coefficients. In this situation, classical regression methods cannot be applied directly. Consequently, different strategies need to be considered to address this problem. Two approaches discussed in this paper are: (i) apply PLS to build a regression model between the response variable and the fitting coefficients, and (ii) place a hard constraint on the number of basis functions such that ordinary least squares can be applied. 2.2. Direct Approach ~ In the case that the predictor is a function and the response is a scalar, the operator L can be considered as an inner product operator and the estimation of the response is the inner product of the functional predictor and the regression coefficient. For example, let the matrix notation for the relationship between the response y and the predictor X be y = Xb + e . Xb is scalar since y is a scalar, consequently, Xb can be considered as the inner product of X and b , hence b should be a function since X is a function λn
y=
³ x(λ )b(λ )dλ + ε =< x, b > +e
(6)
λ0
where [λ0 , λn ] denotes the range of the spectrum, and denotes the inner product. The problem now becomes how to estimate the function b(λ ) . The approach discussed in this paper is to represent the regression coefficient b by a set basis functions directly as opposed to the original spectrum. Let b(λ ) be represented by m basis functions: m
b(λ ) = ¦ cvφv (λ )
(7)
v =1
Thus < x, b > can be calculated as: λn
m
m
λn
λ0
v =1
v =1
λ0
< x, b >= ³ x(λ ) × (¦ cvφ v (λ ))dλ = ¦ c v ³ x (λ )φ v (λ )dλ
(8)
c1 ,!, cm are the parameters to be estimated. The matrix notation for Eqs (7) and (8) is: y = Xĭ T c + e
(9)
The framework was based on Penalized Signal Regression (PSR) with penalized Bsplines representing the regression coefficient (Marx and Eilers, 1999).
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However the choice of basis functions is an issue in FDA. Ideally basis functions should have some features matching those of the estimated functions. Considering the nonperiodic and broad bands combinational shape feature of NIR spectra, three mathematical basis functions considered were penalized B-spline with equally spaced knots, the B-spline with unequally spaced knots and wavelets. 2.3. Basis Functions and Fitting Methods 2.3.1. Penalized B-Spline Splines are the most common basis function for non-periodic curve approximation, as they can accommodate local features. The B-spline developed by de Boor is the most popular for constructing spline bases. Suppose that the spectrum x(λ ) is defined over a closed interval T = [λ0 , λn ] that is then divided into k+1 subintervals by k internal knots ( {ξ i }k : ξ1 , ξ 2 , ! , ξ k ), such that λ 0 < ξ1 < ξ 2 < " < ξ k < λ n . If the B-spline has a fixed degree d, it has continuous derivatives of degree up to d − 1 , and the total number of spline bases is k n = k + d + 2 . When using the B-spline as a smoother, the issue is how to choose the number and position of knots to avoid over or under fitting. Eilers and Marx (1996) proposed using a relatively large number of equi-spaced knots and a penalty on the finite differences of the coefficients of adjacent B-spline to avoid overfitting. This approach was termed the “P-spline”, penalized B-spline. The fitting criterion based on least squares using the penalized B-spline is given by: p
K
SMSSE ( x c) == ¦ [ x j − ¦ c k B j , K j =1
k =1
2 +1
( x j )] 2 + γ
K
¦ (Δm c k ) 2 k = m +1
(12)
where γ is a parameter for controlling the smoothness of the fit, Δm is the difference operator, which is defined as: Δ1c k = ck − c k −1
(13)
Δ2 c k = Δ1 (Δ1ck ) = Δ1 (c k − c k −1 ) = Δ1ck − Δ1ck −1 = c k − 2c k −1 + c k − 2
(14)
When using a P-spline, four parameters require to be chosen: spline degree d, knot number k, differences degree m and γ . 2.3.2. Free knots B-Spline This approach, based on a Bayesian approach, automatically identifies the optimal number and location of the internal knots. The fitting method adopted in this paper was proposed by Dimatteo, et al. (2001). First, a cubic B-spline is assumed. And a reversible-jump Markov chain Monte Carlo (MCMC) (Green. 1995) is implemented to change the knot number k and location ξ = (ξ1, ξ 2 ,!, ξ k ) . Finally, a posterior distribution of the knot number and location is achieved. 2.3.3. Wavelets The fundamental idea of wavelets is multiresolution analysis. The ‘mother wavelet’ ψ plays a primary role in wavelet analysis. Once a wavelet is chosen, a functional datum x (λ ) can be decomposed into different wavelet components
ψ jk (λ ) = 2 j / 2ψ (2 j λ − k ) , with the dilation and translation of the ‘mother wavelet’ forming a set of basis functions that capture features in the frequency and time domain.
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The wavelets considered are Daubechies wavelets and are classified in terms of the number of vanishing moments. The first and third Daubechies wavelets are considered Table 1. Prediction results Method PLS
Indirect Approach
P-spline with PLS
P-spline with limit numbers
Free knots B-spline with PLS
Daubechies wavelets(first)with PLS
Daubechies wavelets(third) with PLS
Direct Approach
PSR
Daubechies wavelets(first)
Daubechies wavelets(third)
Temp(ºC) 30 40 50 60 70 30 40 50 60 70 30 40 50 60 70 30 40 50 60 70 30 40 50 60 70 30 40 50 60 70 30 40 50 60 70 30 40 50 60 70 30 40 50 60 70
Ethanol RMSEP 0.014 0.013 0.038 0.016 0.018 0.016 0.009 0.030 0.013 0.014 0.004 0.007 0.011 0.009 0.014 0.015 0.018 0.048 0.020 0.026 0.016 0.013 0.037 0.018 0.022 0.018 0.011 0.022 0.017 0.021 0.006 0.009 0.016 0.015 0.027 0.003 0.014 0.019 0.014 0.016 0.005 0.013 0.015 0.012 0.016
Water RMSEP 0.012 0.006 0.008 0.008 0.008 0.011 0.007 0.008 0.008 0.005 0.003 0.003 0.008 0.006 0.005 0.009 0.004 0.008 0.008 0.005 0.014 0.007 0.008 0.009 0.005 0.014 0.004 0.008 0.008 0.005 0.004 0.003 0.008 0.006 0.006 0.004 0.006 0.010 0.005 0.008 0.004 0.006 0.010 0.005 0.008
2-propanol RMSEP 0.011 0.016 0.041 0.017 0.017 0.012 0.014 0.031 0.015 0.012 0.004 0.006 0.016 0.004 0.010 0.011 0.022 0.053 0.020 0.026 0.013 0.016 0.039 0.021 0.023 0.011 0.008 0.020 0.018 0.024 0.003 0.009 0.024 0.011 0.020 0.003 0.011 0.022 0.011 0.013 0.003 0.010 0.020 0.010 0.014
3. Case Study A NIR spectral data set is considered (Wülfert et al. (1998)). Spectra of mixtures of ethonal, water and 2-propanol are used to predict the mole fractions of these
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components. Measurements of 19 samples at five temperatures (30, 40, 50, 60 and 70 ºC) in the range, 580-1091nm, with 1nm resolution were recorded. Only the spectral region 850-1049 nm was considered in the analysis. The samples were divided into 13 training and 6 test samples as described in the paper (Wulfert et al. 1998). Features associated with the spectra included an apparent band shift and broadening which introduced nonlinearity into the relationship between the spectra and reference values. Mean centering was first applied. The root mean square error of prediction was used as the performance criteria to evaluate the predictive ability of the different models.
4. Results and Discussion In this section, the results of applying different functional linear regression approaches are considered which are benchmarked against PLS. The indirect approach with Pspline, free knots B-spline, and wavelets and the direct approach with P-spline, and wavelets were applied to the data. The prediction results are given in Table 1. It can be observed that the performance of PLS and the functional linear methods, especially the indirect methods with PLS being used for defining the relationship between the response and fitting coefficients, are comparable. Using a basis functions to fit the data, i.e. performing a transformation on the original data, variations within the original data will be transferred to the variation between the fitting coefficients. If a complete mathematical basis functions (i.e. wavelets) is used, the variation will be nearly totally transferred, which is the reason that PLS and functional linear methods with wavelets achieve similar prediction results. The B-spline is not a complete bases hence greater fitting errors may be introduced to the variations of the fitting coefficients resulting occasionally in a large prediction bias.
5. Conclusions The prediction performance of PLS and functional linear regression methods is comparable except for the indirect method when a hard constraint is placed on the number of P-spline. For the data set studied it outperforms all other methods. The rationale for this needs further investigation. Both approaches can be described within a common framework as the loadings of PLS can be considered as data-based basis function. Future work is on-going on how to choose basis functions.
Acknowledgements CJ acknowledges the financial support of the Dorothy Hodgkin Postgraduate Awards.
References I. Dimatteo, C.R. Genovese and R.E. Kass, 2001, Bayesian curve-fitting with free-knot splines. Biometrica, 88(4), 1055-1071. P.J. Green, 1995, Reversible jump Markov Chain Monte Carlo computation and Bayesian model determination. Biometrica, 82(4), 711-732. B.D. Marx and P.H. Eilers, 1996, Flexible smoothing with B-splines and penalties (with comments and rejoinder). Statistical Science, 11(2): 89-121 B.D. Marx and P.H. Eilers, 1999, Generalized linear regression on sampled signals and curves: A P-spline approach, Technometrics, 41, 1-13. J.O. Ramsay and C.J. Dalzell, 1991, Some tools for functional data analysis, Journal of the Royal Statistical Society, Series B, 53, 539-572 F. Wülfert, W.T. Kok and A.K. Smilde, 1998, Influence of temperature on vibrational spectra and consequences for the predictive ability of multivariate models. Anal Chem.,70, 1761-1767.
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Application of Global Sensitivity Analysis to Biological Models Alexandros Kiparissidesa, Maria Rodriguez-Fernandeza, Sergei Kucherenkoa, Athanasios Mantalarisa, Efstratios Pistikopoulosa a
Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College, London SW7 2AZ
Abstract The ever increasing knowledge and understanding of biological systems necessitates the development and implementation of even more sophisticated and complex mathematical models. An important and necessary step in the process of model validation is analysis of the model parameters, which can identify the parameters that significantly affect the model output. Several methods for parameter sensitivity analysis exist, including global sensitivity analysis (GSA). Herein, various methods for GSA are briefly discussed and a computational comparison between the established Sobol’ indices and a novel derivative based global sensitivity measures is performed on a model describing the growth kinetics of mammalian cell culture systems. Keywords: global sensitivity analysis, Sobol’ indices, derivative based global sensitivity measures
1. Introduction An inherent problem with the development of high fidelity models, especially ones representing complex biological systems, is the increase in the number of parameters. Furthermore, as current analytical techniques in cell biology do not allow the measurement of all parameters, experimental estimation of an extensive number of parameters often is an infeasible task (Sidoli et al. 2005). Previous research in the field of mathematical modelling of biological systems has shown that statistical tools such as GSA can provide a guideline towards optimal experimental design, minimising cost and experimental labour (Kontoravdi et al. 2005, Rodriguez-Fernandez et al. 2007). GSA offers a comprehensive approach to model analysis (Saltelli 2000). Unlike local sensitivity analysis, GSA methods evaluate the effect of a factor while all other factors are varied simultaneously, thus accounting for interactions between variables without depending on the stipulation of a nominal point. Furthermore GSA allows the exploration of the space of possible alternative model assumptions and structure on the prediction of the model, thereby testing both the quality of the model and the robustness of the model based inference. The performance of GSA methods has, up to now, been tested on test functions with known analytical solutions and a limited number of parameters. Herein, we present for the first time an overview of the performance of GSA methods, deemed to be suitable for use in complex ODE or PDE models containing nonlinerities and coupled terms, such as biological or reaction network models. We examine a simple biological model consisting of 6
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differential equations and 16 model parameters. The measured sensitivity for the model parameters is dependant on the variable chosen to be the output variable. 2. Global Sensitivity Analysis The term global is used to characterise methods that posses two basic properties (Salteli 2000): (i) all parameters are varied simultaneously and (ii) sensitivity is measured over the entire range of each input factor. When dealing with a nonlinear model and input factors that are affected by uncertainties of varying magnitude, a global sensitivity approach is the more suitable option. The most widely used methods in GSA are, FAST and extended FAST, the Sobol’ indices and the Morris method and its adaptations. A method developed in 1991 by Morris, classified as a screening method provides a fast and computationally cheap method to rank parameters. Although this method is regarded as global, it is based on the computation of local measures (Saltelli 2000). The method covers the whole space in which the parameters may vary, hence the term global. The ranking is based solely on the main effect each factor has on the output variance. By averaging the local measures over a range of points an estimate of the importance of each factor is gained. The novel derivative based global sensitivity measures (DGSM), developed by Kucherenko et. al.(2007) is a method conceptually based on the Morris method, and is capable of providing information on the total effect for each parameter while maintaining the low computational cost. The basic concept of FAST is the decomposition of the total output variance of the model to summands of increasing dimensionality. In order to acquire these summands, the properties of a Furrier series transformation are utilised. The initial method only provided first order information ignoring any possible influence through parameter interactions. Even though the computation of the total indices using FAST was proposed by Saltelli and Bolado (1998), extended FAST still lacks the accuracy and transparency of the Sobol’ method. The method of global sensitivity indices developed by Sobol’ (2001) is based on an ANOVA type of a high dimensional model representation. It is superior to other SA methods, such as those based on correlation or regression coefficients because it is model-independent. In particular it works for nonlinear and non-additive models. Furthermore it allows the calculation of the total sensitivity indices, which measure the total contribution of a single input factor. The Sobol’ method is superior to the original FAST in that the computation of the higher interaction terms is well defined and easy to interpret. In the past, the Morris method was regarded as inferior to the Sobol’ and FAST methods due to the small amount of information it provided. The DGSM method is believed to yield valuable information since it can both provide the order of significance with respect to the output variance of various parameters as well as capture the relative difference in importance between two parameters. Consequently, a comparison between the Sobol’ global indices and the novel DGSM was examined and the quality of information obtained was compared in
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terms of ranking of parameters, required computational time and ease of implementation. 2.1. Global Sensitivity Methods used A detailed description of the Sobol’ method for GSA is provided by Saltelli (2000) and Sobol’ (2001). Considering a differentiable function f(x), where x = {xi} is a vector of input variables defined within the unit hypercube In. Local sensitivity measures are based on partial derivatives and are of the form: Ei ( x*) =
f ( x i + Δ ) − f ( xi ) ∂f = Δ ∂xi
(1)
Sensitivity measure Ei(x*) depends on a nominal point x * and its value varies according to the value of x * . This deficiency can be overcome by averaging Ei(x*) over the parameter space In. Such a measure can be defined as:
M i = ³ Ei dx
(2)
In
Non-monotonic functions consist of regions with both positive and negative values of partial derivatives Ei(x*), hence due to the effect of averaging, values of M i can be very small or even zero. To avoid such situations measures based on the absolute value of |Ei(x*)| can be used: Another informative measure to consider is the variance of M i which can be estimated by:
Σ i2 = ³ n Ei2 dx − M i2 I
By combining the presented measures a new measure can be derived: Gi = Σi2 + M i2 = ³ n Ei2 dx I
(3) (4)
A normalised version of the new measure can be defined as: s
n
i =1
i =1
G = ¦ Gi / ¦ Gi ,
(5)
Where 1 s n. The G measure can account for the fractional significance of a particular parameter with respect to the total variance, or for a group of parameters with respect to the total variance. Calculation of DGSM is based on the evaluation of integrals (2)-(5), which can be presented in the following generic form: I [ f ] = ³ n f ( x)dx
(6)
I
Monte Carlo algorithm can be used for the evaluation of integrals of the general form (6). The convergence rate of MC does not depend on the number of variables n although it is rather low. A higher rate of convergence can be obtained by using deterministic uniformly distributed sequences also known as low-discrepancy sequences instead of pseudo-random numbers. Methods based on the usage of such sequences are known as QMC methods. The QMC method
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with Sobol' LDS sequences was used in the present work because of its high efficiency (Kucherenko et al. 2007). 1 N (7) I N = ¦ f (qi ). N i =1 The total number of function evaluations required for the calculation of a full set of {M i } and {Σi } is NF = N (n +1). 3. Results and Discussion The investigation of the performance of the two proposed methods for GSA was performed on a model consisting of 6 ODEs and 16 model parameters, based on the model of Jang and Barford (2000) and adapted by Kontoravdi et al. (2005). The model under consideration was initially developed for antibody producing hybridoma cell lines, but with proper adaptation can be used for other mammalian cell lines. The model operates under the assumption of perfect mixing of the cell culture. It also assumes that only two of the key nutrients namely, glucose and glutamine, are considered as growth limiting factors, while their products, lactate and ammonia respectively, are the only inhibitors. The model utilises Michaelis-Menten type kinetics to describe the rate of nutrient uptake and product formation. In the present study the model was operated under batch conditions. All simulations were performed on an Intel Pentium® (D) (CPU 2.80GHz, 2.79GHz) personal computer with 1 Gigabyte of R.A.M. memory. Both the model and the sensitivity analysis were implemented with the use of Matlab® mathematical suite. A stiff stable ODE solver was utilised to perform the necessary model evaluations, namely routine ode15s. The simulations involved the scanning of all model parameters with respect to each of the six possible model output variables. Sensitivity Analysis was performed at 10 hour intervals from the beginning of the culture, until the termination of the culture. Batch processes that involve the secretion of biologically active molecules usually are not left to proceed until completion. Due to the accumulation of toxic products within the bioreactor which threaten to degrade valuable end products and render them biologically inactive, it is common practice for the batch culture to be terminated when the cell viability falls below 50% of the total cell concentration. For the current model, this is observed to occur at 150 h after the initialisation of the culture. Parameters were varied by ± 50% of their nominal value. A meaningful comparison that highlights difference between the two methods, is computational time. While the DGSM method required 2.7e4 sec of computational time, the calculation of the Sobol’ global sensitivity indices required 6.3e5 sec. More importantly when examining the results these methods yield, it was observed that the DGSM performs in a quite similar way as the Sobol’ method. In Figures 1-6, the sensitivity indices for all 16 parameters are presented for 3 time points and 2 possible output variables. The time points were chosen to represent the important phases of a batch cell culture process. The first of the chosen time points corresponds to the initiation of the growth
Application of Global Sensitivity Analysis to Biological Models
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phase, which occurs subsequently to the lag phase, around 20 h into the culture. The second time point is at the end of the exponential growth phase, where the concentration of viable cells obtains its maximal value, and the last time point is in the middle of the death phase towards the end of the culture.
Figures 1-6: Calculated sensitivity indices for various time points and two different output variables; F1-F3: Sensitivity indices for viable cell concentration at time points 20h, 50h and 100h. F4-F6: Sensitivity indices for glucose concentration at time points 20h, 50h and 100h. Model parameters: 1:ȝmax ; 2:kglc ; 3:kgln ; 4:KIlac ; 5:KIamm ; 6:ȝd,max ; 7:kd,gln ; 8:kd,amm ; 9:Ylac,glc ; 10:n ; 11:mglc ; 12:Yx,gln ; 13:Yx,glc ; 14:Yamm,gln ; 15:a1 ; 16:a2.
Both methods are in good agreement in the top ranking parameters, not only in terms of identification but also in terms of relative significance towards the less important parameters. Differences do occur in the ranking of the least significant parameters; however this is insignificant since the indices for these parameters are rather small. As the culture exits the growth phase and enters the death phase, the most significant parameters are bound to change, as different
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mechanisms govern the culture. This transition is successfully captured by both methods. Overall both methods yield the same results; hence the DGSM method appears to be more advantageous due to its significantly lower computational requirements. However it is noteworthy mentioning that the choice of ǻ needs to be made with caution and is problem dependant. In fact, for the current problem, a ǻ value of 10-5 was used for the calculation of the indices with respect to glucose concentration, while for the viable cell concentration the value used was 10-3. It is obvious that the resulting indices depend on the choice of ǻ, which should be looked into before performing the actual analysis. 4. Conclusions The DGSM method appears to be a more desirable method for GSA of biological models, especially complex ones, since it combines the quality of information provided by the established Sobol’ indices with far lower computational requirements. Since the presented difference in computational time was for a minimal biological model the advantage in computational time could prove critical when analysing very complex models. It is imperative, that a comparison of the performance of the two methods in larger scale models, such as the model presented in the work of Kontoravdi et al.(2004) is performed, as well as an investigation for a consistent choice of the value of ǻ. Acknowledgements Alexandros Kiparissides would like to gratefully acknowledge financial support from the PROBACTYS E.U. project. S.Kucherenko and M. Rodriguez-Fernandez would like to acknowledge the financial support by the EPSRC grant EP/D506743/1. References J.D. Jang, J.P. Barford, 2000, An unstructured Kinetic Model of Macromolecular metabolism in batch and fed-batch cultures of hybridoma cells producing monoclonal antibody, Biochem. Eng. J., 4, 153-168. C. Kontoravdi, S.P. Asprey, E.N. Pistikopoulos and A. Mantalaris, 2004, Development of a dynamic model of monoclonal antibody production and glycosylation for product quality monitoring, Comp. and Chem. Eng., 31, 392-400. C. Kontoravdi, S.P. Asprey, E.N. Pistikopoulos and A. Mantalaris, 2005, Application of Global Sensitivity Analysis to determine goals for design of experiments: An example study on Antibody-Producing cell cultures, Biothechnol. Prog., 21, 1128-1135. S. Kucherenko, M. Rodriguez-Fernandez, C. Pantelides, N. Shah, 2007, Monte Carlo evaluation of Derivative based Global Sensitivity Indices, submitted to Reliab, Eng. Syst. Safety, 2007 M. Rodriguez-Fernandez, S. Kucherenko, C. Pantelides, N. Shah, 2007, Optimal experimental design based on global sensitivity analysis. Computer-Aided Chemical Engineering, vol.24 Proceedings European Symposium on Computer Aided Process Engineering, (ESCAPE17, 2007), 63. A. Saltelli, K. Chan, E.M. Scott, 2000, Sensitivity Analysis, Wiley Press. Saltelli A., Bolado R.,1998, An alternative way to compute Fourier amplitude sensitivity test (FAST), Computational Statistics & Data Analysis 26 , 445-460. Sidoli F.R., Mantalaris A., Asprey S.P.,2005, Toward Global Parametric Estimability of a LargeScale Kinetic Single-Cell Model for Mammalian Cell Culture, Ind. Eng. Chem. Res., 44 (4), 868 -878. I. Sobol’, 2001, Global Sensitivity Indices for nonlinear mathematical models and their Monte Carlo estimates, Math. and Comp. in Sim., 47, 103-112.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) . © 2008 Elsevier B.V. All rights reserved.
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Development of a sophisticated framework for complex single- and multi-objective optimization tasks Matthias Leipold,a Sven Gruetzmann,a Georg Fieg,a Dietrich Maschmeyer,b Jörg Sauer,c Holger Wiederholdc a
Hamburg University of Technology, Schwarzenbergstr. 95, 21073 Hamburg, Germany Evonik Oxeno GmbH, Paul-Baumann-Straße 1, 45772 Marl, Germany c Evonik Degussa GmbH, Paul-Baumann-Straße 1, 45772 Marl, Germany b
Abstract This work introduces a general framework for the global optimization of arbitrary single- and multi-objective optimization tasks. The framework covers the industrial demand on a user-friendly toolkit uniting arbitrary optimizations in one graphical user interface. The framework includes a stand-alone solver communicating over a free programmable interface with one or multiple instances of any simulation tool. The functionality of the framework is shown by two highly differing case studies. The first concerns the determination of intrinsic kinetics, carried out at our industrial partners the Evonik Degussa GmbH and Evonik Oxeno GmbH. The second addresses the multiobjective mixed-integer dynamic optimization of a middle vessel batch distillation including the startup. In both case studies the high flexibility of the framework, its easy setup and its robust optimization capabilities will be shown. Keywords: robust optimization, evolutionary algorithm, industrial application, intrinsic kinetics, middle vessel batch distillation.
1. Introduction In the last decade optimization tasks have become a crucial technology in industry. They are one of the main challenges in chemical and process engineering today since they bear an important part to save competitiveness of industrial companies [1]. Optimizations are important in all stages of product and plant life cycles. That means on the one hand regularly occurring optimization tasks e.g. concerning data regression for reaction kinetics, pressure loss correlations or thermodynamic properties like vapor pressure curves. On the other hand there arise extensive optimization problems concerning the modeling and design of whole processes. All these tasks imply complex optimizations including non-linearity, mixed integer problems, dynamic optimizations, structural complexities, boundary conditions or multiple objective functions. In general there are solution methods available for all kinds of optimization problems. These were mainly developed for academic purposes. Today many common engineering programs utilize these developments with user-friendly graphical user interfaces (GUI). However, integrated solution methods often are limited to few optimization tasks with a fixed structure. They lack the possibility to freely setup more complex jobs. By contrast there are comprehensive mathematical toolkits available offering a great freedom to setup models and optimization tasks. Anyway, these programs usually are missing a user-friendly GUI.
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The objective of this contribution is to provide a sophisticated framework for all kinds of single- and multi-objective optimization tasks including an easy to use GUI and usage of arbitrary simulation toolkits.
2. Optimization framework The framework consists of four major elements as shown in Figure 1. The first one covers an evolutionary algorithm (EA) as solver that is provided in a single-objective and a multi-objective implementation. As second element an arbitrary simulation tool with the possibility of remote access is applied. The third element comprises a suitable communication interface for the formulated problem. Finally the fourth element is a GUI covering all other parts in an optimization. graphical user interface
solverapplication (evolutionary algorithm)
communicationinterface
simulation tool
Figure 1: Communication structure of the optimization framework
2.1. Solver algorithm For the solver algorithm an evolutionary algorithm (EA) was chosen. This is for two reasons. First and most important, an EA is not specialized on any kind of problem (e.g. NLP, MINLP or MIDO) [2]. Furthermore, it can perform global optimizations while it is independent of initial values [2]. For single-objective optimizations the Modified Differential Evolution (MDE) algorithm by Angira and Babu is applied and for multiobjective optimizations the non-constrain-dominated sorting MDE presented by Gruetzmann et al. was chosen [3-5]. Besides the EA other more specialized and thus faster solvers can be implemented. Main restriction is that the only information available about the used simulation are input and output values. Accordingly the mathematics of the optimization is fully unknown to the solver. The chosen EA as a general solver is implemented in Visual Basic for Applications (VBA) with the GUI realized in MS Excel. This platform was chosen for two reasons. First, MS Excel is a well known and accepted standard in industry and research. Moreover, most commercial and free simulation tools available comprise communication protocols to VBA or MS Excel. 2.2. Simulation tool Within the framework any simulation tool can be applied. Although it is part of the framework, it is independent of the solver and the frameworks GUI to maintain a standardized working flow within the tool. Precondition for the usage of a software as “simulation tool” in the sense of the framework is a suitable remote access. The given minimum requirements are that at least the necessary input parameters may be changed externally (e.g. by manipulation of a project file), a simulation can be automatically
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started and run without any user input (e.g. run by a shell command) and the solution parameters can be read from the finished simulation (e.g. read from an output file). 2.3. Interface The communication interface is the main part of the framework. It establishes the high flexibility for the setup of simulations since any required external program call supported by the simulation tool is executable. There are no restrictions concerning the type of variables. Even parameters changing the simulation structure are possible. The communication interface, like the solver-algorithm, is implemented in VBA. It is completely freely programmable. This assembly offers a wide range of possibilities. Besides optimizations of a single process it is quite easy to set up more complex scenarios. For example the sequential usage of different simulation programs is imaginable to combine separately developed process elements in a plant wide optimization. Another example is the simultaneous optimization of more then one simulation dependent on the same input parameters as shown in case study one. To fulfill the request of a user-friendly GUI it is possible to build graphical communication interfaces for different programs without the loss of flexibility. For the industrial standard process engineering programs Aspen Plus and Aspen Custom Modeler suitable graphical communication interfaces were developed and can be used for a fast and easy setup of optimizations. For usage of the chemical engineering program Presto Kinetics a similar interface was set up.
3. Case studies – examples of successful application The optimization framework has already been successfully applied to multiple optimization tasks. In this contribution two of them will be presented. First is a singleobjective optimization from our industrial partners (Evonik Degussa GmbH and Evonik Oxeno GmbH) for the determination of complex intrinsic kinetics. The second one concerns a multi-objective optimization of a multi-vessel batch distillation. 3.1. Determination of intrinsic kinetics The first case study considers a single-objective non-linear global optimization for the determination of complex intrinsic oligomerization and isomerization kinetics based on a multitude of measurements at different process parameters. It was performed in a survey of our industrial partners the Evonik Degussa GmbH and Evonik Oxeno GmbH. For simulations a steady-state model realized in Presto Kinetics was applied. Next to the actual intrinsic kinetics it incorporates the description of several physicochemical mechanisms as for example catalyst activity, inhibition or different reaction pathways. The optimization task was set up using a least square formulation as objective function, validating the model versus measurements. In one run measurements of up to ten different operating conditions varying in temperature, pressure, reactant concentration and the properties of the catalyst fixed-bed were optimized simultaneously. The objective function is directly dependent on the measured (wM,i) and calculated (wi) mass fractions. Whereas, the calculated mass fractions are dependent on activation energy, pre-exponential factor, inhibition constants, distribution constants etc. which will be summarized in the mathematical formulations by x . Additionally the set up task is
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constrained by boundary conditions g , the reaction model, and h , parameter boundaries, to a priori exclude physicochemical improper model parameterizations. The optimization problem can be formulated as follows: Min :
F x
¦ «¦ > w ª
n
¬
i
M ,i
@
2 º wi x » ¼
(1)
subject to:
g x 0
(2)
h x ! 0
(3)
where n is the number of simultaneously optimized operation conditions and i the number of measured data points at each operation condition. For the optimization task a communication interface was set up. It is based on an application object provided by Presto Kinetics offering routines to read and write parameters and to run the model. To automatically assign the measured data to Presto Kinetics, the communication interface includes routines to create the required data files for the model. Additionally the capability for the sequential run of a predefined number of simulations was implemented. The result of the optimization is a set of model parameters independent of the process conditions. With these parameters a multitude of measured data can be described reliably. In Figure 2 an example of measured data and the appropriate calculated profiles along the fixed bed length is shown. It can be seen that the optimization setup in the framework is well capable of finding a sufficient set of model parameters, incorporating the boundary condition of a physicochemical acceptable model. 0,45
0,14 reactant B, isomer 1
0,35 0,30 0,25 0,20
reactant B, isomer 2
0,15 0,10
0,10 0,08 0,06
product B 0,04
product C
0,02
reactant A
0,05
product A
0,12
mass fraction w [kg/kg]
mass fraction w [kg/kg]
0,40
0,00
0,00 0,00
0,25 0,50 0,75 normalized reactor length z’ [z/L]
1,00
0,00
0,25 0,50 0,75 normalized reactor length z’ [z/L]
Figure 2: Reactant and product mass fraction profiles along the fixed-bed. measured data point: X; calculated profile: —
1,00
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3.2. Design and control of multivessel batch distillation The second case study discusses the multi-objective mixed-integer dynamic optimization of a middle vessel batch distillation column. For that purpose a rigorous process model in Aspen Custom Modeler by Gruetzmann and Fieg considering the start-up phase of the process was used [6]. The objective was to perform an optimization of investment (IC) and operation costs (OC) for an investment decision. To overcome the problem of an a priori decision for the tradeoff between IC and OC a multi-objective optimization was performed. Whereas, OC is a function of time dependent operation parameters uO while IC is a function of design parameters u D . The simulation is additionally constrained by a given demand of purity. A mathematical formulation of the optimization task can be written as follows:
Min :
f1 uO , t IC
OC
f2 uD
(4)
subject to:
g x, x, t , u D , u O
wi t wmin h wi
¦ 'w
i, j
0
(5)
i 1,2,3
(6)
t0
i 1,2,3 j 1,...N 't
(7)
i 1
where g is the dynamic process-model, x and x are the time dependent and independent state variables and w is the mass fraction of a component.
status information
For the optimization a communication interface based on the Aspen Custom Modeler application object was implemented. The interface incorporates reading and writing of parameters, remote control for running the simulations including full error handling and routines for the manipulation of the simulation structure (e.g. creation of additional internal tasks). An interaction structure of the framework including the Aspen custom Modeler communication interface is given in Figure 3. graphical user interface start initialization optimization by genetic operators
input to ACM run simulation
problem initialization
error handling
simulation
output from ACM
end of simulation
communication interface
simulation program: Aspen Custom Modeler
end solver: ncsMDE
Figure 3: Interaction structure of the optimization framework including ncsMDE-Aspen Custom Modeler communication interface
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In the case study an industrial scale distillation column for the separation of a mixture of 400 kg each of hexanol, octanol and decanol subject of product purity of at least 99 % was performed. In order to assure a reasonable vapor load, the reboiler duties has been set to 200 kW. Illustrated in Figure 4 are the pareto-optimal solutions, that are the best tradeoffs between OC and IC. Shown is generation 2163 this is when the optimization was aborted since no further improvements could be achieved. Also shown are second best (2. Front) and third best (3. Front) tradeoff solutions along with a front of reference points calculated using a temperature control. In the second diagram of Figure 4 the solver efficiency is shown by means of mean violation of constraints. Started at high constraint violations due to the randomly chosen initial values, constraint violation is rapidly decreasing. This once again shows the effectiveness of the solver and the framework. 168750 165000
IC [€/a]
161250 Reference
157500 153750 150000 146250 20500
0,30 mean violation of constraints
Generation 2163 pareto optimal front 2. Front 3. Front
0,25 0,20 0,15 0,10 0,05 0,00
21000
21500 OC [€/a]
22000
22500
0
200
400
600 800 []Generation[]
1000
1200
Figure 4: pareto-optimal solutions of case study two and efficiency of optimization
4. Summary and Conclusions In this contribution, for the first time, a sophisticated framework incorporating a userfriendly graphical user interface combined with a robust solver for arbitrary optimization tasks has been presented. In two highly differing case studies the efficiency of the framework could be shown. The framework or more precisely the communication interface was easily adapted for different programs and various structural setups. The used evolutionary algorithm was shown to reliably solve singleand multi-objective optimization tasks including mixed integer non-linear tasks as well as mixed integer dynamic optimizations. The presented framework is a reliable and easy to handle tool for the application on further optimization tasks.
References [1] L.T. Biegler and I.E. Grossmann, Comp. Chem. Eng., 28 (2004) 1169 [2] K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms, Wiley, Chichester, 2004 [3] R. Angira and B.V. Babu, Proc. IICAI-07, (2005) 911 [4] S. Gruetzmann, M. Leipold, G. Fieg, Proc. ESCAPE17, (2007) [5] M. Leipold, S. Gruetzmann, G. Fieg, Comp. Chem. Eng., (2007) (submitted) [6] S. Gruetzmann and G. Fieg, Ind. Eng. Chem. Res., (2007) (accepted)
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Towards Resilient Supply Chains: Uncertainty Analysis Using Fuzzy Mathematical Programming Kishalay Mitra,a Ravindra D. Gudi,b Sachin C. Patwardhan,b Gautam Sardara a
Engineering and Industrial Services, Tata Consultancy Services Limited, 1, Mangaldas Road, Pune 411001, Maharashtra, INDIA b Indian Institute of Technology, Bombay, Powai, Mumbai 400076,Maharashtra, INDIA
Abstract A multi-site, multi-product supply chain planning problem under demand as well as machine uptime uncertainty has been analyzed in multi-objective Pareto sense in this paper using the fuzzy mathematical programming approach. Fuzzy programming not only keeps the problem size in control which is the prime lacuna of the conventional two stage scenario based stochastic programming approach but also free from any assumption regarding the nature of the distribution of the uncertain parameters. It is seen that the fuzzy approach is generic, relatively simple to use, and can be adapted for bigger size planning problems of industrial scale. We demonstrate the proposed approach on a relatively moderate size planning problem taken from the work of McDonald and Karimi (1997) and discuss various aspects of uncertainty in context of this problem. Keywords: Supply Chain Optimization, Uncertainty, Programming, Multi-objective Optimization, Pareto.
Fuzzy
Mathematical
1. Introduction In the recent era of global economy, competitive pressures force big enterprises to maintain their supply chain spread across the globe where the enterprise having more responsive supply chain network, not the mere size of the network, performs better in meeting customer satisfaction. Planning and thereby leveraging the best out of a supply chain, therefore, is the primary focus of most of the enterprises. Effective coordination and integration of the key business activities undertaken by an enterprise, starting from the procurement of raw materials to the distribution of the final products to the customers is the key in a supply chain network (Shapiro, 2001). Most of the supply chain models assume parameters (cost components etc.) as well as various predictions (demands etc.) are accurately known and hence the models available in commercial enterprise software are deterministic in nature. But in real life situations, the enterprises have to face the volatile market conditions where one has to meet customer satisfaction under changing market conditions. Under these conditions, it is more realistic to consider the effect of uncertainties on supply chain planning and thereby minimize their impact on the final supply chain performance. In this work, we, therefore, present a multi-objective supply chain planning framework under demand as well as machine uptime uncertainty using fuzzy mathematical programming which is one of the three popular methods (two stage stochastic and chance constraint programming being the other two) of handling uncertainty in systems engineering literature (Birge and
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Louveaux, 1994; Sahinidis, 2004). One of the most important merits of fuzzy mathematical programming over other existing approaches is related to the fact that it does not require the knowledge of distributions associated with the uncertain parameters. The second important advantage that fuzzy programming has is related to keeping the problem size small and tractable in the presence of an increase in the number of uncertain parameters (unlike two stage stochastic programming) enabling the fuzzy approach to handle large scale industrial problems without any further modification in the solution techniques. In view of these merits, in this paper, the uncertainty issues associated with a multi-site, multi-product supply chain mid term planning problem, has been analyzed in detail using the fuzzy mathematical programming approach taking the mid term planning model of McDonald and Karimi (1997) as the basis of this work.
2. Adaptation of Deterministic Planning Model Under Fuzzy Framework As opposed to other methods, fuzzy programming considers uncertain parameters as fuzzy numbers and the constraints associated with those uncertain parameters as fuzzy sets. A degree of satisfaction of a constraint is defined as the normalized membership function (0≤Ȝ≤1) of the constraint where the uncertain parameter is allowed to vary within a given range (prefixed by Δ with the uncertain parameter) and the value of this membership function signifies the extent of constraint violation (Ȝ = 0 being the complete violation and Ȝ =1 being no violation, other values of λ linearly varying between 0 and 1). In this way, some amount of constraint violation is allowed. Finally we write the λ optimization problem of Bellman and Zadeh (1970) that attempts to maximize the satisfactions of the constraints including the objective function. The final midterm planning model of McDonald and Karimi (1997) when adapted under fuzzy framework, can be described as follows:
λ
Max
0 ≤ λ ≤1, Pi , j , s , t , RL i , j , s , t ,C i , s , t ,Si , s , c , t , I i , s , t , I i−, c , t ,σ i , s , s ′ , t , I iΔ, s , t , Yf , j , s , t
Pi , j,s,t = R i , j,s ,t RLi , j,s,t RL f , j,s , t =
¦ RL
(1)
∀i ∈ I \ I RM
(2) (3)
i , j,s , t
i∈Φ i , f
C i ,s , t =
¦β ¦ P
i′ ,i ,s i′ ∋ β i ′ , i , s ≠ 0
∀i ∈ I \ I FP
i′, j,s , t
(4)
j
C i ,s , t = ¦ σ i ,s ′ ,s , t
∀i ∈ I IP
(5)
s′
Ii,s,t = Ii,s,t−1 + ¦Pi, j,s,t − ¦σi,s′,s,t − ¦Si,s,ct∀i ∈I \ IRM
(6)
I iΔ,s , t ≥ I iL,s ,t − I i ,s, t
(7)
j
s′
c
∀i ∈ I FP
Towards Resilient Supply Chains: Uncertainty Analysis Using Fuzzy Mathematical Programming
703
RL f , j,s , t − MRL f , j,s , t Yf , j,s , t ≥ 0
(8)
I iΔ,s , t ≤ I iL,s , t
(9)
¦ RL
i , j,s , t
− H j,s ,t ≤ 0
(10a)
i
ª§ º · «¨ ¦ RL i , j,s , t − (H j,s , t − ΔH j,s , t )¸ ΔH j,s , t » + λ − 1 ≤ 0 ¹ ¬© i ¼
(10b)
¦ RL f , j,s , t − H j,s , t ≤ 0
(11a)
ª§ º · «¨ ¦ RL f , j,s , t − (H j,s , t − ΔH j,s , t )¸ ΔH j,s , t » + λ − 1 ≤ 0 ¹ ¬© f ¼
(11b)
f
ª§ − º ½ · − «®¨ I i ,c,t − I i ,c, t −1 + ¦ Si ,s,c,t ¸ − (d i ,c,t + Δd i ,c,t )¾ Δd i ,c, t » − λ + 1 ≥ 0 s ¹ ¿ ¬«¯© ¼» ª§ · «¨¨ ¦ S i ,s ,c , t ′ − ¦ d i ,c, t ′ ¸¸ t ′≤ t «¬© s , t ′≤ t ¹
¦ Δd t ′≤ t
i ,c, t ′
º » + λ −1≤ 0 »¼
Pi , j,s , t ≤ R i , j,s , t H j,s , t
[{P
i, j,s,t
]
−Ri, j,s,t (Hj,s,t −ΔHj,s,t )} Ri, j,s,tΔHj,s,t +λ−1≤0
i , j,s , t
(14b) (15a)
]
− (H j,s, t − ΔH j,s, t )} ΔH j,s , t + λ − 1 ≤ 0
(15b)
RL f , j,s , t − H j,s , t Yf , j,s , t ≤ 0
[{RL
f , j, s , t
(16a)
]
− (H j,s , t − ΔH j,s , t )Yf , j,s , t } ΔH j,s , t Yf , j,s , t + λ − 1 ≤ 0
ª ½ «®S i ,s ,c, t − ¦ d i ,c , t ′ ¾ t ′≤ t ¿ ¬¯ ª§ − · «¨ I i , c, t − ¦ d i ,c , t ′ ¸ t ′≤ t ¹ ¬©
¦ Δd t ′≤ t
i,c , t ′
¦ Δd
i ,c, t ′
[(cos t − cos t ) (cos t
max
min
t ′≤ t
(13b)
(14a)
RL i , j,s , t − H j,s , t ≤ 0
[{RL
(12b)
º » + λ −1 ≤ 0 ¼
(16b) (17b)
(18b)
º » + λ −1 ≤ 0 ¼
)]
− cos t min + λ − 1 ≤ 0
(19)
704
Where
K. Mitra et al.
Cost= ¦FCf , j,s,t Yf , j,s,t + ¦νi, j,s Pi, j,s,t + ¦pi,s Ci,s,t + ¦hi,s,t Ii,s,t + f , j,s,t
i, j,s,t
i,s,t
i,s,t
¦t s,cSi,s,c,t + ¦t s,s′σi,s,s′,t + ¦ζi,s IiΔ,s,t + ¦μi,cIi−,c,t
i,s,c,t
i,s,s′,t
i,s,t
i,c,t
Pi , j,s ,t , RL i , j,s, t , RL f , j,s , t , C i , s , t , S i ,s , c , t , I i,s, t , I i−,c , t , σ i ,s ,s′, t , I iΔ,s ,t 0, Yf , j,s,t ∈{0,1}
(20)
where Pi , j,s ,t , RL i , j,s , t , RL f , j,s , t , C i , s , t , S i ,s , c , t , I i,s, t , I i−,c , t , σ i ,s ,s′, t , I iΔ,s ,t represents the production, run length for each product, run length for each product family, consumption, supply to the market, inventory at production site, missing demand at market, intermediate product, inventory below safety level for product i or family f of several products to be produced at facility j at site s or customer c or market m at time period t respectively. Here Yf , j,s , t represents the binary variable to decide a product family f to be produced at machine j, site s and time period t or not. Few other important parameters are demand (di,c,t), machine uptime (Hj,s,t), minimum run length for the product family f (MRLf,j,,s,t), Safety stock target for product ( I iL,s , t ), effective rate of production (Rijst) whereas various unit cost parameters are inventory holding cost (hist), revenue (μic), raw material price (pis), penalty for dipping below safety level (ζis), fixed production cost (FCf,j,s,t) and variable production cost(νijs) and transportation costs (tss′, tsc). Based on whether the product or product family is chosen with or without fixed associated cost, the final planning model formulation would be a LP / MILP / MINLP. Observing an inherent trade off, we can generate the multi-objective Pareto optimal points for the above formulation using overall planning cost, margin / variation allowed for uncertain parameters and demand satisfaction as different trade-off criteria.
3. Results and Discussion The motivating example considered here is taken from the first case study of McDonald and Karimi (1997). There are two production locations (S1 and S2) having one unit in each and each production unit has a single raw material supplier. Production units S1 and S2 are connected to market M1 and M2 respectively putting demands for 34 products. Unit S1 and S2 manufacture products P1 - P23 and P24 - P34 respectively. Products at S2 are produced from a set of intermediate products produced at S1 e.g. product P24 is produced from product P1, product P25 is produced from product P4 and so on (see McDonald and Karimi, 1997). There are eleven product families F1 – F11 that are composed by clubbing the products at site S1 e.g. products P1, P2, P3 form product family F1 and so on (see McDonald and Karimi, 1997). Market M1 has customers who have demands for products P1-P23 and market M2 has customers having demands for products P24-P34. The demand values for all 34 products are taken from the original work for a 1 year planning horizon (with a time period of duration 1 month). To see the effect of sudden rise in demands, the demand values for time periods 6 and 12 are changed to 300% of the demand values given in the original work while all other demand values for the rest of the 10 time periods are considered to be 20% of the demand values reported in the original problem. These modified demands are henceforth called the baseline values for fuzzy programming or nominal values for deterministic problem. First we analyze the effect of demand uncertainty for two fuzzy formulations: (i) multi-objective midterm planning product formulation without any minimum run length restriction (henceforth called as Model 1 consisting of equations
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1,2,4-7,9,10a,11a,12b,13b,14a,15a,17b,18b,19) and (ii) multi-objective midterm planning product family formulation with minimum run length restriction (hence forth called as Model 2 consisting of equations 1 - 9,10a,11a,12b,13b,14a,15a,16a,17b,18b, 19). The first problem results in an LP formulation (4789 single equations, 3989 single variables) whereas the second problem is an MILP problem (5198 single equations, 4214 single variables, 132 binaries). The complete formulation was coded in the modeling environment of GAMS© and solved using BDMLP (Brooke et al, 1998) as well as COIN-OR SYMPHONY solver for LP and MILP respectively. Model 2 was found to converge to 0.01% of the best possible value spanning over 25 different runs. It is observed that there lies a trade-off between the overall planning cost and margins provided on uncertain demands. These Pareto Optimal (PO) points for model 1 and model 2 with different values of demand margins of the basis values are presented in Figure 1. The PO front of model 2 (MILP) lies marginally above the PO front of model 1 as model 2 (MILP) is a more restrictive case of model 1 (LP) and hence leads to higher cost. Total Cost & Constraint Margin Pareto 10000 9000 8000 Cost
7000 6000 5000 4000 3000 2000 0
20 40 60 80 Demand Constraint Margin
Dmd 30% margin model 1
100
Dmd 30% margin model 2
Fig. 1. Total cost vs. demand margin Pareto fronts for model 1 and model 2 respectively
Next we focus on a few points of the model 1 and model 2 PO front (two points correspond to 30% and 50% margin points). These two cases are compared with the results of the deterministic planning model run for the nominal demands (henceforth called as nominal case). As compared to the nominal case, the plan for the uncertainty cases shows a trend of higher production to handle uncertainty in future (Fig 2). The start of production only around the sixth time period can be explained as the demand till that time period being met by the already existing initial inventory at the production site. More accumulation of inventory for future uncertainty is not visible as there is a cost associated with it. On a relative basis, the unit cost component of the McDonald and Karimi (1997) model is defined in such a way that the model gives higher preference for maintaining inventory at the safety level as long as there is no demand miss and that happens during the time periods of 6 - 11. At the time period 12, the model allows its safety level to get depleted to meet market demand because the cost associated with a missing demand at market is higher than that of the inventory costs. The case is more aggravated when the margin on the product demand uncertainty is higher (50% margin). The relative results of uncertainty analysis for model 2 and model 1 shows products are made at all possible time nodes, if required, because of the
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absence of the minimum run length as well as product family constraint in the case of model 1. Dem and Patterns
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Fig. 2. Demand, Production, Inventory and Shortage patterns for product P1 under various demand margins over the entire planning horizon for model 2 ((a) when demand values are certainly known, (b) demand margins are 30% of the nominal values, (c) demand margins are 50% of the nominal values)
The effect of machine uptime uncertainty when considered in addition to demand uncertainty leads to LP (1,2,4-7,9,10b-15b,17b-19b) and MINLP (1-9,10b-19b) formulations for product and product family formulations respectively. MINLP problem is solved using BARON solver. These results are not presented here for the sake of brevity and will be communicated in future publications.
4. Conclusion In this paper, the multi-objective mid term supply chain planning problem is solved using fuzzy mathematical programming. The slot based planning model of McDonald and Karimi (1997) is adopted under fuzzy programming paradigm and solved for various uncertain scenarios. If the same problem would have been solved using the scenario based two-stage stochastic programming approach considering just 5 scenarios for each of the 34 products for 12 time periods interlinked by inventory balance equations, we would have to solve a very large problem (534×12×12 scenarios) which was not the case for fuzzy approach. In fuzzy approach, the problem formulation is quite generic and easy to model, and the time involved in solving the problem is much smaller in comparison. In addition, it does not require the knowledge of distributions associated with the uncertain parameters. Due to these strong advantages, the fuzzy programming promises a great potential in handling problems under uncertainty.
References J. F. Shapiro, 2001, Modeling the Supply Chain, Duxbury Thormson Learning, USA. J. R. Birge, F. Louveaux, 1994, Introduction to Stochastic Programming, Springer-Verlag, New York, USA. N. V. Sahinidis, 2004, Optimization Under Uncertainty: state-of-the-art and opportunities, Comp. Chem. Eng., 28, 971. C. M. McDonad, I. A. Karimi, 1997, Planning and Scheduling of parallel semicontinuous processes. 1. Production planning. Ind. & Engg. Chem. Res., 36, 2691. R.Bellman, L. A. Zadeh, 1970, Decision-making in a fuzzy environment. Man. Sci., 17, 141. A, Brooke, D. Kendrick and A. Meeraus, 1998, GAMS – A User’s Guide, GAMS Dev. Corp. Washington DC.
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Modeling and Identification of the Bio-ethanol Production Process from Starch: Cybernetic vs. Unstructured Modeling Silvia Ochoaa, Ahrim Yoob, Jens-Uwe Repkea, Günter Woznya, and Dae Ryook Yangb a
Department of Process Dynamics and Operation, Technical University of Berlin, Sekr. KWT 9, Strasse 17. Juni 135, Berlin 10623, Germany. b Department of Chemical & Biological Engineering, University of Korea, Seoul, Korea.
Abstract In this work, an unstructured and a cybernetic model are proposed and compared for the Simultaneous Saccharification - Fermentation process from Starch to Ethanol (SSFSE), in order to have good, reliable, and highly predictive models, which can be used in optimization and process control applications. The cybernetic is a novel model, which especially considers i) the starch degradation into both glucose and dextrins, and ii) the dynamic behavior of the concentration of the main enzymes involved in the intracellular processes, giving a more detailed description of the process. Furthermore, a new identification procedure based on a sensitivity index is proposed to identify the best set of parameters that not only minimizes the error function, but also contains a fewer number of parameters depending on the initial conditions of the process. Finally, an application of the two models for controlling the SSFSE process using an NMPC (following an optimal reference trajectory for the ethanol concentration) is presented, showing the potential and usefulness of each type of models. Keywords: Cybernetic Model, Ethanol, Sensitivity Analysis, Parameter Identification, NMPC.
1. Introduction During the last years, significant improvements have been done in the bio-ethanol industry in order to make it economically more competitive, such as, in purification technologies for ethanol dehydration as well as in the genetic modification of microbial strains. However, the economical feasibility of the bio-ethanol industry is still questioned, and therefore much effort should be oriented to the optimization and control of the process. It is well known that a suitable model of the process should be available for developing optimization and control tasks and that although in chemical processes this is currently not a problem, the complexity of biological systems makes its modeling a difficult task. Bioprocess modeling is usually addressed from two different points of view: the structured and the unstructured modeling frameworks. Structured models (such as cybernetic models) try to describe in detail the intracellular behavior, and although they are more complex (i.e. higher number of ODE and AE with more parameters), they can predict more accurately the actual behavior of the process states. Parameter identification of biochemical models by error minimization is a nonlinear optimization problem that contains multiple local minima. In those cases, stochastic
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optimization methods are more convenient because they usually present a better performance in comparison to gradient search based methods which frequently lead to local solutions, especially if the model contains a large number of parameters and sufficient experimental data are not available. Therefore, trying to avoid local solutions while at the same time finding a minimum number of parameters dependent on the initial conditions of the process, in Section 3 an identification procedure based on a Simulated Annealing method coupled with a sensitivity analysis is presented. The main purpose of this paper is not to answer the question regarding to which kind of model is better or worse; the purpose is to show that depending on the application, these two models can even be used in a synergistic manner. Unstructured models are more suitable for online applications where the simplicity of the model plays an important role especially for saving computation time while the model predictions are still good. In contrast, cybernetic models are preferred for offline applications in which very accurate predictions are needed no matter the computation time. As an example of the potential usefulness of the two types of models, a Nonlinear Model Predictive Control (NMPC) for the fed-batch SSFSE process was implemented for controlling an optimum ethanol concentration profile that guarantees maximal productivity. The unstructured model was run online as the predictive model that is part of the NMPC; whereas the cybernetic was used offline for finding the optimal ethanol profile defined as the reference trajectory on the NMPC calculations. Additionally, the results of the controlled fed batch process are compared to a batch SSFSE process, simulated using the model presented in (Ochoa et al, 2007), in order to show that the productivity reached in the controlled fed batch process is higher than in the batch.
2. Modeling of the SSFSE Process The process modeled on this section is a fed batch process in which two reactions take place simultaneously in the same vessel: i) the enzymatic conversion of starch into glucose (by means of glucoamylase and α-amylase), and ii) the fermentation of glucose to ethanol by means of yeast. A genetically modified Saccharomyces cerevisiae strain is used in the process (as described by Altintas et al, 2002), which is able of both, secreting the required enzymes for the starch saccharification and producing ethanol by glucose fermentation. 2.1. Cybernetic Model The cybernetic modeling framework has been developed by Ramkrishna’s group and presented in several papers. The most remarkable of those is the paper by Varner and Ramkrishna (1999), in which the guidelines for developing cybernetic models of bioprocesses are given, according to the type of pathway that is taking place. Following Ramkrishna’s ideas and the metabolic pathway shown in Figure 1, the cybernetic model for the fed batch SSFSE process is proposed in this section. e5 e1
Glucose (G)
e3
Dextrin (D)
Starch (S)
e2
e4
Ethanol (E) Yeast (X)
Figure 1. Metabolic Pathway for ethanol production from starch.
The cybernetic model for the fed batch process is obtained from the mass balances for Starch (S), Glucose(G), Dextrins (D), Cells (X), Ethanol (E), Glucoamylase (e1= e2), αamylase (e3), hypothetical enzyme 1 (e4) and hypothetical enzyme (e5), as shown in Figure 2. The expressions for the kinetics ri and the cybernetic variables νi (enzyme
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activity) and ui (enzyme synthesis) are given in Figure 3. A detailed description of the nomenclature used in this work can be found in Ochoa et al. ( 2007). F (S − S ) dS = (− r1v1 − r3v3 ) X + in in dt Vol
(
) (
)
(
μ max + β i C s X d ei / eimax X ei F e / e max ui − β i max X − in i i = ei dt K ei + C s ei Vol
dX F X = (r4v4 − K d ) X − in dt Vol
dD F D = (r3v3YD / S − r2v2 ) X − in dt Vol
dG rv rv FG = ( r1v1YG / S + r2v2YG / D − 4 4 − 5 5 ) X − in dt YX / G YE / G Vol
)
dE F E = r5v5 X − in dt Vol
Figure 2. Cybernetic model for the fed-batch SSFSE: Mass balances for the state variables · § r1 ¸ ¨ § ·¨ r1 G ¸ v1 = ¨¨ ¸¸ © max (r1 , r2 ) ¹ ¨ max §¨ r1 , r3 ·¸ ¸ ¸ ¨ ©G D¹¹ © μ (e / e max ) D r2 r2 = max,2 1 1 v2 = K2 + D max (r1 , r2 ) r3 μ (e / e max ) S D v3 = r3 = max,3 3 3 K3 + S §r r · max ¨ 1 , 3 ¸ ©G D¹ r4 (e / e max )G § μ E ·¸ X r4 = max,4 4 4 2 ¨¨1 − v4 = G K Pini , 4 ¸¹ §r r · © G + K4 + max ¨ 4 , 5 ¸ K Sini , 4 ©X E¹ r5 · μ max,5 (e5 / e5max )G § E ¨1 − E ¸ r5 = v5 = G 2 ¨© K Pini ,5 ¸¹ § r4 r5 · G + K5 + max ¨ , ¸ K Sini ,5 ©X E¹ r1 =
§ r1 · ¸ § r ·¨ u1 = ¨¨ 1 ¸¸ ¨ G ¸ © r1 + r2 ¹ ¨¨ r1 + r3 ¸¸ ©G D¹
μ max,1 (e1 / e1max ) S K1 + S
r2 r1 + r2 r3 u3 = D r1 r3 + G D r4 u4 = X r4 r5 + X E r5 u5 = E r4 r5 + X E u2 =
Figure 3. Kinetic expressions and cybernetic variables for the SSFSE process
Altintas et al. (2002) developed a cybernetic model for the same SSFSE process tackled here; but the authors did not consider the starch degradation into dextrins, which is considered in the present work (see Figure 1). The main advantage of including this in the model is that more accurate predictions of the process variables can be made, especially for the starch and for the ethanol concentration, being the latter the most valuable product of the process. This fact is corroborated by the results presented in section 3 (see Figure 7). 2.2. Unstructured Model The unstructured model developed here considers that the starch is composed of two fractions, one susceptible (faster hydrolyzed, represented by Ssus), and one resistant (Sres) as described in Kroumov et al. ( 2006). Although the saccharification is carried out using glucoamylase and α-amylase, the model considers that this two-enzyme action can be simplified and represented by an additive enzyme activity (Enz) (Kroumov et al., 2006). The kinetic expressions used for describing the fermentation, take into account substrate and product inhibition in both cell’s growth and ethanol production rates. The model for the fed batch SSFSE process is given in Figure 4, while the corresponding kinetic expressions are given in Figure 5. dE F E F (S −S ) F (S −S ) dS dS dS F (S − S ) = qX − = −R S + = −R S + dt
= − RSus S Sus − Rres S res +
in
in
Sus
in
dt
Vol
F X dX = ( μ − K d ) X − in Vol dt
Sus
sus
sus , in
sus
Vol
F Enz dEnz = REnz − (μ + β )Enz − in Vol dt
in
res
res
dt
res
res , in
in
res
dt
Vol
Vol
§ μX · § qX · Fin G dG ¸¸ − ¨¨ ¸¸ − = 1.111 ( RSus S Sus + RRes S Res ) − ¨¨ dt © YX / G ¹ © YE / G ¹ Vol
Figure 4. Unstructured model for the fed batch SSFSE process. RSus =
k sus Enz 2 § G · S Sus ¸¸ + K m ¨¨1 + + S Sus + S res © K G ¹ K Starch
REnz =
(μ m + β )(S sus + S res )Enzmax K enz + S sus + S res
Rres =
kres Enz 2 § G · S res ¸¸ + K m ¨¨1 + + S Sus + S res © K G ¹ K Starch
Figure 5. Kinetic expressions for the unstructured model.
q=
qm G k sp + G +
§ · ¨1 − E ¸ G 2 ©¨ Emp ¹¸ K ssp
μ=
μm G ks + G +
§ E · ¨1 − ¸ G 2 ©¨ Em ¹¸ K ss
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3. Identification of Parameters Define n sets of data at different initial conditions
Initial set of Pk parameters
Metropolis Monte Carlo Optimization: n
[
min Fobj(P) = min¦ MSEX ,h + MSE S,h + MSE G,h + MSE E,h h=1
.
]
Caculate the sensitivity index: P0k + ΔP k
S = k I
³F
obj
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For each Parameter Is SI < Tol?
Yes
The parameter is not Sensitive = Fixed Parameter (P=Pns)
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The parameter is Sensitive: P=Ps
Re-optimization of Ps for each n set of data using the Metropolis Monte Carlo Method.
Optimal values for data set 1
Optimal values for data set 2
Optimal values for data set n
Figure 6. Developed Identification Procedure: Optimization coupled with Sensitivity analysis.
The parameters for both models were identified using experimental data reported by Altintas et al. (2002), following the identification procedure proposed in Figure 6. The identification procedure uses different sets of experimental data at different initial conditions and is divided in three main steps: i) An initial optimization routine (for all sets of data simultaneously) is run to calculate a first group of parameters for the various sets of experiments; ii) a sensitivity index is calculated for identifying which parameters have stronger influence on the objective function (according to a pre-established tolerance, Tol), iii) a re-optimization is performed, this time for each set of data independently, but only considering those parameters to which the objective function showed a higher sensitivity. The objective function (Fobj) was taken as the sum of the normalized squared error values for X, S, G and E (comparing to the experimental data). The sensitivity index SI evaluates the sensitivity of Fobj to each parameter when the k-th parameter varies between the integration limits that are defined as a function of the optimized value for k (P0k). It is important to remark that the sensitivity is usually analyzed as the partial derivative of Fobj with respect to the k-th parameter; however in this case an optimum has been already found and if we use the typical sensitivity analysis, we could find that some parameters may have a sensitivity value of zero. That is the reason why we propose here to analyze the sensitivity using the new index shown in the procedure described in Figure 6. Cybernetic and unstructured models presented in Section 2 are composed of 34 and 20 parameters respectively. After analyzing the sensitivity by means of the new sensitivity index, it was found that only 17 and 7 parameters respectively, are sensitive parameters. It is possible to state that for the set of parameters for each kind of model, only those sensitive should be periodically adapted using online information from the process, especially when the process conditions change considerably. On the other hand, non-sensitive parameters can be maintained fixed at their optimal values. As the main advantage of the identification procedure is the reduction of the number of parameters that should be adapted online, it is important to remark that the success of the procedure depends highly on the methods used for the
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optimization and re-optimization steps. Stochastic optimization methods are more suitable due to their ability for escaping out of local minima. In this way, the Metropolis Monte Carlo simulated annealing method (Kookos, 2004; Ochoa et al., 2007) is recommended because of i) its random nature, which allows the exploration of a much wider region, ii) its ability for avoiding getting trapped in a local optimum, which is given by the Metropolis condition and iii) the annealing effect, which takes care of the convergence. In Figure 7 a comparison between the predictions made by the unstructured, the cybernetic and Altintas’ model is presented for starch and ethanol. As can be seen, the models presented in Section 2 not only are in good agreement with the experimental data but also give a better description of the state variables during the whole process. In contrast, Altintas’ model fails predicting the ethanol and starch dynamic behavior. It is important to remark that the main difference is that, in contrast to the cybernetic presented here, Altintas’ model does not consider the conversion of starch into dextrins. This is probably the main reason why their model predicts higher starch concentration in the interval 20-100 h leading to a lower predicted ethanol, and a lower starch for the period 100-140 h leading to a higher predicted ethanol. 30
15
Cybernetic Unstructured Altinta's Model Experimental Experimentaldata data Ethanol Concentration (g/l)
25
10
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20
15
10
5
5
0
0 0
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100
150
0
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Figure 7. Models Predictions for Starch (left side) and Ethanol (right side).
4. Nonlinear Model Predictive Control In this section the usefulness of each kind of model is exemplified in the control of the fed-batch SSFSE process. The objective of the control system is to maximize the productivity of the process, which is calculated as the total mass of ethanol produced. Due to its accuracy for predicting the dynamic behavior of the process, the cybernetic model was used offline to calculate a profile for the ethanol concentration that leads to maximal productivity; whereas the unstructured model was used in the prediction block of the NMPC, because of its simplicity (important for a fast online solution) and still good prediction capability. Figure 8 shows the scheme of the control system. The dynamic behavior of the process and the NMPC performance were investigated through simulation studies considering measurement noise with standard deviation of 3%, 0.02%, 0.01% and 0.02% for X, S, G, and E respectively. During the process, two disturbances were simultaneously considered, i) a 10% of change in the feed starch concentration (Sin) and ii) a 20% of change in the value of the maximum specific growth rate um. The results for the NMPC are compared in Figure 9 to those for the nominal case (optimal operation without disturbances) and to the batch results. The batch case was run in open loop using the unstructured model presented in Ochoa et al. (2007). Despite the disturbances and the model mismatch, the NMPC followed successfully the optimal ethanol reference trajectory calculated offline. Therefore, it can be stated that the cybernetic and unstructured models are quite useful for offline and online
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applications respectively, due to the predicting capability of the cybernetic model and the simplicity (and even good predictions) of the unstructured model. Besides, it is important to highlight that a higher ethanol concentration (and therefore a higher productivity) is obtained in the fed-batch process when compared to the batch process. In the example tackled here, it is shown that by means of a conveniently controlled fedbatch process, the purity of the ethanol in the fermentation stage can be increased, which is translated into a reduction of downstream purification costs. d1(sin), d2 (um) Offline Set point Calculation (Cybernetic Model)
Eref -
NMPC (unstructured model)
+
Fin
Process (unstructured model + noise)
Eprocess
Figure 8. NMPC: Cybernetic and Unstructured models application. 18 16 14
Ethanol (g/l)
12 10 8
Efedbatch(NMPC) Ebatch
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4 2 0
0
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Figure 7. NMPC results. Ethanol concentration: Fed batch controlled process vs. Batch.
5. Conclusions Cybernetic and unstructured models were proposed for the fed batch SSFSE process. The models were compared to a cybernetic model previously reported, showing a better performance than the previous model. The parameter identification of the models was done by means of a new identification procedure in which stochastic optimization is coupled to sensitivity analysis. Using this procedure, it was possible to find which parameters should be adapted online and which could be kept at fixed values, leading to a more robust model. The unstructured model is suitable for online applications such as model-based control, whereas the cybernetic is the best choice for applications where the accuracy of the model is important such as the off-line determination of optimal trajectories to be tracked along the process.
References M. Altintas, B. Kirdar, Z. I. Önsan and K. Ülgen. 2002, Cybernetic Modelling of growth and ethanol production in a recombinant Saccharomyces cerevisiae strain secreting a bifunctional fusion protein, Process Biochem., 37, 1439-1445. A. D. Kroumov, A. N. Módenes and M. C. A. Tait, 2006, Development of new unstructured model for simultaneous saccharification and fermentation of starch to ethanol by recombinant strain, Biochem. Eng. J., 28, 243-255. J. Varner and D. Ramkrishna, 1999, The non-linear analysis of cybernetic models. Guidelines for model formulation, J. Biotechnol., 71, 67-104. I. K. Kookos, 2004, Optimization of Batch and Fed-Batch Bioreactors using Simulated Annealing, Biotechnol. Prog., 20, 1285-1288. S. Ochoa, A. Yoo, J-U. Repke, G. Wozny and D.R. Yang. 2007, Modeling and Parameter Identification of the Simultaneous Saccharification-Fermentation Process for Ethanol Production, Biotechnol. Prog., 23, 1454-1462.
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Particle Swarm Optimisation in Heat Exchanger Network Synthesis Including Detailed Equipment Design Aline P. Silva,a,b Mauro A. S. S. Ravagnani,a Evaristo C. Biscaia Jr.b a
Universidade Estadual de Maringá, Maringá – PR, Brasil,
[email protected] b
PEQ/COPPE/UFRJ, Rio de Janeiro - RJ, BRAZIL
Abstract Heat exchanger network (HEN) synthesis has been a well-studied subject over the past four decades. Many studies and methodologies have been proposed to recover energy between process streams, minimizing the utilities consumption and the number of heat transfer equipment. Most of these formulations assume constant heat-transfer coefficients and counter current arrangement for all stream matches, which can lead to non-optimal results. In the present contribution an optimisation model for the synthesis of HEN that includes a detailed design for each heat exchanger in the network is proposed. Shell and tube pressure drops and fouling have been considered, as well as mechanical aspects, like shell and tube bundle diameters, internal and external diameter of tubes, number of tubes, number of baffles, baffles spacing, number of shells, tube length, tube pitch, tube arrangement and the fluid allocation in the heat exchanger. Particle Swarm Optimisation approach has been applied to determine the HEN that minimizes the total annual cost, considering capital costs of heat exchangers, energy costs for utilities and pumping duties. The algorithm combines two distinct models, a superstructure simultaneous optimisation model for the HEN synthesis and a model for the detailed equipment design according to TEMA. An illustrative example shows the potential of the method, and optimum HEN configuration with the detailed heat exchangers design was obtained. Keywords: Heat exchanger network, particle swarm optimisation, shell and tube heat exchangers design, Bell-Delaware method.
1. Introduction The synthesis of heat exchanger networks (HEN) is an important field in process systems engineering, and has been the subject of considerable research efforts over the last 40 years, according to the review paper of Furman and Sahinidis1. Many studies and methodologies were proposed to make possible the energy recovery between process streams, minimizing the utilities consumption and the number of heat transfer equipment2. Most formulations, however, assume constant heat-transfer coefficients and purely counter-current arrangement for all stream matches, which can lead to nonoptimal results. Over the past few years, several papers have been published considering the heat exchanger design during the HEN synthesis stage. Ravagnani, et al.3 presented a methodology for the synthesis of HEN including the thermo-hydraulic design of the heat exchangers. The HEN synthesis is accomplished by using Pinch Analysis. The network is evolved by identification and loop breaking. After the evolution, the heat exchangers of the network are designed considering pressure drops and fouling with the Bell-Delaware method for the shell side.
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Frausto-Hernandez et al.4 presented a mixed integer non linear programming (MINLP) model to the synthesis of HEN considering pressure drop effects. Heat transfer coefficients are calculated based on the fixed pressure drops, using the equations proposed by Panjeh Shahi5, Polley et al.6 and Polley and Panjeh Shahi7. Mizutani et al.8 presented a Mathematical Programming model to the design of shell and tube heat exchangers. The model is based on the generalized disjunctive programming (GDP) with a MINLP formulation and uses the Bell-Delaware equations to calculate heat transfer and pressure drop for the shell side. The objective function takes in account area and pumping costs. Based on this work, Mizutani et al.9 developed a model for the synthesis of HEN including their heat exchanger design model. Ravagnani and Caballero10 proposed a mathematical model to find the best shell-andtube heat exchanger configuration, using the Bell-Delaware method for the shell side thermal calculation and following rigorously the standards of the Tubular Exchangers Manufacturers Association (TEMA)11. In this paper it is proposed a method based on Particle Swarm Optimisation (PSO) for the HEN synthesis that includes the detailed design of the heat exchanger units. An algorithm similar to the proposed by Yee and Grossmann12, based on a stage-wise superstructure representation, considering stream splitting is used for HEN synthesis. A model proposed in Ravagnani and Caballero10 is used for the design of shell and tube heat exchangers. The model follows TEMA standards and Bell-Delaware method is used to the shell side calculations. Mechanical design features (shell and tube bundle diameters, internal and external tube diameters, tubes length, pitch and arrangement, number of shells, number of tubes and tube passes) and thermal-hydraulic variables (heat, area, individual and global heat transfer coefficient, shell and tube pressure drops and fouling) are variables to be optimised. The equipments are designed under pressure drop and fouling limits. The main contribution of this paper is, besides the incorporation of the equipment detailed design considering TEMA standards, the optimisation with PSO method. PSO is able to avoid local optima and suits very well to non linear problems. HEN Problem Definition: The problem consists of finding the HEN that minimizes the total annual investment plus operating costs. The investment term includes the cost of exchangers and pumps, and the operating costs comprise the energy for utilities and pumps. Given a set of hot and cold streams with their supply and target temperatures, flowrates and physical properties (density, viscosity, heat capacity and thermal conductivity), pressure drop and fouling limits, as well as hot and cold utilities with their temperatures and corresponding costs, the objective is to find the HEN with the detailed heat exchangers design concerning the minimum global annual cost, considering utility, area and pumping costs. The problem consists in to find the best HEN configuration and to optimise the heat exchangers units variables. For the HEN synthesis an algorithm similar to the stage-wise superstructure representation of Yee and Grossmmann12 is proposed. Stream splitting and by pass is considered in the HEN synthesis model. Heaters and coolers are placed at the ends of the streams. This algorithm (master problem) is combined with the heat exchangers design model presented in Ravagnani and Caballero10 for each network equipment, to find the minimum global annual cost, comprising area, utilities and pumping costs. The design of heat exchangers is solved as an inner optimisation loop.
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2. Model Formulation of Heat Exchanger Design Shell and tube heat exchangers are the most used heat transfer equipment in industrial processes due to their resistant manufacturing features and design flexibility. Nevertheless, some difficulties are found, especially in the shell-side design, because of the complex characteristics of heat transfer and pressure drop. In the present paper, Bell-Delaware method, presented in (10), is used to formulate the mathematical model involving discrete and continuous variables for the selection of the configuration and operating levels, respectively. A tube counting table, following the TEMA Standards is proposed, allowing to calculate the shell diameter, the tube bundle diameter, the external tube diameter, the tube pitch, the tube arrangement pattern, the number of tube passes and the number of tubes. Furthermore, some complementing features are proposed. Besides the table counting, shell and tube side pressure drops and fouling factor are calculated and the model has as constraints operational limits, previously fixed, as in industrial applications. The problem to be formulated as an optimisation problem is the design of the optimum shell and tube equipment to exchange heat between a cold and a hot stream. The objective is to find the heat exchanger that presents the minimum cost including exchange area cost and pumping cost, following TEMA standards constrained to allowable pressure drops and fouling limits. Inlet data for both fluids are: Tin (inlet temperature), Tout (outlet temperature), m (mass flowrate), ρ (density), Cp (heat capacity), μ (viscosity), κ (thermal conductivity), allowable ΔPdesign (pressure drop), rddesign (fouling factor) and area and pumping cost data. The mechanical variables to be optimised are tube inside diameter (din), tube outside diameter (dex), tube arrangement (arr), tube pitch (pt), tube length (L), number of tube passes (Ntp) and number of tubes (Nt), for the tube-side. To the shell-side, the desired variables are the external diameter (Ds), the tube bundle diameter (Dotl), baffles number (Nb), number of shells (NS), baffles cut (lc) and baffle spacing (ls). Finally, thermal-hydraulic variables to be calculated are heat duty (Q), heat exchange area (A), tube-side and shellside film coefficients (ht and hs), dirty and clean overall heat transfer coefficient (Ud and Uc), pressure drops (ΔPt and ΔPs), fouling factor (rd), log mean temperature difference (LMTD), the correction factor of LMTD (Ft) and the fluids location inside the heat exchanger. The main equations of the model are related bellow. Clean Overall Heat Transfer Coefficients (Uc) Tube-Side Heat Transfer Coefficients (ht) ht =
Nu t ⋅ k t
1
Uc =
d int
Tube-Side Pressure Drop (ΔPt) § 2 ⋅ fi t ⋅ n t ⋅ Lt ⋅ v t 2 ¨ p ΔPt = ρ t ¨ + 1.25 ⋅ n tp ⋅ v t d int ¨ © Shell-Side Heat Transfer Coefficients (hs) hs = hoi ⋅ J c ⋅ J1 ⋅ J b Pressure Drop Across the Shell-Side (ΔPs) § N · ΔPs = 2 ⋅ ΔPb ⋅ ¨¨1 + cw ¸¸ ⋅ Rb + © Nc ¹
()
+ (1 + N b ) ⋅ ΔPb ⋅ Rb ⋅ R1 + N b ⋅ ΔPw ⋅ R1
·
( ) ¸¸ 2
¸ ¹
( )+ r t
d ext ht ⋅ d int
+
rin ⋅ d ext d int
+
d ext ⋅ log dex d t
in
2⋅k
ex
+
1 hs
Dirty Overall Heat Transfer Coefficients (Ud) Q Ud = A ⋅ LMTD Fouling Factor Calculation (rd) U −Ud rd = c U c ⋅U d Area Cost (Carea)
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Heat exchange area (A) t A = n t ⋅ π ⋅ d ex ⋅ Lt
· § Q ¸¸ C area = a1 ⋅ ¨¨ © U ⋅ Ft ⋅ LMTD ¹
a2
Optimisation Problem Minimize: Ctotal = C area + C pump Subject to:
ΔPt ≤ ΔPmax ; ΔPs ≤ ΔPmax ; rd ≥ rd ,design and Ft ≥ 0.75
3. Particle Swarm Optimisation Particle swarm optimisation (PSO) is a stochastic optimisation technique developed by Kennedy and Elberhart13, inspired by social behaviour of bird flocking or fish schooling. PSO as an optimisation tool provides a population-based search procedure in which individuals called particles change their position (state) with time. In a PSO system, particles fly around in a multidimensional search space. During flight, each particle adjusts its position according to its own experience, and according to the experience of a neighbouring particle, making use of the best position encountered by itself and its neighbour. In the last years, PSO has been successfully applied in many research and application areas. One of the reasons that PSO is attractive is that there are few parameters to adjust. In this work, the particles and the velocity of each particle are actualized according to:
(
)
(
v k(i+)1 = ω k v k(i+)1 + c1r1 p k(i ) − x k(i ) + c 2 r2 p kglobal − x k(i )
)
x k(i+)1 = x k(i ) + v k(i+)1
Where x k(i ) and v k(i ) are, respectively, position and velocity vectors of the particle i , ω k is the inertia weight, c1 and c2 are constants, r1 and r2 are two random vectors, pk(i ) is the position with the best result of particle i and pkglobal is the position with the best result of the group. In above equations subscript k refers to the iteration number.
4. Illustrative Example An example, considered in Ravagnani and Caballero2, is presented to illustrate the potential of applicability of the proposed algorithm for the synthesis of HEN considering the detailed design of the heat exchangers. The objective function considers area, utilities and pumping costs. The purpose is to find the optimal heat exchanger network configuration with the equipments detailed design. The problem has two hot and two cold streams and a hot and a cold utility are available. Temperatures, flow rate and physical properties of the streams and utilities, pumping, area and cost data are shown on Table 1. By applying the proposed methodology, the optimal network configuration obtained is presented in Fig. 1. The value of the HEN global annual cost is 96,007.39 $/year. Table 2 presents the details of the equipments design. Also, the designed heat exchangers are in accordance with TEMA standards. Table 3 shows the comparison with literature.
5. Conclusions In the present paper an algorithm for the synthesis of HEN including the detailed design of the equipments is proposed. It is based in a model for the optimal synthesis of HEN
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considering stream splitting and by pass and a model for the optimal design of a shell and tube heat exchanger design, following rigorously TEMA standards. The global annual cost objective function takes into account investment, utility and pumping costs. An example was used to describe the algorithm applicability. The final results obtained in this paper are consistent with the presented in the literature. The problem was optimised with PSO method, which is a reliable way compared with other methods, because it suits well to MINLP problems. Although with a computational time of 80 minutes the results are better than the presented in Ravagnani and Caballero10.
Table 1 – Streams and Cost Data Stream H1 H2 C1 C2 UQ UF
Tin (K) 368 353 303 333 500 300
Tout (K) 348 348 363 343 500 320
m (kg/s) 8.15 81.5 16.3 20.4
μ
ρ
(kg/ms) 2.4 E-4 2.4 E-4 2.4 E-4 2.4 E-4
(kg/m3) 634 634 634 634
Cp (J/kgK) 2454 2454 2454 2454
κ
ΔP
(W/mK) 0.114 0.114 0.114 0.114
(kPa) 68.95 68.95 68.95 68.95
rd (W/mK) 1.7 E-4 1.7 E-4 1.7 E-4 1.7 E-4
Area cost=1000 + 60A0.6, A in m2. Pumping cost = 0.7 (ΔPtmt/ȡt +ΔPsms/ȡs), ΔP in Pa, m in kg/s and ȡ in kg/m3. Hot utility cost = 60 $/kW year. Cold utility cost = 6 $/kW year.
348 K
368 K
E1 348 K
353 K
E2
363 K
338 K
303 K
328 K
H1 343 K
(1000 kW)
(400 kW)
(1000 kW)
333 K
H2 (500 kW)
Figure 1 – Optimal HEN Table 2 - Detailed equipment design Area (m2) Q (W) Ntp NS Ds (m) Dotl (m) Nt Nb dex (mm) din (mm) pt (mm)
E1 36.76 400 4 1 0.43815 0.4064 168 12 0.01905 0.017 0.0254
E2 73.43 1000 1 1 0.6858 0.64453 286 7 0.0254 0.0225 0.03175
L (m) hs (W/m2 K) ht (W/m2 K) Uc (W/m2 K) Ud (W/m2 K) ΔPt (kPa) ΔPs (kPa) rd (m2 KW) Arrangement Hot fluid allocation
E1 3.658 1662.34 1212.61 524.37 441.36 9299.32 1563.14 3.58E-04 Square Tube
E2 3.658 964.46 995.65 390.29 334.62 1165.84 418.88 4.26E-04 Square Tube
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Table 3 - Final results Global annual cost ($/year) Area cost ($/year) Pumping cost ($/year) Utility cost ($/year) CPU time (min) @ Pentium IV 170 GHz
Ravagnani and Caballero (2007) 96013.65 5844.09 169.56 90000.00
Present paper 96007.39 5783.23 224.16 90000.00 ~ 80
6. Nomenclature a1,a2,a3
Cost parameters
fl
Friction factor for the tube-side Shell-Side Heat Transfer Coefficient for an Ideal Tube Bank Correction Factor for Bundle-Bypassing Effects Correction Factor for Baffle Configuration Effects Correction Factor for Baffle-Leakage Effects Number of tube rows crossed in one crossflow section Number of tube columns effectively crossed in each window Number of Nusselt Correction Factor for Bundle Bypass
hoi Jb Jc Jl Nc Ncw Nu Rb
Rl v ΔPb ΔPw
Correction Factor for the Effect of Baffle Leakage on Pressure Drop Fluid velocity Pressure Drop for an Ideal Cross-Flow Section Pressure Drop for an Ideal Window Section
Index c
Cold fluid
h
Hot fluid
s t
Shell-side Tube-side
References 1. Furman, K. C.; Sahinidis, N. V. A. Ind. Eng. Chem. Res. 2002, 41, 2335-2370. 2. Ravagnani, M. A. S. S.; Caballero, J. A., (2007). Computers and Chemical Engineering, 31, 1432-1448. 3. Ravagnani, M. A. S. S., Silva, A. P., and Andrade, A. L. (2003).. Applied Thermal Engineering, 23, 141–151. 4. Frausto-Hernandez, S., Rico-Ramirez, V., Jimenez-Gutierrez, A., Hernandez- Castro, S. (2003). Computers and Chemical Engineering, 14(1). 5. Panjeh Shahi, M. H. (1992). Ph.D. Thesis, UMIST, U.K. 6. Polley, G. T., Panjeh Shahi, M. H. M., & Jegede, F. O. (1990). Transactions on Institute of Chemical Engineers, 68, 211–220. 7. Polley, G. T., & Panjeh Shahi, M. H. M. (1992). Transactions on Institute of Chemical Engineers, 69, 445–447. 8. Mizutani, F. T., Pessoa, F. L. P., Queiroz, E. M., Hauan, S., Grossmann, I. E. (2003). Industrial & Engineering Chemistry Research, 42, 4009–4018. 9. Mizutani, F. T., Pessoa, F. L. P., Queiroz, E. M., Hauan, S., & Grossmann, I. E. (2003). Industrial & Engineering Chemistry Research, 42, 4019–4027. 10. Ravagnani, M. A. S. S.; Caballero, J. A., (2007). Chemical Engineering Research & Design, 85 (A10) 1–13.
11. TEMA. (1988). Standards of the tubular heat exchanger manufacturers association (7th ed.). New York: Tubular Heat Exchanger Manufacturers Association. 12. Yee,T. F.,Grossmann, I. E. (1990). Computers and Chemical Engineering, 14, 1165. 13. Kennedy, J.; Eberhart, R.; Swarm Intelligence. Academic Press, London, 2001.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A single stage approach for designing water networks with multiple contaminants Krzysztof Waáczyk, Jacek JeĪowski Rzeszów University of Technology, Department of Chemical Engineering and Process Control, Al. PowstaĔców Warszawy 6, 35-959 Rzeszów, Poland
Abstract The paper addresses water network consisting of water using processes (wastewater reuse network - WWRN) modeled as mass transfer operations with multiple contaminants. The objective is to minimize freshwater cost or usage but some structural requirements can be also included. The approach is simultaneous by optimizing WWRN superstructure model. Due to novel logical conditions and some valid simplifications the optimization model is mixed-integer programming (MILP) with small number of binary variables. It can be solved efficiently using widely available solvers even for large-scale cases. This paper presents basis of approach and example of application. Keywords: wastewater reuse network, multiple contaminants, simultaneous approach, linear optimization.
1. Introduction Water network design problem (water allocation problem) has reached mature state. However, there is still a lack of general robust technique guaranteeing global or near global optimum solution for industrial cases. The reason is in nonlinear model of water using processes. More recently a lot of methods applied non-mass transfer model that provide linearity of water network problem, see for instance Prakash and Shenoy (2005). However, these insight-based approaches are limited to single contaminant. This paper addresses wastewater reuse network (WWRN), i.e. the network with water using processes but without regeneration/treatment operations. The problem is simpler than the design of total water system but still requires nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) model if optimization-based method is to be applied without major simplifications. The excellent review given by Bagajewicz (2000) showed power but also limitations of such approaches when applied to solve large scale nonlinear superstructure models. There are also more recent methods available based on this strategy. Genetic algorithms were applied by several authors, among others most recently by Cao et al. (2007). Even though some results are promising the technique is time consuming and does not guarantee global optimum. Gunaratnam et al. (2005) as well as Alva-Argaez et al. (2007) developed optimization approach by sequential linearization. Lee and Grossmann (2003) applied complex two level branch-and-bound optimization solver that provides global optimum for nonlinear (NLP) formulation. Those approaches require advanced solvers and/or long computation time (CPU) for large-scale cases. Bagajewicz et al. (1999, 2000) developed the approach that linearizes the optimisation model using optimality conditions from Savelski and Bagajewicz (2003). Such concept is computationally most efficient since allows solving linear programming (LP) or mixed-integer linear programming (MILP) problem. However, linearization works well for single contaminant case – see Bagajewicz (2000). Multiple contaminants problem requires creating a maximum reuse
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structure, which is solved by tree search enumeration technique. In this work we address the approach that follows some concepts of Bagajewicz et al. (1999, 2000) since we also linearized the water network superstructure model using conditions of optimality from Savelski and Bagajewicz (2003) with some extensions. However, we eliminated the necessity of tree search to calculate WWRN because the method doesn’t require generation of maximum reuse structure. In result our approach reduces largely computation load, and, also produces better results in some cases.
2. Problem formulation and analysis WWRN problem is stated as follows. Given water using processes i ∈ I modeled as counter-current mass exchangers. In each process a water stream has to remove given contaminants c ∈ C . The basic data for each process are: • Mass loads of contaminants Li , c (∀ i ∈ I , ∀c ∈ C ) , •
Upper limits on contaminant concentrations at process inlet and outlet , max C iin,c, max , C iout ( ∀i ∈ I , ∀c ∈ C ) ,c
The objective is to calculate water network that minimizes freshwater usage or its cost. Our approach is based on a solution of superstructure optimization model. The superstructure contains freshwater source and water using processes. One mixer and one splitter are attached to each water using process in order to maintain all wastewater reuse options. One freshwater splitter and one wastewater mixer at outlet from the network are also included. The explanation here is limited to a single freshwater source without contaminants. The assumptions can be easily removed. The variables are concentrations at processes inlet and outlet ( C iin,c , C iout ,c ) well as flow rates listed in the following: Fi w - freshwater flow rate ( ∀i ∈ I ); Fi proc =
¦ F j ,i + Fi w - flow rate of
∀j∈I , j ≠ i
inlet stream to process that combines freshwater and wastewater streams from other processes ( F j ,i ). The model of water using process is given by (1).
(
)
in ½ Li ,c = Fi proc C iout ,c − C i , c °° C iin,c ≤ C iin,c, max ¾∀i ∈ I , ∀ c ∈ C ° out , max C iout °¿ , c ≤ C i ,c
(1)
Nonlinearity in (1) is caused by bi-linear terms: flow rate multiplied by concentrations. In consequence, such bi-linear terms are also in superstructure optimization model. Due to space limitation we will not address the detailed model. The reader is referred to many journal papers. Instead two crucial bilinear equations of the superstructure model are presented here: component mass balances for mixers with inequality limit on concentration (2) and component mass balances (3) for arrangement: mixer-processsplitter. Notice, that other equations in the model are linear. proc ⋅ C iin,c, max ; ∀i ∈ I , ∀c ∈ C ¦ F j ,i ⋅ C out j ,c ≤ Fi
∀j∈I , j ≠ i
(2)
A Single Stage Approach for Designing Water Networks with Multiple Contaminants
Li ,c = Fi proc ⋅ Ciout ,c −
721
¦ F j ,i ⋅ C out j ,c ; ∀i ∈ I , ∀c ∈ C
(3)
∀j∈I , j ≠i
The optimality conditions of Savelski and Bagajewicz (2003) suggest using the maximal concentrations at process inlet and outlet. Then, model (1) becomes linear for single contaminant. In consequence, superstructure model becomes linear, too. In case of multiple contaminants the upper limits on concentration are usually reached by only one pollutant called “key” contaminant. To deal with this problem Bagajewicz et al. (1999, 2000) applied sequentially created maximum reuse structure, which ensures linear models of each process in this structure. To generate the structure a division into two types of processes were used: head processes that uses freshwater only and wastewater processes that can use additionally wastewater from some other processes. The method of linearization of mass balance for the process in (1) is illustrated in details since we applied basically similar concepts. The models are presented in the following, first for head processes (4a,b) and, then, for wastewater processes (5). , head Li ,c = Fi proc ⋅ C iout ; ∀i ∈ I , ∀ c ∈ C ,c
Li ,c
, head C iout = ,c
max(
Li , k , max C iout ,k
(
; ∀c ∈ C , ∀i ∈ I
(4a)
(4b)
, ∀k ∈ C )
)
in Li ,c = Fi proc ⋅ C iout ,c − C i,c ; ∀i ∈ I , ∀ c ∈ C
(5)
, head It is important to note that outlet concentrations from head processes ( C iout ) can be ,c
determined analytically from (4b) while those for wastewater ones ( C out j ,c ) have to be calculated sequentially by optimization when maximum reuse structure is generated. Parameter C iin,c denotes the concentration of inlet combined stream to wastewater process i in the superstructure - this value is calculated in tree-searching procedure. The generation process of maximum reuse structure requires tree search enumeration to provide all possible maximum reuse structures. The novelty of our approach is the elimination of tree search. Basic concepts and techniques are explained in next section.
3. Method overview 3.1. Basis of the approach We have also applied identical types of processes as Bagajewicz et al. (1999, 2000) did. To explain the basis of the mechanism of linearizing model (1) and overall superstructure model in consequence, we will employ here a simple illustrative example with two processes (i=1, 2) such that: • i = 1 – head process, for which outlet concentrations were calculated analytically from (4b), • i = 2 – wastewater process, for which we can only estimate outlet concentrations. As the basic approximation we used, following Savelski et al. (2003), parameters from the data, i.e. maximal values C iout , max . We found that
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this estimation works well though some extensions may produce slightly better results for large-scale cases – they will be mentioned in the following. In addition, we assumed, following also Savelski et al. (2003) that the inlet concentrations for wastewater processes are set at their maximum values C iin,c,max . Notice that the models for both types of processes become linear. Because the outlet and inlet concentrations in wastewater processes are only approximations it is necessary to relax the equality in process model (1) into linear inequality (6). Notice that inequality (6) is met for the key contaminant as equality in optimal solution (optimal in regards to freshwater usage).
(
)
, max L2,c ≤ F2proc C 2out − C 2in,c,max ; ∀c ∈ C ,c
(6)
Note that nonlinear equations (2), (3) from the superstructure model become linear, too. These two models for two types of processes: (4a,b) for head processes and (6) for wastewater ones, have been embedded into single framework of generalized water using process within the superstructure. We developed novel logical conditions that are explained in the following. It is of importance that it is unnecessary in our approach to know whether certain water using process is the head process or the wastewater process. This eliminates the necessity of using maximum reuse structure. Linear superstructure model can be solved directly. First, however, binary variables are defined as follows:
Yi =
{
1− if i is head process 0 − if not
Next the following conditions are included:
( (C (C
½ ) ° ) ≥ CONST ⋅ (Y − 1) °¾∀i = 1, 2, ∀c ∈ C ) ≤ CONST ⋅ (Y )°°¿ −C
, head ≤ CONST ⋅ (1 − Yi ) Li ,c − Fi proc C iout ,c
Li ,c − Fi proc Li ,c − Fi proc
out , head i ,c out , max i ,c
i
in , max i ,c
(7)
i
where CONST is sufficiently large number. The conditions ensure selection of appropriate model for head or wastewater process, i.e. optimization chooses head or wastewater process from the generalized model. Identical conditions are applied to nonlinear equations (2) and (3) causing the whole model to be linear. Notice that the conditions require smaller number of variables (in fact only one binary for one water using process) than standard conditions for coding alternatives – see e.g. monograph by Biegler et al. (1997). Due to this the superstructure optimization model has also small number of binaries. One can apply additional binary variables to account for structural issues such as reduction of the number of connections since the model will still contain moderate number of binaries. It is also of importance that this approach accounts for case of no head process or multiple head processes what may cause difficulties in the method of Bagajewicz et al. (1999, 2000). In this short paper we addressed only the foundation of the approach in some detail. As we mentioned in the preceding the approximation of outlet concentrations by the maximal values given in the data may cause local optimum results in larger scale problems. Thus, we have developed additional alternative for outlet concentrations of contaminants. This requires new binary variable, but still the number of binaries is kept
A Single Stage Approach for Designing Water Networks with Multiple Contaminants
723
in reasonable limits. Finally, the approach contains correction of estimates on concentrations. It is worth noting that the approach allows including such features as: • Multiple freshwater sources • Constraints on network structure such as forbidden or must-be connections • Process model changes such as water gains and/or losses, self-recycles around processes
4. Example Here we present one example taken from Bagajewicz et al. (2000). This is sufficiently large problem with 8 processes and 4 contaminants. The objective was to minimize the freshwater consumption. No additional constraints on structure were accounted for. The data are gathered in Table 1. The final network is defined by parameters in Table 2. The solution from our method has goal function of 160.67 while the best result from Bagajewicz et al. (2000) is equal to 162.59. The approach was tested against many cases from literature. Among others there was a problem with 15 processes and 6 contaminants – the largest we have found in the literature. In all cases we reached the best results from literature or even better ones with CPU of order a few minutes for larger cases. Table 1 Data for the example according to Bagajewicz et al. (2000) Process 1
2
3
4
5
6
7
8
Contaminant
Inlet concentration
Outlet concentration
Mass load
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
300 50 5000 1500 10 1 0 0 10 1 0 0 100 200 50 1000 100 200 50 1000 85 200 300 200 1000 1000 150 200 800 1200 150 200
500 500 11000 3000 200 4000 500 1000 1000 3500 2000 3500 400 6000 2000 3500 350 6000 1800 3500 350 1800 6500 1000 9500 6500 450 400 9500 6500 450 400
0.18 1.20 0.75 0.10 3.61 100 0.25 0.80 0.60 30 1.50 1 2 60 0.80 1 3 3 1.90 2.10 3.80 45 1.10 2 120 480 1.50 0 140 220 1.20 0
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Table 2 Solution for the example
1 2 3 4 5 6 7 8
1
2
3
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Flow rates process-process 4 5 6 7
8
0 0.65 0 0 0 0 0 0
0,9 5,35 7,99 0 0 0 0 0
0.08 0 0.58 0 0 0 0 0
0 0 0 0 0 0 0 0
1.42 10.40 0 0 0 25 0 0
Freshwater flow rates to processes: 3 4 5 6 7 2.4 25 8.57 9.69 12.28 25 50.46 Wastewater from processes to treatment: 1 2 3 4 5 6 7 8 1
0
2
8.61
0
10.35
12.93
0 87.27
8 27.27
41.51
5. Summary Robust and efficient design method has been developed for wastewater reuse network synthesis. It is simultaneous approach that requires the solution of linear optimization model. Due to small number of binary variables the solution of MILP model makes no problem even for large-scale industrial problems. Additionally, it can be extended for water network with reuse and regeneration. The method, which embeds simultaneous heat integration, has been developed on the basis of this technique (paper under preparation). Due to some heuristic elements the approach does not guarantee the global optimum. However, for all literature examples, we reached the best results published to date or even a bit better solutions.
References Alva-Argaez A., A. Kokossis and R. Smith. 2007. The design of water-using systems in petroleum refining using a water-pinch decomposition. Chem. Eng. J. 128:33-46 Bagajewicz, M. 2000. A review of recent design procedures for water networks in refineries and process plants. Comput. Chem. Eng. (24): 2093-2113 Bagajewicz, M.J., Rivas, M. and Savelski, M.J. 1999. A new approach to the design of water utilization systems with multiple contaminats in process plants. Presented at the 1999 AICHE national Meeting, Dallas Bagajewicz, M.J., Rivas, M. and Savelski, M.J. 2000. A robust method to obtain optimal and suboptimal design and retrofit solutions of water utilization systems with multiple contaminats in process plants. Comput. Chem. Eng, (24): 1461-1466 Biegler, L.T., Grossmann, I.E. and Westerberg, A.W. 1997. Systematic Methods of Chemical Process Design. New Jersey: Prentice Hall PTR Cao K., X. Feng and H. Ma. 2007. Pinch multi-agent genetic algorithm for optimizing waterusing networks. Comput. Chem. Eng., 31: 1565-1575 Gunaratnam M., A.Alva-Argaez, A. Kokossis, J-K. Kim and R. Smith. 2005. Automated Design of Total water Systems. Ind. Eng. Chem. Res. 44: 588-599 Lee, S. and Grossmann, I.E. 2003. Global optimization of nonlinear generalized disjunctive programming with bilinear equality constraints: applications to process networks. Comput. Chem. Eng. 27:1557-1575 Prakash, R. and Shenoy, U.V. 2005. Targeting and design of water networks for fixed flowrate and fixed contaminant load operations. Chem. Eng. Sci. 60: 255-268. Savelski, M.J. and Bagajewicz, M.J. 2003. On the necessary conditions of optimality of water utilization systems in process plants with multiple contaminants. Chem. Eng Sci. 58 (23-24): 5349-5362
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Multiscale molecular modeling: a tool for the design of nano structured materials Maurizio Fermeglia
Abstract Atomistic –based simulations such as molecular mechanics (MM), molecular dynamics (MD), and Monte Carlo-based methods (MC) have come into wide use for material design. Using these atomistic simulation tools, we can analyze molecular structure on the scale of 0.1-10 nm. However, difficulty arises concerning limitations of the timeand length-scale involved in the simulation. Although a possible molecular structure can be simulated by the atom-based simulations, its is less realistic to predict the mesoscopic structure defined on the scale of 100-1000 nm, for example the morphology of polymer blends and composites, which often dominates actual material properties. For the morphology on these scales, mesoscopic simulations such as the dynamic mean field density functional theory (Mesodyn) and dissipative particle dynamics (DPD) are available as alternatives to atomistic simulations. It is therefore inevitable to adopt a mesoscopic simulation technique and bridge the gap between atomistic and mesoscopic simulations for an effective material design. Furthermore, it is possible to transfer the simulated mesoscopic structure to finite elements modeling tools (FEM) for calculating macroscopic properties for the systems of interest. In this presentation, a hierarchical procedure for bridging the gap between atomistic and macroscopic (FEM) modeling passing through mesoscopic simulations will be presented and discussed. The concept of multiscale (or many scale) modeling will be outlined, and examples of applications of single scale and multiscale procedures for nanostructured systems of industrial interest will be presented. In particular the following industrial applications will be considered: (i) polymerorganoclay nanocomposites for the estimation of the binding energy and basal spacing of a montmorillonite – polymer – surface modifier system; (ii) mesoscale simulation for diblock copolymers with dispersion of nanoparticels; (iii) polymer - carbon nanotubes system and (iv) applications of multiscale modeling for process systems engineering.
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Energy-preserving method for spatial discretization: application to an adsorption column. Ahmed Baaiu, Françoise Couenne, Laurent Lefevre, Yann Le Gorrec Université of Lyon 1, CNRS UMR 5007, Laboratoire d’Automatique et de Génie des Procédés, Villeurbanne, F-69622, France,
[email protected] Abstract This paper deals with the spatial discretization of distributed parameter systems. The originality of the proposed approach is to combine geometrical modelling and finite element discretization method to preserve the model structure associated with both mass and energy balances during the spatial reduction. The approach is presented through the example of an adsorption process. The methodology is described on the microporous phase. Keywords: spatial discretization, infinite dimensional systems, adsorption process, thermodynamic systems, port-based modeling.
1. Introduction The aim of this paper is to present a method for spatial discretization of distributed parameters systems. The originality of this work is the use of Port Based Modeling (PBM) approach for both process modeling and discretization (Karnopp 2000). Let us recall that the power of PBM is that interconnection is done in a natural way as soon as port variables are chosen as power conjugate variables like in thermodynamics (De Groot and Mazur 1984). Moreover, models of systems are manipulated as a set of interconnected and reusable sub-models whose basic elements are accumulation element, dissipation element and power preserving interconnection structure. The structure issued from PBM (see for instance Couenne et al. (2006), Couenne et al. (2007) ) is used in order to characterize the energetic behavior of the system and as a basis of our discretization mixed finite element method. The final goal of this method is by an appropriate choice of power conjugate variables to preserve during the discretization stage the energy balances as well as the structural properties of the distributed model in terms of energy. In this way the method guarantees the easy interconnection of the discretized model (Couenne et al. 2007) and its reusability. This preservation of structure is important for control purpose since we now possess a reduced model which allows a direct use of the geometric and thermodynamics properties of the PDEs model to develop control algorithms. As an example, passivity based or energy-shaping techniques can be applied (Ortega et al. 2002) for stabilization and regulation purposes on such a model. As an example we will treat the case of an adsorption column with bidisperse pellets based on Maxwell Stefan formulation of diffusion (Krishna 1990). The column is mathematically described by a set of interconnected Partial Differential Equations (PDE's). Traditional modeling of such system does not take into account any structure of the constitutive equations and the choice of the state variables can lead to numerical difficulties, especially during the interconnection of the different levels. The partial
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model (microporous phase) is presented in Couenne et al. (2005). The complete port based model of the column is given in Baaiu et al (2006). In this paper we focuse to the microporous phase modeling and discretization. The modelling and reduction of the other phases will be obtained with the same methodology as it will be seen.
2. Basis of the structured modelling of an adsorption column Let first recall all the assumptions we made over the entire column: 1. We consider an ideal binary mixture constituted of an inert gas and one component that can be adsorbed. 2. The adsorption column is supposed to be at constant temperature and pressure. The velocity v of the flowing fluid is also supposed to be constant. 3. The diffusion onto the surface of the crystal and the diffusion into the macropore volume are represented by using the Knudsen/Maxwell-Stefan formulation (Krishna 1997) . This choice is adequate since flux is expressed thanks to the thermodynamic chemical potential. The Langmuir model for the adsorption equilibrium is used. 4. In the extragranular phase, a dispersion phenomenon is taken into account. It is represented with a constant axial dispersion coefficient D . 5. The column is supposed to be cylindrical with constant cross section. The particles and the crystals are supposed to be spherical with uniform radius. Spherical symmetries are supposed both in the macropore phase and in the adsorbent. As mentioned modelling and discretization methods have been applied to the each phase of the column. From the assumptions each level leads to a 1D model. Let us now review in details the port based model for the microporous scale only. Remarks about the other phases will be made along the section. 2.1. Modelling of the microporous scale From a mathematical point of view, we use the framework of differential geometry (Flanders 1989) to obtain a coordinate free model of the considered process. In this framework d is the exterior derivative (in the general case it is the div or gradient; in catesian 1D it reduces to
w ). The general balance equation for species i is given by: wr
wqi
³ wt ³ d ( N )
(1)
i
:
:
With the concentration qi , the diffusive molar flux N i . : represents the 1D domain
[0, R] , R being the mean radius of the crystals. Since the proposed discretization method must preserve the structure associated with both mass and energy balances, the choice of the manipulated variables must concern mass and energy. In order to obtain the right power conjugate variables, let us write the (Gibbs free) energy density g balance:
d g dt :³
³ ¦ d ( N )P i
: i
i
(2)
Energy-Preserving Method for Spatial Discretization
Pi
with
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wg the chemical potential of species i. Applying Stoke’s theorem to wq
equation (2), its finally results (Couenne et al. 2005):
³P
T
N
w:
³ dP
T
:
N ³ P T dN
(3)
:
with standard vectorial notation. w: ^0, R` and dP corresponds to grad P . Equation (3) expresses the power continuity between internal power variation and the power flow at boundaries. Moreover it imposes the choice of the manipulated power conjugate variables P , dN and dP , N . It makes appear the geometric structure representative of the infinite dimensional mass balance,
§ dN · ¨¨ ¸¸ © dP ¹
§ 0 d ·§ P · ¨¨ ¸¸¨¨ ¸¸ © d 0 ¹© N ¹
(4)
which is with the appropriate boundary pairing
P
N 0 and P
N R a Dirac
structure (Maschke and van der Schaft 2004). The originality of our approach is to use this geometric power conserving structure for the modelling of dissipative systems. This is the price to pay to interconnect easily systems (Maschke and van der Schaft 2004). To summarize, the aforementioned power preserving structure represents the interconnection between the storage, dissipative and boundary parts of the model. It combines two adjoint differential relations, namely the generating force as the gradient of the chemical potential and the conservation law (1) by the divergence of the flux. Moreover it is the central element of the structured modelling of mass transport phenomena. It will appear at each phase of the model. This model has to be completed with two closure equations between effort and flux variables related with accumulation and dissipation terms. The resulting structured model is depicted on Figure1. This model is valid for the microporous level but also for the other level. The element C is related to the accumulation and represents the left hand side of equation (1).
q can be computed from dN and Fdistr by time integration (this is done
to homogeneous P thank to the local equilibrium thermodynamic condition) and from q using the thermodynamic constitutive equation (first closure equation).
P
Remark: In the case of the microporous phase, the distributed flow Fdistr =0. It is not the case for the other levels. For example, in the extragranular level, Fdistr corresponds to the total flow coming from all the crystals present in the macroporous sub domain.
P0
C
P
P Fdistr
P
0 wq wt
N0 dP
D
N
dN
PR
dP
0 NR
N dissip
dP
N conv
1
dP N dissip
R
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Fig 1: Structured representation of the transport phenomena.
The element R is related to the dissipation (diffusion or dispersion). The flux N dissip is computed from the driving force dP using the second phenomenological law. The element D is the power preserving structure described by equation (4). The power continuous junctions 0 and 1 express the continuity of flow variables (extensive variables) and effort (intensive variables) respectively. Remark: It can be seen that in the extragranular phase the convective flux N conv has be added between the elements D and R ( N
N dissip N conv ).
2.2. Interconnection of the level The assumption for the interconnection of phases is that the crystal repartition into the pellets is uniform as well as the pellet repartition within the column. Furthermore all the boundaries of the considered level are at local equilibrium with variables of the upper level. Considering spherical symmetry, the crystals have the same chemical potential than the pellet. This means that there is an equality of efforts at the boundary. Continuity of flux at the boundary of the crystal is also considered. As a consequence, the flux coming from all the crystals present in the sub domain can be seen as a distributed source of flux for the pellet. It can be shown that these relations define a power continuous coupling between the levels (Couenne et al. 2005).
3. Model reduction based on geometrical properties The proposed discretization method consists in splitting the initial structured infinite dimensional model into n finite dimensional sub-models (finite elements) with the same energetic behavior. Structure given in figure 1 is still enforced. 3.1. Approximation of forms For this purpose we consider the local domain
[a, b] [0, R ] . The
Rab
approximation method is based on the separation of variables method. The chosen approximation bases are different according to the degree of the considered differential forms. From the observation of equation (4), P and N are functions (0-form) since
: whereas dP and dN are 1-forms since they For simplicity let us set can be evaluated by integration along : . P d dP and N d dN .
they can be evaluated at any point of
The 1-forms are approximated on ab d
chosen such that and N d (t )
P (r , t )
ab Nd
P dab (t )ZPab (r ) d
ab
and
ab Nd
N (t )Z (r ) where the support 1-forms ZPd (r ) and Z (r ) are
N d (r , t )
ab
Rab by P d (r , t )
³
R ab
³
R ab
ZPab d
³
R ab
Z Nab
d
1 which implies that P dab (t )
³
Rab
P d (t , r )
N d (t , r ) . The 0-form P and N are approximated on Rab by:
P (a, t )ZPa (r ) P (b, t )ZPb (r ) N (r , t )
where the support 0-forms are chosen such that:
N (a, t )Z Na (r ) P (b, t )Z Nb (r )
Energy-Preserving Method for Spatial Discretization
731
ZPa (a) ZPb (b) 1, ZPa (b) ZPb (a) 0, Z Na (a ) Z Nb (b) 1, Z Na (b) Z Nb (a) 0
P (a, t ) P (a, t ) and P (b, t ) P (b, t ) . For simplicity a b we choose the same support 0-forms Z and Z for P and N and the same support ab 1-form Z for P d and N d . This choice is done such that
3.2. Discretization of the interconnection structure The interconnection structure of each submodel is finite dimensional and concerns the
Pd
reduced variables N d and
and their power conjugate variables
P
and N . In
order to have a finite dimensional power preserving structure, the reduced variables have to satisfy (Golo et al. 2004):
E P ab
N ab
>
@
Pwa
Pwb F P dab T
T
N dab
N wa
N wb
T
0
(5)
T
with E F full rank and EF FE 0. For this purpose, we require that the approximation variables satisfy the relation induced by the interconnection structure (4). It leads to the following relations between the approximated variables with
D ab
b
³Z Z
ab
R ab
:
N dab N (b) N (a ) N wb N wa ® ab P (b) P (a ) Pwb Pwa ¯ Pd
(6)
and
° N ab (1 D ab ) N (a ) D ab N (b) (1 D ab ) N wa D ab N wb ® ab (1 D ab ) P (b) D ab P (a) (1 D ab ) Pwb D ab Pwa °¯ P
(7)
Equations (7) are obtained from the net power expressed with approximate variables. We have 8 variables and 4 equations but two are input variables. So we have to characterize two relations consisting in the discretized version of the constitutive relations. 3.3. Discretization of the diffusion equation The purpose of this section is to compute N
ab
ab
structure of the element R is preserved: GR
from the driving force such that energy
P dab N ab
³P
d
N .
R ab
The diffusion represented by Knudsen law can be written as 1-form
f on 1D domain, it can be written f
N
D*q * P d . For a RT
wf dr and the Hodge star operator * wr
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wf . Writing the instantaneous power of this element with wr wGRab ab approximate variables and after identification N 2 K ab RP dab with wP dab D*q K ab ³ Z ab * Z ab depending on support forms and R . Rab RT represents the function *
f
3.4. Discretization of the accumulation The principle is the same than for the R element. The purpose is to compute
q . The approximate energy on Rab of the C element is GCab
P ab from
³ q P . Let us note that
R ab
q lies in the same space than the flow variable q as well as the linear saturation concentration qs appearing in the Langmuir model so the same support
the linear concentration
function can be used. We finally obtain for the discretized chemical potential
P ab (t ) :
wGCab wq ab
P ref (T , P) RT ln(
q ab 1 ) P k (qsab q ab )
Using the same procedure, the other level are also discretized. Mainly only constitutive relations of accumulation and dissipation are changed. Finally the coupling of the different levels is performed.
4. Conclusion In this paper we present a discretization method which preserves both the nature of the interconnection structures and the physical properties of the connected elements. We apply this method with the simplest support forms
Za
br b and Z ba
Z ab
1 dr , ba
ra . Numerical results are presented in (Baaiu 2006). ba
This choice of forms leads to a centered method. The quality of numerical results can be compared advantageously to those obtained with a left finite difference method. References Couenne F., Jallut C., Maschke B., Breedveld P. C., Tayakout M., 2006, Mathematical and Computer Modelling of Dynamical Systems, 12(2-3), 159-174. Couenne F., Jallut C., Maschke B., Tayakout M., Breedveld P., Available online 22 April 2007, Computers & Chemical Engineering. Baaiu A., F. Couenne F., Le Gorrec Y., Lefèvre L., Tayakout-Fayolle M., 2006, Preprint 5th International Conference on Mathematical Modelling MATHMOD, Vienna, Austria. Couenne F., Eberard D., Lefèvre L., Jallut C., Maschke B. , 2005, ESCAPE 15. De Groot S. R., Mazur P. , 1984, Non-equilibrium thermodynamics, Dover. Krishna R., Wesselingh J.A., 1997, Chem. Eng. Science, 52: 861-911. Karnopp D., Margolis D., Rosenberg R.. John Wiley and Sons, New York, 2000. Golo G., Talasila V., Van der Shaft A., Maschke B., 2004, Automatica, 40 :757-771. Ortega R., van der Schaft A., B. Maschke B., Escobar G., 2002, Automatica 38 (4) : 585–596.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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MEXA goes CAMD – Computer-Aided Molecular Design for Physical Property Model Building André Bardowa, Sven Kossackb, Ernesto Kriestenb, Wolfgang Marquardtb a
Process & Energy Department, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands b Aachener Verfahrenstechnik, Templergraben 55, RWTH Aachen University, 52056 Aachen, Germany
Abstract The development of physical property models is an ongoing challenge in chemical engineering. It usually requires both theoretical insight as well as experiments to test and validate the models. Model-based experimental analysis (MEXA) provides a work process for such developments integrating systems tools and experiments. Optimal experimental design is here a key step. In physical property model development, the choice of the optimal test mixture itself is crucial but usually not systematically addressed. For a rational solution to this problem, recent methods for computer-aided molecular design (CAMD) are integrated into the MEXA work process. Thereby, a targeted and efficient approach for physical property model development is achieved. The approach is exemplified for the prediction of multicomponent diffusion in liquids. Keywords: optimal experimental design, computer-aided molecular design, model identification
1. Introduction Modeling in chemical engineering relies on ever better physical property predictions. Ab initio prediction methods are promising but still limited to the simplest cases. Even then, experimental validation is required to test models and methods. In such tests, model-based methods for optimal experimental design (OED) [1] should be employed in order to make best use of experimental resources. OED methods find the best settings for the experimental degrees of freedom for the question of interest. Typically, the degrees of freedom considered are limited to flow rates, temperatures, and the like. In the development of predictive models for physical properties, model discrimination and validation are critical steps [2]. In this work, a rational framework is proposed to identify the components and mixtures that allow for optimal model discrimination and validation. By selection of the right mixtures to test, a targeted and more efficient approach towards predictive models for physical properties becomes viable. For this purpose, methods from computer-aided molecular design (CAMD) [3] are employed. In CAMD, candidate molecule structures are computer-generated for a specific task. Major applications have been process and product design, in particular solvent selection. Here, it is shown how to integrate CAMD methods into the framework of model-based experimental analysis (MEXA) [4]. Suitable problem formulations are explored and discussed. As the prediction of kinetic coefficients in mixtures is particularly challenging, the new framework is exemplified for the study of multicomponent diffusion coefficients.
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2. Framework 2.1. Physical property modeling For illustration, the physical property models considered in this work are indirect property models. Here, the desired physical property ξ is not directly predicted from molecular structure but correlated via other intermediate physical propertiesψ, i.e.,
ξ = f( p, T, ψ(M,p,T), M , θ),
(1)
where θ collects constant coefficients and M captures the chosen test substances and the mixture composition. The most prominent example of this model class are mixing rules where a mixture property is predicted from pure component data. Many other physical property models fall also into this class [5]. Below, the Wilke-Chang equation [6] is considered which correlates diffusion to viscosity. Heat transfer correlations etc. are also of the given form. 2.2. MEXA for physical property model development For the efficient use of experimental resources, a systematic approach should be followed. Model-based methods can lead to significant reductions of experimental effort. The MEXA work process therefore integrates systems tools into the experimental protocol [4]. The major steps in the procedure are common to all work processes for model-based experimentation (e.g., [2]): • A mathematical model (or several candidates) is proposed. • Free variables of the experiment are optimized in model-based experimental design. • The experiment itself is carried out and measurement data are collected. • Inverse problems are solved to analyze and interpret the experimental data. For the problem of physical property model development, this generic work process can be adapted (see Figure 1). While also starting from a priori knowledge and intuition, the developed mathematical model consists of two specific elements in this case: • the description of the experiment itself; • the physical property model candidate(s) to be tested.
Figure 1: MEXA work process for physical property model development integrating CAMD.
The experiment has a number of design settings d to be chosen. The physical property model output depends on the fluid(s) chosen, summarized here as mixture M. The
MEXA goes CAMD
735
mixture M itself is now introduced as a new degree of freedom in OED. This requires adaptation of the tools employed in the experimental design step as outlined next. 2.3. Optimal experimental design In optimal experimental design, the free variables of the experiment are chosen such that the maximum information with respect to the goal of the investigation can be collected. The two tasks typically encountered in model development are [2]: • Model discrimination to find the suitable model structure; • Estimation of parameters in a given model structure. While the concepts developed here are applicable in both cases, we limit the following discussion to model discrimination (MD). Based on a set of candidate models f (i), the goal is then to find an experiment that allows best to identify the correct model. Here, the criterion suggested by Buzzi-Ferraris and Forzatti [7] is employed M
max φ MD = max ¦ d ,ψ
d ,ψ
¦ (y
T
M
m =1 m '= m +1
(m)
)
− y ( m ') S m ,m '
−1
(y
(m)
)
− y ( m ') ,
(2 )
where y(i) is the measurement predicted by model i and the matrices S are defined by
S m , m ' = 2V + W m + W m ' ,
(
)
(
and W m = ∂y ( m ) ∂θ ( m ) Vθ ( m ) ∂y ( m ) ∂θ ( m )
)
T
.
The matrix Wm quantifies the prediction uncertainty in y according to the current parameter covariance matrix Vθ ( m ) . V is the measurement error matrix. The criterion thus places measurements at the conditions where the measurement predictions differ most. Since the objective (2) is related to a t-test, the models are expected to be discriminable if the objective function value exceeds the number of measurements [7]. The considered design variables d usually are temperature, pressure, sampling times, compositions etc. The constituents of the test mixtures have so far not been considered as design variable due to the resulting problem complexity. Here, we follow a two step procedure to address this problem. First, optimal intermediate properties ȥ are determined in the OED problem by adding them to the list of continuous design variables (cf. Eq. (2)). In step two, the optimized values for these properties are used as targets for a CAMD analysis to identify suitable components. 2.4. Computer-aided molecular design Computer-aided molecular design (CAMD) is a systematic tool to find components with desired pure component or mixture properties [3]. CAMD can be interpreted as the inverse of the property prediction problem: Given a set of target properties - obtained here from the optimal experimental design problem (2) – a combination of structural groups is sought that satisfies the property specifications. In this case study, the generate-and-test approach is employed. This CAMD approach consists of three basic steps [8]: • Pre-Design: Define the problem in terms of desired properties of the compound to be designed. • Design: Run the actual CAMD design algorithm to generate compounds and test them against stated criteria from the pre-design stage. • Post-Design: Test the results based on properties that are not easily screened during stage two, such as environmental and safety criteria. For a more detailed discussion, the reader is referred to [8]. Using the extended experimental design problem formulation discussed in Section 2.3, the described CAMD approach thus directly integrates into the MEXA work process (cf. Figure 1). Thereby, the optimal selection of test mixtures can be achieved.
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3. Case study: Prediction of multicomponent diffusion 3.1. Problem formulation The proposed framework is applied to a model discrimination problem for diffusion in liquids. NMR measurements are used to discriminate between five mixing rules that combine binary diffusivities at infinite dilution to predict multicomponent MaxwellStefan diffusion coefficients. In light of the previous classification, the problem formulation consists of the following parts: • Experiment model consisting of: a relation between measured NMR signal intensity and the self-diffusion coefficients as well as intermediate models to relate self- to Maxwell-Stefan (MS) diffusivities and the generalized Vignes correlation for prediction of MS diffusivities. This model needs as input the binary MS diffusion coefficient Dijx →1 between species i,j infinitely diluted in species k. k
• Five candidate physical property models for predicting diffusivity ξ= Dijx →1 based on available binary data ψ= { Dik0 , Dki0 , D 0jk , Dkj0 , Dij0 , D 0ji }. k
The physical property Dijx →1 is very difficult to measure. Its prediction is therefore the problem of interest. A detailed description of the problem formulation is given in [9]. The goal is to perform experiments in a ternary mixture to discriminate between the physical property model candidates. Each component will be diluted in one experiment, i.e., 3 measurements are taken. For the purpose of illustration, the components Toluene (1) and Cyclohexane (2) have been preselected. The remaining design questions are: • Which compound should be employed as third component (3)? • At which composition should be measured? While the latter question is classical in OED [9], the first question is difficult to answer directly using standard methods. k
3.2. OED-CAMD solution strategy In the proposed approach, intermediate physical properties ψ are added to the design variables considered in the OED problem. In the present example, this amounts to the infinite dilution diffusivities with the target compound, i.e., ψ= { D130 , D310 , D230 , D320 }. To employ CAMD methods, a group-contribution-based prediction method for ψ is required. Here, we employ the Wilke-Chang equation for the diffusion coefficients [6]:
Díj0 = 1.1728 × 10−16
(φ j M j )1 / 2 T
η j (θiVbi )0.6
,
(3 )
where φi, θj are correction factors which are assumed to be constant in this work, Mj is the molar weight, ηi the viscosity and Vbi the molar volume at the boiling point. The latter two properties are obtained from group-contribution methods in the CAMD step as described below. As the properties M,η, Vb are known for the preselected components (1) and (2), all four intermediate properties ψ= { D130 , D310 , D230 , D320 } are determined once the molar volume Vb3 and the ratio molar weight over viscosity (M31/2/η3) are specified,. In order to optimize the true target properties, Eq. (3) is therefore added to the design problem. The reduced set of additional design variables that need to be considered thus are ψ={( M31/2/η3), Vb3}. 3.2.1. Molecular target from OED The optimal experimental design problem (2) for discrimination between the five model candidates is solved with the design variables mixture composition and ψ={( M31/2/η3),
MEXA goes CAMD
737
Vb3}. Figure 2 shows the objective as a function of the free intermediate physical properties ψ. It can be seen that the molar volume has a minor influence on the model discrimination capacity. For the ratio (M31/2/η3), high values lead to major improvements. The model discrimination problem therefore yields the CAMD target of finding a component that maximizes this ratio.
Figure 2: Model discrimination objective in physically relevant range of CAMD target properties.
3.2.2. CAMD solution In the pre-design step, the desired and the undesired properties of the new molecules are specified as targets for the generation algorithm. In the present case, the target value is a high ratio between the square root of the molecular weight and the liquid viscosity (Section 3.2.1). Other constraints are the boiling temperature above 50°C, a restriction to non-aromatic hydrocarbons that may contain oxygen and a limitation of molecule size to 6 functional groups. All these constraints can be specified in ICAS [8], a software package that can readily be used for CAMD applications. Given the targets from the pre-design phase, feasible molecules are generated in the design step. The algorithm solves a number of sub-problems of increasing complexity [8]. In the post-design phase, the generated alternatives are ranked and tested. Here, we require that only alternatives included in the DIPPR database are analyzed further. 3.3. Results and Discussion In Table 1, the results of the CAMD algorithm of ICAS are shown. The three topranked molecules after the post-design step, their predicted physical properties and the final model discrimination (MD) objective are given. Table 1: Results of the CAMD algorithm Generate-and-Test (ICAS ProCAMD) Component name
M (g/mol)
Ș (cP)
Vm (cm³/mol)
MD objective
3-methyl-cyclopentene methyl-cyclopentane cyclohexene
82.14 84.16 82.14
0.27 0.41 0.54
119.57 120.69 108.04
129.14 46.0 21.9
All suggested molecules are expected to allow for model discrimination as the objective exceeds the number of measurements. In addition, the results of the combined MEXACAMD approach clearly show that the optimal choice of the chemical component has a
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strong impact on the ability to discriminate between different diffusion models. Objective function values for the top-ranked molecules already range from 21.9 for cyclohexene up to 129.14 for 3-methyl-cyclopentene. As the objective scales with the number of experiments, 6 times more experiments would be required to obtain the same confidence in model discrimination in case cyclohexene is used as compared to 3methyl-cyclopentene. Without a model-based selection strategy, even poorer candidates might have been chosen. Consequently, the use of a systematic selection of a test mixture by the suggested MEXA-CAMD approach seems mandatory to save time and experimental expenses.
4. Conclusions In this work, a novel experimental design approach for the optimal choice of a test mixture to enhance the ability to discriminate between competing physical property models is presented. In a two-step procedure, first characteristic optimal intermediate properties are determined as continuous design variables by model-based experimental design. In step two, these are defined as target properties for a CAMD analysis to get suitable mixtures. The significant potential of this approach is exemplified in the case study. Through the optimal choice of the test mixture the experimental effort can be reduced by orders of magnitude. As the proposed method extends beyond the considered problem class, the systematic selection of test mixtures should now be added to the list of design variables in model-based experimental analysis.
Acknowledgements The authors thank R. Gani for providing the ICAS ProCAMD software. Financial support of CRC 540 by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.
References 1. E. Walter, L. Pronzato, Qualitative and quantitative experiment design for phenomenological models - A survey, Automatica, 26 (1990) 195-213. 2. S.P. Asprey, S. Macchietto, Statistical tools for optimal dynamic model building, Comp. Chem. Eng., 24 (2000) 1261-1267. 3. R. Gani, L.E.K. Achenie, V. Venkatasubramanian, Introduction to CAMD. In: L.E.K. Achenie, R. Gani and V. Venkatasubramanian: Computer Aided Molecular Design: Theory and Practice, Elsevier, Amsterdam, 2003. 4. W. Marquardt, Model-based experimental analysis of kinetic phenomena in multi-phase reactive systems, Chem. Eng. Res. Des., 83 (2005) 561-573. 5. R.C. Reid, J.M. Prausnitz, B.E. Poling, The properties of gases and liquids. 4th edition. McGraw-Hill, New York, 1987. 6. C.R. Wilke, P. Chang, Correlation of diffusion coefficients in dilute solutions. AIChE J. 1 (1955) 264-270. 7. G. Buzzi-Ferraris, P. Forzatti, A new sequential experimental-design procedure for discriminating among rival models, Chem. Eng. Sci., 38 (1983), 225:232. 8. P.M. Harper, R. Gani, A multi-step and multi-level approach for computer aided molecular design. Comput. Chem. Eng., 24 (2000) 677-683. 9. A. Bardow, S. Kossack, E. Kriesten, M.A. Voda, F. Casanova, B. Blümich, W. Marquardt. Prediction of multicomponent diffusion in liquids: Model discrimination using NMR data. In preparation, 2007. 10. A.C. Atkinson, Beyond response surfaces – recent developments in optimum experimental design, Chemometr. Intell. Lab. 28 (1995) 35-47.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Modeling the Phase Equilibria of Nitriles by the soft-SAFT Equation of State Abdelkrim Belkadia, Mohamed K. Hadj-Kalia, Vincent Gerbauda, Xavier Jouliaa, Fèlix Llovellb, Lourdes F. Vegab,c,d a
Université de Toulouse, LGC (Laboratoire de Génie Chimique), CNRS, INP, UPS, BP 1301, 5 rue Paulin Talabot, F-31106 Toulouse Cedex 01, France. b Institut de Ciència de Materials de Barcelona, (ICMAB-CSIC), Consejo Superior de Investigaciones Científicas, Campus de la UAB, Bellaterra, 08193 Barcelona, Spain. c MATGAS Research Center, Campus de la UAB, Bellaterra, 08193 Barcelona, Spain. d Carburos Metálicos-Grup Air Products. C/Aragón 300. 08009 Barcelona, Spain.
Abstract Nitriles are strong polar compounds, and some of them, like acetonitrile (CH3CN) and propionitrile (C2H5CN), play an important role as organic solvents in several industrial processes. There are challenging systems to investigate from the modeling point of view, given the highly non-ideal intermolecular interactions they present. This work deals with results concerning calculations of the vapor - liquid equilibrium (VLE) for nitriles using a modified version of the SAFT Equation of State (EoS): the soft-SAFT EoS, chosen because of its accuracy in modeling associating fluids. In this work, both polar and associating interactions are taken into account in a single association term in the equation. Molecular parameters for acetonitrile, propionitrile and n-butyronitrile (C3H7CN) were regressed from experimental data. Their transferability is tested by the calculation of the VLE of heavier linear nitriles, namely, valeronitrile (C4H9CN) and hexanonitrile (C5H11CN), not included in the fitting procedure. soft-SAFT results are in excellent agreement with experimental data, proving the robustness of the approach. Keywords: soft-SAFT, Nitriles, vapor - liquid equilibrium
1. Introduction In the recent years, the advent of models based on molecular approaches such as the Statistical Associating Fluid Theory (SAFT) [1-2] has opened new possibilities in the modeling of complex molecules. Having a strong statistical mechanics basis, SAFT equations of state have been used to describe a wide variety of compounds, including associating fluids and complex mixtures. Its formulation allows the systematic addition of new terms in order to consider particular physical effects, such as polarity, ring structures, etc. when this is necessary. Accurate thermodynamic properties of pure compounds and mixtures, in particular phase equilibrium properties, are needed over a wide range of temperature and pressure for the optimization of existing processes and the design of new processes and/or materials in chemical industry. Nitriles are industrial solvents and good representative of polar compounds which phase equilibria is not trivial to model with macroscopic thermodynamic models [3]: popular cubic equation of states are suited for the investigation of any pressure condition but poorly applicable to polar molecules. Activity coefficient models handle polar compounds but are valid only at low pressures. Recently, Hadj-Kali et al. [4] used molecular simulation techniques by coupling the
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Gibbs Ensemble Monte Carlo method with a suitable interaction force field to model vapor - liquid equilibrium of such molecules; although this approach is accurate, it requires intensive computational efforts as compared to equation of state models. The approach used in this work concerns the use a molecular based equation of state, namely the soft-SAFT EoS, developed by Blas and Vega [5-6] to investigate the phase behavior of nitriles. Unlike classical PR or SRK equations of state that require molecule properties (critical temperature, critical pressure and acentric factor) to model the PVT properties on compounds, molecular based EoS require to describe the gross chemical structure of molecules in terms of molecular parameters, enabling to find suitable correlations between compounds from the same homologous serie. The present paper is organized as follows: a brief background of the soft-SAFT EoS is exposed. Then, details on former published models and the proposed model are provided. Finally, molecular parameters are regressed for the three lightest nitriles of the linear nitrile family and their transferability is validated for heavier compounds of the same family, in a pure predictive manner.
2. The soft-SAFT approach The soft-SAFT EoS is a variant of the original SAFT equation proposed by Chapman and co-workers [1] and Huang and Radosz [7-8] based on Wertheim’s first order Thermodynamics Perturbation Theory (TPT) [9-10]. Since the SAFT equation and its modifications have been extensively revised elsewhere [11], only the main features of the equation are retained here. SAFT-type equations of state are written in terms of the residual Helmholtz energy:
a res (T , P , N ) = a(T , P , N ) − a id (T , P , N )
(1)
Where a(T,V,N) and aideal(T,V,N) are the total Helmholtz energy per mole and the ideal gas Helmholtz energy per mole at the same temperature and density, respectively. The residual Helmholtz energy is the sum of the microscopic contributions to the total free energy of the fluid, where each term in the equation represents different microscopic contributions to the total free energy of the fluid:
a res = a LJ + a chain + a assoc
(2)
The main difference between the soft-SAFT equation and the original equation [1] is the use of the Lennard–Jones (LJ) intermolecular potential for the reference fluid (with dispersive and repulsive forces into the same term), instead of the perturbation scheme based on a hard-sphere reference fluid plus dispersive contributions to it. This difference also appears in the chain and association term, since both terms use the radial distribution function of the reference fluid. The LJ potential includes a dispersive term in r-6 and a repulsive term in r-12. It exhibits an energy minimum versus the interaction distance and is thus more realistic that the HS + dispersion potential. The accurate LJ EoS of Johnson et al. [12] is used for the reference term. The chain term in the equation comes from Wertheim’s theory, and it is formally identical in the different versions of SAFT. In our case, it is expressed as:
a chain = k BT ¦ xi (1 − mi )ln g LJ
(3)
i
Where ȡ is the molecular density of the fluid, T is the temperature and kB is the Boltzmann constant. In the soft-SAFT case, it is applied to tangent LJ spheres of chain
Modeling the Phase Equilibria of Nitriles by the soft-SAFT Equation of State
741
length m that are computed following the pair correlation function gLJ, evaluated at the bond length ı. The association term comes from the first-order Wertheim’s TPT for associating fluids. The Helmholtz free energy change due to association is calculated from the equation
a assoc = k BT
§
¦ x ¦¨¨© ln X i
α i
α
i
−
X iα ·¸ M i + 2 ¸¹ 2
(4)
Where Mi is the number of associating sites of component i and X iα the mole fraction of component i not bonded at site Į which accounts for the contributions of all associating sites in each species:
X iα =
1
¦x ¦X
1 + N avog ρ
j
j
β α iβ j jΔ
(5)
β
3. Results and discussion 3.1. Modeling nitriles In the comprehensive work of Spuhl et al. [13], acetonitrile (ACN) was modeled by three different schemes: the first considers ACN as a chain of hard spheres, the second as an associative molecule with one associating site on the nitrile contribution CN, and the third one takes into account the dipolar moment of the ACN. Results show that the model which considers the dipolar moment is better than the two others although the associative model also showed good results. Earlier, Jackowski’s experimental studies of the propionitrile by NMR [14] lead to the presumption that self association interactions must be considered in these systems. The soft-SAFT formalism is built explicitly to take into account such self association, being naturally suited, in principle, for the self-associating nitriles. The equation requires at least three parameters for each compound, namely: m, the chain length, ı, the diameter of the LJ sphere forming the chain, and İ, the interaction energy between the spheres. For associative molecules, two additional parameters are needed per association site, the association volume țHB and the association energy İHB. The model proposed in this work describes all nitriles by a single association site located on the CN group. The dipolar moment is not explicitly considered and their effects are embedded into the other fitted molecular parameters [15]. All parameter values are obtained by fitting the saturated liquid densities (ȡliq) and vapor pressures (Psat) from the Design Institute for Physical Properties (DIPPR) available in Simulis Thermodynamics component (http://www.prosim.net/) for each molecule by minimization the following objective function called absolute average deviation:
1 AADY (% ) = P N
§ Yi cal − Yi exp · ¸¸ ¨¨ ¦ Yi exp i =1 © ¹ NP
2
Where Y represents the property data used for the regression, namely ȡliq and Psat .
(6)
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3.2. Methodology The first three linear nitriles (CH3CN, C2H5CN and C3H7CN) are used as reference for the optimization of the soft-SAFT EoS molecular parameters (m, ı and İ) by fitting the available VLE data summarized in table 1. The association parameters (İHB and țHB) are fitted differently for acetonitrile and propionitrile. Light nitriles like acetonitrile and acrylonitrile often display peculiar behavior because of the short radical bonded to the – CN group, which dominates the interactions. As a matter of fact in UNIFAC group contribution method, acetonitrile and acrylonitrile are considered as unique groups while other nitriles can be constructed from -CHx and -CH2CN groups. Here we find that acetonitrile requires a larger association volume than other nitriles, a fact also observed for the alkanol family in previous studies [16]. Propionitrile association parameters are then kept constant for the rest of the nitriles. From the observations of Huang and Radosz [7] about the relation between the association strength İHB and volume țHB value, we can classify nitriles as an associating fluid stronger than alkanols but with a smaller association volume [16], hinting at the fact that associated nitriles may interact at distances smaller than H-bonds (typically 2.8 ǖ) found in alkanols. Table1: Molecular Parameters for the n-nitriles family (C2-C4). molecule
T range (K)
m
ı (ǖ)
İ/kB (K)
İHB/kB (K)
țHB(Å3)
AAD ȡliq(%)
AAD Psat(%)
CH3CN
280-528
1.45
3.70
268.0
8425
69
0.70
2.03
C2H5CN
283-553
1.55
3.97
272.0
8425
49
0.92
2.10
C3H7CN
283-553
1.65
4.22
279.3
8425
49
0.80
3.50
Experimental vapour pressure and density-temperature data are plotted along with the description of the soft-SAFT model in Figure 1. The absolute average deviation on density and vapor pressure is below 1% and in the 2-4% range respectively. Figure 1 shows that the fitting is indeed excellent, except near the critical point. This was expected, since we are using an analytical equation of state, in which the density fluctuations occurring near the critical region are not explicitly expressed. Additional mathematical treatments like renormalization group theory have been shown to correct effectively the VLE near the critical point [16] but, since for the applications we are interested in are far from the critical region and the calculations with crossover only improve the region near the critical point, they are not considered here. An advantage of having parameters with physical meaning is that their physical trend can be investigated within the same family. Therefore, as in previous works, we have linearly correlated the three molecular parameters m, mı3 and mİ with the molecular weight of the compounds within the same chemical family [17-18]. This allows obtaining a set of transferable parameters as a function of the molecular weight (equations 7). These correlations are established from the optimized parameters given in table 1 and are obtained with a correlation coefficient greater than 0.98.
Modeling the Phase Equilibria of Nitriles by the soft-SAFT Equation of State
a)
743
b)
Figure 1 n-nitriles (acetonitrile [circle], propiontitrile [square] and butyronitrile [cross]) phase equilibria (a) temperature-density diagram, (b) Pressure-temperature diagram. Symbols are from DIPPR data [19] while solid lines stand for soft-SAFT calculations.
m = 0.0083M W + 1.1083
(7.a)
mσ 3 = 2.1143M w − 13.878
(7.b)
mε / k B = 3.025M W + 263.53
(7.c)
Units of ı and İ/kB are Å and K, respectively. Using these correlations, VLE properties of heavier linear nitriles of the same family (Valeronitrile (C4H9CN) and Hexanonitrile (C5H11CN)) are predicted, without any further fitting on supplementary experimental data. The maximum absolute average deviation to density is obtained for Hexanonitrile (0.88%) with an absolute average deviation to the vapor pressure near 3% for both molecules leading to a very good agreement comparing to the DIPPR data [19] as highlighted by figure 2.
a)
b)
Figure 2 Vapor-liquid equilibria of valeronitrile [triangle up] and hexanonitrile [triangle down]. (a) temperature-density diagram, (b) Pressure-temperature diagram. Symbols represent DIPPR data [19], while solid lines are soft-SAFT predictions.
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Despite the discrepancy in the near critical region, the absolute average deviation on vapor pressure is higher than 2% in both cases. The overall agreement with experimental data is very good, proving the transferability of the parameters used for these predictions.
4. Conclusion A molecular model for the n-nitrile chemical family with the soft-SAFT approach was developed. n-nitriles were modeled as LJ chains with one associating site mimicking the strong interactions of the –CN group. Once molecular parameters for the first members of the family were obtained by fitting to available VLE equilibrium data, a correlation of these parameters with the molecular weight of the compounds was proposed, which can be used in a predictive manner for heavier members of the family. A good agreement was obtained comparing the DIPPR data with small discrepancies near the critical region, as expected, since the classical version of the soft-SAFT equation was used. The linear correlations were successfully used to predict the phase behavior of heavier compounds, in excellent agreement with experimental data, highlighting the reliability of the model. The authors acknowledges the Ministère de l’Enseignement Supérieur et de la Recherche de France (MESR) for its grants and the CTP 2005 project (Convention Région N° 05018784). This work has been partially financed by the Spanish Government (project CTQ2005-00296/PPQ) and the Catalan government (projects SGR2005-00288 and ITT2005-6/10.05)
References [1]. W. G. Chapman, K. E. Gubbins, G. Jackson, and M. Radosz, Ind. Eng. Chem. Res., 29 (1990) 1709-1721. [2]. W.G. Chapman, G. Jackson and K. E. Keith Gubbins, Mol. Phys., 65 (1988) 1057-1079. [3]. J. Vidal, Thermodynamics: Applications in Chemical Engineering and the Petroleum Industry, Editions Technip, 2003, ISBN2710808005. [4]. M. K. Hadj-Kali, V. Gerbaud, X. Joulia, A. Boutin, P. Ungerer, C. Mijoule and J. Roques, Computer Aided Chemical Engineering, 14 (2003) 653-658. [5]. F.J. Blas and L.F. Vega, Ind. Eng. Chem. Res., 37 (1998) 660-674. [6]. F.J. Blas and L.F. Vega, Molec. Phys., 92 (1997) 135. [7]. S. H. Huang and M. Radosz, Ind. Eng. Chem. Res., 29 (1990) 2284-2294. [8]. S. H. Huang and M. Radosz, Ind. Eng. Chem. Res., 30 (1991) 1994-2005. [9]. M. S Wertheim. J. Stat. Phys., 35 (1-2) (1984) 19-34. [10]. M. S.Wertheim, J. Stat. Phys., 35 (1-2) (1984) 35-47. [11]. E. A. Müller and K.E. Gubbins, Ind. Eng. Chem. Res., 40 (2001) 2193-2211. [12]. J. K. Johnson, J. A. Zollweg and K. E. Gubbins, Molec. Phys. 78 (1993), 591. [13]. O. Spuhl, S. Herzog, J. Gross, I. Smirnova, and W. Arlt. Ind. Eng. Chem. Res., 43 (2004) 4457-4464 [14]. K. Jackowski and E. Wielogorska,. Journal of Molecular Structure., 355 (1995) 287-290. [15]. J. P.Hansen, I. R. McDonald, Theory of Simple Liquids., London Academic Press: 1990. [16]. F. Llovell and L.F. Vega, J. Phys. Chem. B., 121 (110) (2006) 1350. [17]. N. Pedrosa, J. C. Pàmies, J. A. P. Coutinho, I. M. Marrucho, and L. F. Vega, Ind. Eng. Chem. Res., (2005) 44 7027-7037. [18]. J. C. Pàmies, L. F. Vega, Ind. Eng. Chem. Res., 40 (2001), 2532. [19]. DIPPR (Design Institute for Physical Property Data) from Simulis Thermodynamics.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Application of a digital packing algorithm to cylindrical pellet-packed beds Richard Caulkin, Michael Fairweather, Xiaodong Jia, Abid Ahmad, Richard A. Williams Institute of Particle Science and Engineering, School of Process, Environmental and Materials Engineering, University of Leeds, Leeds, LS2 9JT, UK
Abstract A digital packing algorithm is used in an investigation to predict the structures of cylinder packed columns. Simulation results of the computational approach are compared with packing data from experimentally measured beds as a means of model validation. The algorithm has been modified from that reported previously (Caulkin et al., 2005) to include particle collisions that guide pellet movement in such a way that it does not sacrifice the advantage of simulation speed, yet is able to better recreate the packing of non-spherical particles. The results of both the original and modified models are presented, with predicted bulk and local voidage values compared directly with data determined by optical analysis of corresponding experimental columns. The results demonstrate that while the original version of the algorithm qualitatively predicts the trend in voidage for cylindrical pellets, the modified version is capable of providing more quantitative results. Therefore, the influence of physical interactions upon the packing cannot be disregarded if realistic packing structures are to be obtained. Keywords: digital packing algorithm, cylinder-packed beds, particle collisions
1. Introduction Cylinder packed columns are the dominant type of reactor used for catalytic reactions due to their high surface area ratios, and because of this they are employed extensively in the chemical and process industries. The efficiency of fluid flow and transport processes through these beds is affected by their internal structure, which in turn depends on the geometrical make-up and arrangement of the packing material, as well as the size ratio between the container and particle diameter. Therefore, as the final stable geometrical structure of a packed bed greatly influences all subsequent properties of the packing, interest exists in practical models for their improved prediction and design. Computational fluid dynamic (CFD) modelling of flow through porous media, e.g. Dixon et al. (2006), has been developed to the point where it has the potential to become a significant instrument for use in analysis and design. As CFD modelling has developed, the need for concise information about the structure of the porous media has increased. Specific macroscopic properties such as the voidage or packing density are widely accepted parameters used to define bed structure. However, mean porosity, Ȉmean, on its own does not provide a detailed knowledge of the packing. Therefore local voidage information is often used to gain a better understanding of the inhomogeneous structural properties of packed beds. To obtain accurate representations of packed beds, various methods have been proposed.
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A number of advanced packing algorithms exist, but these have been largely limited to simple packing materials (Zeiser et al., 2001; Abreu et al., 2003; Freund et al., 2003) due to the challenges of representing large numbers of randomly orientated objects. Although some of these methods can pack complex shaped particles, the resulting beds do not accurately reproduce the structure of real packed columns. The porosity distributions generated by these packing algorithms are therefore at variance with existing experimental data. Earlier attempts used an approach which advanced an empirical function and adjusted fitting parameters by regression of experimental data. Despite their usefulness, these correlations are limited by the range of data used in their formulation. Most recently, X-ray microtomography (Zhang et al., 2006) and magnetic resonance imaging (Sharma et al., 2001) techniques have been reported as suitable methods for the generation of accurate three-dimensional geometrical representations of bed structure. These are, however, limited by the significant time and financial outlay needed to investigate individual beds.
2. Model Description In this work, a Monte Carlo simulation approach to the prediction of bed structure (Jia and Williams, 2001) is employed. The basis of the code, called DigiPac, is the digitisation of objects and of the packing space. Therefore, regardless of geometric complexity, shapes are represented as coherent collections of voxels and the simulation volume and container into which the particles are to be packed is converted into a threedimensional lattice grid over which the particles move randomly. To simulate the effect of gravity, the upward component of a move is only accepted with a rebounding probability, a user-defined parameter. A value of zero means that particles never move upwards, whereas a value of one gives particles an equal probability to move up or down. A value of 0.3 was used in the simulations presented, resulting in a directional and diffusive motion, similar to a random walk-based sedimentation model, helping the particles to effectively explore every available packing space. The movement of particles over a grid makes collision detection straightforward as it can be checked whether two particles occupy the same grid space at the same time. This shortens computational time compared to other algorithms where overlap detection is mostly based on the use of mathematical comparison techniques. Since particles move only one grid at a time, the overlap detection procedure ensures that one particle will not jump over another during packing. The ease of overlap detection significantly increases the computational efficiency and drastically reduces the coding effort required in software implementation. Additionally, unlike conventional methods, at a given resolution the computing resources (i.e. memory and CPU time) do not increase with shape complexity, and as computations using the DigiPac code are performed mainly on integers used to store locations of voxels, it can be run using desktop workstations. In this work, two versions of the code have been used. The original version is completely probabilistic in nature and uses random walks to simulate particle movement as described above. In the modified version, particles are still represented digitally, so the advantages of ease and speed of collision and overlap detection are retained. While this version is also stochastic, the difference is it makes use of collisions to guide particle movements (Collision Guided Packing or DigiCGP). In this version, collision points are identified in the lattice grid and each pair of colliding voxels is assigned a nominal impact force of one. For torque calculation the direction of the nominal impact force is taken to be normal to the contact face of the colliding pair of voxels. The net torque vector is subsequently used as the axis of particle rotation in the following step.
Application of a Digital Packing Algorithm to Cylindrical Pellet-Packed Beds
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The angle of rotation is still random, but is capped to give a maximum swept distance of no more than a few pixels during rotation. To calculate the net force, the direction of an impact force is taken to be along the line joining the collision point and the centre of gravity of each particle. For translational movement the net collision force is normalised against the largest component, so each force component is now between 0 and 1. This is then used as the probability of moving the particle by at most one grid cell at a time along each principal axis in the lattice grid, as in the original code. It should be noted that the above treatment does not include voxel-level friction or any other forces tangential to a contact. Particle-level friction is partially accounted for by the roughness of the digital surfaces. The method also neglects inertia effects as particle velocity is neither calculated nor stored. All these omissions are for the sake of computational speed and result in a simulation time comparable to that of the original DigiPac code.
3. Experimental Work Cylindrical containers were constructed by boring into PVC rod, with internal tubes fixed in place by adhesion to the container base. Lead ballast was used as the packing material and was introduced a handful at a time, followed by gentle tapping. When each layer was formed, Ampreg 20 resin was poured slowly and uniformly over the particles, ensuring that no air pockets remained. This process was repeated until the container was packed to a height of approximately 60mm and aimed to simulate a poured randomly packed bed. After solidification each packed bed was periodically turned in a lathe and axially ‘sliced’ to expose 50 consecutive cross-sections, shaving off 1mm (±0.001mm) from the base each time. A high resolution image (512x512 pixels) of each exposed cross-section was captured and converted to binary format for analysis.
4. Data Extraction For digital structures, voidage distribution is calculated by counting the number of solid voxels and dividing the count by the total number of grid cells within the corresponding packing space. This procedure applies to both simulated and optically analysed experimental packing structures. The porosity of each bed slice is calculated within the software package once prompted for analysis. To calculate the radial voidage of individual beds, each cross-section is divided into 50 equally spaced concentric rings. Voxel counting is then used for each ring, and the results cumulated with corresponding rings from the remaining cross-sections over the height of the bed. The resulting values are then plotted against radial distance, in particle diameters, from the retaining wall. Each bed, measured and predicted, was re-packed a total of four times and resulting averaged values are presented. For mean voidage calculation, values in the axial direction were calculated. This was done by means of voxel counting for the crosssectional slices of the packed columns in the bulk region of the beds, i.e. with bed ends excluded. The resulting voidage values are then averaged over the number of crosssections used in the calculation to provide a single bulk value for individual beds.
5. Results and Analysis Several beds, examined experimentally and using the DigiPac/DigiCGP algorithm, and packed with cylindrical pellets are presented. Containing different configurations of internal tubes, as detailed in Table 1 and Fig. 1, they were examined in terms of structure by numerical analysis and compared with matching beds created by experimental means. As noted, multiple trials for each bed were undertaken and the results averaged.
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Σmean
Aspect ratio dt/dp
Measured (average)
DigiPac Predicted
DigiCGP Predicted
% error (CGP) Number of tubes Tube dia. (mm)
TA1
8.6
80
9.3
0.409
0.449
0.422
3.18
3
8
TA2
5.3
80
15.1
0.348
0.401
0.362
4.02
3
8
OA1
8.6
80
9.3
0.359
0.386
0.371
3.34
1
8
OA2
5.3
80
15.1
0.359
0.379
0.370
3.06
1
8
Bed dia. dt (mm)
Bed
Pellet dia. dp (mm)
Annuli
Table 1. Dimensions and mean voidage data on the beds investigated.
Fig. 1. DigiPac images of TA and OA beds. From the mean voidage predictions (Table 1), the modified packing algorithm provides good qualitative results, with errors of less than 5% for DigiCGP. The packed bed parameter of radial porosity is also used to compare the prediction accuracy of the algorithm with experimental data. The average CPU time taken to complete a single simulation (with multiple random particle rotation) was approximately two hours using a desktop PC with a Pentium 4, 2GHz CPU and 512Mb RAM. Significant speed-up can be achieved if the simulations are run on a multi-CPU shared memory computer, as the software implementation is multi-threads enabled. The dimensions of the beds were determined by scaling down industrial packed columns. A relatively large outer tube diameter, dt, is used to ensure that the retaining wall is a sufficient distance from the internal tube(s) so as not to have any appreciable effect on porosity in this region. When pellets are introduced into a bed, the container wall influences the orientation of the outermost cylinders, forcing a row of pellets to be formed along the outer wall. The second row of particles then rest in the cusps formed by the first row. Therefore, moving inwards from the wall to the bed centre, the trend is repeated, with each subsequent row more randomly packed than the previous. Fig. 2 presents the measured and predicted local voidage of the TA beds. Analysis of the radial voidage for bed TA1 shows that voidage decreases from 1.0 at the outer wall to a minimum of 0.19 (0.33 DigiPac; 0.23 DigiCGP) at 0.75dp. The radial voidage then proceeds as a damped oscillatory wave until the central structure of the three internal tubes. At this point (2.75-3dp), the waveform ends and the voidage rises to a peak of 0.64 for the experimental bed and 0.60 for the voidage predicted by DigiCGP (0.53 DigiPac). After 4dp, the voidage resumes as an oscillatory wave until the bed centre is reached. Bed TA2, which is packed using smaller cylinders than bed TA1, reveals many
Application of a Digital Packing Algorithm to Cylindrical Pellet-Packed Beds
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of the same features and characteristics. The main difference for bed TA2, however, is that the oscillating radial voidage extends for a greater number of dp, due to the smaller particles in this column. Therefore, the opportunity exists for a greater number of particles to fit into a space which is the same size as that used to pack the particles of bed TA1. The minimum porosity recorded for bed TA2 again occurs at 0.75dp from the container wall, with a measured value of 0.18 (0.22 DigiCGP). At its peak voidage, around the three internal tubes, bed TA2 has a maximum value of 0.57 (0.56 DigiCGP). The most likely reason for this greater span of elevated porosity in the vicinity of the internal tubes is because the small cylindrical particles allow a higher number of pellets to occupy the space between the tubes than in bed TA1. This creates a greater number of boundaries between particles, leading to a cumulatively elevated voidage in this region. However, for this triangular shell-side bed arrangement, the smaller cylindrical particles result in an overall lower mean and radial voidage, suggesting that smaller particles, when unimpeded, form more compact packing within shell-side beds than larger particles. The TA beds investigated in this paper do not provide information on how each internal tube individually affects the voidage in the bed, due to the influence of the neighbouring tubes affecting how the particles are arranged. As a result of this, two further beds containing a single tube, but otherwise identical to the respective TA beds, were investigated for local voidage. Bed TA1
Radial Voidage
1
Bed TA2
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0 0
1
2
3
4
5
0
1
2
Distance from wall, particle diameters
3
4
5
6
7
Radial Voidage
Fig. 2. Radial voidage data for TA beds (symbol-exp, line-DigiCGP, dash-DigiPac).
Bed OA1
1
Bed OA2
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0 0
1
2
3
4
5
0
1
2
Distance from wall, particle diameters
3
4
5
6
7
Fig. 3. Radial voidage data for OA beds (symbol-exp, line-DigiCGP, dash-DigiPac). The OA beds in Fig. 3 contain only one internal tube, located in the same position as one of the tubes in the TA beds. This is to allow a direct comparison between the OA and TA beds, so permitting the effects of multiple tubes on local voidage to be assessed, in addition to investigating the ability of the algorithm in predicting bed structure despite such changes in bed geometry. The similarities that are seen to exist between the two bed types, in not only the measured beds but also the DigiPac and DigiCGP predicted beds, extend throughout the entire bed for each particle size investigated. The radial voidage of bed OA1 once again takes the form of a damped oscillatory wave that continues until the single internal tube is approached. At this point, around 3.5dp, just as
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in bed TA1, the voidage marginally increases to a peak of 0.55 (0.53 DigiCGP) before resuming in a damped manner. Bed OA2 also displays similar characteristics to bed OA1, with an elevated region at 4.3dp, peaking at a value of 0.43 (0.40 DigiCGP). The location at which the peak value occurs again corresponds with that of bed TA2. Comparing the TA beds with the OA beds reveals that TA1 and TA2 consistently have a higher radial voidage than beds OA1 and OA2, respectively. The only difference in these two bed types is the number of internal tubes. In the TA beds, the three tubes give rise to three overlapping wall effects within the bed. Hence, an elevated voidage profile is seen when compared with the single tube of the OA beds. Comparing bed TA1 with TA2, and bed OA1 with OA2, a lower radial voidage results for the second bed group as TA2 and OA2 are packed with smaller cylinders which form a more compact packing throughout the beds. In Fig. 3, the rise in radial voidage for the OA beds, after the profile has taken the form of a damped oscillatory wave (i.e. as the tubes are neared) is not as great as in Fig. 2 for the TA beds. As only one tube is present, the distortion from the true radial voidage is less. It is observed from the beds investigated that the DigiCGP model is able to predict in a quantitative manner, and within reasonable error margins, the mean and local voidage of the experimentally investigated beds.
6. Conclusions This work has considered the prediction of columns packed with cylindrical pellets in order to validate the DigiCGP code against experimentally derived structures representative of realistic scenarios found in industry. The improved calculation method, which makes use of collisions to guide particle movements, has been shown to be reliable and capable of predicting the mean and local voidage of such beds. Combined with its user-friendliness and low running costs, the validated code has potential uses in the design of such beds, particularly if coupled with other methods such as CFD. Work on such coupling has commenced, as has the development of a deterministic version of the packing model to incorporate further interaction forces.
References C.R.A. Abreu, F.W. Tavares, M. Castier, 2003, Influence of particle shape on the packing and on the segregation of spherocylinders via Monte Carlo simulations, Powder Tech, 134, 167-180. R. Caulkin, M. Fairweather, X. Jia, R.A. Williams, 2005, A numerical case study of packed columns, European Symposium on Computer-Aided Process Engineering-15, L. Puigjaner, A. Espuna, Eds., Elsevier, Amsterdam, 367-372. A.G. Dixon, M. Nijemeisland, E.H. Stitt, 2006, Packed tubular reactor modeling and catalyst design using computational fluid dynamics, Adv Chem Eng, 31, 307-389. H. Freund, T. Zeiser, F. Huber, E. Klemm, G. Brenner, F. Durst, G. Emig, 2003, Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation, Chem Eng Sci, 58, 903-910. X. Jia, R.A. Williams, 2001, A packing algorithm for particles of arbitrary shapes, Powder Tech, 120, 175-186. S. Sharma, M.D. Mantle, L.F. Gladden, J.M. Winterbottom, 2001, Determination of bed voidage using water substitution and 3D magnetic resonance imaging, bed density and pressure drop in packed bed reactors, Chem Eng Sci, 56, 587-595. T. Zeiser, P. Lammers, E. Klemm, Y.W. Li, J. Bernsdorf, G. Brenner, 2001, CFD-calculation of flow, dispersion and reaction in a catalyst filled tube by the lattice Boltzmann method, Chem Eng Sci, 56, 1697-1704. W. Zhang, K.E. Thompson, A.H. Reed, L. Beenken, 2006, Relationship between packing structure and porosity in fixed beds of equilateral cylindrical particles, Chem Eng Sci, 61, 8060-8074.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
751
Modelling and simulation of a membrane microreactor using computational fluid dynamics
Paris Chasanis,a Eugeny Y. Kenig,a Volker Hessel,b Stefan Schmitt b a
University of Dortmund, Department of Biochemical and Chemical Engineering, EmilFigge-Str. 70, 44227 Dortmund, Germany b Institut für Mikrotechnik Mainz GmbH, Carl-Zeiss-Strasse 18-20, 55129 Mainz, Germany
Abstract In this paper, the effect of miniaturisation and inlet velocity variation on the performance of a membrane microreactor is studied numerically. The microreactor consists of a reaction channel, in which the water gas shift reaction takes place, and a permeate channel, in which the permeating hydrogen is swept away. These channels are separated by a selective palladium membrane. A 3D CFD model is developed to account for hydrodynamics, mass transfer, chemical reaction and permeation through the membrane. It is found that reactor miniaturisation significantly improves hydrogen yield and recovery. Furthermore, the reaction channel feed velocity is found to exert remarkable influence on reactor performance, whereas the impact of the sweep gas inlet velocitiy can be considered as less important. However, the latter cannot be neglected, and thus, both channels have to be considered simultaneously. Keywords: membrane microreactor, mass transfer, steam reforming, water gas shift reaction, CFD
1. Introduction In recent years, chemical micro processes have attracted significant interest of both chemical process industry and science [1]. These processes occur in equipment with dimensions at micrometer and sub-millimeter scale. As a consequence, high surface areas per unit volume and small diffusion paths are achieved resulting in increased mass transfer rates. Membrane-based microreactors are an important class of micro devices combining reaction and separation inside one single shell [2]. Among a large variety of applications, selective separation of hydrogen by means of palladium membranes seems to be especially promising [3]. Due to the high selectivity of palladium membranes, hydrogen can be separated with purity sufficient for its further use in micro fuel cells [3]. In this work, the water gas shift reaction (WGS) accompanied by a removal of H2 from a reformate gaseous mixture of CO, CO2, H2O and CH4 in a membrane microreactor is investigated numerically. The reaction is represented by
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⎯⎯ → CO 2 + H 2 ↑, ΔH 0R = −41, 2kJ / mol CO + H 2 O ←⎯ ⎯
(1)
The reactor consists of a reaction channel and a permeate channel, which have a rectangular cross-section and the same dimensions. The WGS takes place at the bottom and at the side walls of the reaction channel coated with Pt/CeO2 catalyst. At the top of the reaction channel, a palladium-based membrane (77%Pd-23%Cu) is placed for the selective removal of the produced hydrogen. The hydrogen permeating through the palladium membrane is swept away by a water vapour stream in the permeate channel. Figure 1 illustrates the configuration of the microreactor under study.
Fig. 1: The microreactor configuration: permeate channel (above) and reaction channel (below); the catalyst and membrane surfaces are shown separately.
A 3D model was developed and applied to carry out intensive studies on the influence of miniaturisation on reactor performance. Furthermore, the impact of the reformate and the sweep gas velocity on the reactor behaviour is examined. The reformate composition used in all studies (in mass percentages) is: H2 (8.9%), H2O (35.1%), CO (29.6%), CO2 (25.1%) and CH4 (1.3%).
2. Mathematical model The flows in both microchannels are laminar which is reflected by low Reynolds numbers. Furthermore, ideal gas behaviour is assumed. Under isothermal and steadystate conditions, the transport phenomena in the considered microreactor can be described by the conservation equations of overall mass, momentum and species, which read as
∇u = 0
(2)
∇ ⋅ ρ uu = −∇ p + ρ g + μ Δ u
(3)
(4)
u ⋅∇ C = ∇ ( D ∇C )
A no-slip boundary condition was applied at all walls, whereas inlet velocities and oulet pressures were defined for both channels. Hydrogen permeation molar flux through membranes can be described by the following expression [2]:
Modelling and Simulation of a Membrane Microreactor Using CFD
JM =
kM
⋅ ( pHn 2 ,R − pHn 2 ,P )
δ
753
(5)
where k M is permeability, δ is membrane thickness pH 2 ,R and pH 2 ,P are partial pressures of hydrogen in the reaction and permeate channels, respectively. The exponent n can range from 0.5 (Sievert’s law) to 1 (Fick’s law). We experimentally determined that the membrane under study obeys Fick’s law under the conditions studied. By introducing permeance K M
KM =
kM
(6)
δ
equation (5) transforms to
J M = K M ⋅ ( pHn 2 ,R − pHn 2 ,P )
(7)
To describe the reaction kinetics, we applied the approach suggested by Keiski et al. [4], who investigated the reaction kinetics of the WGS over a CuZnO/Al2O3 catalyst: 0.78 rCO = k1 ⋅ cCO ⋅ cH0.15 ⋅( 1 −τ ) 2O
where
τ is reversibility factor of the reaction, τ =
(8)
cCO2 ⋅ cH 2 cH 2 O ⋅ cCO ⋅ KT
, and KT is
equilibrium constant. The rate constant k1 depends on temperature according to Arrhenius’ law.
⎛ E ⎞ k1 = k0 exp ⎜ − A ⎟ ⎝ RGT ⎠
(9)
where k0 is pre-exponential factor, E A is activation energy and RG is gas constant. Due to the considerably higher activity of the Pt/CeO2 catalyst compared to the CuZnO/Al2O3 catalyst, the reaction rate was assumed to be of one order of magnitude higher [5].
3. Implementation The set of non-linear partial differential equations described in the previous section is solved by means of the commercial CFD tool CFX® (ANSYS Inc) , which is based on
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the finite volume element method. For the discretisation of the advection terms, a high resolution scheme is used. The hexagonal grids are generated using ICEM CFD® (ANSYS Inc). A set of Fortran subroutines is developed to link grid cells on both sides of the membrane and to implement conjugate boundary conditions according to equation (7). In this way, local driving forces and permeation fluxes through the membrane are calculated accurately.
4. Results and discussions 4.1. Effect of miniaturisation on the reactor performance In order to determine the impact of miniaturisation, five geometrically similar microreactors (each consisting of a reaction and a permeate microchannel with identical dimensions separated by a palladium-based membrane) with different cross-sectional diameters are taken into consideration. Table 1 summarises the dimensions of the considered microchannels: Table 1. Dimensions of the microchannels under study Microreactor
Height [µm]
Width [µm]
Micro-1 Micro-2 Micro-3 Micro-4 Micro-5
250 500 750 900 1250
300 600 900 1200 1500
Cross-section diameter [µm] 272.73 545.45 818.18 1090.91 1363.64
Length [µm] 5000 10000 15000 20000 25000
The temperature is 300 °C, whereas the catalyst density is 0.04 kg/m² for all five microreactors. The inlet velocities, which are equal in both channels for each microreactor configuration, range from 0.1 to 0.5 m/s and provide identical residence times. The inlet stream in the reaction channel has the reformate composition given above, while the sweep gas stream flowing into the permeate channel consists exclusively of water vapour. Finally, the pressure difference between the reaction and the permeate side is 1 bar for each microreactor. The permeance of the palladium membrane was experimentally determined and is equal to 1.95 10-9 mol m-2 s-1 Pa-1. Figure 2a illustrates the concentration profiles of the five species in the reaction channel and of hydrogen mass fraction in the permeate channel along the channel length of Micro-3. Hydrogen is continuously transferred from the reaction channel into the permeate channel resulting in a gradual hydrogen mass fraction increase in the latter. Despite the hydrogen production on the catalyst, the hydrogen mass fraction in the reaction channel decreases, which shows that the permeation rate through the membrane is higher than the reaction rate of the WGS under the applied conditions. As expected, mass fractions of both reactands (H2O and CO) decrease, whereas CO2 mass fraction continuously grows. The mass fraction of CH4, which does not take part in the WGS, hardly changes. The simulations were also performed for five microreactors consisting exclusively of one reaction channel with the same dimensions (cf. Table 1)
Modelling and Simulation of a Membrane Microreactor Using CFD a
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b 1.0
0.7
0.9
0.6 0.8 0.7
CO2
0.6
0.4
[-]
mass fractions [-]
0.5
0.3
0.4
H2O 0.2
CO
H2
0.1
yield without hydrogen removal
0.2
yield with hydrogen removal H2-recovery
0.0
0 0
0.3
0.1
H2(permeate)
CH4
0.5
0.002
0.004
0.006
0.008
0.01
channel length [m]
0.012
0.014
0.016
0
200
400
600
800
1000
1200
1400
1600
cross-section diameter [μm]
Fig. 2: Mass fractions of the five species in the reaction channel and of hydrogen mass fraction in the permeate channel along the channel length of Micro-3 (a); impact of miniaturisation on reactor performance (b)
Clearly, in these configurations, no hydrogen is transferred through the membrane. Figure 2b gives a comparison between the achieved total hydrogen yield for both configurations. In both cases, the yield is increased by reducing the channel dimensions. This can be explained by the increase of the surface area per volume of catalyst. However, the yields achieved with the simulataneous removal of hydrogen from the reaction channel are larger than those achieved without hydrogen removal for all microreactor dimensions studied. Obviously, the thermodynamic equilibrium of the WGS is shifted to the product side by hydrogen separation. In fact, the difference between the achieved yields steadily increases with decreasing microreactor dimensions indicating the growing impact of the hydrogen removal. This is also reflected by the increased hydrogen recovery, which is defined as the ratio of permeated hydrogen to the total produced hydrogen. 4.2. Effect of inlet velocities on the reactor performance The impact of the inlet velocities is investigated in two sudies on the basis of Micro-2: in the first one, the reformate inlet velocity is varied between 0.008 and 5 m/s, whereas in the second study, the sweep gas inlet velocity is changed in the range between 0.001 and 5 m/s. While changing the respective velocities, all the others conditions remain unchanged as they are given in the previous section. The results of both studies are illustrated in Figure 3. Figure 3a shows a significant influence of the reformate inlet velocity on the hydrogen yield and on the hydrogen recovery. By decreasing the reformate inlet velocity, the residence time in the reaction channel is increased leading to increasing amounts of produced and permeated hydrogen and thus to higher yields and hydrogen recovery. On the other hand, the reduction of the sweep gas inlet velocity leads to higher hydrogen partial pressures in the permeate channel. Hence, the driving force according to equation (7) is reduced resulting in lower permeate fluxes and, consequently, in lower yields and hydrogen recovery. Figure 3b shows a lower influence of the sweep gas inlet velocity on the reactor performance compared to the reformate inlet velocity. However, this effect is not negligible.
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1.0
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
[-]
[-]
a
0.5 0.4
0.4
0.3 0.2 0.1
0.5
0.3
yield
yield
0.2
0.01
H2-recovery
0.1
H2-recovery
0.0 0.001
0.1
velocity [m/s]
1
10
0 0.001
0.01
0.1
1
10
velocity [m/s]
Fig 3: Impact of the reformate inlet velocity on reactor performance (a) ; impact of the sweep gas inlet velocity on reactor performance (b)
5. Concluding remarks In this work, a 3D CFD model is developed in order to capture hydrodynamics and mass transfer in a membrane micro reactor consisting of a reaction channel and a permeate channel. A particularity of this model is a coupled consideration of both channels. By means of Fortran routines, the local driving forces are calculated accurately, which enables concentration profiles in both channels and thus the actual reactor performance to be exactly determined. By decreasing the reactor dimensions, the reactor performance significantly improves as a result of increasing catalyst and membrane surface per volume. The impact of the reformate inlet velocity is found to be remarkable, whereas the sweep gas inlet velocity has a lower influence. However, in the velocity range under consideration, the achieved yields vary between 0.83 and 0.92 and the hydrogen recovery between 0.18 and 0.4. This indicates that the effect of sweep gas inlet velocity cannot be neglected and justifies the need to take both channels into consideration. In the future, the impact of other process parameters (e.g. temperature, catalyst amount, inlet concentrations) should be examined. Furthermore, the model should be extended to describe nonisothermal conditions.
References [1]. V. Hessel, S. Hardt, H. Löwe, 2005. Chemical micro-process engineering, Wiley-VCH, Weinheim. [2]. A. Zheng, F. Jones, J. Fang, T. Cui, 2000. Dehydrogenation of cyclohexane to benzene in a membrane microreactor, In: R.S. Wegeng, W. Ehrfeld, I. Rinard (Eds.), Proceedings of the Fourth International Conference on Microreaction Technology, March 5-9 2000, Atlanta, GA, pp. 284-292. [3]. K. A. Alfadhel, M. V. Kothare, 2005. Microfluidic modeling and simulation of flow in membrane microreactors, Chemical Engineering Science, 60, 2911-2926. [4]. R. L. Keiski, O. Desponds, Y.-F. Chang, G. A. Somorjai, 1993, Kinetics of the water-gas shift reaction over several alkane activation and water-gas shift catalysts, Applied Catalysis A: General, 101, 317-338. [5]. T. Baier, G. Kolb, 2007. Temperature control of the water-gas shift reaction in microstructured reactors, Chemical Engineering Science, 62, 4602-4611.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
757
Modeling of catalytic hydrogen generation from sodium borohydride André Gonçalvesa,b, Pedro Castroa, Augusto Q. Novaisa, Carmen M. Rangelb, Henrique Matosc a
DMS, Inst. Nacional Engenharia Tecnologia e Inovação, 1649-038 Lisboa, Portugal UEQM, Inst. Nacional Engenharia Tecnologia e Inovação, 1649-038 Lisboa, Portugal c DEQB, Instituto Superior Técnico, 1049-001 Lisboa, Portugal b
Abstract This paper presents a dynamic model compiled in gPROMS that describes the hydrogen production via the catalytic hydrolysis reactions of sodium borohydride (NaBH4) solutions. It extends our previous work for the self-hydrolysis of NaBH4 [1], with the addition of a modified version of Davis et al. [2] empirical correlation to describe the reaction mechanism limiting step rate. The kinetic parameters were estimated using the gPROMS Parameter Estimation tool supported by experimental data in terms of produced gas volume and solution pH. The results have shown that the developed model accurately describes, not only the catalytic hydrolysis but also the self-inhibited self-hydrolysis and the alkaline storage of NaBH4. This model allows the prediction of hydrogen volume, pressure, rate of release and solution stability for this hydrogen generation reaction. Keywords: Hydrogen; Dynamic Modeling; Sodium Borohydride; Self-hydrolysis; Catalytic hydrolysis
1. Introduction New clean and renewable energy sources, which can effectively substitute fossil fuels, are the hopes and challenges for the future role of energy in the world economy. The most preponderant question is related with the energy transportation and storage, as most of these clean energy sources are often found far from the areas with high energy consumption. So far one of the best solutions for a reliable energy carrier for the future is hydrogen, since it can be efficiently and safely stored as a chemical hydride and released ondemand to generate electricity in a PEMFC (Proton Exchange Membrane Fuel Cell). Sodium borohydride (NaBH4) is considered, since the 50’s, as a good hydrogen storage medium [3]. This chemical hydride spontaneously releases hydrogen when placed in contact with water, through a chemical process known as self-hydrolysis. The kinetics for this chemical reaction were initially studied [2] and a sequential mechanism proposed, based on a pH-dependent slow step. Since then other reactions have been proposed that could also describe this transformation, such as the metaborate formation [4], the tetraborate formation [1] and the tetrahydroxyborate formation [5]. Furthermore, it was discovered [3, 6] that if a specific metallic catalyst is added to a borohydride solution, the hydrogen release rate would dramatically increase in comparison with the self-hydrolysis release rate. However the mechanism for the catalytic hydrolysis of sodium borohydride is still a matter of ongoing research.
A. Gonçalves et al.
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The use of mathematical models and simulation software could be instrumental in unveiling the best reaction mechanism for these chemical transformations, by describing the hydrolysis reactions and comparing the results with experimental data. With this aim, the gPROMS software is employed in this work, to implement a modification of a previously presented self-hydrolysis model [1] and to extend it to the catalytic hydrolysis of sodium borohydride.
2. Self-hydrolysis reaction mechanism The general expression that describes the self-hydrolysis of sodium borohydride in aqueous media is: NaBH 4 ( s ) + 4 H 2 O( l ) ⎯ ⎯→ 4 H 2 ( g ) + NaB (OH )4
(1)
As it was observed [6], the self-hydrolysis is dependent on the pH of the reacting solution, and so at high pH values this process can be almost entirely inhibited. This fact is in agreement with preliminary experiments [2] where boric acid is formed after reacting sodium borohydride with water. Davis et al. also proposed an empirical reaction rate equation (eq. 2) that can describe the slow step rate, given the NaBH4, H+ and H2O molar concentrations. (2)
RRLimiting = k H + × C BH − × C H + + k H 2O× C BH − × C H 2O 4
Step
4
However, a consequence of an increasing alkalinity of the solution is the formation of the sodium tetrahydroxyborate, through the boric acid interaction with water and the hydroxide ion [5]. The reaction mechanism that represents the chemical equation (1) is shown in Fig. 1. + − NaBH 4( aq ) ⎯⎯ ← ⎯→ Na( aq ) + BH 4( aq )
BH 4−( aq ) + H (+aq ) ⎯⎯ → BH 3( aq ) + H 2 ( aq )
Sodium borohydride dissolution Borohydride acidic addition (limiting step)
BH 3 ( aq ) + 3 H 2 O( l ) ⎯⎯ → B (OH ) 3 ( aq ) + 3 H 2 ( aq )
Boric acid formation
⎯⎯ → B (OH ) 4− ( aq ) + H (+aq ) B (OH ) 3 ( aq ) + H 2 O( l ) ←⎯ ⎯
Tetrahydroxyborate ion formation
− ⎯ → Na(+aq ) + B ( OH )4 ( aq ) ←⎯ ⎯ NaB ( OH ) 4 ( aq s) )
Sodium tetrahydroxyborate precipitation
Fig. 1. Proposed sodium borohydride hydrolysis reaction mechanism.
Other reactions included in the model are the water autoprotolysis and the sodium hydroxide dissolution (not shown), and the boric acid deprotonation equilibria (eqs. 3, 4 and 5). ⎯ ⎯→ − + ⎯ → B (OH ) 3 ( aq ) ←⎯ ⎯ H 2 BO3 ( aq ) + H ( aq ) ← ⎯⎯ H 2 BO
− 3 ( aq )
⎯ ⎯→ + 2− ⎯ → ←⎯ ⎯ HBO 3 ( aq ) + H ( aq ) ← ⎯⎯
(3) (4)
Modeling of Catalytic Hydrogen Generation from Sodium Borohydride
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⎯ ⎯→ + 3− ⎯ → HBO 32 (−aq ) ← ←⎯ ⎯ BO3 ( aq ) + H ( aq ) ⎯⎯
(5)
3. Dynamic model of the reaction system The gPROMS dynamic model, built up to describe the experimental results of the hydrolysis, consists of three units: the reactor, the gas reservoirs and a connection unit that regulates the flow between the reactor and the reservoirs. The reactor-reservoir connections were expressed in the model using identical reservoir units connected to the reactor through on/off valves. These connections are opened one by one, in order to fill the correct reservoir. A changeover occurs whenever the height of the water column of the active reservoir reaches zero, triggering a routine command that orders the opening of a new valve. The full DAE model is index 1 and consists of a total of 902 equations and variables of which 204 are differential and 698 are algebraic. To accomplish all the physical-chemical operations of the system the model units include: mass balances given by eq. (6) for aqueous phase and eq. (7) for gas phase compounds, where Mi is the molar holdup of compound i, RRj is the reaction rate for the reaction j, ni,j is the respective stoichiometric coefficient, VAqueous represents the solution volume, FiGas-liquid is the gas-liquid transfer rate of component i, FrReservoir-vase is the reservoir-vase exit flow rate from reservoir r and FrReact-reserv is the reactor-reservoir transition flow rate using reservoir r; gas-liquid equilibriums modeled by Raoult and Henry expressions generalized by eq. (8) , where PTotal is the total pressure of the gas phase, yi and xi are the molar fractions of i in the gas phase and aqueous solution phase, respectively, and KiGas-liquid equilibrium is a generic equilibrium constant similar to the component vapor pressure or the Henry constant; flow rates in the system calculated using mass transfer relations for the reactor-reservoir connections (eq. 9), the gas phase and the liquid phase interchange (eq. 10) and the flow of water in the reservoir to the vase below (eq. 11), where the mass transfer constants, Kmass transf, are related to the pressure differential between the reactor and the reservoir r, the gas molar fraction of component i and the water height in the reservoir r; the reaction rate of the limiting step described by eq. (2), which was improved with the addition of partial reaction orders (eq. 12), Įi, to provide a better adjustment between the experimental data and the model results. The rate of the subsequent reactions of the mechanism given in Fig. 1 were defined by the limiting step hypothesis (eq. 13). The rate of the remaining reactions was given by elementary reaction rate expressions. In order to represent the reaction rates at different temperatures the Arrhenius expression was used (eq. 14), where parameter kj is the respective kinetic constant. dM iAqueous = − FrR eservoir−vase reservoir + Fi Gas−liquid + ¦ (ni , j × RR j ) × V Aqueous only dt j∈J dM iGas = ± FrR eact −r eserv − Fi Gas −liquid dt Gas −liquid
P Total × y i = K iequilibriu m × xi FrR eact −r eserv = K
Fi Gas − liquid = K
R eact − r eserv mass transf
Gas − liquid mass transf i
(8)
Total × P(Total Reservoir r ) − P( Reactor )
Equilibrium i
− yi
(6) (7)
, ∀i ∈ I
, ∀i ∈ I
( × (y
, ∀i ∈ I
)
)
, ∀r ∈ R
, ∀i ∈ I
(9) (10)
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FrR eservoir−vase = K
A. Gonçalves et al. R eservoir−vase mass transf
(
× H rBernoulli − H rVolume
α
−
α
α
−
)
, ∀r ∈ R α
RRLimiting = k H + × CBHBH−4 × CHH+ + + k H2O× CBHBH−4 × CHH2O2O Step
RRLimiting ≈ RR j
4
4
(11) (12)
, ∀j ∈ J
Step
Ea j · § ¸¸ k j = A j × exp¨¨ − © Rg × T ¹
(13) , ∀j ∈ J
(14)
4. Self-hydrolysis model results The unknown parameters of the reaction mechanism, namely the limiting step kinetic parameters, were estimated by adjusting the model results to the experimental data. This calculation was handled by the gPROMS Parameter Estimation function. The plots obtained to compare simulated and experimental data of the self-hydrolysis at different temperatures, solution volumes and pH are shown next.
Fig. 2. Graphical comparison of experimental and simulated data for the self-hydrolysis of sodium borohydride (10% wt.): a) at 45ºC, for 5, 25 and 50 ml initial reacting solution; b) solution pH at 45ºC; c) 5 ml initial solution at 45ºC, 55ºC and 65ºC; d) 5 ml initial solution at 45ºC, 55ºC and 65ºC with 3% wt. NaOH added.
The estimated parameter results for the self-hydrolysis mechanism are presented in Table 1.
Modeling of Catalytic Hydrogen Generation from Sodium Borohydride
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Table 1. Kinetic results for the adjustment of the gPROMS model to the experimental data of selfhydrolysis of sodium borohydride (10% wt.).
Ea H Ea H O AH + AH 2O Parameter 4 22 4 Value 8.669x10 6.433x10 9.501x10 2.042x108 −1 6 −2 −1 −1 Units J .mol dm 3.9 .mol −1.3 .s −1 J .mol dm .mol .s +
2
α BH
− 4
1.8 -
αH
+
1.2 -
αH O 2
0.5 -
The simulated data for the total gas produced and different reacting solutions volumes and temperatures, with 10% wt. NaBH4, show a very good agreement with the experimental data. Those obtained for pH and for the system with added NaOH, also adjust satisfactorily to the measured values. Considering these good results, this model can, therefore, be employed to predict, amongst other, NaBH4 storage properties, such as the solution half-life time.
5. Catalytic hydrolysis model results In order to apply the proposed self-hydrolysis mechanism to the catalytic hydrolysis reaction, the new kinetic parameters, equivalent to those shown in Table 1 for the selfhydrolysis, have to be estimated using the gPROMS Parameter Estimation function. The results of this adjustment are presented in Table 2. Table 2. Kinetic results for the adjustment of the gPROMS model to the experimental data of catalytic hydrolysis of sodium borohydride (10% wt.).
α BH 4− α H + α H 2O Ea H O AH + AH 2O Parameter Ea H 4 22 4 7 Value 8.669x10 6.433x10 6.839x10 7.077x10 0 1.2 0.5 Units J .mol −1 dm 0.6 .mol −0.2 .s −1 J .mol −1 mol 0.5 .dm −1.5 .s −1 +
2
With the new estimated kinetic parameters, the catalytic hydrolysis simulated were plotted along with the experimental data, as shown in Fig. 3.
60 ºC
1.6
49 ºC
Gas volume (l)
28 ºC 36 ºC
1.2
0.8
0.4
0.0 0
10
20
30
40 Time (min)
50
60
70
80
Fig. 3. Graphical comparison between simulated (lines) and experimental data (dots) for the gas volume produced during the catalytic hydrolysis of sodium borohydride (10% wt.) at 28ºC, 36ºC, 49ºC and 60ºC for a 5 ml solution.
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The use of the catalytic hydrolysis mechanism enables the operator to gather information on the reactor performance of a number of factors such as the initial reactant concentrations, the solution pH, the conversion and reaction end time, and the concentration of all the final species present in the reactor.
6. Conclusions This paper has presented a dynamic model for hydrogen production through the hydrolysis of sodium borohydride. This model can predict, in good agreement with the gathered experimental data, the behavior of a solution in conditions of alkaline inhibition, neutral pH and heterogeneous catalysis. To this purpose, the limiting step kinetic parameters were adjusted to describe both the self-hydrolysis and catalytic hydrolysis processes. It was shown that the linear behavior of the experimental catalysis can be described by a complex mechanism, based on the self-hydrolysis. This has the advantage, over the commonly used zero order rate law, to enable the testing of different starting conditions in the reactor and predict, for each case, various experimental results relevant for further developments, with a consequent economy in experimental effort. Future work will focus on the identification of all hydrolysis reaction products and their compositions, the effect of borates and initial borohydride concentrations on the reaction rate and the effect of the exchanged heat during the hydrolysis process.
7. Acknowledgements Partial funding by the European Commission DG Research (contract SES6-200618271/NESSHY) is gratefully acknowledged by one of the authors (C. M. R.). The authors also would like to acknowledge the support provided by the laboratory staff working at DMTP/INETI for making available the experimental data.
References [1] Gonçalves A., Castro P., Novais A. Q., Fernandes V., Rangel C., Matos H., 2007, Dynamic Modeling of Hydrogen Generation via Hydrolysis of Sodium Borohydride, Chem. Eng. Trans., 12, 243-248. [2] Davis R. E., Bromels E., Kibby C. L., 1962, Boron Hydrides. III. Hydrolysis of Sodium Borohydride in Aqueous Solution, J. Am. Chem. Soc., 84, 885-892. [3] Schlesinger H. I., Brown H. C., Finholt A. E., Gilbreath J. R., Hoekstra H. R., Hyde E. K., 1953, Sodium Borohydride, Its Hydrolysis and its Use as a Reducing Agent and in the Generation of Hydrogen, J. Am. Chem. Soc., 75, 215-219. [4] Rangel C. M., Silva R. A., Fernandes V. R., 2006, Hydrogen Storage and Production at Low Temperatures from Borohydrides, WHEC, 16, Lyon. [5] Wee J.-H., Lee K.-Y., Kim S. H., 2006, Sodium Borohydride as the Hydrogen Supplier for Proton Exchange Membrane Fuel Cell Systems, Fuel Proc. Tech., 87, 811-819. [6] Amendola S. C., Sharp-Goldman S. L., JanJua M. S., Spencer N. C., Kelly M. T., Petillo P. J., Binder M., 2000, A Safe, Portable, Hydrogen Gas Generator Using Aqueous Borohydride Solution and Ru Catalyst, Inter. J. of Hydrogen Energy, 25, 969-975. [7] Guella G., Zanchetta C., Patton B., Miotello A., 2006, New Insights on the Mechanism of Palladium-Catalyzed Hydrolysis of Sodium Borohydride from 11B NMR Measurements, J. Phys. Chem. B, 110, 17024-17033. [8] Kojima Y., Haga T., 2003, Recycling Process of Sodium Metaborate to Sodium Borohydride, Inter. J. of Hydrogen Energy, 28, 989-993. [9] Shang Y., Chen R., 2006, Semiempirical Hydrogen Generation Model Using Concentrated Sodium Borohydride Solution, Energy & Fuels, 20, 2142-2148.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Towards a new generation heat exchanger models Geert W. Haarlemmer a, Jérôme Pigourierb a
RSI, Parc Technologique de Pré Milliet, Montbonnot 38330, France
b
AXENS, 89 bd Franklin Roosevelt, Reuil-Mailmaison 92508, France
Abstract In the quest for more dependable process models, attending to small detail and integrating increasing their internal complexity will improve dynamic behavior and simulation accuracy. Although detailed heat exchanger models in dedicated steady state design programs are common, steady state process models and dynamic simulations have been based largely on shortcut heat exchanger calculations. However, detailed heat exchanger models can now be employed in dynamic simulations to enhance model performance significantly while maintaining reasonable computational times. An LNG liquefaction process, the new Axens Liquefin process, was modeled employing Indiss Dynamic Simulation Software and results presented in this article. Based on brazed aluminum plate-fin heat exchanger technology it, the process contains two closed refrigerant loops making it essential to provide correct simulation of refrigerant hold-up throughout the entire process. Keywords: Dynamic simulation, Plate-fin heat exchanger, Heat transfer.
1. Introduction Modern process plant developments are often accompanied by dynamic process simulators. Simulators are used initially for studies, later for operator training. The dynamic studies can address equipment integrity (compressor anti surge or thermal stress in plate and fin heat exchangers), controllability or operating strategy development. Dynamic simulation studies (like any other study) cannot realistically be used to cover all operational problems but can and do help to avoid certain problems. The scope of a dynamic simulation study should define the equipment to simulate, the thermodynamic models and the level of detail for the process models. Axens expressed the wish to create a dynamic simulator for the Liquefin process. This novel LNG liquefaction process is based on brazed aluminum plate-fin heat exchanger technology. After careful consideration of the physical phenomena dominating the dynamics of a real plate and fin heat exchanger, it was decided to increase the level of detail in the plate and fin heat exchanger module to include a discretized hold-up model and to rigorously calculate the heat transfer coefficients. The internal hydrodynamic multiphase behavior is solved by a dedicated network solver. To simulate the four heat exchangers as a single heat exchanger is an oversimplification as problems with re- or mal-distribution of the fluids may be overlooked. The common assumption of constant mass flows in the different cold-boxes is no longer valid during transients and changes in fluid distribution can have an important effect on the results.
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Heat exchanger inertia due to the metal and the process fluids can be important, especially at low flow rates. The discretized hold-up model greatly improves the quality of the model’s dynamic response. Another important measure is the rigorous calculation of heat transfer coefficients taking into account multi phase phenomena. A third consideration is the model’s ability to predict the temperature and pressure profiles and the true multi-phase flow profile along the flow path in the heat exchanger. Recent correlations for computing of heat transfer coefficients for all the different fluids under the various regimes encountered during operation were carefully selected, tested and implemented. These regimes include heat transfer in gas or liquid phases, or in two phase mixtures containing vaporizing or condensation regimes. All these phenomena were introduced in a plate and fin heat exchanger code.
2. Heat Transfer Coefficients Heat transfer coefficients vary greatly according to fluid quality, flow rate and heat exchanger geometry. Specialized heat exchanger design codes have sophisticated models to calculate the heat transfer coefficients. In dynamic simulation models, fixed film heat transfer coefficients ( α , in W/Km2) are used most often, frequently adjusted as a function of flow rate (Reynolds number Re). A typical implementation could be: § Re © Re Ref
α = α Ref ⋅ ¨¨
· ¸ ¸ ¹
0.8
(eqn 1)
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This implementation works reasonably well for single phase turbulent flow where the heat transfer coefficients can be predicted from the following well-known equation for continuous fins. Nu = 0.023 ⋅ Re0.8 ⋅ Pr1 / 3 (eqn 2) Here Nu (Nusselt) and Pr (Prandlt) are dimensionless numbers often used in heat transfer characterization. Nu = Dh ⋅ α / λ (eqn 3) Pr = Cp ⋅ μ / λ (eqn 4) Here Cp is the fluid heat capacity, λ is the heat conductivity, μ is the viscosity and Dh is the hydraulic diameter of the fluid channel defined specifically for each geometry. The inconvenience of this implementation is that there is little sensitivity to multi phase phenomena. Phenomena like multi phase intensification and dry-out are not really taken into account. The physical phenomena are very similar among the different geometries. However very few theoretical models exist that predict the film coefficients for a particular geometry. Correlations have been created for each geometry based on experimental results. These correlations either predict film coefficients directly or they predict the Colburn (Jh) number. From the Colburn numbers it is possible to calculate the film coefficient. Some manufacturers of plate and fin heat exchangers can supply the curves Jh as a function of the Reynolds number. The film coefficient ( α ) can be calculated from the Colburn number via the Nusselt number: Nu = Re⋅ Pr1 / 3 ⋅ Jh (eqn 5) Other formulations to calculate the heat transfer coefficients from the Colburn number are available. Care should be taken to use the correlations as they were intended. Correlations are often given for single-component fluids. If these correlations have to be applied to multi component fluids, the Silver correction can be applied (Silver, 1947). The local film coefficient thus obtained is used to predict the local heat transfer (Q in W) between the fluid and the metal, passing through the film.
(
∂Q = α ⋅ Tmetal − T fluid ∂A
)
(eqn 6)
Integrated on a small domain this gives: Q = α ⋅ A ⋅ (Tmetal − T fluid )
(eqn 7)
Each simulated fluid element exchanges heat with the metal. It is the metal that transports the fluid between the fluids. The metal and the fluids have their own thermal inertia. The overall heat exchanger can now be solved using plate-to-plate calculation or a Common Wall model. Both models are essentially the same. The Common Wall model solves for one metal at a single temperature while the plate-to-plate model solves for as many metal temperatures as there are separation walls. The overall equation to be solved for the Common Wall model at cell i is the following: Cp Metal *
i ∂ TMetal − ∂t
¦Į A
i i j j j= All fluides in the zone
And for each of the cells i and each fluid j:
i i * (TFluid - TMetal )= 0
(eqn 8)
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M ij *
∂ H ij ∂t
+ F ji *
∂ H ij ∂x
i i - α ij Aij * (TFluid - TMetal ) = 0
(eqn 9)
The single phase model implemented in the model is based on Shah and London for the laminar part and the equation presented above for the turbulent part. The film condensation model is based on the classical Nusselt analysis with extensions towards wavy and turbulent regimes. The boiling heat transfer is based on a two phase intensification of the heat transfer based on the Lockhart-Martinelli two phase multiplier. A full treatment of the calculation of heat transfer coefficients is not in the scope of this paper; for more information the reader is referred to work by Alpema, 2000; Greth, 1996 and Greth 1999.
3. Pressure Flow Relationship Heat exchanger models can be treated either as a singular pressure drop model much like a valve or it can be treated as a pipeline model where the pressure flow relationship is discretized and the accumulations are taken into account for each element. For the Liquefin simulation project it was decided to discretize the hold-up model to solve the heat exchanger as a multi fluid pipe model in which the fluids are thermally coupled. The basic pressure drop model is the following: ∂P f ⋅ u 2 ⋅ ρ = ∂l Dh
(eqn 10)
Here f is the friction factor. This can either be calculated from manufacturer’s correlations as a function of the Reynolds number, or can be maintained constant throughout the simulations. The pressure in the cells is closely related to the mass accumulations, via the density ( ρ ). The overall mass balance in each of the cells is given as follows. (Fin − Fout )* dt = CellAccumulation − Vol * ρ ( p) (eqn 11) The density should be correctly estimated as a function of the composition, pressure and enthalpy in the cell.
4. Simulation Project The first project to use this new technology was to simulate the Axens Liquefin process. This process has four cold boxes in parallel; it was decided to simplify the simulation to simulate only two cold boxes. Each of these two cold boxes is sized as two times 50%. All heat exchangers are multiple stream plate and fin heat exchangers. The scope of the simulation included the scrubber column, both compressor trains and the final end flash column. The thermodynamic system is based on SRK equation of state with Lee Kessler for the enthalpies. Several dynamic simulation cases were performed; one involved closing the third (low pressure) MR1 Joule Thomson (JT) valve at Cold Box 1 causing an upset. The flow rate through this valve was reduced to zero (Figure 3) in 20 seconds. The control scheme attempted to maintain a temperature difference between the MR1 inlet and outlet of each section by adjusting the position of the JT valves. It is this mechanism that reduces
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the MR1 flow in Cold Box 1, the HP and MP JT valves at the upset cold box close slightly as the MR1, normally passing though the JT3 valve, no longer needs cooling. The lack of liquefaction in the upset cold box causes an increase in pressure drop and the natural gas is directed towards Cold Box 2. This causes the JT valves for this cold box to open (Figure 3). The overall LNG flow rate (Figure 4) is obviously reduced.
Figure 3 – JT flow rates
Figure 4 –LNG flow rate (values removed for confidentiality reasons)
The MR2 is normally liquefied in the first stage cold box. It is used as the refrigerant in the second stage. The MR2 from the upset cold box heats up and is no longer completely liquefied (Figures 5 and 6). The second stage in the upset cold box loses a large amount of its capacity.
Figure 5 – Gas Fraction MR2
Figure 6 – Temperature MR2
The steady state temperature profile descending in the cold box is given below. In reality the cold-box is simulated in five sections as there are numerous inlets and outlets. This profile is initially (Figure 7) identical for each of the trains. The temperature profile in the failed cold box is drastically modified relative to the starting point (Figure 8). The upset part (LP) of the cold box displays a flat profile indicating that there is no heat transfer occurring in this part, the temperatures of the streams entering this part converge rapidly and remain constant. The MR2 flow rates remain constant owing to flow control. The second stage (MR2) of the cold box also displays a flat profile as it is now over-dimensioned relative to its cooling capacity. The expanded
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cold MR2 heats up slightly (Figures 7 and 8) and it has therefore less cooling capacity. For this reason it heats up rapidly and the upper part of the heat exchanger is no longer needed.
Figure 7 – Overall Temperature Profile Base case
Figure 8 – Overall Temperature Profile End of Run
5. Conclusions The results show that it is worthwhile to invest in detailed models to obtain valid predictions of heat exchanger behavior. The obtained results show a realistic evolution of heat exchange coefficients and internal properties, such as fluid temperature and hold-up. The results show how complex phenomena such as condensing and boiling can be taken into account in dynamic simulations and contribute to the accuracy of the conclusions of dynamic studies.
References Alpema Standards, The Standards of the Brazed Aluminum Plate-Fin Heat Exchanger Manufacturers’ Association, Second Edition 2000, Houston Texas. Manuel Technique, Groupement pour la Recherche sur les Echangeurs Thermiques. Chapters TM11, TM14, TE7, TE9 and TC1. CEA Grenoble, 1999. Lois de Transfert et Pertes de Pression dans les Echangeurs a Plaques et Aillettes Braisées, dans Compte-redu du Greth (Amelioration des techniques de transfert par évaporation) Annexe 11, Note Technique du Greth n° 97/422, 1996. Silver, L. (1947). Gas Cooling with Aqueous Condensation, Trans. Inst. Chem. Eng, 25, 30-42. B. Fischer (IFP), M. Khakoo (BP), Plate-fin heat exchangers - An Ideal Platform for LNG Process Innovation, Gastech 2002.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Brownian Dynamics and Kinetic Monte Carlo Simulation in Emulsion Polymerization Hugo F. Hernandez,a Klaus Tauera a
Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, Golm 14476, Germany
Abstract In this work, a generalized structure of a multi-scale dynamic simulation model for emulsion polymerization is presented. A simplified version of this multi-scale structure, a multi-scale kinetic Monte Carlo - Brownian Dynamics simulation, is used to study the competition between the capture of radicals by polymer particles and radical reactions in the aqueous phase in a seeded semibatch emulsion polymerization. In this case, the system is simulated by a kinetic Monte Carlo technique where the kinetic information of radical absorption is supplied by a lower scale Brownian Dynamics simulation model. The kinetics of radical capture by polymer particles is determined by Brownian dynamics simulation using a Monte Carlo random flight algorithm. The multi-scale model developed may be used to optimize the conditions for avoiding secondary particle nucleation in any particular emulsion polymerization system. Keywords: Brownian Dynamics Simulation, Emulsion Polymerization, Kinetic Monte Carlo simulation, Multiscale Modeling.
1. Introduction Radical emulsion polymerization is a widely used technique for the synthesis of polymers for a variety of industrial fields ranging from coatings and adhesives to biomedical applications (Tauer, 2004). Emulsion polymerization is preferred over other polymerization techniques especially because of the higher molecular weight of the polymers obtained, the low viscosity of the latex, the increased safety and productivity of the reaction, and for being friendlier to the environment (Daniel, 2003). However, good product quality control and batch to batch homogeneity are very difficult to achieve because radical emulsion polymerization is a highly complex dynamic process in which several simultaneous and usually competitive colloidal (aggregation, coalescence), chemical (radical generation, polymerization, termination, chain transfer) and physical events (diffusion, nucleation, swelling) occur at very different time scales and dimensions. These events take place, for instance, at rates ranging from about 100 to 109 s-1 and involving entities of very different length scales, such as ions and molecules (< 1 nm), macromolecules (1 – 10 nm), polymer particles (10 nm – 1 μm) and monomer droplets (>1 μm). Additionally, emulsion polymer systems may present a marked spatial heterogeneity on the macroscopic scale (imperfect mixing), making it very sensitive to temperature and composition profiles inside the reactor. For all these reasons, it is clear that a very precise representation of the process is only possible if different simulation techniques –such as Brownian Dynamics simulation, kinetic Monte Carlo stochastic simulation, Molecular Dynamics simulation, Computational Fluid Dynamics, etc.– are integrated into a multi-scale simulation approach (Fermeglia and Pricl, 2007; Kevrekidis et al., 2004; Chen and Kim, 2004).
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2. Multiscale modeling and simulation of emulsion polymerization A general representation of the different scales in emulsion polymerization is presented in Figure 1. At least seven different characteristic scales can be considered for multiscale modeling of emulsion polymerization. At each level, different simulation techniques can be used depending on the type of information required.
Figure 1. General multi-scale structure of emulsion polymerization
The atomistic scale considers the electronic interactions between different atoms of the same or different molecules. These interactions are determined by the corresponding solution of the Schrödinger equation. Therefore, Quantum Mechanics (QM) can be used to obtain valuable information about the system, such as activation energies and reaction rate coefficients, long-range potential parameters (such as the Lennard-Jones parameters) and interaction parameters (such as the χ Flory-Huggins parameter). At the molecular scale, the information obtained by QM can be used to determine transport properties (viscosity, diffusivity, thermal conductivity), chemical potentials and interfacial tensions. For this purpose, techniques such as Molecular Dynamics (MD) simulation or Monte Carlo (MC) simulation can be used. At the macromolecular scale it is possible to use a coarse grained (CG) representations of the structure of matter considering groups of atoms as single units, and it is also possible to use the mean field (MF) approach, by assuming continuity for the most abundant chemical species. This is the case of water in the aqueous phase of an emulsion polymerization, or monomer inside the polymer particles. Kuhn lengths and gyration radii of the polymer segments can be calculated and the conformation and arrangement of macromolecules in the aqueous phase and inside the polymer particles can be determined. Transport properties of small molecules inside polymer particles and transport properties of macromolecules in the continuous phase can be determined using Lattice or Off-lattice chain models. At the colloidal scale Brownian entities ranging from 1 nm to 1 μm are defined, and the kinetics of colloidal events such as collision, aggregation, flocculation, adsorption, etc., can be evaluated. The frequent collisions of small molecules from the continuous phase are responsible for the random motion, and therefore, for the diffusion of Brownian entities. This effect can be represented by Brownian Dynamics (BD) simulation which is based on the solution of Langevin’s equation of Brownian motion. At this level, Population Balances (PB) are also useful for incorporating polydispersity effects. At the
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microscopic scale, an integration of chemical, colloidal and hydrodynamic events is performed using the kinetic Monte Carlo (kMC) technique, also known as Stochastic Simulation Algorithm (SSA). The main condition for this integration is the assumption of perfect mixing inside the reference volume. At the mesoscopic scale, mixing hydrodynamic effects are dominant. In this case, Finite Element Modelling (FEM) techniques such as Computational Fluid Dynamics (CFD) can be used. These methods are able to calculate composition and temperature profiles inside the reactor. Finally, the macroscopic scale, which in this case is the emulsion polymerization reactor, is modelled basically with Ordinary Differential Equations (ODE) according to the laws of conservation of mass and energy (and momentum if necessary). A very important aspect of multi-scale modeling is the processing and exchange of information between the different scales. A lower-scale model requires information about the state of the system (temperature, velocity, composition, etc.) which is determined at a higher scale, while at the same time the upper-scale model requires parametric and structural information of the system obtained at a lower scale. Therefore, top-down and bottom-up information exchange procedures must be clearly defined (Chatterjee and Vlachos, 2006; Maroudas, 2000; Broughton et al., 1999). In the topdown procedure, a suitable grid decomposition method based on the distribution of states of the corresponding system scale must be used, while in the bottom-up procedure, the integration of the lower-scale results must be performed. In the next section, an illustrative example of multiscale modeling in emulsion polymerization is presented consisting only of two scales, the microscopic and the colloidal scales.
3. Application of multiscale modeling to semibatch seeded emulsion polymerization The system considered for this example is the semi-batch surfactant-free emulsion polymerization of vinyl acetate in the presence of a monodisperse polystyrene seed latex, initiated by a water-soluble initiator (potassium persulfate) at 80°C. A multiscale model is developed to simulate the molecular weight distribution of polymers in the aqueous phase during polymerization in the presence of radical-capturing polymer particles. For a monomer-starved feed addition policy, it is possible to assume that the monomer concentration in the aqueous phase is constant, that the monomer concentration in the polymer particles is low enough to give rise to a high viscosity inside the particles (therefore negligible radical desorption rates), and that the particles grow at the rate of monomer addition. 3.1. Microscopic scale: Kinetic Monte Carlo (kMC) simulation The kMC simulation technique is based on the SSA introduced by Gillespie (1976). The basic idea of this method is to randomly simulate competitive events (such as chemical reactions) based on their frequency of occurrence. The kMC method is a very good alternative to the classical deterministic rate equations especially when very infrequent events are considered or when a very low number of reactants are present. The kMC method has been successfully used to describe polymerization processes (Nie et al., 2005; Tobita et al., 1994; Lu et al., 1993). In the present example, the following competitive events are considered: Initiator decomposition in the aqueous phase, radical capture by polymer particles, and propagation and termination by recombination reactions in the aqueous phase. Additional events such as chain transfer reactions or termination by disproportionation can be easily included in the formulation of the kMC, but they are not considered in this example for simplicity. The key state variables at the microscopic scale are the chain length distribution and concentration of polymer in the
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aqueous phase. The kinetic coefficients used for the chemical reactions were taken from the literature (Ferguson et al., 2002). The capture rate coefficients are periodically calculated by lower-scale Brownian Dynamics simulations of the system. 3.2. Colloidal scale: Brownian Dynamics (BD) simulation The BD simulation method is based on the solution of Langevin’s equation for Brownian motion, which contains a random force term caused by the frequent random collision between molecules. BD has been successfully employed for simulating a wide variety of systems including molecules, colloidal particles and macromolecules, and it has been previously used for studying radical capture in emulsion polymerization (Hernández and Tauer, 2007). Radical capture kinetic coefficients can be easily estimated with BD simulation, by determining the average time required by a radical generated in the aqueous phase to enter a polymer particle. When the size of the polymer particles changes above a certain tolerance value in the kMC simulation, a BD simulation of radical capture under the new conditions is triggered. The capture rate coefficients for every chain length of the radicals are calculated and given back to the kMC model, to continue the upper-scale simulation. 3.3. Multiscale kMC-BD simulation 3.3.1. Simulation conditions In Table 1, the full set of conditions and parameters used during the multiscale kMCBD simulation is presented. In all cases the final polymer volume fraction was 20%. Table 1. Parameters used for the multiscale kMC-BD simulation of semi-batch seeded emulsion polymerization of vinyl acetate Parameter
Value
Parameter
Value
Temperature (°C) Seed volume fraction (%) Seed polymer density (g/ml) Poly(vinyl acetate) density (g/ml) Monomer feed rate (mol/l⋅s) Initial initiator concentration (mol/l) Propagation rate coefficient (l/mol⋅s) Primary radical molar volume (l/mol) Monomer unit molar volume (l/mol) Water viscosity (cP)
80 0.01 - 10 1.044 1.15
Simulation volume (l) Seed particle diameter (nm) Water density (g/ml) Aqueous monomer concentration (mol/l) Initiator efficiency Initiator decomposition rate coefficient (s-1) Termination rate coefficient (l/mol⋅s) Primary radical molar mass (g/mol) Monomer unit molar mass (g/mol) Particle size tolerance for BD simulation triggering
1x10-14 10-500 0.972 0.3
3x10-4 1x10-3 1.29x104 0.046 0.075 0.355
0.9 8.6x10-5 1.13x1010 96.16 86.09 5%
3.3.2. Simulation results Figure 2 shows an example of the multiscale integration in the kMC-BD simulation. Whenever the particle size is increased above the tolerance value of 5%, a BD simulation is triggered and the capture rate coefficients are updated. This can be seen in Figure 2 as “jumps” in the value of the rate coefficient. In this example, an increase of almost one order of magnitude in the capture rate coefficient between the start and the end of the simulation is observed.
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Capture rate coefficient, kc (l water/part.s)
1e-10
1e-11
BD simulation updates 1e-12 0
2000
4000
6000
8000
10000
Time, t (s)
Figure 2. Periodic determination of the capture rate coefficient of primary radicals by BD simulation. Seed particle size: 100 nm; seed volume fraction: 0.1%. 5
100 Number average chain length, Ln Weight average chain length, Lw Polydispersity index, PDI Max. chain length, Lmax Seed volume fraction: 1%
1000 Number average chain lenght, Ln Weight average chain length, Lw Polydispersity index, PDI Max. chain length, Lmax
20
3 1
Seed particle size: 100 nm
100
15
Lmax
Lmax
10
Ln, Lw, PDI
Ln, Lw, PDI
4
25
10
10
2
5 1 0
100
200
300
400
Particle diameter, dp (nm)
500
0.1 600
1 0.001
0.01
0.1
1
10
Seed volume fraction (%)
Figure 3. Number average chain length (Ln), Weight average chain length (Lw), Polydispersity Index (PDI) and Maximum chain length (Lmax) of the radicals formed in the aqueous phase for different particle size and volume fraction of the initial seed. The dashed lines represent best fit curves.
The effects of the competition between aqueous phase propagation and radical capture by polymer particles are clearly seen in Figure 3. The chain length of the polymer formed in the aqueous phase increases as the initial seed particle size increases (for a constant volume fraction) or the volume fraction of the initial seed decreases (for a constant particle size). That is, the degree of polymerization in the aqueous phase increases as the rate of radical capture decreases. An additional effect observed is the increase in the polydispersity of the polymer formed in water as the rate of radical capture decreases. This result reflects the fact that smaller radicals are captured by the particles more easily than the larger ones. Therefore, the larger radicals can grow even further in the aqueous phase increasing the polydispersity of the system. For the particular case considered, radical propagation in the aqueous phase is practically suppressed when initial seed particles smaller than 80 nm at seed volume fractions higher or equal than 1% are used. When radical propagation is unavoidable, it is possible to determine the extent of secondary particle nucleation in the system using a suitable nucleation model, like for example, the Classical Nucleation Theory (Becker and Döring, 1935; Tauer and Kuhn, 1995) or a modification thereof (Hodgson, 1984). The nucleation model requires the knowledge of the concentration (obtained from the
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kMC-BD simulation) and the solubility of all the nucleable species. Thus, it is possible to use the kMC-BD multiscale simulation model to optimize the conditions required for avoiding secondary nucleation in any given emulsion polymerization system.
4. Conclusions Multiscale dynamic simulation methods have been shown to be potential tools for the investigation of complex systems, in particular, of emulsion polymerization processes. In this paper, a kMC-BD simulation was presented as an example of the integration of different scales in the modeling of semi-batch seeded emulsion polymerization processes. The results obtained in the simulation can be used to find optimal conditions for the suppression of secondary nucleation in emulsion polymerization.
References R. Becker and W. Döring, 1935, Kinetische behandlung der Keimbildung in übersättigten Dämpfen, Ann. Phys., Vol. 24, pp. 719-752. J. Q. Broughton et al., 1999, Concurrent coupling of length scales: Methodology and application, Phys. Rev. B., Vol. 60, pp. 2391-2403. A. Chatterjee and D. G. Vlachos, 2006, Multiscale spatial Monte Carlo simulations: Multigriding, computational singular perturbation, and hierarchical stochastic closures, J. Chem. Phys., Vol. 124, 064110. J. C. Chen and A. S. Kim, 2004, Brownian Dynamics, Molecular Dynamics and Monte Carlo modeling of colloidal systems, Adv. Colloid Interf. Sci., Vol. 112, pp. 159-173. J.-C. Daniel, 2003, A long history with many challenges to meet in the future, in: Elaissari, A., Colloidal Polymers, Marcel Dekker, pp. 1-22. M. Fermeglia and S. Pricl, 2007, Multiscale modeling for polymer systems of industrial interest, Prog. Org. Coat., Vol. 58, pp. 187-199. C.J. Ferguson et al., 2002, Modelling secondary particle formation in emulsion polymerisation: Application to making core-shell morphologies, Polymer, Vol. 43, pp. 4557–4570. D. T. Gillespie, 1976, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., Vol. 22, pp. 403-434. H. F. Hernández and K. Tauer, 2007, Brownian Dynamics Simulation of the capture of primary radicals in dispersions of colloidal polymer particles, Ind. Eng. Chem. Res., Vol. 46, pp. 44804485. A. W. Hodgson, 1984, Homogeneous nucleation, Adv. Colloid Interf. Sci., Vol. 21, pp. 303-327. I. G. Kevrekidis, C.W. Gear and G. Hummer, 2004, Equation-free: The computer-aided analysis of complex multiscale systems, AIChE J., Vol. 50, pp. 1346-1355. J. Lu, H. Zhang and Y. Yang, 1993, Monte Carlo simulation of kinetics and chain-length distribution in radical polymerization, Makromol. Chem. Theory Simul., Vol. 2, pp. 747-760. D. Maroudas, 2000, Multiscale modeling of hard materials: Challenges and opportunities for Chemical Engineering, AIChE J., Vol. 46, pp. 878-882. L. Nie, et al., 2005, Monte Carlo simulation of microemulsion polymerization, Polymer, Vol. 46, pp. 3175-3184. K. Tauer, 2004, Latex Particles, in: Carusso, F., Colloids and Colloid Assemblies, Wiley-VCH, pp. 1-51. K. Tauer and I. Kühn, 1995, Modeling Particle Formation in Emulsion Polymerization: An Approach by Means of the Classical Nucleation Theory, Macromolecules, Vol. 28, pp. 22362239. H. Tobita, Y. Takada and M. Nomura, 1994, Molecular weight distribution in emulsion polymerization, Macromolecules, Vol. 27, pp. 3804-3811.
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Biodiesel production by heat-integrated reactive distillation Anton A. Kissa, Alexandre C. Dimianb, Gadi Rothenbergb a
Akzo Nobel Chemicals, Research and Technology Center, Arnhem, The Netherlands van’t Hoff Institute for Molecular Sciences, University of Amsterdam, The Netherlands
[email protected],
[email protected],
[email protected] b
Abstract This paper outlines the properties of biodiesel as renewable fuel, as well as the problems associated with its conventional production processes. The pros and cons of manufacturing biodiesel via fatty acid esterification using metal oxides as solid acid catalysts are investigated. A novel sustainable process based on catalytic reactive distillation is proposed as base case and a heat-integrated design as alternative. Significant energy savings of ~45% are possible compared to conventional RD designs. Keywords: reactive distillation, heat integration, green catalysts, sustainable fuels.
1. Introduction The depletion of petroleum reserves, increased energy demands, as well as concerns of rising greenhouse gas emissions, make the implementation of alternative and renewable sources of energy a crucial issue worldwide. Biodiesel has become increasingly attractive because it is sustainable and combines high performance with environmental benefits. Unlike petroleum diesel, biodiesel consists of a mixture of alkyl esters of long chain fatty acids. It can be produced from vegetable oils, animal fat or even recycled grease. Biodiesel has several advantages over petroleum diesel: it is safe, renewable, non-toxic and biodegradable; it contains no sulfur and is a better lubricant.1 Despite the chemical differences these two fuels have similar properties. The presence of oxygen in biodiesel (~10%) improves combustion and reduces CO, soot and hydrocarbon emissions, while slightly increasing the NOx emissions. Table 1 illustrates the biodiesel vs. petroleum diesel emissions. Biodiesel brings also additional benefits to the society: rural revitalization, less global warming, energy supply security. Its production is increasing rapidly as biodiesel can be distributed using today's infrastructure. The current biodiesel manufacturing processes have several disadvantages: shifting the equilibrium to fatty esters by using an excess of alcohol that must be separated and recycled, making use of a homogeneous catalysts that require neutralization hence causing salt waste streams, expensive separation of fatty esters products from the reaction mixture, high production costs due to relatively complex processes involving one or two reactors and several separation units. This paper presents the findings of the experimental work, and the results of the rigorous simulations of the reactive distillation process using AspenTech AspenPlus™. The heat integrated design proposed in this work overcomes these shortcomings of conventional processes, by combining reaction and separation into one unit. Compared to classic reactive distillation, the energy requirements in this heat integrated design are further decreased with –43% and –47% for heating and cooling, respectively.
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Table 1. Average biodiesel emissions compared to conventional petroleum diesel. Emission type Total unburned hydrocarbons Carbon monoxide (CO) Carbon dioxide (CO2) – life cycle production Particulate matter Nitrogen oxides (NOx) Sulfur oxides (SOx) Polycyclic Aromatic Hydrocarbons (PAH) Nitrated PAH's (nPAH)
B20 –20% –12% –16% –12% +2% –20% –13% –50%
B100 –67% –48% –79% –47% +10% –100% –80% –90%
2. Problem Statement Fatty acid methyl esters (FAME) – the main components of biodiesel – are currently manufactured by trans-esterification using liquid Na/KOH catalyst, or esterification of free fatty acids (FFA) using H2SO4 as catalyst. Note that due to the EU restrictions on sulfur content in diesel fuels (< 15 ppm), the catalyst removal is a crucial issue. The problem is that these liquid catalysts require neutralization and an expensive multistep separation that generates salt waste streams, thus making biodiesel an attractive but still costly alternative fuel. To solve these problems, we replaced the homogeneous catalyst with solid acids2 and developed a sustainable esterification process based on catalytic reactive distillation. Previously, we have screened a large number of zeolites, heteropoly-compounds, metal oxides, ion-exchange resins, and carbon-based solid acids.3 In this work, we focus on the application of metal oxides catalysts (based on niobia, zirconia, titania and tin oxide) in a heat-integrated reactive-separation design that is able to shift the chemical equilibrium to completion and preserve the catalyst activity by continuously removing the products. The heat-integrated design is based on the experimental findings and rigorous simulations in AspenTech Aspen Plus™.
3. Experimental work The reaction pathways and the possible products are shown in Figure 1 (left). The solid catalyst for esterification should have high activity and selectivity to avoid the formation of by-products; it should be water-tolerant to avoid catalyst deactivation and stable at relatively high temperatures to achieve high reaction rates. Additionally, it must be an inexpensive material that is readily available at industrial scale. Figure 1 (right) shows the chemical and phase equilibrium (CPE) diagram of the chemicals involved. Obviously, the region with two liquid phases should be avoided. REACTANTS Fatty Acid
Acid, 298ºC
Ester, 267ºC 1
Alcohol
VLE
esterification
dehydration
etherification
X2 (acid+ester)
0.8
Equilibrium reaction
0.6
LLE
0.4 0.2
Fatty Ester Main product
Ether
Water
Alkene
Secondary products
0
Alcohol, 65ºC
0
0.2
0.4
0.6
X1 (water+acid)
0.8
1
Water, 100ºC
Figure 1. Reaction pathways and possible products. Generalised CPE diagram.
Biodiesel Production by Heat-Integrated Reactive Distillation 6
6 Alcohol:Acid = 2:1 T=130°C, 2 %wt cat.
Amb-15
4
10%
5%
3%
1.5%
5 SZ / MMO
Nb2O5
3 2
X / (1-X) / [-]
X / (1-X) / [-]
5
777
4 Alcohol:Acid = 1:1 T=150°C, SZ catalyst
3
0.5%w
2
Cs2.5
1
Non-catalyzed
1
Non-catalyzed
0
0 0
30
60
90
120
0
Time / [min]
30
60
90
120
Time / [min]
Figure 2. Esterification of dodecanoic acid: (left) at 130°C using solid acid catalysts (2 wt%), (right) non-catalyzed and catalyzed (0.5-10 wt% SZ catalyst)
In a previous study we investigated metal oxides with strong Brønsted acid sites and high thermal stability.4 Based on the literature reviews and our previous experimental screening we focus here on application of metal oxide catalysts based on Zr, Ti, and Sn. Sulfated zirconia (SZ) outperformed other solid acids, and by increasing the amount of catalyst the reaction rate can be further increased (Figure 2). SZ also showed good thermal stability, high activity and selectivity for the esterification of fatty acids with a variety of alcohols ranging from C1 to C8. In our experiments using metal oxides as catalysts, no by-products were observed by GC analysis, under the reaction conditions. Remarkably, sulfated titania and tin oxide catalysts performed slightly better than SZ, showing increased conversion of the fatty acid. Nevertheless, SZ is less expensive and it is readily available at industrial scale. Note that the catalytic activity of SZ can be further enhanced by preparing it from using a chlorosulfonic acid precursor dissolved in an organic solvent, instead of the conventional H2SO4 impregnation. Other metals, such as iron, can also be added to enhance the activity. Higher sulfur content corresponds to higher acidity of the catalyst and consequently higher catalytic activity. The pore size plays an important role as the reactants and the products must be able to fit inside the catalyst to take full advantage of the total surface area available. The pore size of metal oxides are sufficiently large (>2 nm) to facilitate the mass transfer into and from the catalyst pores. This compensate for their lower acidity compared to other solid acids. Table 2 gives an overview of the tested catalysts, showing their pro/cons with respect to the fatty acid esterification reaction. Table 2. Advantages and disadvantages of the acid catalysts tested for fatty acids esterification.
Catalyst H2SO4 Ion-exchange resins H3PW12O40 Cs2.5H0.5PW12O40 Zeolites (H-ZSM-5, Y and Beta) Sulfated metal oxides (zirconia, titania, tin oxide)
Advatanges Highest activity Very high activity Very high activity Super acid Controlable acidity and hydrophobicity High activity Thermally stable
Disadvantages Liquid catalyst Low thermal stability Soluble in water Low activity per weight Small pore size Low activity Deactivates in water, but not in organic phase
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4. Results and discussion The design of the process is based on a reactive distillation column (RDC) that integrates reaction and separation into a single operating unit. An additional flash and a decanter or a distillation column, are used to guarantee the high purity of the products. RDC consists of a core reactive zone completed by rectifying and stripping separation sections, whose extent depends on the separation behavior of the reaction mixture. Since methanol and water are much more volatile than the fatty ester and acid, these will separate easily in the top. The conceptual flowsheet of the process is shown in Figure 3. MeOH recycle Reflux drum
Fatty acids
Methanol recovery
sep1
RDC MeOH
Water
reaction
sep2
MeOH
Flash separator
FAME
Figure 3. Flowsheet of biodiesel production by catalytic reactive distillation.
RDC is operated in the temperature range of 70–210 °C, at ambient pressure. Out of the 15 stages of the reactive distillation column, the reactive zone is located in the middle of the column (stages 3-10). The fatty acid stream is fed on top of the reactive zone while the alcohol is fed as saturated liquid, below the reactive zone. The reflux ratio in RDC is relatively low (0.1 kg/kg) since a higher reflux ratio is detrimental as it brings back water by-product into the column, thus decreasing the fatty acids conversion by shifting the equilibrium back to reactants. High purity products are possible, but due to the thermo-stability and high boiling points of the fatty esters (i.e. high temperature in the reboiler) this should be avoided. By allowing ~0.2% of alcohol in the bottom stream, the reboiler temperature in RDC can be limited to ~200 °C. The base-case design (Figure 4) is amenable to heat integration, as the feed stream could be pre-heated using the fatty ester product stream. Obviously, a feed-effluent heat exchangers (FEHE) should replace each of the two heat exchangers HEX1 and HEX2. TOP HEX1 ACID
F-ACID
REC-ACID
DEC
RDC HEX2 ALCO
WATER F-ALCO
REC-ALCO FAME BTM
FLASH
COOLER
Figure 4. AspenPlus flowsheet of biodiesel production by catalytic reactive distillation.
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F-ESTER2
TOP FEHE1 ACID
F-ACID
REC-ACID
DEC
RDC FEHE2 F-ALCO F-ESTER
ALCO
REC-ALCO F-ESTER3 FLASH FAME
BTM COOLER
Figure 5. Flowsheet of biodiesel production by heat-integrated reactive distillation.
The conceptual process design is further improved in this work by adding heatintegration around the reactive distillation column (Figure 5). The hot bottom product of the column, a mixture of fatty esters, is used to pre-heat both reactants: the fatty acid and alcohol feed streams. Figure 6 shows the composition, temperature and reaction rate profiles in the reactive distillation column. The mass balance of these designs is given in Table 2, while Table 3 shows a comparison between the base case and the heatintegrated alternative, in terms of energy requirements. Compared to the conventional reactive distillation design, the energy requirements in the heat-integrated case are further decreased with –43% and –47% for heating and cooling, respectively. Note that both design alternatives are suitable for a large range of fatty acids and alcohol feedstocks. These processes based on RD have no additional separation steps and produce no waste salt streams as water is the only by-product. By combining reaction and separation, one can shift the reaction equilibrium towards products by continuous removal of reaction products, instead of using an excess of reactant. Temperature / °C
Molar fraction 0
0.2
0.4
0.6
0.8
60
1
100
140
180
220
0
0
3
3 Water Acid
6
6
Stage Reaction rate
9
9 12
12
Ester
Methanol
Temperature
15
15 0
0.2
0.4
0.6
Molar fraction
0.8
1
0
0.5
1
1.5
2
2.5
Reaction rate / kmol/hr
Figure 6. Profiles in RDC: liquid composition (left), temperature and reaction rate (right).
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Table 2. Mass balance of the biodiesel production process based on reactive-distillation. F-ACID Temperature K Mass Flow kg/hr METHANOL ACID WATER ESTER-M Mass Frac METHANOL ACID WATER ESTER-M
F-ALCO
BTM
REC-ALCO
FAME
TOP
WATER
418.1
338.6
480.4
480.4
303.1
372.8
323.1
0 1167.607 0 0
188.631 0 0 0
1.883 0.144 0.005 1249.195
0.391 0 0.001 0.834
1.492 0.144 0.003 1248.361
0.011 0.11 104.988 0.01
0.011 0.015 104.986 0
0 1 0 0
1 0 0 0
0.002 0 0 0.998
0.319 0 0.001 0.68
0.001 0 0 0.999
0 0.001 0.999 0
0 0 1 0
Table 3. Comparison of energy consumption: base case vs heat-integrated design.
Operating unit Heating requirements 1. RDC reboiler 2. HEX1 / FEHE1 3. HEX2 / FEHE2 Cooling requirements 1. RDC condenser 2. Decanter 3. Cooler
Base case KW 136 95 8 KW –72 –6 –141
Heat integration KW 136 0 0 KW –72 –6 –38
Difference
–43 %
–47 %
5. Conclusions The integrated design proposed in this work is based on catalytic reactive distillation, powered by metal oxides as solid acid catalysts for fatty acids esterification. By adding heat integration to the conventional reactive distillation setup, significant energy savings of ~45% are possible. This heat integrated alternative improves the HSE benefits and economics of traditional biodiesel processes, and reduces dramatically the number of downstream processing steps. The major benefits of this approach are: 1. Very high conversions, as the chemical equilibrium is shifted towards completion. 2. Increased unit productivity, up to 5-10 times higher than conventional processes. 3. No excess of alcohol required, as both reactants are fed in stoichiometric ratio. 4. No catalyst neutralization step hence no salt waste streams nor soap by-products. 5. Sulfur-free fuel, since solid acid catalysts do not leach into the biodiesel product. 6. Multifunctional plant suitable for a large range of alcohols and fatty acids mixtures. 7. Reduced investment costs, due to less operating units required vs typical designs. 8. Minimum energy consumption, due to heat integrated reactive distillation design. Acknowledgement. We thank Marjo C. Mittelmejer-Hazeleger and Jurriaan Beckers from HIMS (University of Amsterdam) for the technical support.
References B. Buczek, L. Czepirski, 2004, Inform, 15, 186. T. Okuhara, 2002, Chemical Reviews, 102, 3641. A. A. Kiss, A. C. Dimian, G. Rothenberg, 2006, Adv. Synth. Cat., 348, 75. A. A. Kiss, G. Rothenberg, A. C. Dimian, F. Omota, 2006, Top. Catal., 40, 141.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Modeling comparison of high temperature fuel cell performance: electrochemical behaviours of SOFC and PCFC Jean-Marie Klein and Jonathan Deseure LEPMI, UMR 5631 CNRS-INPG-UJF, ENSEEG, BP 75, 38402 Saint Martin d’Hères, France
Abstract Fuel cells are highly efficient in terms of energy production, due to their high power efficiency. Solid Oxide Fuel Cells or Protonic Ceramic Fuel Cell are often proposed. The present paper aims to report on the electrochemical performance comparison between both systems by a Computational Fluid Dynamics approach. The developed model consists of mass, energy balances, and an electrochemical model that relates the fuel, air gas composition and temperature to voltage, current density, and other relevant fuel cell parameters. The electrochemical performances of SOFCs and PCFCs are analysed for several flow configurations. The simulations show that, the flow management should be an essential key during the design optimization. In the PCFC operating conditions, steam is produced at the cathodic side and an excessive steam can involve clogging of PCFC cathode. As a result, electrochemical performance of PCFCs decreases more than SOFCs executions. Keywords: Modeling, CFD, Fuel Cell, SOFC,PCFC .
1. Introduction In recent years, fuel cell technology has attracted considerable attention from several fields of scientific research. Fuel cells are highly efficient in terms of energy production, emit little noise and are non-polluting. The development of solid oxide fuel cells (SOFCs) has reached its new stage with intermediate temperature SOFCs (IT-SOFC). Unfortunately, poor performance can be observed due to the low ionic conductivity of electrolyte at these temperatures. Thus a new class of fuel cells is developed, based on ceramic electrolyte materials that exhibit high protonic conductivity at intermediate temperatures. The protonic ceramic fuel cell (PCFC) is fundamentally different because it relies on proton conduction through the electrolyte and not oxygen ions like SOFCs. Few experimental results on PCFC are reported in literature [1]. However, both SOFC and PCFC operations must be taken into account to clarify the fuel flow management of these devices. It can be added that meaningful flux descriptions are required in order to compare these technologies and to determine the limiting process. The aim of this study is to simulate both PCFC and SOFC operations to assess current, temperature and concentration distributions. We have used a CFD RC commercial package to help decision making on some important flow configurations. It should be noted that this study is theoretical and is based on literature data [2-3].
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2. Description of the planar fuel cells SOFC A planar high temperature fuel cell (700°C for PCFC and 800°C for SOFC) is an assembly of an electrolyte sandwiched between a porous anode and a porous cathode. The oxidant gas and fuel are respectively introduced at the cathodic and anodic side: at the same border (co-flow configuration), at the opposite borders (counter flow) and at the orthogonal borders (cross flow). The cell configuration for modeling is a 15 cm square and the thicknesses of anode, electrolyte, cathode and gas channel are respectively set to 30 μm, 50 μm, 500 μm and 500 μm. In the present model, a finite volume method using a computational grid [4] allows solving mass, charge, energy, momentum balances including transport through porous media, chemical and electrochemical reactions within porous electrodes in a gas diffusion electrode model. This model deals with three-dimension geometry in steady state conditions for PCFCs and SOFCs. The O2/N2/H2O and H2/H2O mixtures are respectively supplied at the air cathode and at the anode gas channel. In the gas phase, the mass conservation equation is described as follows [4]. It can be noted that all parameters definitions are presented in the work of Klein et al. [4].
∂ (ερ) + ∇.(ερ v ) = 0 ∂t
(1)
By neglecting compressibility, turbulence effects, the conservation equations for the transport of Nth species, in a porous media, can be presented in the following vector form: 2 ∂ (ερ v ) + ∇ . (ερ v.v ) = -ε∇p + ∇ . (εδ) + ε μ v ∂t κ
(2)
Gas transport within the porous electrode is described by using the Stefan-Maxwell diffusion with convective transport wherein the electrochemical reaction occurs at the triple phase boundary i.e. at the interface between electronic and ionic conductor and gas phase. Current density (related to charge transports) is thus the sum of two indissociable but different contributions: ionic and electronic conductivities σas, σaM (Ω1 m-1) and potentials φas and φaM (V). For PCFC or SOFC the hydrogen is electrochemically converted into electricity within the anode. Nevertheless, two kinds of electrochemical conversion could be distinguished. The expression of hydrogen oxidation is given by: − for SOFC 1 H 2 + 1 O 2 → 1 H 2O + e - and for PCFC 2 2 2
1 H 2 → H + + e2
(3-4)
The corresponding kinetics of electrochemical reactions (Eq. (3) and Eq. (4)) within the porous electrode is described by a Butler-Volmer equation at the triple phase boundary : § § α SOFC or PCFC F ·§ [H 2 ] or PCFC ¨ η a ¸¸¨¨ jat = jSOFC exp¨¨ a a0 ¨ RT © ¹© [H 2 ] 0 ©
· ¸¸ ¹
SOFCand PCFC
§ α SOFC or PCFC F ·§ [H 2 O] − exp¨¨ − c η a ¸¸¨¨ RT © ¹© [H 2 O] 0
· ¸¸ ¹
SOFC
· (5) ¸ ¸ ¹
Here the exchange current density is expressed in A m-2. The overpotential η (Eq. (5)) is defined as the difference of electronic and ionic potential as:
ηa =φaM −φas −Ea0
(6)
Ea0 is the potential difference between the electrolyte and the nickel in equilibrium, i.e.,
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when no current is produced. If we consider an electrochemical reaction occurring at anode, charge conservation may thus be expressed from the Ohm’s law as Eq. (7) and mass balances for each gas phase species i is given at steady-state by Eq. (8): §S· ∇.(σ as ∇Φ as ) = −∇ . (σ aM ∇Φ aM ) = j t ¨ ¸ © V ¹ eff §S· j ∇ . (ερ v w i ) = ∇ . J i + M i (ν i'' − ν i' )¨ ¸ t © V ¹ eff F
(7) (8)
On the Eq. (8) the first member corresponds to convection and second term of Eq. (9) standing for diffusion of species i uses the effective mass diffusion coefficient Di,eff within the porous medium to be deduced from the free stream diffusion coefficient Di by the so-called Bruggeman model [5]:
J i = ρD i ,eff ∇w i + ρw i ¦ D j,eff ∇w j
D i ,eff = D i ε τ
(9-10)
j
Oxygen reduction reaction occurs at cathode from electrochemical reactions as: for SOFC 1 4 O 2 + e - → 1 2 O 2 and for PCFC 1 4 O 2 + e - + H + → 1 2 H 2 O −
(11-12)
The exchange current jct at cathode is then obtained from a Butler-Volmer equation similar to Eq. (5). The electrolyte material, which is a suitable ionic conductor at high temperature, is completely impermeable to electrons circulation. The electrolyte potential is thus expressed by a classical Ohm’s law without any charge creation or consumption within the electrolyte.
3. Result and discussion Figures exhibit current density at the anode current collector surface for all flow configurations for a cell potential set to 0.3 V. In the case of co-flow configuration (Fig. 1), a linear gradient of current density of 3 mA cm-2 per cell centimeter have been observed for PCFC and SOFC. Nevertheless, the average current density of SOFC is upper than PCFC operation, the order magnitude of this difference is equal to 0.1 A cm2 .This gradient is due to fuel and oxidant consumption along the cell. Moreover, at the cathodic side of PCFC steam is produced and the kinetics of oxygen reduction is slower than the kinetics of hydrogen oxidation. Therefore, two limiting processes occur at PCFC cathode: oxygen reduction and oxygen access to the active area. For SOFC, water production appears at anodic side and the hydrogen conserves a better access to the catalytic area than oxygen in air steam mixture of PCFC. Indeed SOFC have a high kinetics of oxygen reduction and a good access of oxygen to the active sites. Finally we can observe (figure 2 and figure 3) that for counter flow and cross flow configurations, gradients are higher, and the maximum current density increases. Accordingly Larrain et al. [6], flow configurations influence the cell performance in case of SOFC. The SOFC mode shows a largest homogenous area of current density than PCFC mode.
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a)
b)
Figure 1. Current density for the co-flow configuration a) PCFC b) SOFC
a)
b)
Figure 2. Current density for the counter flow configuration a) PCFC b) SOFC
b)
a)
Figure 3. Current density for the cross flow configuration a) PCFC b) SOFC
4. Conclusion These first results show for similar gradients of current density in SOFC mode and PCFC mode, that average current densities of SOFC are higher than PCFC. These gradient are due to the reactant access, in the case of a PCFC the current density is
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lower than SOFC case, but the gas access have the same limiting value. The steam can clog the PCFC cathode, and the simulations have emphasized that it is relevant to operate in cross flow configuration for PCFC. The development of high temperature fuel cell depends on operating temperature and under this condition PCFCs are a promising attainment (700°C for PCFC versus 800°C for SOFC).
References 1. . G. Meng, G. Ma, Q. Ma, R. Peng, X. Liu, 2007, Ceramic membrane fuel cells based on solid proton electrolytes, Solid State Ionics, 178, 7-10, 697-703 2. P. Costamagna, A. Selimovic, M. D. Borghi, G. Agnew, 2004, Electrochemical model of the integrated planar solid oxide fuel cell (IP-SOFC),Chemical Engineering Journal, 102, 1, 61-69. 3. EG&G Services, 2000, Fuel Cell Handbook (Fifth Edition), Science Applications International Corporation, US department of energy, 8-5. 4. J-M. Klein, Y. Bultel, S. Georges, M. Pons, 2007, Modeling of a SOFC fueled by methane: from direct internal reforming to gradual internal reforming, Chemical Engineering Science, 62, 1636-1649. 5. D.A.G. Bruggemann, 1935, Ann. Physik. (Leipzig), 24, 636. 6. D. Larrain, J. Van herle, F. Maréchal and D. Favrat, 2004,Generalized model of planar SOFC repeat element for design optimization, J. Power Sources, 131, 1-2, 304-312
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An integrated framework for model-based flow assurance in deep-water oil and gas production Eduardo Luna-Ortiz,a Praveen Lawrence,b Constantinos C. Pantelides,a,b Claire S. Adjiman,a Charles D. Immanuela a
Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK b Process Systems Enterprise Ltd., Bridge Studios, 107a Hammersmith Bridge Rd, London, W6 9DA, UK
Abstract Flow assurance in deep-water developments has been identified as one of the main technological problems that the oil and gas industry faces today. Extreme conditions such as high pressures and low temperatures promote the formation of gas hydrates that can potentially reduce or completely block the flow path, causing severe financial losses. An integrated framework for model-based flow assurance management is presented. A two-phase flow model describing the thermal-hydraulic dynamics of subsea pipelines is coupled with a hydrate thermodynamic equilibrium calculation module. The model-based flow assurance framework determines whether hydrate formation can occur at every time instant and at every point along the pipe by comparing the hydrate formation equilibrium temperature and the actual pipeline temperature. The injection of hydrate thermodynamic inhibitors (e.g. methanol) is also included in the model. The framework is implemented in a state-of-the-art modelling tool (gPROMS®). In order to demonstrate its capabilities, shut-in and re-start transient production scenarios are evaluated. Our studies illustrate the benefits of a model-based approach in dealing with the complex and multi-faceted problem of flow assurance. Keywords: deep-water production, flow assurance, gas hydrate, two-phase flow, driftflux model.
1. Introduction and Motivation Strong energy demand and high prices of hydrocarbons are stimulating the oil and gas industry to explore and produce in challenging environments such as offshore deep-water (> 500 m water depth). Developing deep-water fields poses challenges that have transformed the industry dramatically (Ezekwe and Filler, 2005). Complex production systems include the entire flow structure from the wells and subsea multi-phase pipelines and risers to the host facilities and represent an investment of over US$1 billion (Sloan, 2005). A major technological challenge in deep-water field development is to ensure the continuous flow of hydrocarbons to the host platform or processing site (Mehta et al., 2000) under the extreme ambient conditions such as low seabed temperatures and high hydrostatic pressures, which can promote the formation of solids such gas hydrates that can clog the pipelines. Such blockages are costly because they interrupt production and require expensive corrective action to rehabilitate the flowlines. Hydrates are ice-like crystals that occur when the
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hydrogen bonds of water form a cage (host molecule) that encloses a small guest molecule (Sloan, 2007). Common guest molecules are light hydrocarbons (C1 through n-C4) and gases such as N2, CO2 and H2S. Low temperatures and elevated pressure conditions influence the hydrate formation. When the multi-phase fluid produced from a reservoir flows along a subsea pipeline, it cools down, and as a result, hydrate formation may occur. Gas hydrates plugs are most commonly formed during transient scenarios, in particular during a planned or unplanned shut-down of the production system. In a shut-in, the pressure increases highly and the flowline cools down until the temperature reaches that of the seabed so that the system is very likely to enter the hydrate formation region. Then, during start-up (or re-start) and shut-in, it is vital to manipulate the flow so that the thermal-hydraulic conditions at all points are outside the hydrate formation domain at all times. Flow assurance refers to the combination of fluid phase equilibria information with transient thermal-hydraulic analysis to develop strategies for the avoidance of hydrate formation (Kaczmarski and Lorimer, 2001; Kopps et al., 2007) and it has a direct impact on the design and operability of the system (Macintosh 2000). Currently, the basic flow assurance philosophy is to keep the subsea pipelines out of the hydrate region during steady-state. Flowlines are insulated to reduce heat losses to the surroundings, and to help the temperature to remain above the hydrate formation temperature. In addition, thermodynamic chemical inhibitors such methanol can be injected. Inhibitors change the phase behaviour of the mixture by moving the locus of hydrate formation to lower temperatures and/or higher pressures, hence extending the hydrate-free domain (Sloan, 2007). As a result of the multi-faceted and complex nature of hydrate formation, the modelling of the thermal-hydraulic dynamics of the oilfield fluid production system and the evaluation of equilibrium thermodynamic conditions for hydrate formation are essential for flow assurance. We present an integrated framework for flow assurance management. A two-phase flow model describing the transient thermal-hydraulic behaviour of gas & oil pipelines is coupled with a hydrate thermodynamic equilibrium calculation module. The hydrodynamic model is based on the mixture model (Ishii and Hibiki, 2006) that considers the relative motion (drift velocity) between the gas and liquid phases, in combination with a transient energy balance. On the other hand, the hydrate thermodynamic model is based on the van der Waals and Platteuw (1959) theory. This approach allows the user to determine whether hydrate formation can occur at each time instant and at each point along the pipe by comparing the hydrate formation equilibrium temperature and the actual temperature in the pipeline. The effect of an inhibitor is also modelled. In order, to show the capabilities of the framework, relevant transient scenarios are evaluated. 2. Model-based flow assurance framework The one-dimensional transient modelling of multi-phase flow in subsea pipelines and risers requires a number of conservation laws and closure
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equations. In this work, we adopt the mixture model (drift-flux model) for the analysis of the two-phase (liquid and gas) flow (Ishii and Hibiki, 2006). In the drift-flux model, the gas-liquid mixture is considered as a whole rather than two separated phases. The basic assumption is that the dynamics of the mixture can be expressed by a single momentum balance with a constitutive equation that specifies the relative motion between the phases. This assumption is valid when the phases are strongly coupled (e.g. dispersed flows). In addition, we assume that mass transfer between phases is governed by thermodynamic equilibrium. 2.1. Mechanistic two-phase flow model The compositional continuity equations are
∂ ª ∂ ª k k kº k k k kº « ¦ ci ρ ε » = − « ¦ ci ρ ε v » ∀i = 1,! , nc ∂t ¬ k = L ,G ∂z ¬ k = L,G ¼ ¼
(1)
The momentum balance for the mixture is
∂ (ρ v ) = − ∂ ρ v 2 + P − ρ g sin θ − τ w ∂t ∂z
(
)
(2)
The total energy balance for the mixture is
∂ (ρ E ) = − ∂ v (ρ E + P ) + Q ∂t ∂z
(3)
where L and G denote the liquid and gas phases respectively, nc is the number components, z is the axial dimension, cik is the mass fraction of component i in the phase k, εk is the volumetric fraction of phase k, ρk is the mass density of phase k, νk is the velocity of phase k, P is the pressure, Q are the heat losses to the surroundings, θ is the inclination of the pipe with respect to the seafloor, τw are the frictional pressure losses, E is the total energy including internal, kinetic and potential contributions. An over-bar represents a property of the mixture. 2.1.1. Closure relationship The hydrodynamic slip equation is given by
v G = Kv + S
(4)
where K is a factor that depends on the concentration and velocity profiles across the pipe section and S is the drift velocity that takes into account buoyancy effects. Several empirical expressions as function of physical and operational parameters exist for K and S in the literature. The correlations from Shi et al. (2005), adopted in this work, are widely accepted in the oil and gas industry and seem to predict accurately the hydrodynamics of disperse flow and counter-courrent flow.
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2.2. Gas hydrate thermodynamic model The thermodynamic gas hydrate model is based on the van der Waals and Platteuw theory. The gas-liquid-hydrate phases are considered in equilibrium. It is assumed that all components (water, hydrocarbons and other species including inhibitors) can appear in all 3 phases. The model consists of a material balance, gas-liquid equilibria, liquid-hydrate equilibria, and equations for hydrate mol fractions and cavity occupancies and can be found elsewhere (e.g. Sloan, 2007). For the purpose of this paper, we simply note that the general form of the model can be written, in compact form, as
(
)
f T * , x L , x G , x H , L, G , H , M , P = 0
(5)
where the model inputs are: M, the molar amounts of all components at a given pipe location and time; P, the pressure and H, the molar amount of hydrate. The model outputs are L and G, the molar amounts of the liquid and gas phases respectively, xH , xL and xG, the molar compositions of the hydrate, liquid and gas phases respectively and T*, the hydrate formation temperature. The incipient hydrate formation temperature can be obtained by specifying H=0.
Figure 1: Integrated multiphase pipeline model for dynamic flow assurance.
2.3. Integrated flow assurance framework The multiphase flow model of section 2.1 is coupled with the hydrate formation module of section 2.2 as shown in Figure 1. Given the pressure of the line and overall (mixture) composition at any point z and at any time instant t, as calculated with the multiphase pipeline model, the (incipient) hydrate formation temperature is computed using the thermodynamic hydrate formation model. We then define the hydrate propensity ΔT(z,t) as the difference between the hydrate formation temperature T* and the actual temperature in the flowline, T, calculated using the multiphase flow model. If the propensity is non-negative, then hydrate formation is thermodynamically favoured and hydrate may form. This approach has been implemented in modular form in the state-of-the-art modeling tool gPROMS® (PSE, 2007). 3. Case-study The strategy proposed is applied to a case study which demonstrates the complexity of the flow assurance problem, and illustrates the wealth of
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information that can be gained from a model-based approach. Consider the simple dry gas production system shown in Figure 2. The mixture consists of 11 components, more than 85% mol methane and very little water (gas-liquid ratio >0.95). The long pipe is slightly inclined and the short riser is vertical. Initially, the system operates at steady state and under a hydrate-free regime.
Figure 2: Flowsheet of deep-water gas production system.
3.1. Shut-in scenario. During shutdown of the production system, the choke valve at the topside is closed. We evaluate the dynamic hydrate propensity along the pipe to determine the time at which hydrate may start to form (touch-time). At 10 km from the wellhead, the touch-time is about 24 hr without inhibitor, while an extra 13 hr are gained if methanol (MeOH) is injected in a ratio of 1% w/w (Figure 3). Touch-time varies as a function of location z, due to the complex interactions within the system.
Figure 3: Hydrate formation propensity at 10 km from the wellhead during a shut-in.
3.2. Re-start scenario. Let us consider the shut-in with inhibitor of section 3.1. After a shut-in, the most common action is to re-start the operation. The line is first depressurised by bleeding the riser at the top, and then the valve is opened until the system is brought back to normal operation. As it was shown in section 3.1, the hydrate propensity increases during a shut-in. When the line is depressurised, the propensity decreases because the system is shifted away from hydrate formation domain. As the valve is opened for re-start, Joule-Thomson cooling occurs, and the hydrate propensity increases sharply along the pipe, leading to a maximum in ΔT with respect to time. Following this, as long as hot fluid circulates
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through the line, the temperature increases and hydrate propensity decreases again, as illustrated in Figure 4. It can be seen that additional MeOH injection may be necessary if a more conservative margin for hydrate propensity is required during re-start.
Figure 4: Maximum hydrate formation propensity in the pipeline during a re-start.
4. Concluding remarks and future work We have presented a model-based framework that incorporates a drift-flux model coupled with a thermodynamic hydrate model. The approach can be used to assess the propensity of hydrate formation during transient operation. The model predicts the complex dependence of hydrate formation on location, time and inhibitor concentration. Such a tool can be used to increase the productivity and reliability of deep-water developments, and for the control and optimisation of gas and oil production systems (e.g. optimal re-start policies). Acknowledgements Financial support from the UK DTI under project TP/2/SC/6/1/10244 is acknowledged. Advice from A. Meredith and M. Williams (Schlumberger Cambridge Research Ltd.) and from A. J. Haslam, A. Galindo and G. Jackson (Imperial College London) is also greatly appreciated. References Ishii, M. and Hibiki, T., 2006, Thermo-Fluid Dynamics of Two-phase Flow, Springer. Ezekwe, J. N. and Filler, S. L., 2005, Paper SPE 95066. Kaczmarski, A. and Lorimer, S., 2001, Paper OTC 13123. Kopps, R., Venkatesan, R., Creek, J. and Montesi A., 2007, Paper SPE 109670. Macintosh, N., 2000, Offshore, 60(10). Mehta, A., Walsh, J. and Lorimer, S., 2000, Ann. NY Acad. Sci., 912, 366-373. Mokhatab, S., Wilkens, R. and Leontaritis, K., 2007, Energy Sources, Part A, 29, 39-45. PSE, 2007, gPROMS® ModelBuilder 3.0.3, www.psenterprise.com Shi, H., Holmes, J., Durlofsky, L., Aziz, K., Diaz, L., Alkaya, B. and Oddie, G., 2005, SPE J., March, 24-33. Sloan, E. D., 2005, , Fluid Phase Equil., 228-229, 67-74. Sloan, E. D., 2007, Clathrates Hydrates of Natural Gas, Taylor & Francis. van der Waals, J. H. and Platteeuw, J. C., 1959, , Adv. Chem. Phys., 2, 2-57.
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Enhanced modeling and integrated simulation of gasification and purification gas units targeted to clean power production Mar Pérez-Fortes, Aarón Bojarski, Sergio Ferrer-Nadal, Georgios M. Kopanos, José Mª Nougués, Enric Velo, Luis Puigjaner Dept. of Chemical Engineering-CEPIMA, Universitat Politècnica de Catalunya, ETSEIB, Av. Diagonal 647, Barcelona, E08028, Spain
Abstract This work presents a structured and validated conceptual model of an integrated gasification combined cycle (IGCC) power plant. A pressurized entrained flow (PRENFLO) gasifier, subsequent gas cleaning operations for fly ashes, ammonia, and sulfur compounds removal, heat recovery steam generator (HRSG) and combined cycle unit operations have been modeled in steady state. The model has been developed using Aspen Hysys® and Aspen Plus®. Parts of it have been developed in Matlab, which is mainly used for artificial neural network (ANN) training and parameters estimation. Predicted results of clean gas composition and generated power present a good agreement with industrial data. This study is aimed at obtaining a support tool for optimal solutions assessment of different gasification plant configurations, under different input data sets. Keywords: conceptual modeling, process simulation, IGCC power plant, gas purification units, clean power production.
1. Introduction Integration of gasification and a combined cycle implies clear advantages as regards to environmental and economical considerations: gasification process contributes to feedstock and product flexibility, and the use of a combined cycle (CC) achieves higher efficiency compared to conventional thermal power plants (around 40-50%) [1]. The aim of this work is to build a decision support platform in order to obtain a wholly integrated and optimized process operation, including modeling and simulation of the gasifier reactor, cleaning and conditioning stages of produced gases and power generation.
2. IGCC power plant model development The model is implemented using two main chemical flowsheeting environments: Aspen Hysys® and Aspen Plus®, which are flexible tools for process simulation by providing thermodynamic models for the estimation of chemical properties and unit operation models for many processes. Aspen Hysys® has been chosen as the platform for the overall process simulation because of its capability of accepting custom models as extensions. These models could be complex chemical reactions (COS hydrolysis) or complicated unit operation (pyrolysis). It also allows creating new chemical components not included in its database, such as non stoichiometric solids for raw material and char definition.
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Alternatively, Aspen Plus® is used for calculations involving water systems and electrolytes. These ionic models are required to solve the phase equilibrium problem for unit operation systems such as venturi scrubbers, sour water strippers or MDEA absorbers. The aforementioned models have been integrated in Aspen Hysys® by means of artificial neural network (ANN) extensions. Data required to train each of the ANN’s comes from sensitivity analysis performed with Aspen Plus® while the neural network training is carried out using the ANN package provided with Matlab 6.5. Matlab is also used for gasifier model parameters estimation. 2.1. Assumptions Several assumptions throughout this work are made regarding the physical behavior of the industrial plant and others related to the representation of such behavior in the simulation software. In the first case, real plant operating conditions have been adapted to the simulation environment and in the latter case they refer to assumptions adopted within the same software. • Data from ELCOGAS IGCC power plant located in Puertollano (Madrid, Spain) are used to define the flowsheet sequence and for testing and model validation purposes. • According to industrial data, fuel raw material is a mixture of coal and petcoke. Ashes are a mixture of oxides primarily SiO2 and Al2O3 with traces of several other metals. Gasifier temperature and pressure operating conditions are shown in Table 1. Percentage of ashes that leave the gasifier reactor as slag and pollutants that pass to chimney emissions together with fly ash, are predicted using experimental correlations [2]. • Suspended solids are separated from the synthesis gas (syngas). Thus, no solids are assumed to be present in all downstream units, simplifying the model since only two fluid phases, liquid and vapor, are considered. • Feedstock particles diameter is considered to be uniform and equal to 5.5 mm. • Three Rankine cycles are set, one for each available pressure at plant site. The assumptions adopted within the software are: • All solid species considered, raw materials, ashes and char, are treated as HypoComponents in Aspen Hysys®. Raw materials and char are defined using their ultimate analysis and heat of formation. • Thermodynamic properties for phase separation are calculated using Peng-Robinson equation of state. • Conceptual models of every unit considered. 2.2. IGCC process description Fig. 1 and Fig. 2 represent two snapshots of the process flowsheet in Aspen Hysys®. An air separation unit (ASU) is used to obtain oxygen at a higher purity (85%) from air at high pressure. Input streams to this flowsheet section (Fig. 1) are: coal and petcoke mixture, air and demineralized water. Air is mainly used for combustion in a Brayton cycle and to obtain the required flow of oxygen for raw material gasification. Residual nitrogen is used in the CC to reduce NOx emissions. Output streams of this section are: electric power generated from steam and gas turbines and flue gas which is sent out through a chimney. Fuel raw material enters the gasifier unit where it is gasified and converted into syngas; this outlet gas is cooled down before entering the purification units. Heat is recovered by producing steam which is used in the CC turbines. Clean gas coming from the purification system goes into the CC where it is burned in a Brayton cycle. Steam is produced in a HRSG taking advantage of the high temperature arising from gas combustion before going through the chimney.
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Fig. 1. Simulated flowsheet: pre-treatment units, gasification and power generation units.
Fig. 2 shows the flowsheet which contains all the models that mimic the plant gas purification stages. Water and pH controlling streams (sodium hydroxide and sulfuric acid solutions) are inlet streams for the venturi and sour water stripper units, respectively. Other inlet streams are oxygen and air to the Claus plant. Water from the sour water stripper, liquid sulfur produced in the Claus plant and fly ashes are outlet streams. In the venturi scrubber, the gas is put into contact with water that absorbs and removes pollutant species (acid and basic species). This water is cleaned downstream in the sour water stripper. Syngas is further purified after its passage through the COS hydrolysis reactor. This unit aims at converting all COS into H2S, which is next removed in the MDEA absorber, maximizing sulfur retention. Polluted streams from sour water stripper, COS hydrolysis reactor and MDEA absorber are sent to the Claus plant, where sulfur is recovered in liquid form. A recycle gas stream from the Claus plant goes to the COS hydrolysis reactor to further increase COS conversion. Finally, the obtained clean gas, after the MDEA absorber, is sent into the CC.
Fig. 2. Simulated flowsheet: syngas purification units.
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3. Plant units modeling In order to test the performance of the model, five sets of raw material compositions have been tested. Base case considered a mixture of 50/50%wt of coal and petcoke. 3.1. Input data Table 1 presents main input parameters and conditions from the real plant that have been directly introduced in the plant simulation. Table1. Operating conditions of ELCOGAS plant (“ar”: as received basis.“mb”: in mass basis). Base Case
Mix2
Mix3
39
45
54
58
61
55
46
42
68.28
64.93
61.95
60.1
3.21
3.16
3.07
3.1
3.46
1.97
2.71
3.37
3.69
Oxygen (% ar)
1.42
1.51
1.29
1.47
1.26
Sulphur (% ar)
3.34
3.79
3.43
3.24
2.97
Moisture (% ar)
2
0.75
1.04
1.29
0.93
25.17 17.3
20.49 16.8
23.44 17.1
25.61 18.2
27.95 18.5
37,847
37,197
37,638
37,997
38,456
2,600 1,600
2,600 1,600
2,600 1,600
2,600 1,600
2,600 1,600
Input Data Coal (%)
50
Coke (%)
50
Carbon (% ar)
61.68
Hydrogen (% ar)
2.93
Nitrogen (% ar)
Ashes (% ar) Volatile Matter (%dry) LHV (MJ/m3) Feed (t/day) Gasification Temperature (ºC)
Mix1
Mix4
Gasifier Pressure (bar)
25
25
25
25
25
O2/feedstock ratio (mb)
0.715
0.715
0.715
0.715
0.715
H2O/feedstock ratio (mb)
0.13
0.13
0.13
0.13
0.13
3.2. Gasifier The conceptual model of the PRENFLO gasifier takes into account several assumptions. Firstly, it considers a non-isothermal reactor by assuming adiabatic behavior, and secondly, a feedstock that enters the reactor with a maximum of 2%wt of moisture. In a previous step to the HRSG, a quench gas cools the syngas from aproximately 1600 to 800ºC. A conversion of around 90% of the char is obtained. The next reaction sequence is considered to take place within the gasifier model: • Pyrolysis is modeled using a series of experimental correlations from specialized literature [3, 4] which depend on temperature and volatile matter. Production of pollutant species (H2S, COS, NH3 and HCN) is represented by correlations taken from [5, 6] and industrial historic data. Every set of correlations is infered from different coal types and analysis. • In the case of volatiles and char combustion, volatiles produced by raw material pyrolisis are considered to be consumed by complete combustion, producing CO2 and H2O. Kinetics of char combustion main reactions have been taken from [7, 8]. This step considers total oxygen consumption. • Char gasification comprises char-CO, char-H2O and char-H2 reactions. Their kinetic parameters have been taken from [7, 8]. • Gas equilibrium reactions are performed by minimizing the Gibbs free energy of all present species. After this last step, syngas is obtained. 3.3. Heat recovery steam generator (HRSG) Heat from gas turbine exhaust gases (at 535ºC) is mainly recovered by the HRSG which produces steam at three different pressures (127, 35 and 6.5 bar). Within the high and
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intermediate pressure steam circuits, extra heat recovery is achieved by cooling syngas (from 800 to 240ºC) and producing saturated steam. 3.4. Gas cleaning units All purification units work at high pressure (22 bar). For the base case, this model shows good agreement between simulated results and industrial data for the outlet streams from venturi scrubber and sour water stripper (Fig. 3). In the case of the venturi, the model predicts lower compositions for all species. Stripper simulation produces values slightly higher than industrial data for CO2 and H2S, and lower for NH3 and HCN.
Fig. 3. Comparison of ELCOGAS data and predicted values for dry gas main components of the outlet gas from the venturi scrubber (left) and from the sour water stripper (right).
Regarding MDEA absorber behavior, (Fig. 4), a remarkable agreement exists between industrial and model predicted composition. Comparing Claus plant results (right, figure 4), main difference between predicted and industrial composition arises in CO composition. Amount of liquid sulfur removed is quite similar for both real and predicted values (3113 and 2810 kg/h, respectively).
Fig. 4. Comparison of ELCOGAS data and predicted values for dry gas main components of the clean gas (left) and the recycle gas (right).
3.5. Global model results and discussion Table 2 shows overall simulation results compared to ELCOGAS data for different raw material mixes. Major differences are found for N2 and water composition in clean gas
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stream. Lower volume percentages are predicted for H2 and CO, while higher values are obtained for H2S, COS and water Simulation of produced power is in good agreement with plant data; this comparison is worst in the case of Mix4. Table2. Power generation and clean gas composition comparison. Error: total power deviation. Mix1
Mix2
Mix3
Mix4
Output Data Clean gas composition H2 (vol. %) CO (vol. %) CO2 (vol. %)
Exp.
Model
Exp.
Model
Exp.
Model
Exp.
Model
21.11 62.06 1.43
19.82 49.76 2.55
21.17 61.1 2.19
19.53 49.76 2.58
21.14 60.36 2.29
19.05 49.9 2.6
19.8 60.7 3.05
18.89 49.88 2.61
N2 + Ar (vol. %)
15.34
27.54
15.47
27.81
16.14
28.11
16.36
28.28
0
0.36
0
0.38
0
0.39
0
0.38
H2O (vol. %)
0.07
0.32
0.07
0.33
0.07
0.33
0.08
0.33
LHV (MJ/m3) Gas turbine power (MW) Steam turbine power (MW) Total power (MW) Error (%)
8.259
7.985
8.126
7.956
8.038
7.923
7.796
7.905
168.7
187.5
173
183.9
163
181.4
137.8
180.6
121.5
112.5
130
109
124.8
108
109.7
105.8
290.2
299.7 3.27
303
293 -3.30
287.8
289.4 0.56
247.5
286.4 15.72
H2S + COS (ppm)
Differences may be caused by a combinated effect of several simplifications that this models relies on. Pyrolisis model estimates char, nitrogen and sulphur compounds production., and it is based on experimental correlations. Char combustion and gasification reactions are also based on experimental correlations. However, these correlations have been taken from the literature and do not exactly correspond to the actual raw material mixtures. ANN results are limited to an interval of variation of gases composition. Also, the combustion of the clean gas is modeled with a Gibbs reactor.
4. Conclusions A validated conceptual model of an IGCC power plant of co-gasification has been performed with a very good agreement between model results and ELCOGAS data. Future work will be envisaged to further improve the model simplifications and optimize the process based on economical and environmental considerations.
Acknowledgement Financial support received from the European Community projects (MRTN-CT-2004-512233; RFC-CR-04006), the Generalitat de Catalunya with the European Social Fund (FI grant) and the Ministerio de Educación y Ciencia (FPU grant) is fully appreciated. ELCOGAS IGCC power plant provision of data for validation purposes is acknowledged with thanks.
References [1] IGCC Puertollano ELCOGAS, 2001, A clean coal gasification power plant. [2] CSIC (Consejo Superior de Investigaciones Científicas), Jaume Almera Institute, Spain [3] S.Balzioc and P.G.W. Hawksley, Ind. Eng. Chem. Process Des. Dev., 9, no. 4 (1970) 521 [4] R. Loison and R. Chauvin, Chimie et Industrie, 91, no. 3 (1964) 269 [5] F. García-Labiano, J. Adánez et al., Fuel, 75, no. 5 (1996) 585 [6] S. Kambara, T. Takarada et al., Energy & Fuels, 7, (1993) 1013 [7] C.Y. Wen and T.Z. Chaung, Ind. Eng. Chem. Process Dev., 18, no. 4 (1979) 684 [8] R. Govind and J. Shah, AIChE Journal, 30, no. 1 (1984) 79
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Absorption of aromatic hydrocarbons in multicomponent mixtures: A comparison between simulations and measurements in a pilot plant Diethmar Richtera, Holger Thielertb, Günter Woznya a
University of Technology Berlin, Strasse des 17. Juni 135, 10623 Berlin, Germany Uhde GmbH, Friedrich-Uhde-Strasse 15, 44141 Dortmund, Germany
b
Abstract In this work the recovery of aromatic components, i.e. benzene, toluene and xylene from coke oven gases is regarded by experimental investigations as well as simulation studies. For the reliable calculation of this process extensive studies are carried out in order to describe the absorption rate and the behavior of the conventional applied multicomponent absorption liquid. In the first part of this work, the implemented models are discussed and validated. In the second part, a comparison between the absorption capacity of the conventional and the alternative absorption liquid biodiesel is taking place based on experimental data. Based on these experiments, the application and innovation of this process will be discussed. Keywords: VOC, absorption, coke-oven gas, rate-based approach, biodiesel
1. Introduction The absorption of aromatic hydrocarbons from coke oven gases takes place on the gas purification side, i.e. the white side of a coke oven plant (fig.1), in order to recover valuable crude chemicals for the chemical industry. In the conventional process a complex mixture of polyaromatic hydrocarbons is applied as absorption liquid with 400 up to 500 different components, similar in their molecular weight and structure. Previous investigations [3], [4] have shown that only ten of these components can be Fig. 1 Coke-oven gas purification process identified which sum up to approx. 54 %mass. Up to now, the simulation of the regarded process fails mainly due to the complexity of the mixture, the lack of thermodynamical data and variations of thermodynamical properties during the process caused by losses of light washing oil components and thereby the accumulation of heavier ones. In order to be able to simulate this process (fig. 2) more accurately, extensive studies are carried out in order to implement a rigorous and robust model approach. For real-time applications the model requirements are defined by model robustness, the required simulation time as well as the accuracy especially for column and process design. The application of structured packing in the absorption column complicates the application of an equilibrium model due to the determination of the HETP value and uncertainties caused by variations of the gas and liquid inlet streams during process operation and thus the
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probability of varying HETP values. In this work a modified rate based approach is presented, it is evaluated through a certain number of measurements for the main components which are recovered from the gas stream. Investigations on the phase equilibrium behavior concerning the main BTX components in the conventional applied coal tar oil and also in the alternative absorption liquid biodiesel have shown that an increase of almost 30% of absorption capacity Fig. 2 Recovery of aromatic hydrocarbons offers a reduction of required washing medium in this process and therefore a significant reduction in the operation as well as investment costs. In this contribution, a comparison between the conventional and the alternative absorption liquid is presented based on experimental results.
2. Thermodynamical investigations Extensive studies were carried out in [3] and [4] for the determination of general thermodynamical properties related to temperature in order to provide more accurate process simulation. These investigations have shown that the high number of components similar in molecular weight and structure complicates the calculation of properties and therefore the simulation of the whole process. Changes in the composition of the applied washing oil occurring during the process are held within certain operation conditions due to the addition of fresh oil and the removal of heavy components. Further experiments were carried out in order to describe the thermodynamical behavior of the regarded BTX components in the coal tar oil. Thereby and due to the adjustment of missing parameters [5] it becomes possible to calculate activity coefficients depending on the molar concentration and the temperature by the application of the modified UNIFAC model. The same set of experiments was also carried out for the alternative absorption liquid biodiesel (Rapeseed oil methyl ester = RME). The experiments for RME, also available in [1], emphasizes that the activity coefficients of benzene, toluene and xylene in biodiesel, with values less than unity, are more desirable than in case of coal tar oil due to the fact that a higher absorption capability is obtained. Table 1 presents a summary of the main results. Table 1: Activity coefficients for the investigated solvents (T = 303.15K)
Ȗ(Benzene)
Ȗ(Toluene)
Ȗ(Xylene)
Density Molecular T=298.15K weight Coal tar oil 1.7 2.7 4.6 1075 180 RME 0.63 0.65 0.68 870 290 Also the solubility of overcritical components expressed by the Henry coefficients was determined for the main coke-oven gas components [3] for more accurate calculations. Solvent
3. Model approach The calculation of the absorption as well as desorption process is based on an equilibrium model as well as rate-based approach implemented in FORTRAN as user-
Absorption of Aromatic Hydrocarbons in Multicomponent Mixtures
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defined subroutine for the application in ChemCAD. Adjusted parameters in the case of the equilibrium model, are the Murphree efficiency for the plate column (desorber), the HETP value for the packed column (absorber) equivalent to the number of theoretical stages. The main requirements for the ratebased approach are model accuracy as well as robustness, in order to carry out real-time simulations for the application of model predictive control. In the general rate-based approach (fig.3) regarding the bulk phases of the liquid and the gas phase separately, mass and heat transfer rates are calculated by the transfer rates crossing the phase boundary between the bulk phases. In this work certain equations are replaced by more robust ones, leading to a better convergence Fig. 3: Mass transfer stage behavior and a higher robustness. The investigations have shown that coupling the mass transfer rates only to one of both bulk phases increases the model robustness significantly for multicomponent mass transfer calculations. Therefore, the original component balances (2) and (3) are replaced by equations (4) and (5). Original rate based equations:
0
Vy i V In y iIn N iVap
(1)
0
Lx i LIn x iIn N iLiq
(2)
0
N iVap N iLiq
(3)
Modified rate-based equations:
0
Vy i V In y iIn N iLiq
(4)
0
Vy i V In y iIn Lx i LIn x iIn
(5)
For the energy balances, the correlation for the liquid side temperature is replaced by the energy equation of the whole section. Investigations on the absorption process have shown that equation (6) leads to higher robustness, whereby variations in the temperature profile due to disregarding the energy transfer coupled to the mass transfer are negligible. Optionally the equation can also be replaced by the general interface energy balance [6]. Alternative energy balance:
0 T I T Liq
T
Vap
T Liq
Liq 1D
D Vap
(6)
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Mass transfer rates, pressure drop in structured packing and liquid hold up are calculated by the correlations from Billet and Schultes taken from [2]. Assuming cross effects negligible, the binary diffusion coefficients are calculated for each component in the mixture of the coke-oven gas by Fuller and in the washing fluid by Wilke & Chang.
N i
NC 1
¦k
ij
(7)
(8)
a I c x j x Ij
j 1
N i | ki ,Solvent a I c xi xiI
Investigations on the off-elements in the matrix of mass transfer coefficients show that the influence of the cross elements are negligible. Therefore, the simulation time can be reduced and the model robustness is improved considerably due to the simplification of equation (7) by equation (8). The calculation of the concentration and the temperature profiles is carried out for an increasing number of discretization elements. For the laboratory column with a packing height of 2.6m an optimal number between 10 and 12 elements can be pointed out.
4. Experimental Setup The experimental validation of the implemented models is carried out in the pilot plant illustrated by fig. 4. The column is equipped with 2.6m of Mellapak 350Y with a diameter of 0.1 m. For the reduction of maldistribution caused by wall effects three liquid distributors are placed along the column height. The gas concentration profile is evaluated taking gas samples continuously at the gas inlet and at the positions of the liquid distributors and are analyzed by a gas transmitter (Dräger Fig. 4: Flow sheet of pilot plant Polytron IRExES). The temperature profiles are determined by the use of eight temperature sensors of type PT100 placed along the column height. The gas load is controlled by a gas blower and the gas load is kept constant at F = 1.5 Pa1/2 (G = 37m³/h) during all experiments. The liquid load is controlled by a radial pump in order to investigate liquid loads between B = 6.8 – 11.3m³/m²h (L = 60-100 l/h).
5. Experimental results 5.1. Model validation During the first set of experiments the absorption capability of the conventional applied coal tar oil concerning the components benzene, toluene and m-xylene is analyzed for constant gas inlet temperatures between 28° and 30°C.
Absorption of Aromatic Hydrocarbons in Multicomponent Mixtures Benzene
803
Toluene
14.0
6.0
12.0
5.0
10.0 simulation
simulation
4.0 8.0 6.0 4.0
3.0 B = 11.3 m³/m³h T=28°C B = 9.1 m³/m³h T=28°C
2.0
B = 9.1m³/m²h T_Gas = 28°C
B = 9.1 m³/m³h T=30°C
B = 11.3 m³/m²h T_Gas = 30°C 2.0
B = 6.8 m³/m³h T=28°C
1.0
B = 11.3 m³/m²h T_Gas = 28°C
0.0
0.0 0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
experim ental data [g/Stdm ³]
experimental data [g/Stdm³]
Fig.5: Comparison between calculated and measured benzene concentration profiles in the gas phase
Fig. 6: Comparison between calculated and measured toluene concentration profiles in the gas phase
In figures 5 and 6 the rate-based approach is evaluated schematically by parity plots. The comparison with the equilibrium model points out that a number of 6 to 7 stages, which corresponds to an HETP value of 0.37 to 0.43m leads to comparable results. Only in the case of higher liquid loads the maldistribution between the liquid distributors and thus the deviation between calculated and measured profiles increases for both models. The calculation of the outlet concentrations are almost within an accuracy of ±0.3g/Nm³ for the regarded components. 5.2. Studies on absorption capacity During the second set of experiments studies on the absorption capability of the alternative absorption liquid were carried out. The comparison between the experimental concentration profiles (fig. 7) of benzene in the different absorption liquids illustrates that the absorption rate is about 35% higher compared to the conventional absorption liquid and, therefore, lower outlet concentration can be obtained for the same liquid and gas load. Concentration profiles for B = 11.3m³/m²h
Concentration profiles for reduction of liquid load
3.00
3.00
2.50
2.50
Coal tar oil B=11.3 m³/m²h RME B=11.3 m³/m²h
1.50
1.50
1.00
1.00
0.50
0.50
0.00 0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
Coal tar oil B=11.3 m³/m²h RME B=7.9 m³/m²h
2.00 Height [m]
Height [m]
2.00
16.00
c (Benzene) [g/Nm³]
Fig. 7: Concentration profiles for coal tar oil and RME for same liquid load B=11.3 m³/m²h
0.00 0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
c (Benzene) [g/Nm³]
Fig. 8: Concentration profiles for coal tar oil and biodiesel for different liquid loads
In the case of biodiesel as absorption liquid the corresponding outlet gas concentration is obtained after 67% of packing height compared to the measurements with coal tar oil, which is equal to 1.7m of packing (Fig. 7). Therefore a reduction of packing height and thus a decrease of investment costs is provided. In the second experiment the liquid load is reduced to B = 7.9 m³/m²h which is equal to a reduction of 30% in the volumetric flow. Fig. 8 illustrates the comparison between the reduced RME flow (B=7.9m³/m²h)
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and the higher coal tar oil flow rate (B=11.3m³/m²h). In this case, the concentration profiles almost corresponds each other.
6. Conclusions The validation of the implemented rate-based approach as well as the equilibrium model have shown that both models are able to predict the absorption rate with sufficient accuracy. Due to the modification of the rate-based approach model, the robustness is increased significantly. The simulation time is reduced by the simplification concerning the mass transfer rates, which are expressed by binary mass transfer coefficients. The concentration profiles for both absorption liquids point out that investment as well as operation cost can be reduced by changing the absorption liquid onto the more favorable biodiesel. Due to the possibility of reducing the required washing oil rate about 30% through savings in investment costs for heat exchangers, pumps as well as column diameter are available.
7. Outlook During ongoing studies the desorption process is studied also in order to analyze the rate-based approach with the focus on the assumed simplifications. For the application in the industrial process the alternative absorption liquid is studied concerning thermal as well as chemical stability especially during the desorption process.
Symbols a B c k L N Q T V x y
Effective interfacial area [m²] Liquid load [m³/m²h] Molar concentration [kmol/m³] Mass transfer coefficient [kmol/m²h] Liquid molar stream [kmol/h] Molar flux across interface[kmol/h] Heat flux across interface [W/h] Temperature [K] Vapor molar stream [kmol/h] Molar fraction liquid side [kmol/kmol] Molar fraction vapor side [kmol/kmol]
Greek letter Į Heat transfer coefficient
[W/m²K]
Superscripts I Related to interphase In Inlet streams Liq Liquid phase Vap Vapor phase
References [1] Bay, K. et. al.; 2006; Absorption of volatile organic compounds in biodiesel: Determination of infinites dilution activity coefficients by headspace gas chromatography; Chemical Engineering Research and design, 84 (A1), pp.1-7 [2] Billet, R.; 1996; Packed towers in processing and environmental technology, VCH; Weinheim [3] Richter, D. et al.; 2006; Investigations on the absorption of aromatic hydrocarbons from cokeoven gases; 17th International congress of chemical and process engineering; Prague [4] Richter, D. et. al.; 2007; Phase equilibrium behavior of volatile organic compounds in complex hydrocarbon mixtures, Chemical and Process Engineering 28; pp. 115-126 [5] Richter, D. et. al.; 2007; Reliable nonlinear parameter estimation for predicting the activity coefficients in complex hydrocarbon mixtures; 17th European Symposium on Computer Aided Process Engineering; Bucharest [6] Thielert, H.; 1997; Simulation und Optimierung der Kokereigaswäsche; Diss.; Berlin
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
805
A Comprehensive Population Balance Model of Emulsion Polymerisation for PSD & MWD: Comparison to Experimental data S. J. Sweetman,a C. D. Immanuel,a T. I. Malik,b S. Emmett,c N. Williamsc a
Department of Chemical Engineering and Chemical Technology, Centre for Process Systems Engineering, Imperial College London, SW7 2AZ, UK b ICI Wilton Applied Research Group, Wilton Centre, UK c ICI Paints, Slough, UK
Abstract A population balance model for emulsion polymerisation has been developed. This model captures PSD and MWD, both of which are key performance indicators for the end latex product. The model employs purely mechanistic kernels and is aimed at maximising predictive capacity. The model is validated against a multi-objective experimental target. The aim is to predict data for PSD, solids, particle number as well as global molecular weight. The experimental system investigated is a vinyl acetate/ butyl acrylate copolymerisation with ionic emulsifier and thermal initiator. The predictive capacity is tested by tuning the model to one set of experimental data, then trying to predict results from a further perturbed experiment, with no further tuning. The results of this study indicate that the model is able to capture the main process trends as well as providing an accurate representation of quantitative data. Keywords: Population Balance, Emulsion Polymerisation, PSD, MWD, Validation
1. Introduction Emulsion polymerisation is a process of considerable industrial and technological significance, utilised to produce an increasing variety of high volume and also hightech, latex-based commodities. It is well known that the key latex characteristic of particle size distribution (PSD) influences rheology [1,2]. In addition, the molecular weight distribution (MWD) of the latex influences end-use properties such as mechanical strength [3] and the fourth moment of MWD is expected to be correlated with the rheology [4]. Thus, the control of PSD and MWD represents an inferential control of end-use properties of the emulsion polymer, and underlines the importance of a detailed mathematical model for PSD and MWD. The difficulty in modelling this highly heterogeneous process lies in describing the complex reaction scheme and capturing the process-driving mechanisms of nucleation, growth and coagulation, which interact in a highly non-linear fashion. Compartmentalisation is an issue in modelling that arises due to the particulate nature of the process and effects termination between radicals contained within particles. The compartmentalisation issue has been addressed by Ghielmi et al. [5] and Butte et al. [6]. Their work was based on the concept of the singly and doubly distinguished particle [7]. They developed models for MWD distinguishing a particle population by the specific pairs of radicals contained. Arzamendi et al. [8] modelled MWD, whilst assessing compartmentalisation, using the so-called partial distinction approach.
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Min and Ray [9] developed the first comprehensive model for PSD and MWD employing a population balance framework. In their model they explicitly account for the radicals of different lengths in different sized particles, enabling an accurate description of termination events. Saldivar et al. [10] extended this model to copolymer systems including an exhaustive kinetic scheme. Solution of the population balance equations was achieved by discretisation, leading to a differential-algebraic system. Comparison of the model was made with experimental results for average particle size and average molecular weight, with a good match between the two. More recently Park et al. [11] formulated and solved a comprehensive model for PSD and MWD for a realistic copolymerisation system with a brief comparison to experimental molecular weight data. In a previous paper [12] a combined PSD and MWD model was developed. The predictive capacity encompassed PSD and average MWs for each particle size class, spanning the particle size domain. A global average molecular weight was also calculated. The model was used to assess the impact of compartmentalisation by varying the rate of termination within the particles. The global MW predictions were strongly effected by compartmentalisation. The aim of this paper is to validate that model through a detailed comparison to experimental emulsion polymerisation data. A semi-batch vinyl acetate/butyl acrylate copolymer system with ionic surfactant and thermal initiator will be studied. The key latex attributes of PSD, solids, number of particles and global-average molecular weight will be investigated simultaneously. Despite ability to predict an average MW for each discrete particle size, it is currently only feasible to measure the global molecular weight or MWD of the entire system. Model predictive capability is demonstrated by tuning the model to data from one experiment and using this tuned model to predict further experimental results. In the next section a brief review of the important model features will be provided.
2. PSD & MWD Population Balance Model and Numerical Solution 2.1. Model The PSD information is incorporated via a 1-D population distribution of the polymer particles with respect to their size, as shown in Eq. (1):
∂ ∂ § dr · F ( r , t ) + ¨ F ( r , t ) ¸ = ℜ nucδ (r − rnuc ) + ℜ coag ∂t ∂r © dt ¹
(1)
Here the particle density F(r,t)dr is defined as the moles of particles between r and dr at time t. The term dr/dt represents the continuous particle growth via polymerisation of radicals inside the particle. The first term on the RHS represents particle ‘birth’ or nucleation. The second term on the RHS represents the rate of coagulation between particles, the kernel being derived based on the ionic net interaction potential in this case. The growth term in the PSD population balance (as well as the MWD equations, to follow) requires information about the number of radicals contained within particles. The average number of radicals per particle is modelled by a first principles population balance over the rates of entry, desorption and termination within particles. MWD information is incorporated via 1-D population distributions of the live radicals and dead polymer chains with respect to their length, in different sized particles. Eq. (2) shows the dead chain balance:
A Comprehensive Population Balance Model of Emulsion Polymerisation for PSD & MWD
∂ l D (r , t ) = ( ktr [ M pj ] + ktrcta [CTAp ]) N l + ∂t tcij p p l −1 2 2 ∞ 2 2 k i j k tdij pi p j N l ¦ N m + ¦¦ N m N l −m ¦¦ ¦ 2 i =1 j =1 m =1 i =1 j =1 m =1
807
(2)
where Dl(r,t) is the number of dead chains of length l (in a particle of size r, at time t). The first term on the RHS accounts for chain transfer reactions, the second and third account for termination via disproportionation and combination respectively (for more details see [12]). The adjustable parameters used for tuning in this model are the mass transfer coefficient (used in the micellar nucleation and particle entry terms), a constant in the coagulation kernel, the critical micelle concentration (used in the micellar nucleation term), the area occupied by a surfactant molecule (used in the micellar nucleation term), the rate of initiator decomposition and the rate constant for chain transfer to chain transfer agent (CTA). 2.2. Numerical Solution Techniques The PSD population balance is solved using a decomposition algorithm [13], with a discretisation of the particle size domain. The algorithm solves separately the rates of nucleation, growth and coagulation, whilst holding the PSD, then uses them to update the PSD at each time interval. For solution of the MWD equations the method of moments is applied to the population distributions over live and dead radicals. The leading moments are used to evaluate the number-average MW (ratio of the first to the zeroth dead moments) and weight-average MW (ratio of the second to the first dead moments). The global-average molecular weight for the entire system is then calculated in Eq. (3):
§ Wglob (r , t ) = ¨ ©
³
rmax
rmin
· § WAMW (r , t )λD1 (r , t ) F (r , t )dr ¸ / ¨ ¹ ©
³
rmax
rmin
·
λD1 F (r , t )dr ¸ ¹
(3)
Here, Wglob is the global weight-average MW, λD1 is the first dead moment and WAMW is the weight-average MW. Consistency is maintained between the PSD and MWD by setting the zeroth moment of live radical populations equal to the average number of radicals per particle.
3. Experimental Studies The system comprises a 0.7 L cylindrical stainless-steel reaction vessel, with mechanical agitation device. Heat transfer is provided by means of an external oil-filled jacket around the vessel. A reflux condenser is connected to the top of the reactor. Reactants are metered via peristaltic pumps or charged via a nitrogen pressurised glass burette. Latex samples are characterised for PSD using capillary hydrodynamic fractionation. Gravimetry is used to determine solids (polymer) fraction. MWD is measured via gel permeation chromatography (GPC). A vinyl acetate (VAc) and butyl acrylate (BuA) copolymerisation recipe is implemented. Sodium dodecyl sulphate is used as the emulsifier, sodium persulphate as thermal initiator and dodecyl mercaptan as CTA. A semi-batch feed addition strategy is implemented. The addition strategy was developed to produce a complex bimodal PSD using ideas discussed in. [14]
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Figure 1: Feed profiles for monomers, initiator (ini) and surfactant (surf)
The nominal feed trajectories are detailed in Figure 1. Case 1 has 1 % CTA dissolved per weight of total monomer, and case 2 has 3 % CTA. Case 1 results are used to tune the model and no further tuning is done in comparison of simulation and data for case 2.
4. Results and Discussion 4.1. Model and experiment comparison for1 wt% CTA case The adjustable model parameters indicated in the modeling section were first tuned to the first set of experimental results, namely those using 1 wt% CTA. Figure 2(a) shows an excellent overall match between model simulation and experiment for end-time weight averaged PSD. Firstly, the bimodal nature of PSD is accurately reproduced, indicating that homogenous nucleation is responsible for the peak centred around 125 nm and a micellar nucleation event is responsible for the smaller mode centred around 35 nm. The magnitude of the two nucleation events is captured, seen here in the reproduction of respective peak heights. The micellar peak resulting from the simulation is shifted towards the left of the experimental micellar peak, indicating that more coagulation may have taken place than predicted. The homogenous peak resulting from the simulation, although it is centred about the same radius, shows a greater degree of broadening than that indicated by experiment, suggesting a more prolonged homogeneous nucleation than that predicted by the model. This is thought to be partly due to the mass transfer coefficient value used to describe the rate of entry into preexisting particles and micelles. This parameter will influence the balance between aqueous phase oligomers that are absorbed by particles or micelles and those which grow long enough to undergo homogenous nucleation. This has an important bearing on the number of radicals contained within particles, shaping the peak via particle growth.
Figure 2: simulation (sim) and experiment (exp) comparison for 1 wt% CTA case for (a) end-time weight-average PSD, (b) particle number, (c) solids and (d) global weight-averaged MW
A Comprehensive Population Balance Model of Emulsion Polymerisation for PSD & MWD
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Figure 2(b) shows that good accord has been attained between simulation and experimental results for particle number. There is good match between the timing of the particle number increase at around 15 mins, indicative of micellar nucleation (coinciding with surfactant addition). The initial jump in particle number of the experiment is not properly captured by the model (the actual homogenous nucleation event evident from experiment was of larger magnitude than predicted). This would explain the apparent broadening of the homogenous peak in Figure 2(a), i.e. the model predicted a smaller number of particles at the start of the reaction, therefore leading to larger radical numbers in particles and causing peak broadening. Figure 2(c) shows a good match at initial times between simulation and experiment for solids content evolution. The experimental results show prolonged rate of rapid increase in solids, possibly due to higher rates of propagation than expected. The experimental solids reach a maximum of around 20 %, after which they decrease due to the dilution effect from the added persulphate solution. Figure 2(d) indicates that despite the relatively low number of experimental sampling points taken for the global MW, there is still a good representation of overall trend demonstrated by the model. The initial peak in MW seems to have been captured, as well as the subsequent rise in MW after around 10 mins. There is however a discrepancy between the results in terms of magnitudes of these MW fluctuations, but the overall MW values are well captured. The initial rise in MW is due to the development of radicals in a monomodal system (homogenous nucleated peak only, at this early time). After the micellar nucleation at around 10 mins there are two modes of particles, which effects the development of MW: decreasing first due to there being many small particles containing short chains, then rising due to growth of both modes of particles. The simulation shows a peak being reached at around 30 mins due to the exhaustion of the more reactive monomer, butyl acrylate, leading to lower propagation rates, the result of which termination and chain transfer reactions become more predominant (lowering MW). 4.2. Model and Simulation comparison for 3 wt% CTA case This section highlights comparisons made between model and experiment, where the model parameters have not been altered from their initial tuned state (based on the first experiment). Figure 3(a) indicates that experimentally, by increasing CTA concentration the PSD is affected such that the micellar nucleated peak (centred around 35 nm) reaches a higher maximum. This trend has been captured by the model, however the model makes somewhat of an over prediction.
Figure 3: comparison between simulation (sim) and experimental (exp) data for 3 wt% CTA case for (a) end-time weight-average PSD, (b) weight-averaged MW
Figure 3(b) indicates that experimentally by increasing the CTA concentration the system MW is considerably lowered (in this case MW peaks at just under 200 k, c.f 500 k peak in previous 1 wt% CTA case). The model also shows the same trend in this
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respect and still captures the dynamic nature of the MW, as discussed in the previous section.
5. Conclusions The model was validated in terms of PSD, number of particles, solids and global weight-average MW. Due to the complex and often non-linearly coupled interactions between underlying process phenomena (nucleation, growth and coagulation), this multi-objective case represents a difficult validation task, however the model simulations were observed to coincide well with the obtained experimental data. With further rigorous tuning of model parameters, an even closer fit with experiment is expected. The predictive capacity of the model was also demonstrated by running a simulation of a second experimental case using only the tuned model parameters from an initial experimental run. The trends observed upon perturbing CTA were accurately reproduced by the model. This highlights the potential use of the first principles model in a truly predictive capacity, with a scope to uncover important mechanistic information about the process. It should also be mentioned in that so far, only the bearest minimum number of parameters have been adjusted. There are a few other uncertain parameters which provide additional degrees of freedom.
References [1]C. Parkinson, S. Matsumoto, and P. Sherman, J. Colloid Interface Sci., 33 (1970), 150 [2]P. F. Luckham and M. A. Ukeje, Journal of Colloid and Interface Science, 220 (1999), 347 [3]R. W. Nunes, J. R. Martin, and J. F. Johnson, Polym. Eng. Sci, 22 (1982), 205 [4]J. E. Puskas, P. Chan, B. McAuley, G. Aszas, and S. Haikh, Polymer Reaction Engineering VI conference, Halifax, Canada, May, 2006 [5]A. Ghielmi, G. Storti, M. Morbidelli, and W.H.Ray, Macromolecules, 31 (1998), 7172 [6]A. Butte, G. Storti, and M. Morbidelli, Macromol. Theory Simul., 11 (2002), 37 [7]G. Lichti, R. G. Gilbert, and D. H. Napper, Journal of Polymer Science: Polymer Chemistry Edition, 18 (1980), 1297 [8]G. Arzamendi, C. Sayer, N. Zoco, and J. M. Asua, Polymer Reaction Engineering, 6 (1998), 193 [9]K. W. Min and W. H. Ray, Journal of Macromolecular Science- Reviews in Macromolecular Chemistry and Physics, 2 (1974), 177 [10]E. Saldívar, P. Dafiniotis, and H. Ray, Journal of Macromolecular Science- Reviews in Macromolecular Chemistry and Physics, 27 (1998), 403 [11]M. Park, M. T. Dokucu, and F. J. Doyle III, Macromol. Theory Simul., 14 (2005), 474 [12]S. J. Sweetman, C. D. Immanuel, T. Malik, S. Emmett, and N. Williams, Macromol. Symp., 243 (2006), 159 [13]C. D. Immanuel and F. J. Doyle III, Chemical Engineering Science, 58 (2003), 3681 [14]C. D. Immanuel, T. J. Crowley, E. S. Meadows, C. F. Cordeiro, and F. J. Doyle III, Journal of Polymer Science: Part A: Polymer Chemistry, 41 (2003), 2232
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Prediction of partition coefficients between food simulants and packaging materials using molecular simulation and a generalized Flory-Huggins approach Olivier Vitraca, Guillaume Gilletb a
Institut National de la Recherche Agronomique, UMR 1145 Génie Industriel Alimentaire, 1 avenue des Olympiades, 91300 Massy, France b Laboratoire National d’Essais, Centre Energie, Mériaux et Emballage, 29 avenue Roger Hennequin, 78197 Trappes CEDEX, France.
Abstract Partition coefficients of n-alkanes, n-alcohols and commercial antioxidants between polyethylene and food simulants (ethanol, methanol), KF/P, have been estimated using an off lattice Flory approximation and satisfactory compared to previously published values. The approach demonstrated the preponderant effect of the configurational entropic contribution on the estimate of KF/P. Keywords: thermodynamics, polymer, desorption, chemical potential, Flory theory
1. Introduction In Europe, all materials intended to be in contact with food must comply with the new framework regulation 2004/1935/EC, which enforces a safety assessment and risk management decision for all starting substances and possible degradation products coming from the material. For plastic materials, article 14 of the directive 2002/72/EC introduces diffusion modeling as an alternative to time-consuming and costly experiments for both compliance testing and risk assessment. The fundamentals of probabilistic modeling of the desorption of packaging substances into food has been analyzed by us [1] and applied to different situations [2] including the assessment of consumer exposure to styrene originating from yogurt pots [3]. The main limitation in the use of predictive approaches for both compliance testing and risk assessment is the availability of physico-chemical properties of a wide range of substances, polymers and thermodynamical conditions (temperature, swelling). Robust approaches have been developed for the prediction of diffusion coefficients in polymers [4-5], but no appropriate method exists to predict partition coefficients between a polymer and a food or a food simulant [6]. A first attempt was made by Baner et al. [7] using the regular solution theory, but it required an empirical factor, which was dependent on the size and shape of the considered substance. This work examines an off-lattice generalized Flory-Huggins approach to predict activity coefficients in polyethylene (PE) and in different food simulants (ethanol, methanol). The excess in mixing enthalpy is assessed by sampling the nearest-neighbor interactions energies for all possible host-substance pairs [8-9]. This method is an alternative to particle insertion or deletion methods [10], which cannot be applied reliably to penetrants much larger than fluctuation volumes in polymers.
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The paper is organized as follows. Section 2 summarizes the theoretical principles used to calculate both the excess in enthalpy and entropy in both phases. Section 3 presents the results obtained for homologous series of alkanes and alcohols as well as for typical hindered antioxidants. When they are available, predictions are compared with values measured between a low density polyethylene and two food simulants with increasing polarity: ethanol and methanol [6-7].
2. Theory and methods of estimation of activation coefficients 2.1. Equilibrium between the packaging material and the food in contact By noting the thermoplastic packaging, P, and the food product in contact, F, the thermodynamical equilibrium between P and F corresponds to a situation, where the cumulated free energy between P and F, noted GP+F, is minimal. For a P+F system at constant temperature and pressure, the evolution towards equilibrium is accompanied by an exchange of matter between P and F. In this work, only a single species initially present in the polymer, noted i, is assumed to migrate. This model situation corresponds in particular to the contamination of an aqueous food or polar simulant by a plastic additive. For an isolated system P+F, GP+F is: μPid + μPexcess
P
μi0 + μiid + μiexcess ,P
P
μi0 + μiid + μiexcess ,F
μFid + μFexcess
P GP + F = Gi + P + Gi + F = nP ⋅ μP + ni , P ⋅ μi , P + nF ⋅ μF + ni , F ⋅ μi , F
Gi+ P =Giid+ P + Giexcess +P
P
Gi + F =Giid+ F
(1)
+ Giexcess +F
where {nk}k=P,F and {ni,k}k=P,F are the number of molecules k and the number of molecules i in k respectively. They are associated to the chemical potential {μk}k=P,F and {μi,k}k=P,F respectively. All energetic terms are further decomposed into an ideal, id, and an excess part, excess. From a microscopic point of view, the detailed mass balance at the interface enforces that the partition coefficient at the interface between P and F, noted KF/P, is equal to the ratio of frequencies of crossing the interface: ki,PĺF and : ki,FĺP. By introducing the free energy of the barrier to cross the interface, Gi†, the transition state theory defines KF/P in the canonical ensemble as:
KF / P =
eq i,F eq i,P
p
p
=
ki , P → F ki , F → P
§ G † − Gi + P kB ⋅ T exp ¨ − i h kB ⋅ T © = † § G − Gi + F kB ⋅ T exp ¨ − i h kB ⋅ T ©
· ¸ ¹ = exp § Gi + P − Gi + F · ¨ ¸ · © kB ⋅ T ¹ ¸ ¹
(2)
Where h is the Planck’s contact, kB is the Boltzmann's constant and T the absolute temperature. Eq. (2) can be used to estimate KF/P in the Gibbs Ensemble [11] but it requires calculating the energy of each subsystem after equilibration. An alternative relies on a macroscopic description of equilibrium (dGP+F=0) for a closed system (dni,F=-dni,P), which leads to: μi,F=μi,P. By choosing the state of pure i as reference and by expressing the activities of both non ideal mixtures from their volume fractions in i, {φi,j}j=P,F, KF/P is approximated as: § μ excess − μiexcess · γ iv, P V ⋅φ ,F (3) K F / P ≈ i i , F = exp ¨¨ i , P ¸¸ = v ⋅ Vi ⋅ φi , P k T γ , B i F © ¹ According to the Flory-Huggins theory [12-15], the activity coefficients {γvi,k}k=P,F can be derived on a rigid lattice, whose mesh size is commensurable to the volume of the penetrant Vi or to its surface. In this work, Vi is chosen as the volume enclosed within
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813
the Connolly surface. For molecules of k with a volume fraction φk and consisting in rk blobs of volume Vi, one gets at infinite dilution of i [16]:
{μ
excess i ,k
}
k B ⋅ T = ln γ iv, k = (1 − 1 rk ) ⋅ φ k + χ iH, k ⋅ φ k2 ≈ (1 − 1 rk ) + χ iH, k
k = P,F
(4)
where χ iH, k ⋅ ni ⋅ φ k = H iexcess k B ⋅ T is the heat of mixing. The first term represents the +k effect of the configurational entropy associated to the increase of microstates due to the distribution of k around i without changing the effective pair interactions between i and k. The absolute value of the first term is expected to be small in polymers (rk>>1) while it is expected to be significant in simulants consisting in molecules much smaller than i. 2.2. Estimation of χi,k from pair contact energies The lattice method has been mainly used to predict the heat of mixing of polymersolvent systems, which present a significant similarity. Since the blob size and the coordination number of the lattice cannot be modified, the lattice approximation is less accurate to sample the interactions between dissimilar structures including flexible penetrants. A continuous representation of interactions was used instead [8-9]:
{χ (T )} i,k
k = P,F
Where ε A+ B
ª zi + k ⋅ ε i + k =¬
T
T
+ zk + i ⋅ ε k + i
T
− ( zk + k ⋅ ε k + k
T
+ zi + i ⋅ ε i + i
2 ⋅ kB ⋅ T
T
)º¼
(5)
stands for an ensemble averaged pair contact energy at the temperature
T (T=313K as prescribed in the EU regulation) by weighting the distribution of energies pA+B(İ) with the Boltzmann factor exp(-İ/kB·T):
{ε
A+ B T
}
A = i , k et B = i , k
= ³ p A+ B ( ε ) ⋅ e
−
ε kB ⋅T
⋅ ε ⋅ dε
³ p A+ B ( ε ) ⋅ e
−
ε kB ⋅T
(6)
The sampling of pA+B(İ) was based on a large set of conformers of A (seed molecule) and B (contact molecule) representative of their condensed state (up to 104 configurations) and based on all possible contacts of their van der Waals envelopes with spherical symmetric probability (up to 106 configurations). Since only the surface farthest away from the center of mass was considered, internal cavities of the seed molecule could only be sampled by a contact molecule smaller than the cavity (e.g. B). The coordination number was determined similarly on a large number of packed configurations (up to 104), where van der Waals envelopes are in contact but not overlapping. Polymers based on few monomers were idealized by preventing head and tail atoms to be in contact with any surface. All conformers and sampling energies were performed using the Materials Studio environment version 4.1 (Accelrys, San Diego, USA), its scripting features and the atom-based COMPASS forcefield, which was applied without any cutoff.
3. Results and discussion Typical configurations related to minimums of İA+B and to typical compaction values zA+B are illustrated in Fig. 1. The volume of each molecule is represented either by calotte models or by their Connolly surface. Hydrogen bonding is depicted in dashed lines.
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Fig. 1. Typical A+B pair interactions and packing. Tested plastic additives are: BHT (2,6-di-tertbutyl-4-methyl-phenol, CAS 128-37-0), Irganox 1076 (octadecyl 3,5-di-(tert)-butyl-4hydroxyhydrocinnamate, CAS 2082-79-3), Irganox 245 (Ethylenebis (oxyethylene)bis-(3-(5-tertbutyl-4-hydroxy-m-tolyl)-propionate), CAS 36443-68-2), Irganox 1035 (thiodiethylene bis[3(3,5-di-tert-butyl-4-hydroxyphenyl)propionate], CAS 41484-35-9).
Since the used off-lattice approach sampled both the conformation and the reorientation phase space, the non-combinatory entropic contribution was accounted in the estimate of χi,k. In Eq. (5), the use of a single coordination number (a non-integer value) assumes however that z and İ are independent quantities, although there are positively correlated for AB. Since the expected deviation is equal to covariance between z and İ, Eq. (5) tends to overestimate the true χi,k. As a result the interaction with the polymer is best estimated when A and B have similar surface areas (i.e. zA+B§zB+A). Fig. 2 plots the corresponding variation χi,PE for typical substances according to number of monomers used to idealize the polymer (head and tail atoms were non-contact). For antioxidants, which do not resemble the polymer, several minima could occur.
Fig. 2. Effect of the number of monomers on the estimation of χi,k.
Typical values of χi,k at 313 K for a series of n-alkanes and n-alcohols and four antioxidants are plotted in Fig. 3. A sensitivity analysis was performed for the series of alkanes and alcohols by generating different independent set of conformers by molecular dynamics at 313 K. The confidence intervals on contact energies were estimated lower than 0.5 kB·T. The interactions were maximal in F and low in PE except for Irganox 245. Since all antioxidants included one or two BHT patterns, the different behaviors observed in PE were mainly related to the stiffness of the side or bridging chain, which was stiffer in Irganox 245 than in Irganox 1035 (see Fig. 1). The high values in simulants were related to the presence of large molecules which reduce the
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possibility of hydrogen bonding. This effect was higher when the surface of the substance i exposed to F was higher (e.g. for linear molecules rather than hindered antioxidants).
Fig. 3. χi,k estimated at 313 K in methanol, ethanol and PE. For PE, the values were derived for the number of monomers, which led to the lowest χi,PE value (see Fig. 2). Irganox molecules are depicted by their numerical codes: 245, 1035, and 1076.
Eq. (3-5) can only estimate partitioning between the amorphous regions of PE and F. Since the dense crystalline regions are assumed to be free of any substance, calculated values were compared with values obtained on a low density PE [6-7] subsequently to a correction according to the amount of amorphous phase. The entropic contribution rF-1 was estimated by considering that the substance i would displace a volume of F commensurable to the volume enclosed into its averaged Connolly surface. This approximation is particularly realistic at high dilution rate (non-interacting substances i), where F molecules smaller than i would act as a continuous phase with a specific volume close to its molar volume at the same temperature. The corresponding results are plotted in Fig 4.
Fig. 4. Estimated and experimental (filled symbols or in italic) partition coefficients between F and amorphous PE regions at 313 K. Error bars represent either 95% confidence intervals or min/max K estimates (symbols are centered on median values).
Without any fitting, the magnitude orders were similar. The deviation was higher in ethanol, where the proposed approach tended to underestimate KF/P of linear molecules while it overestimated the value of hindered additives (BHT and Irganox 1076). A sensitivity analysis demonstrated that the uncertainty was mainly related to the entropic contribution. The number of ethanol molecules associated to the blob of a linear molecule should be higher for alkyl segments and lower for hindered groups (e.g. BHT pattern), which can contribute to hydrogen bonding.
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4. Conclusions The off-lattice generalized Flory-Huggins approach seems a promising approach to predict partitioning between food packaging materials and food simulants. It does not require an explicit representation of the entangled polymer and provides further insight on molecular phenomena, which lead to the contamination of food. In particular, the simulations demonstrated that even if plastic additives have by design a good solubility in polymers, they have a higher chemical affinity for liquids consisting in small molecules. This entropic effect was underestimated in previous studies and would lead to a high migration of antioxidants in food at high temperature when their diffusion and solubility are not limiting.
References [1] O. Vitrac and M. Hayert, 2005. Risk assessment of migration from packaging materials into foodstuffs. AIChE Journal, 51, 4, 1080-1095. [2] O. Vitrac, B. Challe, J.-C. Leblanc and A. Feigenbaum., 2007. Contamination of packaged food by substances migrating from a direct-contact plastic layer: Assessment using a generic quantitative household scale methodology. Food Additives and Contaminants. 24, 1, 75-94. [3] O. Vitrac and J.-C. Leblanc, 2007, Exposure of consumers to plastic packaging materials: assessment of the contribution of styrene from yoghurt pots. Food Additives & Contaminants. 24, 2, 194–215. [4] O. Vitrac, J. Lézervant and A. Feigenbaum, 2006, Application of decision trees to the robust estimation of diffusion coefficients in polyolefines. Journal of Applied Polymer Science, 101, 2167–2186. [5] O. Vitrac and M. Hayert, 2007, Effect of the distribution of sorption sites on transport diffusivities: a contribution to the transport of medium-weight-molecules in polymeric materials. Chemical Engineering Science, 62, 9, 2503-2521. [6] O. Vitrac, A. Mougharbel and A. Feigenbaum, 2007, Interfacial mass transport properties which control the migration of packaging constituents into foodstuffs. Journal of Food Engineering. 79, 3,1048-1064. [7] A. L. Baner and O. G. Piringer, 1991, Prediction of solute partition coefficients between polyolefins and alcohols using the regular solution theory and group contribution methods. Industrial and Engineering Chemistry Research, 30, 1506-1515. [8] M. G. Bawendi and K. F. Freed, 1988, Systematic correction to Flory-Huggins theory: Polymer-solvent-void systems and binary blend-void systems, Journal of Chemical Physics, 88, 4, 2741-2756. [9] M. G. Bawendi, K. F. Freed and U. Mohanty, 1987, A lattice field theory for polymer systems with nearest-neighbor interaction energies. Journal of Chemical Physics, 87, 9, 5534-5540. [10] B. Widom, 1963, Some Topics in the Theory of Fluids, Journal of Chemical Physics, 39, 2808. [11] A. Z. Panagiotopoulos, 1992, Direct Simulation of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review, Molecular Simulation, 9, 1. [12] P. J. Flory, 1941. Thermodynamics of high polymer solutions. Journal Chemical Physics. 9, 660-661. [13] P. J. Flory, 1942, Thermodynamics of high polymer solutions. Journal of Chemical Physics. 10, 51-61. [14] M. L. Huggins, 1942a. Derivation of Molecular Relaxation Parameters of an Isomeric Relaxation. Journal of Chemical Physics, 46, 151-153. [15] M. L. Huggins, 1942b. Theory of Sulutions of high polymers. Journal of the American Chemical Society, 64, 1712-1719. [16] V. J. Klenin, 1999, Thermodynamics of systems containing flexible-chain polymers. Elsevier Science, Amsterdam. 826p.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Shape – The Final Frontier Xue Z Wang*, Caiyun Ma and Kevin J Roberts Institute of Particle Science and Engineering, University of Leeds, Leeds LS2 9JT, UK
Abstract Organic crystals grown from solution are known to exhibit multiple morphology and habits which are of great importance to the end use properties of the product such as the bioavailability and down stream processing such as in filtration and drying. The crystal morphology can also dictate other quality measures such as size. This paper reviews recent developments in on-line crystal morphology measurement and control using online imaging and image analysis. On-line imaging was found to be able to capture with high fidelity crystal shape and polymorphic transitions in real-time. The images were analyzed using a multi-scale image analysis method to extract the crystals from the image background. Preliminary results on estimating crystal growth rates and kinetics parameters for different facets for rod-like crystals were presented. The paper also reviewed recent developments in morphological population balance (PB) modelling which can provide the evolution of the shape and distributions of sizes in all crystal face directions in a reactor. Finally, the perspectives for automatic morphology control which require integration of crystal morphology prediction, morphological PB modelling, on-line 3D imaging and image analysis for shape characterisation as well as computational fluid dynamics are outlined. Keywords: crystal morphology and shape, imaging, image analysis, population balance
1. Introduction The shape, size and polymorphic forms are properties of great importance to crystalline drug products. It is known that certain crystal morphological forms and habits have been related to difficulties in dissolution rate, process hydrodynamics, solid-liquid separations, drug tableting, storage and handling, or in milling and grinding. Although there has been a large amount of research work on on-line measurement of other quality measures such as the size and concentration using various spectroscopy techniques including ultrasound, infrared, near infrared, Uv spectroscopy, X-ray diffraction and Raman spectrometer, the literature on monitoring crystal morphology is scarce. This paper presents recent advances towards developing an enabling technique for real-time measurement and manipulation of the morphology of growing crystals through integrating on-line imaging, image analysis and morphological population balance modelling. The paper also proposes a framework and highlights challenges and future research needs for model predictive control of crystals morphology.
2. Morphology Measurement: Imaging and Image Analysis Laser diffraction techniques were investigated previously for the recognition of nonspherical particles with only limited success mainly due to the difficulty in obtaining a single-particle pattern in mixtures. Use of attenuation acoustic spectroscopy, Raman spectrometer, NIR and X-ray diffraction techniques though can detect polymorphs, but they cannot give detailed quantitative shape information. Several recent studies have demonstrated the effectiveness of on-line imaging as an instrument for monitoring the
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shape of the crystals(Wilkinson, 2000,Patience and Rawlings, 2001,Calderon De Anda, et al., 2005a,Calderon De Anda, et al., 2005b,Calderon De Anda, et al., 2005c). In our work, an on-line imaging instrument Camera Reactor developed by researchers at GlaxoSmithKline was investigated to monitor the onset as well as polymorph transitions during cooling crystallization of L-glutamic acid, an effective multi-scale image analysis technique for segmentation of the crystals from the complex background of image frames was developed, and Fibre optic light subsequently shape descriptors, classification techniques and novel Fig. 1 The on-line imaging system mounted on a 5 litre batch reactor. process monitoring charts were derived. Fig. 1 shows the on-line imaging system mounted on the outside wall of a 5 liter batch reactor which is able to take maximum 30 images per second of the pixel resolution of 480 × 640. Fig. 2 shows polymorphic transition captured in real-time during the cooling crystallization of Lglutamic acid. On-line images of slurries with particles suspended in a solution Fig. 2 Polymorph transition for L-glutamic acid captured in pose much greater real-time, from Į form (left) to ȕ form. The right figure shows challenges to image mixed Į and ȕ indicating transition being taking place. analysis than images of particles obtained with off-line equipment. The major challenges lie in the fact that the slurries in a stirred reactor are in continuous motion, and that the variation of distances from the camera lens of particles captured in a snapshot makes some particles rather vague compared to others. In addition, the light effect and temporal changes of hydrodynamics within the reactor may lead to varied intensity in the image background. As a result a multi-step multiscale approach was developed which proved to be effective in extracting objects from the image background for images obtained by the GSK on-line Fig. 3 crystal images were effectively extracted microscopy system, as well as for from the background of an image frame obtained by the Lasentec PVM imaging system. the Lasentec’s PVM probe(Barrett, 2002), as demonstrated by Fig. 3.
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3. Faceted Crystal Growth Rates and Kinetics
Supersaturation (C/C*-1)
Length (m icrons), W idth (m icrons), Tem perature ( C), Turbidity (-)
Given that the fundamental process of crystal growth and its associated kinetic control is surface controlled, the use of a single scalar parameter, particle size, usually defined as a volume equivalent 0.6 200 diameter, i.e. based on a D 180 spherical assumption of Supersaturation Length 0.55 160 A particle shape can be C misleading for a number of 140 0.5 practical crystallization 120 B Turbidity systems, notably 0.45 100 o pharmaceutical products, 80 where facetted particles 0.4 60 defined by non-unity aspect 40 0.35 ratios. Hence, measurement 20 Temperature Width of the growth rate for each 0 0.3 individual crystal surface in 0 10 20 30 40 real-time and within Time (min) processing reactors could Fig. 4 Crystal length evolution, plotted against open the way for the supersaturation, temperature and turbidity. Each point development of more represents the average of previous 60 seconds effective processes and containing 300 images. product quality control. Using on-line imaging and image analysis, a preliminary study was conducted on the estimation of the growth rates of rod-shaped crystals in two dimensions for ȕ-form Lglutamic acid in cooling crystallization under a cooling rate of 0.100C/min(Wang, et al., 2007). The length and width of each rodshaped crystal were measured every 60 seconds, ranging from x 100 to nearly 200 μm in length and from 30 to 45 μm in width, and the z y values were used to estimate growth rates on both directions (Fig. 4). The growth rate in length was found to be 4 to 6 times greater than for the width. The {101} plane was found to be the fastest growing surface of the morphology studied and an attempt was also made to estimate its growth-kinetics parameters Fig. 5 Morphology of potash alum crystal and the schematic diagram of three size characteristic from measurements of length, whilst it was harder to estimate parameters (x, y, z) used in polyhedral PB model kinetics from measurements of width for other crystal faces. In the temperature range between 68.340C to 67.510C, the length growth rate is estimated as between 2.440×10-8 ~ 2.995×10-8 m/s, while the growth rate for the width is between 0.558×10-8 ~ 0.502×10-8 m/s. The capability to measure crystal growth rates in different directions could be used to estimate the
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parameters associated with growth kinetics in multi-dimensional directions. If a semin
empirical kinetic model is used, R kV , k | 1.761u10-7 m/s, an d n |2.61. It was assumed for ȕ L-glutamic acid, the growth rate in length is very close to the growth rate of the faces {101}.
4. Morphological (or polyhedral) Population Balance Modelling Modelling the growth and dynamic evolution of crystal size distribution within a crystallizer using population balance (PB) has been mainly based on a size definition of volumetric equivalent diameter thus inherently ignoring the shape of crystals. Recently there are a few researchers who have reported two dimensional, i.e. length and width, PB modelling for rod-like crystals. Puel et al.(Puel, et al., 2003a,Puel, et al., 2003b) developed a two-dimensional PB model to simulate the time variations of two internal sizes of crystals, and consequently of a characteristic shape factor. Similar approach was used to investigate the two-dimensional growth of potassium dihydrogen phosphate by Ma et al.(Ma, et al., 2002) using a hybrid of the upwind discretisation and the LaxWendroff method, and by Briesen(Briesen, 2006) employing coordinate transformation method, instead of performing a direct discretisation of the two size parameters, to reduce model size under certain assumptions. We used on-line estimated growth rates for performing two dimensional PB modelling for rod-like ȕ form L-glutamic acid.(Ma, et al., 2007,Wang, et al., 2007) We have recently extended the work and proposed a new model to predict the population distributions for all identified independent crystal faces, which is a unique methodology to integrate population balance with crystal morphology.(Ma, et al., 2008, Ma and Wang, in press, Wang et al., 2008) The critical inputs for the new population balance model are the accurate growth rates for each crystal faces which can be estimated using on-line imaging and image analysis. From the predicted growth of facets at different times during crystallisation process, many important crystal properties such as shape and growth rate can be evaluated. A simple and well-known compound, potash alum (KAl(SO4)2 · 12H2O), as shown in Fig. 5, was selected as a first attempt to test and validate the polyhedral population balance model. A potash alum crystal has total 26 main habit faces in 3 main faces,{111}, {110} and {100}, for which a geometric centre can be found (Fig. 5). The normal distance from each crystal face to the geometric centre represents one dimension in the polyhedral PB model, therefore rigorously speaking the polyhedral PB model should have twenty six size dimensions. However, if some faces, such as the eight {111} faces are symmetry-related, and suppose these symmetry-related faces have identical surrounding growth environments and the same growth rate value, then they can be treated as a single dimension, denoted as dimension x in PB modelling. Similarly, the six {100} faces and the twelve {110} faces will form the second and third independent dimensions, y and z, respectively. Therefore, the morphological PB modelling of crystal growth can be modelled based on these three independent faces. For simplification, if we ignore the effects of both primary and secondary nucleation, and also aggregation and breakage, the polyhedral PB equation can be formed as,
1 w >\ ( x, y, z, t )VT (t )@ w >G1 ( x, t )\ ( x, y, z, t )@ w >G2 ( y, t )\ ( x, y, z, t )@ VT (t ) wt wx wy
w >G3 ( z, t )\ ( x, y, z, t )@ 0 wz
where VT is the total volume of suspension, \ is the number population density function
Shape – The Final Frontier
821
in the suspension, G1, G2, G3 are the growth rates in x, y and z directions, and t is time. The growth rate data for each independent facets of potash alum are obtained from literature. Fig. 6 shows crystal shape variations at different times. It can be seen that with the current growth rates of each face, faces {100} and {110} eventually disappear and the crystal will become the pure octahedral, diamond-like form. Fig. 7 shows the size distribution of three dimensions at three different time points.
Fig. 6 Modelled morphological evolution with time
Fig. 7 x-y and x-z population distribution plots at crystallisation times of 500 (black), 1100 (red) and 1500 (blue) seconds with (a) (110) face located at its corresponding mean values and (b) (100) face located at its corresponding mean values.
5. Perspectives for Shape Control Recent advances on imaging and image analysis for real-time measurement of crystal morphology together with development on morphological population balance modeling make it possible in principle to carry out automatic model-predictive control of crystal morphology. Fig. 8 shows a roadmap towards such a goal detailing the main
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components needed. On the right hand-side of Fig. 8, through on-line imaging, real-time image segmentation analysis, the real-time size distribution for each face of the crystals for a given polymorph can be estimated. The growth rate for that face can then be calculated based on the size of the On-line 3D Imaging current value and the value of a Image Analysis previous time instant. On the left hand side of Fig. 8, based on the Morphology Prediction initial morphology information of Shape Recognition + the crystal, morphological PB Faceted Growth Rates modelling can be carried out Multi-dimensional + and Faceted Population which gives predicted evolution of BalancePopulation Modelling Balance crystal size distributions for all + faces, therefore can be built into + the mode-predictive framework. + Computational Fluid Dynamics
+
Feedback
6. Final Remarks Recent developments in on-line Morphology shape measurement as well as in Control Based on Predictive Models morphological population balance modeling opens the way for Fig. 8 Components for model predictive control developing model-predictive control of the morphology as well as size of crystals grown form solution. This will need integration of on-line 3-D shape measurement, modeling of morphology, multidimensional PB modeling and CFD.
Acknowledgements The work is funded by EPSRC (EP/C009541 and GR/R43860). Thanks are also due to Malvern Instruments, Pfizer, GSK, AstraZeneca and Nexia Solutions Ltd.
References P. Barrett, 2002, PhD thesis, University College Dublin, Ireland. H. Briesen, 2006, Chem Eng Sci, 61, 104-112. J. Calderon De Anda, X.Z. Wang, X. Lai, K.J. Roberts, 2005a, J Pro Cont, 15, 785-797. J. Calderon De Anda, X.Z. Wang, X. Lai, K.J. Roberts, K.H. Jennings, M.J. Wilkinson, D. Watson, D. Roberts, 2005b, AIChE J, 51, 1406-1414. J. Calderon De Anda, X.Z. Wang, K.J. Roberts, 2005c, Chem Eng Sci, 60, 1053-1065. C.Y. Ma, X.J. Wang, AIChE J, in press. C.Y. Ma, X.Z. Wang, K.J. Roberts, 2008, AIChE J, 54, 209-222. C.Y. Ma, X.Z. Wang, K.J. Roberts, 2007, Adv Powder Techn, 18, 707-723. D.L. Ma, D.K. Tafti, R.D. Braatz, 2002, Ind Eng Chem Res, 41, 6217-6223. D.B. Patience, J.B. Rawlings, 2001, AIChE J, 47, 2125-2130. F. Puel, G. Fevotte, J.P. Klein, 2003a, Chem Eng Sci, 58, 3715-3727. F. Puel, G. Fevotte, J.P. Klein, 2003b, Chem Eng Sci, 58, 3729-3740. X.Z. Wang, J. Calderon De Anda, K.J. Roberts, 2007, Chem Eng Res Des, 85, 921-927. X.Z.Wang, K.J. Roberts, C.Y. Ma, 2008, Chem Eng Sci, 63, 1173-1184. M.J. Wilkinson, Jennings, K. H., Hardy, M., 2000, Microsc Microanal, 6, 996-997.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Computational Fluid Dynamics:A tool to the formulation of therapeutic aerosols Nathalie BARDIN-MONNIERa, Véronique FALKa, Laurent MARCHALHEUSSLERa a
Laboratoire des Sciences du Génie Chimique (LSGC),Nancy-Université, CNRS,1rue Grandville B.P. 20451 F-54001 Nancy
Abstract Dry powders inhalation is suitable to deliver drugs in the upper airways up to the deep lung, depending on the particles flow. Therefore, Cascade Impactors (CI) which give access to the particles aerodynamic size distribution are used to develop and control the formulation of such powders. Nevertheless, the interpretation of the experimental data is difficult because of high process variability. It is therefore the objective to improve the understanding of the particles behavior by describing accurately their flow along the CI. This study is focused on the description of the flow of alpha-monohydrate lactose particles in the upper part of the CI (nozzle) and performed with an industrial CFD software (FLUENT®). The turbulence of the continuous phase (air) is simulated via a Reynolds Stress Model (RSM) for a 60 L/min rate. The dispersed phase motion is modeled by a Lagrangian approach coupled with a stochastic model (Eddy Interaction Model). Simulation parameters are the particles diameter which varies from 10 to 100 μm and the velocity restitution coefficient after impaction on the wall. It is shown that particles flow differently depending on their diameter and their position before entering the elbow area. Thus, the process is highly sensitive to small variations in particles diameters which significantly modify the state of the powder entering into the separation part of the CI. Keywords: Aerosols, Cascade Impactor, Computational Fluid Dynamics, Lagrangian Simulation.
1. Introduction Aerosol dispersed phase is made of drug particles adsorbed onto inert excipient particles of 10 to 100 μm diameters. Once being expelled from the inhaler, particles enter the throat where the drug must be desorbed to flow into the deep lung, pass into the blood and thus become efficient. Non-desorbed particles are swallowed or deposited in the throat and become inefficient. Therefore, drug performance depends on the hydrodynamic behavior of the particles in the throat and the lung. To quantify the amount of particles able to reach the deep lung, formulators use CI which separate the particles according to their aerodynamic diameter. However, the interpretation of the experimental data is difficult because of high process variability. The aim of this work is therefore to identify some potential variability sources by simulating the particles flow under different operating conditions.
2. Modeling of the phase flowing The flow studied is a two phases gas-solid flow. It is made of: - an air continuous phase with a density ρc=1.225 kg.m-3 and a viscosity μc=1.789 10-5 kg.m-1.s-1.
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-
a dispersed phase composed of spherical lactose particles with a density of ρp=1525 kg.m-3.
2.1. Continuous phase flow The carrying phase (air) is supposed to be uncompressible because the observed density variations (and thus pressure when the Joule’s law hypothesis is made) are less than 10%. The dispersed phase is made of inclusions and the dispersed phase volume fraction is less than 10%. Under that condition, the interaction of particles with the continuous phase can be considered as negligible. Therefore, the equations governing the continuous phase behavior are limited to the continuity and Navier-Stokes equations. In addition, a 60 L.min-1 rate leads to a weak turbulent flow (Re=4600). Finally, the Reynolds system equations are closed by a second order model (the Reynolds Stress Model (RSM)), in which a transport equation of the Reynolds tensor (turbulent strain tensor) has been used. This model appears to be suitable to take into account intermediate turbulence areas where recirculation phenomena and streamlines of high curvature occur [1]. 2.2. Dispersed phase flow Since the volume fraction of the dispersed phase is rather low (10%), it has been possible to describe the flowing behavior of the particles according to the Lagrangian concept instead of the Eulerian one. The Lagrangian way consists in treating the dispersed phase as a collection of individual particles; each of them is tracked and the averaging occurs afterwards. In addition, the following hypothesis have been made: • Particles are considered as non deformable spheres • Particle-particle interactions are neglected • Since particle-continuous phase are neglected too, the particle-air coupling is one way from the carrying fluid to the particles. The motion of each particle is simulated via the resolution of the Newton’s law (1). Because of the high phase density ratio [2] (ρp=1245ρc), only drag and gravity forces are taken into account. G d 3p du p d 3p d 2p 1 G G G G G ( (1) =π π ρp ρ p − ρ d )g + C x π . .ρ c (u − u P ) u − u P 6 dt 6 4 2 Where : dp : particle diameter (m) ; up : particle instantaneous velocity (m.s-1) ; u : fluid instantaneous velocity (m.s-1) and Cx drag coefficient given by the Morsi and Alexander’s relation (2) [3]. a a C x = a 1 + 2 + 32 (2) Re p Re p where Rep : particles Reynolds number ( Re p =
d p ρc u p − u
μc
) and a1,a2, a3: Rep
dependent coefficients. The fluctuating component of the fluid velocity (turbulent component) at the particle position in each direction is generated via a stochastic method called Eddy Life Time (ELT) model [4]. In this model, particles interact successively with different swirls, each of them being characterized by a threecomponent fluctuating velocity and a lifetime. This model is quite useful in the present study due to the simplified particle equation of motion in the case of gas-solid flows although it records discontinuous velocities which cannot be differenciated.
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2.3. Meshing and geometry The nozzle geometry and meshing are represented in Figure 1. Meshing is composed of 91,000 hexaedric meshes. Particles hydrodynamics have been characterized at 8 different sections located all along the CI nozzle (Figure 1).
Figure 1. Nozzle and meshing
Since CFD results give access to raw hydrodynamic data only, a self-made code has been developed in order to determine the position of the inclusions gravity centre as well as the standard deviation for the particle coordinates. Each section has been divided into 200 subsections to calculate the particles density per unit surface expressed in number of particules.m-2. 2.4. Operating parameters The trajectories of particles having a diameter of 10 to 100 μm are simulated. Inclusions are individually dropped from the same point (x=0, y=0, z=-100 mm) at the centre of the nozzle entry section. A former study [5] has shown that inclusions instantaneously respond to the fluid velocity: as a consequence a zero initial velocity is chosen. The number of simulated inclusions is set to 500 in order to insure an acceptable balance between reproducibility and calculation time [6]. Wall-particles interactions are characterized by different boundary conditions in order to mimic a wide range of real conditions: • Rebound with a restitution coefficient of the normal and tangential velocities varying from 0 (inert impact) to 1 (perfectly elastic rebound). • Particle trapping by the wall each time a contact occurs. This condition is representative of reality since the airways are covered by a highly adhesive mucus layer 3. Results 3.1. Continuous phase It appears first that a recirculation area can be observed at the nozzle elbow level in which fluid velocities are small (Figures 2 and 3). This flow pattern can induce the recirculation of more or less particles depending upon their diameter and disturb the separation process taking place at the exit of the nozzle.
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Figure 2. Side view velocity vectors Sec 3 Figure 3. Side view velocity vectors
Then another small velocity area is observed after the section 4 in the internal part of the elbow (Figure 4 and 5). However, a very low number even no particles cross this area.
Figure 4. Velocity vectors after section 4.
Figure 5. 10 μm particle paths – Elastic rebound
3.2. Dispersed phase 3.2.1 Section 1 and 2 Results presented in table 1 give the average impacts for the whole range of restitution coefficients in section 1 and 2. It shows that the influence of the restitution coefficient can be neglected because of the low number of wall-particle impacts. On the other hand, despite the turbulent flow patterns, the particles start to fall down along the y-coordinate in section 2. The higher the size, the lower the gravity center is. This behavior leads to assert that the mass influence is higher than the drag one in this portion of the CI.
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Computational Fluid Dynamics: A Tool to the Formulation of Therapeutic Aerosols
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In addition, the standard deviation data (figure 7) which reveal the intensity of the dispersion around the gravity center show that the dispersion is higher and comparable for 10 to 20 μm particles compared to larger ones. Gravity effects are balanced by turbulence ones. For 20 to 70 μm particles, the dispersion around the center of mass decreases. Inertial effects become increasingly important. Finely, the dispersion of particles larger than 70 μm is low and remains unchanged: turbulence has a lower impact on these particles while drag and inertia forces exert higher effects. These features show that a slight change in particles diameter can modify the particles path, thereby leading to different drug desorption process and uncontrolled process variability [7]. 3.2.1. Section 3 The nozzle elbow has a sheer geometry which is characterized by a low velocity recirculation area. The number of particles crossing this section is often higher than the initial particle number due to the recirculation. Moreover, particles paths strongly depend on their diameter: 10 and 80 μm particles do not re-circulate, 60-70 μm slightly re-circulate while 40 to 20 μm are strongly affected by the re-circulation whatever the restitution coefficient. In addition, the number of lost particles by impaction is the lowest for 60 μm particles (Figure 8) and is higher with smaller and larger particles. Inertia effects are thus predominant for larger particles while smaller particles are affected by the dispersion effects. Finely, the highest impacted area is located between section 3 and 4 (figure 9). The flowing patterns of these particles are therefore strongly affected by the impaction and this can explain some disturbance of subsequent particles separation process. 3.2.2. Sections 4 to 8 It must be mentioned that the results appear to be quite difficult to analyze in these area. Nevertheless, it appears that particles larger than 20 μm have all impacted on the wall when they reach the section 5 while particles of less than 20 μm need to reach the section 8 to impact at 98.4%.
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4. conclusion Monodisperse particles hydrodynamic behavior inside the nozzle of a CI has been studied via CFD. It has been shown that the particles hydrodynamics depend upon the particles diameters once the section 2 of the nozzle has been passed through. In particular, particles smaller than 20 μm behave differently than particles larger than 20μm. Therefore, different subsequent paths and wall-impacts are observed according to particles diameters. It can then be concluded that the process is highly sensible to small changes in particle size, especially in the usual particle size range of aerosols. Powder samples with small particle size distribution variations will therefore undergo different interactions with the continuous phase and this will modify the state of the powder (adsorbed-non adsorbed ratio) before entering the true separator part of the CI. References [1] STAPLETON K.W., GUENTSCH E., HOSKINSON M.K, FINLAY W.H. On the suitability of k-ε Turbulence Modeling for Aerosol Deposition in the Mouth and Throat : a comparison with experiment. Journal of Aerosol Science, 31 (6) – 739-749 (2000) [2] FEULLEBOIS F., 1980 Certains problèmes d’écoulements mixtes fluids-particules PHD Thesis Université Pierre et marie Curie, PARIS VI [3] MORSI S.A., ALEXANDER A.J. An investigation of particle trajectories in twophase flow systems Journal of Fluid Mechanics, 55 (2) – 193-208 [4] GOSMAN A.D, IOANNIDES E, 1981, Aspects of computer simulation of liquid fueled combuster. 19th Aerospace Science Meeting ST Louis n°AIAA Paper 81-0323 [5] THIBAUT J. Caractérisation des Poudres pour Administration Pulmonaire par l’Impacteur en cascade. Thèse de Docteur en pharmacie,Université Henri Poincaré Nancy I (2002). [6] BARDIN-MONNIER N., DELARUE M., MARCHAL-HEUSSLER L. Etude de l’écoulement de poudres à inhaler dans les voies respiratoires - 21 ème Congrès Français sur les Aérosols, , p89-94 14-15 décembre 05 [7] LI W.I., PERZL M., HEYDER J., LANGER R., BRAIN J.D., ENGLEMEIER K.Aerodynamics and Aerosol Particle Deaggregation Phenomena in Model OralPharyngeal Cavities Journal of Aerosol Science, 27 (8) – 1269-1286 (1996)
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Large eddy simulation of particle dispersion in a straight, square duct flow Michael Fairweather, Jun Yao Institute of Particle Science and Engineering, School of Process, Environmental and Materials Engineering, University of Leeds, Leeds LS2 9JT, UK
Abstract Numerical simulations of three sizes (1, 50 and 100 ȝm) of particle dispersion in fully developed turbulent duct flows at three Reynolds numbers up to 250,000 are reported. Results were obtained using large eddy simulation combined with Lagrangian particle tracking under conditions of one-way coupling between the flow and particles. The results demonstrate that particle dispersion in duct flows is not only affected by particle size, but also by the flow Reynolds number. Small particle size, or high Reynolds number, are found to cause the particles to move more erratically in the flow, and to be more influenced by the flow turbulence and secondary motions. In addition, the secondary flow formed in the cross-section of a duct has a significant effect on particle dispersion in the transverse direction, whilst gravity is more influential on particle dispersion and deposition in the flow direction. The results obtained are of relevance to nuclear waste processing applications where two-phase mixtures need to be kept as homogeneous as possible to discourage the formation of beds of solid particles which can promote pipe blockages. Keywords: Large eddy simulation, particle dispersion, square duct flows
1. Introduction Controlling particle dispersion in turbulent flows in pipes and ducts can be used to improve the efficiency of heat, mass and momentum transfer processes in a number of industrial and environmental applications. Of particular interest in this study are processing applications for nuclear waste treatment where it is desirable that the twophase waste mixtures are kept as homogeneous as possible to prevent, or at least discourage, the settling out of solid particles to form beds which can promote pipe blockages. However, the turbulent dispersion of particles in pipes, and especially in square ducts, is not thoroughly understood due to the limited amount of research conducted on such flows. A number of studies have focussed on turbulent single-phase flows through square ducts, including experimental investigations (Brundrett and Baines, 1964; Launder and Ying, 1972; Gessner et al., 1979), direct numerical simulations, DNS (Gavrilakis, 1992) and large eddy simulations, LES (Madabhushi and Vanka, 1991). All of these studies have demonstrated that turbulence-driven secondary motions that arise in duct flows act to transfer fluid momentum from the core of the flow towards the walls. There exist very few studies of particle-laden turbulent flows in a square duct. Winkler et al. (2004) did, however, utilise LES to investigate the preferential concentration of finite-inertia particles in such flows, especially near the walls of the duct. Sharma and Phares (2006) also employed DNS to predict longitudinal and lateral single particle- and pair-dispersion statistics, although gravity effects were neglected in this work. More recently, Fairweather and Yao (2007) studied particle deposition in a fully developed turbulent flow in a duct at a Reynolds number of 36,500.
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The present work extends the latter to investigate the factors that affect particle dispersion in duct flows at various Reynolds numbers.
2. Mathematical model 2.1 Flow Configuration A schematic diagram of the duct geometry and the co-ordinate system used is shown in Fig. 1. The flow is three-dimensional and described by a Cartesian co-ordinate system (x, y, z), in which the z axis is aligned with the flow streamwise direction, the x axis is in the direction normal to the floor of the duct, and the y axis is in the transverse direction. The corresponding velocity components in the (x, y, z) directions are, respectively, (u, v, w). The cross section of the duct is square with sides Lx = Ly = 2h, and the length of the duct is Lz = 8h, where h = 0.02 m. The boundary conditions for the momentum equations are no-slip at the duct walls. To avoid having to specify inflow and outflow conditions at the open boundaries of the duct, it is assumed that the instantaneous flow field is periodic along the streamwise direction, with the pressure gradient that drives the flow adjusted dynamically to maintain a constant mass flux through the duct. The computational results reported were obtained with cubic grids for which ǻx = ǻy = ǻz, thereby ensuring a constant filter width of the LES equations in each of the three coordinate directions. Three flow Reynolds numbers were considered, with Reb = 4410, 36,500 and 250,000, based on the centerline velocity and duct side length. The corresponding numerical grids used in the computations were 41×41×161, 61×61×241 and 81×81×321, respectively. 2.2 LES Approach In LES only the large scales of motion are directly computed, whilst the small scales are modelled. Any function is decomposed using a localised filter function, such that filtered values only retain the variability of the original function over length scales comparable to or larger than that of the filter width. The present work used a top hat filter as this fits naturally into a finite-volume formulation. This decomposition is then applied to the Navier-Stokes equations, giving rise to terms which represents the effect of the sub-grid scale (SGS) motion on the resolved motion. The SGS stress model used was the dynamic model of Germano et al. (1991), implemented using the approximate localization procedure of Piomelli and Liu (1995) together with the modification proposed by di Mare and Jones (2003). This model represents the SGS stress as the product of a SGS viscosity and the resolved part of the strain tensor, and is based on the possibility of allowing different values of the Smagorinsky constant at different filter levels. In this formulation the model parameter is numerically well behaved, and the method is well conditioned and avoids the irregular behaviour exhibited by some implementations of the dynamic model. Test-filtering was performed in all space directions, with no averaging of the computed model parameter field. Computations were performed using the computer program BOFFIN (Jones, 1991). 2.3 Lagrangian Formulation for Particles The solid phase was modelled using a Lagrangian approach (Fan et al., 2002) in which the particles are followed along their trajectories through the flow field. To simplify the analysis, the following assumptions were made: the particle-laden flow is dilute; interactions between particles are negligible; the flow and particles are one-way coupled, i.e. the effect of particles on the fluid is neglected; all particles are rigid spheres with the same diameter and density; and particle-wall collisions are elastic. The Lagrangian motion of a rigid, spherical particle suspended in a flow is governed by a
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force balance equation, described in detail by Maxey and Riley (1983). Even though a number of possible forces (including Stokes drag, lift, gravity, virtual mass and Basset history) can act on a particle, many of these may be neglected without any appreciable loss of accuracy, depending on the particle inertia. The most important force acting on the particle is the Stokes drag force, with gravity also important depending on the orientation of the flow. In this study, Stokes drag, gravity and buoyancy forces were considered, and a particle was assumed to interact with a turbulent eddy over a certain period of time, that being the lesser of the eddy lifetime and the transition time. A fourth-order Runge-Kutta scheme was used to solve the equation of motion, given the initial particle location and velocity. Particle and liquid densities were set to ȡp = 2,500 and ȡl = 1,000 kg m-3, respectively, with a value vl = 1.00×10-6 m2 s-1 assumed for the kinematic viscosity of the liquid. Three particle diameters were considered, namely dp = 1, 50 and 100 ȝm, corresponding to particle relaxation times of IJp = 1.39×10-7, 6.94×10-6 and 1.39×10-5 s, where IJp = ȡp d2p/18ȡl vl based on Stokes drag law. The particle calculations also assumed a periodic boundary condition in the streamwise direction.
Figure 1. Schematic of the duct geometry and the co-ordinate system. Figure 2. Streamwise mean velocity distribution along the lower wall bisector at different Reynolds numbers: Brundrett and Baines (1964) Reb = 83,000; Gessner et al. (1979) 250,000; Launder and Ying (1972) 215,000; Madabhushi and Vanka (1991) 5,810; and Gavrilakis (1992) 4,410).
3. Results and Discussion 3.1 Flow Field The formation of secondary flows in the duct cross-section has been successfully predicted and reported in previous work (Fairweather and Yao, 2007). The predominant effect of the secondary motion is the induced transport of streamwise momentum towards the corners of the duct, with the iso-contours of the mean streamwise velocity near the wall becoming distorted as a consequence. Velocity vectors, averaged over the four quadrants, reveal two streamwise, counter-rotating vortices in each corner that characterise the flow, with a high degree of symmetry evident about the corner bisectors. The maximum secondary velocity in the simulations was § 2.5% of the bulk velocity, with Brundrett and Baines (1964) reporting a value of 2.2%. The effect of Reb on the mean streamwise velocity is shown in Fig. 2, where the velocity is normalized by the bulk velocity along the lower wall bisector (y/h = 1). It can be seen that the ratio of
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the centerline streamwise to the bulk velocity decreases with increasing Reb. This is because the profiles of streamwise velocity flatten, and gradients in the wall regions steepen, due to increased turbulent mixing at higher Reb. Calculated profiles are consistent with this trend, and in agreement with the experimental and numerical studies of duct flows noted above.
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Figure 3. Mean value of particle displacement in normal direction at various Reynolds numbers (time step = 5.61×10-5 s): (a) Reb = 4,410; (b) 36,500; and (c) 250,000.
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Figure 4. Particle (50 ȝm) dispersion in duct flows at various Reynolds numbers: (a) Reb = 4410, after 2 s; (b) 36,500, after 0.4 s; and (c) 250,000, after 0.2 s. 3.2 Particle Tracking To study particle dispersion in the duct, mean values of the particle distribution in the x direction are considered (Yao et al., 2003); Xm(t)=Xi(t)/ni(t), where ni(t) is the total number of particles distributed in the computational domain at time t, Xi(t) is the particle displacement in the normal direction at t, and Xm(t) is the mean value. Fig. 3 shows mean values of the particle distribution (Xm) in the duct for the three Reb considered. The results demonstrate that for all cases, Xm decreases with time due to the effect of gravity, with the decrease with time steepening with particle size. Moreover, the profiles given in Fig. 3 become more erratic with increasing Reb. This is caused by two effects. First, the flow turbulence increases with Reb, causing the turbulence to have more influence on the particles, as illustrated by the results of Fig. 4. Also, the secondary flow in the x-y section increases with Reb (Madabhushi and Vanka, 1991). It is noted that, in Fig. 3, the profiles also become more oscillatory with decreasing particle size, particularly in Fig. 3 (b) and (c). This is because small particles tend to maintain a near-velocity equilibrium with the carrier fluid which can be evaluated using the particle Stokes number, St, as discussed below. Fig. 4 presents 50 ȝm particle trajectories in the three Reb flows, and shows that in the lowest Re flow, Fig. 4 (a), the trajectories are effectively linear. However, as Reb increases, Fig. 4(b), the trajectories become more erratic and, at the highest Reb, Fig. 4(c), the particles’ trajectory is influenced on very short timescales. This effect is
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caused, as noted, by the increasing influence of flow turbulence and secondary flows in the duct. Madabhushi and Vanka (1991) argue that in duct flows turbulence in the flow normal and transverse directions increases with Reb, and suggest that their contribution to the turbulence kinetic energy budget increases at higher Reb. This is most likely due to the increased turbulent mixing in the transverse plane resulting in higher fluctuations in the instantaneous secondary velocities. From Fig. 4, the density of particles in the low Reb flow is also observed to be greater than that of particles in the higher Reb flows, indicating that particles are more likely to deposit in the former flow since gravity effects are more dominant than the streamwise and secondary turbulent motions.
Figure 5. Time-dependent particle dispersion in duct flow (Reb = 36,500; time step = 5.61×10-5 s): (a) mean value of particle displacement in transverse direction; and (b) transverse dispersion function. To further elucidate particle dispersion in the duct, the dispersion function (Yao et al., 2003) in the transverse (y) direction is introduced; Dy(t)=(((Yi(t)-Ym(t))2/nt ))1/2, where nt is the total number of particles distributed in the computational domain at time t, Yi(t) is the particle displacement in the transverse direction at t, and Ym(t) is the mean value. Mean values of particle displacement (Ym) in the transverse direction at Reb = 36,500 are shown in Fig. 5 (a). It may be noted that Ym values are two orders of magnitude lower than the Xm values shown in Fig. 3. This suggests that gravity is influential on particle dispersion in the normal direction. Fig. 5 (a) shows that for all particles, Ym develops with time in an oscillatory fashion due to the effect of the secondary flow in the cross section of the duct. In comparison with mean values in the normal direction (Xm in Fig. 3), the secondary flow does have a significant effect on particle dispersion in the transverse direction because there is no gravity effect in that direction. Ym also oscillates more with decreasing particle size since smaller particles follow the flow more closely that large particles. To scale particle motion in fluids a useful parameter is the Stokes number which is the ratio of particle response time to a time characteristic of the fluid motion: St=IJp/IJf, where IJp is the particle relaxation time, and IJf is a time scale of the flow structures (IJf = u2IJ/v, where uIJ is the shear velocity and v is the kinematic viscosity). For the Reb = 36,500, uIJ is equal to 0.31 m s-1. Then, for the three particles, of 1, 50 and 100 ȝm diameter, St = 1.33×10-4, 6.67×10-3 and 1.33×10-2, respectively. In the present work, St is therefore significantly less than 1, so the particles can maintain near velocity equilibrium with the carrier fluid (Crowe et al., 1996). Lastly, Fig. 5 (b) shows the particle dispersion function in the transverse direction. The profile is similar to that of Ym(t) in Fig. 5 (a), and again oscillates with time due to the effect of the secondary flow. The magnitude of the oscillations in the dispersion function is seen to increase with decreasing particle size, with an accompanied decrease in the frequency of oscillation.
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4. Conclusions Large eddy simulation has been used to study flows in square ducts at three Reynolds numbers, and results found to agree with previous studies of single-phase flows. Solid particle dispersion within these flows has also been simulated, and in all cases the mean value of the particle distribution in the normal direction decreases with time and with increasing particle size due to the effect of gravity. The particle distribution in the transverse direction is more oscillatory than in the normal direction, and two orders of magnitude lower. This indicates that the secondary flow does have some effect on particle dispersion in the former direction, but that gravity dominates in the normal direction and overall plays the most significant role in particle dispersion. In addition, particle trajectories were found to be affected by the Reynolds number and particle size, with oscillatory motions increasing with Reynolds number and decreasing particle size.
Acknowledgement This work was carried out as part of the TSEC programme KNOO and as such we are grateful to the EPSRC for funding under grant EP/C549465/1.
References E. Brundrett and W.D. Baines, 1964, The Production and Diffusion of Vorticity in Duct Flow, J Fluid Mech, 19, 375-394. C.T. Crowe, T.R. Troutt and J.N. Chung, 1996, Numerical Models for Two-Phase Turbulent Flows, Ann Rev Fluid Mech, 28, 11-43. M. Fairweather and J. Yao, 2007, Investigation of Particle-Laden Flow in a Straight Duct Using Large Eddy Simulation, Proc 11th Int Conf Environmental Remediation and Radioactive Waste Management, Bruges, Belgium, 2nd-6th September 2007. J.R. Fan, J. Yao and K.F. Cen, 2002, Antierosion in a 90° Bend by Particle Impaction, AIChE J, 48, 1401-1412. S. Gavrilakis, 1992, Numerical Simulation of Low-Reynolds-Number Turbulent Flow Through a Straight Square Duct, J Fluid Mech, 244, 101-129. M. Germano, U. Piomelli, P. Moin and W.H. Cabot, 1991, A Dynamic Sub-Grid-Scale Eddy Viscosity Model, Phys Fluids, 23, 1760-1765. F.B. Gessner, J.K. Po and A.F. Emery, 1979, Measurements of Developing Turbulent Flow in a Square Duct. In, F. Durst, B.E. Launder, F.W. Schmidt and J.H. Whitelaw (Eds.), Turbulent Shear Flows I, Springer-Verlag, New York, 119-136. W.P. Jones, 1991, BOFFIN: A Computer Program for Flow and Combustion in Complex Geometries, Dept Mech Eng, Imperial College of Science, Technology and Medicine. B.E. Launder and W.M. Ying, 1972, Secondary Flows in Ducts of Square Cross-Section, J Fluid Mech, 54, 289-295. R.K. Madabhushi and S.P. Vanka, 1991, Large Eddy Simulation of Turbulence-Driven Secondary Flow in a Square Duct, Phys Fluids A, 3, 2734-2745. L. di Mare and W.P. Jones, 2003, LES of Turbulent Flow Past a Swept Fence, Int J Heat Fluid Flow, 24, 606-615. M.R. Maxey and J.J. Riley, 1983, Equation of Motion for a Small Rigid Sphere in a Nonuniform flow, Phys Fluids, 26, 883-889. U. Piomelli and J. Liu, 1995, Large Eddy Simulation of Rotating Channel Flows Using a Localized Dynamic Model, Phys Fluids, 7, 839-848. G. Sharma and D.J. Phares, 2006, Turbulent Transport of Particles in a Straight Square Duct, Int J Multiphase Flow, 32, 823-837. C.M. Winkler, S.L. Rani and S.P. Vanka, 2004, Preferential Concentration of Particles in a Fully Developed Turbulent Square Duct Flow, Int J Multiphase Flow, 30, 27-50. J. Yao, F. Ji, L. Liu, J.R. Fan and K.F. Cen, 2003, Direct Numerical Simulation on the Particle Flow in the Wake of Circular Cylinder, Prog Nat Sci, 13, 379-384.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Test bench dimensioned by specific numerical tool Nicolas Gascoin1, Philippe Gillard1, Gregory Abraham1, Marc Bouchez2 1 2
LEES, 63 avenue de Lattre de Tassigny, Bourges, 18000, France MBDA-France, 18 rue Le Brix, Bourges, 18000, France
Abstract One of the main issues of hypersonic flight is the thermal management of the overall vehicle. In order to simulate the behaviour of a complete actively cooled Supersonic Combustion Ramjet, a one-dimensional transient numerical model has been developed with heat and mass transfer particularly in a cooling channel for supercritical fuel under pyrolysis. It uses a detailed pyrolysis mechanism for n-dodecane (1185 reactions and 153 species). A further validation of the model, based on experimental and numerical data, is presented in this paper. The hydrodynamic behaviour is considered to be good enough for this numerical tool as the accuracy of fluid velocity computation is about few percents. The model is quantitatively validated under stationary conditions for both hydrodynamic and thermal aspects. The discrepancies between computed and experimental data remain close to 5 % or less on a thermal point of view. Furthermore, good agreement is found with transient experimental test case. Discrepancies are analysed and they remain in an acceptable range of a tenth of degree. A validation of the chemistry is provided thanks to experimental results. The pyrolysed mixture’s compositions are well reproduced with only few percents of error. RESPIRE is now considered to be validated and it brings further analysis of the experimental data obtained with the new pyrolysis bench. Some interesting examples of use are given. Keywords: Process Design, Multiphysic Process, Fuel Pyrolysis.
1. Introduction Hypersonic flight is expected to be achieved with SCRAMJET engine. Because the total temperature of external air reaches temperatures as high as 4950 K for example at Mach 12, even composite materials could not withstand such large heat load. Thus, an active cooling system has to be used. Furthermore, the time allocated to the combustion in the engine is about 10-3 s. These two points lead to use the fuel to cool down the engine’s wall and then to burn it in the combustion chamber. Fuel is injected in a composite channel which surrounds the engine. When heated above 800 K, the fuel is pyrolysed and thanks to its endothermic behaviour, it ensures the active cooling of the hot walls. This pyrolysis produces lighter hydrocarbons species, which are easier to ignite. It is important to note that the expected high pressure in the cooling loop (>3 MPa) causes the fluid to become supercritical in the channel. The principle and advantages of SCRAMJET and the interest to use hydrocarbon fuel have been fully studied (Powell et al., 2001). The modelling is a more feasible method than experiments for conducting engineering studies and for furthering research related to this topic. As both the pyrolysis and the combustion chemistry are never treated in the literature, coupled phenomena are not considered and the relationship between fuel composition and SCRAMJET thrust cannot be taken into account. The need of a specific tool considering the overall vehicle, its cooling as its thrust, is thus evident to study the entire coupled phenomena involved in the SCRAMJET's cooling. The present work falls within the framework of the COMPARER project (COntrol and Measure of
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PArameters in a REacting stReam). It aims at understanding the pyrolysis of endothermic hydrocarbon fuel under supercritical states with complementary numerical and experimental approaches. This work should help to respond to the industrial need, which is related to mass flow rate measurement and burning capacity determination. A numerical code, called RESPIRE (a French acronym for SCRAMJET Cooling with Endothermic Fuel, Transient Reactor Programming), has been specifically developed. Its purpose is mainly to understand the relationships between the phenomena involved in the process. The aim of RESPIRE is to determine temperatures in the system to a tenth of a degree and the chemical composition at a mole fraction of 1 %. An experimental test bench has also been realised to serve as a validation apparatus for RESPIRE and also as a comprehension tool. This bench allows for studying fuel pyrolysis under stationary and transient conditions, particularly under supercritical state. The maximum operating parameters are about 1800 K, 8 MPa and 0,6 g.s-1 inside the chemical reactor heated by a furnace. It is notably composed of a Gas Chromatograph and a Mass Spectrometer. Coupling experimental and numerical approaches is hoped to improve knowledge about pyrolysis. The test bench is described in a previous paper (Gascoin et al., 2007). The fuel is the n-dodecane because of its representativity of aeronautic kerosene and of its purity. The purpose of this present work is firstly to give a numerical and experimental validation of the pyrolysis channel. Secondly, some very interesting examples are provided to show the capacities of the code. The simulations are used to furnish information, which are not measured during the experiments.
2. Governing equations of the full transient model RESPIRE considers a complete hypersonic cooled vehicle. It allows for studying under transient conditions, the coupling between the pyrolysis inside the cooling channel and the combustion inside the engine, so as to the thermal consequences on the engine and the thrust of the vehicle. All the governing equations are given in details in previous work (Gascoin 2006). The cooling channel can be studied alone to simulate a chemical reactor. The related equations are written in transient state and the resolving method is a finite differences one. Partial derivative equations are discretized in space (centred scheme) and solved in time (explicit scheme). An average temperature is computed in the wall, considering radiative, convective and conductive heat fluxes. The fluid is treated as an average single phase flow but possibly multi-species. The velocity of the fluid is determined by the momentum equation and its enthalpy by the energy equation. The effusion through the walls can be investigated thanks to the Darcy Law. RESPIRE could treat several fluid types. The main one is n-dodecane, for which a full mechanism (Dahm et al., 2004) is used (1185 reactions and 153 species, designed by the French laboratory DCPR). The transport equation is solved for each species. An equation of state is used to determine the density considering the perfect gases law modified by the compressibility factor. The Pitzer acentric factor is used. The LeeKesler tables are needed. The heat capacity is corrected following the temperature and the pressure. Pressure of fluid is determined by use of Bulk Modulus.
3. Results and discussion 3.1. Stationary hydraulic numerical validation of the fluid flow The numerical stationary reference data have been obtained with NANCYNETIK, a former "in-house" MBDA code (Daniau et al., 2004). A chemical reactor is considered and is heated by a furnace, whose temperature depends on the position. It is comprised between 1500 K and 1900 K. The mass flow rate is equal to 0.05 g.s-1. The fluid is the
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Fluid flow velocity, m.s
-1
n-dodecane. It is injected at a temperature of 300 K and at a pressure of 3.5 MPa. Such a test case is representative of the experimental COMPARER bench. If velocity trend are of good agreement in the chemical reactor (Figure 1a), numeric values between the two codes are slightly different. This is attributed to the physical fluid properties calculations. Indeed, data tables in temperature and pressure are used in NANCYNETIK whereas RESPIRE computes these data with the method described above in the section 2. As the fluid temperature given by RESPIRE is lower in the first 0.4 m (Figure 1b), the density is higher and the resulting fluid velocity for a fixed mass flow rate is lower. Furthermore, as the fluid compressibility is taken into account by RESPIRE and not by NANCYNETIK, it may be possible to observe an accumulation of fluid, particularly in the critical region (0.2 m for almost 1 m of supercritical fluid), near 658 K. This would result in a velocity decrease in this region and in a Reynolds number decrease too. Consequently, the fluid temperature is lower than without accumulation. Furthermore, for the same computed fluid temperature with both numerical codes (around 0.42 m, 0.48 m and 0.52 m), the velocity is the same. This highlights the fact that for similar conditions, discrepancies are lower than few percent. 0.5 0.4 0.3 0.2 0.1 0
FUEL
NANCYNETIK
0
0.2
0.4
0.6
0.8
RESPIRE
1
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Mixture temperature , K
Position in the channel, m
1500 1300 1100 900 700 500 300
FUEL
NANCYNETIK
0
0.2
0.4
0.6 Position in the channel, m
Fig. 1
a)
0.8
RESPIRE
1
1.2
b)
Velocity (a) and mixture temperature (b) profiles in the cooling channel at equilibrium.
3.2. Stationary thermal experimental validation of fluid flow An experimental test case from MBDA-France and its partners of the Prométhée program is used to validate thermal behaviour of fluid inside the cooling channel. A cylindrical one meter long reactor is heated by its external surface. The fluid temperature is measured at the reactor outlet. For different temperature of the system, the validation is conducted on the outlet fluid temperature, witness of all the thermal aspects involved in the channel. The geometry of the chemical reactor considered numerically is not cylindrical because it is not taken into account by the RESPIRE code. A panel with pin fins is considered with the corresponding empiric correlations for the Prandtl and Nusselt numbers calculation. The internal height and width of the reactor are respectively 5.10-3 m and 8.10-3 m; the wall thickness is about 2.5.10-3 m. The thermal discrepancies (Figure 2) are lower than 10 % between the numerical and experimental data. They are attributed to the geometric configuration because the pin fin geometry corresponds to a gap of 30 % for thermal exchange surface and hydraulic diameter. Nevertheless, results are good enough for the COMPARER project. Furthermore, for such pyrolysis configuration, the thermal radial gradient in the
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Outlet Fluid Temperature, K
cylindrical reactor has been numerically determined to be around 40 K, thanks to the CFD commercial software CFD-ACE. As RESPIRE is a 1-D code, discrepancies remain acceptable. Another calculation has been conducted for the 873 K external face temperature test case considering a pin fin geometry but with modified hydraulic diameter (5.10-3 m) and external exchange surface. The latest is computed for a given computation space step for a cylindrical tube of 9.5.10-3 m external diameter. This calculation gives an outlet fluid temperature of 774 K against 690 K with the previous geometric data. As the pin fin geometry still overestimate the thermal exchange compared to cylinder configuration, the results are consistent and they remain in the 40 K gradient numerically observed in the 2-D configuration by CFD approach. 950 900 850 800 750 700 650 850
Experiment RESPIRE 900
950
1000
1050
1100
1150
1200
External Face Temperature, K
Fig. 2
Comparison of experimental and numerical data for thermal validation.
3.3. Transient validation on outlet fluid temperature An experimental test case from MBDA-France and its partners is used to test transient validity of RESPIRE. A chemical reactor is equipped by thermocouples, located on the upper external face. Along the channel, the fluid (initially hot) is simply subjected to natural cooling with walls, which exchange by convection with external environment. The transient temperatures and pressures are measured at the inlet and outlet of the channel. The injected fluid inside the channel is changing from air to kerosene after 27 s of experiment and again to air after 70 s. The outlet fluid temperatures are investigated during 160 s with the two fluids alternatively (Figure 3a). If the trend of calculated data looks like the one of measured data, their values can be 40 % higher. 800
OutletOutlet measurementmeasurement Isentropic Isentropic Expansion Expansion Inlet measurement Inlet measurement
1000
Temperature, K
900
kerosene
air
Temperature, K
air
800 700 600 500
Outlet Measurment Inlet Measurment RESPIRE
400
700 600 500 400 300
300
0 0
20
40
60
80 100 Time, s
120
140
160
a)
3
6
9
12
15
Time, s s Time,
18
21
24
27
b)
Fig. 3 Outlet fluid temperatures for transient calculations and experimental measurements (a) and Effect of an isentropic relaxation on numerical calculation (b).
This result is attributed to the pressure variations, which have been experimentally measured at the entrance. The pressure is typically measured to be equal to 1.5 MPa in entrance and 0.16 MPa at the outlet. This cannot be due to regular pressure loss over a so small panel of few centimeters. Inlet temperature and pressure measures are taken just before a singular pressure loss. Consequently, an expansion of the fluid appears and modifies the fluid temperature. An isentropic expansion is chosen at the panel entrance from measured inlet pressure (roughly 1.5 MPa) to 0.25 MPa; even if a polytropic
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expansion should be more realistic. Then, with an inlet pressure of about 0.25 MPa, the regular pressure loss inside the channel conduct to furnish an outlet pressure of roughly 0.16 MPa, which has been experimentally measured. The figure 3b shows the good agreement between calculated and measured data with discrepancies lower than 10 K. 3.4. Experimental validation of pyrolysis The COMPARER bench has successfully furnished a detailed comprehension of pyrolysis phenomena (Gascoin et al. 2007). The n-dodecane has been studied (Gascoin 2006) on a wide range of parameters (700 K to 1100 K, 10 bars to 50 bars, residence time from 20 s to 100 s). These data allow to test RESPIRE to verify its validity. On a first example for extreme temperature and pressure conditions (Figure 4a), the mole fractions of gases at ambient conditions are measured experimentally and compared to numerical results. The lack of hydrogen obtained with the experiments is attributed to its high diffusivity, which makes it difficult to measure. The code shows here a first interest because it enables to consider hydrogen in a better way. The other discrepancies are due to measurement uncertainties on the temperature. For a 20 K thermal gradient, the pyrolysis rate can vary by 10 %, which explains the observed differences. Indeed, the fluid temperature cannot be measured inside the process but only in the furnace, outside the chemical reactor.
a)
b)
Fig. 4 (a) Composition of gaseous products obtained for a pyrolysis at 1100 K, 10 bars, 0,05 g.s-1. (b) Composition of pyrolysed products obtained at 773 K, 50 bars, 0,05 g.s-1.
For moderate temperature and pressure conditions (Figure 4b), the mole and mass fractions of gases and liquids are observed. The discrepancies are, in these conditions, due to 2-D effects (hydraulic and thermal ones) in the reactor. Indeed, RESPIRE considers one phase whereas two phases can appear depending on operating conditions. Thus, a gliding can be observed at the reactor outlet. Due to high residence time between the process and the analysis, this conducts to some experimental uncertainties. For low pyrolysis rate, RESPIRE also shows a good agreement with experiments. The differences on composition (some percents) are acceptable for the COMPARER project because it is preferred to take all the system with detailed chemistry into account with a moderate accuracy rather than a simplified configuration with higher accuracy. 3.5. Some interesting use of RESPIRE After validation, RESPIRE has been used to provide additional information on the experiments. For example, it gave firstly a justification of using the maximum temperature measured in the furnace, outside the chemical reactor, to characterize the thermal conditions of the pyrolysis. Indeed, the maximum temperature reached by the fluid is closed to the maximum one measured in the process (Figure 5a). A cooling of the fluid has been shown in the last third of the reactor thanks to the code. In addition, it is proved that no chemical reaction appear during this cooling and after the reactor outlet. Consequently, the chemical composition depends on the maximum temperature reached by the fluid, which directly depends on the one of the process. Furthermore,
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RESPIRE allows studying the residence time in the process and it appears that three different times are observed. The first one (75 s) is dedicated to the heating of the fluid (until 800 K) during which no pyrolysis appears (Figure 5b). Then, a short period (10 s) corresponds to the pyrolysis (from 800 K and above) whereas the cooling of the fluid takes place during the last 15 s. Finally, only 10 % of the global residence time is allocated to the fuel pyrolysis. This parameter is not accessible experimentally.
a)
b)
Fig. 5 (a) Fluid temperature computed in the reactor of the given experimental thermal profile. (b) Fluid temperature computed in the reactor and given as a function of time and position.
4. Conclusion The COMPARER project studies the active cooling of a scramjet for hypersonic flight application. It is needed to have at our disposal a numerical tool able to take into account all the phenomena involved in this technology with a low computational cost. A one-dimensional transient model, called RESPIRE, has thus been developed. A complete pyrolysis mechanism (1185 reactions and 153 species) has been implemented. The hydraulic and thermal behaviour of the code is confirmed to be good enough for the project. The transient validation has shown a good agreement of RESPIRE despite the complexity of study cases, with alternative and sudden changes in fluid nature. A validation of the chemistry has been realized with the dedicated experimental bench. The differences have been understood and remain acceptable for this project. Some examples have been presented in this paper to show the interest of RESPIRE to deeply investigate the experimental results, particularly for the fluid temperature and the residence time inside the process. RESPIRE continues to be systematically used on the experimental test cases to give additional information about unknown parameters. Presently, RESPIRE is used to investigate the relationship between the pyrolysis of the fuel and the quantity of product gases obtained at ambient conditions.
Acknowledgements The present work was realised thanks to the "Conseil Général du Cher", of the "Conseil Régional du Centre", of the FRED, of the FEDER, of the FSE, of MBDA-France.
References Dahm K.D. et al., 2004, Experimental and Modelling Investigation of the Thermal Decomposition of n-Dodecane, J. Anal. Appl. Pyrol., 71, pp. 865-881. Daniau E., Bouchez M., Gascoin N., 2004, SCRAMJET Active Cooling Analysis Using ndodecane as a Generic Endothermic Fuel, TPPA, St Petersburg, Russia, 12-14 July. Gascoin N., 2006, Etude et mesure de paramètres pertinents dans un écoulement réactif, PhD Thesis, Orleans University, 30/11/06, Bourges. Gascoin N. et al., 2007,"Pyrolysis of Supercritical Endothermic Fuel: Evaluation for Active Cooling Instrumentation.", Récents Progrès en Génie des Procédés, N°96, Ed. Lavoisier. Powell O.A. et al., 2001, Development of Hydrocarbon-Fueled Scramjet Engines: The Hypersonic Technology (Hytech) Program, J. Prop. Power, Vol. 17, No. 6, Nov–Dec.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimization of SOFC Interconnect Design Using Multiphysic Computation Dominique Grondin,a,b Jonathan Deseure,a Mohsine Zahid,b Maria José Garcia,b Yann Bultela a
Laboratoire d’Électrochimie et de Physico-chimie des Matériaux et des Interfaces (LEPMI), UMR 5631 CNRS-INPG-UJF, ENSEEG, BP 75, 38402 Saint Martin d’Hères, France b European Institute For Energy Research (EIFER), Emmy-Noether Strasse 11, D-76131 Karlsruhe, Germany
Abstract The aim of this work is to optimize an interconnect design. A three-dimensional model have been developed in order to investigate the effect of interconnect design on electrical performance and degradation process. Oxygen concentration, potential, current density and temperature distribution in interconnect and SOFC cathode have been calculated. Cathode degradation has been supposed to be due to temperature gradient non-uniformity. Our studies have demonstrated the impact of cathode/interconnect contact on thermal and electrical behavior. Thus, an optimization of the cathode/interconnect contact using COMSOL Multiphysics® software has been investigated. In this investigation, the effects of the two geometrical parameters are considered. This paper presents the modification of cathode/interconnect contact area and electrical collecting pins size. Simulations show a decreasing power density and a reduction of temperature gradient for an increasing contact area. With a decreasing size of collecting pins, better temperature homogeneity and power density are recorded. Keywords: SOFC, modeling, optimization, transfer phenomena, design
1. Introduction For the generation power, especially for stationary applications, planar SOFC stack is a promising device that converts chemical energy into electric and thermal energy using Fuel like hydrogen or methane and air in temperature ranges between 750 and 1000°C. The serial repeating unite that forms such a stack consists of an interconnect structure and a three-layer region which is composed of two ceramic electrodes separated by a dense ceramic electrolyte. SOFC can convert hydrogen into electricity with a high efficiency (§ 60%). Unfortunately, performance of SOFCs is strongly limited by thermal stress induced by dilatation of the ceramic layers. Since all SOFC components are solid state, in principle there are no restrictions on cell configuration. In planar configuration, interconnect plays a critical role. It is the element which ensures electrical bond between cells and supplies reactive species on the electrodes. Research efforts are mainly focused on increasing lifetime and performance. The experimental investigations have shown that interconnect decreases fuel cell electrical performance and cell durability. Several electrochemical SOFC models focus only on cathode side of fuel cell [1], because cathode activation potential is the largest source of losses in fuel
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cells. Oxygen-reduction reaction at cathode (Eq. (1)) plays a significant role in SOFC electrochemical behavior. 1 O + 2e → O 2− 2 2
(1)
Nevertheless, a multi-physic approach is required to describe cathode side. Many relevant investigations [2-4] have been carried out using three-dimensional computational fluid dynamics software. These studies consider an entire SOFC cell or a SOFC stack and emphasize the complex interactions between electrochemistry, mass and heat transfer.
2. Model development A model of a planar half-cell SOFC was developed using the COMSOL Multiphysics® software. Electrochemical reaction within porous electrodes is described using the Butler-Volmer equation at electrode/electrolyte interface. Modeling is based on solving conservation equations of mass, momentum, energy and electric current by using a finite element approach. Simulations allow calculation of temperature, velocity, oxygen concentration, current density and potentials distributions within the cathode side (i.e. interconnect and electrode). 2.1. Geometry Figure 1 shows the simulated design of current interconnect design. Air channel is formed by space between pins. Air flow inlet is in the centre. It is impossible to consider the problem using only two directions due to symmetry plan absence. Threedimension simulations need high memory capacity. To cut down this difficulty, symmetry axes make it possible to consider only an eighth part of this configuration (Fig. 1). Regardless element sizes of this module, the porous cathode is a very thin component. Therefore, to increase chances to attain a solution and to reduce computing time, it is required to reduce the great scale difference. The thickness of the cathode has been extruded from 35μm to 1mm so as to reach the same scale order of the interconnect thickness. In this new geometrical arrangement, cathode parameters such as thermal and electric conductivities and diffusion coefficient are anisotropic in the extrusion direction. Indeed, we have multiplied by the ratio of computed thickness divided by the real one (1/0.035 § 28.6) in the dilatation direction.
Figure 1: Scheme of the SOFC metallic interconnect (design of pins distribution).
2.2. Momentum The mass and heat transport is done in some measure by convection route. So, velocity (u) distribution in gas channels is needed. To calculate this one, momentum equations of Navier-Stokes have been solved see Eq. (2-3). An isothermal flow and a constant air density (ȡ) are assumed.
(
( ) ) + ρ (uG.∇)uG + ∇p = 0 and ∇G .uG = 0
G GG GG − ∇.η ∇u + ∇u
T
G
G
G
(2-3)
Optimization of SOFC Interconnect Design Using Multiphysic Computation
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Where Ș is dynamic viscosity and p is pressure. 2.3. Mass In air channels, mass transport is ensured by convection and diffusion processes. Oxygen transport in the porous cathode and along gas channels has been considered. Eq. (4) describes this phenomenon and is expressed as follows:
(
)
G G G ∇. − D∇c + cu = R
(4)
D is oxygen diffusion coefficient, c is oxygen concentration and R is volume reaction rate. The electrochemical reaction occurs only at electrode/electrolyte material, thus R = 0. Inside the porous cathode, only diffusion process is solved. According to J. Deseure et al. [1], the Knudsen diffusion process is a non-negligible diffusive phenomenon in SOFC cathodes. Thus, pore walls could control the diffusion process in the cathode.
1 1 1 = + DO2 Dknudsen D eff
D knudsen = d p and
ε
8 RT
3τ
πM O
(5-6)
2
Where, Deff is effective oxygen diffusion coefficient in cathode,
DO2 is oxygen
diffusion coefficient in air and Dknudsen is oxygen Knudsen diffusion coefficient. This coefficient depends on gas temperature T, ideal gas constant R, oxygen molar mass M O2 , average pore diameter dp, porosity İ and tortuosity IJ. 2.4. Charge Electrical current continuity equation has been solved. There are no current sources in cathode and interconnect volume. Cathode and interconnect electronic conductivities are assumed to be constants. The solved equation in our problem is given by:
G G J = σE
(7)
J is current density, ı is electronic conductivities and E is potential. It is assumed that most part of overpotential is located at the cathode side and the current density is given by the Butler-Volmer law [6]. 2.5. Heat There are three domains for heat transfer. In the first domain, transfers by conduction and radiation are modeled in interconnect and cathode. In the second domain, transfer by conduction-convection is studied in gas phase (air). Finally, in the third domain, alumina, only the transfer by conduction is solved. Constant thermal conductivities, negligible thermal resistance between cathode and interconnect and laminar flow in air channel have been assumed. In the first domain (cathode side material), the following equation is solved:
(
)
G G − ∇. k∇Ts1 = Q
(8)
Ts1 is the solid temperature in the first domain, k is thermal conductivity and Q is volume heat source. The heat source Q involves the Joule effect. According to the conclusions of Damm et al. [7] concerning temperature distribution impact on SOFC anode supported, it should be noted that the radiative heat transfer can be neglected inside cells. Nevertheless, a radiative flux coming from the furnace of experimental device is taken into account such as a constant flux at cathode / air interface at centre inlet gas feeding (qinlet). At outlet of gas channel, hydrogen and air are mixed and burnt
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(qoutlet). The resulting heat flux is scrutinized from thermodynamic data and gas flux burnt. The Newton’s law of cooling has been taken into account. In the second domain (gas phase), the non-conservative form of convection-conduction is considered. In air, there is no heat source, therefore Q = 0 and the computed equation is:
G G G G ∇.( − k∇Ta + ρCp∇Ta u ) = 0
(9)
Where Ta is air temperature, ȡ is air density, Cp is air specific heat capacity. In alumina (the third domain), only the transfer by conduction is solved, ( Q = 0 ), this relation is similar to Eq. 8. Table 1 gathers main parameters values considered in simulations. Table 1. Multi-physic Model Parameter Values Parameter Furnace heat flux at inlet (qinlet)
Value 3
8 10
4
Unit
Reference
W/m²
This study
Furnace heat flux at outlet (qoutlet)
3.2 10
W/m²
This study
Ta_inlet
1073
K
This study
T_furnance
1077
K
This study
Cathode overpotential
0.22
V
This study
Exchange current density
1484
A/m²
This study
Porosity (İ)
0.3
Tortuosity (IJ)
6
Average pore diameter (dp)
0.5
Oxygen molar ratio (y02)
0.25
Inlet air velocity
1.25
[8] [8] μm
[8] This study
m/s
This study
3. Design Optimization In current SOFC operation and configuration, interconnect collecting pins impact on oxygen concentration and heat distribution. Indeed, our simulations show low oxygen concentration and temperature in the cathode under pins contact area (Fig. 2 and Fig. 3). Interconnect design have been modified to reduce the thermal gradient and improve electrical behaviour. The pin shape (square) is maintained. Mainly two geometric parameters are investigated. The first one was air channel width which matches a contact surface percentage. The second one was pins size. 3.1. Contact surface For the current design, the contact surface is equal to 25%. It corresponds to a 2 mm air channel width. Pin size is maintained constant and contact surface varies from 12% to 60%. The smaller is the contact surface; the better is electrical performance (Fig. 4). Nevertheless, the temperature gradients increase with decreasing contact surface (Fig. 5). Pin/cathode contacts involve temperature variations: lower temperatures are recorded at pin/cathode contact.
Optimization of SOFC Interconnect Design Using Multiphysic Computation
Figure 2: Simulated oxygen concentration in the cathode
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Figure 3: Simulated temperature in cathode and interconnect
0,37
0,8 0,32
0,75 0,7
0,27
0,65
0,22
0,25
0,35
0,45
0,55
Power density (W/cm²)
Cell potential (V)
0,85
Cathode temperature (°C)
797 0,42
796 795 794 793 792 791 790 0,01
0,65
0,02
0,02
0,03
0,03
Radius distance (m)
Densité de courant (A/cm²)
Figure 4: Simulated polarization curves as function of contact surface (Ŷ: 12%, Ƈ: 25%, Ÿ: 50%, Ɣ: 60%; — : cell potential, ---: power density)
Figure 5: Simulated temperature on cathode surface as function of contact surface (Ŷ: 12%, Ƈ: 25%, Ÿ: 50%, Ɣ: 60%)
0,41
0,8
0,36
0,75
0,31
0,7
0,26
0,65 0,25
0,21 0,35
0,45
0,55
Current density (A/cm²)
Cathode temperature (°C)
0,85
Power density (W/cm²)
Cell potential (V)
3.2. Pin size To study pin size influence, contact surface is maintained constant and equal to 25%. For the current interconnect design, the square pin size is 2 mm. When the pin size decreases, electric performance increases (Fig. 6). It should be due to better oxygen access on reactive sites. Under pin/cathode contact diffusion process is controlled by distance of oxygen pathway. Moreover, small pins involve low temperature gradient on cathode surface (Fig. 7). Good temperature homogeneity (small-scale temperature variation) and an increasing performance using small pins (1mm) have been observed. 795 794,5 794 793,5 793 792,5 792 791,5 791 0,01
0,02
0,02
0,03
0,03
Radius distance (m)
Figure 6: Simulated polarization curves as Figure 7: Simulated temperature on cathode function of pin size (Ŷ: 1mm, Ƈ: 1.5mm, Ÿ: 2mm, surface as a function of pin size (Ŷ: 1mm, Ƈ: Ɣ: 2.5mm; — : cell potential, ---: power density) 1.5mm, Ÿ: 2mm, Ɣ: 2.5mm)
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795 794,5 794 793,5 793 792,5 792 0,010
0,015
0,020
0,025
Radius distance (m)
0,030
Power density (W/cm²)
Cathode temperature (°C)
3.3. Selected solution Small pins are more advantageous than larger ones. Nevertheless, at 25% contact surface, small pins involve small gas channel width. Pressure drop should be more important in this configuration. In the previous section, it has been shown an increasing surface contact implicates a decreasing electrical performance. Thus, from the interconnect design 1mm – 25%, contact surface have been diminished to improve cell behavior. The main goal of the optimization is a temperature variation below 1°C. Indeed, 16% contact surface is the best value allowing good electric performance (Fig. 9) and suitable temperature variation (Fig. 8). 0,43 0,41 0,39 0,37 0,35 0,33 0,31 0,29 0,27 0,25 0,28
0,38
0,48
0,58
0,68
Current density (A/cm²)
Figure 8: Simulated temperature on cathode surface as a function of contact surface with 1mm Figure 9: Simulated power density curves with initial and optimized interconnect pin size (Ŷ: 14%, Ƈ: 16%, Ÿ: 20%, Ɣ: 25%) design (Ŷ: 25%-2mm, Ÿ: 16%-1mm)
4. Conclusion A multi-physic model has been developed and solved with COMSOL Multiphysics® software. These simulations highlight controlling process and allow a good understanding of different phenomena. An optimization is proposed by varying two parameters: contact surface and pin size. The present study reveals that the interconnect design 1mm – 16% allows optimal performance. So, simulations let us expect a temperature variation two times lower and 5% gain of power density at 0.5 A/cm².
References 1. J. Deseure, Y. Bultel, L. Dessemond and E. Siebert, 2005, Theoretical optimisation of a SOFC composite cathode, Electrochimica Acta, 50, 10, 2037-2046 2. Jinliang Yuan, Masoud Rokni and Bengt Sundén, 2003, Three-dimensional computational analysis of gas and heat transport phenomena in ducts relevant for anode-supported solid oxide fuel cells, International Journal of Heat and Mass Transfer, 46, 5, 809-821 3. B.A. Haberman and J.B. Young, 2005, Numerical investigation of the air flow through a bundle of IP-SOFC modules, International Journal of Heat and Mass Transfer, 48, 25-26, 5475-5487 4. K. P. Recknagle, R. E. Williford, L. A. Chick, D. R. Rector and M. A. Khaleel , 2003, Three-dimensional thermo-fluid electrochemical modeling of planar SOFC stacks, Journal of Power Sources, 113, 1, 109-114 5. P. Costamagna, A. Selimovic, M. D. Borghi, G. Agnew, 2004, Electrochemical model of the integrated planar solid oxide fuel cell (IP-SOFC),Chemical Engineering Journal, 102, 1, 61-69. 6. P. Aguiar, C.S. Adjiman and N.P. Brandon, 2004, Anode-supported intermediate temperature direct internal reforming solid oxide fuel cell. I: model-based steady-state performance, Journal of Power Sources, 138, 1-2, 120-136 7. David L. Damm and Andrei G. Fedorov, 2005, Radiation heat transfer in SOFC materials and components, Journal of Power Sources, 143, 1-2, 158-165
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Multi-objective Scheduling for Environmentallyfriendly Batch Operations Iskandar Halima and Rajagopalan Srinivasana,b a
Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833 b Department of Chemical and Biomolecular Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Abstract The push towards sustainable operation has pressurized the batch process industries to implement energy minimization. One technique proven in the continuous industries is heat integration – matching the hot streams that require cooling and the cold streams that require heating to reduce the overall utilities consumption. In this work, we present a methodology for heat integration in multipurpose batch plants. This is done by optimizing the schedule to simultaneously minimize an economic objective such as make-span and utilities. We illustrate the framework by solving a literature case study. Keywords: Short-term scheduling; Energy integration; Pinch analysis; Simulated annealing; MILP
1. Introduction Due to its intrinsic flexibility, batch process has been the preferred option in the production of high-value added materials such as pharmaceuticals, and fine and specialty chemicals. However, unlike in continuous processes, the same process unit in a batch process can be used for multiple operations. For example, a jacketed vessel may be used to blend reactants, carry out a reaction, boil off solvent or distil the product. Thus, optimal scheduling of tasks to be performed in different units is very crucial for improving the plants’ bottom-line. This is particularly true in the case of multipurpose production plant, where a variety of products are produced using different recipes, all of which use the same processing units. In the mean time, the continuing global concern over the carbon emissions has pressurized the batch process industry to reduce its energy consumption – this can be achieved through heat integration technique. Such heat integration approach, which has been the standard tool in the design of an optimal heat exchanger network (HEN) in continuous plants, is now being adapted for energy recovery of batch plants (Kemp, 2007). Traditionally, process scheduling and heat integration of batch process have been solved as single objective optimization problem, such as profit maximization involving product sale values, cost of raw materials and utilities consumption (Papageorgiou et al., 1994; Barbosa-Povoa et al., 2001; Majozi, 2006). Another optimization approach is by Adonyi et al. (2003), who formulated the problem as energy minimization with additional constraint on the makespan. In this paper, we propose a multi-objective framework for simultaneous process scheduling and utilities minimization. We illustrate the framework on a well-known literature case study and discuss the findings in detail.
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2. Problem Statement The problem addressed in this paper can be defined as follows. Given information on a multipurpose batch plant in the form of: (1) sequence of operation tasks I (i = 1, 2, …, I) as represented through the state-tasknetwork (STN) model, (2) plausible set of unit operations J (j = 1, 2, …, J) with their storage capacity, (3) processing time of each task, and (4) heating and/or cooling duty requirements of the tasks, determine the optimal allocation of tasks on each unit so that minimum make-span as well as utilities consumption can be achieved. To solve this problem, we make the following assumptions (Sundaramoorthy and Karimi, 2005; Papageorgiou et al., 1994): (1) all materials are stored in a storage facility; a task starts by withdrawing the required materials from storage (real or pseudo) and ends by transferring materials to storage (real or pseudo), (2) processing time already includes storage, transfer and setup times of each task, (3) processing time varies linearly with the size of the batch in process.
3. Multi-objective Optimization Framework Figure 1 shows the multi-objective optimization framework. Schedule optimization is first performed through task-unit operation allocation with the objective of minimizing the make-span. We have implemented the slot-based continuous-time MILP approach of Sundaramoorthy and Karimi (2005) for designing optimal tasks. Here, we seek multiple solutions (alternate optima) to the scheduling problem. In the next stage, a heat integration scheme is designed so that minimum utilities are consumed in the proposed schedules. We have applied the batch pinch analysis of Kemp (2007) for designing optimum heat integration network. Both the make-span and utilities next used as objectives for manipulating the decision variables to obtain Pareto-optimal solutions. Decision variables Slot-based scheduling
Minimum make-span
TSM-based heat transhipment model
Minimum utilities
Multi-objective SA
Pareto solution set Figure 1. Multi-objective optimization framework 3.1. Slot-based Process Scheduling for Makespan Minimization In this approach, the entire batch horizon H is divided into K (k = 1, 2, …, K) slots of variable lengths SLk. The objective function to be optimized can be described as follows: K
Min Makespan =
¦ SL k =1
k
.
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As slot k runs from slot time Tk-1 to slot time Tk , thus Tk-1 + SLk = Tk . At any Tk,, as only one task can start on a unit j, the following expression is used Zjk = Yijk , 0 ≤ k < K ,
¦
i∈I j
where Yijk and Zjk are binary variables defined as follows: 1 Yijk = ® ¯0 1 Z jk = ® ¯0
, i ∈ Ij, 0 k < K ,
if unit j begins task i at time Tk otherwise
if unit j begins a task (including i = 0) at time Tk otherwise
, 0 k K.
A balance over the status of unit j is written as yijk = yij(k-1) + Yij(k-1) - YEijk , 0 < k < K, in this case yijk and YEijk are binary variables: 1 if unit j is continuing to perform task i at time Tk , i ∈ Ij,0 k K , y = ® ¯0 otherwise 1 if unit j ends task i and releases its batch at time Tk YEijk = ® ¯0 otherwise ijk
, i ∈ Ij, 0 k K.
As a unit j can start a new task only after the preceding task is completed on that unit, the following equation is applied Zjk = YEijk , 0 < k < K. Similarly, a unit j can start
¦
i∈I j
a new task only if it is not continuing any task, thus
¦y
ijk
+ Zjk = 1, 0 < k < K.
i∈I j
A mass balance over a unit j is written as bijk = bij(k-1) + Bij(k-1) – BEijk , i > 0, k > 0, where bijk and bij(k-1) are the amount of batch that exists in unit j just before a new task begins at Tk and Tk-1, respectively; Bij(k-1) is the batch size of unit j where task i begins at Tk-1; and BEijk is the batch size discharged by task i at its completion time Tk.. A time balance at Tk-1 is defined as tj(k) + (α Y + β B ) - SL(k+1) tj(k+1) , k < K, where
¦
ij
ijk
ij
ijk
i∈I j
tj(k) is the time remaining at Tk to complete the task that was in progress on unit j during slot k. The term α ij Yijk + β ij Bijk denotes the batch processing time of task i on unit j, where Įij and ȕij are the fixed and variable processing time, respectively, and Bij is the size of the batch in process. 3.2. Heat Integration Scheme The result of scheduling can be represented as a Gantt chart which shows the allocation of tasks to different units in different time slots. In this case, the solution is not unique instead multiple solutions exist for the given objective function (makespan minimization). In the next step, we perform heat integration on each of the scheduling solutions. This is done by pairing the process hot streams that require cooling and the cold streams that require heating to reduce the overall utilities requirement. We consider only direct heat integration as the heat exchange mode between streams without heat storage unit. We have implemented the concept of time-average model (TAM) and time-slice model (TSM) (Kemp, 2007) in the analysis. In TAM, the heat flows of process streams are averaged over the period of the batch. The objective is to allow weighting of process streams with different time periods. As an illustration, consider a cold stream of 250 kg of materials with specific heat capacity (Cp) of 4 kj/kg0C being heated from 200C to 1200C over a duration of 0.5 hour. The total heat load of this stream is 100 MJ, while the average heat flow of the stream is 200 MJ/h. Now, if this stream is integrated with a
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hot stream for 0.2 hour, the amount of heat saving is then calculated as 40 MJ, which is the average heat flow multiplied by time duration. In the TSM approach, the batch period is split into different time intervals within which the heat transfer process is assumed to take place like in a continuous one. In this case, we have used the schematic slots distribution of the process schedule as the basis for time intervals. Figure 2 illustrates this approach which shows the matching between the hot and cold streams of task 2 and task 3 over a time interval of 4 to 6 hour. We have adopted an MILP based heat-transshipment model of Papoulias and Grossmann (1983) for solving the utility minimization problem. In this model, heat acts as the commodity to be shipped from sources (i.e., hot streams/utilities) to sinks (i.e., cold streams/utilities) according to temperature intervals (Shenoy, 1995). Potential heat transfer time slot
unit U1
T1
T4
T3 (cold) T2 (hot)
U2
time (hour) 2.5
4
6
7.5
Figure 2. Heat integration between different tasks
4. Application to Case study We have tested our framework on a case study based on Kondili et al. (1993). Figure 3 illustrates the recipe diagram (STN model) of this process. The process involves scheduling of five different tasks in four plausible unit operations (HR, RR1, RR2, and SR). Table 1 and 2 display information on the description of the tasks, processing times of each task in unit and the stream temperature requirement. Figure 4 to 6 represent three alternative schedules, all with the same makespan. When heat integration is implemented on these, the utility consumption is calculated to be 76.2, 67.8, and 52.7 MJ, respectively. The latter is hence the preferred schedule. Prod 0
50 C Feed A
Heating {HR}
Hot A 700C
Reaction-2 {RR1, RR2} Int BC
QH1
700C
QC1
1000C Int AB
Separation {SR} 1000C
120 C Feed B 0
0
50 C
100 C QH2
Impure E
QC2 0
Reaction-1 {RR1, RR2}
1300C Reaction-3 {RR1, RR2}
Feed C 100 0C Figure 3. Recipe diagram of a case study
Prod2
Multi-Objective Scheduling for Environmentally-Friendly Batch Operations
Task (i)
ID
Heating Reaction-1
1 2
Reaction-2
3
Reaction-3
4
Separation
5
Table 1. Unit operation information Description Unit Max Bij (j) (unit vol) Heat A for a time period HR 100 React 50% B and 50% C to RR1 50 form Int BC RR2 80 React 40% hot A and 60% Int RR1 50 BC to form Int AB and Prod1 RR2 80 React 20% C and 80% Int AB RR1 50 to form Impure E RR2 80 Distill Impure E to 90% Prod2 SR 200 and 10% Int AB Table 2. Energy stream data Tin (0C) Tout (0C) Duration (h) 50 70 0.667 50 100 1.334 120 70 1.334 130 100 1.334
Stream Feed A Feed B Int BC Impure E
ȕij (h)
0.667 1.334 1.334 1.334 1.334 0.667 0.667 1.334
0.006670 0.026640 0.016650 0.026640 0.016650 0.013320 0.008325 0.006660
5 2
3
3
3
4
RR1
2
2
2
3
4
4
5
HR
Įij (h)
Cp (kJ/kg 0C) 2.5 3.5 3.2 2.8
SR RR2
1
Slot
1 1
Time (h)
1 2
2.68
3
5
2
4
851
3
4
3
1 3
5.37
8.06
6
7
10.75 12.02 14.71
8
17.24
19.93
Figure 4. Schedule-A with utility demand of 76.2 MJ
5
SR RR2
2
3
3
RR1
2
2
3
HR
1
Slot Time (h)
1 1
4
3 4
4
3
3
4
2
3
6
7
8
1 2
2.69
2
5
3
5.38
4
8.07
5
10.59 13.28 14.55 17.24
Figure 5. Schedule-B with utility demand of 67.8 MJ
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SR
5
RR2
2
3
3
RR1
2
3
2
HR
1
Slot Time (h)
1 1
4
3 4
4
3
3
4
2
3
6
7
8
1 2
2.69
2
5
3
5.38
4
8.07
5
10.59 13.28 14.55 17.24
19.93
Figure 6. Schedule-C with utility demand of 52.7 MJ
5. Conclusions Unlike in continuous plants, process scheduling is of paramount importance especially in multipurpose batch plants. We propose a multi-objective framework for scheduling the optimal sequence of tasks to be performed in different process units with the objective of minimizing the make-span and utilities. The optimization is performed on a three-stage procedure: MILP for minimizing the makespan, MILP for utilities minimization and simulated annealing for multi-objective optimization. We illustrate the framework by solving a case study and obtain satisfactory results.
References R. Adonyi, J. Romero, L. Puigjaner and F. Friedler, 2003, Incorporating Heat Integration in Batch Process Scheduling, Applied Thermal Engineering, 23, 17431762. A. P. F. D. Barbosa-Povoa, T. Pinto, A.Q. Novais, 2001, Optimal Design of HeatIntegrated Multipurpose Batch Facilities: A Mixed-integer Mathematical Formulation, Computers and Chemical Engineering, 25, 547-559. I.C. Kemp, 2007, Batch and Time-dependent Processes, Pinch Analysis and Process Integration. Elsevier, Oxford, UK. E. Kondili, C.C. Pantelides, R.W.H. Sargent, 1993, A General Algorithm for ShortTerm Scheduling of Batch Operations–I. MILP Formulation, Computers and Chemical Engineering, 17, 211-227. T. Majozi, 2006, Heat Integration of Multipurpose Batch Plants Using a ContinuousTime Framework, Applied Thermal Engineering, 26, 1369-1377. L.G. Papageorgiou, N. Shah, C.C. Pantelides, 1994, Optimal Scheduling of HeatIntegrated Multipurpose Plants, Computers and Chemical Engineering, 33, 3168-3186. S.A. Papoulias and I.E. Grossmann, 1983, A Structural Optimization Approach in Process Synthesis II. Heat Recovery Networks, Computers and Chemical Engineering, 7(6), 707. U.V. Shenoy, 1995, Mathematical Programming Formulations for HENS, Heat Exchanger Network Synthesis. Dulf Publishing Company, Houston, USA. A. Suppapitnarm, K.A. Seffen, G.T. Parks, P.J. Clarkson, 2001, A Simulated Annealing Algorithm for Multiobjective Optimization, Engineering Optimization, 33, 59-85. A. Sundaramoorthy and I.A. Karimi, 2005, A Simpler Better Slot-based Continuoustime Formulation for Short-term Scheduling in Multipurpose Batch Plants, Chemical Engineering Science, 60, 2679.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Operability Analysis and Conception of Microreactor by Integration of Reverse Engineering and Rapid Manufacturing André L. Jardini,a Maria Carolina B. Costa,a Aulus R.R. Bineli,a Andresa F. Romão,a Rubens Maciel Filho,a a
Department of Chemical Processes, School of Chemical Engineering, State University of Campinas, 13083-852, Campinas, SP, Brazil
Abstract The propose of this work is to develop high precision microfabrication facilities using computer aided technologies as Reverse Engineering (RE) and Rapid Manufacturing (RM) process to analyze and design of microreactor. The microreactor is usually a continuous flow reactor in contrast to a batch reactor. The goal of microreactors is the optimization of conventional chemical plants, and also to open the way to research new process technologies and to synthesis of new products. In this work, microreactors fabricated using FDM method (Fused Deposition Modeling), were digitalized, using a 3D scanning, to redesign the object. The widths and thickness of the microchannels produced were analyzed by RE, and alterations and adjusts were performed in redesign strategies for better application. The approaches presented are also fundamental to verify microreactor’s geometry and for modeling/simulation by finite element analysis (FEA), to assure the metrological accuracy of geometry and optimization of process parameters. The integration of RE and RM computer aided technologies to conception and analysis of microreator, has been used to produce several different small scale microchannel devices for chemical processing applications. Keywords: rapid manufacturing, reverse engineering, microreactors, simulation.
1. Introduction In this new millennium, much effort has been devoted to developing microdevices for reaction, mixing and separation. The emergence of microreactor generation has been attracting for these application fields. Microreaction technology is sometimes regarded as a key strategy for economic growth, by means of cost and time saving, and for the ecology, by sustainable development and saving of natural resources (Ehrfeld, 2000). Microreactors are studied in the field of micro process engineering, together with other devices (such as micro heat exchangers, micromixers, microdispersers, and microcombustors) in which physical and chemical processes occur (Watts, 2005). Microreactors can be used to synthesize material more effectively than current batch techniques or conventional devices. They may involve very efficiently liquid-liquid, gas-liquid and also solid-liquid systems with for example the channel walls coated with a heterogeneous catalyst. The benefits here are primarily enabled by the mass transfer, thermodynamics, and high surface area to volume ratio environment as well as engineering advantages in handling unstable intermediates (Cordero, 2002; Jahnisch, 2004).
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Conventional chemical processing equipment typically holds a relatively large volume of materials and consequently has a relatively large volume to surface area ratio. As a result, different portions of the reactant materials contained within such equipment are exposed to different histories of conditions. In the case of a conventional tank reactor, for example, even when temperature conditions at the walls of the reactor are well controlled, the portions of the reactants that are not in close proximity to the walls of the reactor may experience different temperature histories, especially if a significant temperature gradient exist, which might occur if the chemical reaction is strongly exothermic. In extreme situations reaction rates may accelerate to uncontrollable levels, which may cause safety hazards, such as potential explosions. If, however, the volume to surface area ratio of the processing apparatus is substantially reduced, the degree of control precision of homogeneity of temperature history of the reactants can be substantially improved. The small characteristic dimensions of microstructured reactors should improve process safety by enhancing heat transfer. Indeed, for exothermic reactions, small dimensions facilitate transfer of heat generated by reaction from the process fluid to the reactor walls. This accelerated heat transfer can prevent hot spot formation and subsequent thermal runway. The combustion of hydrogen, for example, has been operated safety and controlled in the explosive regime in microchannels with diameters of several hundred micrometers, due to enhanced heat transfer (Commenge, 2005). In this paper, a system of Rapid Prototyping, denominated FDM (Fused Deposition Modeling), is used for microreactor fabrication in ABS (Acrylonitrile Butadiene Styrene) material. FDM system allows building physical objects directly by model in CAD system (Computer aided design) providing very precise control of dimension and design. The flow chart of the rapid design, analysis and optimization of microreactor with microfluidics channels is initially performed in CAD software and constructed in rapid prototyping system is reported in Figure 1. The fluidic properties of microreactors (fluid dynamics, mixing behavior) can be analyze using both experimental measurements and simulations (computational fluid dynamics, CFD). CFD calculations are also used in the design and specification of new microreactor developments. The potential advantages of using a microreactor, rather than a conventional reactor, include better control of reaction conditions, improved safety, and portability.
Figure 1. Flow chart of the rapid design and manufacture of microreactor.
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2. Design of Microreactor: CAD Modeling RM uses Rapid Prototyping (RP) technology to directly produce useable parts from CAD system, and Reverse Engineering (RE) to digitalize the fabricated part aiming optimization and verification of design. The aim of RE is to reproduce a physical object to digital exactly like it is or at least it, as comparison original model. Computer aided systems is the technology concerned with the use of computer systems to assist in the creation and modification of a design. CAD software provides a special kind of file back to the RP system. The generated information for this system can later be exported according to the following formats (IGES, STL, VDA, STEP etc) and imported in the same way by CAE, where the numerical model simulations can be done based on the analyses by finite elements (FEA). The integration these computer aided technologies can be of significance in a process line for fabrication of microreactors applying to control and optimization of chemical processes. In this paper, a FDM system is used for microreactor fabrication in ABS (Acrylonitrile Butadiene Styrene) material. FDM system allows building physical objects directly by model in CAD system (Computer aided design) providing very precise control of dimension and design. Figure 2 shows a cross section of microreactor with microchannels created in SOLIDWORKS software.
Figure 2. Detailed view of a microreactor created in SOLIDWORKS software.
3. Fabrication of Microreactor Fabrication of the microreactor by FDM starts with the generation of three-dimensional CAD models (Figure 2) of the microdevice components to be produced. In the FDM process the material filament is transported into the heated chamber by two drive wheels which effects the discharge of the molten material (Figure 3). The data are then converted into the standard FDM file format “STL” and the 3D model is subjected to triangulation, i.e. it is approximated by a structure consisting of triangles. By varying the number of these triangles, the amount of data and the resolution of the FDM component are influenced. These data are used to control FDM head that deposits a ABS filament on a construction platform layer by layer (Fig. 3).
Figure 3. Working principle of the FDM process (Stratasys, 1995).
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4. Reverse Engineering Recent fields of technology innovation related to computer based manufacturing, such as the use of 3D digitizing, are being explored to be integrated in the chain process of industries, for applications as: Reverse Engineering; Quality Control; Differential Inspection; Direct Replication; Detection of Inaccuracies; Redesign of Parts; Manufacturing Tools. The 3D digitizing (Ferreira, 2007) and reconstruction of 3D shapes by RE has numerous applications in areas that include manufacturing, virtual simulation, science, and consumer marketing. This is an actual research and development field that is related to the problem of processing images acquired from accurate optical triangulation (Dorsch, 1994), and is presented as a RE methodology for surface reconstructing from sets of data known as range images. 4.1. 3D Scanner Digitizer Principle and Application To perform the RE recurring to a 3D scanning technique an Orcus 3D Scanner (Spatium, 2007) is used that allows the digitizing of objects by taking coordinates on the surfaces at selected points. This device scan without contact using a structured light projection to acquire the surface of the object to be digitized, and CCD cameras capture profile images that by triangulation algorithms generate digital data (Figure 4). Projecting patterns over the object enables triangulation and the collecting of surface data (XYZ) of over One million points per acquisition.
Figure 4. (a) 3D Scanner machine (“Orcus”), (b) 3D Scanner digitiser principle.
The Orcus system, which is a flexible scanning machine, was used to scanning tests for evaluate the accuracy of RM-FDM patterns, and its specification is: Working area Resolution Scanning rate
2000 x 2000 mm 0.010 mm 400.000 points per second
The interface between the 3D Scanner and a digital model was done through Spatium FORM software. For optimum digitalization, three acquisition of microreactor constructed in FDM system, was performed. The software calculates each detected coordinate point and translated that into a 3D virtual space generating a network array of points (points cloud), as shown in Figure 5.
Figure 5. Surface from the digitalized points in Spatium FORM software.
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After 3D digitized in Spatium FORM, the next step is to reconstruct the CAD model of the microreactor from the point cloud. The imported point cloud first must be processed in reverse engineering software (Geomagic Studio) to reduce the file size. The points are then wrapped as polygonal surfaces. Certain defects such as holes in the surface must be removed to obtain close manifolds (Figure 6).
Figure 6. Reconstruction process of the defect microreactor.
A new CAD model is rebuilt from the several points digitized on the RM-FDM surface. This was a RE reconstitution of actual RM-FDM surface that present some diverse coordinates when compared with the original CAD model. The resulting dimensional geometry when compared with the original 3D CAD dimensions allows to control of the metrological accuracy and re-design of the microreactor, as shown in Figure 7.
Figure 7. Inspection from RE compared with original CAD.
The CAD data for the microreactor with correspondent resection template is translated into STL file format and imported into the Rapid Prototyping machine (FDM) to fabricate the new microreactor. The STL format is a standard export/import data file for CAD software’s and analyze and simulation software (ANSYS, FEMLAB). This allows transferring design data via the intermediate step of STL from a CAD to another CAD system graphics program. Finally, the FDM microreactor is directly used in injection molding for the rapid manufacturing for production of the ceramic microcomponents. Ceramic microcomponents are of particular interest for applications in microtechnologies when their good mechanical and tribological properties, their thermal and chemical resistance or special physical, i.e. dielectric or piezoelectric properties, qualify them for uses that can not be covered by polymers or metals.
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5. Conclusion The Reverse Engineering methodology starting from 3D digitizing of physical parts allows to rebuild promptly physical models and to manufacture faster Rapid Prototypes. The Reverse Engineering via 3D digitizing it is a potential methodology to make Virtual Prototyping (VP) models for computer simulation. The computer simulation analysis grant optimized shapes to manufacture improved Rapid Manufacturing. The RE methodology aided by 3D digitizing make available a faster shape metrology control of prototype for foundry by calculating the deviation between 3D digitizing data and 3D CAD model, before manufacturing processes.
6. Acknowledgements The authors wish to acknowledge the financial support provide by FAPESP (The Scientific Research Foundation for the State of São Paulo).
References W. Ehrfeld, V. Hessel, H. Lowe, 2000, Microreactors: New Technology for Modern Chemistry, Wiley-VCH, 15. P. Watts, C. Wiles, 2007, Recent advances in synthetic micro reaction technology, Chem. Communication, 443–467. J.M. Commeng, L. Falk, J.P. Corriou, M. Matlosz, 2005, Analysis of Microstructured Reactor Characteristics for Process Miniaturization and Intensification, Chem. Eng. Technol., 28, 4. N. Cordero, 2002, Thermal Modelling of Ohmic Heating Microreactors, Proc. Therminic 2002, Madrid, 173-176. K. Jahnisch, V. Hessel, H. Löwe, M. Baerns, 2004, Angew. Chem. Int. Ed. 43, 406. H. Löwe, V. Hessel, and A. Mueller, 2002, Microreactors. Prospects already achieved and possible misuse, Pure Appl. Chem., 74, 12, 2271–2276. R. Ferreira, I. Leal, N. Alves,, P. Bartolo, 2007, Agile CAD for reverse engineering, Virtual and Rapid Manufacturing, 3, 257-261. R. Dorsch, G. Hausler, J. Herrmann, 1994, Laser Triangulation: fundamental uncertainty in distance measurement, Appl. Opt. 33, 7, 1306–1314. Stratasys, 1995, ``FDM1600 User Manual''.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimisations with Energy Recovery for Oxidative Desulphurization of Heavy Gas Oil Hamza A. Khalfalla a, Iqbal M. Mujtaba.a, Mohamed M. El-Garnib, Hadi A. El-Akramic a
School of Engineering Design & Technology, University of Bradford Bradford BD7 1DP, UK.b Libyan Petroleum Institute, P.O. Box 6431 Tripoli-Libya c Chemical Engineering Al-Fateh University P.O. Box 13335 Tripoli Libya
Abstract A lab-scale batch reactor is used to study deep desulphurization of a model sulfur compound dibenzothiophene (DBT) and heavy gas oil (HGO) with hydrogen peroxide (H2O2) as oxidant and formic acid (HCOOH) as catalyst. The results are quite promising and therefore a large scale oxidation process using a continuous stirrer tank reactor (CSTR) is considered further. In this process, a large amount of energy is required to carry out reaction at temperature close to that of the batch reactor, the recovery of which is very important for maximizing the profitability of operation and reducing environmental impact. Therefore a heat integrated CSTR system is proposed here. In the absence of a real plant a model for the system is developed. The kinetic model for the CSTR is based on the batch reactor experiments. An optimization problem to minimize the overall annual plant cost is formulated and solved using gPROMS. A cost saving of 22% for the integrated process is obtained compared to a non-integrated process. Keywords: Desulfurization, Heavy Gas Oil, Integrated Process, Energy Recovery.
1. Introduction Both economics and environment dictates the removal of sulfur from petroleum or its products. Sulfur in petroleum products poisons catalytic converters, corrodes parts of internal combustion engines and refineries because of the formation of oxy-acids of sulfur. Traditionally catalytic hydrodesulfurization (HDS) method is used for reducing sulfur which requires high partial pressure of hydrogen and high temperature. This makes HDS a costly option for deep desulfurization. Furthermore HDS is not effective for removing hetrocycilc sulfur compounds such as dibenzothiophene (DBT) and its derivatives. Faced with continuing fuel quality challenges, refiners have begun to look at oxidative desulfurization (ODS), under much milder conditions, as an alternative complementary process to HDS for deep desulfurization (Aida et. al., 2000). The ODS is basically a two-stage process, oxidation, followed by liquid extraction. In the oxidation step, the sulfur containing compounds are oxidized using appropriate oxidants to convert these compounds to their corresponding sulphones. These are preferentially extracted from oil based on their increased relative polarity (Babich and Moulijn, 2003, Gore; 2001). In the extraction step, the oxidized compounds are extracted from the oil by using a non-miscible solvent. With this back drop, the aim of this work is two fold. Firstly, the oxidation of model sulfur compound (DBT) and sulfur present in heavy gas oil (HGO) with H2O2 in the presence of a catalyst (HCOOH) is studied. A series of batch experiments are carried out using a small reactor (500 ml) operating at various temperatures ranging from 40 0C to 100 0C. Kinetic model for the oxidation is also developed based on the experimental
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data. Secondly, a CSTR model is developed for the oxidation process for evaluating the viability of a large-scale operation. Note that while the energy consumption and recovery issues could be ignored for batch experiments those are certainly not the case for large scale operation. To carry out the reaction even at 30-40 0C, the large scale operation will demand large amount of heating. The recovery of heat therefore, is very important for maximizing the profitability of operation. For industrial operation, the calculation of the minimum heating and cooling requirements reveal significant energy savings (Douglas, 1988). Therefore an integrated process where most of the energy is recovered is proposed here. However, this leads to embedding a number of heat exchangers in the system requiring capital investment. Therefore an optimization problem is formulated to minimise the total cost while optimising several design and operating parameters such as reaction temperature, residence time, minimum approach temperatures and splitter ratio. Here, the modelling and optimization are carried out by using gPROMS software (2005).
2. Batch Reactor Experimentation with Small Scale Oxidation Process The oxidation reaction was carried out in a 500 ml four necked flask containing 30 ml of model oil (sulfur was 940 ppm) and 1.25 ml of 30 % H2O2 (oxidant). Dibenzothiophene (DBT) was dissolved in dodecane to make the model oil. The flask is placed into the heating mantel equipped with a temperature controller and stirred at 750 rpm. When the required reaction temperature has been reached 30 ml of HCOOH (catalyst) was added to the flask to initiate the reaction. This procedure was carried at different temperatures (40, 60, 80 and 100 0C) for different time intervals. The resulting mixture was cooled to room temperature, and the sulfur content of the organic layer was detected by X-ray fluorescence. The same procedure was used for the heavy gas oil (HGO, sulfur was 1066 ppm) using equal volumes of the catalyst and HGO (30 ml) and half the volume of oxidant (15 ml). 2.1. Experimental results The results of oxidation of dibenzothiophene with H2O2 as a function of reaction time and reaction temperatures are shown in Figure 1 (Khalfalla et al, 2007). The initial reaction rate was found to be high, therefore, ninety eight (98) percent (wt %) conversion of DBT has been achieved after 5 minutes for all reaction temperatures. The oxidation of HGO with H2O2 as a function of reaction time over various temperatures is shown in Figure 2. The results indicated that the oxidation activities increased with the increasing temperature up to 600C but the conversion is only 40 %. A linear relationship of ln(CA /CA0) versus time was obtained for DBT and total sulfur in HGO for all temperatures (Figures 3 and 4 shows the plot for 40 0C). These results suggest that the oxidative reaction can be treated as a first-order reaction. Therefore, the reaction rate constants at various temperatures can be obtained from the slops of ln(CA /CA0) vs time. The apparent activation energies (E) and Arrhenius factor (A) with model oil and HGO were obtained from the Arrhenius plots (ln K vs 1/T). For HGO, E =7622 J/mol, A= 0.2279 min-1 are obtained. (Khalfalla et. al., 2007)
Optimisations with Energy Recovery for Oxidative Desulphurization of Heavy Gas Oil
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Figure 1. Oxidation of DBT at different
100
Figure 2. Oxidation of HGO at different
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ln(CA/CA0)=-0.7379t
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Figure 3. First-order plots DBT at 40 0C
6
0
0.5 1 1.5 2 Reaction time (min)
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Figure 4. First-order plots of HGO at 40 0C
3. Heat Integrated Large Scale Oxidation Process For large scale oxidation a CSTR is chosen. Batch reactor experiment (section 2) shows that oxidation reaction of model sulfur compound and total sulfur in heavy gas oil is favourable at higher temperature (>40 0C). The energy consumption for batch reactor (lab-scale) was negligible (as the volume is small) and natural cooling after the reaction was sufficient and therefore, no additional utility was required. However, in the large scale operation even to raise the HGO at 40 0C, energy consumption is a big issue. Therefore while scaling up a heat integrated of CSTR process (Fig. 5) is considered to reduce the overall energy consumption. The objective is to determine a retrofit design that can reduce the energy consumption, maximize energy recovery and minimize the capital investment. The exchangers, heaters and cooler are represented in Figure 5 by E, H and C respectively. The feed and product temperatures will be considered fixed and equal (TF0). For simplicity a simple CSTR model with the assumption of perfect mixing is used. 3.1. Process model In Figure 5, three feed streams were fed into the reactor. The first stream S1 (cold stream) containing HGO is preheated from TF0 to TF1 in the heat exchanger E1. Then, the HGO is fed into the heater H1 to preheat from TF1 to the reaction temperature (Tr). The second stream S2 (cold stream) containing HCOOH is preheated from TF0 to TF2 in the heat exchanger E2, and then from TF2 to Tr through the heater H2. The third stream S3 containing oxidant (H2O2) is fed into heat exchanger E3 to preheat from TF0 to TF3 and then to heat up to the reaction temperature (Tr) in the heater H3. The stream leaving the reactor (hot stream) is divided into two streams (S5 and S6) according to the splitter
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ratio (Sr). Stream S5 is cooled from Tr to T0 by exchanging heat with the feed stream S1 through the heat exchanger E1. Stream S6 is cooled from Tr to T01 by stream S2 in the heat exchanger E2. The product streams (S5 and S6) are mixed and cooled from TP to TA by exchanging heat with feed stream S3 through the heat exchanger E3, and then from TA to product temperature TF0 (same as feed temperature) in the cooler (C) by using utility water at Tw1.The model equations for the whole process are shown in Figure 6. There are forty six equations and fifty seven variables (fifty three unknown and four specified) and nineteen fixed parameters (shown in Table 1) in these equations. TF0, Tw1, Ts and V0 are specified and ǻT2, ǻT4, ǻT6, Tr, Tw2, IJ and Sr are relaxed and optimized.
Figure 5. Process flowsheet of heat - integrated reaction system
4. Optimization Problem Formulation The optimization problem can be described as follows: Given feed and product temperature (TF0), steam temperature (Ts), water temperature (Tw1) and volumetric flow rate of feed (V0); Optimize residence time (IJ), reaction temperature (Tr), outlet temperature of cooled water (Tw2), splitter ratio (Sr), minimum approach temperatures (ǻT2, ǻT4, ǻT6) So as to Minimize the total cost of the process (Ct) including capital investment Subject to constraints on the conversion (0.40<XAA @, >B @,...,>M @
(2)
The rate constant (kr) is a function of temperature and typically follows the Arrhenius equation
Industrial Applications of Multi-Phase Thermochemical Simulation
lnkr
ln D r
Er
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(3)
T
where Dr and Er are parameters defining the frequency factor and the activation energy of the reaction r. The expressions for global reaction rate laws vary considerably according to the particular application under consideration. In Fig. 1 a volume element of the dynamic chemical system is shown. It is assumed that no external force fields are present and that no external work is done for the system. The volume element is defined by its temperature, pressure and chemical composition. The element encounters an entering reactant flow (mR) and the respective output of products (mp) is leaving the element (diffusive side streams are omitted for simplicity). The volume element is characterised with measurable temperature and pressure as well as composition in terms of the molar amounts of substances nk. Further, the exchange of heat (Q) between the control volume and its surroundings is shown.
mR
mP T, p, nk Q
Figure 1. The volume element of a chemically reactive system.
As the temperature, pressure and the molar amounts of substances are known, the Gibbs energy G = G(T,P,nk) is defined for the volume element. The minimisation of Gibbs energy at given T and p in terms of the molar amounts is the traditional method to calculate the global equilibrium composition of the system. The optional constraints then may partly replace the elemental balance and T-p-conditions of the original minimisation procedure and are usually introduced with algorithmic techniques (Koukkari et al., 2001, Koukkari and Pajarre, 2006). The versatility of the Gibbsian process simulation is presented in a simple block diagram in Fig. 2. Elemental balance constraints Conditions Heat/mass transfer constraints Reaction rate constraints
- input amounts - T, p (optional) (optional)
min (G) at given conditions • concentrations • activities • chemical potentials • other intensive properties (p, T, pH, redox, etc.) • extensive state properties (G, H, S, C, V etc.)
Figure 2. The Gibbsian method in process simulation.
The thermochemical technique is applicable in all such situations where thermodynamic (e.g. temperature) measurements can be made and where sufficient data is available to
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define the free energy of the system and its constituents. Then, as far as we follow only the physico-chemical changes in the system, it is possible to define the Gibbs energy at any such stage of the process. Following the thermodynamic relations, the mutually interdependent properties are available for the validation of the model.
3. Models for Pulp and Paper-making Chemistry A typical example of an industrial multi-phase system is the chemical state of a fibre suspension in which N) 4 , viz. the gas phase, two aqueous phases and one or several precipitating phases (Table 1). Applying the Donnan equilibrium theory, the fibre acidity can be taken into account by describing the fibre in the model as a secondary aqueous phase characterised by its protolysing acid groups and separated from the primary aqueous phase by a semipermeable wall (Pajarre, Koukkari 2006). This interface allows the transfer of mobile ions while the anionic groups of the protolytes remain in the secondary phase. Table 1. Multi-phase system of a pulp suspension Gas N2, O2, H2O, CO2… External solution H2O, H+, OH-, Na+, Ca2+, Cl-, HSO4-, SO42-, HCO3-, CO2-, CO2,… Fibre phase H2O, H+, OH-, Na+, Ca2+, Cl-, HSO4-, SO42-, HCO3-, CO2-, CO2,…, AcidaH, Acida-,… Solid phases CaCO3, MgCO3, CaSO4,…
Donnan ion exchange theory combined with multi-phase thermodynamic model provides an efficient method to quantify the important process variables. Aqueous volumes inside and outside fiber walls are treated as separate solution phases. The use of general thermodynamic formalism also enables the use of non-ideal solution models and the simultaneous consideration of a large number of solubility equilibria. The method allows for efficient calculation of cation distributions in bleaching and pHalkalinity control in the wet end of paper machines. Fig. 3 shows comparison of calculated alkalinity values to process measurement in five subsequent mill test runs, where the multi-phase model was applied as a steady state process simulation during mill trial runs of non-stoichiometric bicarbonate (CO2/NaOH) pH-buffering. The values have been scaled to highest measured value Ł 1.
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Figure 3. Comparison of the modeled alkalinity values with experimental results from five subsequent mill tests.
4. Models for Chemical Reactors Principles presented in equations (1)-(3) can be generally applied for various chemical reactors. The combination of reaction kinetic and heat transfer equations with the thermodynamic multicomponent calculation is of particular interest in kiln reactors, as direct measurement from inside a rotary kiln is quite difficult to perform. Yet, rotary kilns are common separator reactors in the mineral processing, metallurgical and chemical industries. Usually they operate in counter-current fashion, where the condensed raw material is fed into the kiln from the ’feed end’ and the hot gas enters from the opposite ’burner end’.
Cell1 Gas out
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CellN
Gas in eq.
Gas in eq.
convection+ diffusion
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Gas in eq. convection+ diffusion
dust+ volatiles
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dust+ volatiles condensed
Bed in eq.
condensed
Bed in eq.
condensed
Mass transfer of gas species between bed and gas. Convection and diffusion between gas and bed.
Gas in Mass transfer of condensed species between bed and gas. Dusting of solid particles and formation of liquid phases.
Bed out
Bed in eq.
Figure. 4. The thermochemical model of a countercurrent kiln
In the Gibbs’ian model the kiln is divided into number of successive calculation cells, in which the temperature of bed, gas, and inner and outer wall of the kiln are assumed as constant. The volume elements of material bed and gas are described as open thermochemical systems, which transform mass and heat with each other. For simplicity, heat transfer is assumed to be radial. The state properties of the volume elements are calculated by minimizing their Gibbs energy and by taking into account the mass and heat transfer between the volume elements and the surroundings. The time-dependent reactions in material bed are taken into account by separating the phases into reactive and inert parts in each calculation cell according to reaction rate parameters. Axial plug flow is assumed for both the gas and the bed phase in the steady state model.
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Figure 5. Calculated one-dimensional temperature profile and the amounts of mixture constituents (solution phases) in a countercurrent kiln used in cement production.
5. Summary Multi-phase thermodynamic computation provides an efficient tool for chemical engineering. Concepts developed in physical chemistry and thermodynamics are applied for complex industrial conditions, giving a rigorous approach to solve practical problems. The range of potential applications of the Gibbs’ian multi-phase method is broad, as basically macroscopic thermodynamics can be used combined with reaction kinetics and transport processes.
References: G. Eriksson, 1975. Thermodynamic studies of high temperature equilibria XII, Chemica Scripta, 8, 100-103. P. Koukkari, 1993. A physico-chemical method to calculate time-dependent reaction mixtures, Comput. Chem. Eng., 17(12), 1157 – 1165. P. Koukkari, R. Pajarre, K. Hack, 2001. Setting kinetic controls for complex equilibrium calculations, Zeitschrift fur Metallkunde, 92, 1151-1157. P. Koukkari, R. Pajarre, 2006. Introducing mechanistic kinetics to the Lagrangian Gibbs energy calculation, Comput. Chem. Eng., 30, 1189– 1196. R. Pajarre, 2001. Modelling of equilibrium and non-equilibrium systems by Gibbs energy minimisation, Master’s Thesis, Helsinki University of Technology R. Pajarre, P. Koukkari, 2006. Inclusion of Donnan Effect in Gibbs Energy Minimization, Journal of Molecular Liquids, 125, 58-61.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
895
Prediction of the Melting Point Temperature Using a Linear QSPR for Homologous Series Inga Paster,a Mordechai Shacham,a Neima Braunerb a
Dept. Chem. Eng., Ben-Gurion University, Beer-Sheva, Israel School of Engineering, Tel-Aviv University, Tel-Aviv, Israel
b
Abstract Prediction of normal melting temperature (Tm) using linear Quantitative Structure Property Relationships (QSPR) whose applicability domain is limited to a particular homologous series is considered. It is shown that by limiting the applicability domain of the QSPR and using a very large bank of descriptors it is possible to identify a small set of descriptors whose linear combination represents Tm within experimental error level, even if the change of Tm with the number of C atoms is highly irregular. Confidence in the predicted values in both interpolation and extrapolation is considerably enhanced by ensuring random residual distribution in the training set used. The proposed method yielded prediction errors lower than reported in the literature in all the homologous series that were included in this study. Keywords: property prediction, QSPR, molecular descriptors, homologous series, melting point.
1. Introduction Normal melting temperature (Tm) is an important property for assessing the environmental impact of compounds as it indicates the physical state of the chemical at ambient temperatures, thus dictates how the chemical is handled and treated. Furthermore, it is widely used in quantitative structure-activity relationships (QSARs) for predicting toxicity and aqueous solubility. Methods for the prediction of physical properties of pure compounds based on their molecular structure are challenged by the prediction of solid properties, Tm in particular. This is due to the numerous factors that affect the solid state properties, but have much less (or no) effect on the liquid or gas phase properties. These factors include ionic, polar and hydrogen bonding forces, crystal packing, and positional, expansional, rotational and comformational entropy effects (Dearden, 2003). Consequently, property prediction techniques are significantly less reliable when applied to solid properties compared to their reliability in predicting liquid and gas phase properties (Godavarthy et al., 2006, Dearden, 2003). We have tested the hypothesis that the prediction of Tm can be improved by the use of Quantitative Structure Property Relationships (QSPR) for which the applicability domain is limited to "similar" compounds. To this aim, compounds belonging to a particular homologous series were selected as applicability domain for the QSPR. A QSPR whose applicability domain is limited to a particular series is denoted HS-QSPR. To carry out the studies described in this paper, a molecular descriptor database for homologous series of hydrocarbons (n-alkane, 1-alkene and alkyl-benzene) and oxygen containing organic compounds (aliphatic-alcohol and alkanoic monocarboxylic acid) have been prepared. The Dragon program (version 5.4, DRAGON is copyrighted by TALETE srl, http://www.talete.mi.it) was used to calculate 1280 descriptors for the
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compounds in the database. Melting point data were taken from the DIPPR (Rowley et al., 2006) database. A modified version of the stepwise regression program (SROV) of Shacham and Brauner (2003) was used for the identification of the most appropriate QSPRs.
2. The HS-QSPR method For development of the QSPR the members of the homologous series are divided into a training set which includes only compounds for which Tm data are available and an evaluation set in which Tm data are available only for part of the compounds. Shacham et al., (2007) have shown that using ten compounds is sufficient as a training set. For predicting Tm for the members of the homologous series, a linear structure-property relation is assumed of the form:
y
E 0 E1ȗ1 E 2ȗ 2 ! E mȗ m İ
(1)
where y is a p-dimensional vector of the respective property (known, measured) values (p is the number of compounds included in the training set), ȗ1, ȗ2 … ȗm are m pdimensional vectors of predictive molecular descriptors, are the corresponding model parameters to be estimated, and İ is a p-dimensional vector of stochastic terms (due to measurement errors). The descriptors are selected to the model in a stepwise manner according to the value of the partial correlation coefficient, |Uyj| between the vector of the property values y, and that of a potential predictive descriptor ȗj. The partial correlation coefficient is defined as
U yj
y ȗ Tj , where y and ȗ j are row vectors, centered (by subtracting the mean)
and normalized to a unit length|Uyj|. Values close to one indicate high correlation between molecular descriptor and the property value. The training set average percent error can be used for estimating the expected prediction error. It is defined as:
Ha
1 p ¦100 yi E 0 E1] 1,i E 2] 2,i ! E m] m,i / yi pi1
(2)
Addition of new descriptors to the model may continue as long as the calculated average error is greater than the pre-specified error tolerance (İa > İg ) and the signal-to-nose indicators of the SROV program are not violated. The stepwise regression program SROV (Shacham and Brauner, 2003) is used, which selects in each step one molecular descriptor that reduces the prediction error most strongly. Tm values for the members of the evaluation set are estimated by:
~ yt
E 0 E1] t1 E 2] t 2 ! E m] tm
(3)
where ~ yt is the estimated (unknown) property value of the respective compound and ȗt1, ȗt2 … ȗtm are its corresponding molecular descriptors values.
3. Predicting Tm for the alkanoic, monocarboxylic acid series. The first 19 members of the alkanoic, monocarboxylic series (shown in Table 1) were included in this study. Experimental Tm values (shown in Table 1 and Figure 1) are available for all of them in the DIPPR database. The estimated experimental error (reliability) of the data is < 1%.
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Table 1. Reference data and results for predicting Tm of alkanoic, monocarboxylic acids Tm (K)1 HS - QSPR Experimental Prediction % error
no. of C atoms
Acid 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Methanoic Ethanoic Propanoic Butanoic Pentanoic Hexanoic Heptanoic Octanoic Nonanoic Decanoic undecanoic dodecanoic tridecanoic tetradecanoic pentadecanoic hexadecanoic heptadecanoic octadecanoic eicosanoic
281.55 289.81 252.45 267.95 239.15 269.25 265.83 289.65 285.55 304.75 301.63 316.98 315.01 327.37 325.68 335.66 334.25 342.75 348.23
281.67 289.94 251.08 267.73 238.59 269.35 269.84 288.66 284.91 304.18 302.43 316.20 316.13 326.82 325.02 333.30 333.49 341.80 348.69
1
Data from the DIPPR database
2
Members of the training set are shown in bold letters
0.04 0.04 0.54 0.08 0.24 0.04 1.51 0.34 0.22 0.19 0.26 0.25 0.35 0.17 0.20 0.70 0.23 0.28 0.13
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Descriptor IVDE EEig06x
1 1 0.5 1 0.667 1 0.75 1 0.8 1 0.833 1 0.857 1 0.875 1 0.889 1 1
0.918 0.811 1.371 1.459 1.449 1.406 1.352 1.295 1.241 1.189 1.14 1.095 1.053 1.014 0.978 0.944 0.913 0.884 0.832
PJI2
IVDE
6
8
Mor16v
0 0 0 0 -0.754 -0.255 0.217 0.425 0.571 0.853 1.138 1.382 1.588 1.76 1.904 2.027 2.13 2.219 2.362
EEig06x
0.016 -0.015 -0.073 -0.056 -0.066 -0.095 -0.091 -0.098 -0.097 -0.115 -0.096 -0.09 -0.092 -0.084 -0.078 -0.067 -0.081 -0.083 -0.097
Mor16v
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Normal Melting Temp. (K)
PJI2
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260
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240
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0
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No. of C Atoms
Figure 1. Experimental Tm values of alkanoic, monocarboxylic acids
Figure 2. Descriptor values vs. the number of C atoms for the alkanoic acids.
Observe that the behavior of Tm versus nC is very irregular. For low carbon numbers the general trend is decrease of Tm with the increasing nC. Starting at nC = 6 the trend is reversed. However, in addition to the general trend there are also oscillatory changes between neighboring compounds. It is rather difficult to model such an irregular behavior. To identify the molecular descriptors that should be included in the regression model all 18 out of the 19 compounds shown in Table 1 were included in the training set. The SROV program has identified the descriptor EEig06x as having the highest correlation with Tm (|Uyj| = 0.967). EEig06x is a two dimensional (2D) descriptor belonging to the category of "edge adjacency indices", described by Dragon as "eigenvalue 06 from edge adjacency matrix weighted by edge degrees". In Figure 2 several descriptors are plotted versus nC. Observe that EEig06x represents well the general trend of the Tm curve, but not the oscillations. It is important to point out that there are several additional descriptors which are highly correlated with Tm however their (|Uyj| values are slightly lower than that of EEig06x. One of these descriptors, for example, is SIC3 which is also a 2D descriptor belonging to the "information indices" category ("structural information
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content (neighborhood symmetry of 3-order)" for which |Uyj| = 0.965. Thus, from among the 1280 descriptors several combinations can possibly be found, which yield predictions of Tm of a similar precision. The next descriptor to enter the QSPR is PJI2 ("2D Petitjean shape index" from the "information indices" category) with |Uyj| = 0.965. Observing the behavior of this descriptor in Figure 2 reveals that this descriptor represents only the oscillations. The combination of these two descriptors provides very precise representation of Tm for most compounds involved (prediction error < 1%) except for ethanoic-acid and butanoic -acid for which the prediction error is ~ 4%. Two additional descriptors have to be added to the QSPR in order to reduce the error in the representation of Tm for these two compounds. To validate the extrapolation capabilities of the QSPR for predicting Tm of the alcanoic acid series, the parameters of the QSPR are derived using a training set of 10 compounds which are identified in Table 1. The HS-QSPR obtained is Tm = 277.32 + 44.84 PJI2 - 41.98 IVDE + 21.02 EEig06x -121.81 Mor16v. The prediction errors when using this QSPR are below experimental error level (< 1%, see Table 1) in all except one case (for heptanoic acid the error is 1.51 %). The mean absolute error is 0.9 K. Dearden (2003) provides a summary of the prediction errors reported in connection to using various QSPRs for predicting melting points of various groups of compounds. Average errors are reported in the range of 8.1 K through 47.8 K. Thus, the precision of the HSQSPR is considerably higher than that of the other QSPRs reviewed by Dearden (2003).
4. Predicting Tm for the 1-alkene series. Twenty seven members of the 1-alkene containing between 4 to 30 carbon atoms were included in this study (Table 2). For the first 17 compound Tm values (either measured or predicted) are available in the DIPPR database with reliability ranging between 0.2 % and 1.0. All the compounds for which the data are marked as experimental(except 1heptene, 9 compounds) were included in the training set. The first descriptor to enter the QSPR was TIC5 (a 2D descriptor belonging to the "information indices" category: "total information content index, neighborhood symmetry of 5-order" ) with |Uyj| = 0.99985. The meaning of such a high value of the correlation coefficient can be understood in reference to Figure 3. In this Figure the reported Tm values as well as the descriptor values are plotted versus nC, for the 1-alkene series. Observe that, for this series, there is a smooth, monotonic increase of Tm with increasing nC. Furthermore, the descriptor TIC5 is almost completely collinear with Tm. This can be verified by plotting Tm versus TIC5 (Figure 4) which yields an almost perfect straight line. The one descriptor QSPR: Tm = 75.4013+1.0267TIC5 yields predictions with error smaller than 1% for most of the compounds, however there are excessive error values for 1-pentene (4.7%) and 1nonene (2.0%). An even more serious deficiency of this model can be detected by inspecting its residual plot (not shown). The residuals of the one descriptor model exhibit a definite curvature, with a decreasing trend at high carbon numbers. Consequently, there is a consistent increase in the error starting from Tm = 184.4 K. If this model is to be used for extrapolation (as required, according the data available in Table 2) we can expect the prediction error to grow even further. The three descriptor HS-QSPR reads: Tm=106.47+0.7336TIC5+42.83BELp5-57.96L2p. Its prediction errors are within experimental error level (Table 2). Furthermore, it provides residual plot (not shown) with randomly distributed residuals which indicates that the model is safer for extrapolation than the one descriptor model.
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Table 2. Reference data and results for predicting Tm of 1-alkenes
Name 1-butene 1-pentene 1-hexene 1-heptene 1-octene 1-nonene 1-decene 1-undecene 1-dodecene 1-tridecene 1-tetradecene 1-pentadecene 1-hexadecene 1-heptadecene 1-oktadecene 1-nonadecene 1-eicosene 1-heneicosene 1-docosene 1-tricosene 1-tetracosene 1-pentacosene 1-hexacosene 1-heptacosene 1-octacosene
no. of C atoms 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
1-nonacosene 1-triacontene 1
T m (K)1 HS - QSPR Reported Prediction 87.8 87.78 108.016 109.31 133.39 133.78 154.12 154.07 171.45 172.34 191.91 190.97 206.9 207.36 223.99 224.94 237.95 237.96 250.08 250.75 260.3 260.15 269.42 269.24 277.51 276.65 284.4 284.04 290.76 290.35 296.55 296.65 301.76 302.15 307.74 312.65 317.74 322.29 326.92 331.13 335.45 339.38
29 30
-
343.46 347.23
% error 0.03 1.19 0.29 0.03 0.52 0.49 0.22 0.42 0.01 0.27 0.06 0.07 0.31 0.13 0.14 0.03 0.13 -
TIC5 11.651 36.697 57.651 75.268 93.284 109.627 126.452 143.71 157.362 169.866 179.722 188.404 196.304 203.626 210.499 217.01 223.22 229.177 234.917 240.468 245.854 251.094 256.204 261.196 266.083
-
270.873 275.576
Descriptor BELp5 0 0.094 0.343 0.511 0.675 0.822 0.949 1.057 1.149 1.228 1.295 1.353 1.403 1.446 1.485 1.518 1.548 1.574 1.597 1.618 1.636 1.653 1.668 1.682 1.694 1.706 1.716
L2p 0.47 0.485 0.512 0.509 0.543 0.537 0.561 0.556 0.572 0.568 0.58 0.576 0.585 0.582 0.589 0.587 0.593 0.591 0.596 0.594 0.597 0.596 0.599 0.598 0.601 0.6 0.602
Data from the DIPPR database
5. Conclusions Prediction of the normal melting temperatures of alkanoic acids has demonstrated that by limiting the range of applicability of the QSPR to a particular homologous series and using a very large bank of descriptors it is possible to identify a small set of descriptors whose linear combination represents Tm within experimental error level, even if the change of Tm with the number of C atoms is highly irregular. In cases when the change of Tm with the number of C atoms is smooth and monotonic an HS-QSPR containing only one descriptor can provide prediction of acceptable precision if interpolation is involved (as shown in the example of 1-alkenes). However, if the available data dictate prediction by extrapolation addition of more descriptors, until reaching random residual distribution, can provide some confidence in the predicted values. A more extensive discussion on the advantages of the proposed method over other property prediction methods (such as the ones using PCA or neural networks) can be found in Kahrs et al (2007). Results of applying the proposed method for additional homologous series and comparison of the accuracy of the predicted Tm with other methods are presented in Brauner et al. (2008).
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References N. Brauner, R. P. Stateva, G. St. Cholakov, M. Shacham, 2006, A structurally “targeted” QSPR method for property prediction, Ind. Eng. Chem. Res., 45, 8430-8437. N. Brauner, G. St. Cholakov, O. Kahrs, R. P. Stateva, and M. Shacham, 2008, Linear QSPRs for Predicting Pure Compound Properties in Homologous Series, (AIChE J, Accepted ). J. C. Dearden, 2003, Quantitative structure–property relationships for prediction of boiling point, vapor pressure, and melting point. Environ. Toxicol. Chem., 22, 1696–1709. S. S. Godavarthy, R. L. Robinson, K.A.M Gasen, 2006, An improved structure-property model for predicting melting point temperatures, Ind. Eng. Chem. Res., 45, 5117–5126. O. Kahrs, N. Brauner, G. St. Cholakov, R. P. Stateva, W. Marquardt and M. Shacham, 2007, Analysis and Refinement of the Targeted QSPR Method, Computers chem. Engng., doi:10.1016/j.compchemeng.2007.06.006. R. L. Rowley, W. V. Wilding,J. L. Oscarson,Y. Yang,N. A. Zundel,2006, DIPPR Data Compilation of Pure Chemical Properties Design Institute for Physical Properties. http//dippr.byu.edu, Brigham Young University Provo Utah. M. Shacham, N. Brauner, 2003, The SROV program for data analysis and regression model identification. Comput. Chem. Eng., 27, 701–714. M. Shacham, O. Kahrs, G.St. Cholakov, R. P. Stateva, W. Marquardt, N. Brauner,2007, The Role of the Dominant Descriptor in Targeted Quantitative Structure Property Relationships", Chem. Eng. Sci. 62 (22), 6222-6233.
Normal Melting Temp (K)/Descriptor Value
350 300 250 200 150 Tm
TIC5
100 50 0 4
6
8
10
12
14
16
18
20
No. of C atoms
Figure 3. Reported Tm and descriptor TIC5 values of 1-alkenes 350
Normal Melting Temp. (K)
300 y = 1.0267x + 75.401 R2 = 0.9992 250
200
150
100
50
0 0
50
100
150
200
250
Descriptor TIC5
Figure 4. Reported Tm values versus descriptor TIC5 of 1-alkenes
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A general mathematical model for a moving bed gasifier Sauro Pierucci and Eliseo Ranzi Politecnico di Milano, CMIC, Piazza L.da Vinci 32, 20133 Milano, Italy
Abstract Cocurrent and countercurrent units are common configuration of biomass and coal gasifiers. Moving solid beds contact a flowing gas phase, usually air, steam or their mixtures. Batch and fluidized bed reactors, or drop tube gasifiers are also alternative units. The complexity of these systems relies in several aspects: the chemistry of the released species in the first devolatilization and gasification step, the large number of species and reactions in the gas phase, the definition of a well balanced description of the gasifier and finally the necessity to adopt a stable ODE solver to numerically handle the large system of balance equations. The different process units are schematized in terms of a series of elementary cells where the solid particles release volatile components with effective material and energy exchanges with the flowing gas phase. Gasification reactions in the coal or biomass particles are properly accounted including mass and thermal diffusion limitations. Reactions in the gas phase are finally accounted by using a detailed kinetic scheme of pyrolysis and combustion reactions. Preliminary comparisons with experimental measurements support the proposed approach. Keywords: Gasification, Combustion, Mathematical modeling, Biomass.
1. Introduction Although pioneer works on gasifier modeling date the seventies (Anthony and Howard 1976) only recently a higher publication frequency appeared in literature. This is probably due to a continuous demand of alternative and renewable fuels as a consequence of a lower availability of canonical raw materials. The approaches adopted for modeling such equipment, largely vary with the applications: from thermochemical equilibrium models (Ruggiero and Manfrida 1999, Jayah et al. 2003) to very detailed CFD descriptions (Gao et al. 2006, Watanabe and Otaka 2006). Independently on the approach chosen, it seems that a low attention has been paid to mass and thermal diffusion limitations, which limit the release of volatile components and the successive reactions on the gas phase. In addition to this fact a necessary compromise between details and assumptions in model description has not been yet clearly stated. Aim of this paper is to contribute to the solution of these existing problems and a mechanistic and intrinsic model at the particle scale is presented. Although a moving bed is the most common configuration of a gasifier it is worth to include it in a framework of ancillary configurations that may be encountered as valid process alternatives.
2. Kinetic Models It is necessary to distinguish two different kinetic models: the devotalilization, gasification and combustion in the solid particle and the pyrolysis and combustion in the gas phase. The biomass devolatilization, gasification and combustion scheme refers to about 30 species and 25 global reactions (Cuoci et al., 2007). The gas phase kinetic
902
S. Pierucci and E. Ranzi gi0 ,Tg0 SJ ǻrJ
Vp0 ,Ș0
z Gi
mJ,i
Gi
N0
D -D
rJ z TJ
G0i
G0i
N
a)
b)
c)
Fig.1 Particle and Gasifier sketches, a) Fixed bed, b) Moving bed, c) Drop tube
model has been extensively validated by Ranzi et al. (2001) and refers to more than 100 species involved in thousands of elementary and lumped reactions. Due to limited space available, the kinetic model will be only referenced and is available as supplementary material.
3. Reactor and particle model Fig. 1 sketches the solid particle and three configurations of different reactors. The particle is supposed of spherical shape, divided into NR spherical sectors (j =1 to NR). The components are supposed to be NCP, identified by i =1 to NCP. ‘ Sector j’ means the particle volume included within the radius rj and r j-1. 3.1. Fixed bed (or semi-Batch Reactor) Fig. 1. a) sketches the reactor bed that is supposed divided along its vertical axis into a defined number of elements. Here for sake of simplicity in exposition a single element is assumed. Extrapolation to a different number requires only minor nomenclature changes. (See 'Nomenclature' chapter for variables meaning) The component mass balances for each spherical sector are given by: dm j ,i (1) J j 1,i J j ,i R j ,i dt where Rj,i [kg/s] is the production rate due to chemical reactions. The mass flux Jj,i results from two different contributions: Diffusion
D j ,i
dC j ,i dr
S j porj
Pression
y j ,i
j rj
Da j dPj
P j dr
U j S j porj j rj
At the external surface, the diffusion contribution is replaced by the flux exchanged with the bulk phase (analogously the pressure contribution takes into account of the bulk pressure): Diffusion U i (CNR ,i CBi ) S NR porNR The enthalpy balance around each sector j is mainly dependent on conduction and reactions duties: NCP
d ¦ m j ,i Cp j ,iT j i 1
dt
NCP
NCP
i 1
i 1
JC j 1 ¦ J j 1,i h j 1,i JC j ¦ J j ,i h j ,i HR j
(2)
JCj [kj/s] is the heat flux due to conduction exiting the sector j. At the external surface, JCNR becomes the flux exchanged with the bulk phase.
A General Mathematical Model for a Moving Bed Gasifier
903
HRj [kj/s] is the total heat production rate in the sector ‘j’ due to chemical reactions. The mass component equations and enthalpy balance in the gas phase are: dg i (3) G 0 , i J NR , iK R g , i G i dt NCP
d ¦ g i CpiTg i 1
NCP
¦G
0 ,i
dt
i 1
NCP
NCP
i 1
i 1
hg 0,i ¦ J NR ,i hNR ,iK JC NRK HRg ¦ Gi hg i
(4)
where HRg [kj/s] is the total heat production rate due to gas phase reactions, Ș is the total number of particles in the bed. Finally ancillary equations are added to complete the model at hand: x Continuity on total gas flowrate ¦ Gi ¦ (G0,i J NR ,iK ) x
Shrinking of particle sectors (solved for rj) NCP * 4 S ( r 3 r 3 ) U *j (1 . por j ) ¦ m j ,i 3 i 1 (NCP* is the total solid and liquid components number, ȡj*is the density of such a mixture) Shrinking of the reactor bed (solved for Z) A Z K V p /(1 H ) Pressure inside each particle sector (solved for new Pj): j
x x
Pj
j 1
4 S ( r j3 r j31 ) U *j * por 3
R GAS T j j
M
wj
NCP * *
¦m
j ,i
i 1
(NCP** is the total gas components number, ȡj** is the density of such a mixture, Mwj is its molecular weight and RGAS is the gas constant) Dependence of the porosity and the bed void fraction on the particle morphology is here neglected. The model of the single element is constituted by a system of [(NCP+1)*NR + NCP+1] ODE equations (1-4), with the initial conditions at t=0. The ancillary equations form a disjoint system of algebraic equations that is sequentially solved at each integration step. The large ODE system has been solved by using BzzMath library, which is available on the Internet and is downloadable as freeware software for noncommercial use from www.chem.polimi.it/homes/gbuzzi/ 3.2. Moving Bed Model The standard moving bed gasifier requires a ash continuous removal from the bottom to maintain the combustion zone in a relatively fixed vertical position and a top feed rate modulated to maintain a fixed top of bed level within the gasifier (Fig. 1. b). The particle discretization is the same of the one used in the previous batch model description. Again for sake of simplicity in exposition a single reactor bed element is assumed. The nomenclature adopted by the fixed bed model is valid also in this description. The extent of the bottom extraction depends case to case from several controlling variables including the concentration reached on the bottom by inert components. For sake of example let suppose the following simple relation: S
x ash x 0 Sm 1. x0
where S [kg/s] is the extraction rate, xash is the actual ash mass fraction, x0 is its initial value equal to that one in the top feed and Sm stands for the maximum expected value of S. The extraction rate S may be rewritten as the product N*mp, where N is the number of particle extracted per second and mp the mass of a single particle. N0 and mp0 will denote the same quantities in the top feed. Assuming that both the particle porosity and the bed void fraction are constant along the time, the constant reactor volume (Vr) is obtained by imposing the following condition:
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S. Pierucci and E. Ranzi
NR 1 NCP dm j ,i Nm p dVr N 0 m p 0 K¦ 0 ¦ dt U dt U0 j 1 Uj i 1 The hold-up Ș (number of particle in the bed) changes in the time according to: dK
dt
N0 N
(5)
(6)
The integration of (6) allows obtaining the desired value of N0 from the algebraic equation (5). The balance equations governing the whole process are directly derived from those ones already presented for the fixed bed model with slight modifications. dm j ,i (7) J j 1,i J j ,i R j ,i N 0 m0 j ,i Nm j ,i dt NCP
d ¦ m j ,i Cp j ,i T j i 1
dt
NCP
NCP
NCP
i 1
i 1
i 1
JC j 1 ¦ J j 1,i h j 1,i JC j ¦ J j ,i h j ,i HR j ¦ ( N 0 m 0 j ,i h0i Nm j ,i h j ,i ) (8)
It is reasonably acceptable that the gas phase may be described by the previous equations (3) and (4), due to the limited entrainment of gas into the solid feed. The system of equations 3-8 when solved simultaneously provides the desired process description. 3.3. Drop Tube Model For sake of kinetic modeling studies of gasification and combustion of biomasses, many experiments are conducted inside entrained flow or drop-tube reactors (Fig. 1. c). Gas and particles are continuously fed at the top of the tube through two different nozzles. Gas enters at temperature, mass flowrate and velocity usually higher than the solid particles. Steady conditions are easily reached by the system and this allows to make all the desired experiments. Again with the same previous particle discretization and nomenclature, the steady conditions of this system are described along the reactor height. Contact time of solid particles is given by the definition of the particle velocitys derived from momentum equation: dv p (9) mp ( U p U g ) a V p sin(D ) 0.5 f U g (v p v g ) (v p v g ) dt where vg [m/s] is the gas spatial velocity, a [m/s2] is the gravity, Į[deg] is the inclination of the reactor vs. horizontal line; f is the friction factor depending on Reynolds number. The particle behavior is described by the equations (1) (2) adopted in the fixed bed model. The mass gas component equations are: dwg i (10) v A (J K P ) dt
p
NR , i
g ,i
where Ș indicates the number of particles per m3 of reactor (Ș0 at reactor inlet), J NR ,iK [kg/m3 s] is the total mass exchanged by the gas phase with the particles. The gas enthalpy balance is: NCP
d ¦ wg iCpiTg
NCP
(11) dt i 1 HRg [kj/m3 s] is the total heat production rate due to gas phase reactions Two further ancillary equations, continuity on total particle number and on total gas flowrate, are added to complete the model. i 1
v p A ( ¦ (J NR ,i hNR ,i )K JCNRK HRg )
A General Mathematical Model for a Moving Bed Gasifier
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4. Example Biomass is pyrolysed under high temperatures and flash heating rates conditions in a drop tube reactor. Particles of 0.4 mm diameter are fed to the reactor and the gas released is more than 70 wt % of the initial weight. The particle residence time is about 1 s while the gas residence time is about 3.5 s. The equivalent initial composition of the biomass C6H8.8O3.9 becomes C6H2.9O1.1 at 1073K and C6H1.4O0.5 at 1273K, at the reactor outlet. These results are in good agreement with the experimental measurements indicating a composition of C6H2.7O0.8 and C6H1.5O0.4, respectively. The predicted char yield is ~14 wt% of the initial dry biomass, in a very good agreement with the experimental measurements.Experimental (Dupont et al. 2007) and predicted results are compared in Fig. 2. CO is the major species in both model and experiments, followed by H2 and H2O. There is a good agreement on CO2, which is present only in small amounts. Tar species decompose in the gas phase and significantly contribute to the formation of methane, acetylene, ethylene and heavier hydrocarbons. While acetylene and ethylene predictions agree with the experimental measurements, methane predictions are underestimated by the model. The temperature effect on CO and H2 is not very sensible because the devolatilization process is practically completed even at 1073 K. On the contrary, it is possible to observe that the model properly predicts the different trends of ethylene and acetylene. In fact, C2H2 is more abundant than C2H4 at high temperature, while the reverse behavior is predicted and measured at 1073 K. The results of Fig. 2 clearly indicate not only the possibility of the model to correctly predict the amount and composition of the solid residue, but also show the importance of the successive decomposition of the released products. 0.025
0.004
dp=.4 mm T=1273 K CO
0.003
Mole fractions
Mole fractions
0.02
0.015
H2 0.01
T=1273 K 0.002
T=1073 K
0.001
0.005
CH 4
CO 2 0
dp=.4 mm
0 0
0.2
0.4
0.6
0.8
1
0
0.2
0.0016
0.4
0.6
1
0.8
Reactor length [m]
Reactor length [m] 0.002
dp=.4 mm T=1073 K
dp=.4 mm T=1273 K
0.0014 0.0016
C2H4
0.001
Mole fractions
Mole fractions
0.0012
0.0008 0.0006
0.0012
0.0008
C2H4
C2H2
0.0004
C2H2
0.0004
0.0002 0
0
0
0.2
0.4
0.6
Reactor length [m]
0.8
1
0
0.2
0.4
0.6
0.8
1
Reactor length [m]
Fig. 2. Comparisons between experimental data (points) and model predictions (lines) at 1073 K and 1273 K for 0.4 mm particles
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S. Pierucci and E. Ranzi
As far as the kinetics of gasification and combustion of char residue is concerned, it is assumed that only the final char residue is reactive and usual kinetic laws of pure carbon are used.
Nomenclature A CBi Cj,i Cpj,i Da j Dj,i gi Gi hj,i hgi Jj,i m j,i Pg,i Por j Rg,i Tg Vp yj,i wgi Z Oj Ș H P , μj ȡg , ȡj ȡp
[m2] [kg/m3] [kg/ m3] [kj/ kg K] [m2 ] [m2/s] [kg] [kg/s] [kj/ kg] [kj/kg] [kg/s] [kg] [kg/m3 s] [m3/m3 ] [kg/s] [K] [m3] [kg/s] [m] [kj/mKs] [m3/m3 ] [kg/m s] [kg/m3] [kg/m3]
reactor cross section gas bulk concentration of component i gas concentration of component i in the sector j heat capacity of component i in the sector j Darcy coefficient in the sector j effective diffusivity of component i in the sector j mass of component i in the gas phase flowrate of i in the gas at bed exit (G0i at bed inlet) specific enthalpy of component i in the sector j specific enthalpy of component i in gas phase (hg0i at bed inlet) mass flux of component i exiting the sector j mass of component i in the sector j (mp is the total mass) total mass production rate due to gas phase reactions particle porosity (pore volumes / total volume of sector j) total mass production of component i due to gas phase reactions Temperature in the gas phase particle volume gas mass fractions gas flowrate of component i (wgi,0 at the bed inlet) reactor height thermal conductivity of sector j number of particles in the reactor bed bed void fraction gas viscosity and gas viscosity in the sector j gas density and gas density in the sector j density of the particle
References D. B. Anthony, J.B. Howard, 1976, Coal Devolatilization and hydrogasification, AlCHE Journal, 22, 4, 87-101 A. Cuoci, T. Faravelli, A. Frassoldati, S. Granata, G. Migliavacca, E. Ranzi, S. Sommariva, 2007, A General Mathematical Model of Biomass Devolatilization, Italian Combustion Institute, July, 2007, Ischia
C., Dupont, G. Boissonnet, J.M. Seiler, P. Gauthier, D. Schweich, Fuel, 2007, 86, 32-40 K. Gao, J. Wu, Y. Wang, D. Zhang , 2006, Bubble dynamics and its effect on the performance of a jet fluidised bed gasifier simulated using CFD, Fuel, 85, 1221–1231 T.H. Jayah, L. Aye, R.J.Fuller, D.F. Stewart, 2003, Computer simulation of a downdraft wood gasifier for tea drying, Biomass Bioenergy, 25, 459–469. E. Ranzi, M. Dente , G. Bozzano, A. Goldaniga, T. Faravelli, 2001, Lumping Procedures in Detailed Kinetic Models of Gasification, Pyrolysis, Partial Oxidation and Combustion of Hydrocarbon Mixtures, Progr. Energy Comb. Science, 27, 99-139 M. Ruggiero, G. Manfrida, 1999, An equilibrium model for biomass gasification processes, Renew Energy, 1999, 16, 1106-1115. H. Watanabe , M. Otaka,2006, Numerical simulation of coal gasification in entrained flow coal gasifier, Fuel, 85, 1935–1943
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Modelling of an hybrid wastewater treatment plant Marie-Noëlle Pons,a Maria do Carmo Lourenço da Silva,a Olivier Potier,a Eric Arnos,b Philippe Battaglia,b a
Laboratoire des Sciences du Génie Chimique – CNRS, Nancy University, ENSIC, 1 rue Grandville, BP 20451, 54001 Nancy cedex, France b GEMCEA, 149 rue Gabriel Péri, 54500 Vandoeuvre-les-Nancy
Abstract A simplified dynamic model of a hybrid wastewater treatment plant which combines activated sludge + biofilm carriers in a fluidized bed has been developed, based on information collected on a full-scale plant. High nitrification yield can be achieved but denitrification requires a tight dosing of external carbon, for which a PI controller has been implemented. Keywords: activated sludge, biofilm, hybrid, denitrification, controllability.
1. Introduction Treatment of urban and industrial wastewater by activated sludge is widespread around the world. More stringent discharge regulations imply in many places retrofitting and extension of capacity. It might be difficult to maintain a classical activated sludge system with suspended biomass if available space is limited. Hybrid systems have been proposed to intensify the process with a limited footage requirement. They combine sections with fixed (on sand, plastic supports, etc.) and suspended biomass and sections where only the suspended biomass is circulating (Müller, 1998; Lee et al., 2002). The experience gained with such systems is still limited and model efforts are scarce (Fouad and Bhargava, 2005). In order to investigate the controllability of such a system, a dynamic model had to be developed. The methodology which has been followed is based on the Benchmark Simulation Models (BSM)’one (Copp, 2002; Jeppsson et al., 2008). The design parameters and the influent wastewater characteristics have been adapted from a full-scale wastewater treatment plant (WWTP) based on the Biolift® process (Nancy-Maxéville, France, 300000 equiv. inh).
2. Plant layout description The global plant layout is present in Figure 1 and the biological reactor in Figure 2. It is composed of six compartments and has a total volume of 12000 m3. The fluidized section, which handles the fixed biomass, has a volume of 3000 m3. The volume occupied by the supporting material represents 10% of this volume. Upstream of this unit, there are two anoxic reactors (2000 m3 each). Downstream, after a degassing unit (volume = 1000 m3) there are also two anoxic reactors (2000 m3 each). External carbon (i.e. methanol) can be fed into the first of them to favor denitrification. The mixed liquor is partially recycled from the exit of the degassing unit to the inlet of the bioreactor. The clarifier has a volume of 6000 m3 and a depth of 4 m. Most of the sludge exiting the clarifier is recycled to the inlet of the bioreactor. The wasted part is thickened prior to anaerobic digestion together with the primary sludge collected from the 900 m3 primary settler. The present contribution is focused on the biological section of the wastewater treatment.
M.-N. Pons et al.
908
Figure 1: Schematic plant layout. TSS = Total Suspended Solids From primary settler
Qq ecec
Q0
External carbon feed To clarifier
A1
A2
FBAS
DG
A3
A4
Q0 Q0 Sludge recycle from clarifier
Figure 2: Schematic biological reactor layout: A1 to A4: anoxic units, FBAS: fluidized bed + activated sludge unit (aerated), DG: degassing unit. Q0 and Qec are feedrates.
3. Model description The activated sludge behavior is described through the Activated Sludge Model 1 (ASM1) (Henze et al., 1987) which is summarized in Figure 3. The same model is used for the fixed biomass but two new variables have been added: XB,Hf and XB,Af which represent respectively the heterotrophs and the nitrifiers (autotrophs) fixed on the supporting material. The concentration gradients in the biofilm around the supporting media are not taken into account explicitly (i.e. the substrates and metabolites concentrations are equal in the bulk and the biofilm). This choice has been made to keep the computation simple. To take into account the effect of limitation due to diffusion of substrates through the biofilm, some of the kinetic parameters (intrinsic heterotrophs and autotrophs growth and decay rates, ammonification and hydrolysis rates) are assigned lower values than the equivalent kinetic parameters in the bulk phase through a multiplying factor [ (Table 1). The effect of biofilm detachment due to shear in the fluidized section is taken into account by a transfer of heterotrophs and autotrophs from
Modelling of an Hybrid Wastewater Treatment Plant
909
the biofilm to the bulk. The clarifier is modeled as in the BSM1 according to Takács et al. (1991).
Figure 3 : Schematic representation of the basic ASM1. See Table 2 for symbols Table 1: Biological reactions main kinetic parameters ; [ [0.5, 1.]
Kinetic parameter Heterotrophs growth rate (d-1) Autotrophs growth rate (d-1) Heterotrophs decay rate (d-1) Autotrophs decay rate (d-1) Ammonification rate (m3 (g COD . day)-1) Hydrolysis rate (g slowly biodegradable COD (g cell COD . day)-1) Heterotrophs detachment rate (d-1) -1
Autotrophs detachment rate (d )
Activated sludge 4 0.5 0.3 0.05 0.05
Biofilm 4·[ 0.5·[ 0.3·[ 0.05·[ 0.05·[
3.
3. ·[ 0.025 0.025
4. Influent model Two sets of constant influent flowrate and composition have been tested (Table 2). Set 1 is based on BSM1, with the flowrate adapted to the size of the simulated plant. Set 2 is based on actual wastewater composition at the inlet of the Nancy-Maxéville wastewater treatment plant. It is much more diluted due to a high infiltration rate of groundwater in the sewer network. For that purpose the daily average values of COD, TSS, Kjeldahl nitrogen and ammonia corresponding to a 2.5 yrs period have been extracted for the plant historical data. A fractionation experiment of wastewater COD has been conducted (Lourenço et al., 2008): 2hrs-composite samples have been collected on the full-scale WWTP primary settler. Filtrated (1.2 μm) and raw aliquots of the samples have been placed in 500 mL aerated reactors. After inoculation with activated sludge, the biodegradation has been monitored for 21 days. The various wastewater COD fractions (SI, SS, XI and XS+XB,H) have been determined from the COD balance over the experiment. Nancy wastewater has a higher fraction of SI and XS and a lower percentage of SS than the BSM1 wastewater.
M.-N. Pons et al.
910 Table 2: Steady-state wastewater flowrate and composition
Variable Flowrate Soluble inert organic matter Readily biodegradable substrate Particulate inert organic matter Slowly biodegradable substrate Active heterotrophic biomass Active autotrophic biomass Particulate products arising from biomass decay Oxygen Nitrate and nitrite nitrogen NH4+ + NH3 nitrogen Soluble biodegradable organic nitrogen Particulate biodegradable organic nitrogen Alkalinity Total Chemical Oxygen demand Biological Oxygen Demand – 5days Kjeldahl nitrogen
Symbol Q0 SI SS XI XS XB,H XB,A XP
Set 1 61920 30. 69.50 51.20 202.32 28.17 0. 0.
Set 2 61920 15. 21. 48.9 130. 10. 0. 0.
Unit m3.d-1 g O2.m-3 g O2.m-3 g O2.m-3 g O2.m-3 g O2.m-3 g O2.m-3 g O2.m-3
SO SNO SNH, SND
0. 0. 31.56 6.95
0. 18. 4.
g O2.m-3 g O2.m-3 g N.m-3 g N.m-3
XND
10.59
6.
g N.m-3
SALK COD BOD5
7. 381 272
7. 207 96
moles.m-3 g O2.m-3 g O2.m-3
NTK
49
28
g N.m-3
Two dynamic files, describing the variations with respect to time of the wastewater flowrate and composition at the inlet of the biological reactor, have been then applied. The first one (Dyn1) is based on the BSM1 dry weather file with a linear adjustment of the flowrate so that the average flowrate is equal to 61920 m3.d-1. For the second one (Dyn2) typical daily influent flowrate variations recorded on the Nancy-Maxéville WWTP have been collected and a typical pattern has been extracted with a 15 min period. A submersible UV-visible spectrophotometer (S:can Messtechnik, Vienna, Austria) has been installed for two weeks on the Nancy-Maxéville WWTP primary settler and total COD variations have been extracted from the spectra collected every 15 min. The variations of the different wastewater fractions have been estimated from them and the fractionation experiment previously described.
5. Results 5.1. Steady-state The oxygen mass transfer rate in the fluidized bed has been set to 480 d-1. High nitrification rates can be achieved but there are strongly dependent upon the efficiency of the bioreactions in the biofilm, which is parameterized by [. Figure 4 summarized the steady-state concentrations (obtained after 100 days of simulated time) in the fluidized bed (FBAS) and the last compartment of the biological reactor (A4) for a constant feed of external carbon (concentration = 400 kg COD.m-3) Qec = 5 m3.d-1. There is some nitrification still taking place in the degassing unit due to dissolved oxygen carried over
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35 30 25 20 15 10 5 0
SNO SNH
SNO, SNH (gN.m-3)
SNO, SNH (gN.m-3)
from the fluidized bed. Efficient post-denitrification requires the addition of an external carbon source as most of the rapidly biodegradable substrate present in the wastewater is consumed in the first reactors. Figure 5 shows the effect of Qec on the nitrates and ammonia concentrations in FBAS and A4. Increasing the external carbon increases also the anoxic growth of autotrophs and the production of ammonia through their death (Figure 3). In FBAS unit In FBAS unit 20 15 SNO SNH
10 5 0
0.4
0.6
0.8
1
0
10
[
In unit A4
50
30
40 30
SNO SNH
20 10
SNO, SNH (gN.m-3)
In unit A4 SNO, SNH (gN.m-3)
20
30
40
Qec (m3.d-1)
0
25 20 SNO SNH
15 10 5 0
0.4
0.6
0.8
1
0
10
20
30
40
Qec (m3.d-1)
[
Figure 4: Effect of [ on nitrates and ammonia in FBAS and A4 units (Qec = 5 m3.d-1)
Figure 5: Effect of external carbon feed on nitrates and ammonia in FBAS and A4 ([ = 0.6) units
5.2. Dynamic behavior Once the steady state achieved, dynamic simulations have been run (with [ = 0.6). Due to the importance of the external carbon feed, a PI control has been added (as on the full-scale plant) to manipulate Qec depending upon the nitrate concentration in A4. The controller has not been optimized however. The setpoint has been set to 10 mgN.m-3. In Figure 6a, a part of the influent file Dyn1 is shown. In Dyn1, the effect of the weekdays is considered with lower wastewater flowrate and concentration on Saturdays and Sundays. (a) (b) 20
30000
250
25000
200
20000
150
15000
100
10000
SS
5
16 SNO (gN.m-3)
Q0
12
3
8
2
4 50
SNH 0
1
2
3
4
Time (day)
5
0 6
7
1
Qec
5000
0
4
SNO
0 0
10
20 30
Qec (m3.h-1)
35000
XS
300
Q0 (m3.d-1)
SS, XS (gO2.m-3), SNH (gN.m-3)
350
40
50
60
70 80
0 90 100
Time (day)
Figure 6: (a) Subpart of the Dyn1 file; (b) nitrate concentration in A4 under PI control
M.-N. Pons et al.
912
Figure 7a presents the daily variations of SS, XS and the flowrate for the Dyn2 datafile. As the wastewater is more diluted than in the Dyn1 case, a lower Qec flowrate is needed to maintain the nitrate concentration at the exit at its setpoint. (a) (b) 20
80000
16
120 60000
100
Q0
80
40000
60
SS
40
5 4
SNO
12
3
8
20000
4
0
0
2
Qec
Qec (m3.h-1)
XS
140
100000
SNO (gN.m-3)
SS, XS (gO2.m-3)
160
Q0 (m3.d-1)
180
1
20 0 0
0.2
0.4
0.6
Time (day)
0.8
1
0
10
20 30
40
50
60
70 80
0 90 100
Time (day)
Figure 7: (a) Subpart of the Dyn2 file; (b) nitrate concentration in A4 under PI control
6. Conclusions A model for a hydrid system (activated sludge + fixed biomass) has been set up to study the dynamic behavior of the plant and its controllability with respect to various perturbations, especially related to wastewater composition and flowrate. The obtained behavior is in agreement with information collected on the full-scale treatment plant which inspired the model. The actual work is focused on the sensitivity of the model to parameters such as [ (biofilm bio-efficiency) and biocarrier volume and to the modeling of the full plant, i.e. including the sludge treatment.
7. Acknowledgements The authors are thankful to the Greater Nancy Council for permission to access plant data and to Mr David Drappier (Tradilor) for his help.
References J.B. Copp (ed.), 2002, The COST Simulation Benchmark – Description and Simulator Manual, ISBN 92-894-1658-0, Office for Official Publications of the European Communities, Luxembourg. M. Fouad, R. Bhargava, 2005, A simplifed model for the steady-state biofilm-activated sludge reactor, J. Environ. Manag., 74,3, 245-253. M. Henze, C.P.L. Grady Jr, W. Gujer, G.V.R. Marais, T. Matsuo, 1987, Activated Sludge Model No. 1, IAWQ Scientific and Technical Reports No. 1, London, UK. U. Jeppsson, M.N. Pons, I. Nopens, J. Alex, J. Copp, K.V. Gernaey, C. Rosen, J.P. Steyer, P. A. Vanrolleghem, 2008, Benchmark Simulation Model No.2 – General protocol and exploratory case studies, Wat. Sc. Technol., 56,8,67-78. H.S. Lee, S.J. Park, T.I. Yoon, 2002, Wastewater treatment in a hybrid biological reactor using powdered minerals: effects of organic loading rates on COD removal and nitrification, Process Biochem., 38,1, 81-88. M.C. Lourenço, S. Pontvianne, M.N. Pons, 2008, Fractionnement de la matière organique pour la caractérisation des eaux usées urbaines, TSM, in press. N. Müller, 1998, Implementing biofilm carriers into activtaed sludge process – 15 years of experience, War. Sc. Technol., 37, 9, 167-174. I. Takács, G.G. Patry, D. Nolasco, 1991, A dynamic model of the clarification thickening process, Wat. Res. , 25, 10, 1263-1271.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
913
Dimension reduction of two-dimensional population balances based on the quadrature method of moments Andreas Voigta, Wolfram Heinekenb, Dietrich Flockerzib, Kai Sundmachera a
Otto von Guericke University Magdeburg, PF 4120, D-39016 Magdeburg, Germany Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, D-39106 Magdeburg, Germany
b
Abstract Crystallization models that take into account direction-dependent growth rates give rise to multi-dimensional population balances that require a high computational cost. We propose a model reduction technique based on the quadrature method of moments (QMOM) that simplifies a two-dimensional population balance to a one-dimensional advection system. Our method returns the crystal volume distribution and other volume dependent moments of the crystal size distribution, in contrast to many other QMOM based reduction methods that lose all the volume dependent information. The method is applied to the direction-dependent growth of barium sulphate crystals, showing a close agreement with the solution of the full two-dimensional population balance. Keywords: barium sulphate crystallization, direction-dependent growth, twodimensional population balances, quadrature method of moments
1. Introduction Crystallization processes are often modeled using one-dimensional population balances. Models of this kind are able to describe the distribution of crystals in a reactor with respect to one size coordinate, e.g. the diameter of spherical crystals. However, crystalline particles are in general of a far more complex shape which, in addition, may change during a crystal’s growth process. The growth rate is often different along certain directions of the crystal, which results e.g. in needle-shaped or plate-like crystals. In order to simulate crystallization processes more accurately, one is interested in models that cover the complicated structure of crystal shape and growth mechanisms. As a motivating example one could look at the reaction crystallization of benzoic acid presented in [1]. There the authors showed that appropriate modeling is possible only when the shape evolution of crystal population is taken into account. In this regard several authors have included more than one length coordinate and direction-dependent growth rates, resulting in multi-dimensional population balances, see e.g. Puel et al. [2], Ma et al. [3] and Gunawan et al. [4]. Multi-dimensional population balances can be solved numerically, but are often computationally expensive. To overcome this problem, several model reduction techniques have been suggested. Some of them are based on the quadrature method of moments (QMOM), a method originally introduced by McGraw [5] to simplify one-dimensional population balances. Extensions to multi-dimensional population balances have been proposed, e.g. the method DQMOM of Marchisio and Fox [6]. However, this higherdimensional variant of QMOM returns only moments of the crystal size distribution (CSD) that are averaged over all length coordinates. Thus the moments obtained from
A. Voigt et al.
914
DQMOM contain much less information than the CSD. It is, for example, not possible to reconstruct the crystal volume distribution (CVD) from these moments. Recently Briesen [7] has proposed a model reduction technique resulting in moments of the CSD that are still volume dependent. Therefore, this method is able to keep important information like the CVD, and only the additional shape information is sacrificed. This method approximates the CSD with a Gaussian distribution ansatz. It gives very good results if the ansatz is closely met by the CSD. However, for a more general CSD, e.g. a multi-modal one, Briesen’s approach is not well suited. In this paper we introduce a method to compute the same volume dependent moments as in Briesen’s approach, but the Gaussian distribution ansatz is replaced by a QMOM ansatz. Therefore, our method combines the advantage of Briesen’s method, to keep the volume dependence, with the flexibility of QMOM which can also cover crystal distributions that are far from a Gaussian one. We apply our method to a model of direction-dependent growth of plate-like barium sulphate crystals. The model As an example for a two-dimensional crystal growth process we consider the following model for a direction-dependent growth of barium sulphate crystals in a batch reactor of volume Vreac. It is assumed that every crystal has the shape of a prism with hexagonal base. Crystals of this particular form have been observed in our precipitation experiments, see Fig. 1, and are reported in the literature, see Voigt and Sundmacher [8], and Niemann and Sundmacher [9]. The dimensions of the hexagonal base are indicated in Fig. 2. The thickness of the prism is denoted by L2 and is assumed to be always less than a given value L2,max > 0. All hexagonal bases are assumed to be self-similar, i.e. the relations L3 = ȕL1 and L4 = ȖL1 hold for all crystals with given constants ȕ,Ȗ > 0. We set Į = ȕ + Ȗ. Let f(t,L1,L2) be the crystal size distribution (CSD). The volume of one crystal is given by Vcr(L1,L2) = ĮL12L2/2, the total volume of crystals in the reactor is f f ³0 ³0 Vcr ( L1 , L2 ) f (t , L1 , L2 )dL1dL2 . It is assumed that for all crystals Vcr(L1,L2) > V0 > 0 holds, where V0 is a given minimum crystal volume. In our example we set Vreac = 10 m3, V0 = 10-20 m3, L2,max = 3·10-6 m, ȕ = 2 and Ȗ = 1.5, which gives Į = 3.5. The crystal growth in the direction of L1 and L2 is given by the growth rates G1(c) = dL1/dt = G(c) and G2(L2,c) = dL2/dt = (1 – L2/L2,max)G(c), where c is the concentration of barium sulphate in solution and G is defined according to Baádyga et al. [10] as
Vcr, tot (t )
L1
Figure 1: Hexagonal barium sulphate crystals from a precipitation experiment.
L4
L3
Figure 2: Hexagonal base of the crystals.
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Dimension Reduction
G (c )
§ 2 · °k D ¨ c csat c c 2c (c csat ) ¸, ¹ ® © °¯ 0,
½ c t csat ° ¾ c d csat °¿
(1)
with kD = 4·10-8 (m/s)(m3/mol), csat = 1.05·10-2 mol/m3, and c = 0.345 mol/m3. Remark. In Baádyga et al. [10] direction-dependent growth is not considered, and G(c) is derived there as a uniform growth rate for barium sulphate crystals. Since we have observed plate-like crystals in the experiment, we introduce the growth rates G1 and G2 as a simple model that would result in such flat crystals. We would like to stress that our growth rates are not based on empirical measurements; they are rather taken to provide a simple test example for our model reduction technique. The crystal size distribution f(t,L1,L2) satisfies the two-dimensional population balance wf (t , L1 , L2 ) wf (t , L1 , L2 ) wG2 ( L2 , c) f (t , L1 , L2 ) G1 (c) wt wL1 wL2
0.
(2)
for all L1,L2 with Vcr(L1,L2) > V0. As an initial crystal size distribution we consider f(0,L1,L2) = a d(L1,L2) exp(–b((L1 – L1 )2 + (L2 – L2 )2) with a = 1025 m-2, b = 2·1012 m-2, V1 = 5·10-19 m3, L1 = (2/Į)1/2V11/3, L2 = V11/3, and d ( L1 , L2 )
° 1 cos 2 ® °¯
ln Vcr ( L1 , L2 ) ln V1 ln V1 ln V0
S 12 , 1,
V0 d Vcr ( L1 , L2 ) d V1 ½° ¾. °¿ V1 d Vcr ( L1 , L2 )
(3)
The factor d(L1,L2) is chosen such that f(0,L1,L2) is zero at the minimum volume, i.e. for Vcr(L1,L2) = V0. We impose zero boundary conditions at the inflow boundary that is located at Vcr(L1,L2) = V0. It is assumed that under batch conditions the concentration c decreases with increasing time t since barium sulphate from the solution is needed to grow the crystals:
c
c0 Vcr,tot (t ) Vcr,tot (0) U mol / Vreac .
(4)
Here ȡmol = 1.928·104 mol/m3 is the molar density of crystalline barium sulphate and c0 is the initial concentration. In our example we set c0 = 2 mol/m3.
2. Transformation to a volume based distribution In this section we are going to derive an ODE system for volume based moments of the crystal size distribution f. Following Briesen [7], we transform the coordinates (L1,L2) to new coordinates (v,ț), where v is the volume of a crystal and ț2 is the area of its hexagonal base. The transformation is given by v = ĮL12L2/2 and ț = (Į/2)1/2L1. This results in the transformed CSD F(t,v,ț) = (2/Į)1/2ț-2f(t,L1,L2). The population balance, Eq. (2), transforms to wF (t , v, N ) wF (t , v, N ) wGv (v, N , c) F (t , v, N ) GN (c) wN wt wv
0
(5)
with Gv(v,ț,c) = (ț2 – v/L2,max + (2Į)1/2vț-1)G(c) and Gț(c) = (Į/2)1/2G(c). We introduce the moments M i (t , v)
f i ³0 N F (t , v, N )dN for i
and assume that all moments required
A. Voigt et al.
916
in the method below are finite. Note that M0 is the crystal volume distribution. Eq. (4) is equivalent to c
c0
U mol
f
v M 0 (t , v) M 0 (0, v) dv . Vreac ³V
(6)
0
If we multiply Eq. (5) with ți and integrate, we obtain the following PDE system for the moments Mi: wM i wM i 1 vG (c ) wM i wM i 2 2D vG (c) G (c ) wt wv L2, max wv wv (2 i ) D / 2G (c) M i 1
G (c ) Mi L2, max
0,
(7)
iI
where I is chosen to be a set of 2n integers. This is a system in only one spatial variable v, while the population balance (5) contains two spatial variables v and ț. However, the system of moments is not closed. This means that from whatever index set I the indices i are taken, the system will always contain more moments than equations. In the next section we apply the quadrature method of moments (QMOM) in order to close the system (7).
3. Closure of the system of moments using QMOM In QMOM, the moment Mi(t,v) in Eq. (7) is replaced by the sum ¦ nj 1N j (t , v) i w j (t , v) . The functions țj(t,v) and wj(t,v) are the abscissae and weights of a Gaussian quadrature rule. This leads to the PDE system n
ª wN j
wN j
º B (c ) » wv j 1 ¬ wt ¼ n wN j ww j ª ww j º ¦ N ij « C (N j , w j , v, c ) A(N j , v, c) D(N j , w j , c)» wv wv j 1 ¬ wt ¼
¦ iN ij1w j «
A(N j , v, c)
(8) 0,
iI
for the unknown functions țj(t,v) and wj(t,v), where the functions A, B, C and D are given according to A(țj,v,c) = ((2Į)1/2v/țj – v/L2,max + țj2)G(c), B(c) = –(Į/2)1/2G(c), C(țj,wj,v,c) = (–(2Į)1/2v/țj2 + 2țj)G(c)wj, D(țj,wj,c) = ((2Į)1/2/țj – L2,max-1)G(c)wj, and c is given in Eq. (6). Introducing the matrices P = (Pij) = (ițji-1wj), Q = (Qij) = (țji) and the line vectors r = (rj) = (wNj/wt + AwNj/wv + B), s = (sj) = (wwj/wt + CwNj/wv + Awwj/wv + D) for i = 1,…,2n and j = 1,…,n, system (8) can be written in matrix form as (P Q)(r s)T = 0. The matrix (P Q) is almost everywhere regular, i.e. it is singular only for (N1,…,Nn) Ks, where Ks is a set of measure zero in n. Thus, system (8) is almost everywhere equivalent to the system (r s) = 0 which we are going to solve. Note that this system is independent on the choice of I. The subsystem r = 0 decouples into n independent advection equations. The system is equipped with initial values țj(0,v) > 0, wj(0,v) > 0 and boundary values țj(t,V0) > 0, wj(t,V0) > 0 for j = 1,…,n. It follows that țj(t,v) > 0, wj(t,v) > 0 and A(țj,v,c) > 0 hold for all t > 0, v > V0, j = 1,…,n. The latter inequality means that advection is directed towards increasing v. Thus the boundary condition is imposed correctly, i.e. at the inflow boundary of the problem. The initial and boundary values țj(t ,v ), wj(t ,v ) for (t*, v*) * : {0} u >V0 , f >0, f u {V0 } are derived from
917
Dimension Reduction
the initial and boundary moments Mi(t ,v ) using the PD-algorithm of Gordon [11], see e.g. McGraw [5]. If this algorithm produces a solution țj(t ,v ) > 0, wj(t ,v ) > 0, then Mi(t ,v ) = ¦ nj 1N j (t*, v*)i w j (t*, v*) holds for i = 0,…,2n – 1. The initial and boundary moments Mi(t ,v ) are calculated from the known initial and boundary values of f by quadrature. The advection system is numerically solved using a splitting scheme that consists of a second order upwind scheme [12] for the advection part and a second order Runge-Kutta method for the source term. The numerical method returns a solution țj(tk,vl), vj(tk,vl) on a time-volume grid. The moments Mi are then approximated at the grid by M iQ (t k , vl ) ¦ nj 1N j (t k , vl ) i v j (t k , vl ) , where the superscript Q stands for QMOM. Off the grid, MiQ(t,v) is linearly interpolated. The concentration c is approximated at the time grid by c Q (t k )
c0 ( U mol / Vreac ) ³Vf0 v M 0Q (t k , v) M 0 (0, v) dv .
Here the integral is evaluated by quadrature. The above mentioned PD-algorithm is not applicable if M0(t ,v ) = 0 holds for any (t*, v*) *. Therefore, it is numerically problematic if the CSD f is zero in the initial or boundary condition. We overcome this problem by adding a negligibly small positive perturbation to the initial and boundary conditions on f which are given in Section 2.
4. Numerical results In this section we compare the moments MiQ obtained with the QMOM based closure method with the moments Mi that are calculated from a reference solution of system (2), (4). Since an exact solution of this system is not known, the reference solution is computed numerically using a second order finite volume method [13], see also [4], for the two-dimensional advection problem (2). Fig. 3 shows contour plots of f(0,L1,L2) and f(400s,L1,L2) obtained from the reference solution. The problems are computed on such a fine grid that any further refinement would lead only to negligible changes in the moments. The relative error of MiQ is estimated by the expression f f Q ³V0 | M i (t , v) M i (t , v) |dv / ³V0 M i (t , v)dv .
K ( M iQ , t ) x 10
−6
est. relative error η(Mi ,400 s)
3
t = 400 s
L2 in m
2 t=0
path of maximum
Q
2.5
3.59x1025m−2
1.5 1
25 −2
10 m 0.5 0 0
2
L1 in m
4
6 −6
x 10
Figure 3: Contour plot of the crystal size distribution f at times t = 0 and t = 400 s.
0.065 0.06
i=0 i=1 i=2 i=3
0.055 0.05 0.045 0.04 2
3 4 number of quadrature points n
5
Figure 4: Estimated relative error Ș(MiQ,400 s).
A. Voigt et al.
918 29
29
x 10
x 10
2.9 n=5
2.8
0
0
n=3
n=4
ref. sol.
0
2
3 M , MQ in m−3
n=2 n=5 ref. sol.
0
M , MQ in m−3
3
1
2.7 2.6
0
0.6
0.8
1 1.2 3 v in m
1.4
1.6 −16 x 10
n=2 7.5
8
8.5 3 v in m
9 −17 x 10
Figure 5: M0 and M0Q at time t = 400 s. Right plot shows zoom into left plot.
In Fig. 4 we show the estimated error for t = 400 s, i = 0, 1, 2, 3 and n = 2, 3, 4, 5. As expected, it turns out that the estimated error can be decreased by increasing the number n of quadrature points in QMOM. However, for n > 6 the numerical method solving the advection problem in QMOM was unstable. In Fig. 5 the moments M0 and M0Q are shown for time t = 400 s and n = 2, 3, 4, 5. In the left plot the cases n = 3, 4 are omitted to enhance visibility. The moments M0Q are shown to lie close to M0.
5. Conclusion We have proposed a QMOM based dimension reduction method for the numerical simulation of direction-dependent crystal growth. Our method reduces a twodimensional population balance to a small system of advection equations. The method returns volume-dependent moments of the CSD which might be an advantage over reduction methods that exclude all information on volume dependence of the CSD. Our dimension reduction was shown to give satisfactory results when it was applied to a problem that models the growth of hexagonal barium sulphate crystals. The method could be extended to cover additional processes like crystal nucleation.
References [1] M. Stahl, B. Aslund and A.C. Rasmuson, Ind.Eng.Chem., 43 (2004) 6694. [2] F. Puel, G. Févotte, J. Klein, Chem. Eng. Sci., 58 (2003) 3715. [3] D. Ma, D. Tafti, R. Braatz, Ind. Eng. Chem. Res., 41 (2002) 6217. [4] R. Gunawan, I. Fusman, R. Braatz, AIChE J., 50 (2004) 2738. [5] R. McGraw, Aerosol Sci. Tech., 27 (1997) 255. [6] D. Marchisio, R. Fox, J. Aerosol Sci., 36 (2005) 43. [7] H. Briesen, Chem. Eng. Sci., 61 (2006) 104. [8] A. Voigt, K. Sundmacher, Chemie Ingenieur Technik – CIT, 79 (2007) 229. [9] B. Niemann, K. Sundmacher, in: Proceedings of the 3rd International Conference on Population Balance Modelling, Quebec, Canada, 2007. [10] J. Baádyga, W. Podgórska, R. Pohorecki, Chem. Eng. Sci., 50 (1995) 1281. [11] R. Gordon, J. Math. Phys., 9 (1968) 655. [12] E. Toro, in: E. Toro, J. Clarke (eds.), Numerical methods for wave propagation, Kluwer, Dordrecht, 1998, pp. 323-385. [13] R. LeVeque, Finite volume methods for hyperbolic problems, Cambridge University Press, 1st ed., 2002.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
919
Predictions of the consequences of natural gashydrogen explosions using a novel CFD approach Robert M. Woolley,a Michael Fairweather,a Samuel A.E.G. Falle,b Jack R. Giddingsc a
School of Process, Environmental, and Materials Engineering, University of Leeds, Leeds LS2 9JT, U.K. b School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K. c Mantis Numerics Ltd., 46 The Calls, Leeds LS2 7EY, U.K.
Abstract There is increasing interest in the use of hydrogen as an energy carrier. A hydrogen delivery system is required, and one solution is its addition to existing natural gas pipeline networks. A major concern is the explosion hazard may be increased should an accidental release occur, and this paper presents results from the mathematical modelling of confined, vented explosions of mixtures of methane with 0%, 20% and 50% hydrogen dilution by volume. The flow field in an explosion was predicted through solution of the averaged forms of the Navier-Stokes equations, with these equations closed using both k-İ and second-moment turbulence models. Accurate representation of the turbulent burning velocity of the various mixtures was necessary, and this was achieved using correlations obtained from the analysis of extensive experimental data sets on H2-CH4 mixtures. Results, derived for explosions in a 70m3 confined vessel with and without pipe congestion, demonstrate that hydrogen addition can have a significant effect on overpressure generation, particularly if turbulence generating obstacles are present. Keywords: CFD, deflagration, safety, hydrogen
1. Introduction There is presently an increasing interest in the use of hydrogen as an energy carrier as an essential part of achieving a sustainable economic development. The work described was carried out as part of the NATURALHY project (see http://www.naturalhy.net), the main objective of which is to considering the potential for using the existing natural gas system as a means of transporting the hydrogen from a site of production to a point of use. Hydrogen would be transported in the gas network as a mixture and some hydrogen extracted for hydrogen powered applications. However, some hydrogen would remain mixed with natural gas and be delivered to existing gas customers where it would be burned as a mixture. One major concern in this work is that the explosion hazard may be increased, as in contrast to natural gas, hydrogen has a relatively high burning velocity, and can easily make the transition from deflagration to detonation. It is therefore essential to investigate the possible behaviour of such gaseous mixture releases in both confined and unconfined areas of industrial relevance. Subsequently, the information obtained can be used in the design of equipment and plant, and to improve safety and reduce the risk of both deflagrations, and deflagration to detonation transitions.
R.M. Woolley et al.
920
This paper presents results from the mathematical modelling of confined, vented explosions with and without internal pipe-work congestion. The mixtures investigated comprised methane, used to represent natural gas, with 0%, 20% and 50% hydrogen dilution by volume. One objective of this study was the comparison of turbulence model performance, and the turbulent flow field was resolved by the application of both a twoequation and a second-moment turbulence closure, supplemented with transport equations for the reaction progress variable and the total energy. Accurate representation of the turbulent burning velocity of the various mixtures is necessary, and this was introduced into the calculation via the diffusion coefficient and the source term of the reaction progress variable. The burning velocity was represented by correlations obtained from the analysis of recent experimental data gathered at the University of Leeds, and a simple eddy break-up reaction model using a one-step irreversible reaction was applied in the prescription of the turbulent combustion model. The calculations presented are representative of confined, vented explosion experiments undertaken by Loughborough University in a 70m3 confined vessel with and without internal pipe-work congestion. The results are conforming to experimental observation (Hankinson and Lowesmith, 2007), however a full experimental dataset remains in preparation and as such, is not reported in the present work. Future publication will provide full comparisons.
2. Experimental Arrangement The predictions presented in this paper are a selection taken from a number of simulations of large-scale experiments undertaken by Loughborough University (Hankinson and Lowesmith, 2007). A full account of the experiments performed and the results obtained will be presented elsewhere, hence only a brief overview is given here. The experimental rig was of steel construction, and measured 8.25m in length, 3.0m in width, and 2.8m in height. One 3.0 × 2.8m end was effectively open to the atmosphere for the purpose of the tests, being covered with a polythene sheet to retain the gas-air mixture prior to ignition. Figure 1 depicts the rig, and indicates the configuration of pipe-work congestion and the spark ignition points, although not to scale.
3.0m
Polyethylene IN
OUT
External recirculation system
Pipes 0.18m diameter
OUT
2.8m IN
Ignition position 8.25m
Figure 1. Schematic diagram of the experimental rig.
Predictions of the Consequences of Natural Gas-Hydrogen Explosions Using a Novel CFD Approach
921
The gases investigated were mixtures of methane, hydrogen and air, with the methaneto-hydrogen ratio by volume being 100:0, 80:20 and 50:50. Five tests for computational investigation were chosen as a representative sample of the total number of experiments performed, and these configurations are reported in Table 1. Table 1. Experimental conditions. Experiment number
Fuel / CH4:H2
Congestion / pipes
Ignition location
7 8 9 10 13
80:20 50:50 80:20 50:50 100:0
None None 17 17 None
Rear Rear Rear Rear Rear
3. Mathematical Modelling 3.1. Turbulent Flow Field The flow fields within the experimental rig were resolved by solution of the two- and three-dimensional forms of the density-weighted, partial differential equations describing the conservation of mass, momentum, and total energy. Time-dependent, and written in their high Reynolds number forms, the averaged equation set was closed in the first instance by the standard k-ε turbulence model of Jones and Launder (1972). Modelling constants used were the widely accepted standard values, as reported in Jones and Whitelaw (1982). For comparison, a second-moment method of turbulence closure was investigated, being that described by Jones and Musonge (1988). In this original aspect to the modelling approach, the shear and normal stress terms are closed by the solution of their individual transport equations, the modelling constants employed being a modified set, as described in Jones (1994). The geometry was modelled using three approaches. In the first instance, a central section of that shown in Fig. 1, assuming symmetry properties of two of the computational boundaries, was used. Fig. 2 depicts this geometry, where the left boundary represents a solid wall, and the right an outflow. Initially, a small area of burned gas, represented by a region where the progress variable, c, equals 1.0, is located adjacent to the former boundary, which is used to instigate the numerical reaction. Secondly, a two-dimensional slice of the geometry was modelled using three solid wall boundaries, and containing a representation of all the specified obstacles. Thirdly, a full three-dimensional version of the confined region was modelled. 3.2. Combustion Model In addition to that for total energy, E, the premixed combustion model implemented requires the solution of a conservation equation describing the reaction progress variable. The source term of this equation is represented by a modified form of the eddy break-up reaction rate expression as:
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averaged mean values. Also, R represents the reaction rate established in line with discussion in Catlin et al. (1995), and ȡ the densities of the burned and unburned gases indicated by the subscripts. This form of the reaction rate expression eliminates the cold-front quenching problem by prescribing variation of the reaction rate through the flame using a power law expression (Catlin et al., 1995). Equation (1) can be subsequently used in the closure of the source term for total internal energy by convolution with a representation of the specific heat release. The two components of this model are to firstly provide solutions which give rise to a flame which accurately reproduces specified burning velocities, and secondly provide a representative prescription of these velocities given known mixture and flow field parameters. Following Catlin et al. (1995), the source terms and diffusion coefficients in the equations for E and c can be defined as functions of the turbulent burning velocity, and here, correlations derived from the most recent experimental evidence (see, for example, Burluka et al., 2007) have been implemented. 3.3. Method of Solution Integration of the equations employed a second-order accurate finite-volume scheme in which the transport equations were discretised following a conservative control-volume approach, with values of the dependent variables being stored at the computational cell centres. Approximation of the diffusion and source terms was undertaken using central differencing, and a second-order accurate variant of Godunov’s method applied with respect to the convective and pressure fluxes. The fully-explicit time-accurate method was a predictor-corrector procedure, where the predictor stage is spatially first-order, and used to provide an intermediate solution at the half-time between time-steps. This is then subsequently used at the corrector stage for the calculation of the second-order fluxes. A further explanation of this algorithm can be found elsewhere (Falle, 1991). An adaptive-grid method was employed to allow the generation of fine grids in regions of steep spatial and temporal variation, and the implementation of coarser grids in smooth regions of the flow. Adaption of the rectangular mesh was employed by the overlaying of successively refined layers of grids, with each layer generated from its predecessor by the doubling of the computational cell number in each spatial dimension. Again, further details regarding the algorithm can be found in Falle and Giddings (1993).
4. Results and Discussion
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Figure 2 provides an example of a sample stage of solution during the calculation of experiment number 10, using the Reynolds-stress approach to the turbulence closure. From an assembly of a time-lapse sequence of the reaction progress variable such as this, the behaviour of the flame front can be seen to be in-line with expectation. Initially progressing at a relatively slow rate, the reaction zone subsequently accelerates through the unreacted fluid upon each obstacle interaction, returning to a constant velocity in between these areas of turbulence generation.
Figure 2. Sample two-dimensional symmetry progress variable predictions of experiment 10.
Analysis of the results provides the maximum overpressures achieved and the flamefront vessel-exit velocities predicted by the models, which are presented in Fig. 3. It is
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evident from these results that, in general, the magnitude of the predictions, and hence ultimately their conformity with experiment, depends upon the turbulence model, which in turn has a performance dependency upon the domain geometry and the fuel investigated. This is less evident for the three-dimensional approach, although results based on the Re-stress model are generally more in line with available data. For the two-dimensional symmetry simulations run involving internal pipe-work, the more reliable Reynolds-stress model is seen to be at variance with its two-equation counterpart with respect to recorded maximum overpressures. Predicted exit flamespeeds do, however, show little difference in the performance of the two turbulence models. At the higher turbulence levels associated with the congested cases, the flow becomes increasingly less isotropic and it appears a notable component of the turbulence stress-tensor is not being represented in the k-İ case. Scrutiny of the calculated results also reveals a relative deterioration of the k-İ model’s predictive ability in the cases of higher hydrogen content, this being due in part to the introduction of hydrogen effecting an increase in both the laminar and turbulent burning velocity, and hence an increase in the turbulence generated. The varied performance of the models is further highlighted when the results obtained from the calculations of the empty rig are considered. Here, conversely to that seen in the relatively high turbulence case, the Reynolds-stress model is seen to predict lower maximum overpressures than its k-ε counterpart, over the three fuels considered. Again, predictions of exit flamespeed velocity are similar for the three cases investigated, with little difference observed between the two turbulence model predictions. 2500
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With reference to the two-dimensional calculations (Fig. 3b), the increase in geometry complexity is seen to bring predicted overpressures more in line in the congested cases, although a less conforming result is seen for the empty vessel. Also, predicted exit flame speeds comply with this observation, which raises questions regarding the validity of the model in such low turbulence regimes. Based on these observations, and the long computational time of approximately 80 hours using a 3 GHz processor, three-
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dimensional calculations were undertaken of the high-turbulence cases only, and results are depicted in Fig. 3(c). Both predicted overpressure and flame speed are noted to be of lower magnitude than the previous approaches, with the k-İ model typically over predicting Re-stress results in the cases with the higher hydrogen concentration and hence the higher level of turbulence. One further consideration is the accuracy to which either of these turbulence models can be expected to predict a flow that is substantially laminar, as in the case of explosions within vessels without internal obstacles. Further work has therefore focussed on those experimental tests performed using internal, turbulence generating pipes. Additional investigations are also being undertaken to assess the model’s performance in the modelling of similar, but unconfined cases.
5. Conclusions For the first time, a Reynolds-stress turbulence model has been applied to the prediction of large-scale vented explosions, coupled to a turbulent premixed combustion model. Maximum predicted overpressures and flame-front velocities for five test cases are presented, and comparisons made to calculations based on the k-ε model. The Reynolds-stress model is seen to generally be at variance with the isotropic approach, although in terms of predicted overpressures and flame-front velocities these differences are often small. However, the increase in turbulence anisotropy caused by internal pipe work within a vessel necessitates the use of a Reynolds-stress model on physical grounds alone. These observations are valid for the three approaches used to represent the geometry considered, with the level of conformity observed in the two-dimensional cases making them viable for use in future studies.
6. Acknowledgements The authors gratefully acknowledge financial support for the work described from the EC’s 6th Framework Programme (Integrated Project NATURALHY – SES6/CT/2004/50266).
References A.A. Burluka, M. Fairweather, M.P. Ormsby, C.G.W. Sheppard and R. Woolley, 2007, The Laminar Burning Properties of Premixed Methane-Hydrogen Flames Determined Using a Novel Analysis Method, Proc. 3rd European Combustion Meeting, Paper 6-4. C.A. Catlin, M. Fairweather and S.S. Ibrahim, 1995, Predictions of Turbulent, Premixed Flame Propagation in Explosion Tubes, Combust. Flame, 102, 115-128. S.A.E.G. Falle, 1991, Self-Similar Jets, Mon. Not. R. Astr. Soc., 250, 581-596. S.A.E.G. Falle, and J.R. Giddings, 1993, Flame Capturing, In, M.J. Baines and K.W. Morton, (Eds.), Numerical Methods for Fluid Dynamics 4, Clarendon Press, 337-343. G. Hankinson, and B. Lowesmith, 2007, private communication. W.P. Jones, 1994, Chapter Six: Turbulence Modelling and Numerical Solution Methods for Variable Density and Combusting Flows. In, P.A. Libby and F.A. Williams, (Eds.), Turbulent Reactive Flows, Academic Press, New York, 309-373. W.P. Jones and B.E. Launder, 1972, The Prediction of Laminarization with a Two-Equation Model of Turbulence, Int. J. Heat Mass Transfer, 15, 301-314. W.P. Jones and P. Musonge, 1988, Closure of the Reynolds Stress and Scalar Flux Equations, Phys. Fluids, 31, 3589-3604. W.P. Jones and J.H. Whitelaw, 1982, Calculation Methods for Reacting Turbulent Flows, Combust. Flame, 48, 1-26.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Support of strategic business decisions at BASF’s largest integrated production site based on site-wide Verbund simulation Stefan Brüggemann,a Nanette Bauer,a Eberhard Fuchs,a Axel Polt,a Bernhard Wagner,a Michael Wulkowb a b
BASF AG, 67056 Ludwigshafen, Germany CiT-Computing in Technology GmbH, 26180 Rastede, Germany
Abstract The paper presents a novel large-scale sequential-modular simulation tool for expansion and refinement of Verbund sites with highly-interconnected networks of chemical production and infrastructure plants. The simulation uses a hierarchical model based on the site’s cost centers, plants and unit operation modes which hold the stoichiometry and utility demand of each production step. A semi-automatical interface to the SAP database of the site is used for routinely updating the model with respect to the latest changes regarding structure and recipe parameters. Based on this model the impact of modifications in a single plant, for example a capacity increase, can be analyzed by giving a quantitative prediction of all relevant consequences across the linked value chains of the site. The new simulation tool is used to support strategic business decision making with respect to new investments, capacity adjustments and production planning. In addition, the gathered and consolidated data of the Verbund models are a valuable resource for strategic and operative business units. Keywords: Simulation, Integrated production, Verbund model, Business decision support, Enterprise resource planning, SAP.
1. Introduction Verbund is one of BASF’s core competencies: At all major sites, the production plants are connected in a sophisticated complex network which link basic chemicals to specialties along value-adding chains. Byproducts are integrated into subsequent production steps either as a secondary fuel source, or, preferably, as raw materials for other plants (see Kröner et al., 1988, and Lenz et al., 1989). Hence, the Verbund network supports sustainable production by reducing energy and raw material consumption, cuts down logistic costs and allows the jointly use of infrastructure facilities by synergy management. In order to maintain its competitive advantage, BASF continuously cultivates and refines its Verbund structures. However, the high level of integration of the network in which chemical products, side-products, waste fractions and utilities are transferred between and shared by a large number of chemical plants also leads to a high degree of complexity when assessing the impact of strategic business decisions on the Verbund site as a whole. For example, the expansion of a plant for a sales product automatically triggers an increased demand for its respective feedstock intermediates. The resulting make-or-buy decision for these intermediates requires a quantitative prediction of all relevant effects on the other plants of the site as well as the utility systems.
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In this contribution, we present some experiences on successfully modeling and simulating BASF’s largest Verbund site worldwide, Ludwigshafen, consisting of more than 200 plants and 8,000 sales products, each processed from several intermediates or raw materials. One of the key challenges is the enormous amount of data which is required to reproduce the network of chemicals, utilities and plants. A new tailor-made simulation software has been developed which provides interfaces to the databases of the site’s procurement and resource planning systems (SAP).
2. Structure and characteristics of the Verbund model Modern modeling and simulation programs have become indispensable tools for the design and rating of chemical processes. The vast array of different tools can be categorized by the level of detail of the respective models. Figure 1 illustrates this categorization and names some industrially important tools. Plant information systems collect historical measurement data from existing plants. Trend detection and reconciliation features allow a data-driven assessment and rating of single pieces of equipment and the performance of the production process as a whole. Equipment design software targets the sizing and rating of key equipment such as distillation columns or heat exchangers based on thermodynamics, physical property packages and high-detail models for heat and mass transfer as well as fluid dynamics. The use of process simulators such as Aspen Plus has long become state-of-the-art for the design of complete process flowsheets. They allow capturing the interdependence between major pieces of equipment and the influence of recycles. Integrated optimization packages and sizing model libraries assist the identification of cost-optimized operating points (Wiesel et al., 2006). In principle, the simulation of a complete Verbund site can be regarded as a flowsheet simulation which operates on a very large-scale model encompassing all chemical components, utilities and plants on the site. Regarding the sheer number of components on a single site, which can easily reach several hundred to thousands, it is, however, easy to imagine that standard process simulation tools are not well suited for this task. Instead, BASF decided to create the new custom-made simulation tool SiteMod for sitewide simulation with a highly aggregated model which has been implemented and jointly developed by CiT. A Verbund model is built up based on a three-level hierarchy which is closely related to the structure of the SAP database of the site. Figure 2 illustrates the structure of the Verbund model with an example. The first level comprises of the plants Level 0: BASF Worldwide All sites
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Figure 1: Levels of detail in modeling chemical processes
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Figure 2: Hierarchical structure of the Verbund model
or, respectively, cost centers on the site. Each plant is subdivided into several production units (cost subcenters) which define an independent chemical production facility, e.g. a single production line of a polymer plant. The description of the chemical process itself is stored in unit operation modes attached to the production units. The chemistry is given in form of a recipe which balances the input and output streams of the production unit with respect to chemicals and utilities. The example shown in Figure 2 describes the recipe for the production of a liquid intermediate product in the polyamide value chain. Extractsolution 75% is the main raw material. A small quantity of an alkaline side product is formed in addition to the target component. The process requires steam at two pressure levels and a small amount of electricity. Large-scale single-purpose lines, like the one shown here, only have one single operation mode. On the other hand, multi-purpose units can own several competing unit modes. Depending on the type of plant the amount of different unit modes in one unit can grow quite large, e.g. several hundred for compounding and confectioning lines. In addition to the recipe each unit operation mode has a so-called alternative capacity which denotes the maximum yearly production if the production unit is operated with this unit operation mode exclusively. The amount to which the main product of the unit operation mode is produced is stored in the portfolio of the unit. Using the concept of the alternative capacities the amount of produced material per operation mode can be converted to an operating time. Comparison of the sum of these partial operating times with the total yearly operating time of the unit then yields the level of capacity utilization. In addition, the overall material and energy balances of units and plants can directly be deduced from the portfolios.
3. Integration with the electronic procurement database of the site The development of Verbund models for site scenarios started in 2002 with the engineering of BASF’s most recent Verbund site in Nanjing. The availability of a tool for site-wide balancing offered a significant contribution to the successful conceptual planning and startup of this new site where the integration of the new plants into several value chains and utility networks was basically derived from the drawing board. In the following years, the concept of Verbund simulation was expanded to the sites in Geismar, Freeport and Antwerp. Up to this point, the models were mainly constructed
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and maintained by hand. When work started on a Verbund model for BASF’s largest and most diversified site Ludwigshafen in 2004, it soon became apparent that this approach is not suitable anymore. More than 200 plants with over 900 production units, approximately 5,800 main products and a total of around 18,000 different chemical and utility components correspond to an increase of complexity of at least one degree of magnitude in comparison to any of the other sites. In addition to the monstrous task of collecting all relevant information at one point in time, the high rate of modifications with respect to plants, recipes and new products, especially in the specialties and customized polymers sectors, makes it nearly impossible to keep the model up-to-date manually. This claim is probably best illustrated by the fact that in 2007 alone more than 800 new components have been introduced on site. In order to keep up with the sheer mass of information required for an adequately concise representation of the Ludwigshafen Verbund, SiteMod has been equipped with an interface for data import. The enterprise resource planning database (SAP) of the site is used for the compilation of the raw data. This approach is similar to modern logistics optimization (see Stadtler et al., 2007). Figure 3 shows the software architecture and respective interfaces. As part of its administration and accounting modules, the SAP database contains the current cost center structure and most of the main parameters such as the alternative capacities as well as planned and historical recipes. These parameters are collected in a business warehouse (BW) and extracted to an XML-file which is then imported into a given SiteMod model. A fine-granular parameter blocking mechanism allows to selectively spare certain parameters from being overwritten by the extracted input file. Currently, a present-state site model is generated and updated on a monthly basis. After importing, the model undergoes a data verification process. The model information is aggregated into cost center reports which are published in a restricted-access intranet database. This database is routinely scanned by a data validation team. In case of doubt this team discusses the respective data with plant management and controlling, whereby inconsistent SAP information is corrected. As a beneficial side effect of the data verification process, plant management and controlling are provided with a web access to a very compact overview of the plants.
Figure 3: Software architecture and integration with the SAP database
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SiteMod also provides additional interfaces for the import of parameter tables, e.g. sales plans for selected components, and the generation of tabular and graphical output for the documentation of different case studies.
4. Calculation and analysis of site scenarios In principle, Verbund simulation can be used to target either strategic site development scenarios or operative optimization. Historically, the main application is the assessment of the Verbund aspects of investment projects, e.g. new plants or capacity increases in existing plants. This is done in the form of case studies called site scenarios. These case studies target questions such as how the degree of utilization of all upstream plants is affected, if the market prognoses for the related sales products support the planned capacity of an intermediate, or whether there is additional demand for investment in order to supply the required raw materials or utilities. Hence, the scenarios provide important input for the support of strategic business decision making with respect to the investment. Figure 4 illustrates the application of Verbund simulation for the benchmarking of an investment project. A new site scenario usually starts from a collection of historical information stored in the reference model of the site. This model basically describes the balances of the plants according to the sales and production data of the previous financial year. However, the balances are revised in order to remove effects from singular events such as shortfall of production due to unplanned shutdown, technical problems or raw material shortage. In essence the model, therefore, describes a perfectly operated site. The reference model also contains a set of manually edited parameters and rules which describe constraints on the balances of special components. For example, the demand of some concentrated acid is first covered by re-concentrating available amounts of spent diluted acid before it is synthesized from fresh raw material. Another example is the preferred allocation of production to the most cost-effective of multiple production lines. In order to create a new scenario the model is augmented with project-specific information, such as new plants and new components with their respective market prognosis. Finally, the model is recalculated by iteratively setting the amounts of production of all unit operation modes in the portfolio of each production unit to a desired target. This target is determined according to the desired sales and the internal demand for the specific component. Rule parameters partition the production in case Historical Historical information information
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multiple unit operation modes exist for the production of the same component. A sequential-modular approach has proven to be most suitable for converging the overall site balance out of two reasons. First, it readily supports a step-by-step analysis of the balance changes and, if necessary, adjustment of the rule parameters. Secondly, it allows isolation of singularities and other numerically unwanted effects in the model. For example, singularities frequently arise when component A is not only produced from component B in one unit operation mode but also reprocessed to B in another one. Whereas this situation is perfectly valid for accounting in SAP, it can, depending on the rule parameters, be a major hassle for the simulation. The resulting balances of the scenario can readily be compared to the reference model or, respectively, to alternate scenarios in form of a Δ-assessment. This assessment shows the changes of the site balance with respect to the overall component balance and the utilization of the plants. Successive scenario calculations can then be used to refine and optimize the integration of productions within the Verbund.
5. Use of Verbund simulation as an operative site information tool In addition to the economic assessment of investment projects the data in the Verbund model can also be used as a site information tool for midterm operative planning. Based on a five-year sales forecast the corresponding plant portfolios are calculated using the reference model. Where applicable, scheduled capacity increases resulting from debottlenecking and, vice versa, capacity decreases, e.g. from planned turnarounds, are considered. The resulting production plan is published in a SAP BW/Intranet database and provides the plant managers with information on the expected utilization of their plant and, in case of multi-product plants, on the distribution of the product portfolio (cf. Figure 3). Recently, this planning module has been expanded to additionally propose a site-wide forecast of energy and utility consumption.
6. Conclusions and future work A novel software tool for site-wide balancing of chemicals and utilities has been introduced. The tool enables visualization and refinement of integrated production at a Verbund site based on data from an enterprise resource planning database (SAP). It is used for the economic benchmarking of the site aspects of investment projects. In addition, it is the basis for setting up the midterm operative production and utility forecast of the site. Future work will focus on exploiting the data contained in the Verbund model for additional operative aspects. Ideas range from optimization of product allocation during periods of raw material shortage to the application for tolling purposes. On a long-term scale the extension to multi-site Verbund simulation is targeted.
References H. Körner, 1988, Optimaler Energieeinsatz in der chemischen Industrie, Chemie Ingenieur Technik, 60, 7, 511-518. H. Lenz, M. Molzahn and D. W. Schmitt, 1989, Produktionsintegrierter Umweltschutz – Verwertung von Reststoffen, Chemie Ingenieur Technik, 61, 11, 860-866. H. Stadtler and C. Kilger, 2007, Supply Chain Management and Advanced Planning: Concepts, Models, Software and Case Studies, Springer Verlag, Berlin. A. Wiesel and A. Polt, 2006, Conceptual steady state process design in times of value based management, Proc. ESCAPE 16, Elsevier, 799-804.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A generic scientific information management system for process engineering Sylvie Cauvina, Mireille Barbieuxb, Laurent Carriéb, Benoît Celseb a
IFP- 1 & 4, avenue de Bois Préau - 92852 Rueil Malmaison, France
b
IFP-Lyon, Rond Point de l'échangeur de Solaize, BP3, 69360 Vernaison, France
Abstract The development of new and innovative refining or petrochemical processes involves various activities ranging from analysis tools development, catalysts or separation agents elaboration, laboratory and pilot tests, models and simulators development1. At each step, a huge amount of very valuable and heterogeneous data is collected. It must be exploited by all the actors of a project. This paper presents the scientific data management system which has been developed in order to deal with this data, therefore enhancing the process development cycle. It focuses on the conceptual foundations which allowed us to reach the aim of having generic applications which are directly configured by the end-user. The system being in use since 2006, feedback and lessons learnt are presented. Keywords: Scientific data management system, Process development, Databases and Data mining.
1. Introduction and requirements Developing new industrial refining or petrochemical processes requires a wide range of activities. First of all, catalysts or separation agents are elaborated which involves specific methods of preparation. All the variables such as temperature and duration of calcination, are important. Then many tests are conducted in laboratories in order to estimate the performances of the product which is considered. When this step is successful, more tests are conducted on pilot plants which are units measuring several meters but much smaller than industrial units. These tests cover wide ranges of operating conditions (several kinds of feeds, ranges of pressure and temperature). Collected data is used to build models which will be used to design industrial units and be able to guarantee some yields in specific conditions. Therefore, collected data is very valuable (a wrong design would lead to huge economic penalties). The set of data is big: a lot of physical analyses are made to get the detailed information that is required, the range of the data must be representative, there is redundancy in the data in order to be able to guarantee its quality. At the same time, the tests being very expensive, the number of experiments and measurements must be restricted to the bare necessity. As new processes must be developed quicker and quicker to be on time on the market, it is absolutely necessary to deal with the collected data with very efficient tools (Moore 2000). In this paper, we detail the information management system which was set up in 1
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our Research and Development Institute. It allows us to optimise the daily work of the process engineers, to optimise the use of the data, to minimise the cost of software development and adaptation, and constitutes an important item of the quality policy. The system interconnects the experimental devices, data bases, simulation and request tools. All the tools are configured by the end-users, which allows them to use the same tools from one process to another without any further software development. Each data is entered only once, checked manually (using results of the calculations and comparisons between several experimental points), and tracked. Nevertheless, this genericity (or possibility to use the same software for different purposes) involves complexity in the conceptual foundations of the applications. Figure 1 presents the global organisation of all the devices used and connected. Pilot plants are controlled using the Fix Control System2 which is connected to iHistorian3 Software which centralises synthetic values (average, mean, max). On-line and off-line analyses are stored in the LIMS (Laboratory Information Management System) when special chromatography systems are managed by the Galaxie application. The collected data is then transferred in two applications: CataSepa which is dedicated to studies concerning catalyst and separation agents, and B-DEXP which manages pilot plant information. These applications have different aspects: data management, data exploitation with query tools and models connection. Figure 1 also mentions Oleum, an application for managing the location of the products and security aspects (it provides information to B-DEXP) and Correl which is an application dedicated to the elaboration of correlative models using analyses results. Finally, on the catalysts, some information is entered manually in Excel files which are loaded directly in CataSepa.
Fig. 1: An interconnected information management system
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The paper is organised as follows: Section 2 focuses on the LIMS developed with SQL*LIMS4 from ABI, using Oracle database, Section 3 focuses on the two applications dedicated to catalyst and process development (CataSepa and B-DEXP) which are distributed Intranet applications developed with Oracle 9i Application Server, Oracle data base, Java and Business Objects, and Section 4 focuses on the lessons learnt.
2. The LIMS application 2.1. Main functionalities and specificities The LIMS application manages the submissions and the results of almost all the analyses which are made within the Institute. A submission with its samples follows a complete workflow in the LIMS application from the customer - who generates the submission – to the analysts who enter the results, method by method, and then finally to the customer again when the results are approved. The standard functionalities of SQL*LIMS software have been adapted to meet the requirements of our process research Institute which are much different from those of the pharmaceutical industry (Kimber 2006). In particular, due to the fact that tests are conducted in a wide range of conditions, specific functionalities had to be developed. For instance, "frameworks" were made available to manage complex submissions, with multiple samples and numerous analyses, which are frequently used. The "frameworks" are used to generate the new submissions. The development was not easy as it had to take into account the structure of the LIMS. Nevertheless, the database being Oracle, it has been possible to develop such functionalities which make users save a lot of time. Another important specificity of the application relies in the connections with other tools. The following connections were set-up: • automatic data entry with IDM LimsLink5, • automatic creation of submissions for on-line analyses, • connection to the databases CataSepa and B-DEXP (cf. § 2.2), • connection to the ANALIMS application which generates statistics and quality indicators, using QlikView6, a Business Intelligence solution, • Business Objects module to request the LIMS database, especially for answering questions from the technical assistance. 2.2. Standard connections This section focuses on the generic connection between the LIMS and the databases CataSepa and B-DEXP. When a customer generates a submission, he can specify the database where the results have to be inserted, if any. The mechanism is based on an Oracle view, one per database where the results to be transferred are to be "stored". Every night, a batch is executed (one per client database). It inserts the results into the database. Information is then stored in a journal table in the LIMS database which is used as a filter to generate the view. 2.3. Use of the application The LIMS application is in use since mid-2003. It's now fully integrated in the daily work of about 600 persons. A high availability and reliability is therefore required. 4
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About 150 distinct users connect every day to the LIMS. Concerning the amount of managed data, the number of submissions in a week is quite stable – about 150 – but the number of analyses is increasing: roughly 800 per week in 2006, and 950 per week in 2007. In order to guarantee good performances, a distributed architecture had to be designed. Specifically, one machine is in charge of the LIMS database, one is in charge of the interactive application, another is in charge of the application dealing only with on-line analyses, and one is in charge of the batch printing system.
3. Catalyst and Process data management 3.1. Main functionalities and specificities CataSepa and B-DEXP are two Intranet applications which are used to store information on catalysts (preparation, or characterization) and test results (laboratory test results for CataSepa and pilot plants test results for B-DEXP). As several kinds of catalyses are studied within IFP (adsorbents, solvents, homogeneous catalyses, heterogeneous catalyses), and tests are conducted on different kinds of processes (FCC, HDT, Isomerisation, etc), the applications require a high level of flexibility (cf. 3.2). They allow each group of users: • to define all the key information to be collected and stored in the database, • to define calculus in order to calculate test results (selectivity, activity, etc). All these activities are conducted through configuration screens. No software development is required. Thus, it allows researchers to adapt quickly the application to any change in the way research is conducted. In order to automate data collection, those applications have been connected through generic links to: • iHistorian7 in order to import automatically sensor values • Chromatographic results (Galaxie8) and LIMS results in order to import analyses results (cf. §2.2) • Pilot Plant in order to create automatically tests (using information stored in the pilot plant controller). Moreover, specific modules have been developed in order to import/export tests results contained in Excel spreadsheets, and a connection between CataSepa and B-DEXP has been developed in order to be able to use information from one database in the other, especially for calculations and requests. To obtain such a flexible architecture, a specific Oracle structure has been designed and associated with a specific data base (Data Mart) in order to facilitate Queries (cf. 3.2), the connection of different kind of calculation tools was made available (cf. 3.3) and a standard framework was developed (cf. 3.4). 3.2. Conceptual foundations In order to obtain a flexible application, the data base structure is not usual. Each variable of the application is not stored as the column of a table but as rows of a specific table. Then, to add/delete a variable, it is only needed to add/suppress a row without any structure modification of the data base and then of the application. For example, the following variables are stored for homogeneous catalysis: • Molecular Formulation • Ionic Liquid used 7 8
www.gefanuc.com www.varianinc.com
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when the following variables are used for heterogeneous catalysis: • Calcination Temperature • Porous Volume • Mass and the following variables are defined for tests in heterogeneous catalysis: • Pressure (set points, mean value) • Temperature (set points, mean value) • Catalyst DRT • H2/HC • GC Results • Activites, Selectivites, Conversion All the variables are defined for each kind of catalyst, each kind of processes and each kind of application, by the users (who have the configuration profile) themselves. This architecture is very powerful for flexibility. However, it decreases drastically the possibilities to query the data base. A new data base dedicated to query had then to be developed. Tables are built dynamically (one table per analysis method, preparation method). Each variable is then one column. Each day, data is inserted in the datamart using PL/SQL scripts. This database is then classical and can be easily requested using conventional tools (Business Objects or MS Query). 3.3. Connecting calculation modules First of all, users wanted to be able to enter formulas which use data from the database and to store the results which are key variables very often used when requesting the database. A tool was developed to select variables and mathematical functions, to generate the JAVA classes in charge on the calculation (using JAVAcc library), and to create the variable containing the results and insert them in the database. Nevertheless, some calculations relying on others (100 formulas can be defined for one test), a preliminary treatment is organising the calculations. This tool is dedicated to simple calculations such as activities, selectivities, yields. In other cases, users mainly want to be able to connect existing Fortran or C++ codes. In this case, they can specify the input data, which is sent to an XML file used by the external code, which itself generates an XML file read by the application to create new variables which store the values in the database. 3.4. Standard framework In order to reduce development costs, a specific framework following J2EE Design Patterns has been developed in 2000 and used in all our Intranet applications. It is based on the design pattern MVC (Model View Controller). MVC encompasses more of the architecture of an application than is typical for a design pattern. The application is divided in three layers (Burbeck, 1992): • Model: The '''domain'''-specific representation of the information which the application operates. Domain logic adds meaning to raw data (e.g., selectivity, activity, etc). It uses a persistent storage mechanism (oracle DataBase) to store data. • View: Renders the model into a form suitable for interaction, typically a user interface element. Multiple views can exist for a single model for different purposes. • Controller: Processes and responds to events, typically user actions, and may invoke changes on the model. This module is similar to Struts and Barracuda frameworks but it implements functionalities dedicated to IFP:
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• Model layer uses BC4J components provided by Oracle (Muench, 2002). • View layer uses JSP pages and Oracle taglib provided by BC4J. • Traces (debug or log) are managed by the framework, as well as user management (login pages, password authentification), and security aspects for database queries. 3.5. Use of the applications CataSepa and B-DEXP are used daily since 2006 by about 200 people. Today, about 50 000 catalysts, 5000 tests, 9000 full experiments have been stored. The tools are used for conducting the experiments (for preliminary calculations, data validation) as well as for research (analysis of the data, models and correlations elaboration and validation).
4. Lessons learnt and conclusion In the past, the situation within the Institute was very heterogeneous. For some processes such as the Reforming process, specific databases were in operation, for others, each engineer had his own Excel files. Many applications were mastered by only one person and nobody else could make it evolve. Each of them being specific, many connection tools were developed in order to put the data in the correct form. Moreover, some data (and some formulas) were defined at different steps of the development cycle. The deployment of the new system solved those problems. Therefore, it increases the quality insurance and optimises the work of the process engineers. Nevertheless, it involved a lot of work from the different teams in order to define the common use of the data and to configure the applications. The deployment of such a system requires the involvement of everybody in the company, comprising decision makers. Deployed step by step, the system is now fully used in some departments and some configurations are going on in others. It looks very important to develop performing query tools. When dedicated Business Objects reports are made available, the users really benefit from the system and can answer quickly very accurate questions. In the future, it should be examined how data from the different databases can be exploited in order to develop new kinds of processes using existing data, thus minimising the number of tests to be conducted. Concerning the software aspects, the genericity created some constraints and difficulties. The data model is rather complex and generates complexity for the datamarts and for the calculations. So, a skilled team is required for the maintenance of the applications.
References R. Moore, 2000, Data Management Systems for Scientific Applications, IFIP conference, Volume 188, Pages 273-284 Kimber M., 2006, Choosing and Using a LIMS, Tessella Support Services PLC, Issue V1.R2.M1, http://www.tessella.com/literature/supplements/pdf/lims.pdf S. Burbeck, 1992, Applications Programming in Smalltalk-80(TM):How to use Model-ViewController (MVC), http://st-www.cs.uiuc.edu/users/smarch/st-docs/mvc.html Steve Muench, 2002, Simplifying J2EE and EJB Development with BC4J, http://www.oracle.com/technology/products/jdev/collateral/tutorials/903/j2ee_bc4j/prnt/j2ee_b c4j.html
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Rapid Process Design and Development of Complex Solution Copolymers Yadunandan L. Dara and Tahir I. Malikb a) ICI Applied Research, 10 Finderne Avenue, Bridgewater NJ 08807 USA b) ICI Applied Research, ICI Wilton Centre, Redcar, Cleveland TS10 4RF UK
Abstract: New, compositionally complex, Free Radical, solution co-Polymers (FRPs) are synthesized in our research laboratories to develop specialty materials with very specific and challenging combinations of product properties for advanced technology end applications. The co-polymer composition and polymer molecular weight distribution (MWD) are key factors in achieving the required properties and need to be reliably maintained in the scaled-up processes. We present significant developments involving use of thermodynamics, dynamic heat transfer, heat and mass balance models as well as polymerization kinetics models combined with selective experiments to rapidly progress to pilot and full scale production despite limited data. We also report development of a new, innovative, sparse matrix based representation for chain-length dependent polymerization kinetics that has potential to deliver rapid solutions without loss of detail for MWD. Future publications will elaborate each aspect further. Keywords: Solution Polymerization Modelling, Thermodynamics, Equation Based Dynamic Modelling, Scale-up, Batch processes
1. Introduction 1.1. The need for specialty co-polymers The design of specialty polymers is of significant interest to the specialty polymers industry. The requirements on product performance are rapidly evolving with simultaneous demands on material properties such as adhesion, permeability, strength, conductivity, rheology etc. One way to satisfy diverse requirements is through a controlled combination of several different monomers where each monomer introduces an element of desired functionality into the product. Free radical solution copolymerization is usually one of the most suitable processes to generate such materials, provided the monomers can be polymerized by this route via an industrially suitable process. A variety of monomers including acrylates, methacrylates, styrenics, and acrylonitrile have been used for this purpose (1). For example n-butyl acrylate (n-BA) is a commonly used monomer to lower copolymer glass transition temperature and modulus. Acrylonitrile (AN) has also been frequently used to tailor the glass transition temperature and bulk/ interfacial properties. The synthesis of n-BA and AN copolymers has been a topic of interest in the scientific literature for the last three decades (2-3). 1.2. Scale-up challenge A key criterion for good scale-up for solution polymerization is the ability to reproduce copolymer composition and MWD. This is challenging in an industrial setting because: • It is challenging to dose required amounts of minority reagents at small amounts/ rates repeatably and reproducibly across different scales.
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• Manufacturing/ pilot plant/ laboratory equipment configuration and operational philosophy are usually different. • Vapor-liquid phase compositions at different scales may vary due to piping and instrumentation difference that may lead to compositional and MWD variation. • The heat transfer system details e.g. type of jacket and utility fluids used will usually be different and may follow different control strategies and response times. • Mixing and related aspects of heat and mass transfer can vary significantly at different scales, especially for viscous systems. • Sufficient data to comprehensively characterize and model the system may be difficult to generate within the project scope and time scale It is critical to understand and address these and related issues to ensure successful scale-up and robust/ reliable manufacturing. 1.3. The role of CAPE Despite the usual scarcity of data, we advocate a systematic application of CAPE based methods with judicious approximations and use of selective experiments to gather essential data. ICI have a strong pedigree in the use of CAPE, (4-9) with respect to process and control aspects of reactive systems. We use combinations of models (thermodynamics, heat transfer, dynamic heat/ mass balances, reaction kinetics and MWD modeling) at different levels of approximation to gain sufficient insight on system behavior in order to rapidly progress process development and scale-up. For example, unusual and novel monomers are often used in small quantities to provide specific product functionality. When considering the overall system thermodynamics, it is sometimes feasible to lump these species with one of the (closest, more volatile) bulk monomers. This reduces the thermodynamic system complexity significantly while maintaining the ability to make reasonable predictions of properties of interest e.g. phase compositions and reflux conditions.
2. Thermodynamics for Batch Processes We use thermodynamics to study phase behavior at different reaction stages. For processes operating at reflux, it is essential to characterize the reflux conditions such as vapour/ liquid composition of the bubbling reactor, reflux temperature and expected latent heat of condensation. This analysis can provide estimates for reactor temperature as the batch composition evolves and predicts likely control and scale-up issues. Computational challenges arise if a large number of species are present due to the need to estimate binary interaction parameters (BIPs). For example, the reaction system described here comprised of 3-7 monomers with the bulk monomers being n-BA and AN. The Uniquac method was used to carry out vapour-liquid equilibrium (VLE) calculations with BIPs obtained from literature or existing databases and estimated from group contribution methods (Unifac). For species that comprise chemical groups not present in the Unifac database, experimental determination of BIPs is needed. However, in this case, all other monomers were heavier than n-BA and could be lumped with it, with good predictions of bubble and dew points. In addition to the bubble point temperature of the reactor, the bubble point of the vapour formed is of interest as the temperature where all non-inert species condense. Fig.1 shows condensation curves for different monomer to solvent ratios for this example. These are quite non-linear with a widely varying rate of condensation with temperature. The difference between the two temperatures is accentuated for the higher monomer fraction case in this example. Fig.2 shows a laboratory overhead temperature measurement as compared to the calculated bubble point of the vapour going through
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the condenser (solid line). The temperature measurement point is upstream of the condenser with the liquid drops falling back on it. Even though at the small scale the agreement is diverging, one would expect better agreement with a different measurement point and full condensation. Thus, the solid line is still the correct one for total condensation at the large scale. In this case, the weight average condensed temperature for the vapor and liquid phases (dashed line) gave a closer agreement with the experimental results. Overhead Temperature
1 0.8 0.6 0.4 0.2 0
Temperature oC
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Temperature C Bubble with 40% monomer
Fig.1 Condensation curves with monomer ratio
Expt.Ovhd.Temp
Model TBub of vapour
Wt.cond.temp.avg.
Fig.2 Reflux overhead temperature.
0.6
Temp. vs. % acetone replaced
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0 0 20 Batch End
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% acetone replaced by MEK
Thermodynamics helped to understand the changes that would arise when replacing the solvent (from acetone to Methyl Ethyl Ketone MEK) while polymerizing the system at reflux. Fig. 3 shows the impact of this for both near batch start and batch end conditions. As the overall monomer to solvent ratio has not changed, the difference between the two bubble points remains despite the switch to MEK but the absolute value increases, thus giving a higher boiling and condensing temperature with MEK, with consequential impact on reaction kinetics. The bottom two curves show the batch end conditions when the monomers have nearly depleted and hence the collapsing of the two bubble points on each other with the maximum difference occurring in the middle where the two solvents are in similar amounts. Fig.4 shows the change in vapour composition for batch start (top set of curves) and near batch end (bottom set of curves) for the two solvents and their mixtures. There is significant change in the total monomer obtained in the vapour phase between the two solvents at batch start.
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3. Heat Transfer and Dynamic Heat and Mass Balance Models. The approach advocated here is based on evolutionary development of a family of equation based dynamic models that allow the mechanistic detail to be increased as it becomes available and easy scale-up and mapping between the different equipment setups and recipies. Initially, even if the detailed kinetics are not available, these models can be run with assumed or estimated (from compositional measurements) individual monomer reaction rates. The heat transfer models can start at the level of assumption of a reasonable value of Overall Heat Transfer Coefficient (OHTC). As detailed information becomes available on batch viscosity profiles and other properties, these can be incorporated in correlations that estimate film coefficients both on the reactor and the utility sides. Then the OHTC is obtained from the individual contributions. Similarly, initially the overhead condenser may be modelled as being capable of just condensing all the non-inert vapour. This enables the capacity of the rest of the system to be determined assuming the condenser is sufficiently over-designed. However, if there are significant excess exotherms present, the condenser capacity may be stretched in part of the batch and an actual heat transfer model of the condenser will be required to assess the possible loss of vapour that may occur as a result. In terms of the utility system, there may be a need to include the utility circuit in the model, e.g. the oil circuit. The lag of the utility system depends on the thermal inertia inside it and thus its total size as well as the speed and response of the valves and the controllers. It is possible to superimpose controller and logic models on the open loop dynamic process models and see the impact on system stability. Both the open loop and closed control loop studies can be carried out with the system stretched to its limits, e.g. in terms of maximum throughput or shortest cycle time. Finally, equation-based models also provide a point for integration with procedure based models. The thermodynamic models can be called from the equation based models, as can the comprehensive kinetic and MWD models, to provide an integrated and holistic view. This level of integration is appropriate once the process has been settled and even further optimisation is required.
4. Kinetic and MWD modelling There are a range of complex kinetic events during the synthesis of FRPs. The system density and viscosity change with increasing conversion, and in turn affect transport properties and reaction kinetics. These changes depend both on polymer concentration as well as chain length distribution (CLD). The modelling of CLD and related MWD is not a trivial matter and full treatment leads to an unrealistic number of equations in the model. Therefore simplifying approaches are employed e.g. method of Moments, use of Galerkin methods and other approximations (10-12). The new approach described here is directed towards explicit consideration of chain length effects on kinetic parameters and developing an exact numerical solution to the problem, while allowing for the application of suitable computation techniques that reduce the time and effort needed for simulation. This approach is based on a novel sparse matrix (13) representation of the polymerization kinetics. This representation can be subjected to sparse matrix manipulation techniques like partitioning and tearing to reduce solution effort and time (14-19). These techniques use concepts from graph theory to model information flows in large systems of equations. We report an innovative way to specify the polymerisation equations for facilitating easy implementation and fast solution. The derived equations for the homopolymerisation case are shown here where, [I] is the initiator concentration (mol.L-1),
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[M] is the monomer concentration (mol.L-1), [R]is the primary initiator radical concentration (mol.L-1), [P1] is the primary polymer radical concentration (mol.L-1), [Pn] is the concentration of polymer radicals of length n (mol.L-1), [Dn] is the concentration of dead polymer molecules of length n (mol.L-1), [M0] is the initial monomer concentration (mol.L-1), x is conversion, V0 is the initial volume (L), V is the volume (L), Vsolvent is the volume of solvent (L), ε is the relative change in density as defined in Eq. 9, β is the relative fraction of solvent defined in Eq. 10, fs is the fraction of solvent volume defined in Eq. 11, ρp is the polymer density (g.cm-3), ρm is the monomer density (g.cm-3), kp is the propagation rate constant (L.mol-1.sec-1), ktc is the rate constant for termination by combination (L.mol-1.sec-1), ktd is the rate constant for termination by disproportionation (L.mol-1.sec-1), kt is the rate constant for termination (combination and disproportionation) (L.mol-1.sec-1), and kd is the rate constant for initiation (sec-1). Equations (1)-(11) can be converted to a set of four mass-balance vector ODEs (Equations (12)-(15)) after some manipulation. The assembly of matrices used in these equations can completely address the kinetics of free radical polymerization and can then be implemented on a computer using relatively straightforward matrix manipulations. Chain transfer, copolymer formation, and any other side reactions can also be added as separate terms to Equation (12)-(15) when applicable. All symbols used are the same as in Equations (1)-(11), except λo, which is the sum of the concentrations of all polymer radicals of all chain lengths. The one and two dimensional matrices used are compilations from the equation terms and have been described in reference 13. d[I ] εkp (1 − x)λ 0 ½ = ®− kd + ¾[ I ] dt (1 − εx + β ) ¿ Eq.12 ¯
1 d([I]V) = - k d [I] Eq.1 V dt 1 d([M]V) = - k p [M]P Eq.2 dt V
dx = kp (1 − x)λ 0 Eq.13 dt
1 d([R]V) = 2 fk d [I] - k t [R][M] Eq.3 dt V
T d [ P] εkp (1 − x)λ 0 [ P] = A ⋅ [ P *] − (ktd + ktc ) P ⋅ I n,1 ⋅ [ P] + dt (1 − εx + β )
1 d([ P1 ]) = k i [R][M] - k p [M] - k t [ P1 ]P Eq.4 dt V
Eq.14
Eq.5 1 d([ P n ]V) = k p [M](([ P n -1 ]) - [ P n ]) - k t ([ P n ])P V dt 1 1 d([ Dn ]V) 1 = k td [ P n ]P + k tc Σnm-=1 [ P m ][ P n ] Eq.6 dt 2 V x=
ε=
(ρ
p
[M]0 Vo - [M]V Eq.7 [M]0 V0
− ρ m ) Eq.9
ρp
β =
fs
(1 − f s )
V=
Eq.10
εkp(1 − x)λ 0 d [ D] = ktd Q ⋅ I 1, n ⋅ [ P ] + ktc ⋅ C ⋅ [ P] + [ D] dt (1 − εx + β ) Eq.15
V0 (1 - εx + β ) Eq.8 (1 + β ) fs =
Vsolvent V0
Eq.11
Most of the matrices used here are one-dimensional and require minimum computing resources for both storage and processing. Bottlenecks in computation will mainly arise from handling the larger two-dimensional matrices, A and C, which are both sparse matrices. Matrix A is a predominantly block diagonal matrix and has very low occupancy (< 1 % for n > 200, < 0.01 % for n> 20,000) whereas matrix C has an average occupancy of 0.25, for all n, where n is the number of species in the system. These equations can be solved on a platform that facilitates vector or parallel solution
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techniques, along with a suitable numerical algorithm and methods for the utilization of sparse matrix techniques. The simulation can be easily set up and carried out on a standard desktop using a variety of computational environments e.g. it was successfully implemented in MATLAB (13). Future publications will give more details of results and extension to complex polymers.
4. Conclusion A practical methodology is presented, which combines traditional chemistry and process development approaches with insights from CAPE based models. This approach has been used for rapid, reliable and reproducible scale-up of complex solution polymers while keeping within equipment, manpower and time constraints. It is suggested that eliminating large changes during the batch in temperature, free monomer concentration and reaction rates is important for reliable scale-up. This can be achieved by changing temperature and addition profiles for the reagents or using subreflux vs. reflux processes based on equipment limitations and process requirements. Thermodynamic studies can help identify the right solvent for the ideal temperature regime required for favourable kinetics. Good and fast kinetic models that retain detailed MWD information are required and a matrix based representation is presented that has potential to provide rapid solutions through exploitation of sparsity. In addition to the above observations, complex polymer innovation and process technology development requires excellent interaction between chemists, engineers, R&D staff, business personnel and CAPE experts.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
G. Odian, “Principles of Polymerization”, 4th ed, 2004, Wiley, New York C. Zhang, Z. Du, H. Li, E. Ruckenstein, Polymer, 2002, 43(20), 5391. C. Tang, T. Kowalewski, and K. Matyjaszewski, Macromolecules, 2003, 36(5), 1465. S. Garlick, T. I. Malik, and M. J. Tyrrell, Comp. Chem. Eng., 1994, 18. Suppl., s493. M. James, T.I. Malik and J.D.Perkins, “The Introduction of Speedup into ICI” , PSE’91 Montebello, Canada, 1991. S. N. Collins, M. Falgowski and T. I. Malik, Comp. Chem. Eng., 1997, 21 Suppl., s911. S. P. Walsh, S. Chenery, P. Owen and T. I. Malik, Comp. Chem. Eng., 1997, 21 Suppl., s391. T. I. Malik and L. Puigjaner, “Batch User Needs & Specialties Chemical Processes”, in Software architectures and tools for CAPE, 2003, Elsevier, London. S. J. Sweetman, C. D. Immanuel, T. I. Malik, S. Emmett, and N. Williams, Macromol. Symp., 2006, 243, 159. N. A. Dotson, R. Galvan, R. L. Laurence, M. Tirrell, “Polymerization Process Modeling”, 1996, VCH Publishers, New York, NY. K-D. Hungenberg, U. Nieken, K. Zollner, J. Gao, and A. Szekely, Ind. Eng. Chem. Res., 2005, 44 (8), 2518. R. D. Skeirik, E. A. Grulke, Chem. Eng. Sci., 1985, 40, 535. Y. L. Dar, Ph.D. thesis, 1999, Dept. Chem. Eng., Mich. Tech. Univ., Houghton MI. D. M. Himmelblau, Chem. Eng. Sci., 1966, 21, 425. R. E. Tarjan, SIAM J. Comput., 1972, 1, 146. D. V. Steward, J. SIAM Numer. Anal. (B), 1965, 2, 345. B. W. Kernighan, S. Lin, Bell Syst. Tech. J., 1970, 49, 291. J. W. H. Liu, ACM Trans. Math. Soft., 1989, 15, 196. A. Pothen, C. J. Fan, ACM Trans. Math. Soft., 1990, 16, 303.
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Troubleshooting and process optimisation by integrating CAPE tools and Six Sigma methodology Dr. Guido Dünnebier Bayer Technology Services GmbH, Advanced Process Control, 51368 Leverkusen, Germany
Abstract The application of state-of-the-art process systems engineering technologies like simulation and optimisation for small scale (life science) processes is limited. The limitation due to the cost-benefit ratio is particularily high when attempting to optimise process operation, in comparison to process design topics. There is an enormous potential for process systems engineering in the life science area though, since a larger number of smaller improvements is resulting in an enormous economic impact. SixSigma is an established methodology supporting process improvements which originated from american manufacturing industries with a strong focus on statistical methods. It is problem oriented, identifies causes for (operational) problems based on statistical data and economic drivers, and is open to the use of any suitable tool to solve the problems identified. This contribution discusses the special requirements of process industries and some useful extensions of the Six Sigma toolbox, like establishing multi-variate statistical methods as a standard tool in the Six Sigmal toolbox, and also shows how the identification and priorisation of problems leads to the application of CAPE tools in areas where otherwise the hurdle for their application would have been to high. This is being illustrated using an industrial example from a biotechnological production of pharmaceutical, where the original project scope to stabilise product yield and impurities led to applying advanced control, dynamic simulation and dynamic optimisation in addition to the “low hanging fruits” being related to, e.g., improvements of manual process steps. Keywords: Process Operations, Dynamic Simulation, Biotechnology, Six Sigma.
1. Introduction The application of state-of-the-art process systems engineering tools like simulation and optimisation tools for small scale (life science) processes is limited. Even though some areas like scheduling even originated in this sector, most of the model-based methodologies orginating from large scale processes (like refinery, petrochemicals, ..) are by far less often economically applied in small (batch) production units. This is, amongst others, due to the fact that these processes have a different cost-benefit ratio and the processes are more numerous and different in the technologies applied. Commercial modeling, optimization and control technology is dedicated to “classical” gas-liquid processes, whilst the applicability and maturity is limited for life-science processes, including, e.g. solids or biological processes. The limitation due to the costbenefit ratio is particularily high when attempting to optimise process operation, in comparison to process design topics. There is an enormous potential for process systems engineering in the life science area though due to the large number of processes present. A potentially large number of
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smaller improvements is then resulting in an enormous economic impact. There is, on one hand, a significant research need to adapt the well-know techniques for chemical and petrochemical processes to small scale life science processes, delivering customized solutions for batch processes, small scale production and multipurpose plants. On the other hand, the community needs to exploit new workflows to identify the fewer and less obvious opportunities where current tools can well support process improvements in particular in process operations. This contribution will give a brief introduction in the SixSigma process improvement methodology in the next section, followed by an general introduction of potential applications and an illustrative example of yield optimisation for a biotechnological API (Active Pharmeceutical Ingredient) production in section 3.
2. Six Sigma Process Improvement Six Sigma is a formalised concept initiated in 1987 by Motorola. It combines project philosophy and cost control with proven methods derived from quality and project management and industrial statistics. Six Sigma is an initiative that aims to reduce errors with a view to improving efficiency. The Six Sigma philosophy is divided into a guideline (or philosophy) for project management, including the commitment of the entire hierarchy and a toolbox of (well known) statistical tools to support process anlysis and data driven decision making. Six Sigma can also be applied solely as a project philosophy, particularly when the commitment to the project goal is already forced by economic needs, and no prejudices exist that could hinder an project approach where the technical solution is not known at the start of the project. The project management philosophy enforces four distinct project phases: 1. Define (D): After identifying a relevant project on the basis of its economic potential in the preproject phase, the project goal is specified in this phase (expressed in expected savings), along with nomination of the project team and a time horizon of usually less than a year. The goalt is usually determined by a reduction of process variation towards a stable operation along the demonstrated best practise. Exact limitation of the project is also important if the achievement of success within the stipulated time is to be a realistic possibility (“don’t boil the ocean!”). 2. Measure (M): The characteristics (e.g. measurements existing or to be introduced) that are relevant to the process in terms of the project goal are defined in the Measure phase and process data is to be collected and its accuracy to be quantified. All decisions are to be based on process data! 3. Analyze (A): Here, an effort is made to locate root causes for for process variation to be reduced to achieve the required quality characteristics (project goal). The effectiveness of current process control and at whichever ı level one is as a result is determined from the measurements. Result of this phase is also a list of potential improvements ranked by their impact on the project goal. 4. Improve (I): Modifications are realised in this phase that improve an existing process and, consequently, lead to a higher ı level. These include finding optimum settings, their realisation and the subsequent verification of process improvements. Systematic experiments (statistical test planning) enable quantifying of the effects of the most
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important process variables; a model is created and improved settings are determined. 5. Control (C): While success is determined in a typical project on the basis of realisation of process changes, Six Sigma also includes a Control phase. It is not only relevant that the process has been raised to a higher ı level but remains there. This ensures that the effects of improvements are sustained and an improved process does not drop back . This also aids identification of further improvement potential which can be exploited or lead to new projects. Beside the tools from industrial statistics listed in standard SixSigma handbooks, several tools developed and applied by the CAPE community well fit in this framework when applied to chemical processes. The Six Sigma module principally contains classic statistical methods that originate from a limited number of process variables and, moreover, are only conditionally applicable for strongly correlated variables (e.g. single and multiple regression). Multi-variant methods such as PCA (Principal Components Analysis) and PLS (Partial Least Squares) certainly offer a practical addition in this respect, as they are not only capable of practical processing of correlations, but also provide valuable assistance during data analysis where numerous process variables are involved. The CAPE community also employs non-statistical methods which can be utilised in Six Sigma projects. In the case of a continuous process with redundant measurements, information on the accuracy of individual process variables can be gained from mass and energy balances over stationary periods of time using data reconciliation Rigorous process models can generally provide useful service when determining whether the operating status, plant utilisation or use of individual plant components lie within the boundaries of design constraints. In the event of sufficient analogies being detected between the experimental results for the plant and the model simulation, an attempt can also be made to simulate fully-factorial test plans with many factors and factor levels (i.e. an enormous number of “experiments”) and conclusions drawn from this. More details on the application of SixSigma methodology in the process industry can be found in Bamberg et al. (2007) and NAMUR (2007). This formal procedure and the tools included within can be applied to any type of process, from discrete manufacturing to business and support processes. It has proven to be very efficient in application where the exact technical solutions are not known beforehand, or when a prioritization between different (potentially costly) technical solutions is not straightforward. To the authors experience, these criteria hold for optimisation of batch process operation, in particular for small scale processes and/or multipurpose plants. The next section illustrates this using an industrial example.
3. Applications 3.1. General Scope of industrial applications The industrial applications for troubleshooting of existing batch processes using CAPE technologies can be distinguished into two mayor groups: 1. Improve / Reduce variation of throughput / cycle times / capacity. This is the classical debottlenecking problem where logistic simulation, scheduling and mixed integer optimisation technologies are applied.
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2. Variation in quality parameters like impurities or yield. Here mainly data driven technologies like multivariate statistical analysis are usually applied. The SixSigma methodology is a selection of choice for both groups, since it can be applied if an economically significant variation with unknown root causes appears. It then helps to identify the mayor candidates for potential root causes, prioritize the further actions using the process data and also motivate the application of classical cape tools. First principle modelling is seldom applied for these problems at the first stage since the implementation costs, in particular when physical and chemical property data are scarce, and the building of an expensive model can only be justified economically at a later stage (e.g. after the economical potential of a particular process improvement has be quantified in the course of a SixSigma project). To illustrate the broad range of potential application, [Klatt, 2007] presented a list of industrial problems from the area of optimisaton of batch process operation from his or his coworkes experience, some of the technologis applied to solve them (without claiming the lists completeness): 1. Improve cycle times and quality for a batch process with solids and raw materials from natural ressources. The problem has been solved by two parallel activities, one using data driven (statistical modelling) leading to a quick implementation, and the other establishing a first principle process model and at a later stage joining these two models. 2. Yield improvement of a chemical API The problem had been solved by purely data driven (statistical modelling) methods. The improvements implemented concentrated on minor technical modifications of the plant and some manual operational steps. 3. Improve cycle times and quality of multipurpose (Semi)Batch polymer plants Usually first principle models are not economically feasible in this context, therefore often no systematic optimisation and advacned control, or approaches on a purely data driven basis. 4. Cycle time optimisation for a batch destillation with a reaction. Since reaction kinetics are only partially known, only a combination of data driven and first principle models (including several experiments) can be applied. 5. Monitoring of the continuous perfusion fermentors for Kogenate production. Early detection of unnormal operating conditions using dynamic statistical control charts. This is just another illustration of the need of tailormade extended statistical tools for industrial applications in this area. [Warncke, 2007] The next section describes the yield optimisation for a biotechnological API production in more detail. 3.2. Biotechnological API production Biotechnological API (Active Pharmaceutical Ingredient)-processes are often characterised by variation in product yield and impurity levels in fermentation, and varying product yield (and potential impurity excursions) in purification, whilst manufacturing costs tend to be significantly higher than comparable chemical API’s. The reduction of this yield and impurity variation and a quantification of the resin condition in the chromatographic separation where defined as project goals in the definition phase of this extensive SixSigma improvement project at Bayer Healthcare. Subject of the investigation where both the fed batch fermentation for the production of the API and the purification section including, amongst others, several chromatographic steps. To identify the root causes for the existing process variation in yield and
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impurities, several statistical tools including multivariate statistics (PCA / PLS) based on all available process data from various sources have been used (see figure 1).
Figure 1: PLS Analysis of process data
The most crucial step in the course of the project was the formulation of process engineering based hypothetical cause-relationships based on the results of the statistical anylsis. These have been developed by combining the statistical results with the experience and sound background knowledge from both production and development.
Figure 2: pO2 variation before introduction of control concept
These hypotheses have then, as far as possible, been verified in plant trials and in parallel or in sequence improvements in the production process have then been proposed. Of those, most could be implemented within the current license. Some of these have been of relative simple technical or organisational complexity, but some of them included the usage of advanced control and simulation technologies. The first project included the implementation of an advancd control concept for the dissolved
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oxygen in the fermentor (Figure 2 shows the variation in this process variable during the previous uncontrolled operation), the second the optimisation of online analyzers to improve the control of the fractionating points during chromatographic separatin (see figure 3, the variation in fractionation time) and the third the use of a dynamic process model and dynamic optimisation to improve the feeding profile during fed batch operation and another one the implementation of statistical process control to monitor the resin quality of several crucial chromatographic columns. The project delivered two mayor beneits: The primary goal was the yield improvement by reducing variation within the process leading to payback times of less than a year, and the second was the, in particular for an established process, significant insight gained during the project.
Concentration
Fractionation
Time Figure 3: Concentration profile during chromatographic separation
4. Summary and Conclusions After introdroducing the SixSigma concept, this contribution motivates how the identification and priorisation of problems leads to the application of CAPE tools in areas where otherwise the hurdle for their application would have been to high. This is being illustrated using an industrial example from a biotechnological production of an API, where the original project scope to stabilise product yield and impurities led to applying advanced control, dynamic simulation and dynamic optimisation in addition to the “low hanging fruits” being related to, e.g., improvements of manual process steps. To further enforce the implementation of classical CAPE technologies to flexible multipurpose plants, research effert is required to facilitate its use also in case of the unfavourable cost-benefit relationship.
References A. Bamberg, G. Dünnebier, C. Jaeckle, S. Krämer, J. Lamers, U. Piechottka, 2007, “Six Sigma in der Prozessindustrie”, atp Automatisierungstechnische Praxis, 49(1), p. 42-50 K.U. Klatt, 2007, Presentation on GVC Fachausschuss “Prozess und Anlagentechnik” NAMUR, 2007, “Six Sigma in Process Industries”, NA119, www.namur.de M. Warncke, 2007, Dynamic Control Charts for Monitoring Fermentation Processes, BPI Analytical and Quality Summit, San Diego, CA
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A Compliance Management System for the Pharmaceutical Industry Julie Fishera, Arantza Aldeaa, René Bañares-Alcántarab a
School of Technology, Oxford Brookes University, OX33 1HX Oxford, UK Department of Engineering Science, University of Oxford,OX1 3PJ, UK
b
Abstract The management of compliance with rules, policies, guidelines, practices, and standards is largely done through a manual and labour-intensive process. This process can be facilitated through the use of a computer-based Compliance Management System (CMS). A CMS identifies compliance tasks, tracks the performance of these tasks with respect to a set of requirements and documents their compliance status. The output from a CMS can be used to satisfy a variety of reporting requirements and initiate alerting mechanisms. A CMS can be particularly useful in managing regulation change and overlap. This paper presents the first step in the development of a decision and compliance management tool, in particular, a prototype CMS for the pharmaceutical industry is described. The CMS has been tested with a simulated case study. Keywords: Compliance Management, Regulation, Information System, Pharmaceutical Industry.
1. Introduction The regulatory authorities are empowered to issue and enforce regulations for the manufacture of pharmaceutical products with the aim to strike a balance between the therapeutic advantages of a drug and its possible risks to the patients. The regulatory authorities approve the sale of only those drugs produced with manufacturing processes that comply with the regulations. As a result, individual pharmaceutical companies produce a set of internal guidelines, rules, and policies to implement the regulation imposed by the regulatory authorities. The development and maintenance of these internal guidelines, rules and policies is an arduous and tedious process that requires substantial human resources. To begin with, the regulations must be interpreted to make them applicable to a specific manufacturing process. However, quite often regulations are vague, subjective and ambiguous, and thus with the potential to produce inconsistencies. A second complication is that there are national and international regulations, and products and processes must comply with all regulations of the places where they are produced and sold. Lastly, regulations change in time and companies must update their procedures accordingly. The process of interpretation finishes when all the regulations have been translated into a set of tasks to be performed with a given frequency and by individuals with specific roles. A Compliance Management System can be used to keep track of these tasks. A CMS identifies compliance tasks, tracks the performance of these tasks and documents their compliance status; the output can be used to satisfy a variety of reporting requirements and initiate alerting mechanisms.
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This paper describes the initial approach in the development of a CMS for the pharmaceutical industry. The case study is built around rules regulating pharmaceutical production; however, the purpose of this research is more general: to create a domain independent CMS that operates for different regulations retrieved from a library. The principles of this research are applicable to any other regulated activity such as trading, construction, and industrial SHE (Safety, Health and Environmental) compliance. The CMS under development consists of a MySQL database that stores the information related to the compliance tasks and a JAVA front end that displays the data and interacts with the different users. XML (eXtensible Markup Language) will be used in the future so the CMS can communicate with other applications. Specifically, XML will be used to store the tasks to be read by the CMS and the reports it generates. The generic features of a Compliance Management System are described in the next section. Section 3 focuses on the pharmaceutical industry and how a CMS can help to cope with the regulations imposed in this domain. The implementation of our CMS for the pharmaceutical industry is described in Section 4 and the preliminary results with a test case are presented. The future steps in our research are discussed in Section 5.
2. Compliance Management Systems A Compliance Management System (CMS) should be able to identify compliance tasks, track their performance and document their compliance status; its output being amenable to be used to satisfy a variety of reporting requirements [Boland 06]. Science based industries are increasingly using CMSs because competitive and regulatory pressures push them to consider the role that automation can play in converting data to useful knowledge [Conley 00]. The number of regulations with which companies have to conform nowadays is so vast that automating their compliance is a natural progression. There are three main components in a basic CMS: a library of applicable requirements, another library of tasks created to meet those requirements, and a set of means to administer status reporting and record keeping. Tasks can be defined in terms of a vocabulary of actions (e.g. monitor, collect, perform, review, document, verify) applied to objects (e.g. materials, equipments, reports) at a required frequency (e.g. once, daily, weekly) done by an individual with a role (e.g. technician, process engineer, plant manager). Compliance with a regulation can be assessed in terms of “checkpoints” [Yip et al. 06]. Other types of information are goals/intentions and criteria, which are necessary to evaluate task compliance [Boland 06]. Additional CMS features are e-mail notification, escalation and recurring tasks. An e-mail notification system sends e-mails to the employees due to carry out the tasks prior to the due date, whereas an escalation system sends additional warning e-mails to the employee’s supervisors when a task is either overdue or has failed. [Conley 00] looked at automating regulatory compliance, focusing on the NuGenesis Scientific Data Management System, when the acceptance of electronic record keeping was relatively new to the Food and Drug Administration (FDA). NuGenesis does not appear to store information about regulations and their associated data, and so does not have the functionality to notify when these regulations are due to be carried out. [Yip et al. 06] presented XISSF, an XML-based compliance audit system that enforces rules
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and information security policies. However, many of the functions associated to a CMS, such as describing a regulation in terms of tasks and roles, are not included. [Boland 06] investigated how CMSs aid business and compared the features of some commercial available CMSs in the market. The common features of all those systems are e-mail notification and escalation. Many of the commercial CMSs do not appear to be business specific; however there are some expressly aimed at the pharmaceutical industry. For example EtQ for Pharmaceuticals/Biotechnology (see www.etq.com), which is an integrated FDA CMS. This system includes several modules, allowing to tailor its application to a company’s needs, e.g. for archiving, escalation/delegation and monitoring. The EtQ system is aimed for companies that want to put their products in the American market.
3. A CMS for the Pharmaceutical Industry An important concern in the pharmaceutical industry is the large volume of regulations and their constant update. The regulations need to be analysed and validated to create a set of task, rules and procedures. 3.1. Regulations in the Pharmaceutical Industry All licensed medication put onto the market has to comply with a regulatory body to ensure it is effective and safe. It is essential for any company that all the criteria imposed by the regulatory body are met, as a rejection of the application can be very costly. However, regulation does not end after the approval of the manufacturing process; there is a continuous monitoring of the medication during its market lifetime. The most important regulatory bodies for the UK are MHRA (Medicines and Healthcare products Regulatory Agency) at the UK level, EMEA (European Agency for the Evaluation of Medicinal Products) at the EU level, and FDA (Food and Drug Administration) for the American market. Each regulatory body provides a number of principles and guidelines such as GMP (Good Manufacturing Practice) and GLP (Good Laboratory Practice). These are written at an abstract level and their aim is to provide guidance to the company. To aid in the management of the large volume of guidelines there are books that collate all the relevant information, e.g. Rules and Guidance for Pharmaceutical Manufacturers and Distributors 2007 [Pharma Press 02], commonly referred to as the “orange guide”. The orange guide is produced in association with MHRA and has all the guidance required for a company wanting to sell their products in the UK or EU. There are also books that aid in the compliance with the FDA guidelines, e.g. Pharmaceutical Master Validation Plan [Haider 01] and Validation Standard Operating Procedures [Haider 06]. The first book describes how a pharmaceutical company can put together a compressive plan to achieve the validation requirements, while the second looks into every aspect of validation for each of the guidelines. Our aim is to create a tool that facilitates the validation process and hence the translation of the regulations imposed by the regulatory bodies into a specific set of tasks. The CMS is used to manage the tasks and the people involved in them. This paper focuses on the first part of a prototype.
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3.2. Requirements for a CMS The CMS must be able to track the performance of compliance tasks and document their status; notification of pending tasks and an escalation process to flag overdue tasks are also required. To make the system more robust a regulation should be associated with a role rather than a specific employee. The quantity of data that a CMS is required to manage is large and must be preserved accurately, ensuring that only those with the appropriate permission access it. Easy and quick access to data is also desirable. Lastly, the system must be able to create accounts for users with different levels of access and functionality. No prior knowledge of the underlying software technologies should be expected of the users, who will interact with the CMS using a Graphical User Interface (GUI). This GUI needs to be simple and convenient for the user.
4. Implementation and Initial Results The CMS has been developed in JAVA and all the information about tasks, regulations and personnel was stored in a MySQL database. A JAVA GUI was also developed to facilitate the introduction of all the information and the communication with each one of the operators. More details about the system can be found in [Fisher 07]. Once the company has identified the set of task required to comply with the regulations, those tasks and regulations must be introduced in the CMS. At the moment the tasks are introduced manually through the CMS GUI (see Figure 1). In the near future we are planning to introduce a connection between the output of a validation process tool based on an organisational memory system (OMS) and the CMS. When a regulation is entered, the type of personnel that will be in charge of the regulation must be identified as well as the domain. After a regulation is successfully introduced into the database, the CMS asks the user to input the associated tasks and displays the ADD TASK panel (see Figure 1). By declaring tasks consecutively the user can ensure that prerequisite tasks are entered previously. If there are concurrent users adding regulations and associated tasks at the same time, the system is able to cope by storing the IDs of the regulation or task that has just been created to be used in the creation of subsequent tasks.
Figure 1. Windows used to enter regulations and their associated tasks.
A Compliance Management System for the Pharmaceutical Industry
Figure 2a. Customised “To Do” list for an employee. supervisor when tasks are overdue.
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2b. Warning sent to the
Tasks can be assigned to employees by the manager, and the employees will have then access to a window that lists all the tasks that need to be completed as shown in Figure 2. The CMS keeps track of all the tasks and their assigned employees and will make sure that all the tasks are completed on time by highlighting the pending tasks and sending regular emails to the employees (see Figure 2a). If the employee does not carry out a task, a report is generated and the corresponding line manager will be informed (see Figure 2b). To showcase the CMS some information was created for a small fictitious company, e.g. there are employees in three different roles (administrators, supervisors and analysts). Examples of regulations were taken from Chapter 18 of [Haider 2001] “Qualification of Process Equipment”. Figure 3. Example results written after performing some verification tasks.
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In particular, the regulation in the example applies to a Commuting Mill process, with each of its functions split into tasks. No frequencies for carrying out the tasks are suggested in the guidelines, as they depend on the manufacturer’s manual for the machine; weekly tasks were set for this example. With further knowledge about the machine, such as its calibration system or details about its workings, the tasks could have been made more specific. The interface developed to introduce the results from the tasks is shown in Figure 3.
5. Conclusions and Future Work This paper has presented the initial results in the development of a CMS for the pharmaceutical industry. The CMS has been tested with a case study built around rules regulating pharmaceutical production. The purpose of this research is more general: to create a domain independent CMS as the principles of this research are applicable to any other regulated activity. We are investigating the creation of a support decision making tool based in Compendium [Shum et al. 06]. Given a set of regulations and guidelines, this tool will support a quality assurance expert to parse those regulations (also policies, rules and procedures) into tasks that need to be performed to comply with the regulations. These tasks will then be saved in a XML ontology and incorporated in the CMS system; XML will be the communication language with other applications. Specifically, XML will be used to store the tasks to be read by the CMS and the reports it generates.
References Boland, R. 2006. Reduce business risk with a CMS. Chemical Engineering Progress 102 (10), pp. 39-44. Conley, J. 2000. Automating regulatory compliance. Scientific Computing and Instrumentation 17(3), pp. 25-26. Fisher, L. 2007. Development of a Compliance Management System for the Pharmaceutical Industry. MSc dissertation in Computing. Oxford-Brookes University Haider, S. I. 2001. Pharmaceutical Master Validation Plan: The Ultimate Guide to FDA, GMP, and GLP Compliance. Florida: CRC Press LLC, pp. 1-3 and 115-146. Haider, S. I. 2006. Validation standard operating procedures: a step-by-step guide for achieving compliance in the pharmaceutical, medical device, and biotech industries. 2nd ed. Florida: CRC Press LLC, pp.3-18. Pharmaceutical Press. 2007. Rules and Guidance for Pharmaceutical Manufacturers and Distributors. 2007 ed. London: Pharmaceutical Press, pp. xvii-8. Shum, S. J. B., Selvin, A. M., Sierhuis, M., Conklin, J., Haley, C. B. and Nuseibeh, B. 2006. Hypermedia Support for Argumentation-Based Rationale: 15 Years on from gIBIS and QOC. In: Dutoit, A.H., McCall, R., Mistrik, I. and Paech, B. (eds.) Rationale Management in Software Engineering. Berlin: Springer, pp. 111-132. Yip, F., Ray, P. and Paramesh, N. 2006. Enforcing Business Rules and Information Security Policies through Compliance Audits; XISSF - A Compliance Specification Mechanism. In: The First IEEE/IFIP International Workshop on Business-Driven IT Management (BDIM 2006)- Information Technology Management from a Business Perspective. pp. 81-90
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Business Process Model for Knowledge Management in Plant Maintenance Tetsuo Fuchino,a Yukiyasu Shimada,b Masazumi Miyazawa,c Yuji Nakad a
Tokyo Institute of Technology, Tokyo, 152-8552, Japan National Institute of Occupational Safety and Health, Tokyo, 204-0024, Japan c Mitsubishi Chemical Corporation, Kurashiki, 712-8054, Japan d Tokyo Institute of Technology, Yokohama, 226-8503 , Japan b
Abstract The physical state of chemical plants changes with deterioration. The mechanism of deterioration is very complicated and its occurrence and progress speed can not be measured during operation directly. Thus, the maintenance is planned based on the presumption, and the information acquired from inspection and repair is integrated into knowledge in the from of technological standard. This knowledge represents the presumption, and consistency between the technological standard and the results of inspection and repair decides the safety of the plant. In this study, a business process model for knowledge management in plant maintenance is developed, and the system requirement for knowledge management supporting environment is defined. Keywords: business process model, plant maintenance, knowledge management.
1. Introduction The plant maintenance aims at restoring the plant which is deteriorated with operation to a desired condition for its safety operation. Therefore, the plant maintenance plays an important role for the life-cycle safety, and proper integrity is required. However, the mechanism of deterioration in chemical plants is very complicated, and its occurrence and progress speed can not be measured directly during operation, generally. Thus, the plant maintenance is carried out by using so called PDCA (Plan, Do, Check, Action) cycle, i.e. the presumption against occurrence and progress speed of deterioration is applied in planning of maintenance, the inspection verifies the presumption, and repair is planed and executed on the basis of further presumption. On the other hand, there exist huge number of equipment items and pipes to be maintained in a chemical plant, and it is required to maintain them exhaustively and effectively. To satisfy these opposing necessary conditions, the trend of deterioration captured by inspection of equipment units for many years is integrated into knowledge such as causality of deterioration occurrence and progress speed, residual life expectation and so on, and the knowledge is put in the form of technological standard to be applied for the presumption against occurrence and speed of deterioration. Accuracy of the presumption, which effects on safety in operation, greatly depends on the consistency between the technological standard and the results of inspection and repair. However, the technological standard provision form the results of inspection and repair is carried out implicitly, and system requirement for knowledge management in plant maintenance can not be specified properly. The inconsistency between the technological standard and the plant actual state possibly causes serious problem in the lifecycle. In this study, business process model for knowledge management in plant maintenance is developed under the cooperation of plant maintenance experts in
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chemical industries in Japan, and IDEF0 (Integration Definition for Function) model [1] to integrate maintenance information into knowledge and technological standard is provided. The system requirement for knowledge management supporting environment in plant maintenance is specified. We have already proposed a business process model for plant maintenance [2], which defined activity from planning to execution of plant maintenance by using IDEF0 model. The proposing business process model here becomes an upper model of the previous one, so that from the lifecycle engineering viewpoint, the previous IDEF0 activity model is extended to include the knowledge management.
2. IDEF0 Activity Model for Lifecycle Engineering In IDEF0 activity model, the rectangle represents activity, and the arrows describe information. The information is classified into four categories; i.e., 'Input' to be changed by the activity, 'Control' to constraint the activity, 'Output' to be results of the activity and 'Mechanism' to be resources for the activity. The 'Input', 'Control' and 'Mechanism' are fed to left side, top and bottom of the activity respectively, The 'Output' is to go out from right side of the activity. Each activity is developed to sub-activities hierarchically. In this study, a modified PIEBASE template [3], which categorized activities into four types; i.e. 'Manage', 'Do', 'Evaluate' and 'Provide Resources', and two step approach; i.e. (1) generate and define hierarchical structure of activities, (2) provide ICOM (Input, Control, Output, Mechanism) information, which are proposed in the previous study [2], are applied in making IDEF0 activity model.
Fig. 1 Perform Lifecycle Engineering
To generalize the maintenance information into knowledge, information from design and operation, which are activities compose plant lifecycle as well as maintenance, is indispensable. Therefore, the top activity of this study should be ‘Perform LCE (Lifecycle Engineering)’, and is developed into seven sub-activities; ‘A1: Manage LCE’, ‘A2: Perform Design’, ‘A3: Construct Plant’, ‘A4: Perform Operation’, ‘A5: Perform Plant Maintenance’, ‘A6: Perform PHA (Process Hazard Analysis)’, and ‘A7: Provide Company Technology’, as shown in Figure 1. The activity model for plant maintenance
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proposed in the previous study [2] is developed under ‘A5: Perform Plant Maintenance’ activity. From the view point of lifecycle engineering, information generated in each lifecycle (sub-)activities; i.e. design, construction, operation and maintenance, is to be integrated and shared through the lifecycle. Therefore, the ‘A7’ activity receives the results of lifecycle activities, and outputs knowledge on each lifecycle activity, tools, and technological standards. The respective lifecycle activity performs their engineering on the basis of the technological standard. However, various changes are carried out during the lifecycle, for example it is in such cases as the change of the raw material, the change of the production rate, the change of the product specifications, the change of the product mix, and the change of plant structure (revamp). The effect of such changes is recognized at respective lifecycle activity. Especially in maintenance, A deterioration tendency is likely to change, and the difference between the presumption and the result of inspection would be increased. When this difference spread than the threshold value decided beforehand, the cause is investigated and the change of the technological standard must be required. In Figure 1, this requirement is once fed to ‘A1’ activity, and is informed to the ‘A7’ activity to prevent local inconsistent revision of technological standard. In the next section, based on the above mentioned consideration of lifecycle engineering, the mechanism of knowledge management for plant maintenance is developed under ‘A7’ activity.
3. Knowledge Management Model for Plant Maintenance
Figure 2. Provide Company Technology
The knowledge and technological standard for respective lifecycle activity are provided separately, because the cycle and timing of performing engineering are different with each other, and these provided standards should be consistent with each other to manage safety through the lifecycle. Thus, the ‘A7’ activity in Figure 1 is developed into six sub-activities as shown in Figure 2. The ‘A72’ to ‘A74’ activities provide technology, knowledge and technological standard to perform design, operation and maintenance. The ‘A75’ controls consistency among technological standards, and if inconsistency is found, then revision requirement for any technological standard is outputted. The
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occurrence and progress speed of deterioration are influenced by design specification and operational history, and the residual life prediction depends on production plan in future. Therefore, design information, operational log and production plan is fed to ‘A74’ activity in Figure 2. 3.1. Generation of Technological Standard for Plant Maintenance
Figure 3 Provide Resources, Knowledge and Technological Standard to Perform Maintenance
Figure 4 Provide Management Standard for Maintenance
The ‘A74’ activity is decomposed into five sub-activities as shown in Figure 3. There are two types of technological standard for maintenance; i.e. one is technological standard to decide framework of maintenance method, and the other is that to decide the individual maintenance method according to the framework. The former is called ‘management standard’, and the latter is called ‘individual standard’, here. The management standard is provided on the basis of design information in the ‘A742’ activity, and the individual standard is provided in the ‘A743’ activity, on the basis of public information stored in ‘A745’ activity in the beginning. Other than the revision requirement from ‘A75’ activity, when inspection and repair information increases, and knowledge is accumulated in ‘A745’ activity, then a revision is added to the ‘A743’ and/or ‘A742’ activities, if necessary, from ‘A745’ activity.
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The ‘A742’ and ‘A743’ activities are developed into four sub-activities as shown Figures 4 and 5 respectively. It is obvious form the ‘A7422’ and ‘A7423’ activities in Figure 4 that the framework, which the management standard is to prescribe, is the relation between deterioration and its causal factors, and the individual standard offers the prediction mechanism and relating methods based on the causal factors for respective equipment items. Therefore, the ‘A745’ activity should receive operational history, design information and results of inspection and repair, and integrate the results of maintenance into the knowledge in the form of the causal factors related to deterioration and the prediction models with related methods.
Figure 5 Provide Individual Standard for Maintenance
3.2. Integration of Maintenance Information into Knowledge
Figure 6 Integrate Maintenance Information into Knowledge
In order to make maintenance plan, three types of knowledge are necessary; i.e. residual life prediction, inspection method and repair method, and these types of knowledge, and the technological standard provided from the knowledge are implemented in the maintenance information system. Therefore, the ‘A745’ activity is developed into five sub-activities as shown in Figure 6. In predicting residual life, the assumed prediction method in design is provided from ‘A7455’ activity in the beginning. According to increase of the inspection and repair information, the parameters in prediction equation are revised. The revised parameters are stored in the ‘A7455’ activity, and it is utilized
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in prediction next time. When the deviation between predicted and inspected deterioration is increased, diagnosis of the error should be performed. Therefore, the ‘A7455’ is developed into four sub-activities as shown in Figure 7, and the ‘A74554’ activity analysis the reason of the error. There are three types of reasons for the errors; i.e. prediction model, inspection and repair. According to the reason of the error, the proper revision request is fed back to the ‘A743’ and/or ‘A742’ activities.
Figure 7 Provide Residual Life Prediction Method
4. Conclusion In the plant maintenance, the information acquired from inspection and repair is integrated into knowledge, and is put in the form of technological standard. The consistency between maintenance and the technological standard decides safety in lifecycle. In this study, a business process model for knowledge management in plant maintenance is developed, and IDEF0 activity model to manage the consistency explicitly is developed. Consequently, the system requirement for knowledge management supporting environment in plant maintenance can be specified. Acknowledgements The authors are grateful to the following plant maintenance experts for their cooperation in modeling; Mr. Sadayoshi Hano (Mitsubishi Chemical), Mr. Kazutaka Hosoda (Fuji Oil), Mr. Kiyoshi Matsuoka (ZEON), Mr. Shizuo Ishizuka (Kashima Oil), Mr. Hitoshi Shinohara (Tokuyama), Mr. Shinji Takagi, Mr. Tatsuo Gamon (Asahi Kasei Chemicals), Mr. Tsuyoshi Takehara (Tonen General Sekiyu)
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References
[1] Federal Information Processing Standards Publications; “Integration Definition for Function Modeling (IDEF0),” http://www.itl.nist.gov/fipspubs/ [2] Fuchino,. T., M. Miyazawa and Y. Naka, “Business Model of Plant Maintenance for Lifecycle Safety,” 17th European Symposium on Computer Aided Process Engineesing - ESCAPE17, Bucharest Romania, Elsevir(2007) [3] PIEBASE; “PIEBASE Activity Model Executive Summary”, http://www.posc.org/piebase/own
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Practical Challenges In Developing Data-Driven Soft Sensors For Quality Prediction Jun Liu,a Rajagopalan Srinivasan,a,b P N. SelvaGuruc a
Institute of Chemical and Engineering Sciences, A*STAR (Agency for Science, Technology and Research), 1 Pesek Road, Jurong Island, Singapore 627833, Singapore b Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore c Singapore Refining Company, 1 Merlimau Road, Singapore 628260, Singapore
Abstract With improved quality control, a refinery plant can operate closer to optimum values. However, real-time measurement of product quality is generally difficult. On-line prediction of quality using frequent process measurements would therefore be beneficial. In this paper, our learnings from developing and deploying a data-driven soft sensor for a refinery unit are presented. Key challenges in developing a practicable soft sensor for actual use in a plant are discussed and our solutions to these presented. Finally, this paper reports results from the online deployment and demonstrates their value for the plant personnel. Keywords: Soft sensors, quality prediction, neural networks.
1. Introduction Quality control relies on real-time measurement of quality, which is generally difficult and usual too infrequent to be used directly for good quality control. On the other hand, process measurements such as temperatures, pressures, and flow rates are available on a more frequent basis (every minute or every few seconds) than the lab or analyzer measurement. Soft sensors are inferential models that use such easily available process measurements to predict the values of other useful but difficult to measure quantities. They can serve as an important tool to improve quality control and process operation, as they can provide frequent, timely and accurate estimations of product quality. In recent years, various inferential models have been developed to predict product quality using first principles, linear regression or neural networks (NN) models [1-4]. In this work we have developed a NN-based soft sensor for a refinery. The process considered is a crude distillation unit as shown in Figure 1. LPG
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ASTM 90% distillation temperature (D90) is commonly used to characterize quality in the refinery, and both lab and online analyzer measurements are available for this quality variable. However, the analyzer measurements are slow (total time delay of about an hour), infrequent (one sample every half an hour) and sometimes unreliable; the more accurate lab measurement of the same variable is even slower (time delay of hours) and less frequent (about one or two samples per day). It is not easy to build a first-principle model to predict product quality due to the complexity of the process. Because of the easy availability of large volumes of historical process data, empirical models are considered in this work. Furthermore the process is significantly nonlinear, and operates with varying feedstock, and at different operation conditions. A simple linear regression model would not work well for such case. Therefore a neural network approach combined with process knowledge has been selected in this work. In this paper, our learning from developing and deploying this data-driven soft sensor is presented. The key challenges and some solutions to these are also discussed. Finally, this paper presents results from online deployment of the soft sensor in the plant.
2. Key Challenges in Developing Soft Sensors Data-driven soft sensors require less process knowledge; they exploit historical operating data to extract the correlations between variables. In practice, the quality and quantity of data available for training pose hurdles, specifically • Good quality data are not uniformly available. Erroneous samples in process variables, as well as analyzer and lab measurements occur due to poor calibration, measurement error, computer interface errors, etc. For example, Fig. 2 shows that sometimes the data is quite noisy with outliers or even measurement failures. These complexities must be taken into account during both model development and realtime use of the sensor. • In the current situation, there are two independent measurements of quality. There could be a mismatch between analyzer and lab measurements, in terms of both time and value. Analyzer and lab measurements have different sampling intervals and time delays, which causes mismatch in time of measurement. Sometimes there is also a mismatch between the analyzer value and the lab value as shown in Fig. 3 (the difference could be as much as 100C in contrast to required accuracy of 30C). Therefore, alignment of the data to counteract the mismatches is necessary. • Change of process operating conditions in the refinery is quite common. For instance, there were 7 significantly different types of crude feed in a given month as shown in Fig. 4. Each feed corresponds to a different operating condition. In addition, new crudes and unit operation conditions are likely in the feature. Extrapolation beyond the range of the training data is called for with the concomitant difficulties. Analyzer
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Figure 4: Variation in density of crudes used during a month
• The process is a large scale one with hundreds of variables. It is impossible to include all of them in the inferential model. Therefore, some analysis must be done to identify the important variables as inputs to the soft sensor.
3. Soft Sensor A soft sensor based on neural networks and process knowledge has been developed to predict the refinery D90 quality variable. The process variables that serve as input to the network were selected offline based on process understanding and correlation analysis. As these input variables represent different quantities – temperature, flow, pressure, etc – and have different scales, they were first normalised (auto-scaled) before being input to the neural network. Standard back propagation was used to train the network offline. To improve generalization, the available data was divided into 3 sets: training, validation, and test. The training set is used for computing the gradient and updating the network weights and biases. The validation set is monitored during the training process. Normally when the network begins to over-fit the training data, the error on the validation set will begin to rise. When the validation error increases consecutively, the training is stopped. The test set is used to select the best model via prediction error compared to lab measurements and prediction correlation with analyzer measurements. This general neural network training strategy was supplemented with several additional solutions to systematically address the challenges described above. In order to shortlist the key input variables, correlation analysis was augmented by process understanding. Data analysis schemes for offline and online validity check was developed to uncover erroneous data. Metrics for performance evaluation were also developed in order to account for the mismatch between the two independent measures of quality. These are described next:
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3.1. Validity Check Sufficient historical data with good accuracy is essential to build a good inferential model. Historic data over two years sampled at 10 minute-intervals were collected from the process historian. Of these, data outside a prescribed range were removed as outliers. Further offline analysis was done to extract good quality training data where analyzer and lab measurements matched well. Only about 10% of the original data met these criteria and were used to train the neural network. For online deployment of the soft sensor, process data is also accessed through the process historian. A separate input validity check was also implemented for the online case; the last valid input is used when an invalid measurement is detected online. 3.2. Analyzer/Lab data treatment The online analyzer samples the process automatically every 30-40 minutes and takes about 30 minutes to estimate the quality. To correlate the analyzer measurements with the process conditions, we evaluate various effective time delays between the process change and online analyzer measurement. The correlation between the analyzer and the process variables seem to be the highest when the overall time delay is set to an hour. This was also consistent with the plant engineer’s process knowledge. Therefore, the analyzer data are shifted by an hour during offline analysis and modelling. During online implementation, analyzer data are also aligned with the process data an hour ago. Unlike input and analyzer data which come from the instruments directly, the lab data is manually recorded into the lab information management system, which is then reflected in the process historian. The time between taking the sample and updating the measurement in the process historian varies significantly, from an hour to several hours. This irregular availability of lab data complicates the online performance evaluation. 3.3. Performance Evaluation As the key process time constants are about 1 to 2 hours, lab measurement available typically at 8 hour intervals is not enough to capture dynamics of the system. Therefore, the performance of the soft sensor has to be gauged from both the analyzer (of limited reliability) and the lab measurements. Two metrics – prediction error and correlation are used as the objective functions for developing the inferential model, so as to balance the performance requirements. The mean of absolute error and standard deviation are used for quantifying the prediction error. Correlation coefficient between the prediction and the analyzer measurement (corrected for the time delay) is used for prediction movement quantification. Several factors affect the correlation analysis including analyzer faults (outlier, drift, bias, etc.) and noise, analyzer measurement accuracy, analyzer bias change, and analyzer sampling time and delay. Analyzer
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4. Results The soft sensor described above has been implemented using Visual C++ and deployed in the refinery. Some example results from online tests are reported next. Fig. 5 shows an overview of the prediction result during a 2-week window (a server shutdown and restart occurred on Aug 23; results during that period should be ignored). The correlation coefficient between prediction and analyzer measurement was found to be 0.71 for the whole data and 0.76 for data excluding analyzer errors. This is considered to be acceptable. It can be visually seen from the figure that the prediction movement pattern is similar to that of the analyzer. Table 1 shows the prediction error (between prediction and lab measurement) compared to the analyzer error (difference between analyzer and lab measurement). It can be seen that the prediction error (in terms of both mean and standard deviation) is smaller than the analyzer error. As a further comparison, according to ASTM D86 standard [5-6], the analyzer has an accuracy of about 40C (one out of twenty will exceed this value; standard deviation is 20C for normal distribution). The soft sensor developed in this work compared favorably with this standard.
Table 1. Prediction error compared to analyzer error Error (0C)
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5. Conclusions This paper presents our experience from developing and deploying a data-driven soft sensor for a refinery. The initial online test results are encouraging. The prediction output of the soft sensor tracks the analyzer movement pattern well, and matches the lab measurement better than the online analyzer. The key advantage of the soft sensor is the complete absence of any time delay which would enable closed-loop control. Further, estimates are at regular intervals and higher frequency compared to the analyzer. Our current work is focused on extending the sensor with online learning – when a new crude is used or operating conditions go out of the range of training data, the model will update itself once it has enough data to recalibrate with adequate confidence.
Acknowledgement This work was supported by the Science and Engineering Research Council of A*STAR (Agency for Science, Technology and Research), Singapore. We also would like to thank Mr Wee Leong Hu and Mr Leong Kitt Mum from SRC for their continual help and support during the project
References G. Martin, G. Barber, Z. Friedman and E. Bullerdiek, Refining and petrochemical property predictions for distillation, fractionation and crude switch, NPRA 2000 Compute Conference, Nov 13-15, 2000, Chicago, Illinois, USA. N. Bonavita and T. Matsko, Neural network technology applied to refinery inferential analyzer problems, Hydrocarbon Engineering, December 1999 A. Adnan, N. Sani, S. Nam and Z. Friedman, The use of first-principles inference models for crude switching control, ERTC Computer Conference, May 2004, London, UK S. Lakshminarayanan, A. Tangirala, S. Shah, K. Akamatsu and S. Ooyama, Soft sensor design using partial least square and neural networks: Comparison and industrial applications, AICHE annual meeting, Nov 15-20, 1998, Miami, USA G.P. Sturm and J.Y. Shay, Comprehensive report of API crude oil characterization measurements, American Petroleum Institute, 2000 ASTM Standard D86, 2007a, Standard Test Method for Distillation of Petroleum Products at Atmospheric Pressure, ASTM International, West Conshohocken, PA, www.astm.org
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Process Analytical Technologies (PAT) – the Impact for Process Systems Engineering Zeng Ping Chena, David Lovettb and Julian Morrisc a
CPACT, Pure and Applied Chemistry Strathclde University, Glasgow, Scotland Perceptive Engineering, Daresbury Innovation Centre, Daresbury,Cheshire, UK c CPACT,Chemical Engineering and Advanced Materials, Newcastle University, UK b
Abstract With the increasing take-up of Process Analytical Technologies (PAT) by the pharmachem, bio-pharma , specialty chemicals and materials manufacturing industries there is a critical need for robust data verification, particularly as this information is being included in real-time control or at least advisory feedback applications. In particular the accuracy and reliability of spectral calibrations for processes which are subject to variations in physical properties such as sample compactness, surface topology, etc are becoming a hot topic The variation in the optical path-length materializing from the physical differences between samples may result in multiplicative light scattering influencing spectra in a nonlinear manner leading to the poor calibration performance. In this paper a number of new approaches are shown to overcome the limitations of existing methods and algorithms. Space precludes detailed descriptions of the new algorithms, which are fully referenced, with some of the main results being presented and the justification why these data validity issues need to be addressed by the Process Systems Engineering and CAPE communities. Keywords: Process Analytical Technologies, calibration, data validity, process control
1. Introduction Pharma-Chem and bio-pharma, alongside speciality chemicals and materials development and production are now being heavily influenced through the recent FDA PAT2 initiative with spectroscopic instrumentation being increasingly applied for, or at the very least explored, on-line real-time process control applications. This drives the urgent need to incorporate and integrate the detailed spectral information into process performance monitoring schemes. The enhancement of spectroscopic data analysis techniques, calibration algorithms and robust software thus becomes even more important if PAT (and Quality by Design - QbD) is to be widely applied and accepted. As it is generally chemical information (in most cases the concentrations of the chemical or biological compounds) inherent within the spectroscopic measurements, rather than the spectroscopic measurements themselves, that are used for efficient management and optimization as well as for quality control; calibration models are therefore needed to transform abundant spectroscopic measurements into the desired concentration information. The accuracy of the calibration models is influenced by a number of factors, chemical and physical, the need for sophisticated chemometric methodologies and algorithms for advanced spectral data analysis,the initial modelling data and most critically for on-line deployment the “real-time” data quality. The real2
FDA, PAT - A Framework for Innovative Pharmaceutical Development, Manufacturing, and Quality Assurance, http://www.fda.gov/cder/guidance, 2004
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time application of these calibration models provides a corner stone of PAT and hence is of significant importance to the process systems engineering community in the broader application of QbD
2. Challenges for PAT in Quality by Design Robust and transferable calibration models are essential for the full implementation of PAT/QbD. To achieve this two areas of complexity need to be addressed. One relates to the variations in external process variables which can have different impact on different chemical species in mixtures. For example, (i) fluctuations in temperature will provoke non-linear shift and broadening in spectral bands of absorptive spectra of constituents in mixtures, where such temperature-induced non-linear spectral variations can have detrimental effects on predictive performance of multivariate calibration model if not being properly taken into account when developing the model; (ii) uncontrolled variations in optical path length due to the physical variations such as particle size and shape, micro-organism growth, sample packing and sample surface which may cause dominant multiplicative light scattering perturbations which will mask the spectral variations related to the content differences of chemical compounds in samples. 2.1. Correction of Temperature Induced Spectral Variations for In-line Monitoring and Control (Using Loading Space Standardization) The routine application of PAT within a process control environment requires that the building of calibration models becomes a routine, non-expert, application embedded within a process systems engineering context. Typically variable selection models tend to require special expertise and software; non-linear effects are often not removed by filtering or resolved through orthogonal basis transformations such as a wavelet transformation, etc. In practice a full account of the effect of temperature on the spectra is therefore only possible through the application of nonlinear methods. Due to the nonlinear characteristic of temperature effects, neither implicit modelling through the inclusion of temperature into the calibration experimental design nor explicit inclusion of temperature into the calibration model (such as treating the temperature of samples as an extra independent variable appended to the spectra or as another dependent variable can successfully eliminate the temperature influence on the predictions of calibration models. There are a large number of methods attempting to resolve these and related calibration issues methodologies2 and these are referenced in the papers by Chen et al). E.g. calibration based on robust variable selection (PDS) and its extensions, CPDS for compensation of temperature effects on spectra, With a view to compensating for temperature effects on spectra, and ICS which was first proposed by Chen et al, 2004 to eliminate temperature effects on the predictive abilities of calibration models for white chemical systems, A full description of temperature influence is only possible using nonlinear methods. Loading Space Standardization (LSS) was developed to generalize the ideas behind ICS to correct temperature-induced spectral variations for grey chemical systems (Chen et al, 2005). The underlying proposition is that if process temperature variations have not been taken into account during the data collection phase of the calibration task the calibration model built on the spectral data measured at particular temperatures can only provide accurate predictions for reactions operating at 2
FT: Fourier Transform; WT: Wavelet Transform; CPDS: Continuous Piecewise Direct Standardization;: PSR: Penalized Signal Regression; ICS: Individual Contribution Standardization; DS: Direct Standardization; PDS: Piecewise Direct Standardization; MSC: Multiplicative Signal Correction; ISC: Inverted Signal Correction; EMSC: Extended MSC; EISC: Extended ISC; LSS: Loading Space Standardization; OPLEC: Optical Path Length Estimation and Correction
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the same temperatures. Temperature is a continuous variable in process analytical control applications. It is not possible to build calibration models for every possible temperature that will be encountered during process manufacturing. In order to apply the calibration models established at training temperatures to future on-line measurements under different temperature profiles it is necessary to model the temperature effects and then standardize the spectra for future process measurements to the corresponding spectra as if they were measured under calibration training temperatures. In LSS the absorbance of each chemical species in every wavelength follows polynomials with respect to temperature which are used to predict the loading vectors at test temperature which play an important role in correcting spectral variations caused by temperature differences between calibration models and measurements made during production process control.
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Fig. 1a. Raw Data Fig. 1b. LSS pre-processed spectra Fig.1a shows the raw spectra of samples with different monosodium glutamate (MSG) crystal concentrations with Fig. 1b the LSS pre-processed spectra of samples. These results confirm the validity of the basic assumption underlying LSS. A recent extension to LSS addresses the enhanced improvement of the linearity of spectroscopic data subject to fluctuations in external variables such as temperature (see Chen et al 2007). 2.2. Improving the signal-to-noise ration through Smoothed Principal Components (XRD for on-line monitoring of crystal morphology) X-ray diffraction spectroscopy is one of the most widely applied methodologies for the in-situ analysis of kinetic processes involving crystalline solids. However, due to its relatively high detection limit, it has limited application in the context of crystallizations from liquids. Methods that can lower the detection limit of x-ray diffraction spectroscopy are therefore highly desirable. Most methods tend to only utilize the frequency information contained in the single spectrum being processed to discriminate between the signals and the noise and as a result may not successfully identify very weak but very important peaks especially when these weak signals are masked by severe noise. Smoothed principal component analysis (SPCA) which takes advantage of both the frequency information and spectral common variations is proposed as a methodology for the pre-processing of the x-ray diffraction spectra. SPCA was used to provide enhanced extraction of polymorphic form information from high signal to noise ratio x-ray diffraction spectra in a crystallization process (Chen et al 2005). The resulting sensitivity was sufficiently high to enable the detection of the formation of polymorphic structures at an early stage in the reaction. Figs. 4a (upper plot) shows the X-ray diffraction profiles of the desired ȕ-form and the corresponding (un-smoothed) PLS calibration model (Fig. 4b upper plot) of the GA slurries. Fig. 4a (lower plot) shows the corresponding smoothed PCA diffraction profiles and resulting PLS calibration model Fig.4b (lower plot). Compared with other signal processing methods such as the wavelet transformation, SPCA achieves lower detection limit of the ȕ-form
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of GA with concentrations as low as 0.4% by weight being detected from GA-methanol slurries comprising mixtures of both Į and ȕ forms (see Chen et al, 2005).
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2.3. Extracting Chemical Information from Spectral Data with Multiplicative Light Scattering Effects (Optical Path-Length Estimation and Correction) Spectroscopy in solid and heterogeneous types of samples that exhibit sample-to-sample variability, the variation in the optical path length materializing from the physical differences between samples, due to particle size and shape, sample packing, and sample surface, for example, may result in the multiplicative light scattering effect masking the spectral variations relating to the differences between the chemical compounds present. The effect of multiplicative light scattering is difficult to handle through the application of standard bilinear calibration methodologies as these are based on the construction of latent variables that are a linear combination of the wavelengths. Consequently if the spectral data are not appropriately preprocessed, the underlying behavior of the data, relating to the chemical properties, will be masked due to the effect of multiplicative light scattering. Many chemometric pre-processing methods have been proposed to explicitly model the effect of multiplicative light scattering (MSC), e.g. multiplicative signal correction and its variants. A new correction method enabling the improved extraction of chemical information from spectral data with MSC problems (Optical Path-Length Estimation and Correction – OPLEC does not place any requirement on prior chemical knowledge and can be generally applied in unit. Figs. 5a and 5b show the impact of the new spectral pre-processing approach, space precludes a full discussion – see Chen, et al. 2006. 3.2
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3. Challenges for PAT in Closed Loop Systems The management of real time data, including pre-processing, outlier detection, outlier isolation and record of uncertainty associated with data is vital in a validated environment, to ensure complete traceability of all actions deployed by either a closed loop control system or operator. This management housekeeping, underpins the credibility for any software used for PAT and “real time” applications. This is an area that has been considered in depth for safety critical systems, for instance, in the Nuclear Industry, and one that again emphasizes the Process Systems Engineering approach from input to final output. There are a number of data quality monitoring approaches to strengthen the integrity and robustness of predictive engines that are worth consideration and are likely to be a pre-requisite for real time PAT. This section provides the results from an industrial application of a multivariate data quality monitoring system on a biological process that supports analysers, by providing real time data quality analysis to increase the availability, robustness and confidence in the process sensors and analyzers prior to use in any subsequent computational action. These spectroscopic developments were demonstrated by application to a commercial pilot scale batch cooling crystallization. Fig.6a and b show the industrial pilot plant, the supersaturation control system and a typical the resulting crystallization control run. 1.225 1.175 1.125 1.075 1.025 0.975 0.925 0.875 0.825 0.775 0.725 0.675 Concentration (g/500ml) 0.625 0.575 Turbidity (%) 0.525 Slimit 0.475 0.425 0.375 0.325 0.275 0.225 0.175 0.125 0.075 0.025 900 1000 1100 1200 1300
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3.1. Model-based Multivariate Statistical Process Performance Monitoring In multivariate statistical process control (process performance monitoring) the monitoring statistics depend upon the model residuals being ‘IID’. In practice, the monitoring model (eg PCA or PLS model) will not be perfect and the residuals will contain structure. A modified model-based approach (McPherson et al. 2002) incorporates an additional residual modelling stage to remove structure from the residuals as shown in Fig 7a. Examination of the model-plant mismatch residuals, Figs. 7b and 7c shows that both serial correlation and non-normal behaviour is still present. A modified model-based approach is proposed where an additional residual modelling stage is incorporated, as shown in Fig 7a, to remove the remaining structure and to obtain a set of unstructured residuals suitable for process monitoring. Finally, Fig. 8 shows the structure of a commercial real time data quality monitoring and dynamic model based control system designed for pharma and other PAT based applications.
4. Conclusions Real time chemometrics and the incorporation of PAT Sensors into real time process control need to be part of the CAPE toolkit. PAT devices capable of 1-2 second or sub-
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second measurement rates, real-time control based on a PAT measurement is a reality. Richness of measurement: not just a single data point per sample but a vector of data per sample. Sensor calibration models can give real time inference of product property. Real time pre-processing - no control system is going to control a spectrum of several hundred simultaneous values; so what is important? Is there is a calibration model to infer product property? Are there particular features/segments of the spectrum of interest? Should the scores of the PCA/PLS calibration model be controlled? Online Spectral methods coupled with closed loop process control will be both critical and useful tools for process transfer and comparability – process systems engineering has much to offer the PAT initiative. Outputs
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Acknowledgements EPSRC grant GR/R19366/01 (KNOW-HOW) and GR/R43853/01 (CBBII).
References ZP. Chen, Morris, J.; Martin, E., (2004),Modeling temperature-induced spectral variations in chemical process monitoring, Dycops. ZP. Chen, Morris, J.; Martin, E., (2005), Correction of temperature-induced spectral variations by loading space standardization, Anal. Chem. 77, 1376-1384 ZP. Chen, Morris, J.; Martin, E.; Hammond, R.B.; Lai, X.J.; Ma, C.Y.; Purba, E.; Roberts, K.J.; Bytheway, R., (2005), Enhancing the signal to noise ratio of x-ray diffraction spectra by smoothed principal component analysis, Anal. Chem. 77, 6563-6570 ZP. Chen, Morris, J.; Martin, E., (2006), Extracting chemical information from spectral data with multiplicative light scattering effects by optical path-length estimation and correction, Anal. Chem., 78, 7674-7681. L. McPherson, E.B. Martin, & A. J. Morris (2002). Super Model Based Techniques for Batch Process Performance Monitoring, ESCAPE 12, 523–528. ZP. Chen, Morris, J., Improving the Linearity of Spectroscopic Data with Fluctuations in External Variables by the Extended Loading Space Standardization,(2007), Under Review for Anal. Chem.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Decision Support for Control Structure Selection During Plant Design Jan Oldenburga, Hans-Jürgen Pallascha, Colman Carrollb, Veit Hagenmeyera, Sachin Aroraa, Knud Jacobsena, Joachim Birka, Axel Polta, Peter van den Abeelc a
BASF SE, D-67056 Ludwigshafen, Germany Cornell University, Ithaca, NY 14853, USA c BASF Antwerpen N.V., B-2040 Antwerpen 4, Belgium
b
Abstract During the design of chemical processes, considerable effort is put into developing and refining stationary process models. Once a process model has been developed, significant value can be added by its subsequent reuse for plant design, design of operational strategies, control concepts and even for operational support of an existing plant. In this work, we present a methodology for the simple and efficient re-use of the steady-state simulation data in the context of the process control structure selection which follows basic ideas of the self-optimizing control paradigm of Morari et al. (1980). It is shown how the approach is integrated into a decision support tool, which has already been successfully applied to one of our large-scale investment projects. Keywords: Control structure selection, Process modeling and simulation, Model re-use, Economic performance measures.
1. Introduction Process modeling and simulation play a prominent role during the development of new chemical processes. The modeling of a new or modified chemical process typically starts during the conceptual design phase. Based on a physico-chemical process model, which is steadily refined and further developed, a systematic screening and economic evaluation of design alternatives is possible using commercial process simulation and/or optimization tools such as e.g. Aspen Plus. Once a process model has been developed, significant value can be added by its consequent reuse for plant design, design of operational strategies and control concepts and even for operational support of an existing plant. During the engineering phase, which is concerned with the transformation of a chemical process design into a highly profitable and reliable plant, the reuse of process models can already been considered to be an established practice. In this context, an important ingredient is a methodology named intelligent total cost minimization (i-TCM) (Wiesel and Polt, 2006). By incorporating short-cut equipment sizing and costing routines into the process model, this method translates the conventional results from a process simulation into costs for raw materials, utilities and annualized costs for equipment, i.e. the lifecycle costs of the process. This helps us to obtain a plant lifecycle cost-centric view of the process design alternatives – based on a total cost minimization by numerical optimization – which allows an objective decision-making process based on quantitative information. Successful plant design should also take into account operability rather than only design aspects. Therefore, we have adopted a method for decision support for control structure
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selection during plant design, which follows the approaches of Morari et al. (1980) and Skogestad (2000) to systematically find favorable control structures by i. making use of stationary process models to the extent possible, ii. employing an economic measure to classify different control structures. Engell (2007) gives a nice explanation of (ii) by stating: “From a process engineering view, the purpose of feedback control is not primarily to keep the plant at their setpoints, but to operate the plant such that the net return is maximized in the presence of disturbances and uncertainties, exploiting the available measurements.”. Following this paradigm, we advocate the use of economic measures for the evaluation of process control structures in an analogous fashion to the way lifecycle costs are used to compare process design alternatives. While a cost-centric view has become an established best practice in industrial process design, this is not the case for control structure selection. Interestingly, we found that neither (i) nor (ii) is a well defined industrial practice up to now. The present contribution is organized as follows: The control structure selection procedure is presented in Section 2. To illustrate the method, we elaborate on the control structure design for a particular distillation column in our large-scale plant in Section 3. The main results related to plant-wide control are briefly outlined in Section 4. The findings of our work are summarized in Section 5.
2. From optimal design to optimal operation: Identifying economically attractive control structures The starting point of our analysis is the development of a stationary simulation model of a chemical plant under consideration. For this purpose, we typically employ Aspen Plus extended by our i-TCM functionality, which was developed by BASF engineers. The first stage in the i-TCM procedure is the identification of the degrees of freedom (DOF) that are available for steady-state optimization. These include operational DOF (such as boilup rates, reflux ratios), and equipment-related DOF (e.g. reactor volumes, number of trays in distillation columns). A total cost function is then established, and the operational and design constraints are identified. The next step is to perform a total cost minimization to obtain minimal nominal lifecycle costs in €/a and the corresponding optimal (nominal) operating point and equipment geometries. During plant operations, the actual total lifecycle costs will, of course, differ from the nominal case due to the fact that the operational costs vary in the presence of external disturbances such as fluctuating feedstock qualities or prices, or model uncertainties/plant malfunction. The goal of process control is – in addition to keeping process operations feasible and stable – to run the plant as efficiently as possible by minimizing the operational cost for all operating conditions within a range around the nominal operating point. The question of which control structure, i.e. which set of controlled (measured) and manipulated variables is used and how they are paired with each other, is suited to meet these requirements best is usually addressed using heuristics, best practices and process engineering insight. The control structure selection problem of a large-scale investment project motivated us to look for a more systematic approach which makes an explicit and quantitative re-use of process engineering insight contained in our steady-state process models. This is achieved by extracting data from these process models including the equipment and operational cost models that were already used for the process design and by following ideas from Morari et al. (1980) and Skogestad (2000) as will be seen in the following sections.
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2.1. Identifying attractive candidate controlled variables For the selection of the controlled variables, all equipment-related DOF are fixed within the Aspen Plus i-TCM model. The next step is to identify candidate controlled variables. These variables are typically quantities that represent the current state of the process, such as flows and temperatures. These examples are favored choices for controlled variables since they can be measured reliably, accurately and easily. However, sometimes more sophisticated controlled variables, such as compositions, that have to be measured online, are required. For such cases, the investment and maintenance cost for measurements needs to be taken into account. The trade off we typically face between the additional cost of installing complex measurement systems versus the actual benefit created in terms of control performance can nicely be estimated using the proposed method as will be seen later. Finally, a controlled variable should be sensitive to changes in the manipulated variable associated with it via the respective control loop. In the subsequent step important disturbance scenarios that are most likely to act on the process have to be defined. These can include external disturbances as well as model uncertainties or measurement errors in the controlled variables. For each disturbance scenario, operational cost optimization calculations using the operational DOF are repeated to obtain the corresponding objective function. Each of these operational cost minima represents the optimal process cost for the respective scenario assuming ‘perfect control’, i.e. assuming the corresponding disturbances could be measured and an advanced process control setup involving a real-time optimizer would be available during process operations. These minima related to ‘perfect control’ are used to perform an economic evaluation of each potential set of controlled variables selected to control the chemical plant. For each set of controlled variables this measure calculates the difference in terms of cost between the operational cost of the plant with closed loop control (with constant setpoints) and with a re-optimization of the respective setpoints. Among the various alternative candidates that can be selected as controlled variables, the loss that is to be expected by fixing controlled variables to their setpoint values should be minimal. It should be noted that the i-TCM operational cost and equipment models in conjunction with the equation-oriented (EO) simulation mode of Aspen Plus constitute important ingredients of these variational calculations. 2.2. Control Loop Pairing and Verification by Dynamic Simulation Analysis Once promising candidate sets of controlled and manipulated variables have been selected, an appropriate control loop pairing needs to be determined. Sensitivity considerations as well as the relative gain array (RGA) method (Bristol, 1966) help in selecting one or a few out of the various potential pairings that are left from the previous selection process. Based on sensitivity information, which is available from the solution of the stationary process model, and a few simple matrix operations the RGA method can effectively be used to identify instable pairings. All the steps presented so far can be conducted using information derived from stationary process models. Dynamic simulation studies are the next step towards building up and testing the control structures that are initially proposed based on stationary simulation studies. Several aspects of dynamic simulations are discussed in the following that give a lot of information about the dynamics of the process and on controllability issues, which are relatively hard to extract from the stationary models: Firstly, the disturbance scenarios identified in the previous subsection are assessed. Then, different possible combinations of the control structures are examined in view of operational feasibility. RGA analysis gives possible guesses for good loop pairing but
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may not always lead to the best results (it may even lead to unstable loop pairings). This is checked and verified. After a suitable control structure has been selected, care must be taken in choosing ranges for the controllers (actuator limitations on the manipulated variables), its effect on the controlled variables and the coupling effect on the whole process (e.g. undesirable overshoots or long delays). Further on, partial control schemes in which an important key variable is controlled and some other operational specifications during big disturbances are allowed to be off-spec are also checked. Dynamic simulation is also useful to get ideas of control parameters if desired.
3. Case Study: Control Structure Selection for a Distillation Column In order to illustrate the above procedure, we examine a particular section of our largescale process: a distillation column used to separate the key product P from the raw material R as well as from a set of inert components. Though the distillation column is operated under high pressure, the top product has to be condensed at very low temperatures, a fact which makes process operations expensive. A schematic of the system can be seen in Fig. 1, left. D (Inerts, R)
FC
FC 1
TI
5 FC
S (mainly R) Inerts, P, R
TI
FI
TI
9
0
0.2
0.4
0.6
0.8
1
dTi / dFQ dTi / dFC dTi / dS
13 17 21 FC
25 FQ 29 B (pure P)
Figure 1: Schematic of the distillation process (left) and normalized sensitivity plot of the temperature profile in the column (stage 1:= condenser, stage 29:= reboiler) with respect to the manipulated variables condensing fluid flow rate FC, evaporator steam flow rate FQ and side stream flow rate S (right). D, B and S refer to the distillate, bottoms and side draw streams.
The first step is to determine an optimal design of the column based on minimizing the total cost. Due to confidentiality issues we do not elaborate on equipment-related issues but instead concentrate on the three operational DOF available for steady-state optimization (thereby assuming that the liquid holdups in the condenser and the reboiler are controlled by the reflux and bottoms streams respectively, and that the pressure is controlled by the vapor stream D): the condensing fluid flow rate FC, the evaporator steam flow rate FQ and the side stream flow rate S. Two important operational constraints are imposed: The product P should contain less than 5 w-ppm of R while the side stream S should contain less than 50 w-ppm of P. The nominal lifecycle costs in Euro per annum are obtained by a total cost minimization using i-TCM.
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3.1. Identifying attractive candidate controlled variables For the design of an appropriate control system, we proceed with selecting flows and temperatures as candidate controlled variables, which can be measured easily and reliably. In order to simplify the list of candidate control variables a sensitivity check is conducted. We are principally interested in examining which temperatures within the column are most sensitive to changes in the manipulated variables FC, FQ and S (see e.g. Luyben, 2006). These sensitivity values are obtained conveniently as a by-product of the Aspen Plus EO solution. The results calculated for the column are shown in Fig. 1, right. For this system, it is seen that there are two areas of good temperature sensitivity, one around stage 14, and another around stage 19. This suggests that temperature sensors could be effectively used at these positions. Additionally, the condenser temperature T1 as well as the ratio rFFQ of the feed flow rate and the evaporator steam flow rate FQ are selected as candidate controlled variables. With these considerations, the following two sets of controlled variables are identified: Set 1 composed of variables T1, T14, rFFQ and set 2 composed of variables T1, T14, T19. Normalized operating cost
120
110
100 Perfect control Controlled variables set 1
90
Controlled variables set 2
80 -20%
-10%
0%
10%
20%
Change in feed mass flow of component R [%]
Figure 2: Economic comparison of controlled variables sets 1 and 2, distance to ‘perfect control’.
For an economic comparison of the two sets of controlled variables, disturbance scenarios are to be defined. The project team argued that a change in the amount of R in the feed is, amongst others, a realistic and important scenario for testing our control system. Fig. 2 shows the influence of a change in the feed mass flow of component R on the operating cost of the column for three different control schemes. The cost for ‘perfect control’, which is calculated as explained in Section 2.2, indicated by the circles in Fig. 2 serves as a reference for the two sets of candidate controlled variables. By comparing the operational cost for varying feed compositions (+/- 20% in component R), it can easily be seen that set 1 is worse than ‘perfect control’ and set 2. This first result shows that set 2 should be used rather than set 1. Furthermore, Fig. 2 also reveals that set 2 is rather close to the performance of ‘perfect control’. Hence, it would not be worth spending the effort required for an advanced control scheme with an economic performance close to ‘perfect control’. These general findings are confirmed for all remaining disturbance scenarios. Thus, it can be concluded that set 2 is the favorable set of controlled variables. 3.2. Control Loop Pairing and Verification by Dynamic Simulation Studies Having identified a set of controlled and manipulated variables, an appropriate control loop pairing remains to be determined. For this purpose, we again make use of
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stationary process information by using sensitivity information to calculate the RGA matrix for the system. This is especially important for the control design problem considered here, since controlling a distillation column with more than one temperature is known to potentially cause stability problems. Whereas several pairings of controlled variables T1, T14, T19 with the manipulated variables FC, FQ, S are found to be unstable, the following control loop pairing is found to be stable: FC controls T1, FQ controls T19, S controls T14. By converting the stationary into a dynamic model using Aspen Custom Modeler, this control system is tested and confirmed to be well suited for our purpose.
4. Plant-Wide Control Structure Selection The proposed methodology has not only been applied to design the control structure for the distillation column discussed in the previous section, but also for the plant-wide control structure selection of a large-scale BASF process (of which the distillation column is a part). The confidential process consisting of multiple units (reactor, several separation columns, many heat exchangers) is described using a non-standard chemistry and thermodynamic model. Despite the system complexity, the methodology could be applied in a precisely analogous manner. Important elements of our considerations included product relevant specifications, hydraulic calculations, product and materialrelevant temperatures as well as several internal concentrations. In our experience, the breakdown of the overall process into smaller subsections (process modules) proved to be a key element for success. Finally, the chosen control structures were validated by a dynamic simulation of the complete plant. The application of this method was seen to greatly facilitate the selection of a favorable control structure for the process.
5. Conclusions A decision-support tool for control structure selection has been proposed in this paper. The two core elements of the method are (i) a re-use of stationary process model information and (ii) the use of an economic measure in order to objectify decisions to the extent possible. The method has proven its ability to support decision-making in the project team with quantitative information and to greatly simplify dynamic simulation studies required to design the control structure of an industrial process. In this respect, the proposed method is an effort to overcome the break between model-based design and control reported by Bausa and Dünnebier (2005).
References Bausa, J., Dünnebier, G., 2005, Durchgängiger Einsatz von Modellen in der Prozessführung, Chemie Ingenieur Technik 77, 12, 1873-1884 Bristol, E. H., 1966, On a new measure of interaction for multi-variable control systems, IEEE Transactions on Automatic Control, 11, 1, 133-134 Engell, S., 2007, Feedback control for optimal process operation, Journal of Process Control, 17, 3, 203-219 Luyben, W. L., 2006, Evaluation of criteria for selecting temperature control trays in distillation columns, Journal of Process Control, 16, 2, 115-134 Morari, M., Arkun, A., Stephanopoulos, G., 1980, Studies in the synthesis of control structures for chemical processes, AIChE Journal, 26, 2, 220-232 Skogestad, S., 2000, Plantwide control: the search for the self-optimizing control structure, Journal of Process Control, 10, 5, 487-507 Wiesel, A., Polt A., 2006, Conceptual steady-state process design in times of value-based management, In: Proceedings of ESCAPE 16, Germany, Eds.: W. Marquardt, C. Pantelides, 799-805
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Production-line wide dynamic Bayesian network model for quality management in papermaking Aino Ropponen, Risto Ritala Tampere University of Technology, Institute of Measurement and Information Technology, P.O. Box 692, 33101 Tampere, Finland
Abstract The quality parameters of paper are managed with rather independent decisions made by many process operators through the production line. Improving one quality parameter typically deteriorates another, and hence incoherent decisions tend to lead to suboptimal overall quality. Vast amount of laboratory measurements data support these operator decisions, yet how this information is utilized in practice, is not well known and appears to vary from production line to production line and operator to operator. We aim at coherent quality management of a paper production line through both optimizing the operator actions and scheduling the measurements of quality management optimally. We have chosen a Bayesian network formalism to integrate qualitative human knowledge and the measurement data about quality. We present an application with a Bayesian network as a model within stochastic dynamic programming. We demonstrate our modeling approach in a realistic case study, yet not in full-scale production-line wide quality management case. Keywords: Bayesian network, Dynamic programming, Quality management, Decision Support, Papermaking.
1. Introduction The quality of end product in papermaking is a result of management actions through the entire production line. These actions are decided upon by several process operators based on process knowledge and data about the process state. Measurements of raw materials and material flows as well as product quality measurements in laboratory support these decisions. In principle, the actions are made coherent with coordinated subgoals for these decision makers. However, under dynamic disturbances the coherence easily breaks down and corrective actions are not made where it would be economically most beneficial. Depending on paper grade, there are 4-8 key quality variables, e.g. strength, roughness, brightness, opacity, and hue. Quality management attempts to keep these properties in prescribed balance while minimizing costs. Typically improving one property deteriorates another. We shall present a production-line wide quality model that informs the operative decision makers about action consequences to the other quality management decisions. Furthermore, if the balance amongst quality variables can be expressed as a single objective function and as a set of constraints, the model is suited for optimization, including scheduling of quality measurements.
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Paper consists of wood fibers that have a wide distribution of properties. Hence, physico-chemical quality models are scarce. There exist huge amounts of process data at paper mills. The model sought in this work would require open-loop data with appropriately designed experiments but the existing data is closed-loop one with little input variations. The useful information about relationship between quality and operative actions is either qualitative human knowledge or data of small sections of the production line. In this study, we have chosen a Bayesian network formalism to integrate qualitative knowledge and process data. Bayesian network (BN) is a probabilistic graph model for the dependences between [1]. BN allows probabilistic inference on quality dynamics. Dynamic programming is a method to find the actions maximizing a given objective. We shall demonstrate the use of a Bayesian network as a model for stochastic dynamic programming. This paper is organized as follows. In Section 2, we review Bayesian network as stochastic dynamic model. Section 3 presents the dynamic programming problem with uncertain state measurements and the measurement scheduling problem. Section 4 shows how the methods can be applied for quality management and measurement scheduling in papermaking and presents examples of results obtained. Section 5 discusses the challenges remaining to take the methods in use for practical quality management at paper mills.
2. Bayesian network Bayesian network is a probabilistic graph model, which describes dependences between variables. Dynamics can be described as BN as shown in the Fig. 1a, where x is the state variable, z is the uncertain measurement about the state and u is the control action to the process. Fig. 1b shows how a linear state model can be interpreted as a BN, corresponding to x k 1
Ak x k Bk u k wk
v k ~ N 0, 6 w
z k 1
C k x k 1 H k 1
H k ~ N 0, 6 H
(1)
Hence, BN of Fig. 1a can be understood as a non-linear stochastic dynamic model that can be expanded to discrete-valued states.
Figure 1a. Dynamic Bayesian network.
Figure 1b. BN of linear state model.
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Independently on whether the state in BN is continuous or discrete the dynamic model is written as conditional probabilities p x k 1 | x k , u k and p z k 1 | x k 1 . Then the state, given measurement and action history is inferred about as p x k 1 | Z k 1 , U k C p z k 1 | x k 1 p x k 1 | Z k , U k
(2)
C p z k 1 | x k 1 p x k 1 | x k , u k p x k | Z k , U k 1 dx k
³
xk
where Z k 1 >z k 1 Z k @ is a collection of measurements, U k >u k U k 1 @ collection of control actions to the process and C is a normalization factor. T
T
is a
Table 1 shows an example of discrete state dynamic process model. Table 1. Example of probability density table with two control actions uk1 and uk2. p(xk+1|xk,uk1)
xk =
xk =
xk =
high
ok
low
xk+1 = high
0.8
0.15
0.05
xk+1 = ok
0.15
0.7
xk+1 = low
0.05
0.15
p(xk+1|xk,uk2)
xk =
xk =
xk =
high
ok
low
xk+1 = high
1
0.9
0.8
0.15
xk+1 = ok
0
0.1
0.2
0.8
xk+1 = low
0
0
0
3. Dynamic programming Dynamic programming (DP) is an algorithm to compute an action sequence so that a given objective is optimized over a given time horizon. Typically the objective is to minimize costs, due to actions and resulting quality, taking into account the expected future with future optimal actions. 3.1. DP-algorithm for uncertain state information If the state of the system is known exactly through measurements, dynamic programming is solved with backwards recursion [2]. As a result, optimal action sequence is obtained. However, if the state of the system is known only through uncertain measurements the solution becomes much more complex. In our application, there is considerable uncertainty in quality measurements, and hence this more complex problem must be addressed. If the state is known through uncertain measurement, the information must be expressed as probability densities, c.f. measurement equation in Eq.(1). For uncertain state information the DP-algorithm takes the form [2,3]
J k pk , u k
H ku u k H kx x k p x k | Z k , U k 1 dx k E ^J k 1 p k 1 , u k 1 `,
³
xk
J N pN
³
xN
H Nx x N p x N | Z N 1 , U N 1 dx N ,
z k 1
(3) k
0...N 1
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where H ku u k is the cost function of the control action and H kx x k is the cost function of the state and we have assumed the overall cost additive of these two components. The future state is defined as p k 1 p x k 1 | Z k 1 , U k . The optimal sequence of actions is then obtained by solving uk
opt
arg min^J k pk , uk J N p N `
k
(4)
0,..., N 1
uk
This problem cannot be solved backwards since the cost function depends on probability p k p x k | Z k , U k 1 which cannot be solved independently as shown in the Eq. (2). Instead a tedious but manageable solution that propagates the priors forward was applied. 3.2. DP-algorithm with measurement control subsystem Let us consider a case when only a limited number of measurements can be done at any given time step. In that case not only the actions to the process need to be optimized, but also the measurements must be scheduled. Let us denote the choice of the measurement by m and the collection of choices up to time N by MN = [mN MN-1]T. Now the cost at time k depends not only the state and the control to process, but also of the measurements chosen. The DP-algorithm takes the form J k p k , u k , mk
H ku u k H km m k H kx x k p x k | Z k , U k 1 , M k dx k
³
xk
E ^J k 1 p k 1 , u k 1 , mk 1 `,
k
z k 1
J N pN
³H
x N
0...N 1
(5)
x N p x1 | Z N 1 ,U N 1 dx N
xN
with p x k 1 | Z k 1 , U k , M k 1 C p z k 1 | x k 1 , mk 1 p x k 1 | Z k , U k , M k C p z k 1 | x k 1 , mk 1 p x k 1 | x k , u k p x k | Z k , U k 1 , M k dx k
³
(6)
xk
The optimal sequence of actions is then obtained by solving ª u k opt º « opt » ¬«mk ¼»
arg min^J k p k , u k , mk J N p N `,
k
0,.., N 1
(7)
uk mk
However, the measurement scheduling problem needs not to be solved together with optimal control policy, but it can be solved separately solving the Eq. (4) with varying measurement policy as m k opt
° ½° arg min ®arg min^J k p k , u k J N p N `¾ °¯ u k °¿ mk
k
0,..., N 1
(8)
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4. Case: Quality management in papermaking As a case we consider quality management problem in papermaking. Within quality management the balance between brightness and strength by manipulating fiber fraction ratio and dosage of bleaching chemicals is an important subtask. The Bayesian network of this case is shown in the Fig. 2.
Figure 2. Bayesian network of the quality management case.
Four states have been defined for brightness (critical, low, ok, too high) and three states for strength (critical, low, ok). Measurements of brightness are discretized into eight values and measurements of strength into seven values. The control actions are also discretized, both into five values. Such discretization is appropriate for practical decision making at paper mills. Brightness is mainly controlled by dosage of bleaching chemicals and strength by fiber fraction ratio, but both control actions have impact on both quality variables. The delay for fiber fraction ratio is one time unit and for dosage of bleaching chemicals delay is two time units. One time unit corresponds to manufacturing time of one machine reel. The parameters for the model have been identified by combining information from operator interviews and quality data [4]. If the optimization horizon is three (N=3) and if only one measurement can be made at time, 8 measurement scheduling options exists. We now present a small example in which the process is simulated to behave according to the model in optimization (Table 2). This is a recovery from poor brightness state. After initial measurement of brightness the actions measurements are chosen to monitor the recovery while keeping track on the strength development in case of sudden disturbance in this property. Note that one-stepahead optimal measurement at t 6 deviates from that of two-step-ahead optimal calculated at t 5 . This is because at t 5 surprisingly good brightness was observed and hence switching the measurement over to strength is justified.
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Table 2. Summary of simulation results with optimization horizon N = 3. The first line shows the values of measurement chosen to be made. As only brightness or strength can be measured, the one not measured is denoted with '-'. The second line gives the optimal and implemented actions based on the measurement value. The third line gives the true process states (note the different scale of measurements and states) that are not observable to optimizer. At N = 2 and 3, only the optimal measurement is given, M denoting a measurement, '-' not a measurement. In all pairs in the table, the first value refers to brightness and the second to strength. t=0 N=1
t=1
t=2
t=3
t=4
t=5
t=6
Meas. value
2
-
-
6
-
6
6
-
-
7
6
-
-
6
Opt. control
4
4
3
3
4
3
3
3
3
3
3
3
3
3
True state
1
3
1
3
2
3
3
3
3
3
3
3
3
3
N=2
Opt. meas.
-
M
-
M
M
-
-
M
M
-
M
-
M
-
N=3
Opt. meas.
M
-
M
-
M
-
M
-
M
-
M
-
M
-
If both measurements can be made simultaneously but with higher uncertainty, measurement scheduling options are increased to 27, and if one option is to measure neither, 64 measurement scheduling options exists with the optimization horizon of three.
5. Conclusion In this paper we have shown the use of Bayesian network as a model for dynamic programming. We have presented the quality management problem in papermaking and shown a method to optimize the control action to the process and the control to measurement subproblem. An obvious problem in the presented approach is the curse of dimensionality. As the number of variables, states and controls and the dimension of measurements increase and as the time horizon increases, the recursion becomes deeper and the calculation time consuming and memory intensive. One solution to somewhat manage the dimensionality problem is reducing the discretized values of measurements further down in time horizon. Identifying a Bayesian network is non-trivial. The verification of probability models based on human knowledge would require open-loop data, but only a closed loop data with little input variations is available. Therefore tuning the model is time-consuming and interactive process. The models applied within this study are versions that will need further analysis and practical testing.
References [1] F.V. Jensen, 2001, Bayesian Networks and Decision Graphs, Springer Verlag, New York. [2] D.P. Bertsekas, 1995, Dynamic Programming and Optimal Control, volume 1, Athena Scientific, Belmont, Massachusetts. [3] L. Meier, J. Peschon, R.M. Dressler, 1967, Optimal Control of Measurement Subsystem, IEEE Transactions on Automatic Control, vol. AC-12, no. 5, 528-536. [4] A. Ropponen, R. Ritala, to be published.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
OntoMODEL: Ontological Mathematical Modeling Knowledge Management Pradeep Suresha, Girish Joglekara, Shuohuan Hsua, Pavan Akkisettya, Leaelaf Hailemariama, Ankur Jainb, Gintaras Reklaitisa , and Venkat Venkatasubramaniana1 a b
School of Chemical Engineering, Purdue University, West Lafayette IN 47907, USA Enterprise Optimization, United Airlines, Chicago IL 60007, USA
Abstract In this paper we describe OntoMODEL, an ontological mathematical model management tool that facilitates systematic, standardizable methods for model storage, use and solving. While the declarative knowledge in mathematical models has been captured using ontologies, the procedural knowledge required for solving these models has been handled by commercially available scientific computing software such as Mathematica and an execution engine written in Java. The interactions involved are well established and the approach is intuitive, therefore not requiring model user familiarity with any particular programming language or modeling software. Apart from this key benefit, the fact that OntoMODEL lends itself to more advanced applications such as model based fault diagnosis, model predictive control, process optimization, knowledge based decision making and process flowsheet simulation makes it an indispensable tool in the intelligent automation of process operations. This paper also discusses the shortcomings of existing approaches that OntoMODEL addresses and also details its framework and use. Keywords: Ontology, Mathematical modeling knowledge, knowledge management.
1. Introduction Mathematical knowledge is a very broad term that could be used to describe various components of mathematics such as theorems, lemmas, proofs etc. In this work we use the term ‘Mathematical Modeling Knowledge’ to denote the vast amount of knowledge that exists as mathematical models, the modeling assumptions and the model solving procedures associated with them. Compared to other forms of knowledge, like rules, decision trees, guidelines etc., mathematical knowledge is more abstract and highly structured (Farmer 2004). Most forms of mathematical knowledge are either embedded in specific software tools such as unit operation models in simulation software, or have to be entered into a more general mathematical tool following a specific syntax, like Matlab or Mathematica. Much of this knowledge, however, concerns specific applications and expressed procedurally rather than declaratively. For example, in the application domain of chemical process development, Aspen Custom Modeler (See URL) uses a specific modeling language for user to provide or create new models in order to be used with other Aspen products. The need for an automated, systematic, reusable mathematical model knowledge capturing environment is very real and justified in the context of the large amounts of process and product information and 1
Corresponding author
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knowledge generated and stored. In this work we will propose an ontological approach to address these needs.
2. Existing Modeling Approaches and Limitations In almost all of the mathematical modeling knowledge management approaches mentioned below, the model is unique to the format it is created in and hence cannot be shared/reused, and even if so, interfacing is neither user friendly nor transparent. 2.1. Microsoft Excel Perhaps the most popular approach to handle simple mathematical models is Microsoft Office’s spreadsheet application, Excel. It provides basic calculation and plotting abilities and can copy formulae and refer values based on cell names. Clearly, Excel is not capable of handling complex models (e.g. differential equations). Models created in Excel are sometimes difficult to interpret and cannot be shared across most software packages 2.2. Commercial Mathematical Modeling Packages It is possible to solve mathematical models in commercial mathematical packages, such as Matlab, Mathematica or Aspen Custom Modeler, so as to utilize the equation solving and visualization capabilities of these tools. This approach provides better usability compared to Excel since the variable names are directly used instead of cell locations or aliases as in Excel. The users who need to use the model however, have to be familiar with the specific syntax designed for that package. Thus, it would be difficult for users other than the developers/experienced users to utilize the knowledge. 2.3. Commercial Flowsheet Simulators Commercially available flowsheet simulators such as Aspen Plus, Batches provide another approach for mathematical model solving where the model usually exists as a “blackbox” giving the user no freedom to create new models or manipulate existing models. The process of model solving typically is embedded in the form of a flowsheet simulation and the user has drag/drop options to pick operations that have parameters to be solved for. The models behind these operations have been hardcoded by the software developer beforehand. 2.4. Other related work Bogusch et al. (1997) refer to an ontology based approach for managing process model equations that defines the semantics between the equation and the variables in them. Although many research groups have tried to use such an ontological structured framework for managing mathematical knowledge in process models e.g. ModKit (Bogusch et al., 2001), ProMot (Mangold et al., 2005) etc, most of them have had to rely upon the simulation environment/engine to analyze and solve the systems of equations while powerful dedicated solvers are available.. Marquardt et al (2004) describes design and implementation of ROME (Repository of a Modeling Environment), a model repository to support maintenance of heterogeneous process models and their integration from a data management point of view. The CAPE-OPEN (See URL) standard aims at supporting the modeling process by providing interoperability between modeling tools. While the actual model can exist in any tool by itself, a wrapper has to be written around each model in a markup language called CapeML which creates the input and output ports of the model so that it can interact with other models. While both ROME and CAPE OPEN initiatives try to address the goal of model interoperability and communication, the individual models are still in a format that is specialized and therefore requires familiarity to manipulate models.
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3. Ontological approach In the proposed approach (mentioned briefly in Venkatasubramanian et al., 2006) for modeling mathematical knowledge, the declarative and procedural parts of the mathematical knowledge have been separated. The declarative part consists of the information required by the model to be solved, the information generated from the model, and the model equations. The procedural part consists of the details of model solving such as the algorithms being used and variable initializations. Mathematical Markup Language (See URL) which is based on XML has been used as a standard way of describing the mathematical equations. There are two dialects in MathML: the presentation markup which concentrates on displaying the equations; the content markup concentrates on the semantics (meaning) of the equations. Among the ontology development tools available for OWL, Protégé 3.2 was selected due to its maturity, ease-of-use, its scalability and extensibility (Castells et al 2004b). The Web Ontology Language (OWL) provides an ontology modeling language with defined formal semantics. There are already tools available both for authoring and parsing various forms of OWL documents as well as tools for reasoning over ontologies expressed in OWL (Obitko et al. 2003). Thus OWL is used to model the ontologies as described below. Fig 1 shows a schematic of the intercommunications in the proposed approach. The declarative part of the approach consists of a ModelDefinition ontology (or Model ontology) which contains the definition of the models and an information repository, Model Use ontology (or Operation ontology) containing design data such as operating conditions, equipment parameters for the use of models. The model ontology consists of a model class that has as attributes, instances of Equations class that denote the model equations (which in turn can be DAE’s, PDE’s, Integral eqns, Algebraic eqns or function Fig 1. Proposed Approach evaluations) and instances of the assumptions, model parameters, dependent variables, independent variables, universal constants classes. All the above attributes of a model class essentially describe the knowledge about the model in an intuitive and explicit manner which makes the model representation systematic, computer interpretable and generic in nature. One of the biggest strengths of this approach is that the components of the model thus created are entirely reusable i.e. equations, variables, assumptions from one model can be reused while creating another model. Several web based graphical editors are available to create mathematical equations and store them in Content MathML (WebEq, See URL). Thus, the process of creating a mathematical model becomes very intuitive and user friendly compared to the existing approaches. Each model in this approach is an instance of the model class of the ontology. Model variables are linked to their values using a namespaces recursively which essentially provide the hyperlink to the placeholder of the value in the operation ontology. The ModelDefinition ontology also contains the functional representation of the model in the form of Signed Directed Graph (Maurya et al., 2003) for advanced model based fault diagnosis. Fig 2 shows a subset of concepts and relationships captures in the model ontology
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Fig 2: Block diagram of the Model ontology The ModelUse ontology consists of the operation class whose subclasses are the different unit operations in chemical/pharmaceutical product development and instances contain the operating conditions of the operation. This ontology also consists of the results class wherein the link to file containing the results of model solving is stored. The procedural part of this approach consists of a Java based engine for constructing statements that parse the equations in MathML and translating them to expressions interpretable by the Mathematica, which was chosen as the solver. The engine also creates statements to (1) initialize the model parameters with values provided in the instance of the model class chosen, (2) create associations between variable indices and quantities it stands for, (3) initialize universal constants, (4) put together the actual model solving command and (5) invoke the Mathematica kernel to solve the set of equations. Mathematica provides us with many readily useful features, including the symbolic processing capability which handles equations in MathML formats directly and the extensibility with programming languages like Java. A Graphical user interface (GUI) is used to display results from the solver (plots or expressions) along with storing results back to the ModelUse ontology and is also used to select the instance of the model to be solved and the operation to be modeled.
4. Batch Filling model Example Fig 3 shows an example of how a batch tank filling operation is modeled using OntoMODEL. The model equations (in this case, mass and species balances) are converted to Content MathML strings and stored in the hasEqn attribute. The assumptions, dependent, independent variables and model parameters are also defined. The JAVA engine on execution lets the user pick the model instance and operation instance after which it constructs Fig 3. Tank filling model
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Mathematica statements that construct equations from MathML strings, initialize model parameters based on operation instance, and finally create solve statements that let Mathematica know which variables to solve for. On computation, the results are given back by the Mathematica kernel to the GUI and plots, other results are either shown graphically in the GUI or stored back in the operational instance.
5. OntoMODEL The resulting tool using the ontological approach described above acts as an ‘one-stop shop’ for systematic model creating, manipulating, solving, searching and querying which is completely transparent, user friendly and automated. The tool has been shown to work for DAE’s, ODE’s, and Algebraic equations with unit operation models from pharmaceutical product development, e.g. Johanson’s Rolling theory (Johanson et al 1965). The GUI shown in Fig 4 is undergoing constant updates and later versions have features to search and query models, equations etc. Apart from this standalone application, the model repository is also being investigated for use in model predictive control, fault diagnosis and ontology based decision making frameworks.
Fig 4. User interface for OntoMODEL
6. Summary Despite progress in individual fronts of mathematical modeling knowledge management such as sophistication of solvers and standardized markup languages for model representation, progress towards a framework that provides a reusable, user friendly, portable, integrated model management environment was lacking, especially for pharmaceutical product development. In this work, an integrated framework that facilitates the process of mathematical model creation, manipulation, reuse and solution is described. An ontological information-centric approach to model the mathematical information and knowledge is proposed which offers a variety of advantages from the developer and user perspective. Various other applications of this framework, apart from being a useful standalone tool, such as being part of an ontological decision logic framework, model based process operations such as fault diagnosis, control and optimization are being explored.
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References Aspen Custom Modeller, http://www.aspentech.com/product.cfm?ProductID=54 R. Bogusch, W. Marquardt, 1997, A formal representation of process model equations, Computers & Chemical Engineering, 21 (10): 1105-1115 R. Bogusch, B. Lohmann, W. Marquardt, 2001, Computer-aided process modeling with ModKit, Computers & Chemical Engineering, 25 (7-8): 963-995 The CAPE Open Laboratories network, http://www.colan.org/ P. Castells, B. Foncillas, R. Lara, M. Rico and J.L. Alonso, 2004, Semantic Web technologies for economic and financial information management, Lecture Notes in Computer Science 3053 473-487 W. M. Farmer, 2004, MKM: A New Interdisciplinary Field of Research., ACM SIGSAM Bulletin, 38(2) J. R. Johanson, 1965, A rolling theory for granular solids, Trans. of the ASME: J. Appl. Mech., Series E, 32(4), 842-848 M. Mangold, O. Angeles-Palacios, M. Ginkel, A. Kremling, R. Waschler, A. Kienle, and E. D. Gilles, 2005, Computer-aided modeling of chemical and biological systems: Methods, tools, and applications, Industrial & Engineering Chemistry Research 44 (8): 2579-2591 M. R. Maurya, R. Raghunathan, and V. Venkatasubramanian, 2003, A Systematic Framework for the Development and Analysis of Signed Digraphs for Chemical Processes. 1.AlgorithmsandAnalysis, Industrial & Engineering Chemistry Research 42, 4789-4810 W. Marquardt, M. Nagl, 2004, Workflow and information centered support of design processes - the IMPROVE perspective, Computers & Chemical Engineering 29 (1): 65-82 MathML, http://www.w3.org/Math/ M. Obitko and V. Marik, 2003, Adding OWL semantics to ontologies used in multiagent systems for manufacturing, Lecture Notes in Artificial Intelligence 2744 189200 V. Venkatasubramanian, C. Zhao, G. Joglekar, A. Jain, L. Hailemariam, P. Suresh, P. Akkisetty, K. Morris, G.V. Reklaitis, 2006, Ontological informatics infrastructure for pharmaceutical product development and manufacturing, Computers and Chemical Engineering 30, 1482–1496 WebEq, http://www.dessci.com/en/products/webeq/
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OntoCAPE 2.0 – a (Re-)Usable Ontology for Computer-Aided Process Engineering Jan Morbach, Andreas Wiesner, Wolfgang Marquardt AVT-Lehrstuhl für Prozesstechnik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
Abstract This contribution gives an overview on version 2.0 of OntoCAPE, a formal ontology for the domain of Computer-Aided Process Engineering (CAPE). We argue that a useful ontology must simultaneously strive for usability and reusability, explain how these goals are achieved by OntoCAPE, and present some application examples. Keywords: Ontology, CAPE, information modeling, knowledge representation.
1. Introduction An ontology is an explicit specification of a conceptualization, typically involving classes, their relations, and axioms for clarifying the intended semantics [1]. It constitutes a structured framework for the storage of information and knowledge, which can be reused and shared across different software applications. Particularly, ontologies have been suggested as a means to efficiently build knowledge-based software from reusable components [2]. To this end, the (generic) ontology must be transformed (i.e., extended and customized) into an application-specific knowledge base. OntoCAPE is a formal ontology designed for use with different types of CAPE tools that support such diverse tasks as mathematical modeling [3, 4], knowledge management [5], and data integration [6]. OntoCAPE emerged from two large, interdisciplinary research projects: the COGents project [3] and the IMPROVE project [7]. In IMPROVE, the conceptual basis for OntoCAPE was established by the information model CLiP [8]. Based on CLiP, the COGents project created version 1.0 of OntoCAPE [4], aiming at applications in the area of modeling and simulation. After the completion of COGents, the further development of OntoCAPE was taken over by IMPROVE. In 2007, version 2.0 was released [9], which has a broader scope than version 1.0, additionally aiming at applications in the area of process design. In the following, we will exclusively refer to OntoCAPE 2.0. Related efforts are, amongst others, the ISO 15926 Upper Ontology [10] and the POPE ontology [11]. An extensive review of these and other ontologies, including a comparison with OntoCAPE, can be found in [12]. The remainder of this paper is organized as follows: Sect. 2 gives an overview on OntoCAPE; in Sect. 3, the goals of ontology usability and reusability are introduced and discussed; Sect. 4 explicates how these goals are achieved by the design of OntoCAPE; Sect. 5 describes some prototypical software applications that demonstrate the practical applicability of the ontology; Sect. 6 concludes the paper by summarizing our findings.
2. An overview on OntoCAPE OntoCAPE is organized through three types of structural elements: layers, modules, and partial models (cf. Fig. 1).
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The layers subdivide OntoCAPE into different levels of abstraction, thus separating general knowledge from knowledge about particular domains and applications. The topmost Meta Layer, is the most abstract one; it holds a Meta Model that introduces fundamental modeling concepts and states the design guidelines for the construction of the actual ontology. Next, the Upper Layer of OntoCAPE defines the principles of general systems theory according to which the ontology is organized. On the subjacent Conceptual Layer, a conceptual model of the CAPE domain is established, which covers such different areas as unit operations, equipment and machinery, materials and their thermophysical properties, chemical process behavior, modeling and simulation, and others. The two bottommost layers refine the conceptual model by adding classes and relations required for the practical application of the ontology: The ApplicationOriented Layer generically extends the ontology towards certain application areas, whereas the Application-Specific Layer provides specialized classes and relations for concrete applications. notation
Meta Model Meta Layer
Upper Layer
meta_model module module OntoCAPE
Layer
includes
upper_level system
module module partial model
chemical_process_system Layer
partial model
CPS_realization Conceptual Layer
plant plant_equipment fixture machine
Application Oriented Layer Application Specific Layer
apparatus
applications e-procurement
Fig 1: A detail of OntoCAPE demonstrating the overall structure of the ontology
A module assembles a number of interrelated classes, relations, and axioms, which jointly conceptualize a particular topic (e.g., the module ‘plant’ provides a conceptualization of chemical plants). The boundaries of a module are to be chosen in such a way that the module can be designed, adapted, and reused to some extent independently from other parts of an ontology [13]. A module may include another module, meaning that if module A includes module B, the ontological definitions specified in B are valid in A and can thus be directly used (i.e., extended, refined …) in A. That way, OntoCAPE can be organized as an inclusion hierarchy of loosely coupled modules. Modules that address closely related topics are grouped into a common partial model (e.g., the partial model ‘plant_equipment’ clusters the thematically related modules ‘fixture’, ‘apparatus’, and ‘machine’). Unlike modules, partial models may be nested
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and may stretch across several layers. While the boundaries of the modules are chosen for practical considerations (such that the interdependencies between the individual modules are minimized), the boundaries of the partial models reflect the “natural” categorization of the domain. At present, OntoCAPE, including the Meta Model, has a total of 62 modules, which are clustered in 27 partial models; the modules on the upper three layers (down to and including the Conceptual Layer) comprise about 500 classes, 200 relations, and 1000 axioms. Additionally, OntoCAPE can be combined with other, specialized ontologies representing documents, work processes, and decision-making procedures, as described in [5, 12]. An extensive documentation of OntoCAPE as well as an implementation of the ontology in the OWL modeling language [14] are accessible at http://www.avt.rwthaachen.de/AVT/index.php?id=486
3. The challenge of (re-)usability Principally, any ontology has to meet two major goals: to be usable and to be reusable: The usability of an ontology denotes the degree to which the software component is useful for a specific task or application. The term also has the connotation of “ease of use” pertaining to the effort required by a user to operate the system. By definition, an ontology is never ready for use, but must always be adapted and refined to result in a knowledge base for the envisioned application. Therefore, the goal of ontology usability can be phrased as minimizing “the effort required to customize the ontology so that it can be used by humans or machines in a given application context” [15]. The reusability of an ontology can be defined as “the adaptation capability of an ontology to arbitrary application contexts” [15], including those contexts “that were not envisioned at the time of the creation of the ontology” [16]. Note that it is neither feasible nor desirable to design an ontology that is equally appropriate for all application contexts [17]; rather, the goal of reusability is to come up with an ontology that can be adapted to a preferably large number of applications. Unfortunately, it is difficult to simultaneously achieve high degrees of usability and reusability: Specializing in one kind of task makes the ontology more useable for this particular task, but it also decreases the likelihood of its reusability. A highly abstract ontology, on the other hand, may be applicable to a variety of different tasks, but it is unlikely to prove very useful for any of these without extensive modification and detailing. This challenge is known as the reusability-usability trade-off problem [18] in the literature.
4. Design features of OntoCAPE To resolve the aforementioned trade-off problem, OntoCAPE adopted a number of design features that were suggested in the literature. For lack of space, we will only discuss the most important ones: First to mention is the structuring of OntoCAPE into levels of abstraction, which has been recommended by numerous authors (e.g. [16, 17]). According to the trade-off problem, the general knowledge, which is located on the upper layers of OntoCAPE, can be reused in a variety of application contexts, but it is not immediately usable. By contrast, the knowledge located on the lower layers is ready for use, but problemspecific and thus hardly transferable to other applications. Thus, depending on the respective application, the appropriate level of abstraction for knowledge reuse must be found. In practice, this means that one needs to move up the ontology (starting from the Application-Specific Layer) until the encountered knowledge is generic enough to fit
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the respective application context. As an example, consider a CAPE tool, for the development of which a preferably large part of OntoCAPE is to be reused. The knowledge on the bottommost layer is application-specific and therefore of little value for any new tool. But already the above Application-Oriented Layer may contain some reusable knowledge (provided that the tool operates in an application area that is covered by OntoCAPE at all). If this is not the case, we need to move up to the Conceptual Layer; here, at the latest, some reusable knowledge can be found. Thus, one may reuse the ontology down to and including the Conceptual Layer, at least. A second design feature recommended by many ontologists (e.g., [13, 19]) is modularization, that is, the subdivision of the ontology in self-contained modules. By definition, modules have strong internal coherence but relatively loose coupling with the other parts of the ontology [17], which facilitates (i) their selective reuse and (ii) the obligatory customization effort. As for (i), one may choose to reuse only a selected part of the ontology; in this case, it is relatively simple to cut the connections between the modules to be reused and the remainder of the ontology. As for (ii), a single module can be more easily adapted and refined. The reason for this is that the newly defined terms do not have to be compatible with the entire ontology, but only with a subset, thus reducing the likelihood of inconsistencies between new and existing ontological definitions. A positive side-effect of modularization is that the modules are concise and therefore easier to deal with than a complete ontology, hence bringing further advantages with respect to maintenance and intelligibility. A third feature to be mentioned is the Meta Model, which is located on top of OntoCAPE. Its primary function is to guide the development of OntoCAPE. To this end, the Meta Model explicitly states the underlying design principles and establishes general standards for ontology engineering. Due to these properties, the Meta Model has also proven beneficial for the reuse of the ontology: Firstly, when the ontology needs to be modified for a particular application, the Meta Model ensures a consistent modeling style. Secondly, by means of so-called ‘design patterns’ – i.e., templates suggesting best practice solutions for recurring design problems – the Meta Model provides valuable guidance for extending the ontology. Thirdly, by examining the Meta Model, new users can quickly familiarize themselves with the modeling style of the entire ontology. Consequently, the users may evaluate at an early stage if the ontology is generally compatible with the target application. This is of special importance, since assessing the suitability of an ontology for a given application is one of the most time-consuming tasks in ontology reuse [15].
5. Applications of OntoCAPE Some prototypical software applications have been developed around OntoCAPE, which demonstrate the ontology’s capability for reuse as well as its wide range of applicability: • In the COGents project [2], OntoCAPE forms part of a multi-agent framework, which supports the selection and retrieval of suitable process modeling components from distributed model libraries. Within this framework, OntoCAPE serves as a communication language between interacting software agents, and between the software agents and the human users. Concepts from OntoCAPE are used to formulate a modeling task specification, which is then matched against available process modeling components also described through OntoCAPE. • OntoCAPE has also been applied for the computer-aided construction of process models following an ontology-based approach [4]. This approach constructs a
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mathematical model in two successive steps. In the first step, a human modeler constructs a conceptual model of the chemical process; this is accomplished by selecting, instantiating, and connecting appropriate concepts from OntoCAPE that reflect the structural and phenomenological properties of the chemical process. Based on these specifications, the mathematical model is automatically created by a model generation engine in the second step: The engine selects and retrieves appropriate model components from a library of model building blocks; these model components are subsequently customized and aggregated to a mathematical model, according to the specifications of the conceptual model. • OntoCAPE has furthermore been reused for the implementation of a Process Data Warehouse (PDW), which supports the management of experience knowledge in process design [5]. Within the PDW, OntoCAPE is utilized for the annotation of electronic documents and data stores. That way, one obtains a consistent, integrated representation of the contents of these heterogeneous information sources. These content descriptions can then be processed and evaluated by the semantic searching and browsing functions of the PDW, which support the navigation between and the retrieval of information resources. • Currently, OntoCAPE is applied in an industrial project that is run in cooperation with partners from the chemical and software industries. The goal of this project is the development of an ontology-based software prototype for the integration and reconciliation of engineering data from distributed information sources [6]. In each reuse cycle, OntoCAPE has been tested and revised. As part of this process, a number of modeling errors and inconsistencies have been detected and eliminated. Moreover, the ontology has been remodeled such way that it is now applicable to a large number of tasks. Consequently, the quality of the ontology has gradually improved throughout these projects.
6. Conclusion We have presented OntoCAPE, a formal ontology for the domain of computer-aided process engineering that is explicitly designed for reuse. An implementation of OntoCAPE in OWL, supplemented by extensive documentation, can be downloaded free of charge at our website. OntoCAPE’s modular, layered structure, supports the partial, selective reuse of the ontology and allows an easy adaptation to various task requirements. The Meta Model provides guidance for extensions and modifications of the ontology and enables a fast screening for compatibility with application requirements. OntoCAPE has been applied in a number of software projects covering the application areas of modeling and simulation as well as process design and engineering. In the course of these projects, the quality of the ontology has gradually improved: Some former errors and deficiencies could be detected and corrected. Moreover, certain parts of the ontology have been reformulated – either to better support efficient reasoning or to enable a more user-friendly representation. As a result, OntoCAPE now constitutes a validated ontology of proven usability, with a high degree of reusability.
References [1] M. Uschold and M. Gruninger, Ontologies: Principles, Methods and Applications, Knowl. Eng. Rev., 11 (1996) 93-155. [2] R. Neches and R. Fikes and T. Finin and T. Gruber and R. Patil and T. Senator and W.R. Swartout, Enabling Technology for Knowledge Sharing, AI Magazine, 12(3) (1991) 36-56.
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[3] B. Braunschweig and E.S. Fraga and Z. Guessoum and D. Paen and D. Pinol and A. Yang, COGents: Cognitive Middleware Agents to Support e-CAPE, in: B. Stanford–Smith and E. Chiozza and M. Edin (eds.): Challenges and Achievements in E–business and E–work, IOS Press, Amsterdam, 2002, pp. 1182–1189. [4] A. Yang and W. Marquardt, An Ontology-Based Approach to Conceptual Process Modeling, in: A. Barbarosa-Póvoa and H. Matos (eds.): Proceedings of the European Symposium on Computer Aided Process Engineering – ESCAPE 14, Elsevier, 2004, pp. 1159-1164. [5] S.C. Brandt, J. Morbach, M. Miatidis, M. Theißen, M. Jarke, W. Marquardt (2008): An ontology-based approach to knowledge management in design processes. Comp. Chem. Eng. 32, 320-342. [6] J. Morbach and W. Marquardt, Ontology-Based Integration and Management of Distributed Design Data. To appear in: M. Nagl and W. Marquardt (eds.): Collaborative and Distributed Chemical Engineering Design Processes: From Understanding to Substantial Support, Springer, Berlin, 2008, Chapter 7.1. [7] W. Marquardt and A. Nagl, Workflow and information centered support of design processes – the IMPROVE perspective, Comput. Chem. Eng., 29 (2004) 65-82. [8] B. Bayer and W. Marquardt, Towards integrated information models for data and documents, Comput. Chem. Eng., 28 (2004) 1249-1266. [9] J. Morbach and A. Yang and W. Marquardt, OntoCAPE - a Large-Scale Ontology for Chemical Process Engineering, Eng. Appl. Artif. Intel., 20(2) (2007) 147-161. [10] R. Batres and M. West and D. Leal and D. Price and K. Masaki and Y. Shimada and T. Fuchino and Y. Naka, An Upper Ontology Based on ISO 15926, Comput. Chem. Eng., 31 (2007) 519-534. [11] V. Venkatasubramanian and C. Zhao and G. Joglekar and A. Jain and L. Hailemariam and P. Suresh and P. Akkisetty and K. Morris and G. Reklaitis, Ontological Informatics Infrastructure for Pharmaceutical Product Development and Manufacturing, Comput. Chem. Eng., 30(10-12) (2006) 1482-1496. [12] J. Morbach and M. Theißen and W. Marquardt, Integrated Application Domain Models for Chemical Engineering, To appear in: M. Nagl and W. Marquardt (eds.): Collaborative and Distributed Chemical Engineering: From Understanding to Substantial Design Process Support, Springer, Berlin, 2008, Chapter 2.6. [13] H. Stuckenschmidt and M. Klein, Integrity and Change in Modular Ontologies, in: Proceedings of the International Joint Conference on Artificial Intelligence - IJCAI '03, Acapulco, Mexico, Morgan Kaufmann, 2003, pp. 900-905. [14] S. Bechhofer and F. van Harmelen and J. Hendler and I. Horrocks and D.L. McGuinness and P.F. Patel-Schneider and L.A. Stein, OWL Web Ontology Language Reference, W3C Recommendation, available at http://www.w3.org/TR/owl-ref/ (2004). [15] E. Pâslaru-Bontaú, Contextual Approach to Ontology Reuse: Methodology, Methods and Tools for the Semantic Web, PhD thesis, FU Berlin, available at http://www.diss.fuberlin.de/2007/230/index.html (2007). [16] T. Russ and A. Valente and R. MacGregor and W. Swartout, Practical experiences in trading off ontology usability and reusability, in: Proceedings of the Knowledge Acquisition Workshop (KAW99), Banff, Alberta, 1999. [17] W.N. Borst, Construction of engineering ontologies for knowledge sharing and reuse, CTIT PhD-thesis series, Universiteit Twente , No. 97-14, available at http://doc.utwente.nl/17864/ (1997).. [18] G. Klinker and C. Bhola and G. Dallemagne and D. Marques and J. McDermott, Usable and Reusable Programming Constructs, Knowl. Acquis., 3(2) (1991) 117-135. [19] A. Rector, Modularisation of Domain Ontologies Implemented in Description Logics and Related Formalisms Including OWL, in: S. Haller and I. Russell (eds.), Proceedings of the 16th International FLAIRS Conference, AAAI Press, Florida, 2003. [20] T.R. Gruber and G.R. Olsen, An ontology for engineering mathematics, in: J. Doyle and P. Torasso and E. Sandewall (eds.), Fourth International Conference on Principles of Knowledge Representation and Reasoning, Bonn, Germany, Morgan Kaufmann, 1994, pp. 258-269.
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CAPE Methods and Tools for Systematic Analysis of New Chemical Product Design and Development Merlin Alvarado-Morales,a Naweed Al-Haquea, Krist V. Gernaeyb, John M. Woodleyb, Rafiqul Gania a
CAPEC, bBioEng, Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
Abstract This paper highlights the use of CAPE methods and tools for systematic analysis of chemical product-process development. Through a conceptual case study involving the production of four chemical (intermediate) products via a second-generation biorefinery route, the steps of analysis and the need for, as well as the use of, CAPE methods and tools are highlighted. Keywords: Chemical product, Process design, Property model, CAPE, Biorefinery
1. Introduction Conventionally, computer-aided process engineering (CAPE) has been concerned with the development and solution of problems related to chemical process design, control and operation through systematic computer-aided techniques. The oil and gas industry, the petrochemical industry and to some extent, the chemical industry have been the traditional users of the methods and tools, including software, from the PSE/CAPE community. Problems related to process optimization, process integration and process synthesis/design are currently solved through knowledge-based methods as well as mathematical optimization techniques. To date systematic (and/or computer-aided) methods and tools have been developed and applied successfully to solve many industrial problems. However, future applications will not only demand CAPE methods and tools, but also require new tools and models. This is well illustrated by the application of CAPE to the second generation of biorefinery concept discussed in this paper. As resources decrease and demand for products in terms of quantity (as well as quality) increase, it is necessary to continuously develop better and significantly improved chemical-based products in order to satisfy the needs of the modern society. On the other hand as Gani and Grossmann (2007) noted, we continually face the questions ⎯which of our current products should be replaced, which products will we need for the future and how do we search for sustainable alternatives? In addition we can ask whether it will be possible for the CAPE/PSE community to provide and develop the necessary methods and tools to address these problems, or can the methods and tools currently available be used to solve these problems? These questions can be addressed through the formulation and solution of integrated product-process design problems that can be viewed as new opportunities and challenges for CAPE/PSE. In particular, the areas of energy and sustainability clearly provide new challenges and opportunities. One example is the shift towards renewable resources with respect to energy, most notably
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through the increasing use of biomass as a renewable energy source, which requires addressing processes that have quite different characteristics than the traditional petrochemical processes in as much as the reactions are only mildly exothermic and take place at relatively moderate temperatures and pressures. Furthermore, the separations tend to involve highly dilute aqueous systems. The objective of this paper is to highlight the use of CAPE methods and tools in the different stages of the design and development of chemical products and their sustainable production. In particular, some of the design and development issues related to the production of important intermediate chemicals from alternative renewable resources are analyzed.
2. Chemical product-process development The design of chemical products and their sustainable production involves analysis of the product-process needs; generation of process alternatives (for a specified product); evaluation of the product-process performance; final selection and validation of the product-process (Gani, 2004). Systematic model-based methods and tools can be applied at every step, depending on the availability of appropriate models. Consider, for example, an intermediate chemical (product) that can be produced from a range of renewable resources. A pre-analysis of the product qualities and its characteristics, defines the process needs. Even though a product may be obtained through many processing routes, the objective must be to identify those that are sustainable. Here, algorithms that can quickly generate and evaluate processing alternatives are needed together with a set of performance criteria and product-process specifications. Productprocess specifications help to identify the set of feasible alternatives, while more sustainable alternatives can be identified by using sustainability metrics and/or life cycle assessment as the set of performance criteria. The main supporting CAPE tools are: modelling tools (models need to be generated, tested, and validated before use, as an example: MoT); property tools (truly predictive but reliable calculations are needed: ProPred, TML); process synthesis/chemical synthesis (generation of flowsheet and molecules/mixture alternatives: ProCAFD, ProCAMD); design tools (driving force based design of operations: PDS); process simulation (for verification/analysis of design: PROII£ and ICAS); databases (database of chemicals, reactions, enzymes, etc., are always useful to have: CAPEC database). As a proof of concept case study, the development of four intermediate chemical products and their corresponding processes is highlighted below. The objective is to identify four intermediate chemical products that can be produced from renewable resources, which may be corn, straw, and/or lignocellulose. The methods and tools listed above, ICAS (Gani et al., 1997), MoT, ProPred, TML, ProCAMD, ProCAFD, PDS, CAPEC-database (Gani, 2002), and PROII£ have been used in the case study. The same methods and tools can also be used for product-process development in pharmaceutical, food, and agrichemical industries. 2.1. Product-process analysis: biorefinery Considering the concept of a biorefinery ⎯ a facility that integrates biomass conversion processes and equipment to produce chemicals, fuels and power - the four chemical products can be identified from multiple products that are commonly attributed to a biorefinery. A biorefinery might, for instance, produce one or several low-volume (but
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high-value) chemical products as well as low-value (but high-volume) products such as intermediate chemicals and/or liquid transportation fuel, while generating electricity and process heat for its own use. The high-value products enhance profitability while the high-volume products may also enhance profitability by producing other high value chemicals in the product supply chain, or, as fuel helping to meet increasing energy needs. In addition, the power production reduces over-all production costs and avoids greenhouse-gas emissions. Based on the above discussion, four chemical products (as listed in table 1) have been selected.
Figure 1. Basic principles of a biorefinery.
An interesting feature for the four selected chemical products is that they can be produced from the same source – that is, conversion of glucose, which can be produced from corn, straw or lignocellulose (see Figure 1). The product palette of a biorefinery not only includes the products produced in a petroleum refinery, but also in particular products that are not accessible in petroleum refineries. For instance, furfural and 5hydroxymethyl-furfural (HMF) are interesting by-products from lignocellulose feedstock biorefinery. Furfural is the starting material for the production of nylon 6,6 and nylon 6. 2.2. Setting of targets for product-process design The first step is to evaluate a base case design and define targets for generation of more sustainable alternatives. In this way, an analogy may be drawn with computer aided molecular design (CAMD), where molecules matching a set of target properties are identified. In this case, using the same principle, process flowsheets matching a set of design targets (improved sustainability metrics) will be analyzed. Figure 2 shows a simplified version of the flowsheets for the conversion of corn as the raw material to produce the four chemical products listed in table 1 (the detailed flowsheet for each product can be obtained from the authors).
Figure 2. Simplified flowsheet for the production of bio-based chemicals from corn.
Figure 2 also shows the results of a mass balance based on the amount of products obtained per kg of raw material (in this case, corn) and the amount of water used in the principle processing steps using collected data from the open literature. Based on this
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mass balance and an added energy balance, a cost analysis for the 4-products biorefinery has been performed. The results are summarized in table 1. It can be noted that the three high value products have an acceptable rate of return while the low value product is not economically feasible for the production rates listed in table 1. This means that the targets for more sustainable design alternatives should be focused on production of ethanol for this biorefinery. From figure 2 it can be seen that economic feasibility of the process for ethanol can be improved through higher product yields and/or more efficient product recovery. Table 1. Cost analysis of 4-products biorefinery Product Production (kg/h) Profit ($)/kg Payback time (yr) Price ($/kg) Lactic acid 1271.23 0.042 6 1.10 1, 3-propandiol 1256.76 0.058 4.1 1.34 Succinic acid 1226.67 0.043 7.4 1.10 Ethanol (corn) 1135.25 0.019 11.62 0.75 Ethanol (lignocellulose) 18557.0 -0.166 0.75
As the reactor effluents are dilute aqueous solutions of the product, recovery is not straightforward. Furthermore, separation by distillation is both difficult and expensive because of the ethanol-water azeotrope. In this work, we have considered alternative product recovery strategies for ethanol and succinic acid (to identify another alternative to crystallization for product recovery). The option of increased product yield in the reaction is beyond the scope of this work as it involves the design/selection/testing of new catalysts or enzymes. 2.3. Generate-test design alternatives The traditional succinic acid recovery method is based on precipitation and crystallization technology. However, the recovery of succinic acid by this process is costly and complex. From an analysis of succinic acid-water binary mixture, it is clear that solvent-based separation is an option worth considering, for example liquid-liquid extraction (LLE). ProCAMD (Harper and Gani, 2000) has been used to find solvents for LLE of succinic acid from water. Figure 3(a) shows the LLE driving force diagram for succinic acid-water-solvent (butyl acetate and propyl acetate) on a solvent free basis. From figure 3(a) it can be seen that between the two solvents that have been identified, butyl acetate is better as it provides a larger driving force. For the case of ethanol purification, we are highlighting the process with lignocellulose as the raw material (see bottom row of table 1). The product stream from the fermentation stage is a mixture of ethanol, cell mass and water. In this stream, ethanol (produced from lignocellulosic biomass) has concentrations that are lower (less than or equal to 5 wt %) than ethanol produced from corn. To obtain anhydrous ethanol, the first step is to recover ethanol from the product stream of the fermentor. The product (37 wt % ethanol) is then concentrated to obtain anhydrous ethanol (more than or equal to 99.5 wt %). Here also we can employ the driving force concept (Gani and Bek-Pedersen, 2000) to investigate the different separation techniques. From figure 3(b) it can be seen that it is impossible to obtain anhydrous ethanol in a single distillation column (curve 1).Therefore, solventbased or hybrid separation processes are necessary. By solvent-based distillation using ethylene glycol (curve 2) or ionic liquid (curve 4), it is possible to achieve the desired purity.
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Figure 3. (a) Solvent-free driving force curves for succinic acid-water mixture based on LLE. (b) Curves for driving force as a function of composition (curves 1-4) and as constants (curves 5-7) for ethanol-water mixture.
Distillation followed by pervaporation is also a feasible (curves 1 and 3) separation process. As reported by Seiler et al. (2004) compared with the organic solvent-based separation which uses ethylene glycol (curve 2), a saving in overall heat duty of 24% can be achieved by using ionic liquid [EMIM]+[BF4]− (curve 4). This can be very quickly verified through the driving-force based process group contribution approach for flowsheet synthesis and simulation (d’Anterroches, 2005). From table 1, it can be seen that the ethanol from lignocellulosic biomass has a negative profit value. However, with the ionic liquid based distillation process, an improvement to the profit (-0.099 $/kg) can be achieved. This however is still not enough to produce a positive profit, indicating there are costs related to pretreatment and water-use that also need to be targeted (note that the purification step counts for only about 30 % of the total operating cost). 2.4. Final selection and validation From the above analysis, it is clear that applying solvent-based liquid-liquid extraction for recovery of succinic acid and ionic liquid based ethanol purification will lead to lower operating costs without increasing the environmental impact. In addition, the use of resources would be improved through better and more efficient solvents. Thus, these alternatives will improve sustainability metrics related to waste, environmental impact and economics. The final optimal design, however, is not possible to obtain until the production rates for each of the four products are simultaneously optimized. Note that as listed in table 1, the production rate of ethanol is not particularly high, due to imposed constraints on the availability of biomass as the raw material. The flowsheet of a biorefinery could reach a high degree of compactness by using process intensification and specifically bio-reactive separations. For example, in the bioethanol production process, where enzymatic hydrolysis is applied, different levels of process integration are possible. In Consolidated BioProcessing (CBP) all required enzymes are produced by a single microbial community in a single reactor. CBP would appear the logical endpoint in the development of biomass conversion technology. Application of CBP implies no capital or operating costs for dedicated enzyme production (or purchase), reduced diversion of substrate for enzyme production, and compatible enzyme and
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fermentation systems (Hamelinck et al., 2005). Here the major challenge for the CAPE community is how to provide meaningful and useful simulation and optimization tools for modeling these complex systems that in turn require integration with data-intensive experimentation.
3. Conclusions One of the greatest challenges for the future is to use renewable raw materials in an efficient way. The biorefinery concept enables the structuring of the technology needed to ensure efficient biomass conversion to fuels and chemicals (as shown in the example here). There are still some unsatisfactory parts within the lignocellulosic feedstock biorefinery (LCF), such as the utilization of lignin as fuel, adhesive or binder, its pretreatment and hydrolysis steps. In principle, a biorefinery is not only able to produce a variety of chemicals, fuels and intermediates or end-products, but can also use various types of feedstocks and processing technologies to produce products for the industrial market. The flexibility of its feedstock use is the factor of first priority for adaptability towards changes in demand and supply for feed, food, and industrial commodities (Kamm and Kamm, 2004). The integration necessary to provide the optimal blend of fuels and chemicals is complex and CAPE methods and tools are essential to achieve this goal. As exemplified here, a major contribution has been to reduce the time and resources to obtain the analysis/design results. In particular a key opportunity for the CAPE community is that it can play the role of the integrator (Gani and Grossmann, 2007). That is, develop systematic solution approaches that combine methods and tools from different sources into flexible, reliable, and efficient problem specific systems. This will not only require the development and adaptation of current systems, but in many cases will also require the development of entirely new approaches and advanced modelling tools.
References L. d’Anterroches, 2005, Process Flow Sheet Generation & Design through a Group Contribution Approach, PhD thesis, Technical University of Denmark R. Gani and I. E. Grossman, 2007, Process Systems Engineering and CAPE ⎯ What Next ?, 17TH ESCAPE Proceeding Book, Bucharest, Romania 24, 1-5 R. Gani, 2004, Chemical product design: challenges and opportunities, Computers and Chemical Engineering, 28(12), 2441-2457 R. Gani, 2002, ICAS documentation. CAPEC, Technical University of Denmark R. Gani, E. Bek-Pedersen, 2000, Simple new algorithm for distillation column design, AIChE Journal, 46(6), 1271-1274 R. Gani, G. Hytoft, C. Jaksland, A. K. Jensen, 1997, Integrated Computer Aided System (ICAS) for integrated design processes, Computers and Chemical Engineering, 21(10), 1135-1146 C. N. Hamelinck, G. van Hooijdonk, A. P.C. Faaij, 2005, Ethanol from lignocellulosic biomass: techno-economic performance in short-, middle- and long-term, Biomass and Energy, 28(4), 384-410 P. M. Harper, R. Gani, 2000, A multi-step and multi-level approach for computer aided molecular design, Computers and Chemical Engineering, 24(2), 677-683 B. Kamm, M. Kamm, 2004, Principles of biorefineries, Applied Microbiology and Biotechnology, 64(2), 137-145 M. Seiler, C. Jork, A. Kavarnou, W. Arlt, R. Hirsch, 2004, Separation of azeotropic mixtures using hyperbranched polymers or ionic liquids, AIChE Journal, 50(10), 2439-2454 PROII User’s Guide (2006). Simulation Sciences Inc, Brea, USA.
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HAZOP SUPPORT SYSTEM AND ITS USE FOR OPERATION Koji Kwamuraa), Yuji Nakab), Tetsuo Fuchinoc), Atsushi Aoyamad) and Nobuo Takagie) a) Techno Management Solutions Ltd. 4259-3 Nagatsuta, Midoriku, Yokohama, 226-8510, Japan. b) Chemical Resources Laboratory, Tokyo Institute of Technology 4259 Nagatsuda, Midori-ku, Yokohama, 226-8503, Japan. c) Dept. of Chemical Engineering, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-0033, Japan. d) Graduate School of Technology Management, Ritsumei University, 1-1-1 Nojihigashi, Kusatsu, 525-8577, Japan. e) Systems Safety Consulting Ltd., 1279-18 Bukkocho, Hodogaya-ku, Yokohama 240-0044, Japan.
Abstract In their effort to improve safety, process industries have relied on a variety of information systems for managing safety. However, current information systems are limited in their ability to integrate information along the life-cycle. This paper proposes a Hazop support system, which has three functions as follows. (F1) An intelligent CAD system (DFD, Dynamic Flow Diagram) to visualize plant structure, operation with process behavior, (F2) Intelligent user interfaces to make Hazop analysis easer as well as to edit analyzed results (F3) Interface to generate information models to be used in real-time operation. Specifically, this paper describes the knowledge management strategy which is responsible for carrying out potential hazard identification and safety protection layer design systematically. Finally, a case study illustrates the proposed system.
Keywords: Hazop, life-cycle engineering, intelligent CAD, knowledge management, logging system 1. Introduction In their effort to improve safety, process industries have relied on a variety of information systems for managing safety (safety information management systems). One of the challenges in developing such systems is the variety of information. For example, hazard identification requires engineering diagrams such as P&IDs, design specification data, process chemistry, and design information on currently installed/considered protection layers. Furthermore, it is necessary to record, keep and store the hazard identification itself, which is complicated by a number of issues such as: (1) Because hazard identification results and Hazop in particular are recorded in natural language expressions their degree of fidelity and quality are dependent on the particular scribe. (2) It takes long time to carry out hazard identification because searching proper
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information in the relevant documents tends to be time-consuming. (3) Contents in current safety information systems cannot be easily reused when revamping its process because investigation processes are not clear. Two types of Hazop supporting systems have been developed: logging systems and Hazop execution systems (McCoy and Chung, 2001). As most of logging systems have no plant structure models in detail, it is not easy to understand the documents. Execution systems are computer tools for performing Hazop automatically. Automic Hazops requires precise knowledge of process behaviors. Its quality of analysis results is dependent on this knowledge. In a previous research, we have developed technological information models known as MDOOM/MDF (Batres, Naka and Lu, 1998) which cover a wide range of information along the life cycles of product, process and plant (Bayer, 2003). MDOOM/MDF is an integrated model of characterized by physical structure, operation and process behavior information. This paper describes the knowledge management strategy of the proposed Hazop support system which supports potential hazard identification and safety protection layer design for plant life-cycle engineering systematically. Finally, a case study illustrates the proposed system. 2.
Scope of Hazop Support System
The proposed Hazop support system (HazopNavi) has three main functions as follows. (1) Facilitates Hazop analysis for chemical plants at various design stages All Hazop analytical data stored in a database and integrated with PFDs and P&IDs. (2) Assists in the supervision of process states during the operation of the plant while guiding safety operation We design operational information to supervise process state in operation with the database and design rationale. (3) Supports management of change Operation & HazopNavi has been developed based on Management the MDF concept (Multi- Dimensional Model Formalism) as shown in Figure 1. Behavior Plant Structure HazopNavi provides specific Model Model engineering functions for supporting Hazop by using PlantNavi and OpeNavi Figure 1 Multi-Dimensional which are commercially available (Kawamura, 2008). The PlantNavi is an intelligent CAD system (PFD & P&ID) based on the plant structure model of ISO 15926 and include a number of function including searching plant and line queries, equipment specifications as well as drawing expressions. The OpeNavi represents relationships between plant structure and its operating procedures corresponding to CGU (controlled group unit) derived from plant structure (Naka, Lu, and Takiyama, 1997). HazopNavi has the following functions: (F1) It shows plant areas where failures may propagate and indicates equipment of plant structure where may be changed to other failure. In addition, it lists candidates of sensors to detect failures. It helps Hazop by visualizing the parts of plant, where individual failures propagate. This function clearly defines an area where Hazop is being carried out. These propagations are carried based on whether valves are open or closed, so not only steady state operation but also various transient operations such as start-up or shut-down can be analyzed easily.
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(F2) Intelligent user interface: It has two functions to support investigating process of failure propagation and store analysed results and additional evaluation results of likelihood of its failure and degree of its criticality. Its Hazop editor enables users to store Hazop results easily. (F3) Interface to generate information models to be used in real-time operation: It can transform the stored knowledge to the information models for diagnosing abnormal situations in real-time operation. 3.
Methodology
Users
DFD
Operation Support
3.1 System Architecture HAZOP Searching & Plant Structure Logging System With use of MDF model, we have Simulation engine Model developed the system architecture of a Library technological information infrastructure Operation Expert 䊶Behavior Model as shown in Fig. 2, which supports Model 䊶Guide Phrase supervising editing safety engineering information based on Figure 2 System Architecture ‘design rationale’. It is composed of four modules of Dynamic Flow Diagram (DFD), qualitative simulation, library and HAZOP logging system. The DFD share functions of other intelligent CAD systems and also has capabilities of visualizing relationships between plant structure and dynamic process behavior. With its visualization, in order to support users, each symbol in DFD has various features of style change in color, line pattern, line thickness and fill pattern. For example, its characteristics distinctly show valve state of open/closes, pipeline with/without flowing/stagnant fluids, pump working state and so on. HazopNavi has a qualitative simulation engine which can be used instead of existing quantitative dynamic process simulators, thus saving the time it takes to provide various kinds of process models. It is not easy to apply these approaches for entire process hazard identification. HazopNavi can cover entire process plant represented by DFD (PFD and/or P&ID). Safety engineers carry out Hazop by their engineering decisions with qualitative judgment rather than by quantitative simulation. HazopNavi manages kinds of expert engineers’ knowledge for process behavior model. 3.2 Information representation Hazop specific information in the Hazop support system includes: failure propagations, a mechanism that links initiating causes to effects, severity and likelihood, sets of sensors to detect initiating causes or effects. The Behavior model library has two types of models associated to each piece of equipment: deviations caused by equipment failure modes and new deviations caused by other deviations propagated from other equipment. When choosing equipment failure mode, qualitative simulation starts using propagation mechanism as follows. Failure modes provide process deviations, d(0,2) in equipment and d(0,3) at a port from the initiating deviation library. It is called internal propagation. Then, port deviation d(0,3) is propagated through piping line to next equipment and raises an effect as shown in Figure 3. d(0,3) = f etyp,T2 (d(0,2), pt3 ) ........(2) d(0,2) = fetyp,T1(failure mode).............(1) d(i,1) = d(i-1,3) ................ ...(3) d(i,2) = f etyp,P1( d(i,1), pt1 ) ...........(4) d(i,3) = f etyp,P2( d(i,2), pt3 ) .... ..(5) where, d(i, k) is deviation (i=equipment No., k=1 propagation inlet port, k=2 PBE, k=3
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propagation outlet port), f etyp,T1 and f etyp,T2 are initiating behavior model, f etyp,P1 and f etyp,P2 are propagation behavior model, etyp is equipment type, and pt1 and pt3 are port roles of a liquid inlet and gas outlet, respectively. propagation equip.
trigger equip.
port d(i,1)
PBE port d(0,2) d(0,3)
evaluation equip.
port
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port PBE d(n,1) d(n,2) i ( I =1 ..n-1 )
failure mode
final effect
PBE : process behavior in equipment,
port : line connection point to equipment
: internal propagation,
: external propagation
Figure 3 Propagation Mechanism a. Initiating and propagation behavior models are specified for each type of equipment. b. Deviations d( , ) are shown by “Pmore” (more pressure), “Fless” (less flow rate) etc. c. If deviation change is required in piping path, some virtual transforming equipment is added between two equipments as a propagation model. During the design of operating procedures for abnormal situations, engineers require the list of available sensors to detect respective deviations. Each sensor has different sensing capability of propagation mechanism. Figure 4 shows an example for temperature and pressure sensors. HazopNavi’s qualitative model can distinguish between flow and no-flow situations in piping segment. Hazop results are represented in terms of the following elements: (1) initiating cause and final effect (see Figure 5), (2) criticality evaluation, (3) protection and countermeasure, (4) further study required. In order to ease the scribing efforts as well as to keep consistency in the entries of the Hazop results, users construct sentences using a controlled vocabulary by choosing guide phrases in the guide library (Fig. 2). sensor detectable
stagnant pressure deviation
P
Trigger trigger equipment
sensor detectable
temperature deviation
P
P~
not detectable
stagnant
T
P
T~
T
T
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Figure 4 Sensing of Deviation 3.3 Use of HAZOP Database Hazop results from manually executed Hazop studies are generally recorded in spread sheets, which contain very limited cause-effect information. Hazop database stores not only original causes and final effects but also all intermediate propagation cause-effect chain as shown in Fig. 3. Hazop database has information of all sensors on propagation paths. Sensor information is used to recognize that each deviation can be detected by DCS or local instrument, and to decide whether or not protection control logic and countermeasure against the failure works. If it is not sufficient, further study should be
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required so as to improve facilities or additional instrument, interlock or alarm system. All these propagation behaviors are confirmed graphically with DFD functions. Finally, HazopNavi can support operators by using surveillance mechanism based on cause-effect relationships and design rationale. a. When DCS sends an alarm signal and sets of monitoring data to HazopNavi, it identifies cause-failure relationships and recommendation actions. Its function has been made empirically and is installed already into DCS. The proposed appoach logically designs such function and easily maintains it when a plant revamping situation occurs. b. When several abnormal signals happened simultaneously, HazopNavi searches Hazop database to find a cause which satisfies all abnormal signal conditions. 3
Case Studies
The above-mentioned approach has been applied to several process plants. Fig.5 shows case studies of typical pump failure in HDS plant.
Figure 5 DFD representation (Left) Pump failure with over-speed (Right) Pump failure stop Description for Left case; a. Equipment P-201 failed control and becomes over speed (initiating cause). b. Initiating behavior model of pump produces deviation ‘more Flow’ corresponding to eq. (1) and shows it on DFD in Fig. 5. d(0,2) = ‘Fmore’ = fpump,T1(‘over speed’ ) c. All possible propagation paths of normal/reverse flow directions and candidate equipment are highlighted on DFD using plant structure model. d. When analyzing reverse flow P-201 to tank D-201, its propagation behavior model generates PBE deviations of ‘Liquid level down’ and ‘no Liquid’, corresponding to eqs. (4) and (5), respectively. d(1,2) = ‘Lless’ = ftank,P1(‘Fmore’, ‘liquid out’ )
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d(1,3) = ‘LIQnil’ = ftank,P2(‘Lless’, ‘liquid out’ ) ‘LIQnil’:no LIQUID In this case P-201 is both the initiating cause and the recipient of the final effect. Initial deviation ‘more Flow’ is propagated to tank and transformed to ‘no Liquid’, and propagates back to the pump. The right side of Fig. 5 shows more sophisticated example. 4
CONCLUSIONS
This paper proposes an intelligent Hazop support system and describes its core components. The Hazop support system provides the following functions. 1) Integrated information models can support to carry out Hazop with use of DFD interactively. 2) DFD can visualize engineer’s creative thinking processes. 3) Hazop database is reusable and understandable because it clearly keeps relationships between plant structure and failure propagation paths. 4) Hazop database which has information sets of sensors and propagation paths can be used for operation support system. We are develping an information infrastructure to support advanced plant lifecycle engineering by using PlantNavi, OpeNavi as well as HazopNavi. We will support more logical approaches to safety concious production environment as follows. a. operators protection and countermeasure guidelines against abnormal situations, b. alarm management and interlock system design c. preventive maintenance d. management of change in plant facilities and operation e. redesign of plant and process engineering activities.
Acknowledgement The authors would like to thank Hiroshi Sumida for his valuable suggestions on the classification of knowledge of Hazop.
References McCoy, S.A. and P.W.Chung, 2001, ‘Trial of the HAZID Tool for Computer-Based Hazop Emulation on a Medium-sized Industrial Plant’, HAZARDS XVI: Analysing the Past, Planning the Future, Institution of Chemical Engineers, IChemE Symposium Series No. 148, Manchester, UK, pp. 391-404, ISBN 0-85295-441-7. Batres, R. Y. Naka and M. L. Lu, 1998, ‘A Multidimensional Design Framework and its Implementation in an Engineering Design Environment’, Proc. of 5th International Conference on Concurrent Engineering, Tokyo, pp. 15-17 Naka, Y, H. Seki, K. Tazawa and K. Kawamura, 2006, ‘On information Infrastructure For Safety Conscious Design And Operation of Chemical Processes’, Chem. Eng. Transactions Vol. 9, 275-280. Bayer, B., 2003, ‘Conceptual information modeling for computer aided support of chemical process design’, pp43, ISBN 3-18-3 78703-2 Kawamura, K. 2008, ‘Operation, safety and facility management support system by integrated model’, Kagaku Kogaku, Vol.72 (1) pp58-61 (in Japanese) Naka, Y., M.L. Lu and H. Takiyama, 1997, ‘Operational Design for Start-up of Operational Procedures of Chemical Processes’, Comp. Chem. Engng, vol.21 (9), 997-1007.
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Acceleration of the Retrieval of past experiences in Case Based Reasoning: application for preliminary design in Chemical Engineering. Stephane Negny, Jean-Marc Le Lann INPT- LGC- ENSIACET, UMR-CNRS 5503, PSE (Génie Industriel) 118, Route de Narbonne 31077 – Toulouse Cedex 04, France Keywords: Knowledge Management, Case Based Reasoning, Design, Fuzzy Sets.
Abstract : The way to manage knowledge accumulated is one of the firm’s trends, in order to capitalize and to transmit this knowledge. Some Artificial Intelligence methods are devoted to preserve and to reuse past experiences. Case Based Reasoning (CBR) is one of these methods dedicated to problem solving, new knowledge acquisition and knowledge management. CBR is a cyclic method where the central notion is a case which represents an earlier experience. Several cases are collected and stored in a memory: the case base. The goal of this paper is to soften the way to describe problem and to increase the effectiveness of the system during the retrieval of relevant cases.
1. Introduction The design of a process or a product includes several steps. It starts with the requirements formulation and ends with a product (process…) which satisfies most of the requirements. In the chemical engineering field, there are numerous studies dedicated to different design steps: detailed design, simulation, experimental tests or validation… Nevertheless, there are very few on the preliminary design, because this step is often based on the knowledge and past experiences of experts. But this step is essential for the remainder of the design because it gives a starting point for the future solution. In this context, there is a need for a method focused on capitalizing expert knowledge in order to propose quickly a preliminary solution with high quality. In an industrial context, seeking to reduce the time during the whole design process, an effective tool dedicated to preliminary design allows a saving of time thereafter. Case Based Reasoning (CBR) is one method coming from Artificial Intelligence, very useful for capitalizing and reusing past and new experiences, and knowledge deployed in the resolution of problems. After several evolutions, nowadays it is commonly accepted that CBR is a cyclic method (figure 1, R5 model) based on the general principle: Similar problems have Similar solutions. The problems and their solutions are objects of a CBR system, and a case is the representation of an episode problem solving. Most of the time, a case is composed of the descriptions of a problem and its associated solution (with eventually some comments). Many cases are gathered and stored in a memory called the case base. In practice, a new facing problem (target problem) is compared with other problems stored in the case base (source problem) and the most similar one and its solution are extracted, then adapted to propose a solution to the initial problem. For the problem and its solution descriptions, we used a formalism with feature-value pairs: the features or attributes represent the main and the most relevant characteristics
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of the problems and solutions. The first step is the filling of the problem attributes for the target problem (represent). The next step retrieves in the memory one or various similar cases with the help of a similarity measurement in order to rank them (retrieve). Because there are some differences between the source and target problems, the source solution must be adapted to correspond to the target problem (reuse). In the next step the previous adapted solution is tested and revised to eliminate the discrepancies between the desired and adapted solutions (revise). Finally, after its resolution, the target problem and its associated solution form a new case that is retained in the case base (retain). This is an advantage for this method because the storage of a new problem increases the effectiveness of the CBR system by enlarging the cover of the problem space. On the other hand it is also a drawback because by increasing the number of cases in the memory, the time to retrieve a similar case will be increased too. The goal of this paper is to help the user during the retrieval of past cases. This amelioration concerns the retrieved step and can be decomposed in two points: a method to soften case representation and similarity measurement in one hand, and to anticipate the adaptation step in the other hand. Target problem Represent
New Case
Retrieve
New Case
Learned case
Retain
Reuse
Case base
Validated solution
Retrieved Case
Solved Case Revised and tested Case Revise
Figure 1: CBR Cycle
2. Retrieval 2.1. Case Base Organization The number of cases in the case base is going to grow because of the Retain step or memorization of new cases. Without case base organization, the cost to estimate the global similarity between the target problem and all the source cases in the memory becomes prohibitive. In order to decrease the research time and to increase the effectiveness of the retrieval, the latter is decomposed in two steps. The first one consists in selecting a subset of relevant source cases. The second one is dedicated to the similarity measurement and the ranking of source cases included in the subset. To select the subset of the more relevant cases for aresearch, we index the case base to constrain the research space to the nearest source cases. The organization of the memory is based on the decision tree approach. In this approach, the case base is successively restricted thanks to decision sequences. All the cases of the base are gathered at a root node. Starting from this node, intermediate nodes are generated to restrict the number of case by an evaluation on a discriminate feature. And the end of the tree, at final nodes,
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called the leaves, there are the source cases. Finally in this approach, leaves represent the classification and branches represent conjunction of features that lead to these classification. In the tool, the decision tree can be automatically built with an algorithm based on the ID3 algorithm. Nevertheless, the organization of the case base must reflect the point of view of the user, therefore he can generate its own decision tree corresponding to the aim of his retrieval. 2.2. Similarity Measurement Generally in CBR systems, during the retrieval step, the most relevant case is the most similar one: the one which has the highest value for the similarity function. The global similarity between the target problem and some source ones is evaluated by a weighted sum of the local similarities on each attribute of the problem description. SIM ( X , Y ) =
¦ wi sim( xi , y i ) i
(1)
¦ wi i
μs(x)
μs(x)
1
1
min(f)
max(f)
c di
ds
dom(f)
min(f)
c1 di
max(f)
c2 ds
dom(f)
Figures 2: Fuzzy Sets representation
In chemical engineering, the attributes for the problem description can contain different type of values: semantic for the chemical compounds of mixture, and numerical values for operating condition. For the local similarity of chemical compounds, Avramenko et al, 2004 proposed an approach based on the chemical structure of compounds which is implemented in our system. Concerning the local similarity for attributes with numerical values, the most use formula is to measure the normalized distance (to avoid distortions of the results when features have different variation scales) between both source and target values on the same attribute. But during the preliminary design, the numerical values for the target problem description, are not often precisely known: an operating condition around a central value for example. Here we take into account this imprecision in the target problem description by the way of a percentage of imprecision around the central value specified by the user and a relation, for each attribute. Six different choices are available for the relation: equ, sup, sup-equ, inf, inf-equ, between the central value(s). For one attribute ai, the local similarity measurement is achieved with the fuzzy set theory developed by Zadeh, 1965. We have considered two possible representations for the fuzzy sets: triangular (for the first five relations) or trapezoidal (only for the relation between) (figures 2). A fuzzy set S, on a domain D is defined by a characteristic function ȝs, which has values in [0;1]. ȝs(x) indicates the degree to which x is a possible value in S. With c (or c1 and c2); the central value for ai for the target problem, the relation coupled with the imprecision allow to build the specific domain Si
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(to calculate di and ds). The local similarity for ai is calculated by ȝsi(zi) where zi is the value of the source problem attribute corresponding to ai. 2.3. Retrieval Guided by adaptation The success of any CBR system is contingent on the retrieval of a case that can be successfully reused to solve the target problem. Consequently, the most similar case is unwarranted to be the most appropriate from the reuse point of view: it is not necessarily the easiest to adapt. Sometime, the most similar case may be difficult or impossible to adapt: technically, in terms of cost... Smyth and Keane, 1998, implement the idea of coupling the similarity measurement with a deeper adaptation knowledge traducing the easiness to modify a case to fit the target problem and to ensure case adaptation requirements. They called this technique: adaptation guided retrieval. With this technique, the research of source cases is based on two criteria: similarity and adaptability. Several methods exist to measure this adaptability, but we use the method proposed by Pralus and Gineste, 2006. For each attribute tsi of the target solution an adaptation domain is built from the definition domain of the same attribute in the source solution ssi, figure 3a. The definition domain of ssi is defined by a distribution possibility, which is specified when the case is retained in the base. The intersection of this distribution possibility with the relation (coming from the target problem description, previous part) is projected on the axis of the possible values for tsi, figure 3b. Finally we obtain a distribution of possible values for tsi. We state the assumption that the shape of this distribution determines the easiness to adapt this attribute. The more the range is large, the more this attribute is easiest to adapt (more choice to find an available value for tsi). The concept of specificity introduced by Yager, 1992, measures the degree to which a fuzzy set contains one and only one element (Specificity=1 for a very specific fuzzy set, with one value). Consequently the adaptability (adi) of each tsi is calculated with the measurement of the specificity of its distribution: ad i = 1 − S p (F )
with
S p (F ) = ³0
1
1 dα sup Fα − inf Fα
(2)
n
And the global adaptability of a case : ad s = ¦ ad i / n
(3)
i =1
relation 1 1
intersection
0, 8
0, 8
0, 6
0, 4
tsi 0
projection
0, 2
0, 2
0
0
ssi 0
0, 6
0, 4
tsi
distribution of possibility
ssi 0 0
Figures 3: Graphical representation of the adaptation domain
The user selects source cases with the two criteria and then the adaptation is made with the method described by Avramenko et al, 2004. This adaptation method is based on the main idea that the relative distances between the target problem and the selected source problems in the problem space are transferred in the solution space. To improve
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adaptation, the Constraint Satisfaction Problem (CSP) method will be implemented, and it will also use the tsi distribution, this is why we choose this adaptability measurement.
3. Example This example is presented in order to illustrate several parts of the method for the design of packing for separation. The mixture to separate is a three components distillation Methanol/Ethanol/Water. The target problem is a column which is operated at finite reflux, at atmospheric pressure, with feed flow rate between 0.1877 and 0.8123 mol/s. This distillation corresponds to the work of Mori et al, 2006. Moreover, in our problem description we impose that the distillation is at atmospheric pressure to exemplify the option EXACT, to impose a specific value to a feature. In their operating conditions, the authors do not give the range of temperature, consequently we suppose that it is not known. Of course, this range can be easily calculated with a thermodynamic analysis of the mixture at atmospheric pressure. But in order to show how our system treat the partial description of a problem, we do not fill this feature and we use the option IGNORE. The first five columns of table 1 sum up the problem description. Relation Central Value(s) Imprecision Ignore ȝs Function Mixture Pressure
equ equ
Methanol/Ethanol/Water 1
EXACT
Off Off
ȝs 1
z 1
Temperature Inlet Flow
-between
-0.1877 and 0.8123
-20%
On Off 1
ȝs
Rate
z 0.14 0.18
Reflux
equ
4.5
40%
Off
0.81 0.97
ȝs 1
z 2.7 4.5 6.3
Table 1: Problem description
For the retrieved step, the first work is to build automatically the function ȝs for each numerical feature, except for the temperature because the option IGNORE is activated. Therefore, this feature is not included in the global similarity calculation. These functions are represented in the last column of table 1. Before to calculate the global similarity, the case base is restricted to the subset of the most relevant cases thanks to a decision tree with the following succession of feature evaluation: at the root node the evaluation is on the Reflux, then the Pressure, then the Inlet Flow rate. Here again the temperature is ignored. For each cases in the selected subset, the global similarity measurement is calculated on four features; compounds, pressure, inlet flow, reflux, with the same weight for each one. After the retrieved step, the ranking gives three structured packing (and two random packing, which are eliminated). The two different Montz-pak B1 are retained for adaptation. Finally, after adaptation, the proposed target solution is the Montz-pak B1 30, table 2. The second column of table 2 gives the characteristics of the structured packing used by Mori et al, 2006. In this example, the tools gives a good starting point for the resolution of the initial problem. It is to notice that the material of the two retrieved cases selected are: stainless steel (in case 1) and carbon steel (in case 2).
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Consequently, for adaptation we search in the subset of metal. Then, the choice is oriented to the stainless steel because, under operating conditions in the same magnitude, the mixture of case 1 is most similar to the mixture of the target problem than the one of case 2. Therefore the choice is made with the following assumption: under operating conditions in the same magnitude, the most the mixtures are similar, the most the risk of degradation is reduced. This way to proceed is just a first approximation, and of course it needs to be improved because this assumption is not completely satisfactory. The CSP method will be useful for that. Type of Packing
Material Specific Area (m2/m3) Geometrical Characteristics angle element height (m) corrugation height(m) corrugation base (m) corrugation side length (m)
Proposed Solution
(Mori et al, 2006) Solution
Structured Packing Montz pak B1 300
Structured Packing Montz pak B1 250
Stainless Steel 350
Metal (not specified) 247
45° 0.201 0.008 0.0167 0.0116
45° 0.197 0.012 0.0219 0.016
Table 6: Solution description
4. Conclusion This paper focuses on the retrieval step in CBR and gives two ways to improve this step. In one way, it proposes a method to soften case representation by taking into account some imprecisions during the problem description. It also defines another criteria to determine if a retrieved case is relevant or not. Most of the time the similarity is the only criteria to choose a source case. Unfortunately, the most similar case is not often the most adaptable one. Here the similarity is coupled with an adaptability criteria. An improvement of our system concerns the next step of the CBR cycle, i.e. adaptation. Currently there is a general method which gives good results if the retrieved cases are very near the target problem (like in the presented example). With the adaptability criteria calculation, we generate the definition range for all the attribute of the target solution, this is a first step. The second one, is to fix the values of these attributes (numerical or not) in these intervals, with CSP method. Moreover with this method some constraints would be added like: user preferences, technical constraints…
References Avramenko Y., Nyström L., Kraslawski A., 2004, Selection of internals for reactive distillation column – case based reasoning approach, Comp. and Chem.Eng., 28, 37-44. Pralus M., Gineste L., 2006, Recherche et adaptation d’expériences structutrées, imprécises et incomplètes, Raisonnement à Partir de Cas 1, Hermes, 65-93. Mori H., Ibuki R., Taguchi K., Futuma K., Olujic Z., 2006, Three-component distillation using structured packing: performance evaluation and model validation, Chem. Eng. Sci., 61, 17601766 Smyth B., Kean M. T., 1998, Adaptation-guided retrieval: questioning the similarity assumption in reasoning, Artificial Intelligence, 102, 249-293. Yager R.R., 1992, On the specificity of a possibility distribution, Fuzzy Stes and Systems, 50, 179-292. Zadeh L.A., 1965, Fuzzy sets, Information and Control, 8, 338-353.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Visual Exploration of Multi-state Operations Using Self-Organizing Map Yew Seng Nga and Rajagopalan Srinivasana,b a
National University of Singapore, 10 Kent Ridge Crescent,117576, Singapore. Institute of Chemical & Engineering Sciences, 1 Pesek Road, Jurong Island, 627833, Singapore.
b
Abstract Multi-state operations are common in chemical plants and result in high-dimensional multivariate, temporal data. In this paper, we develop self-organizing map (SOM) based approaches for visualizing and analyzing such data. The SOM is used to reduce the dimensionality of the data and visualize multi-state operations in a three-dimensional map. During training, neuronal clusters that correspond to a given process state – steady state or transient – are identified and annotated using historical data. Clustering is then applied on SOM to group neurons of high similarity into different clusters. Online measurements are then projected on to this annotated map so that plant personnel can easily identify the process state in real-time. Modes and transitions of multi-state operations are depicted differently, with process modes visualized as a cluster and transitions as trajectories across SOM. We illustrate the proposed approach using data from an industrial hydro-cracker. Keywords: Self-organizing map, visualization, multi-state operations, data mining.
1. Introduction Multi-state operations are increasingly common even in petrochemical plants that have traditionally been considered as operating in a ‘continuous’ fashion. In general, the process operation can be classified into modes and transitions. A mode corresponds to the region of continuous operation under fixed flowsheet conditions; i.e., no equipment is brought online or taken offline. During a mode, the process operates under steady state and its constituent variables vary within a narrow range (Srinivasan et al., 2004). In contrast, transitions correspond to the portion of large changes in plant operating conditions due to throughputs, product grade changes etc. Transitions often result in suboptimal plant operations due to production of off-specification products. Understanding transitions and minimizing their duration can lead to major savings and increase periods of normal operation. Advancements in sensors and database technologies in chemical plants have resulted in the availability of huge amount of process data. Visual exploration methods, which facilitate humans to uncover knowledge, patterns, trends, and relationships from the data is hence crucial in understanding process operations, especially when multi-state operation and transitions between them is common. In this paper, we exploit the dimension reduction ability of the self-organizing map (SOM) for visualizing multi-state operations. The organization of this paper is as follows: Section 2 provides the literature review of data visualization methods and principles of SOM, Section 3 describes the proposed methodology for visualizing multistate operations. The proposed method is illustrated using an industrial hydrocracking unit in section 4.
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2. Visualization of Multi-variate Data Visualization techniques use graphical representation to improve human’s understanding of the structure in the data. These techniques convert data from a numeric form into a graphic that facilitates human understanding by means of the visual perception system. The Principal Components Analysis (PCA) has been a common visualization technique used widely for high-dimensional data. PCA is a popular statistical technique for dimensionality reduction and information extraction. It finds combination of latent variables that describe major variation in the data (Wise et al., 1990). In general, only a few principal components are necessary to adequately represent the data. In cases where the dimensions of multivariate data can be reduced effectively through PCA, visualization can be achieved through the biplot of the first few scores as they would explain the most important trends in the data. However, the linear approximation of PCA might not be sufficient to capture nonlinear relationships in the multivariate data. Also, the first two or three principal components are often not adequate for capturing all important variance in the data, so depiction of observations in a 2- or 3-dimensional coordinate plot is not adequate. Finally, when multi-state operations are visualized, the scaling of each variable is dominated by the large variation during transitions; significant changes within a steady state would be obscured by the depiction. To overcome these shortcomings, a self-organizing map based methodology is developed in this work for visualizing high-dimensional, multi-state operational data. 2.1. Self-Organizing Maps The Self-Organizing Map (SOM) is an unsupervised neural network first proposed by Kohonen (1982). It is capable of projecting high-dimensional data to a two dimensional grid and thus can serve as a visualization tool. Self-organization means that the net orients and adaptively assumes the form that can best describe the input vectors. The SOM employs nonparametric regression of discrete, ordered reference vectors to the distribution of the input feature vectors. A finite number of reference vectors are adaptively placed in the input signal space to approximate the input signals. Consider a dataset X containing I samples, each N-dimensional. X is therefore a 2dimensional matrix of size I x N, with the ith sample xi = {xi1 ,..., xin ,..., xiN } . The SOM is an ordered collection of neurons. Each neuron has an associated reference vector m j ∈ ℜn . Consider a SOM M SOM = {m1 ,..., m j ,..., mJ }T with J neurons, which has to
be trained to represent and visualize X. This involves the calculation of the reference vector of every neuron. Initially, let each mj be assigned a random vector from the domain of X. When a sample xi ∈ X is presented to the SOM for training, the neuron whose reference vector has the smallest difference from xi is identified and defined as the winner or the Best Matching Unit (BMU) for that input: bi = arg m in x i − m j , ∀ j ∈ [1 , J ] j
The distance
(1)
between xi and mj is measured here using the Euclidean metric, but
other metrics can also be used. During training, when each sample xi ∈ X is presented, the reference vector of the BMU, mbi, as well as those of its topological neighbors in the grid are updated by moving them towards the training sample xi. In its simplest form, the SOM learning rule at the tth iteration is given as:
Visual Exploration of Multi-State Operations Using Self-Organizing Map m j (t + 1) = m j (t ) + α (t ) hbi j (t ) xi (t ) − m j (t )
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(2)
where Į(t) is the learning rate factor, and hbij(t) is a neighborhood function centered on the BMU bi but defined over all the neurons in MSOM. The SOM can be used for visualization. One way of visualizing clusters in X is by means of the distance between a neuron and each of its neighbors (Ultsch and Siemon, 1990). The unified distance matrix (U-Matrix) visualizes the SOM by depicting the boundary between each pair of neurons by a color or gray shade that is proportional to their jj ' , jj ' = m j − m j ' j ' ∈ & j , with & j being the set of neurons that are
topological neighbors of neuron j. Clusters in the trained SOM can be labeled and directly used as a two-dimensional display to depict a new sample xi from the space of X. This is particularly useful for identifying the class (cluster) of a new sample. SOM has been used successfully in diverse fields. Deventer et al. (1996) demonstrated how disturbances in a froth flotation plant can be visualized using the SOM. Features were extracted from gray-level images of the froth and then visualized using the SOM. A change in the hits from one region of the SOM to another indicated a change in the froth and hence a change in the underlying operating conditions. Kolehmainen et al. (2003) used SOM to visualize the various growth phases of yeast based on data obtained from ion mobility spectrometry. They showed that hits from the same phase cluster together, but are separated from those from other phases by “mountains” of high distance between the neurons. In summary, previous work have largely focused on exploiting the clustering capability of SOM for grouping multivariate data. In this paper, we extend SOM to visualize in real-time the multivariate samples originating from multi-state processes.
3. SOM for Representing Process Operations In this section, we propose a SOM-based methodology to depict multi-state process operations. In the proposed representation, data from different process states (steady state and transient) demonstrate different characteristics in the SOM space. Steady states form clusters of adjacent BMUs while transient operation is reflected as a trajectory. Differences between two states can be observed easily based on the location and evolution of the BMUs. A SOM has to be suitably trained to represent various process states. During training, the neurons on the SOM will orient themselves and evolve into a process map representing all the operating conditions in the training data while preserving the topology (geometric form) of the measurement space. The trained SOM model can then be used to visualize the process state in real-time. 3.1. Visualization of Process States For visualizing process operations, data from online sensors, xi, are first projected on the trained SOM and the BMU of xi, mbi, identified. The location of mbi on the SOM indicates the current state of the process. Process modes and transitions display different characteristics on the SOM space. When a process is in a mode, all its variables have near-constant values. Therefore, online measurements from such a state should be projected on the same BMU. Noise and minor variations in process operation could result in projection of the online measurement to different BMUs, however these would be neighboring neurons because of the topology preserving feature of SOM training. Process modes can thus be identified when a high frequency of BMUs are found within a small neighborhood in the map.
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In contrast, process transitions are characterized by large changes in plant operating conditions. Such evolution of the variable values during the transition would cause the BMUs to traverse over a wide region in the SOM space. The transition can be visualized by connecting the successive BMUs and displaying the trajectory of process evolution. During transition operations, continuous variables would cause the BMU to advance through adjacent neurons, resulting in a smooth trajectory on the SOM space. However, discrete variables would cause abrupt jumps to a BMU since they correspond to abrupt changes in plant operations. They are hence exhibited as discontinuous evolution in the trajectory. 3.2. Neuronal clusters Next, consider the relationship between the process states and their depiction on the SOM map. A larger SOM with more neurons would offer finer resolution of operating conditions and is required to precisely visualize transition conditions and progression. However in large SOMs, even small changes in the operating condition would lead to different neurons (although in the same neighborhood) becoming the BMU, i.e., the “noise” absorbed by each neuron is low. To meet the conflicting requirements of finer resolution and better noise absorbance, a second layer of abstraction can be defined by grouping neurons into neuronal clusters. A neuronal cluster is defined as a set of contiguous neurons in the SOM map with high similarity in mj. The neuronal cluster exploits the topology preserving feature of SOM and are defined by clustering the neurons in the trained SOM based on their reference vectors. Let all the neurons in MSOM be grouped into K neuronal clusters {S1 ,...Sk ,...S K } . The assignment of neuron j to cluster k is specified by a membership function ujk: 1 if neuron j is assigned to cluster k u jk = ® . ¯0 otherwise
(3)
Any clustering technique can be used to specify ujk. We used the k-means clustering algorithm, which identifies the K clusters so as to minimize the total squared distance, İp (Seber, 2004): K
εp =
J
¦¦ || m j ⋅ u jk − ck || ,
(4)
k =1 j =1
where, ck is the centroid of the kth neuronal cluster. In the following sections, these characteristics of SOM are exploited for representation and visualization of highdimension process operational data.
4. Transition Identification & Visualization in an Industrial Hydrocracker The process analyzed in this section is the boiler of a Hydro-cracking Unit (HCU) in a major refinery in Singapore (Ng et al., 2006). Hydro-cracking is a versatile process for converting heavy petroleum fractions into lighter, more valuable products. The objective of HCU is to convert heavy vacuum gas oil (HVGO) to kerosene and diesel with minimum naphtha production. The detailed description and flowsheet of the process can be found in Ng et al. (2006) and will not be reiterated here. The operations of the HCU considered are complex, and involves catalytic hydro-cracking reactions in a hydrogen-rich atmosphere at elevated temperatures and pressures. The HCU includes two sections, a reactor section and a fractionation section. Integrated to both these
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sections is a waste heat boiler (WHB) unit for heat recovery. This section illustrates the application of SOM for visualizing different operating states in the WHB unit. 4.1. Analysis of operating data from Waste Heat Boiler In this study, one month of operating data consisting of 21 measured variables from the WHB unit sampled at five-minute interval is considered. The data was auto-scaled (through mean centered and scaled to unit variance) and used to train a SOM with 468 neurons and dimension of 39 × 12 . The trained SOM was then clustered with K = 70. The clustered SOM was annotated with the typical regions of operation. Next, we demonstrate how the SOM can be used for decision support in the WHB. As can be seen from Figure 1, the WHB unit operates in 5 different modes, shown as M1 to M5. Mode M2 corresponds to the production of steam at a throughput of 22T/hr, mode M3 corresponds to 12T/hr, and mode M4 corresponds to 17T/hr. Analysis of the SOM shows that the unit underwent 7 different transitions during the period under consideration. Five instances of these transitions are shown in the figure. In one instance, depicted as TA34, the unit transitioned from mode M3 to mode M4 in 140 mins. Another instance of the same transition TB34 required only 85 mins. The operating strategy for the latter instance can therefore be used as the basis for all future transitions of this class. To illustrate the robustness, the same trained SOM was also used to visualize the operation during another 15-day period. Since data from this period was not used during the training, it demonstrates the SOMs generalization-ability. The mean quantization error (averaged sum of squared error between each sample and its BMU) for this period was 0.906, indicating that SOM provides a good representation for these as well. During this period, the plant was observed to operate in mode M3 for 83% of time, about 3% in M2 and 4% in M4. The process underwent transitions for a total of 32.5 hours (~10%) during this period. All the transitions could be easily visualized with the previously trained SOM. For the purpose of comparison, we also attempted to visualize the same data using PCA. The first three PCs captured 85.47% of the variance as shown in Figure 2. Data from the five modes identified from the SOM are shown in the biplot. In contrast to the SOM, the different modes of operation are not as clearly delineated by PCA.
Figure 1: Visualization of transition trajectories for the refinery WHB unit
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5. Conclusions Methods that enable effective visual exploration are crucial for extracting knowledge from complex, high-dimensional, temporal, multi-state data. In this work, we have shown that the self organizing map provides a method to reduce dimensionality and visually depict high dimensional process data in an intuitive graphic. Process operation can be represented in the SOM with each state – mode or transition – having a distinct representation. Application of the proposed approach to the operations of an industrial boiler within a hydro-cracker in a major refinery illustrates the benefits of visualization in extracting process knowledge even from complex, multi-state operations. The different states that the process operates in can be segregated. If multiple instances of the same state are present in the data, they can be compared. The trained map can also be used for real-time state identification by identifying the location of the latest BMU on the annotated SOM. In contrast to traditional dimensionality reduction approach such as PCA, which preserve global distances, the SOM dedicates neurons to an operating region only if it is present in the training data. It thus offers a more compact and rich representation of the operation.
References J.S.J.V. Deventer, D.W. Moolman, C. Aldrich, (1996). Visualization of plant disturbances using selforganizing maps, Computers and Chemical Engineering 20, 1095-1100. T. Kohonen, (1982). Self-organized formation of topologically correct feature maps, Biological Cybernetics 43, 59-69. M. Kolehmainen, P. Rönkkö, O. Raatikainen, (2003). Monitoring of yeast fermentation by ion mobility spectrometry measurement and data visualization with self-organizing maps, Analytica Chemica Acta 484, 93–100. Y.S. Ng, W. Yu, R. Srinivasan, (2006). Transition classification and performance analysis: A study on industrial hydro-cracker, International Conference on Industrial Technology ICIT, Dec 15-17, Mumbai, India, 1338-1343. G.A.F. Seber, (2004). Multivariate observation, Wiley-Interscience, Hoboken, N.J., 2004. R. Srinivasan, C. Wang, W.K. Ho, K.W. Lim, (2004). Dynamic principal component analysis based methodology for clustering process states in agile chemical plants, Industrial and Engineering Chemistry Research 43, 2123-2139. A. Ultsch, and H.P. Siemon, (1990). Kohonen’s self organizing feature maps for exploratory data analysis, Proceedings of International Neural Network Conference (INNC’90), Kluwer academic Publishers, Dordrecht, 305-308. B.M. Wise, N.L. Ricker, D.J. Veltkamp, B.R. Kowalski, (1990). A theoretical basis for the use of principal components model for monitoring multivariate processes, Process Control and Quality 1(1), 41-51.
Figure 2: Visualization of the WHB unit operation using first three scores
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Multi-Criteria Decision Making in Product-driven Process Synthesis Kristel de Riddera,b, Cristhian Almeida-Riveraa, Peter Bongersa, Solke Bruinb, Simme Douwe Flapperc a
Unilever Food and Health Research Institute, Olivier van Noortaan 120, 3130 AC Vlaardingen, The Netherlands b Eindhoven University of Technology, PO Box 513, Helix, STW 1.47, 5600 MB, Eindhoven, The Netherlands c Eindhoven University of Technology, PO Box 513, TBK Pav. F06, 5600 MB, Eindhoven, The Netherlands
Abstract Current efforts in the development of a Product-driven Process Synthesis methodology have been focusing on broadening the design scope to consumer preferences, product attributes, process variables and supply chain considerations. The methodology embraces a decision making activity to be performed at different levels of detail and involving criteria with, sometimes, conflicting goals. In this contribution we focus on the development and implementation of a decision making process based on criteria accounting for the above mentioned issues. The developed multi-criteria decision making method is based on Quality Function Deployment and the Analytic Network Process, involving benefits, risks, opportunities and costs. The application of the method provides a more structured scenario for decision making processes in R&D and also forecasts the stability of the outcome with respect to changes in the decision making criteria and relevance of benefits, risks, opportunities and costs. To clarify and illustrate the steps of this method, it has been applied to decision making in a R&D environment. Keywords: multi-criteria decision making, product-driven process synthesis, analytic network process, quality function deployment
1. Introduction Decision making (DM) in product and process design in all Fast Moving Consumers Goods (FMCG) companies can still be improved. These improvements originate from the unstructured way of defining and including consumer preferences, product and process characteristics, and supply chain considerations in the DM activity. The synthesis of new products and processes involves usually multidisciplinary teams with experts in different areas. Quite often, the synthesis activity is performed sequentially (Figure 1-top), resulting in people of the multi-disciplinary team being involved at different stages of the process. This approach leads to non-smooth feedback opportunities and to a lengthy synthesis process. Aiming at a more structured approach towards the synthesis of product and processes, a novel methodology has been developed. This approach -termed product-driven process synthesis (PDPS) - exploits the synergy of combining product and process synthesis
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workstreams. Current efforts in the development of PDPS methodology have been focusing on broadening the design scope to consumer preferences, product attributes, process variables (Almeida-Rivera et al., 2006). In this contribution we focus on the development and implementation of a decision making process based on criteria accounting for the above widened scope including supply chain considerations (Figure 1 – bottom). Supply chain criteria include lead time, time to market and equipment transferability, seasonality, among others.
Fig.1. Sequential synthesis of product and process (top); extended product-driven process synthesis (bottom).
2. The Product-driven Process Synthesis (PDPS) Approach Since its introduction, process systems engineering (PSE) has been used effectively by chemical engineers to assist the development of chemical engineering. In tying science to engineering, PSE provides engineers with the systematic design and operation methods, tools that they require to successfully face the challenges of today's industry (Grossmann and Westerberg, 2000). One such method is the PDPS approach, which focuses on the creation of the best conversion system that allows for an economical, safe and environmental responsible conversion of specific feed stream(s) into specific product(s). Although the definition of PDPS might suggest a straight-forward and viable activity, the synthesis is complicated by the nontrivial tasks of identifying and sequencing the physical and chemical tasks to achieve specific transformations; selecting feasible types of unit operations to perform these tasks; finding ranges of operating conditions per unit operation; establishing connectivity between units with respect to mass and energy streams; selecting suitable equipment options and dimensioning; and control of process operations. Moreover, the synthesis activity increases in complexity due to the combinatorial explosion of potential options. The number of possible combinations can easily run into many thousands (Douglas, 1988). The PDPS methodology is regarded in this context as a way to beat the problem complexity. This synthesis strategy is supported by decomposing the problem into a hierarchy of design levels of increasing refinement, where complex and emerging decisions are made to proceed from one level to another. Moreover, each level in the PDPS methodology (Fig. 2-left) features the same, uniform sequence of activities (Fig. 2-right), which have been derived from the pioneering work of Douglas (1988), Siirola (1996) and further extended by Bermingham (2003) and Almeida-Rivera et al. (2004).
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The generic design structure of the methodology includes an “evaluation and selection” activity, which traditionally has been driven by the satisfaction of economic performance. Hereafter, it is indicated how this “evaluation and selection” space is extended to encompass a wide range of aspects involving consumer preferences, product and process characteristics and supply chain considerations on top of the financial performance. start
From previous level
Level Description 0
Framing level
1
Input/output level
2
Task network
scope & knowledge
generate alternatives Knowledge is generated to fill gaps but without exceeding the degree of complexity of the level
3
Mechanism and operational window
4
Multiproduct integration
5
Equipment and selection design
6
analyse performance of alternatives
Development programme
evaluate & select
Feasibility
N
Multi product-equipment integration
Y
report
end
Each conclusion, assumption, and decision at each level has to be reported
To next level
Fig. 2. Levels of the PDPS methodology (left); activities at each level in the PDPS methodology (right)
3. Multi-criteria Decision Making (MCDM) Improvement of DM processes for the creation and operation of supply chains has been identified as one of the key challenges for the Process Systems Engineering community in the years to come (Grossmann and Westerberg, 2000). This DM process involves different aspects, characterized by different criteria with, sometimes, conflicting goals. To deal with the above, a multi-criteria decision making (MCDM) activity is suggested, including not only financial criterion but also criteria related to consumer preferences, product and process characteristics and supply chain considerations. Next to the definition of the criteria to decide upon, a structured method for DM needs be envisaged to improve the systematic DM. 3.1. Selection of the Benchmarking Technique Benchmarking techniques are DM methods, consisting of DM models and meant to continuously review business processes (Watson, 1993). Based on expected applicability within a FMCG environment, three such techniques have been further studied. Data Envelopment Analysis (DEA) is a mathematical benchmarking technique normally applied to compare the performance of DM units (e.g. production processes). The main advantage of this technique is that the efficiency of multiple inputs and multiple outputs can be evaluated, without the necessity of using weighing factors. On
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the other hand, this technique is limited by the fact that all inputs and outputs must be quantifiable and measurable for each DM unit (Cooper et al., 2006). Analytic Hierarchy Process (AHP) is a technique to compare alternatives. According to this technique, a DM problem can be hierarchically decomposed in: goal, criteria, levels of sub-criteria and alternatives. All criteria are assumed to be independent and pair-wise comparisons are made by experts to determine weighing factors of the criteria. Pair-wise scores for all alternatives per criteria are given by the experts. For further details, see Saaty (1990). Analytic Network Process (ANP) is a generalization of the AHP, where the assumption of a hierarchical structure is relaxed. It resembles a network, consisting of clusters of elements, which are the DM criteria and the alternatives. The relations between elements depend on the DM case. For further details, see Saaty (2005). The selection of the benchmarking technique is based on the applicability of the technique in the product and process DM process within an industrial setting and on whether the criteria are quantifiable and interdependent (Fig. 3). In view of the scope of the PDPS approach, where the dependencies of product and processes characteristics are of relevance, we selected the ANP technique as benchmark.
Fig. 3. Tree diagram for the selection of the benchmarking technique
3.2. Development of the MCDM Method Like Partovi (2007), we combined the concepts of Quality Function Deployment (QFD) and ANP to develop the MCDM methodology. However, the concept of QFD was further extended to cover consumer driven product design, process design and supply chain design. Thus, the extended QFD uses four matrices that integrate consumer preferences, product and process characteristics and supply chain considerations. The network structure of this extended QFD concept and the financial factors are implemented in ANP models of different levels of complexity (simple network, small template (Fig. 4) and full template). The small template structure (Fig. 4), for instance, is composed of two layers. In the first layer, the goal is divided into merits (Benefits, Risks, Opportunities and Costs; BROC); in the second layer, subnets of these four merits are obtained by using a QFD subdivision of the DM criteria; according to this subdivision, clusters for DM problems are divided into three groups: QFD factors, financial factors and alternatives. The clusters and nodes (i.e. DM criteria) in the subnets are pair-wise compared. The overall decision is reached provided that the BROC merits are a-priori weighted. The DM process involves going through various phases as indicated by Saaty (2005). The following changes of and additions to Saaty’s outline of steps are: inclusion of group decision; introduction of a step related to individual influence of decision makers;
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extension of the QFD concept covering consumer driven product, process and supply chain; introduction of a structured way to arrive at the criteria; specification of the timing of the different steps of the method is given; reverting of the order of the steps related to the weighing of the merits and the cluster and nodes comparisons.
Fig. 4. Small-template structure
4. Application of MCDM Method The MCDM method has been applied to a decision making case in a R&D project of a specific product category. The project involves different regions and parallel tasks involving design, development, implementation and launching of products and processes. In this project many decisions need to be made. An example of a decision making problem is the choice between two types of production equipment, types A and B. The performance of type A is proven, whereas type B seems promising, but has a higher risk because its performance is not (yet) fully proven. Equipment type B is less expensive than type A. After having composed the appropriate DM team, a long list of DM criteria per merit has been compiled for the category products and processes. These criteria have been divided into consumer preferences, product characteristics, process characteristics, supply chain characteristics and financial factors. This list does not include any nonnegotiable criteria; however, in the event that alternatives conflict with one or more of these criteria the alternatives are not further considered for the DM process. Next, a short list of criteria has been compiled for the particular case of deciding between equipment type A and type B. The short list has been compiled and agreed upon by key decision makers. Also this short list of criteria has been divided into benefits, risks, opportunities and costs and further divided into consumer preferences, product characteristics, process characteristics, supply chain characteristics and financial factors. The small template was chosen as structure of the ANP model, as the number of clusters per subnet does not exceed 10 (Fig. 3). Per merit, the priority of the alternatives has been calculated using the software Super Decisions 1.6.0. and then multiplied by the weighing factors of the merits to come to the overall decision. According to the outcome of the software, equipment type A seemed to be the best option when it comes to deciding between equipment type A and equipment type B.
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Also, a sensitivity analysis has been performed, where each merit weight was increased while keeping the others constant. The following results were obtained from this analysis: if the benefits became more important, both alternatives had equal priorities; if the costs became more important, alternative B was preferred; if the opportunities became more important, both alternatives had equal priorities; when the risks became more important, alternative A was preferred. The change of relative importance of the alternatives with a fixed priority for the BROC merits has been also analysed. For the case of opportunities merit, for instance, there was a threshold score, above which the equipment type B became preferred over equipment type A, keeping the weighing factors of the merits constant. This sensitivity analysis can be used effectively to establish the DM criteria that should be changed and the extent of change to swap the decision in favour of equipment type A or type B.
5. Conclusions The presented MCDM method is based on Saaty’s outline of steps of the ANP benchmarking technique. In the development of the MCDM method, points for improvement for and positive aspects of the current way of DM were combined: a more structured way to come to the criteria, a more structured way to come to the importance of the criteria, taking into account dependencies between criteria and dealing with objective and subjective criteria. The use of the method is limited, however, by the need of high number of comparisons, considerable time-investment and knowledge availability of all factors. The application of the MCDM method to the industrial R&D project helped to improve the current DM processes in R&D projects, while retaining the strong points. Although the presented MCDM method is extensive, it is important that consumer preferences, product and process characteristics and supply chain considerations are taken into account in all decisions made also during the early stages of the PDPS methodology.
References C.P. Almeida-Rivera, P. L.J. Swinkels, J. Grievink (2004), Designing Reactive Distillation Processes: Present and Future, Computers and Chemical Engineering, 28(10), 1997-2020 C.P. Almeida-Rivera, P. Jain, S. Bruin and P. Bongers (2006), Integrated Product and Process Design Approach for Rationalization of Food Products, Computer-Aided Chemical Engineering, 24, 449-454 S. Bermingham (2003), A design procedure and prdicitive models for solution cristallisation processes, PhD thesis, Delft University of Technology, The Netherlands, ISBN 90-407-2395-8 W. W. Cooper, L.M. Seiford, K. Tone (2006), Introduction to Data Envelopment Analysis and its Uses. Springer, New York. J. Douglas (1988), Conceptual Design of Chemical Processes, McGraw-Hill, USA I. Grossmann and A. Westerberg (2004), Research challenges in Process Systems Engineering, AIChE Journal, 46, 9, 1700-1703 F.Y. Partovi (2007), An analytical model of process choice in the chemical industry, International Journal of Production Economics, 105, 1, 213-227. T. Saaty (1990). How to make a decision: The Analytic Hierarchy Process. European Jorunal of Operational Research, 48, 9-26 T. Saaty (2005), Theory and Applications of the Anlalytic Network Process: Decision Making with Benefits, Opportunities, Costs and Risks. RWS Publications, Pittsburgh J. Siirola (1996), Industrial application of chemical process synthesis. In: Advances in Chmeical Engineering. Process Synthess (J. Anderson, ed.), book chapter 23, (1-61), Academic Press G. Watson (1993), Strategic Benchmarking, John Wiley & Sons, Inc., New York
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Improvement of the production process of leached optical fibers in a technological and organizational context Daniëlle T. Stekelenburga, Zofia Lukszoa, Jeff Loweb a b
Delft University of Technology, P.O. Box 5015, 2600 GA Delft, The Netherlands SCHOTT North America Inc., Southbridge, USA.
Abstract Many contemporary products are relatively small-volume high-value added items which are generally produced in batch production processes. These types of processes are becoming more and more important as markets change quickly and require markets to adapt. Batch-wise production provides the necessary flexibility to respond to these changes. This research project focuses upon complex batch processes with high quality demands which are hard to meet. The production of leached optical fibers at SCHOTT North America Inc (SCHOTT) is examined to identify, apply and test a method which is generally applicable for improving and stabilizing the yield of complex batch processes. The fibers produced at SCHOTT are used in health care and must satisfy strict quality requirements. The yield of fibers meeting the quality standards varies greatly and it is unknown which factors determine the yield and the extent of their influence. The company-dedicated goal of this research was to assist the plant of SCHOTT in implementing and executing a quality improvement process. Existing literature offers little support to the organizational aspect of quality improvement trajectories. Therefore specific attention is paid to the organizational consequences of implementing an improvement process. In this research, response surface methodology is successfully applied to identify causal relationships between factors that impact production process performance and the yield. The optimal settings of these factors are then defined through the use of a regression model. The regression model that is used incorporates the factors of influence on product quality and their relative importance to the production of leached optical fibers at SCHOTT. The same technique can be applied to other production processes. Lastly, an implementation plan is defined to guide organizations towards successful implementation of improvement measures. In order to successfully execute this quality improvement trajectory, a guideline for managing such processes is proposed and applied. Keywords: Response surface methodology, design of experiments, optimization, quality management, organization.
1. Introduction Leached optical fibers are used in health care (in endoscopes) to guide images from inside the body of a patient to a screen. This is accomplished by bouncing the image within the fiber from the point of origin to the screen where it is ultimately displayed. This is demonstrated by Figure 1.
Figure 1 Transmission of light in an optical fiber
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The overall production process consists of three main steps: drawing the fiber rods, leaching the fiber bundles and sheathing and inspecting the end product. The focus of this research was on the first sub-process, the rod-stage.
Figure 2 Multi-multi fiber
Fibers are made from a bar of core glass and two cladding-tubes around it. This cladding, which consists of glass that has a lower refraction index than the fiber, protects the fibers and keeps the signal that needs to be transported inside. Fiber rods are drawn in three steps. The first draw produces mono fibers. These fibers are then assembled for the second draw which creates multi fibers. In the third draw, multi-multi fibers are produced. These multi-multi fibers consist of thousands of fibers which resemble a honeycomb when viewed through a microscope. See Figure 2. The leached optical fiber production process is order-based. Batches of fibers are produced according to the specific wishes of the customer and quality requirements are demanding. The yield of the fiber rods is very low and unpredictable, as many rods do not meet the quality requirements. Process knowledge is limited throughout the fiber optics industry and it is unknown which factors influence the quality of the fiber rods at this stage of production. There is a large financial incentive to improve the yield by limiting production losses at the fiber rod stage. Nonetheless, despite low yield and financial losses, leached optical fibers remain a very profitable business.
2. Research question and methodology The objective of this article is to identify how the production process of leached optical fibers at SCHOTT North America may be improved. To find improvement strategies the following research question is answered: What are optimal settings, both functionally and organizationally, for the process conditions to improve the yield of leached optical fibers with respect to the current situation? To answer this question, response surface methodology (RSM) is employed (Myers, 2002). In the production process of leached optical fibers the relationship between the yield and the independent factors influencing the process performance is unknown. RSM is particularly suitable for optimizing the performance of production processes where process knowledge is limited. The first step in the response surface methodology is to determine a function that describes the response through analyzing the factors of influence. RSM employs experimental design and multiple regression methods. This approach permits the study of multi-variable interactions. Experimental design refers to experimental methods used to quantify the relationship between factors (x1, x2, x3,…) affecting a process and the output of that process (y) in a well-structured approach.
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Figure 3 presents a schematic representation of a full-factorial design for three factors. Three factors x1, x2, x3 are varied at two levels: low (corresponds to “-1”) and high (corresponds to “+1”) with respect to a nominal (zero) situation, which results in 8 experiments. A factorial design with k factors, each varied at two levels in such a way that all the settings of every factor appear in all possible combinations with settings of other factors, is called a 2k factorial design, whereby 2k indicates the number of experiments to perform.
Figure 3 Example of full factorial design of experiments for three factors
Accordingly RSM is very suitable to estimate the response of the production process of leached optical fibers to the input factors. The second step in RSM consists of an analysis of the validity of the model. The final step of an RSM project specifies the relationship between factors in the production process which can be then used for the optimization of the performance of the system by determining the optimal settings of the process parameters (Verwater-Lukszo, 1998). However, knowing the optimal process settings is not enough. Concrete improvement measures need to be formulated to address organizational complexity. Current system improvement tools often do not include this part of the improvement process. To address that deficiency this article investigates both the definition of the improvement measures and the way they should be implemented in a complex organization.
3. Modeling and optimization of leached optical fiber production This section describes two steps of the RSM approach: model formulation and optimization. 3.1. Model formulation Using RSM, a regression model has been estimated. The purpose of the regression model is twofold. On the one hand, the model is focused upon identifying those factors which influence the quality of the fiber rods. On the other hand, the regression model will be used to define the optimal settings of the factors of significant influence. Through interviewing and monitoring employees a list of 25 possible factors of influence was previously identified (Stekelenburg, 2007). The Design of Experiment portion of RSM is a structured, organized method for determining the relationship between factors of influence and the output of that process. Fractional factorial design is one of the most widely used methods for process improvement. Screening experiments employ a linear regression model to reduce influencing factors. If we can assume that certain higher-order interactions are negligible, a fractional factorial design involving fewer runs than the well-known factorial design can be used to obtain information on the main effects and low-order interactions (Montgomery, 2004).
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In this project the estimated ultimate regression model has an explained variance of 72% which is fairly high for an industrial process. The final model of yield y consists of 13 factors and 13 significant interaction effects: 13
13
i =1
i =1
y = β 0 + ¦ βi xi + ¦
13
¦β
x xj + ε
ij i
j >i
The 13 factors influencing response are divided into three groups: easy-to-adjust control variables, not-easy-to-adjust variables and noise factors, which cannot be adjusted by the company. Main factors in the first group include the type of furnace used and the experience level of operators. The second group includes the quality of raw materials, humidity and temperature profiles. The last group addresses the difficulty level of the product which is determined by the quality demands of the customer. 3.2. Process optimization To increase the yield of the production process of fiber rods at SCHOTT, the response to the factors that influence the yield must be improved. The non-linear objective function y is optimized for three anticipated noise factor levels. Further, the lower and upper bound on all factors are taken into account. This straightforward optimization results in concrete improvement measures. This research reveals that different furnaces are optimal for different process stages within each difficulty level. Moreover, the optimal performance of the operator was also variable in relation to the difficulty level. To improve yield SCHOTT must also purchase better quality raw materials. It is recommended that suppliers be stimulated to provide consistently higher quality raw material tubes. Further, the humidity in the draw area is an important and currently unstable factor which impacts the product quality. A humidity control system should be implemented to address this variable. Finally, SCHOTT is advised to either implement an advanced temperature control system, or make smart use of ‘natural’ temperature fluctuations in the draw areas by scheduling blanket orders in seasons with the optimal temperature.
4. Quality improvement process All of the identified improvement measures have consequences for the organization and require effort and commitment from the employees at SCHOTT in order to be successfully implemented. Through observing and conversing with SCHOTT employees many of the general characteristics of the leached optical fiber department were identified. These organizational aspects need to be taken into account when implementing a quality improvement process in the company. Many of the organizational traits identified match features of a professional bureaucracy, as formulated by Mintzberg (Mintzberg, 1992). In order to implement the quality improvement process, the cooperation of the operators is indispensable. However, complete cooperation is often difficult to acquire. It is necessary to develop an environment which facilitates quality improvement processes. By successfully integrating operator and management responsibility, SCHOTT ensured that these parties supported the quality improvement trajectory. From the experience at SCHOTT and from studying quality principles (ISO 9000:2000, 2000), a guideline is proposed for addressing the management changes necessary for the implementation of a quality improvement process. This guideline, which can be found in Table 1, is focused on SCHOTT. However, it may be applied successfully to quality improvement trajectories in similar professional bureaucracies as many of the
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challenges will be the same. The four aspects of the proposed guideline will be explained in more detail. The views of the different parties that are involved should be made to converge in order to create dedication to the quality improvement process. A process approach is very suitable for this goal. A process should be negotiated and designed that guides the quality improvement process for all parties involved. This will serve to reduce interdependencies. Additionally, by establishing a fixed process which the operators agree with will make them less hesitant to committing to changes in their production environment. An external party with experience in designing quality improvement processes may be involved to guide the process negotiation. Aligning the viewpoints and goals of all committed parties is an excellent starting point for a quality improvement process. The involvement of all parties that are necessary to make the quality improvement process a success should be facilitated. Management must strive to commit the operators to the entire quality improvement trajectory. Management should demonstrate dedication to the process by enhancing their presence which will inspire the goodwill of other parties. This approach will increase the transparency of the production process and provide opportunities to assess individual employee performance. The commitment of all relevant parties to the quality improvement trajectory will speed up the process and enhance results. Table 1 Guideline for quality improvement trajectories implementation Guideline
Of who/what?
By who/what?
Quality Principle
Characteristic
Converge views
Operators Management Other Parties
Process
Customer focus Process approach
Interdependencies Stability of work environment Performance assessment difficult Fear of rationalization Autonomy
Involve
Operators Other Parties
Management
Involvement of people Process approach
Convince
Operators Other Parties
Management / External Party
Leadership Factual approach to decision making
Fear of rationalization
Support
Operators Other Parties Process
Management
Continual improvement
Stability of work environment Autonomy Interdependencies
Support is required to facilitate and ensure continuous efforts in the quality improvement process during and after the identification and implementation of the improvement measures. Management should be committed to providing all necessary support to employees who are negatively affected by the changes being made during the quality improvement trajectory. It is important that the parties involved are supportive of the quality improvement process. This is especially true of the operators who are responsible for making the greatest adjustments. Their endorsement of this method is necessary to prevent
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frustration of the improvement objectives. In order to involve and acquire the support of the operators, a three step action plan is proposed. This action plan is shown in Table 2. Table 2 Operator involvement and support action plan
5. Conclusions Response surface methodology is applied successfully for the optimization of the factors that influence the performance of the production process of leached optical fibers. Functional optimal settings for these variables have been identified. However, response surface methodology does not offer any guidance on the implementation of the improvement measures. A systematic analysis of the organizational complexity at SCHOTT has been performed and an implementation plan has been formulated. The consequences of each improvement measure for the company have been identified; SCHOTT is advised in the use of their position, the financial trade-off of improvement measures and methods for enhancing the dedication of employees of different departments. The steps which need to be taken to ensure successful implementation of the improvement measures are identified, bringing the actual implementation one step closer. In addition, in order to guide the implementation of these types of quality improvement trajectories, an implementation guideline of general application is proposed. These two steps are indispensable for successful process improvement.
References ISO 9001:2000, Quality management systems – Requirements, ISO,2004. Mintzberg, H., Structure in Fives, Designing Effective Organizations, Prentice Hall, 1992. Montgomery, D. C., Design and Analysis of Experiments, Wiley, 2004. Myers, R.H., D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Wiley-Interscience, 2002. Verwater-Lukszo, Z., A Practical Approach to Recipe Improvement and Optimization in the Batch Processing Industry, Computers in Industry, pp. 574-281, 26, 1998. Stekelenburg, D.T., A brighter view of the fiber world. Yield improvement of complex batch processes with high quality demands, TPM-TU Delft, Delft, 2007.
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"Quality Assurance of simulation results" "Laurent Testard,a" "aHALIAS Technologies, Le Soubon, Revel, F-38420, France,
[email protected]"
Abstract This paper discusses the automation of the tests of Process Simulation results, and the way that the tests can be integrated in a typical simulation project. Based on existing experiences in another domain (such as micro-electronics), we propose a novel approach by introducing a tool dedicated to the automation of tests of simulation results. This tool is the Quality Testing System (QTS), developed by HALIAS Technologies. Keywords: Quality Assurance, Tests Automation, Time Series, Process Simulation, CAPE-OPEN
1. Introduction 1.1. Concepts and definitions The subject of this paper is the testing of Process Simulation software, mainly from two points of view: firstly Process Simulators, in the field of Operator Training Simulators or Engineering Simulators (i.e. simulators dedicated to engineering studies), and secondly Process Simulation Software, for the design of these simulators. Because simulators are software environments, techniques related to software tests [1] apply to simulation software. Simulation Software Testing is the process of ensuring that the data computed by a software simulator fulfils the expectations of the users of the simulator. These expectations can be of functional nature (based on physical criterion, for example a simulated variable value must be greater than a physical limit) or non functional (typically performance related or quality related). This process mainly uses two techniques: Acceptance tests and Regression tests. Acceptance tests (known as FAT – Factory Acceptance Tests - or SAT – Site Acceptance Tests) are the tests performed on the software in order to ensure that it fulfills all the client's expectations, in terms of contractual functional or non-functional requirements. Acceptance tests are generally performed at the end of a project or at intermediate milestones in a project's life-cycle. • Regression tests are tests performed on successive releases of software, to assert that successive integrations of functionalities did not degrade existing ones. These tests can be applied in different situations: • •
During the software development process, nightly builds can be tested against a battery of reference tests. Those tests can be expressed as business rules or in terms of comparisons to reference values. Between each major release of a software product. Reference business tests cases must be validated on the new version of the software. Those test cases
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include functional and non functional (such as performance or quality related) requirements testing. A Test Case is an elementary test that can be performed on a value or a set of values. A set of Test Cases is generally called a Test Suite, and the Test Cases that are part of a same Tests Suite are generally related from one to each other. 1.2. Analysis of existing simulation projects This section sums up conclusions of a survey we conducted on two different projects in the field of Process Simulation, and from personal experience in the field of MicroElectronics circuit simulation whose techniques are quite similar to the Process Simulation domain, but which makes extensive use of tests tools to improve designs as well as simulation environments. 1.2.1. Development of an Operator Training Simulator Tests results are deliverables of a typical Operator Training Simulator project. At specification time, the tests express the client's requirements. Tests are important during the project life time because intermediate tests (i.e. tests performed during the design and development of the simulator) can guide technical orientations and provide useful information on the process design. The final phases of a typical OTS project involve processing of acceptance tests. From our studies, the global test effort on this particular project is estimated to at least 20% of the global project effort: this effort is divided in tests specifications and tests execution. As a direct consequence, an improvement in this field can then lead to important gains in the development of the simulator. 1.2.2. Complex Unit Operation development The studied project consists in the refactoring (rewriting of a functionally equivalent code with higher quality standard or interoperability requirements) in the form of several CAPE-OPEN Unit Operations [2], to be used in steady state simulators. For this particular project, the global budget is 1.5 person.year for software development. The tests processing is central in this context because there exist a reference implementation of the software that can be used to generate reference test cases. The global testing effort on the project is approx. 30%, including the execution of acceptance tests and the collection of reference values to run regression tests on a nightly basis. Tests also include interoperability tests (i.e. the use of the Unit Operations in conjunction with several types of Simulation Environments such as Aspen + or Pro/II). The acceptance test suites include more than fifty Tests Suites, each one including several hundreds of Test Cases. 1.3. Micro-electronics examples SPICE [3] is general simulation software whose first version was issued in the beginning of the 70s. SPICE simulators perform Steady-State and Transient analysis of electronic components circuits (capacitors, resistances …). This project was forked to commercial implementations and is the basis for a multi-billion dollars market.
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Many tools and techniques related to tests exist in the SPICE world, and the simulation methods can be compared to the ones that exist in the Process Simulation world. We propose the following comparison matrix for the key characteristics of the domains of Micro-electronics and Process Simulation. Characteristic Simulation modes Problem Size
Process Simulation Steady State, Dynamic 1,000 Æ 100,000 variables
Model types Connections between simulation nodes Numerical methods
Complex, multi-physics Simple (INFORMATION) Complex (MATERIAL) Constant step size ODEs and DAEs resolution, non linear systems
Interoperability Test Suites size
CAPE-OPEN N/A
μElec. Analog simulation Steady-State, Transient 100,000Æ 100,000,000 variables Simple Simple Elaborate, variable step size ODEs and DAEs resolution, non linear systems None > 100,000 Test cases for each simulation software
Table 1: Comparison matrix between Process Simulation and Micro-electronics
Temperature
The interoperability subject is not suitable to the field of micro-electronics, because the execution of a code in another vendor's environment is generally prohibited by the vendors. As a direct consequence, every software vendor in the field of SPICE simulation has its own testing environment for its internal QA process and generally provides it to its clients for benchmarking purposes. Objective +/- 5%
Max Bound
Reference value Up time Noise detection
Min Bound
•
time
Figure 1: Examples of tests of a Time Series
1.4. Difficulties Efficient testing is generally difficult because of the numerical nature of the values that are computed: numerical values cannot be tested directly and may require precise mathematical techniques (for example, filtering or statistical methods). This is especially true for dynamic simulation where the results of a simulation are Time Series.
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Figure 1 shows a typical test suite for a given Time Series (corresponding to a single process variable in a dynamic simulator, the simulated values of a temperature variable) which gives a good idea of the complexity for dynamic simulation testing. In order to circumvent these difficulties, the kinds of tests relevant to Simulation Software must be identified. Each one of these tests must individually address a specific problem, whether on the nature of the data that is being tested or the kind of defects that it must detect. 1.5. A first classification of Tests The following classification is based on our experience in micro-electronics and classical usages in the field of test automation. It can be expanded to reflect new usages and specific problems. • Behavioral tests verify a functional characteristic of a simulator (e.g. a function point, the stabilization of a signal …). On Figure 1, we illustrate a bound test, an objective test and an up-time test in this category. The failing of one of these tests indicate that the simulated value is not correct (for example, the minimum bound can be a physical limit and the maximum bound a process limit). • Performance tests aim to enforce the time-related constraints for a given objective such as simulated time / sec, memory bounds, real-time simulation enforcement. • Regression tests consist in the comparison of the values to a reference value (as shown on Figure 1, where the reference value is a time series). • Business related tests are virtually any tests that deal with the specific business of a component of a simulator: for instance, reference phase envelopes for thermodynamic servers. • Statistical / Frequency tests are based on Time Series analysis [4] or statistical processing to extract hidden information from the Time Series. On Figure 1, we illustrate this category with a noise detection test based on frequency analysis techniques, which can indicate that there is a problem in the design of the simulator. • Others: every user has potentially specific tests to perform, depending on the particular project context, the physical nature of the simulation, own experience … 1.6. First conclusions This study highlights the need for a generic, interoperable, open (new test kinds can be added depending on the clients' needs) and automated testing solution. This software tool can be used for static and dynamic simulation and must propose some tests in the categories that were identified. The next section presents the QTS system that fulfills these requirements by providing a framework for tests performed on simulation data.
2. Description of the QTS System 2.1. Architecture QTS (Quality Testing System) is a software system developed by HALIAS Technologies that automates the tasks of testing simulation results. QTS can be installed on an existing network infrastructure as shown on Figure 2 : QTS architecture.
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Unlike distributed modeling approaches such as DOME [5], QTS proposes a test dedicated toolbox for the launching of simulators on remote workstations and the acquisition of values from these simulators that handles the diversity of simulation environments and requires no modification on the simulation environments. The QTS system is intended to be used by Process, Software or Quality engineers working on a project as identified in the previous sections. The first task is to instrument existing simulation software by inserting a CAPE-OPEN compliant Unit Operation in the flow sheets, the DIABOLO Unit Operation (see [6] for details). Because of CAPEOPEN interoperability, this operation does not require modifications in the simulation software as long as it is CAPE-OPEN compliant (all major Simulation Software vendors provide a CAPE-OPEN compliant version of their software), for steady-state simulation modes or even for dynamic ones such as INDISS developed by RSI. 2.2. QTS features The system supports the tests categories identified in section 1.5, suited to both steady state and dynamic simulation. For each kind of tests, a specific page is presented to the user that displays the reason of the failure, via graphical curves, values, text, or any form suitable for the test. Test Cases can be organized in a multi-level hierarchy (Test Case, Test Suite and Test Campaign), to reflect the finality of the tests. Finally, QTS is open to other tests, as it allows users to integrate specific tests in the system. At run-time, the system supports immediate execution as well as several modes of scheduled execution (fixed dates, nightly, external events). It supports major Simulation Environments due to the CAPE-OPEN interoperability. Finally, the system can launch simulations on multiple remote workstations at the same time, enabling both the management of the licenses of the simulation software that are used and the clustering of computers for higher volumes of tests. Test results appear on feature-rich web pages. Web technologies allow the presentation to the user of the status of the simulation. By following hypertext links, the user can analyze results with more precise reporting tools including images, graphics, or specific
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numerical methods. Many standard reporting methods are present on the system (mail, syndication flows, PDF reports), allowing the integration of QTS into existing workflows.
3. Conclusions 3.1.1. Gains estimation on typical simulation projects The QTS system automates the execution and the analysis of the results of the tests on a Process Simulator. The use of the system saves the time needed to launch and analyze the results of a simulation. Because it consists in the wiring a specific Unit Operation in existing flow sheet using the flow sheet editors of major Simulation Design tools, the integration of QTS in a CAPE-OPEN compliant Simulation Environment is painless. As a consequence, the cost of this integration phase is very low. As a conclusion, a significant part of the test effort can be saved by using the QTS system, which can be as high as 30% of the global project effort. 3.2. Conclusion The QTS system is a powerful, feature rich system that introduces a new way of testing Simulation Software. QTS increases productivity on Process Simulation related tasks, or during the development of Simulation Software tools. It can be profitably used on existing projects such as Simulation Projects (Operator Training Simulators as well as Engineering Simulators) or during the development of Simulation Software environments. 3.3. Perspectives The major evolutions of the system include clustering services, instrumentation automation (special agreements with software vendors will be necessary), timelines visualization, powerful reporting methods, and integrating new tests.
References [1] M. Fewster, D. Graham, 1999, Software Test Automation, Addison Wesley [2] B. Braunschweig, R. Gani (Eds), 2002, Software Architectures and Tools for Computer Aided Process Engineering, Vol. 11, Elsevier. [3] D. Pescovitz, http://www.coe.berkeley.edu/labnotes/0502/history.html [4] R. H. Shumway, D.S. Stoffer, 2005, Time Series Analysis and its Applications (Springer Texts in Statistics), Springer-Verlag [5] David R. Wallace, Shaun Abrahamson, Nicola Senin, Peter Sferro, Integrated Design in a Service Marketplace, Computer-aided Design, volume 32, number 2, pp. 97-107, 2000. [6] L. Testard, 2007, Remote Operation of CAPE-OPEN compliant software, http://colan.org/News/Y07/news-0701.htm
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Decision tree based qualitative analysis of operating regimes in industrial production processes Tamás Vargaa, Ferenc Szeiferta, József Rétib, János Abonyia a
University of Pannonia, Egyetem street 10., Veszprém H-8200, Hungary BorsodChem Ltd., Bólyai square 6., Kazincbarcika H-3700, Hungary
b
Abstract The qualitative analysis of complex process systems is an important task at the design of control and process monitoring algorithms. Qualitative models require interpretable description of the operating regimes of the process. This work shows a novel approach to discover and isolate operating regimes of process systems based on process models, time series analysis, and decision tree induction technique. The novelty of this approach is the application of time series segmentation algorithms to detect the homogeneous periods of the operation. Advanced sequence alignment algorithm used in bioinformatics is applied for the calculation of the similarity of the process trends described by qualitative variables. Decision tree induction is applied for the transformation of this hidden knowledge into easily interpretable rule base to represent the operation regions of the process. The whole methodology is applied to detect operating regimes of an industrial fixed bed tube reactor. Keywords: qualitative analysis, decision tree, operating regime, sequence alignment
1. Introduction The improvement of product quality, the need for the reduction of energy and materials waste, and the increased flexibility and complexity of the production systems, process operators require more and more insight into the behavior of the process. Next to these requirements supporting expert systems should also be able to detect failures, discover the source of each failure, and forecast false operations (e.g. thermal runaway) to prevent from the development of production breakdowns. Data mining of historical process data along advanced process modeling and monitoring algorithms can offer effective solution for this problem. Quantitative data intensive methods are widely applied because of their statistical nature, but it always claim prior knowledge to analyze the results. Usually prior knowledge is available in the form of qualitative or tendency models of the process. Hence, qualitative analysis of complex process systems is an important task at the design of control and process monitoring algorithms. Qualitative models require the interpretable description not only the historical process data but also the operating regimes of the process. A common method for decreasing the size of a data set and to get qualitative instead of quantitative information is time series segmentation. Segmentation means finding time intervals where a trajectory of a state variable is homogeneous [1]. Segments can be linear, steady-state or transient, indicative for normal, transient or abnormal operation. Cheung and Stephanopoulos in [2] proposed a second order segmentation method for process trend analysis, the application of episodes with a geometrical representation of
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triangles. Triangular episodes use the first and second derivatives of a time series on a geometrical basis, hence seven primitive episodes can be achieved as characters. To extract useful feature from time series of the state variables one needs to lower the size and dimension of the data and define a distance measure from a theoretically optimal solution to help operators in their work (i.e. the process trends can be easily compared and evaluated with comparing each sequence of primitive episodes). For sequence comparement, in [3] it was shown as an example that dynamic time warping (DTW) is able to compare DNA sequences if mutation weights (as distances) exist. Going towards this dynamic alignment technique, we applied global pairwise sequence alignment, a well-known technique in bioinformatics developed by [4], to handle not only mutation and substitution but injection and deletion operators in a sequence. Decision trees are widely used in pattern recognition, machine learning and data mining applications thanks to the interpretable representation of the detected information. This is attractive for a wide range of users who are interested in domain understanding, classification capabilities, or the symbolic rules that may be extracted from the tree and subsequently used in a rule-based decision system. To emphasize how decision trees can be applied to extract useful information from the sequences of process trends, and how they are able to represent the operating regimes, an industrial heterocatalytic reactor was analyzed. The results show that the proposed hybrid quantitative qualitative modeling approach can be effectively used to build a process monitoring and operation support system for industrial reactors. The paper is organized as follows: in Section 2 the method of qualitative analysis of process trends is briefly introduced, it is followed by the introduction of the developed algorithm for detection of operating regimes. Further sections show an application example and results of the analysis.
2. A novel qualitative time series analysis algorithm for the detection of operating regimes 2.1. Qualitative analysis of process trends As described in [2], to get from a quantitative to a qualitative representation of a realvalued x(t) function, it has to be reasonable function. It is clear that all the psychical variables in a plant operation are reasonable. It is considered, if we know the value and derivatives of a reasonable function, the state of that function is completely known. The continuous state (CS) over a closed time interval can be defined as a point value, which is a triplet (if x(t) is continuous in t) CS(x,t)Łpoint_value(x,t)=<x(t),x’(t),x”(t)> Consequently, a continuous trend can be defined as continuous sequence of states. For discrete functions, as an approximation, an underlying continuous function has to be known since the derivatives of single points cannot be performed. These definitions lead to a qualitative description of a state (QS) and trend if x is continuous at t, otherwise it is undefined QS(x,t)= where [x(t)],[x’(t)] and [x’’(t)] can be {-; 0; +}, depending if they have negative, zero or positive values. Obviously, a qualitative trend of a reasonable variable is given by the continuous sequence of qualitative states. QS(x; t) is called an episode if it is constant for a maximal time interval (the aggregation of time intervals with same QS), and the final definition of a trend of a reasonable function is a sequence of these maximal episodes. An ordered sequence of triangular episodes is the geometric language to describe trends. It is composed of seven primitive notes as {A, B, C, D, E, F, G} illustrated in Fig. 1.
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2.2. Sequence alignment to determine the similarities of the segmented process trends Sequence alignment is typical expression of bioinformatics, where amino acid or nucleotide sequences have to be compared, how far the evolved new sequences are from the elders, i.e. how old they are, and how many mutation steps were needed to result in the new sequence. The algorithm tries to find the least mutation steps between the elder and offspring sequence applies, that is called minimal evolution. In this paper the most advanced algorithm was used (incorporated in the MATLAB Bioinformatics Toolbox) to determine the minimal sum of transformation weights (which means the similarity of the sequences). For this project therefore we extended the toolbox so it is now not only able to handle amino acid sequences, but the sequences of episodes of time series. For this purpose the similarity of the episodes had to be defined, which becomes the elements of the new transformation matrix. 2.3. Visualization and characterization of segments of process trends Based on these alignment scores (i.e. matching scores), one is able to compare and classify process trends to get a qualitative analysis. The Multidimensional Scaling algorithm (MDS) was applied to visualize the similarity of each process trend to other so the operator can easily check a new trend and in the possession of the necessary a prior knowledge the operator is able to improve the process performance. MDS is a statistical technique for taking the preferences and perceptions of respondents and representing them on a visual grid, called perceptual maps. MDS is a good tool to "rearrange" objects (in our case the process trends) in an efficient manner, so as to arrive at a configuration that best approximates the observed distances (in our case similarities of time series). It actually moves objects around in the space defined by the requested number of dimensions (in our case in three dimension), and checks how well the distances between objects can be reproduced by the new configuration. 2.4. Qualitative analysis of operating regimes The obtained virtual space (shown in Fig 2a) can be easily used to reveal how the process trends are clustered. Since the aim of the proposed methodology is the classification of these process trends and the characterization of the operating regimes of the process variables that affects the shape of these trends, the application of decision trees seems to be a straightforward solution. Binary decision trees consist of two types of nodes: (i) internal nodes having two children, and (ii) terminal nodes without children. Each internal node is associated with a decision function to indicate which node to visit next (e.g. if the temperature is smaller than 235° visit node 25, otherwise visit node 26). Each terminal node represents the output of a given input that leads to this node, i.e. in classification problems each terminal node contains the label of the predicted class (e.g. the 25th terminal node represents reactor runaway). The algorithm has the following basic steps (as shown on Fig 2b):
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x Randomly generating inlet conditions and calculating the temperature profiles; x Time series segmentation into a sequence of triangular episode primitives; x Alignment of two episode chains and determining the distance of sequences in a three dimensional virtual space; x Classifying the time series by a decision tree and based on inlet conditions and the corresponding class of sequence another decision tree is inducted.
3. Application to an industrial fixed bed tube reactor 3.1. Process description To emphasize how decision trees can be applied to extract the relevant information from process trends and how the rules characterize the operating regimes a detailed case study has been worked out based on a sophisticated model of an industrial catalytic fixed bed tube reactor. The studied vertically build up reactor contains a great number of tubes with catalyst (as shown on Fig 2b). Highly exothermic reaction occurs as the reactants rising up the tube pass the fixed bed of catalyst particles and the heat generated by the reaction escapes through the tube walls into the cooling water. Due to the highly exothermic reaction which takes place in the catalyst bed makes the reactor very sensitive for the development of reactor runaway. Reactor runaway means a sudden and considerable change in the process variables. The development of runaway is in very close relationship with the stability of reactor/model. Runaway has two main important aspects. In one hand runaway forecast has a safety aspect, since it is important for avoiding the damage the constructional material or in the worst case scenario the explosion of reactor; on the other hand it has a technology aspect, since the forecast of the runaway can be used for avoiding the development of hot spots in catalytic bed. The selection of operation conditions is important to avoid the development of reactor runaway and to increase the lifetime of catalyst at same time. The worked out mathematical model has been presented in the previous ESCAPE conference by the authors [5]. The model has been implemented in MATLAB and solved with a low order Runge-Kutta method. The obtained simulator was applied to calculate profiles in case of randomly generated inlet conditions. product
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3.2. Results and discussion Example for learning samples are plotted on Fig 3a where the vertical lines present where runaway occurs. Such process trends can be easily segmented as it is shown in Fig 3b. It is interesting to note that the algorithm detected that the in this case there was no runaway, since it has inserted an E type episode between the D and A episodes, otherwise D-A episodes would mean the change of the sign of the second derivative of the profile that would indicate runaway according to the classical inflection point based runaway detection method. 100 process trends were analyzed. The similarities of the sequences of the episodes generated from these trends were determined by the previously presented sequence alignment. These similarities were used to map the sequences into a three dimensional space to evolve the hidden structure of the trends. A decision tree was inducted to characterize the trends. Four classes were detected. The tree generated based on these new class labels can be seen on Fig 4b. On this figure the branches of the tree leading from the root to the leaves should be followed from left to right. In a decision tree the leaves contain the label of the class of the typical temperature profiles. Runaway occurs in case of the first class as shown of Fig 5. Based on this tree the instability regime can be determined (pG,in > 1.69 bar and TW,in > 289 K). 420
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Fig. 4. (a) Sequences mapped into a three dimensional “virtual” space based on their similarity. (b) The extracted decision tree that represents the operating regimes and able to estimate the class (1-4) of the temperature profiles (shown in Fig. 5).
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4. Conclusions This work demonstrated how advanced data mining techniques such as time series segmentation, sequence alignment, and decision tree induction can be used to determine the operating regimes in a heterocatalytic reactor. The results show that the proposed approach is able to distinguish between runaway and non-runaway situations based on a set of linguistic rules extracted from classified process trends obtained by the segmentation of time series generated by the model of the process. The analysis of the extracted rules showed the critical process variables determine the shape of the temperature profiles.
Acknowledgement The authors would like to acknowledge the support of Hungarian Research Found (OTKA T049534) and the Cooperative Research Centre (VIKKK) (project III/2). János Abonyi is grateful for the support of the Bolyai Research Fellowship of the Hungarian Academy of Sciences.
References [1] E. Keogh, S. Chu, D. Hart, M. Pazzani, 2001, An Online Algorithm for Segmenting Time Series, IEEE International Conference on Data Mining, 289-296. [2] J. T. Cheung, G. Stephanopoulos, 1990, Representation of process trends. Part I. A formal representation framework, Computers and Chemical Engineering, 14, 495-510. [3] R. Srinivasan, M.S. Qian, 2006, Online fault diagnosis and state identification during process transitions using dynamic locus analysis, Chemical Engineering Science, 61, 6109-6132. [4] S.B. Needleman, C.D. Wunsch, 1970, A general method applicable to the search for similarities in the amino acid sequence of two proteins, Journal of Molecular Biology, 48, 443453. [5] T. Varga, F. Szeifert, J. Réti, J. Abonyi, 2007, Analysi of the runaway in an industrial heterocatalytic reactor, Computer-Aided Chemical Engineering, 24, 751-756.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Mobatec Modeller - A flexible and transparent tool for building dynamic process models Mathieu R. Westerweelea, Jan Laurensa a
Mobatec, Veestraat 10, 6134 VJ Sittard, The Netherlands, www.mobatec.nl
Abstract The software tool that is explored in this paper, Mobatec Modeller, builds on a modelling methodology that was originally developed by prof.dr.dipl-ing H.A. Preisig and dr.ir. M.R. Westerweele [1]. With the tool, dynamic process models of any size can be build - from a single unit to entire processing plants (resulting in more than 50.000 equations). There is a wide application range for these models in, for example, research activities, on-line predictions and/or control and operator training simulators. User-friendliness, functionality and good user-assistance are a prerequisite for being able to manage large models. To demonstrate user-friendliness of Mobatec Modeller, several distinguishing features are discussed, such as automatic component distribution, automatic balance equation generation, easily extendable (equation, component, reaction) databases, consistent initial value calculations, code generation for several solvers, very elaborate and useful search functionality. Keywords: Mobatec Modeller, Dynamic Models, User Friendliness, Transparent Modelling.
1. Introduction Solving process engineering problems without the help of computer-based tools is for almost any problem an unthinkable proposition. Process simulation, process design, controller design, controller testing, data acquisition and model identification, parameter fitting, valve and pump selection, column sizing are just a few examples taken from a very large catalogue of chemical plant related operations that are almost exclusively done with computer-based tools, nowadays. Although several good software tools are on the market to build dynamic process models, it often seems that an expert is needed to setup or modify these models. It is also difficult to build models that are transparent for users that were not involved with the model development. Mobatec Modeller [2] is a computer-aided modelling tool to interactively define and modify transparent process models. It can be seen as a shell around existing dynamic modelling packages. It aims to effectively assist in the development of process models and facilitate hierarchical modelling of process plants through a user friendly interface. With Mobatec Modeller process models are constructed from primitive building blocks, being simple thermodynamic systems and connections. It does not, in distinction to existing flow sheeting packages, build on unit models. The “Unit models” that are available in libraries are also built from the primitive building blocks. Mobatec Modeller generates (and solves) symbolic models in the form of differentialalgebraic equations consisting of component mass and energy balances, augmented with transfer laws, physical and geometrical property relations and kinetic laws.
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2. Modelling Methodology The modelling methodology implemented in Mobatec Modeller is based on the hierarchical decomposition of processes (in which material and energy exchange are playing a predominant role during normal operation) into networks of elementary systems and physical connections. Elementary systems are regarded as thermodynamic simple systems and represent (lumped) capacities able to store extensive quantities (such as component mass, energy and momentum). The connections have no capacity and represent the transfer of extensive quantities between these systems. The construction of a process model with this methodology consists of the following steps: 1)
Break the process down into elementary systems that exchange extensive quantities through physical connections. The resulting network represents the physical topology. The process of breaking the plant down to basic systems and connections determines largely the level of detail included in the model. It is consequently also one of the main factors for determining the accuracy of the description the model provides.
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Describe the distribution of all involved chemical and/or biological species as well as all reactions in the various parts of the process. This represents the species topology, which is superimposed on the physical topology and defines which species and what reactions are present in each part of the physical topology. The species distribution is fully automated by Mobatec Modeller and is initiated by introducing species at the battery limits of the modelled process.
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For each elementary system and each fundamental extensive quantity (component mass and energy) that characterises the system write the corresponding balance equation. Mobatec Modeller automatically generates all the needed balance equations for component mass and enthalpy of each system, since these balances can be trivially formed from the model designers’ definition of the physical and species topology of the process. The user cannot edit the generated balance equations!
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Add algebraic equations to the model definition: • Choose the transfer laws and kinetic laws that express the flow and production rates that appear in the balance equations. • Express the fundamental extensive variables that characterise each system as a function of intensive variables characterizing the same system. • Look for dependencies between the intensive and geometric variables that have been introduced and write these dependencies out as equations of state. The dynamic balance equations (step 3) and the algebraic equations, which are placed on top of the physical topology and species topology, represent the equation topology.
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Add the (dynamic) behaviour of the information processing units, such as transmitters, adjusters and controllers.
These steps for building a model do not have to be done strictly in this sequence - at least not for the overall model. It is left to the model designer when the details are being specified in each part of the model. This five step procedure of building dynamic process models always results in a set of differential algebraic equations (DAE) with an index of one (i.e. structurally solvable by most available solvers). The model can be used for solving certain problems related to the process or it can be further modified by applying mathematical manipulations, such as linearization or model reduction.
3. What is User-Friendliness? According to Wikipedia [3] “usability (i.e. user-friendliness) is a term used to denote the ease with which people can employ a particular tool or other human-made object in order to achieve a particular goal. In human-computer interaction and computer science, usability usually refers to the elegance and clarity with which the interaction with a computer program or a web site is designed.” Imported considerations for user-friendliness include: Who are the users? What is their general background? What do they want or need? What is the context in which the users are working? Can users accomplish intended tasks at their intended speed? Is working with the tool easy to learn? Etc. When people speak about a tool that is “easy to use” or “user-friendly” they often actually mean that it is “easy to learn” or “easy to use without learning”. Easy to learn means that if you sit somebody with no experience down with a tool, it will be (relatively) easy for them to learn how to use it. Useful aspects for learnability are ‘intuitiveness’ and ‘obviousness’. If something is intuitive or even obvious, it's far easier to learn than if it is not. Unfortunately intuitiveness and obviousness are very subjective and often depend on background knowledge; different people find different things intuitive or obvious. Luckily, the group of users we are aiming at in this case roughly (should) have the same background and interests. Another important aspect of user-friendliness of a tool is its documentation. Good documentation is indispensable. It should be correct, up-to-date and cover a reasonable range of the functionality. Unfortunately, typical users will not read the documentation until they are “in trouble”. Therefore the documentation should be kept as short and as to the point as possible. A very good way of “documenting” the functionality of a tool is to make use of ‘Tool Tips’ that appear, for example, after your mouse cursor hovers for a few seconds or when the right mouse button is pressed on an item in a toolbox.
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4. User-friendly Interface of Mobatec Modeller This section discusses some aspects of the implementation and user interface of Mobatec Modeller, a computer-aided modelling tool with the objective to provide a systematic model design method. A software tool cannot reach to its full potential if the software developers of the tool do not exactly know what problems the end users want to solve and what questions these users want to see answered. More often than not the end users of a tool and the developers of this same tool live in two different worlds (computing, implementing vs. engineering, chemistry, academics) and have a hard time communicating with each other. This, of course, makes the software development difficult, slow and time consuming. We found ourselfs in the fortunate situation that we were (and still are) doing industrial projects (for several companies) whilst, at the same time, being able to develop the software that is used for the implementation of these projects. The best way of finding out what the user wants, is to be a (real!) user yourself. During the PhD study of M. Westerweele the focus was on the algorithms behind the mathematical modelling of physical/chemical processes. Afterwards, the focus needed to be shifted to applicability, needs of industry and user-friendliness. The focus of Mobatec Modeller is primarily on modelling and not on problem solving (although both activities are supported in the tool). Most of the currently available modelling languages and simulation packages focus on the manipulation, specification, analysis and/or solution of existing or predefined models and more or less leave out the model building part. In general it is assumed that the mathematical model of the process under investigation is known or easy to assemble. The development of process models, however, is slow, error prone and consequently a costly operation in terms of time and money. Dynamic modelling is an acquired skill, and the average user finds it a difficult task. A modeller may inadvertently incorporate modelling errors during the mathematical formulation of a physical phenomenon. Formulation errors, algebraic manipulation errors, writing and typographical errors are very common when a model is being implemented in a computing environment. Mobatec Modeller automates several of the needed modelling operations and therewith eliminates a lot of simple, low-level (and hard to detect) errors. The modelling methodology implemented in Mobatec Modeller also forces the model builder to make assumptions that are closer to the “physical reality” than when more conventional tools are used. Take, for example, the very well known and often used model of a CSTR with a flow in and out. The commonly used assumption that the liquid volume is fixed holds several other assumptions (e.g. fixed density and infinitely fast adaptation of the outflow to changes in the inflow) of which the implications are often not clear to novice modellers. While this approach is nice for academic examples, since the resulting set of equations can be solved algebraically, it is hardly ever appropriate when building dynamic models for ‘real’ processes. It also tends to let novice modellers make wrong sequential assumptions when the model becomes a bit more elaborate. Mobatec Modeller therefore promotes the use of flow equations that depend on the states (e.g. the pressure or the level) of the interconnected systems.
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We found that “typical” model engineers are not particularly interested in the exact mathematics behind the solving of a problem. They do, however, often want to know how a model or sub model is setup (Which equations are used? What are the assumptions?). They want to be able to understand the used model and possibly make certain adaptations to make it better fit their needs. Mobatec Modeller therefore supports an open model structure in which all used equations can always be viewed and edited (except for the balance equations, that are generated automatically and purposely cannot be edited). A drawback of several (dynamic and/or steady-state) flow sheeting and modelling packages is that the equations of predefined sub models (i.e. units) cannot be edited. In some cases the accompanying documentation lists (partially) which equations are implemented in the sub model, but that is as far as it goes. The disadvantage of this approach is that it is not flexible and a lot of documentation is needed. To make a sub model more flexible, either a lot of options need to be implemented (implying a lot of overhead to be carried along with the model) or a lot of slightly different sub models need to be available. Whilst it is, of course, handy and even necessary to have a large database of predefined sub models (i.e. unit operations); it is not user-friendly to confine the user to the particular implementation of the model builder. To promote user friendliness, Mobatec Modeller has several distinguishing features: • Context sensitive, non-modal properties toolbox. A rather annoying feature of many programs is the use of so-called modal dialog boxes for displaying properties. This means that the user must first close the box before he can continue with the program. This can be very inconvenient if the user wants to view the properties of several objects. In Mobatec Modeller the properties toolbox directly adapts to the active selection. • Unlimited Undo/Redo functionality. All actions can be undone and redone, if necessary. This eliminates the need for modal dialog boxes with questions like “Are you sure you want to ….” • Visible time-scale assumptions. On a high level, the screen of Mobatec Modeller may resemble a typical flowsheeter. It is, however, always possible to zoom in to a lower level in which the user can graphically see which time-scale assumptions have been made in each sub model. Due to the used modelling methodology, all mass transfers, heat transfers, phase transitions, etc. must be explicitly visible. A (sub) model is always an interconnected network of systems. • Automatic species distribution. The definition of the species topology is initialised by assigning sets of species and reactions to some elementary systems. To aid in this definition, species and reaction databases are used. The user may also specify the directionality (i.e. uni or bi-directional) and permeability (i.e. selective transfer of species) of individual mass transfer connections. The distribution of the species over all systems is automated and uses the facts that assigned species can propagate through permeable mass connections and species may generate “new” species (via reactions), which in turn may propagate and initiate further reactions. • Ample user preference settings. User-friendly also means that a user can do his work “his own way”. The working environment can therefore be adjusted via several user preferences and there are several ways to perform actions: via the toolbar, menus, context-sensitive popup menus or single-key keyboard shortcuts. • Powerful search functionality. Mobatec Modeller has an elaborate and useful search functionality, which is especially handy for larger and more complex models.
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The user can easily find unproper equation sets, uninitialized variables, duplicate names, species, reactions, equations, variables, domains, properties, etc. Easily extendable databases for equations, variables, species and reactions. All used equations only have to be defined once. Equations are parsed as they are defined. Low-level errors are therefore minimized and the variables that are used in the equation are automatically detected. Automatic equation sorting and, consequentially, declaration of constants and variables. Due to the division of the model into a set of interconnected systems, typically, only somewhere between one and ten equations are associated with each modelling object (system, connection or reaction). The equations can be selected from user-extendable databases. The user is helped with defining a set with an equal number of equations and unknowns. Mobatec Modeller automatically determines which variable should be solved from which equation and places the used constants and variables of each object in the correct declaration lists. Consistent initial value calculations. For dynamic simulations a consistent starting condition, the so-called initial values for all defined variables, needs to be present in order for the solver to find a solution. This, often cumbersome task, is easy with Mobatec Modeller. The variables of an object are related to each other via the defined algebraic equations. Therefore their values can, in principle, not be chosen independently. The initial values of each object can be calculated from a set of independent variables. Code generation for several solvers. Apart from the code that can be generated for the integrated equation solver, Mobatec Modeller can make input for several other problem solver tools, such as Aspen Custom Modeler, gProms, Matlab, e-Modeler, Modelica, or any other DAE solver. Frequent updates. Our software is constantly further developed and about twice a month a new release is available. Since a compact programming style is used, the size of the installer is small and the updates take less than a minute.
5. Conclusion Mobatec Modeller is a user-friendly tool to define and modify dynamic process models. Even beginning users can relatively quickly setup rather complex models that are transparent for others without much documentation. The constructed models can be used in several existing problem solver tools.
References [1] Westerweele, M. R.: 2003, “Five Steps for Building Consistent Dynamic Process Models and Their Implementation in the Computer Tool Modeller”, PhD thesis, TU Eindhoven, Eindhoven, The Netherlands. [2] Information on Mobatec Modeller and technical consultation: www.mobatec.nl. [3] Wikepedia. Multilingual, web-based, freecontent encyclopedia project. www.wikipedia.org.
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Sustainable Energy Futures, and what we can do about it Cav. Prof. Sandro Macchietto Imperial College, London, U.K (
[email protected])
Abstract Energy underpins every society’s ability to meet most of its primary needs. Its demand has been traditionally been governed by supply, technology and economics. The new constraint posed by energy’s environmental impact is radically changing the playing field, making energy a global issue and one of the key challenges of this century. The scale of this challenge is daunting, and several approaches may be taken. We will briefly discuss the need for and benefits of taking a very broad view of energy, with emphasis on whole systems and sustainability, in addressing the wide ranging and crosscutting energy problems that we face. It will be shown how a systems approach, applied to meeting the primary societal needs, gives key, sometimes surprising insights and indicates key directions for technology and policy development. A series of examples, at various scales of complexity and potential impact, will then be used to highlight the key role of Systems Engineering methodology and tools in improving the efficiency of energy utilisation and in devising new energy supply, conversion, distribution and demand management solutions. Some of the initiatives undertaken at Imperial College to address the above challenges will be discussed. At the research level, these include a series of large scale, multidisciplinary projects within the Energy Futures Lab. At the teaching level, a new Masters Course in Sustainable Energy Futures has been launched, aimed at meeting the need for skilled people able to take a quantitative, strategic view of energy. The course is highly multidisciplinary, involving academic staff from 11 departments in three faculties. The rationale for the course and its structure will be discussed, together with some key challenges arising from its broad nature and the need to straddle organisational boundaries. Final comments will address the need for the traditional process systems community to collaborate with researchers in other key disciplines such as biosciences, materials, energy economics and policy, and behavioural sciences.
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A Methodology for Designing and Evaluating Biomass Utilization Networks Nasser Ayoub1,2, Hiroya Seki1, Yuji Naka1 1. Process Systems Engineering Division, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku Yokohama 226-8503, Japan. 2. Production Technology Department, Helwan University, Helwan, Egypt.
Abstract This paper presents a methodology for designing and evaluating Biomass Utilization Networks, BUN, in local areas. Therefore, the proposed methodology assumes the great importance of establishing the BUN superstructure for the area under study, which relates the biomass resources to their products, available processes and possible future processes of utilization. Using the developed network superstructure, the quantitative data of the local biomass resources, the bioproducts demands, the redundant resources and processes, due to low amount, low demand, or technical problems, are excluded. Then two types of network structures were set upped, the first is the reference models that show the current situation with its possibilities for improvements and the second type is future network structures that can be established excluding, or partly including, the current utilization strategy. The resulted network structures are used as a blue print for different scenarios of integrated biomass utilization systems that can be evaluated in comparison to the reference scenario. Optimizing the different scenarios allows us to define the bottlenecks in the biomass utilization system that limits its total throughput. Solving the optimization problem of the selected network structure in the local level needs high rank of details where each resource’s supply chain includes wide range of Unit Processes, UPs, that meet domestic circumstances e.g. logistics, production facilities, and so on. The GA was used to solve this optimization problem as a powerful tool in solving such combinatorial problems considering three optimization criterions, e.g. costs, emissions, energy consumption to congregate the different economical and environmental burdens of the established BUN. Keywords: Biomass Utilization Networks, Superstructure, Biomass, Genetic Algorithms, Bottleneck.
1. Introduction Traditionally biomass has been used to provide heat for food preparation and worming up (Fanchi, 2004). Nowadays, the technologies used in processing biomass resources are very different and ranges from fundamental processes such as wood fuels in cooking, charcoal production to sophisticated once like thermo-chemical conversion of biomass to gas or power. Furthermore, every local area has its own Biomass Utilization Network, BUN, superstructure, as shown in Fig.1, depending on factors such as; biomass resources available, lifestyle, weather, etc. Hence, the decisions about establishing the BUN, for certain area, have to rely on a robust design and evaluation methodology to overcome the problems that arises from its interconnected processes and their allocation systems. In the definition of the superstructure more detailed classifications are exist for biomass resources, processes and products. For example, the biomass resources are classified as wet or dry, the bioproducts are categorized as finished products or byproducts and so on. The main difference between the network superstructure and the network structure is that the former gives a general outline for
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available resources and processes that is available for certain locality, while the second includes the detailed processes and jobs that are applied in the real situation.
Fig. 1 Biomass Utilization Network Superstructure.
In section 2, the definition of BUN, problem definition and the background are discussed. In section 3 and 4, the proposed methodology and its evaluation criterion are explained. Conclusions and future work are stated in section 5.
2. Biomass Utilization Network 2.1. What is Biomass Utilization Network and why it is important? Our recent research works about biomass utilization as energy source have recommend including bioenergy production systems as a part of local BUNs (Ayoub et al., 2006a; Ayoub et al., 2006b; Ayoub et al., 2007). The BUN in the context of this work can be defined as; “A group of dependant and interconnected processes for utilizing one or more biomass resources that leads to the production of single or multiple bioproducts”. The structure of BUN in a local area is mainly depends upon the biomass resources available, the existing biomass utilization systems, and the demand from various bioproducts. To overcome the differences in nature between different localities in a country, it is important to establish standard classes of localities that share similar characteristics, i.e., land, weather, locations, etc. In this case, establishing a network in one instance of specific class can be applied on the other instances of the class with moderate effort, time and resources. Therefore, the classes of biomass utilization systems suitable for the area under study has to be first established based on local data. 2.2. Problem Definition Many research works are made or being made for promoting biomass utilization that range from biomass potential estimation to technology research and development (Voivontas et al., 2001; Kim and Dale, 2004; Parikka, 2004; Albertazzi et al., 2005; Caputo et al., 2005). However, utilization of biomass to bioproducts is facing many environmental, economical and social problems that may exist from one or more
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processes along the production system. In reviewing the related literature, much work is done in the analysis of individual biomass utilization technologies as well as the biomass supply chains for both single and integrated systems of biomass resources, (Ayoub et al., 2006a; Ayoub et al., 2006b; Ayoub, 2007; Ayoub et al., 2007; Ayres, 1995; Albertazzi et al., 2005; Caputo et al., 2005). However, it reveals that there is lack in literature that study designing and evaluating systems of multiresources and multiproducts like BUNs. For example, none of them analysis the bottleneck processes that may control or obstruct the production flow in the BUN. Dornburg (Dornburg and Faaij, 2006; Dornburg et al., 2006) proposed an optimization model that identifies the optimal strategies for biomass and waste treatment systems in terms of primary energy savings and their economical performance and energy saving however it neglects the environmental effects. Another limitation of their model is neglecting the effect of different technologies along the individual biomass resources supply chains i.e., machines, vehicle, storage, etc. Almost all production processes have bottlenecks in a step or process that limits total plant throughput, and biomass utilization systems are not exception. Defining the bottleneck processes can direct future researches to be more specific and concentrated on the improvement or development of technologies and models used in debottlenecking theses processes or improving unfavorable operating conditions. The research results can be given in form of suggestions of specific network class(s) to each group of localities with the same characteristics. From the authors point of view technologies assessment for each process can help in finding the bottleneck processes in biomass network systems which form main driving force for resuming this research.
Fig. 2. The Proposed Methodology
3. Methodology In this research work, various BUNs in local areas are studied and analyzed aiming at finding general classes of local biomass networks, finding the bottleneck processes, defining suitable evaluation methods to optimize the problem, and suggesting suitable solutions or recommendations for debottlenecking. The methodology proposed here is performed in three steps, as shown in Fig 2, namely; 3.1. Data collection and classification The BUNs are classified based on locality topology, weather, geographical location and the time frame. Based on the renewable resources, the renewable institution classes are defined to be used in allocating the suitable institution for the local area under study. Also, by collecting and analyzing the inputs to the local biomass network, such as available classes of biomass resources, similar classes of local areas, suitable renewable institutions, available processing methods and future trends the biomass utilization superstructure are established.
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3.2. Problem formulation Using the data collected, the BUN classes, which relates the biomass resources to their products, available processes and possible future processes of utilization is defined. In the development of biomass network, the different qualitative characteristics and specifications of biomass resources are taken into consideration such as production location, frequency of production, mode of production etc. At this stage, the scenarios, structures, for BUN are set by defining the primary quantities of biomass resources and their mass balance along each network structure as shown in Fig. 3 for a simple BUN structure of two input resources QR1, QR2 to produce 3 bioproducts P1, P2, P3 through network processes from A to O. This simple network generates seven supply chains; A-B-C-D-E, A-B-C-I-J, A-F-G-H-I-J, A-F-M-N-O, A-FM-N-J, K-L-M-N-O and K-L-M-N-I. For each UP of the supply chain there is a number of models , (Ayoub, 2007; Ayoub et al., 2007) to be optimized. The network optimization can be performed processed quantities or UP models. B
x QR1
C
D
E
H
I
N
O
P1
A QR1- x-y
QR1- x F
G
J
P2
y QR2
QR2 + y K
L
M
P3
Fig. 3. Schematic representation of Biomass Utilization Network
The optimization is performed only over the UPs with fixed biomass resources quantities using the bottom up approach. The cost objective function can be given as: c
MinZ1
m
n
¦¦ ¦UPC
ijk
k 1 j 1
( Re v ETax)
(1)
i 1
where i unit process index; i=0,1, 2, …, n j resource index; j=1, 2, …, m k UP model index k=1, 2, …,c UPCijk annual cost of the unit process i for processing resource j that will be converted at facility k (yen/year) Rev is the revenue from selling the bioproducts (yen/year) ETax is the profits from applying the emission taxes (yen/year) 3.3. Suggested solutions Solving the optimization problem of biomass network models is a challenging task as the local planning needs high rank of details where individual resource’s supply chain includes a wide range of Unit Processes, UPs, that meet domestic circumstances e.g. logistics, production facilities, and so on. The appropriate mix of UPs, equipment sizes, new plants locations, etc., is another complicated issue. As the number of biomass resources and their associated models increase, so does the number of combinations. The GA is used to solve this optimization problem as a powerful tool in solving such combinatorial problems considering three optimization criterions, e.g. costs, emissions, energy consumption. A sensitivity analysis for each class of BUN model is performed in order to define the bottleneck processes. By optimizing the available biomass
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resources via data mining methods the optimal locations of biomass network facilities are defined.
4. BUN Evaluation Criterion and Constraint Handling It is important to consider the concerns of the active stakeholders whom controlling or at least affecting the decision making process. For this reason, three evaluation criterions are considered in this research work for the BUN and explained in the following subsections. 4.1. BUN Cost Minimization The production cost of the bioproducts in a selected BUN is represented by the sum of the costs of the UPs that are forming the individual bioproducts supply chains. 4.2. BUN Emission Minimization The environmental impacts of emission functions expressed as the sum of all emissions resulted from the individual products’ UPs. 4.3. Minimization of Energy Used to Produce Bioproducts The energy objective function measures the amount of energy needed to realize the BUN. The energy objective function is expressed as the sum of annual energies consumed in the individual UPs used in the BUN. 4.4. Constraints Handling The optimization problem includes constraints over total biomass availability and total annual investment. The most common strategy to handle constraints is the use of penalty functions that decrement the value of the fitness associated to the individual if the corresponding solution does not fulfill some constraints of the problem (Michaelwicz, 1992). Another effective strategy is to invoke, just before the actual fitness evaluation, a fast constructive heuristic procedure that is able to convert any individual created by the GA into a fully feasible solution (Naso et al., 2006). The second approach is applied in this work. For example, to control the annual investments for BUN establishment the cost of the best-selected individual is compared to the investment constraint value; if the value doesn’t fulfill the constraint, another individual that fulfill the constraint is selected.
5. Conclusions and Future Challenges The proposed methodology for designing and evaluating BUN is an integration of ideas and methods used for the first time in this research field to consider the BUN. A general explanation about the methodology and its common features is presented. Using the proposed method, designing and evaluating BUN is performed considering various points i.e. environmental, economical, and social and at the same time the possibility of defining the bottleneck processes in a specified network. The results show that approaching the optimization problem by GA is helpful in solving the combinatorial problems of the UP models defined in the BUN. The GA is recommended for its flexibility in handling the problems of combinatorial nature, like the problem under study, where the decision maker is provided by quite a number of solutions using similar high fitness values that are of his expectations. Extending the proposed model to evaluate the hybrid biomass based renewable energy systems through the different life cycles of resources and products is one of the challenges a head. The evaluation is applied over, product costs, CO2 emissions, energy saving/consumption and the number of personnel required for the business realization. The results of applying the proposed methodology as a case study to a local Japanese area with more is to be published as a second part of this work.
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Acknowledgments The authors wish to thank the Ministry of Education, Culture, Sports, Science and Technology, Japan for generously financing this work through biomass leading project.
References S. Albertazzi, F. Basile, J. Brandin, J. Einvall, C. Hulteberg, G. Fornasari, V. Rosetti, M. Sanati, F. Trifiro and A. Vaccari ,2005 , The technical feasibility of biomass gasification for hydrogen production. Catalysis Today, International Conference on Gas-Fuel 05 - International Conference on Gas-Fuel 05 106,297-300. N. Ayoub ,2007 , A Multilevel Decision Making Strategy for Designing and Evaluating Sustainable Bioenergy Supply Chains, PhD thesis in Process System Engineering, Tokyo Institute of Technology, Yokohama. N. Ayoub, K. Wang, H. Seki and Y. Naka ,2006a , Towards sustainable electricity production from Japanese forestry residues, supply chains scenarios and parameters estimation model. Journal of Life Cycle Assessment, Japan 2,212-221. N. Ayoub, R. Martins, K. Wang, H. Seki and Y. Naka ,2007 , Two levels decision system for efficient planning and implementation of bioenergy production. Energy Conversion and Management 48,709-723. N. Ayoub, K. Wang, T. Kagiyama, H. Seki and Y. Naka ,2006b , A Planning Support System for Biomass-based Power Generation, in European Symposium on Computer Aided Process Engineering (ESCAPE, 16) and 9th International Symposium on Process Systems Engineering (PSE, 2006), pp 1899 -1904, Elsevier, GarmischPartenkirchen,Germany. R. U. Ayres ,1995, Thermodynamics and process analysis for future economic scenarios. Environmental and Resource Economics 6,207-230. A. C. Caputo, M. Palumbo, P. M. Pelagagge and F. Scacchia ,2005 , Economics of biomass energy utilization in combustion and gasification plants: effects of logistic variables. Biomass and Bioenergy 28,35-51. V. Dornburg and A. Faaij ,2006 , Optimising waste treatment systems: Part B: Analyses and scenarios for The Netherlands. Resources, Conservation and Recycling 48,227-248. V. Dornburg, A. Faaij and B. Meuleman,2006 , Optimising waste treatment systems: Part A: Methodology and technological data for optimising energy production and economic performance. Resources, Conservation and Recycling 49,68-88. J. R. Fanchi ,2004 , Energy,Technology and Directions for The Future. Elsevier Academic Press., Amsterdam. S. Kim and B. E. Dale ,2004 , Global potential bioethanol production from wasted crops and crop residues. Biomass and Bioenergy 26,361-375. Z. Michaelwicz ,1992 , Genetic algorithms + data structures = evolution programs. Springer-Verlag, Berlin, New York. D. Naso, B. Turchiano and C. Meloni ,2006 , Single and Multi-objective Evolutionary Algorithms for the Coordination of Serial Manufacturing Operations. Journal of Intelligent Manufacturing 17,251-270. M. Parikka ,2004 , Global biomass fuel resources. Biomass and Bioenergy, Pellets 2002. The first world conference on pellets 27,613-620. D. Voivontas, D. Assimacopoulos and E. G. Koukios ,2001 , Aessessment of biomass potential for power production: a GIS based method. Biomass and Bioenergy 20,101112.
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Integrated Gasification Combined Cycle (IGCC) Process Simulation and Optimization F. Emun, M. Gadalla, L. Jiménez Department of Chemical engineering, School of Engineering, University Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain
Abstract Integrated Gasification Combined Cycle (IGCC) technology is increasingly important in the world energy market, where low-cost opportunity feedstocks such as coal, heavy oils and pet coke are among the best alternatives. IGCC technology produces low-cost electricity while meeting strict environmental regulations. To further improve IGCC’s efficiency, operating the process at the optimum values, process integration and modifications of the process flow diagrams are typical approaches, where process simulation is used as a tool for implementation. A process simulation model is developed with Aspen Plus£ for IGCC system employing Texaco gasifier. The model is applied to conduct sensitivity analyses for key performance parameters and integration options to improve system efficiency and environmental performance. As a result, a significant improvements in process efficiency and environmental performance is attained. Thermal efficiency as high as 45% can be reached and a significant decrease in CO2 and SOx emissions is observed. The CO2 and SOx emission levels reached are 698 kg/MWh and 0.15 kg/MWh, respectively. Keywords: IGCC, Process simulation, Process Optimization, Process Integration
1. Introduction Increasingly expensive oil and global warming are causing an energy revolution by requiring oil to be supplemented by alternative energy sources and efficient utilization of existing energy sources (e.g. coal, natural gas, nuclear power). Due to the availability and relatively wide geographic distribution, coal is a representative energy source for power generation. The emission of different pollutants, specially green house gases, urged the environmental regulations to be a strong driver for new developments. These developments aim principally at coal based electric power technologies, where IGCC is an alternative technology to pulverized coal (PC) combustion systems [1]. The reason is that IGCC have the potential to obtain higher efficiency and better environmental performance for power generation. They also offer greater fuel flexibility (biomass, refinery residues…) and can offer multiple products (electricity, hydrogen and other chemicals like methanol and higher alcohols) and byproducts (sulfur, sulfuric acid, slag…). In addition, IGCC technology has the potential for CO2 sequestration [1, 2] . This paper presents an optimization scheme for IGCC through process simulation and sensitivity analysis of the key operating parameters. Then a heat integration scheme is presented for the different sections of the process.
2. IGCC Process Description and Modeling IGCC is developed for a Texaco gasifier with radiant/convective cooling system. The process flow diagram is shown in Figure 1. The coal, (Illinois #6), is crushed and mixed
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with water to produce a slurry (35.5 % w/w water) and pumped into the gasifier with oxygen. The gasifier operates in a pressurized, down flow, entrained design and gasification takes place rapidly at temperatures higher than 1200 ºC. The raw fuel gas produced is mainly composed of H2, CO, CO2, and H2O. The coal's sulfur is primarily converted to H2S and smaller quantity of COS. This raw fuel gas leaves the gasifier at 1370 ºC along with molten ash and a small quantity of unburned carbon. No liquid hydrocarbons are generated. This gas/molten solids stream enters to a radiant syngas cooler (RSC) and convective syngas cooler (CSC) sections. In this design, the mix of gas/solids from the gasifier enters a radiant syngas cooling (RSC) system where cooling (≈815 ºC) is accomplished by generating a high-pressure steam. A convective syngas cooling (CSC)/gas scrubbing system cools the raw fuel stream to about 150 ºC (27.5 bars) by generating additional steam. It uses a gas scrubber and a low temperature gas cooling/heat recovery section to reduce the raw fuel gas stream to 40 oC, prior to entering a cold gas cleaning unit (CGCU) for sulfur removal. The properties of Illinois #6 coal and the data are reported by the Process Engineering Division of the American Energy Institute (2000) [3]. Some data (operating conditions, range of variables) are retrieved from the literature [4-6].
Sulfur
Coal
Water
Figure 1. Simplified diagram for IGCC [7].
3. Methodology The flowsheet has several naturally grouped sections: coal preparation, gasification, gas cooling and cleaning, acid gas removal, gas turbine, HRSG, steam cycle, etc... All sections were rigorously modeled using Aspen Plus®. Simulation was controlled using FORTRAN routines and design specifications to reduce the number of initial conditions and to adjust automatically those associated variables. The main functional relationships (i. e. control structures) are: the amount of coal input is a function of the gas turbine net power (272 MW), the amount of slurry water depends of the coal input (35.5 %), the make-up water for the steam cycle depends on the temperature of the stack gas (125oC), the air input to the ASU is determined by the gasifier net duty and the air to the gas turbine (GT) combustor is fixed by the combustor net heat duty or the stoichiometric amount of air required.
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Since this is a large and complex model (seven nested loops, five control blocks and many design specifications) it is very sensitive towards the loop’s break points (i. e. tear streams) and their initial conditions. After detailed analysis, a specific computational sequence was set up for the model, and the ranges of initial conditions were established to improve the convergence. Sensitivity analysis and process integration are applied to improve the efficiency and environmental performance of the process.
4. Process Optimization The sensitivity of the process for different variables is analyzed. The variables studied are: gasification temperature, combustion temperature, level of N2 injection and solid concentration of the coal slurry. The main parameters analyzed within each analysis are thermal efficiency (LHV) (εLHV), cold gas efficiency (εCG), net power output per ton of coal, O2:carbon ratio (O2:C) and air:clean syngas ratio (air:syn). 4.1. Effects of Gasification Temperature The sensitivity of the process for the gasification temperature is done under the operational range of temperatures where gasification can take place with slagging of the ash (1250 ºC and 1550 ºC) [1]. As the gasification temperature increases, the thermal efficiency decreases due to a decrease in the cold gas efficiency. This decline in cold gas efficiency is due to a rise in the O2:C ratio in order to combust more carbon to reach high temperature. On the contrary, the total net power increases because the steam turbine power output rises due to a higher amount of the slurry used for the same quantity of gas turbine output; however, the net power output per ton of coal consumed has a decreasing trend as the thermal efficiency. The CO2 and SOx emissions per unit of power output increases due to the rise in the coal consumption for the same level of GT power output. But the NOx emission per unit of power output decreases very slightly due to a decline in the air:clean syngas ratio, thereby lessening the thermal NOx formation. 4.2. Effects of Gas Turbine Inlet Temperature (Syngas Combustion Temperature) The analysis is performed for a range of temperatures (Tcomb) around the base case (1250-1550 oC). For an increase in Tcomb by 300 oC, thermal efficiency (εLHV) increases by 5%. Along with an increase in εLHV, the CO2 and SOx emissions per unit power output also decrease. This is due to the decrease in the level of coal consumption for the same GT power output. But, the NOx emission increases because of an increase in thermal NOx formation at higher temperatures. The carbon conversion efficiency, the cold gas efficiency and the O2:C ratio remain almost constant because they are independent of the combustor operating temperature. 4.3. Effects of Level of N2 injection As the fraction of N2 injection to the GT combustor increases: 1. The thermal efficiency increases, due to a decrease in the slurry (coal) requirement as more N2 is used to drive the turbine. 2. The net power output decreases due to a decrease in the steam turbine power output as a result of the reduction in the coal flow. 3. The net power output per ton of coal input increases because of the decrease in coal requirement for the same level of GT output. 4. The CO2, SOx and NOx emissions decrease due to the decrease in the coal consumption and the diluting effect of the N2, thus inhibiting thermal NOx formation. The carbon conversion efficiency, the cold gas efficiency and the O2:C ratio remain constant because they are independent of the varying parameter.
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4.4. Effects of Solid Concentration in Coal Slurry With the rise in solids concentration, the O2:carbon ratio decreases because the required energy to vaporize and superheat the water decreases. Therefore the syngas heating value increases because less coal is being used to supply energy for the gasification. Due to this, the thermal efficiency and the net power output per ton of coal input increase. The emissions per unit power of CO2, SOx and NOx slightly increase because of the slight decrease in the total net power. The net power gets minimized with the rise in solids concentration because the amount of steam produced in the HRSG gets down as the coal consumption decreases. 4.5. Simultaneous analysis of the effects of Level of N2 injection and Syngas Combustion Temperature The thermal efficiency increases almost linearly with the increase in the combustor temperature for all levels of N2 injection to the combustor (Figure 2). Therefore, the power augmenting effect of the N2 flow is greater than its diluting effect in the combustor.
Figure 2. Effects of simultaneous variations of the level of N2 injection and combustion temperature on the thermal efficiency.
N2 injection level of 98% represents the practical upper bound on the total amount of N2 available for injection, as venting is inevitable and N2 can be used as a coolant in the gas turbine [4]. This value supposes that the combustor operates at the highest possible temperature (depending on the turbine inlet temperature specification), thus producing power with relatively high thermal efficiency.
5. Heat Integration With the aim to improve thermal efficiency and environmental performance, the effects of heat integration of the gasifier and GT combustor is analyzed. This study is complemented by the integration of the air separation unit (ASU) and the gas cleaning unit. 5.1. Heat integration of the Gasifier and the GT-Combustor In this analysis, the gasifier is heat integrated with the GT-combustor and the level of integration is optimized by varying the oxygen and air requirements of the gasifier and combustor, respectively. As the gasification reaction is endothermic, its net heat duty is kept zero so that no external heat is added to the system (except from the combustor).
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Integrated Gasification Combined Cycle (IGCC) Process Simulation and Optimization
Figure 3. Dependence of a) Thermal efficiency; b) Cold gas efficiency and carbon conversion efficiency; on heat integration of GT-combustor and gasifier. Table 1. Stream data for the heat integration
Optimized Texaco gasifier o
o
Heat integrated case o
Tin( C)
Tout( C)
Duty(MW)
Tin( C)
Tout(oC)
Duty(MW)
Cond. regen.
347
332
-12
347
332
-12
Oxygen
150
150
0
150
340
5.8
Figure 4. The sensitivity of the combustor and gasifier level of integration for the case of ASU and gas cleaning units heat integration. With the increase in the level of heat integration, the net power output increases, but the net power per ton of coal consumed increases until it reaches a flat maximum (Figure 3a). The decrease in the O2:C ratio with the increase in the level of integration has a positive effect on the thermal efficiency at first, because it favors the gasification reaction (compared with the combustion reaction) and increases the cold gas efficiency. Then, with further decrease in the O2:C ratio, the carbon conversion efficiency and, in turn the cold gas efficiency, start to decrease (Figure 3b), thereby decreasing the thermal efficiency. The air requirement in the combustor also decreases as the net heat duty of the combustor increases. The last effect is to minimize the heat absorbed by the excess air, to maintain the operating temperature. 5.2. Heat integration of the air separation unit (ASU) and the gas cleaning unit The oxygen from the ASU to the gasifier is heat integrated with the condenser of the amine regenerator (condenser regenerator) in the gas cleaning unit. This is proposed due to the availability of high quality heat from the amine regenerator unit (Table 1).
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The integration is done together with the analysis of the sensitivity of the process for the level of combustor and gasifier integration which is already done in section 5.1. As shown by Figure 4, the trend is similar with the previous analysis, and the maximum is shifted to the left and the efficiency improved. The maximum efficiency is reached at a combustor duty of 150MW (unlike 200MW in the previous case) due to the further decrease in the O2:C ratio as the O2 inlet temperature to the gasifier increases.
6. Conclusions Sensitivity of the process for different operating variables has been studied by taking the best case (i. e. with high efficiency) as a base for the next analyses. At the end of these analyses, the maximum thermal efficiency (LHV) attained is 45% with CO2 and SOx emissions of 698 kg/MWh and 0.15 kg/MWh, respectively. This result corresponds to a gasification temperature of 1250 ºC, a combustion temperature of 1550 ºC, 98% of N2 injection to the GT combustor, and a slurry solid concentration of 80%. For a practical application of this improvement, among other considerations like the capacity of the equipments and their cost, the flowability of the slurry at the high level of solids has to be considered. Heat integration of the gasifier and the combustor has revealed that the best value of net heat duty for the integration is around 200 MW; but, the analysis for the heat integrated case of the ASU and the gas cleaning units reveals that the best value of net combustor duty for the integration is 150 MW. Figure 3 shows that the slope of variation in thermal efficiency is very high in the right side of the maximum and therefore a slight variation in operating conditions could lead to a significant loss of efficiency. Therefore, it is advisable to operate at a slightly lower value of the net duty those problems during operation.
Acknowledgement F. Emun wishes to express his gratitude for the financial support received from the Agencia de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) from Generalitat de Catalunya.
References 1. L. Zheng, E. Furinsky, 2005, Comparison of Shell, Texaco, BGL and KRW gasifiers as part of IGCC plant computer simulations, Energy conversion and management, 46, 2005, 1767-1779. 2. G. Ordorica-Garcia, P. Douglas, E. Croiset, L. Zheng, 2005, Technoeconomic evaluation of IGCC power plants for CO2 avoidance, Energy conversion and management, 47, 2006, 2250-2259. 3. W. Shelton , J. Lyons, 1998, Texaco gasifier base cases PED-IGCC-98-001, US Department of Energy, Process Engineering Division, 2000, 1-52. 4. H. Christopher, Y. Zhu, 2006, Improved system integration for integrated gasification combined cycle (IGCC) systems, Environ. Sci. Technol., 40, 2006, 1693-1699. 5. S. Sugiyama, N. Suzuki, Y. Kato, K. Yoshikawa, A. Omina, T. Ishii, K. Yoshikawa, T. Kiga, 2005, Gasification performance of coals using high temperature air, Energy, 30, 2005, 399-413. 6. J. Minchener, 2004, Coal gasification for advanced power generation, Fuel, 84, 2005, 2222-2235. 7. G. Booras, N. Holt, 2004, Pulverised coal and IGCC plant cost and performance estimates, Gasification technologies conference, Washington DC, October 2004.
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IDEF0 Activity Modeling for Integrated Process Design Considering Environmental, Health and Safety (EHS) Aspects Masahiko Hiraoa,*, Hirokazu Sugiyamab, Ulrich Fischerb, Konrad Hungerbühlerb a
Department of Chemical System Engineering,The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan b Institute for Chemical and Bioengineering, ETH Zurich, Wolfgang-Pauli-Strasse 10, Zurich 8093, Switzerland *
[email protected] Abstract We present an activity model of novel chemical process design. This model defines different stages of early process design, i.e. process chemistry and conceptual design, with appropriate process evaluation indicators. Environmental, health and safety (EHS) aspects are considered new assessment criteria together with conventional economic and technical indicators. The type-zero method of Integrated DEFinition language or IDEF0 is selected as a method for activity modeling. The activity model is described from the viewpoint a design-project manager who leads a group of process chemists and engineers. Application of IDEF0 enables systematic and transparent description of complex design activities, where the manager has to consider different types of design constraints and resources at different design stages. Keywords: IDEF0, activity modeling, integrated process design, multiobjective design
1. Introduction Companies need a new business process model when implementing a new strategy. Various methods are brought into focus, e.g. traditional block-flow diagram or Gantt chart for analyzing work flow or scheduling, or UML (Unified Modeling Language) for systems development. In chemical engineering, several authors have presented applications and merits of such business-process modeling techniques, e.g. Schneider and Marquardt (2002). Among other methods, the type-zero method of Integrated DEFinition language or IDEF0 (Ross, 1977; NIST, 1993) is a standardized method of enterprise-resource planning or business-process re-engineering. In process systems engineering, different authors applied this activity modeling technique to the integration of new software tools to existing process- or operation-design (Fuchino et al., 2004; Gabber et al., 2004; Kikuchi and Hirao, 2007). Within ISO’s standards development, there is a project called Process Industries Executive for Achieving Business Advantage Using Standards for Data Exchange (PIEBASE, 2007) where IDEF0 is used to standardize work processes and information requirements within process industries. In regard to new philosophies that will be incorporated in the chemical industry, the concept of sustainable process design is receiving increasing attention. Environment, health and safety (EHS) was the center of the interest of many authors who developed evaluation methods for processes, e.g., Hilaly and Sikdar (1995), Kheawhom and Hirao (2004), Sugiyama et al. (2006, 2007). So far, various indicators or methods have been proposed (see Adu et al., 2007 for review), and they are getting more sophisticated with
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the incorporation of broader issues. However, many papers left it unclear, how a user can apply it in industrial process development. We present an IDEF0 activity model based on our multiobjective process design framework (Sugiyama, 2007; Sugiyama et al. 2008). The viewpoint of the activity model is the user of this design framework, i.e., a design-project manager who leads a group of process chemists and engineers. Application of IDEF0 enables us to make systematic and transparent description of complex design activities, where the manager has to consider different types of design constraints and resources at different design stages. We also present important know-how of the design manager in executing the activity model for increasing its industrial applicability.
2. Integrated Process Design Framework Figure 1 shows an overview of the framework. It covers the early phase of a grass root design and defines four design stages, i.e. Process Chemistry I/II, Conceptual Design I/II. These stages are separated according to the available information for process modeling and to the character of process assessment. As design objectives the following three aspects are considered: economy, environmental impacts through product’s lifecycle, and hazard in terms of EHS. Life Cycle Assessment (LCA) and ETH-EHS (Koller et al., 2000) methods are selected for non-monetary evaluation. As an impact category of LCA, the Cumulative Energy Demand (CED; Verein Deutscher Ingenieure, 1997), which is an energy equivalency of different primary sources used for the production, is selected. At Process Chemistry I/II, proxy indicators are defined to estimate consequential process energy consumption, as a complement to raw material cost/LCA. These quantitative indicators are applied with expanding evaluation scopes, e.g., from substance level to process levels for EHS hazard. In contrast to the above objective functions, technical constraints are considered qualitatively throughout all four stages. A stage-gate approach is taken in our framework: at each stage, reaction and/or process alternatives are modeled and evaluated, and promising one(s) survive(s) to the next design stage. It is assumed that product quality, production scale and location are fixed prior to the first stage. In Process Chemistry I, reaction routes to synthesize the product are searched, and they are screened on the basis of ideal performance i.e. 100% yield. Here, technical difficulties can be a basis for decisions rather than multiobjective evaluation results. More reaction information such as side reactions, catalysts and solvents are included in Process Chemistry II, and promising routes are selected. In Conceptual Design I, the analysis scope is broadened to the whole process including separation part. Process structure is determined by simulation with simple physical property data, e.g. temperature averaged volatility factors. Such short-cut models are replaced by rigorous ones in Conceptual Design II including non-ideality, e.g. azeotropes. Precise mass and energy balances, equipment sizes become available here. With this rigorous model, detailed analysis such as parameter optimization is performed.
3. Activity Modeling of the Design Framework 3.1. Top-activity A0 Figure 2 shows the top-activity A0: Design a chemical process at early phase levels with syntax of IDEF0. In IDEF0, a box represents a function or an activity, which has a verb as a name. The input arrows entering the activity box from the left side represent the objects that are transformed by the function into the output arrows on the right side. The control arrows associated with the top side indicate the conditions required to
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produce the correct output. The mechanism arrows on the bottom indicate the means of performing the function. Although inputs and controls generally consist of similar objects, e.g., data, products, information, they are distinguished in terms of whether or not the objects are transformed by the function. Every activity can be decomposed into a sub-level activity model that has the same boundary as the parent activity. Sub-activities can be defined hierarchically with information and tools consistent with the parent activity. The box at the highest level called “top-activity A0” represents the aggregation of all sub-activities. Process Chemistry I (PC I)
Design objectives
O
Methyl methacrylate (product)
Stoichiometry
educts, solvent, catalyst
product coupled/ byproducts
conversion/selectivity; temp/pressure
Conceptual Design II (CD II)
dist
Design Constraints
O
ps
abs
te 3s
reac
Design stages
4 steps
Modeled aspects
Process Chemistry II Conceptual Design I (PC II) (CD I)
Shortcut models
Rigorous models
Decision structure
No decision forced
Select some reaction route(s)
Select process Optimize parameters option(s) &/or route(s)
Economy
Raw material cost + MLI1 as proxy
Raw material cost + ELI3 as proxy
Production cost
Net present value
Life-cycle environmental impacts
Raw material LCA + MLI as proxy
Raw material LCA + ELI as proxy
Cradle-to-gate LCA
(updated)
EHS hazard
ETH-EHS method2 (substance level)
ETH-EHS method (process level)
(updated)
(updated)
Technical aspects
e.g. market situation; raw material access; e.g. catalyst activity patent situation; blacklist substances
e.g. existing know-how; legislation
e.g. equipment specification
Figure 1. Overview of framework: definition of design stages and appropriate modeling approaches as well as evaluation indicators attached to each stage. 1: Mass Loss Indices (MLI) by Heinzle et al. (1998); 2: ETH-EHS method by Koller et al. (2000): 3: Energy Loss Index (ELI) by Sugiyama (2007). Prior decisions on the process (scale, quality, location)
Control
Market situation Raw material availability Patent situation Legislation/Social aspects Company culture/Existing know-how Time and budget
Output Ideas for the design project
Design a chemical process at early-phase levels
Optimized process flowsheet
A0
Input
Accumulated knowledge/ feedback from the project
Selection methods/tools/databases
Mechanism
Evaluation methods/tools/databases Modeling methods/tools/databases Experimental methods/tools/databases Process chemists/engineers Resource allocation know-how Management skills/facilities
Figure 2. Top-activity A0: Design a chemical process at early-phase levels with syntax of IDEF0.
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The viewpoint of this model, i.e. subject of activity boxes, is the manager of a process design project. This manager has the power to make decisions within the framework, i.e., decisions on reaction chemistry and process technology. The overall input is “Ideas for the design project” that triggers the whole project. There are seven project-external constraints. “Prior decisions on the process” is the necessary constraint of the design regarding production scale, product quality and process location. “Market situation”, “Raw material availability”, “Patent situation”, and “Legislation/Social aspects” are enterprise-exogenic constraints, whereas “Company culture/Existing process” and “Time and budget” are enterprise-endogenic ones. On the side of the mechanism, the “Management skills/facilities” and “Resource allocation know-how” are defined as general management resources. The remaining mechanism arrows are “Process chemists/engineers” and “Methods/tools/databases” for experiments, modeling, evaluation and selection. These resources are available but unallocated in the beginning of the project, i.e. the manager needs to apply them appropriately during a project. Based on these incoming information and resources, the overall outputs “Optimized process flowsheet” and “Accumulated knowledge/feedback from the project” are produced. The former output is a direct input for the successive process development phases, e.g., piloting and detailed engineering. The latter can also be used in the following design phase, e.g., as safety warning on a particular part of the process, or can trigger other design projects, e.g., as motivation in improving reaction performance. 3.2. Main-level activities Figure 3 shows the main-level activities or the decomposition of top-activity A0. Activities A1 and A6 are defined as managerial activities, where the design manager receives and allocates design constraints (A1) and resources (A6) appropriately to different design stages. Activities A2 to A5 correspond to four stages in Figure 1. The design-project manager makes individual steps performed by process chemists or engineers that he/she provides in Activity A6. In this activity, these project members are trained to get familiar with methods, data and tools for experiments, modeling and evaluation. Chemists and engineers, when allotted to each design stage, know-how to perform LCA and EHS hazard evaluation. This is new to conventional practice, and this activity A6 determines the quality of EHS-based design. Multiobjective decisions on process alternatives are made step by step in Activities A2 to A5, and “Optimized process flowsheet” is finally produced in Activity A5. Different non-ideal cases of project execution are represented in the iteration loops, e.g., a case when more experimental resources are requested from a design stage. Another particular non-ideal case in process design is the gap between opinions of process chemists and process engineers. For instance, specifications on reaction chemistry considered only by reaction chemists can serve as a severe constraint on designing separation processes. To avoid such a situation, the model shown in Figure 3 defines a direct iteration loop of “Feedback from process engineers” between Activities A3 and A4, as a desired exchange of information between chemists and engineers. 3.3. Impact of Design Constraints on Decision-making Characterized by Methyl Methacrylate (MMA) Process Development Table 1 shows impact of different design constraints on decisions at four design stages. The basis of this analysis is the Japanese MMA process development during the 1970s/80s where several alternative production processes were launched against the dominating acetone cyanohydrin (ACH) process. Project-external constraints listed in the table are more relevant at earlier design stages. At Conceptual Design, decisions on the process at previous stages, i.e. project-internal constraints, becomes also important.
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Prior decisions on the process (scale, quality, location) Market situation Raw material availability Patent situation Legislation/Social aspects Company culture/Existing know-how Time and budget Feedback from main-level activities Ideas for the design project
Manage mainlevel activities A1
Accumulated knowledge/feedback from the project Constraints to main-level activities: instructions, conditions or time-limit Initial condition
Make Process Chemistry I performed
Feedback from process engineers (desired) Selected routes
A2 Make Process Chemistry II performed
Status of the design project, needs for additional resources
Further selected routes
A3 Make Conceptual Design I performed
Selected route(s)/ process(es)
A4 Make Conceptual Design II performed
Optimized process flowsheet
A5 Provide resources A6 Allocated resources to a specific design stage (allocated methods/tools/data/manpower)
Management skills/facilities
Selection methods/tools/databases Evaluation methods/tools/databases Modeling methods/tools/databases Experimental methods/tools/databases Process chemists/engineers Resource allocation know-how
Figure 3: Decomposition of A0 shown in Figure 2. Table 1. Characterization of project-external design constraints on the basis of Japanese MMA process development in the 1970s/80s. Constraints
Effects on decision-making at Process Chemistry (PC) or Conceptual Design (CD) stages in MMA process development
Market situation
Strong growth in MMA market (PC: need to develop a reaction system starting from well-available raw material)
Raw material availability
Limited availability of HCN as a byproduct of acrylonitrile processes (PC: hindrance to further develop ACH process starting from HCN)
Patent situation
Competition with domestic MMA producers (PC/CD: restricted choice for reaction/process technologies)
Legislation/S ocial aspects
Legislation forbidding MTBE (C4) as a fuel additive (PC: motivation to use inexpensive and abundant C4 remaining as a starting material for MMA) Pressure against landfilling NH4HSO4 (PC: motivation to develop H2SO4-free reaction system)
Company culture/Existi ng knowhow
Strong motivation in developing catalyst technology (PC: potential to purify isobutene as raw material; CD: potential to simplify a separation process in sequential oxidation steps) Possession of acrylic acid process (CD: know-how of operating similar process)
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Character
Process Chemistry I/II
Conceptual Design I/II
Decision-making
Highly influential
Fine tuning and optimization
Constraint
Mainly project-external
Both project-external and -internal
Mechanism
General/Wide scoped
Specific/narrow focused
3.4. Summary of Important Know-how for Design-Project Manager Table 2 summarizes the changing character of decision-making, and mechanisms over design stages. Based on this general summary the following findings are drawn. For making influential decisions at Process Chemistry stages, the design-project manager should consider a broad range of project-external constraints and provide wide-scoped resources. For fine-tuning-type decisions at Conceptual Design stages, the manager should look for various constraints inside and outside the project, and allocate elaborate mechanisms for specific purposes. This is also the case for EHS assessment of a process. With regard to safety, various categories need to be considered e.g. gas release, fire/explosion, at earlier stages, while at later stages it may be rational to concentrate on a relevant category in a detailed manner, e.g. technical prevention of explosion.
4. Conclusions We presented an activity model of chemical process design integrating EHS evaluation as a new element with conventional economic and technical considerations. Important know-how is drawn to execute the activity model. IDEF0 modeling can play as a key approach for implementing the concept of integrated process design in practice.
Acknowledgements Authors would like to acknowledge Nagai Foundation Tokyo for financial supports.
References Adu, I., Sugiyama, H., Fischer, U., Hungerbühler, K., 2007. Trans IChemE Part B. in press. Fuchino, T., Wada, T., Hirao, M., 2004. Proceedings of KES 2004, 418-424. Gabber, H. A, Aoyama, A., Naka, Y., 2004. Comput. Ind. Eng. 46, 413-430. Heinzle, E., Weirich, D., Brogli, F., Hoffmann, V.H., Koller, G., Verduyn, M.A., Hungerbühler, K., 1998. Ind. Eng. Chem. Res. 37, 3395-3407. Hilaly, A.K., Sikdar, S.K., 1995. Ind. Eng. Chem. Res. 34, 2051-2059. Koller, G., Fischer, U., Hungerbühler, K., 2000. Ind. Eng. Chem. Res. 39, 960-972. Kheawhom, S., Hirao, M., 2004. Comput. Chem. Eng. 28, 1715-1723. Kikuchi, Y., Hirao, M., 2007. Proc. ESCAPE 17, 1223-1228. Nagai, K., 2001. Applied Catalysis. 221, 367- 377. National Institute of Standards and Technology (NIST), 1993. Federal Information Processing Standards Publication 183, Department of Commerce, Gaithersburg, MD, U.S. PIEBASE, 2007., Online at http://www.posc.org. Ross, D. T. 1977. IEEE. T. Software Eng. 3, 16-35. Schneider, R., Marquardt, W., 2002. Chem. Eng. Sci. 57, 1763-1792. Sugiyama, H., Hirao, M., Mendivil, R., Fischer, U., Hungerbühler, K., 2006. Trans IchemE Part B. 84, 63-74. Sugiyama, H., Fischer, U., Hirao, M., Hungerbühler, K., 2007. Proc. ESCAPE 17, 1157-1162. Sugiyama, H., 2007. PhD Thesis No. 17186, ETH Zurich. Sugiyama, H., Fischer, U., Hirao, M., Hungerbühler, K., 2008. AIChE J. in press. Verein Deutscher Ingenieure, 1997. VDI-Richtlinie 4600, Düsseldorf.
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A Prototype Agent-Based Modeling Approach for Energy System Analysis Bri-Mathias Hodge,a Selen Aydogan-Cremaschi,b Gary Blau,b Joseph Pekny,a,b Gintaras Reklaitisa a
School of Chemical Engineering, Purdue University, 480 Stadium Mall Drive, West Lafayette, IN 47907, USA b e-Enterprise Center, Discovery Park, Purdue University, 203 S. Martin Jischke Drive, West Lafayette, IN 47907, USA
Abstract The current world energy system is highly complex and is rapidly evolving to incorporate emerging energy technologies. An understanding of how these technologies will be incorporated into the existing system is needed in order to make intermediate and long term research and infrastructure decisions. We propose an agent-based modeling and simulation approach for energy system analysis that can be used to investigate the mechanisms by which changes occur within the system. The approach has been applied to the Indiana state energy system. Keywords: Multi-Agent Systems, Energy Systems Analysis, Learning Curves
1. Introduction Dwindling hydrocarbon reserves, energy supply security and environmental concerns have driven the development of a number of energy technologies which are on the cusp of ubiquitous use. The marketplace will determine the details of how these technologies are adopted, but a deeper understanding of options and implications will allow the marketplace to be more efficient. As such long-term research and infrastructure planning on energy systems are best made with an understanding of the current state of the system, the evolving performance of emerging technologies and the process by which these technologies can be incorporated into the existing energy system. This challenge shares similarities with process synthesis and retrofitting problems in the chemical industry, but at a much larger scale. Despite the difference in scale both are concerned with technology selection, system integration, and scheduling/timing the adoption of innovations. Many energy systems models have already been developed in order to analyze energy systems, including models by international and national institutions such as the International Energy Agency (IEA, 2007) and the United States Energy Information Administration (EIA, 2007). Macroeconomic equilibrium, or top-down, models have been used to study the effects of greenhouse gas reduction policies (Zhang & Baranzini, 2004), the role of energy in a national economic system (Papatheodorou, 1990), as well as specific technologies in a national economy (Galinis & van Leeuwen, 2000). A limitation of these top-down models is that they do not explicitly represent the technical potential of energy technologies, but only the markets in which the energy technologies operate, which can lead to difficulties in representing the effects of emerging technologies. Bottom-up models are better at showcasing the effects of new
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technologies but do not consider the market adoption of those technologies. The MARKAL model (Loulou et al., 2004), which minimizes global cost through investment and operating decisions has been widely used for such diverse purposes as: comparing coal and natural gas electricity generation (Naughten, 2003), district heating with combined heat and power (Ryden et al., 1993) and greenhouse gas abatement (Gielen & Changhong, 2001). A more extensive review of energy system modeling efforts can be found in (Wei et al., 2006), which displays the breadth of models developed and illustrates many instances of their use for energy system analysis on the regional, national and international scale. Agent-based modeling is a growing area with successful applications in many fields including: manufacturing (Monostori et al., 2006), consumer markets (Guerci et al., 2005), and supply chains (Julka et al., 2002). Agents are a type of distributed artificial intelligence algorithm engineering technique. Unlike most other types of distributed algorithms, agents can be developed in a relatively independent fashion and then loosely interact to arrive at solutions; instead of serving as slaves to a master program. The defining characteristics of an agent are: autonomy, modeling of social features, reactivity, and pro-activeness (Wooldridge & Jennings, 1995). Multi-agent systems are particularly adept at showcasing the interactions between individual entities in complex systems and the aggregate system behaviors that result from these interactions (Bonabeau, 2002). Because they can provide a mechanistic view of complex system interactions multi-agent systems are suitable for analyzing energy systems, and have already been applied to electricity market analysis (Koritarov, 2004). In this paper a framework for an agent-based simulation of energy systems will be presented. The agent architecture enables an accurate portrayal of energy systems and is ideal for displaying the mechanisms by which changes occur within existing energy systems. A refined and extensively validated simulation based on the proposed framework would serve as a useful tool for evaluating the effects of government and corporate energy policies on technology growth and the integration of new technologies into the current energy system. A demonstrative model of the state of Indiana is presented below.
2. An Agent-Based Model for Energy Systems Analysis 2.1. Model Framework In order to accurately simulate energy systems, so that energy policies can be tested and insights into the system behavior can be gleaned, a framework for an agentbased model of energy systems has been developed. Each type of entity that plays a role within the energy system is represented as an agent. Since each agent is capable of making independent decisions, the system interactions emerge from the interaction of the agents. For this reason the structure through which the agents communicate is of critical importance. For this paper the communication is accomplished through the use of a network model where the network nodes are agents and the network edges are the lines of communication between agents. 2.2. Model Agents After defining the system through the choice of the energy technologies which will be included in the model, we have pooled the entities to be represented into six classes of agents. While the behaviors of agent types within the classes may differ slightly, each agent class represents a basic model function that is carried out by the particular agent type. The agent classes have been broadly defined in order to enable the addition of new energy technologies within the framework specified.
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2.2.1. Raw Material Agents The modeling of the extraction or growth of basic energy system materials, such as fossil fuels or biomass, is handled by the raw material class of agents. These agents have limited reserves of a material corresponding to their geographic placement and have the responsibility of bringing these materials into the energy system through their sale. The materials may be further processed into consumer energy products or consumed directly themselves. Energy crops, such as soybeans or corn, are regulated and produced by agents of the raw material agent class. 2.2.2. Producer Agents Producer agents model the conversion of raw materials into end-use energy products. Refineries which produce gasoline and diesel fuel from crude oil, biofuel plants which convert agricultural products into fuel products and electric power plants are all types of producer agents. The producer agent interacts with both raw material agents, to acquire feedstocks, as well as consumer agents to sell the resulting products. 2.2.3. Consumer Agents The demand levels of the energy system are driven by the individual agents of the consumer agent class. Energy product demand is split into four distinct sectors: residential, industrial, commercial and transportation. After the area to be modeled is split into geographic regions of known population and energy use patterns, an agent is assigned to represent the consumer use in that region for one of the energy sectors defined. Consumer agents cooperate with producer and raw material agents in order to access the energy products through which they may fulfill their demand. 2.2.4. Research Agents Research agents are used to model the advancement of technologies within the energy system. Research conducted can lower the costs associated with the respective technologies or bring a new technology into a production ready state. Research agents receive their charge from government agents wishing to foster certain technologies, as well as producer and raw material agents looking to gain a competitive advantage. A further explanation of the implementation of technological innovation can be found in section 2.3.3. 2.2.5. Government Agents Government agents may influence the system by choosing to tax or subsidize particular technologies, or by providing direct support in the form of research funding. Government agents perform no regulatory functions in this model, all agents are assumed to be law abiding. 2.2.6. Environment Agents The goal of environment agents is to represent the effects of the world outside of the system boundaries on the system under study and vice versa. These effects are manifested through the competing supply and demand of materials used within the system. The environment agent is also responsible for maintaining the status of the technologies present in the system. 2.3. Model Implementation 2.3.1. Agent Behavior In order to ensure that the agents can interact symmetrically within the simulated environment, the agent logic has been divided into two distinct stages. The first stage is a decision making step. As an example, consider a producer agent. In the decision making stage the producer agent forecasts demand for the product, determines how much to produce and determines the amount of raw materials necessary for
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production. In addition, the agent makes decisions on whether to expand capacity or invest in research. Once every agent has made the necessary decisions, the interaction stage may begin. Agent decisions are made by consulting a set of rules established for each agent class. Let us consider a production agent. After examining the percent utilization of production capacity and the average price received for the product in the previous tick and knowing the amount of unsold product remaining in inventory, where applicable, a production agent will choose the quantity to produce and the price at which to initially offer it for sale. From this information the amount of raw material necessary for production and the maximum allowable price to purchase it at are calculated. Additionally, the historical percent utilization and inventory remaining are examined and a decision on whether to proceed with a capacity expansion is taken. 2.3.2. Agent Interactions The most important interaction between agents is the buying and selling of energy products. These market actions determine the price of the products and are the mechanism by which consumer demand is fulfilled. Negotiation is accomplished through a “take it or leave it” approach. An offer to buy or sell a set quantity of a product at a specified price is made to a random potential partner and either accepted or rejected. If rejected, the initiating agent may not make another offer to the rejecting agent during the same time frame, but may change the terms of the offer made to other potential partners. This process is repeated until the required goods are completely bought or sold, or until the list of potential trading partners is exhausted. 2.3.3. Learning Curves A two-factor learning curve (Kouvaritakis et al., 2000) is used to represent the state of each technology within the model. Using the learning curve the current cost of a technology can be computed by using the cumulative production capacity of the technology and the research spending on the technology as inputs. Each agent within the system keeps a personalized learning curve for all of the technologies with which it deals. In addition there is a global learning curve for each technology that updates the individual curves after a time delay. The learning curve equation used is shown in equation (1). TCit = į0 * (CCitlog2(1-Į)) * (Kitlog2(1-ȕ))
(1)
Here TCit is the installed cost per unit energy for entity i at time t, į0 is the base cost of the technology, CCit is the cumulative installed capacity for entity i at time t, Į is the production learning ratio, Kit is the knowledge stock of the technology for entity i at time t and ȕ is the research learning ratio. The knowledge stock variable is further defined in equation (2). Kit = (1-Ȝ) * Kit-1 + Rit-ij
(2)
The knowledge depreciation rate is Ȝ, Rit is the amount of research spending from entity i at time t and ij is the time until impact for research spending.
3. Illustrative Example – Indiana Energy System Model The energy system of the state of Indiana was chosen as a test case for the modeling approach, because it contains sufficient complexity to assess the framework proposed while providing clear system boundaries. The state was divided into six geographic regions based on the regions defined by the Indiana Economic Development Corporation. Each region possesses an agent for
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each of the four consumer sectors and a raw material agent which represents the agricultural sector. In addition there are 38 producers throughout the state including: two oil refineries, two biodiesel plants, four ethanol production plants, seventeen coal electricity plants, nine natural gas electricity plants, two oil electricity plants and three hydroelectricity plants. Where possible the history of the producer entity was taken into account. For example, the Norway and Oakdale hydroelectric dams are rated at 7.2 MW and 9.2 MW of generating capacity, however the historical maximum outputs of 4 MW and 6 MW are the values used in the model. There are also raw material agents that represent the oil, coal and natural gas extraction that occurs predominantly in the southwestern corner of the state. Ten energy products or product precursors are considered within the model: crude oil, coal, natural gas, gasoline, diesel fuel, biodiesel, ethanol, electricity, corn and soybeans. Sixteen energy technologies which produce, extract or convert the above energy products and are at varying stages of maturity are also accounted for: crude oil extraction, crude refining to gasoline, crude refining to diesel, coal mining, electricity production from coal, natural gas extraction, electricity from natural gas, corn agriculture, corn ethanol production, solar photovoltaics, wind electricity, nuclear electricity, biodiesel from soy production, soybean agriculture, electricity from crude oil and hydroelectricity. Since consumer demand drives many of the decisions made within the energy system, we examine the consumer agents’ demand projection capabilities. Since the starting point for our model is the year 2006, the best data with which to compare our projections is that of the State Utilities Forecasting Group (Rardin et al., 2005, Figure 2). A base case model in which all taxes and subsidies would remain at current levels for a ten year period was examined. This base case preliminary electricity demand profile (Figure 1) is used in order to validate the model results and verify that the consumer agents are functioning properly.
Figure 1: Model Projected Electricity Demand
Figure 2: Indiana SUFG projections
As can be seen from Figures 1 and 2, the aggregation of the twenty four different consumer agents within the Indiana energy system yields electricity consumption patterns which track well over this short time frame with the projections of
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the state utilities forecasting group. The model projections tend slightly lower than the base case scenario, but still well within the lower bound case.
4. Conclusion A framework for an agent-based model of energy systems has been developed. The approach uses autonomous agents to represent the entities within the energy system and allows the agents to interact with other agents and the environment. A model of the state of Indiana energy system has been developed in order to demonstrate the advantages of such an approach, which include the illustration of the effects of interactions between entities within the system. Partial validation of the model has been shown. Further work will include the complete validation of the Indiana model and the testing of Indiana government energy system policies through scenario analysis.
References E. Bonabeau, 2002, “Agent-based modeling: Methods and techniques for simulating human systems”, PNAS, Vol. 99, suppl. 3, pp. 7280-7287 Energy Information Administration, 2007, Annual Energy Outlook 2007, DOE/EIA – 0383 A. Galinis, M.J. van Leeuwen, 2000, “A CGE model for Lithuania: the future of nuclear energy”, Journal of Policy Modeling, Vol. 22, pp. 691-718 D.Gielen, C. Changhong, 2001, “The CO2 emission reduction benefits of Chinese energy policies and environmental policies; a case study for Shanghai, period 1995-2020”, Ecological Economics, Vol. 39, pp. 257-270 E. Guerci, S. Ivaldi, S. Pastore, S Cincotti, 2005, “Modeling and implementation of an artificial electricity market using agent-based technology”, Physica A: Statistical Mechanics and its Applications, Vol. 355, Iss. 1, pp 69-76 International Energy Agency, 2007, World Energy Outlook 2007 – China and India Insights N. Julka, R. Srinivasan, I. Karimi, 2002, “Agent-based supply chain management-1: framework,” Computers & Chemical Engineering, Vol. 26, Iss. 12, pp 1755-1769 V. Koritarov, 2004,“Real-World Market Representation with Agents: Modeling the Electricity Market as a Complex Adaptive System with an Agent-Based Approach”, IEEE Power and Energy Magazine, July/August, pp. 39-46 N. Kouvaritakis, A. Soria, S. Isoard, 2000, “Modelling energy technology dynamics: methodology for adaptive expectations models with learning by doing and learning by searching”, International Journal of Global Energy Issues, Vol. 14, Iss. 1-4, pp. 104-115 R. Loulou, G. Goldstein, K.Noble, 2004, “Documentation for the MARKAL Family of Models”, Energy Systems Technology Analysis Programme L. Monostori, J. Vancza, S.R.T Kumara, 2006, "Agent-Based Systems for Manufacturing", CIRP Annals - Manufacturing Technology, Vol. 55, Iss. 2, pp. 697-720 B. Naughten, 2003, “Economic assessment of combined cycle gas turbines in Australia. Some effects of microeconomic reform and technological change”, Energy Policy, Vol. 31, pp. 225245 Y.E. Papatheodorou, 1990, “energy in the Greek economy: a total energy approach at the macro level”, Energy Economics, Vol. 12, pp. 377-395 R. Rardin, D. Gotham, F. Holland, Z. Yu, D. Nderitu, A. Thomas, 2005, “Indiana Electricity Projections: The 2005 Forecast”, Indiana State Utilities Forecasting Group B. Ryden, J. Johnsson, C-O. Wene, 1993, "CHP production in integrated energy systems examples from five Swedish communities", Energy Policy, Vol. 21, pp.176-190 Y-M. Wei, G. Wu, Y. Fan, L-C. Liu, 2006, “Progress in energy complex system modelling and analysis”, International Journal of Global Energy Issues, Vol. 25, Iss. 1/2, pp. 109-128 M. Wooldridge, N. Jennings, 1995, "Intelligent agents: theory and practice", Knowledge Engineering Review,Vol. 10, Iss. 2, 115-116 Z.X. Zhang, A. Baranzini, 2004, “What do we know about carbon taxes? An inquiry into their impacts on competitiveness and distribution of income”, Energy Policy, Vol. 32, pp. 507-518
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A Systematic Framework for Biorefinery Production Optimization Norman E. Sammons, Jr.,a Wei Yuan,a Mario R. Eden,a Burak Aksoy,b Harry T. Cullinanb a
Department of Chemical Engineering, Auburn University,AL 36849, USA Alabama Center for Bioresource Engineering, Auburn, AL 36849, USA
b
Abstract The integrated biorefinery has the opportunity to provide an independent and sustainable alternative for the production of bulk and fine chemicals. Because of the shift towards producing sustainable energy with minimal environmental impact, there is a need for a methodology capable of evaluating the integrated processes in order to identify the optimal set of products and production pathways. The complexity of the product allocation problem for such processing facilities demands a process systems engineering approach utilizing process integration and mathematical optimization techniques to ensure a targeted approach and serve as an interface between simulation work and experimental efforts. The objective of this work is to assist the bioprocessing industries in evaluating the profitability of different possible production routes and product portfolios while maximizing stakeholder value through global optimization of the supply chain. To meet these ends, a mathematical optimization based framework has been developed, which enables the inclusion of profitability measures and other technoeconomic metrics along with process insights obtained from experimental as well as modeling and simulation studies. A case study has been included which highlights the robustness of the framework and its utility in decision making. Keywords: Biorefining, sustainability, optimization, process modeling
1. Introduction The process of separating biomass constituents and converting them to high value products is known as biorefining, and the integrated biorefinery provides a unique opportunity for reinvigorating an entire manufacturing sector by creating new product streams from a renewable resource [1]. Economic and environmental sustainability are achieved through the optimal use of renewable feedstocks, and a need exists for a process systems engineering (PSE) approach to ensure maximum economic and societal benefit through minimizing the usage of raw material and energy resources as well as the cost involved in supply chain operations intrinsic to biorefining. The bioprocessing industries are slowly becoming aware of the benefits of infusing PSE methods to this emerging field. To maximize the applicability of such systematic methods and to integrate experimental and modeling work, a unique partnership has been established consisting of researchers in academia and industry along with government entities, equipment vendors and industry stakeholders to procure the wide range of information necessary such as data needed for process simulation models, information on capacity constraints, financial data, and nonlinear optimization techniques. This information is obtained from a variety of collaborations involving industrial partners, internal academic partners in both chemical engineering and business, and external academic
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sources. This ensures that the data used in the decision making process is realistic and that the research addresses problems of industrial and regulatory interest. The overall goal of this work is to develop a system that will enable decision makers to evaluate different production pathways in biorefining in order to maximize value while measuring and minimizing environmental impact.
2. Methodology for Integrating Modeling and Experiments In biorefining, the large number of possible process configurations and products results in a highly complex problem that cannot be solved using simple heuristics or rules of thumb. Business decision as well as policy makers must be able to strategically plan for and react to changes in market prices and environmental regulations by identifying the optimal product distribution and process configuration. Thus, it is necessary to develop a framework which includes environmental metrics, profitability measures, and other techno-economic metrics. Such a framework should enable policy and business decision makers to answer a number of important questions like: x For a given set of product prices, what should the process configuration be, i.e. what products should be produced in what amounts? x For a given product portfolio, how can process integration methods be utilized to optimize the production routes leading to the lowest environmental impact? x What are the discrete product prices that result in switching between different production schemes, i.e. what market developments or legislative strategies are required to make a certain product attractive? x What are the ramifications of changes in supply chain conditions on the optimal process configuration? In the following sections, the developed framework for answering these questions is presented along with a discussion of some preliminary results. The introduction of PSE methods into biorefining research provides a systematic framework capable of seamlessly interfacing results generated in simulation studies as well as experimental work. Such a framework is imperative when attempting to combine knowledge and information from a variety of research areas and disciplines. The objective of this approach is to create a library of rigorous simulation models for the processing routes along with a database of corresponding performance metrics. Wherever possible, experimental data is used to validate the performance of the simulation models, and for processes that commercial software packages are incapable of describing adequately, the performance metrics are initially based on experimental results until a satisfactory model has been developed. Figure 1 shows a schematic representation of the strategy employed for identification of characteristic performance metrics of the individual subprocesses. The simulation models for each process are developed by extracting knowledge on yield, conversion, and energy usage from empirical as well as experimental data. If a given process requires the use of a solvent, molecular design techniques like CAMD and property clustering techniques are employed to identify alternative solvents that minimize environmental and safety concerns [2, 3].
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Figure 1 – Strategy for identification of performance metrics.
Process integration techniques are then used to optimize the simulation models. This is an integral step in the model development as it ensures optimal utilization of biomass and energy resources. Finally, the optimized models are used to generate data for the economic as well as environmental performance metrics. The estimation of environmental performance is achieved through the use of the US-EPA Waste Reduction (WAR) algorithm [4]. It should be noted, that only the economic and environmental performance metrics are incorporated in the solution framework described below, thus decoupling the complex models from the decision making process. This approach allows for continuously updating the models as new data becomes available without having to change the selection methodology. Similarly, if new processes are to be included for evaluation, an additional set of metrics are simply added to the solution framework, thus making it robust and flexible.
3. Generalized Biorefinery Model A generalized biorefinery model has been used to develop the structure of the optimization framework and is given in Figure 2. The model structure was formulated to include a variety of basic complexities encountered in the decision making process, e.g. whether a certain product should be sold or processed further, or which processing route to pursue if multiple production pathways exist for a given product. The objective function maximizing the overall profit of the biorefinery is illustrated in Equation 1.
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Figure 2 – Generalized biorefinery model to illustrate possibilities in decision making tree.
Profit
§
¦ ¨ ¦ TS m
©
k
mk
· P C ks ¦ ¦ Rmij C mij C mBM ¦ Rm1 j ¸ i j j ¹
(1)
Using this nomenclature, the first set of terms in Eq. (1) represents the sales revenue from the products made from each bioresource m. TSmk is a variable that denotes the production rate of product k from bioresource m that is sold to the market. Cks is the sales price of product k which is a scalar and is determined through a survey of published prices and vendor quotes. The second set of terms represents the total processing cost incurred by the pathways pursued in production. Rmij is a variable that represents the processing rate of route ij while CmijP is a scalar that represents the cost of processing bioresource m through route ij and is determined through simulation models and process economics. The third set of terms represents the total cost of the biomass resource m, and this is broken down into the scalar purchase price of bioresource m in CmBM and the combined rate of biomass processed by the plant in Rm1j. Although both TSmk and Rmij are variables in the optimization program, they are not independent since the variables are related via mass balance constraints around the product points. The model may be utilized for short-term decision making with existing equipment and market arrangements, or long-term planning that will involve extensive capital expenditure, market forecasts on the future prospects of targeted products, and supply chain considerations. This generalized model, where the objective function and constraints are linear, is easily solved using commercially available software. It should be noted here that while earlier work such as the proposed solution by Sahinidis and Grossman incorporate process models into the optimization problem, the proposed framework separates the wide range of biorefining models from the optimization portion, thus reducing the complexity of the problem for the solver while maintaining the robustness achieved with proven optimization techniques [5]. Without including any constraints on capacity of the processing steps, the solution is a single-product configuration in which all available biomass is converted into the most profitable product. However, if constraints are imposed on the most profitable route, the framework identifies the additional products and processing routes required to maximize the overall profit, thus leading to a polygeneration facility [5]. Approximate capacity constraints are based on a variety of sources, e.g. existing equipment, vendor data and qualitative process information provided by academic and industrial collaborators. In order to effectively address the strategic planning objectives of business decision makers, it is necessary to incorporate the total capital investment as a
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constraint in the formulation. The capital investment for a given unit or process can be approximated as a function of its capacity or processing rate, and both linear and nonlinear expressions have been successfully implemented in the framework. Inclusion of capital cost constraints is crucial for practical application of the results, i.e. enabling evaluation of the potential benefits to be obtained for a given maximum investment by retrofitting an existing facility or constructing new plants.
4. Model Demonstration Many adjustments were made to the parameters such as sales price, processing cost, processing rate conversions, and capital investment functions, and constraints were added on capacity as well as minimum and maximum sales quantities. These modifications were made to determine if the code would give the product distributions that were intuitively determined to maximize profit. In every case, the code returned the solutions including predictable results on the product distribution as well as the pathways necessary to manufacture the product while maximizing value. A case study was performed on a potential biorefinery involving the conversion of chicken litter to syngas, hydrogen, and electricity. Actual data on conversion rates were obtained from experimental work performed by the university and affiliated agencies as well as simulations constructed in ASPEN. Figure 3a shows the possible pathways for production and sale of these chemicals on the commodity market. The execution of the optimization code verified the results obtained from manual calculation; producing syngas from chicken litter and selling it on the market would maximize profit due to the high costs involved in converting the syngas to hydrogen or electricity. Figure 3b illustrates the active pathway chosen by the optimization program. This simple case study will be expanded to include a much wider range of products, production pathways, and feedstocks in order to become a crucial decision support tool in the emerging field of biorefining.
Figure 3 – Illustration of case study. (a) Unsolved decision making tree with variable designations. (b) Solved decision making tree with flowrate values and objective function.
5. Conclusions and Future Work A general systematic framework for optimizing product portfolio and process configuration in integrated biorefineries has been presented. Decoupling the process models from the decision-making framework reduces problem complexity and increases
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robustness. The next phase of this work involves development of additional process models for the generation of performance metrics, specifically information on conversion, yield, and production cost for economic metrics and data to be used to generate a measure of environmental impact. From there, process integration will be utilized to optimize the process models by reducing energy usage, material consumption, and waste streams. An alternative formulation of the product allocation problem will be developed using a combination of general disjunctive programming (GDP) with the use of genetic algorithms (GA) as proposed by Odjo et al [7]. The current formulation of the problem is a mixed-integer nonlinear problem (MINLP), and the use of GA and GDP has been shown to solve nonconvex, discontinuous optimization problems more efficiently than the iterative MILP-NLP approach used in many solver programs. The computation time and objective values of optimal solutions between the GA-GDP solution method and the MINLP method will be compared to determine which formulation and solution style is more effective in solving this general problem [6]. The framework will also become a stronger financial tool through the incorporation of various economic ideas and analyses. The use of net present value as a profitability measure in a similar fashion to Sahinidis and Grossmann will enable the inclusion of the cost of capital, interest expenses, depreciation, and tax consequences of pursued decisions [5]. The development of qualitative predictive models for capital investment and inclusion of capital amortization into the objective function will also increase the strength of the framework. Incorporation of options theory into the framework will allow management to develop financial strategies in response to events in the market or legislative environment. Finally, optimization under uncertainty will be studied to quantify the effects on process configuration resulting from minute changes in product prices [7]. This, in combination with implementing superstructure generation techniques, will lead to increased robustness of the methodology and thus better recommendations [8].
References 1. Bridgwater, A.V. (2003). Renewable fuels and chemicals by thermal processing of biomass. Chemical Engineering Journal, 91, 87-102. 2. M. R. Eden, S. B. Jørgensen, R. Gani and M. M. El-Halwagi. (2004). A novel framework for simultaneous separation process and product design. Chemical Engineering and Processing, 43, 595-608. 3. P. M. Harper and R. Gani. (2000). A multi-step and multi-level approach for computer aided molecular design. Computers and Chemical Engineering, 24, 677-683. 4. D. M. Young and H. Cabezas. (1999). Designing sustainable processes with simulation: the waste reduction (WAR) algorithm. Computers and Chemical Engineering, 23, 1477-1491. 5. N. V. Sahinidis, I. E. Grossmann, R. E. Fornari and M. Chathrathi (1989). Optimization model for long range planning in the chemical industry. Computers and Chemical Engineering, 13, 1049-1063. 6. A. Odjo, N. Sammons, A. Marcilla, M. Eden and J. Caballero. (2007). A disjunctive-genetic programming approach to synthesis of process networks. Computers and Chemical Engineering (in preparation). 7. I. Banerjee and M. G. Ierapetritou. (2003). Parametric process synthesis for general nonlinear models. Computers and Chemical Engineering, 27, 1499-1512. 8. A. Chakraborty and A.A. Linninger. (2003). Plant-wide waste management 2: Decision making under uncertainty. Industrial and Engineering Chemical Research, 42, 357-369.
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Economic Analysis and Process Integration of Hydrogen Production Strategies Wei Yuana, Norman E. Sammons Jr.a, Kristin H. McGlocklina,b, Mario R. Edena a b
Department of Chemical Engineering, Auburn University, Auburn, AL 36849, USA 3M Corporation, Decatur, AL 35601, USA
Abstract Hydrogen is a promising energy carrier for future transportation uses. Its combustion produces no greenhouse gases, no ozone layer depleting chemicals, little or no acid rain ingredients and pollution (Barreto et al, 2002). In addition, hydrogen has the highest gravimetric energy density of any known element (U.S Department of Energy, 2004). Furthermore, since the proton exchange membrane fuel cell (PEMFC) is believed to be the best future vehicular power source for clean transportation and zero emission (Steele et al, 2001), the study of novel hydrogen production strategies is important. Experimental researchers in the Consortium for Fossil Fuel Science (CFFS) are developing novel technologies for hydrogen production and storage, however the economic and environmental viability of the technologies are mostly evaluated separately rather than in an integrated manner. In this work, we aim to address this gap through the development of integrated system engineering strategies for modeling, integration and optimization of hydrogen polygeneration plants. Keywords: Hydrogen production, process integration, economic analysis
1. Introduction A hydrogen polygeneration plant aims at increasing the economic and environmental sustainability potential of coal, biomass and petroleum based production facilities by combining novel conversion processes with conventional production capabilities to include a wider range of co-products, e.g. fuels, chemicals and/or renewable energy along with the primary hydrogen product. The complexity of the co-production problem as it applies to liquid fuels and hydrogen production is illustrated in Figure 1. The main focus of the polygeneration plant is to produce high purity hydrogen, while increasing the profitability of the overall plant by manufacturing other valuable coproducts. Although many of the fundamental processing steps involved in polygeneration are well-known, there is a need for a methodology capable of evaluating the integrated processes in order to ensure optimal hydrogen production and identify the optimal set of co-products along with the best route for producing them. The complexity of the co-product allocation problem for such processing facilities demands a process systems engineering approach utilizing process integration and mathematical optimization techniques to ensure a targeted bi-level approach and serve as an interface between theoretical modeling/simulation work and experimental efforts. Polygeneration plants inherently possess tremendous integration potential, not just limited to recycling unused material, but also in terms of energy recovery. Process integration techniques can be employed to realize this potential by providing global process insights and identifying overall process performance targets. It is imperative to
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apply a holistic approach in order to guarantee a truly optimal solution to the problem, since optimizing each unit individually might lead to suboptimal designs as one bottleneck is replaced by another. Bioproducts
Combustion
Power
Carbon Source Biomass, coal, natural gas, crude oil
Chemical and Biochemical Processing
Gasification
Liquefaction
Synthesis Gas
Chemicals
Fischer -Tropsch Synthesis
Methanol
Liquid Fuels
Reformate Cleanup WGS , PROX , CO2 Removal
Reforming SR , POX , CPOX , ATR, SCWR, Dry, Aqueous Phase
Hydrogen
Fuel Cell Stack
Figure 1. Hydrogen polygeneration complexity
2. Model Development and Solution Methodology A generic, robust optimization framework has been developed that enables identification of economically optimal production schemes for carbon resource processing in hydrogen polygeneration plants (Sammons et al, 2007). The simulation models for each process are developed by extracting knowledge on yield, conversion, and energy usage from empirical as well as experimental data. Process integration techniques are then used to optimize the simulation models. Finally, the optimized models are used to generate data for the economic as well as environmental performance metrics. The estimation of environmental performance is achieved through the use of the US-EPA Waste Reduction (WAR) algorithm (Young et al, 2000). Only the economic and environmental performance metrics are incorporated in the solution framework, thus decoupling the complex models from the decision making process. This approach allows for continuously updating the models as new data becomes available without having to change the selection methodology. Similarly, if new processes are to be included for evaluation, additional metrics can be added to the solution framework. The objective of the optimization step is to identify candidate solutions that maximize economic performance and then the candidates are ranked according to environmental performance. If a candidate satisfies the environmental objectives, then the optimal production scheme has been identified. If none of the candidates satisfy the environmental impact constraints, then the desired economic performance requirements
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are relaxed until a solution with acceptable environmental performance has been identified. It should be emphasized that by decoupling the complex models from the optimization and decision making framework, the methodology is more robust and also provides added flexibility by only having to update the performance metrics for a given process as new information, e.g. a new catalyst with higher conversion, is identified (Sammons et al, 2007).
3. Modeling of Hydrogen Production Strategies Process models have been developed for a variety of hydrogen production schemes. Using process integration techniques and advanced computer-aided tools, the systems have been optimized and the economic potential of the technologies evaluated. Several reforming techniques including four developed within CFFS have been studied for small and large scale production of hydrogen. Literature data along with data obtained in another research project at Auburn University has been used to develop models for partial oxidation (POX), steam (SR) and autothermal reforming (ATR) of a variety of hydrocarbon resources (Wilder et al, 2007; Godat and Marechal, 2003; Seo et al, 2002). In addition, data provided by other researchers in CFFS has been used to build similar models for super critical water reforming (SCWR) of methanol (Gadhe and Gupta, 2005) and biomass (Byrd et al, 2007), dry reforming (DR) of methane (Shao et al, 2005) and finally a catalytic dehydrogenation (CDH) of methane (Shah et al, 2001). The last process is a single step process that in addition to high purity hydrogen also produces a valuable carbon nanotube byproduct. Specifically, we have investigated hydrogen production schemes from four different fuels: • • • •
Natural gas (approximated by methane) Diesel (approximated by dodecane) Methanol Biomass (approximated by glucose)
POX, SR, ATR, DR and CDH POX, SR, ATR SCWR SCWR
Additional models are under development to increase the range of possible products that can be handled by the optimization framework including a comprehensive study of converting waste biomass (poultry litter) to hydrogen. Simulation models were developed in Aspen Plus for small scale (1,000 Nm3/hr) and large scale (100,000 Nm3/hr) hydrogen production plants. The models included all the feed pretreatment steps along with the reforming reactors and effluent treatment including the water-gas-shift reactors. Once material recycles had been implemented and optimized, thermal pinch analysis was utilized to identify the minimum energy requirements. Aspen HX-Net was used to design the corresponding minimum cost heat exchanger networks that optimize the trade-off between capital and utility. Representative results for the large scale production plants are presented in Table 1 below. It should be noted that two scenarios were investigated for each process, i.e. 1) the reactors were allowed to be included in the heat exchanger network, and 2) the reactors were ONLY heated/cooled using external utilities. It is apparent from Table 1, that technologies like POX and ATR due to their exothermic nature are much less sensitive to changes in heating utility cost like the recent spike in natural gas prices. However it is worth noting that all processes can be improved immensely by implementing process integration strategies (the percentage
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reductions are given in parenthesis for each technology). In addition, two scenarios for providing any external heating utilities were investigated for all the cases, i.e. 1) combustion of a fraction of the individual fuel source and 2) combustion of natural gas. Table 1. Process integration analysis (large-scale production) Methane (CH4) POX SR ATR Dry Diesel (C12H26) POX SR ATR Methanol (CH3OH) SCWR
Heating Utilities (kW) w/o Reactors w/ Reactors 16120 (-73%) 2836 (-95%) 127600 (-19%) 117800 (-25%) 27040 (-61%) 11990 (-83%) 93860 (-24%) 90890 (-27%) Heating Utilities (kW) w/o Reactors w/ Reactors 22510 (-71%) 775 (-99%) 142400 (-19%) 133400 (-24%) 43710 (-57%) 1028 (-99%) Heating Utilities (kW) w/o Reactors w/ Reactors 389700 (-46%) 389700 (-46%)
Cooling Utilities (kW) w/o Reactors w/ Reactors 13870 (-76%) 578 (-99%) 10180 (-74%) 394 (-99%) 15850 (-73%) 795 (-99%) 24360 (-56%) 21390 (-61%) Cooling Utilities (kW) w/o Reactors w/ Reactors 66090 (-45%) 44360 (-63%) 9383 (-95%) 422 (-100%) 57850 (-51%) 15170 (-87%) Cooling Utilities (kW) w/o Reactors w/ Reactors 3352 (-99%) 3352 (-99%)
4. Results of Economic Analysis
Relative Hydrogen Production Cost (SR Natural Gas = 1)
An economic analysis of all the generated case studies was performed to evaluate the hydrogen production cost. The initial equipment cost analysis was based on sizing data from the models themselves coupled with Lang factors provided by contacts in the chemical processing industry. Standardized process economics methods were employed to translate the equipment and utility cost into the total production cost, which accounts for everything from engineering to construction, monitoring, supervision and operation. The total product cost was then normalized using the results for steam reforming of natural gas, which is the prevailing means of producing hydrogen. The results are shown in Figure 2 below. Large Scale (100,000 Nm3/hr)
Small Scale (1,000 Nm3/hr)
14 12 10 8 6 4 2 0 SR NG ATR NG POX NG DRY NG
ATR Diesel
Figure 2. Relative hydrogen production cost
POX Diesel
SR Diesel
SCWR SR NG CDR NG SCW R SCWR MeOH (high P) BM (1%) BM (5%)
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The analysis of the various hydrogen production schemes clearly shows that for industrial scale production only the dry reforming (DR) of natural gas has the potential to compete with the traditional steam reforming (SR) process. The conversion of more complex liquid hydrocarbon fuels, e.g. diesel and methanol are not competitive given the current market prices, however such fuels have other benefits such as ease of storage and transportation etc. that can lead to different conclusions in specific cases. The supercritical water reforming (SCWR) process does have one major benefit compared to the other technologies, i.e. the hydrogen is produced at very high pressures, which may be attractive for some applications. For comparison, the hydrogen produced from conventional steam reforming was compressed to the SCWR conditions (276 bar), which resulted in the new process to be only 30% more expensive than the traditional approach. If more efficient separation of the supercritical water phase from the hydrogen product can be developed, e.g. membranes or hydrogels, then the production costs could be significantly reduced by recycling the reaction phase without having to reheat and/or recompress the water to these extreme conditions. The same considerations apply to SCWR of biomass, which is not profitable without the ability to recycle the water phase directly. Two different feed concentrations were investigated (Byrd et al, 2007), i.e. 1 wt% and 5wt% glucose. Although a significant reduction in production cost was observed when increasing the glucose concentration, I it was not enough to offset the high compression and recycle cost. Even if biomass waste, e.g. wood trimmings etc. was used as feedstock, a significant tipping fee would still be needed to make the process profitable. The average tipping fee for unspecified biomass is approximately $30/ton in the United States. This tipping fee would make the current SCWR process comparable in cost to conventional methods if the glucose feed concentration could be increased to around 18 wt%.
Figure 3. Multiwalled nanotubes (MWNT) (left) and stacked cone nanotubes (SCNT) (right) produced by dehydrogenation of methane over Fe-Ni/Mg(Al)O at 650ºC and 500ºC, respectively.
The catalytic dehydrogenation process (CDH) as described by Shah et al, 2001 could potentially be a very attractive alternative to existing hydrogen production schemes. The process produces a valuable byproduct of carbon nanotubes as illustrated in Figure 3. In addition, since the process has the benefit of integrated carbon capture, additional revenue can be secured through credits for reduced CO2 emissions compared to conventional production schemes. Currently carbon credits are traded at approximately $35/ton (www.pointcarbon.com). To break even with steam reforming of natural gas, the carbon nanotube byproduct would have to be sold at approximately 0.20$/lb.
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Although this breakeven sales price of the carbon nanotubes is significantly lower than the open market sales value of carbon nanotubes, it is questionable whether a market exists for such huge amounts of nanotubes that would be available if/when the CDH process is introduced on an industrial scale.
5. Conclusions and Future Work It is apparent that the current technologies for producing hydrogen from liquid fuels are not attractive if evaluated only on the production cost. Benefits such as transportability etc. will need to be quantified for all types of fuel in order to better compare the technologies. However, the dry reforming technology being developed by CFFS researchers appears to be a potentially cheaper alternative to the current state of the art. Furthermore, supercritical water reforming shows significant promise for biomass waste processing, but requires additional research focused on separation of the reactive water phase and the high pressure hydrogen. The catalytic dehydrogenation process developed by CFFS researchers also shows great potential to be competitive with current technologies due to the integrated carbon capture and marketable carbon nanotube byproduct.
6. Acknowlegements This work was supported by the U.S. Department of Energy, Office of Fossil Energy through a contract administered by the Consortium of Fossil Fuel Science (DOE contract number DE-FC26-05NT42456). Additional financial support from the National Science Foundation CAREER Program (NSF-CTS-0546925) is highly appreciated.
References L. Barretoa, A. Makihira and K. Riahi (2002), The hydrogen economy in the 21st century: a sustainable development scenario, International Journal of Hydrogen Energy, 28, 3, 267-284. A.J. Byrd, K.K. Pant and R.B. Gupta (2007), Hydrogen Production from Glucose Using Ru/Al2O3 Catalyst in Supercritical Water, Ind. Eng. Chem. Res, 46, 11, 3574-3579. J.B. Gadhe and R.B. Gupta (2005), Hydrogen Production by Methanol Reforming in Supercritical Water: Suppression of Methane Formation, Ind. Eng. Chem. Res., 44, 4577-4585. J. Godat and F. Marechal (2003), Optimization of a fuel cell system using process integration techniques, Journal of Power Sources, 118, 411-423. Y.S. Seo, A. Shirley and S.T. Kolaczkowski (2002), Evaluation of thermodynamically favourable operating conditions for production of hydrogen in three different reforming technologies, Journal of Power Sources, 108, 231-225. N. Shah, D. Panjala and G.P. Huffman (2001), Hydrogen Production by Catalytic Decomposition of Methane, Energy & Fuels, 15, 1528-1534. H. Shao, E.L. Kugler, W. Ma (2005), Effect of Temperature on Structure and Performance on InHose Cobalt-Tungsten Carbide Catalyst for Dry Reforming of Methane, Ind. Eng. Chem. Res., 44, 4914-4921. B.C.H. Steele and A. Heinzel (2001), Material for fuel-cell technologies, Nature, 414, 345-352. U.S. Department of Energy (2004), Hydrogen, Fuel Cells & Infrastructure Technologies Program: Hydrogen Production. J. L. Wilder, R.M. Hanks, K.H. McGlocklin, N.E. Sammons Jr, M.R. Eden, B.J. Tatarchuk (2007). Process Integration under Size Constraints: Logistical Fuels for Mobile Applications., Computer Aided Chemical Engineering 24, 1059-1064. D.M. Young, R. Scharp and H. Cabezas (2000). The Waste Reduction (WAR) Algorithm: Environmental Impacts, Energy Consumption, and Engineering Economics. Waste Management, 20, 605–615.
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Design of Heat-integrated Power Systems with Decarbonisation Xuesong Zheng, Jin-Kuk Kim and Robin Smith Centre for Process Integration, The University of Manchester, PO Box 88, Manchester, M60 1QD,United Kingdom
Abstract A systematic methodology for driver and power plant selection for low temperature processes has been developed, using a MILP optimisation framework, which generates the optimal number, type, size and model of the main drivers, helper motors/ generators and power plants, as well as the compressor stage arrangement. New synthesis methodology allows a more comprehensive exploitation of the trade-offs when steambased utility network is simultaneously designed with power-dominated systems. Economic and design implications from the introduction of decarbonisation has been also investigated. Industrial case study is presented to demonstrate the significant improvements made by new design method. Keywords: Power Systems; Driver Selection; Steam Systems, Carbon Capture; Optimization.
1. Introduction Intelligent application of process system engineering has gained more attentions in the design of power systems recently because of high energy price as well as greenhouse gas emission. The current study focuses on the application of system engineering to the power-dominated energy systems, in order to achieve high thermodynamic efficiency and sustainable use of fuels. Power-dominated energy systems shows different characteristic, compared to conventional steam-based energy systems, as the provision of shaft (driver) power is more important in the design of utility systems, while conventional utility systems focuses on about how to produce and utilize the steam in a steam distribution network (Varbanov et al, 2004). For example, natural gas liquefaction plant requires several mechanical demands for compressors in refrigeration systems. For such power-dominated processes, a key decision in the design is to select most appropriate driver to satisfy mechanical shaft demands. The design task is very challenging, as there are many driver options for power supply and electricity generation, which leads to a very complex and combinatorial decision-making (Figure 1). The decision on driver selection is to determine optimal number, type and size of the drivers, helper motors/ generators and power plants, subject to a set of mechanical and electricity demands and economic scenarios. Holistic approach is required to deal with design interaction in power systems as the driver selection has different implications in the overall design (i.e. overall cost, fuel consumption, performance, plant availability, carbon emissions, etc). The complexity for the synthesis significantly increases when steam systems are to be considered together with power-dominated systems (Figure 2). This is the case where large amount of heat (steam) is required in processes or a steam turbine, as a direct
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driver, is preferred to gas turbine or electric motor. The steam-based utility system is often employed to generate and distribute steam to the end-users, as well as to utilize steam for power supply or electricity generation by expansion of steam between headers in the steam network. Most of existing works (Wilkendorf et al., 1998; Maréchal and Kalitvenzeff, 1998; Bruno et al., 1998) often focuses on the optimization of steam or utility systems without fully investigating the arrangement of equipment for driver.
Supply
N
Demand
1 2
N
W
1 2
Steam turbine
W N 1 2
Mechanical shaft N
W 1 2
Gas turbine N 1 2
Electricity demand
W
~
Electric motor N 1 2
Power export/ import
Power plant
Figure 1. Driver Selection in Energy Systems
Figure 2. Interactions between steam systems and power systems The separation of carbon dioxide from flue gas (e.g. gas turbine exhaust) is required to regulate the quality of gas emitted to the environment, and an absorption-based postcombustion decarbonisation is considered in this study (Figure 3). When this capture process is implemented to the plant, there are two major impacts from the viewpoint of energy supply. First, additional compression duty is required for CO2 separated from the decarbonisation, and second, considerable amount of steam is needed in the operation of stripper. The additional steam and power requirements should be considered during the design of power and steam systems, as overall thermodynamic efficiency could be
Design of Heat-integrated Power Systems with Decarbonisation
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improved if this heating and power demand could be integrated in the power system design. However, previous studies (Del Nogal et al., 2005; 2006) have not reflected decarbonisation in the design stage, and therefore, in this study, the integrated design methodology will be developed for heat-integrated power systems, subject to decarbonisation. CO2 (compression required)
Treated flue gas
Absorber
Recycle solvent
Stripper
Flue gas Spent solvent
Steam
Figure 3. Absorption-based CO2 capture
2. Synthesis and Optimization The synthesis for the power-dominated energy systems is envisaged with the aid of superstructure-based mathematical optimization. The proposed superstructure (shown in Figure 4) includes all the possible design options, and the optimization is carried out to systematically screen and evaluate potential flowsheets, and perform economic trade-off between capital and operating cost. BO-1 HG/HM
GT-1
VHP
GT-N
DR / EG
HRSG
HP ST
EM-1
BO-N
HRSG ST
HG/HM
....
~
DR / EG
PP-1
MP ST
EM-N
~
DR / EG LP
PP-N ST
ExE
DR / EG CON
Figure 4. Superstructure for Energy Systems in Low Temperature Processes For building superstructure, all the potential direct drivers (i.e. gas turbine, electric motor, steam turbine) are linked to mechanical demand, while process electricity demand is fulfilled either power plant or generation from steam turbine. For gas turbine for direct drive, helper motor or generator is attached for power balance; HRSG is attached for steam production. The steam required at site (i.e. process steam demand) or for electricity generation in steam turbine, is generated from boilers or HRSGs. For
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steam distribution systems, four steam headers are considered and multiple-passout steam turbines are interconnected to headers. The objective for the optimization is to minimize the overall cost (i.e. capital and operating cost), with the considering model constraints: • energy/material balances • choice of driver and electricity generation • maximum/minimum size • compressor stage arrangement • logic constraints, and • mass/energy balances for decarbonisation. The problem is formulated with MILP (mixed integer linear programming), with using piecewise linearization in capital costing. The optimization was carried out using the CPLEX 7.0 solver in GAMS (Brooke et al., 1998).
3. Case study The developed design and optimization method is applied to the case study in which 157.8MW of mechanical shaftpower in overall is demanded together with process electricity and steam demands (Table 1). The base case is identified by optimizing the decomposed sub-optimization problems sequentially. The power system is first optimized without considering steam systems and carbon capture, and then the steam system is optimized to accommodate steam demand from process and carbon capture, as well as shaftpower demand for CO2 compression. Shaftpower demand compressor stage demand (MW) C1 S1 2.5 S2 7.0 S3 12.4 S4 32.3 C2 S1 57.6 S2 18.7 S3 27.3 Electricity demand = 42.6 MW (Power expert and import is not allowed.) Process steam demand MP 34.2 t/h 15 bar / 280 oC LP 26.3 t/h 3 bar / 140 oC Fresh fuel cost: 6 $/MMBTU Table 1. Data for Case Study Figure 5 shows the result from non-integrated sequential optimization, in which three gas turbines are combined with helper motor or generator to meet the mechanical demand, and one power plant is introduced to supply electricity demand. The steam system is configured to accommodate the compressor duty and low pressure steam demand from decarbonisation. All the exhaust gases from gas turbines are further utilized in HRSG with/without supplementary firing, which produces HP steam.
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SF
C2-S2/3
228 t/h HG 1.5 MW
GT
HRSG
HP
48.3 MW
ST
C2-S1 HM 10.5 MW
GT
CC 24.9 MW MP 34.2 t/h
HRSG
48.3 MW
LP 189.4 t/h
C1-S1/2/3/4 HM 6.6 MW
GT
HRSG
48.3 MW
~
PP
60.9 MW
Figure 5. Case study: design from a sequential optimization SF
~
PP
HRSG
123.1t/h
47.0 MW
VHP
CC & C1-S1/2/3
115.6t/h HG
1.3 MW
GT
10.2 MW
GT
C1-S/4
HRSG
HP
48.3 MW
ST
C2-S1 HM
ST
~ 5.5 MW MP 34.2 t/h
HRSG
48.3 MW
LP 189.4 t/h
C2-S/2/3 HG 1.5 MW
GT
HRSG
CON
48.3 MW
Figure 6. Case Study: Optimal design from new design The integrated optimization for decarbonised power and steam systems is presented in Figure 6, where three gas turbines in power systems and one steam turbine in steam systems are employed as direct drivers, and another steam turbine is introduced to supplement the electricity demand. Due to an integrated design, mechanical demand for CO2 compression is allocated to gas turbine, compared to the non-integrated design. The overall cost is 1614 MM$ with 27 MM $ saving.
4. Summary The synthesis of power-dominated energy systems has been studied, and complex design interactions and combinatorial driver selections are systematically explored with the aid of superstructure-based optimization. The integrated design between power systems and steam systems, together with CO2 capture process, has been implemented in the developed methodology, which provides synergetic benefits from the simultaneous consideration in steam systems for the power-dominated plant. Nomenclature BO Boiler CC Compressor for carbon capture CON Condensate C1…N Shaftpower demand (1,2,….N)
HM HP HRSG LP
Helper motor High pressure Heat recovery steam generator Low pressure
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Driver Electricity generator Electric motor External electricity grid Gas turbine Helper generator
MP PP SF ST VHP 1,2..N
Medium pressure Power plant Supplementary firing Steam turbine Very high pressure Number of units
References A. Brooke, D. Kendrick, A. Meeraus, R. Raman and R. Rosenthal (1998) GAMS – A user’s guide, GAMS Development Corporation, 1998. J. Bruno, F. Fernandez, F. Castells and I. Grossmann (1998) A Rigorous MINLP Model for the Optimal Synthesis and Operation of Utility Plants. Trans IChemE, 76, Part A, 246-258 F. Del Nogal, J. Kim, S. Perry and R. Smith (2005) Systematic driver and power plant selection for power-demanding industrial processes, AIChE Spring Meeting, Atlanta, US F. Del Nogal, J. Kim, S. Perry and R. Smith (2006) Integrated Approach for the Design of Refrigeration and Power Systems, GPA meeting, Oslo F. Maréchal and B. Kalitventzeff (1998) Process Integration: Selection of the Optimal Utility System, Computers and Chemical Engineering, 22, S149-S156 P. Varbanov, S. Doyle and R Smith (2004) Modelling and Optimization of Utility Systems, Chemical Engineering Research and Design, 82 (A5), 561-578 F. Wilkendorf, A. Espuña and L. Puigjaner (1998) Minimization of the Annual Cost for Complete Utility Systems. Chemical Engineering Research and Design, 76, Part A, 239245
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Mathematical modeling of limestone dissolution in batch stirred tank reactors in presence of a diluted strong acid. Cataldo De Blasio, Jarl Ahlbeck, Frej Bjondahl Åbo Akademi University Faculty of Technology, Biskopsgatan 8 FIN-20500 Åbo, Finland
Abstract The rate of limestone dissolution determines the need for limestone excess in flue gas desulfurization processes and therefore affects the cost of makeup and waste disposal. For this reason a better understanding of the limestone performance toward desulfurization can have reasonable economical effects. Utilizing a good mathematical model it is possible to optimize the parameters involved in flue gas desulfurization. In the present work a mathematical model describing the transport phenomena occurring in limestone-strong acid reaction in small BSTRs (Batch Stirred Tank Reactors) was developed and evaluated. The particle size distribution and the chemical reactivity were considered as primary factors determining the volume variation of the natural limestone. The model together with the experimental procedure provides a new tool for measuring the properties of chemicals used in flue gas desulfurization FGD. Keywords: mathematical modeling, desulfurization, reaction rate, limestone.
1. Introduction Limestone is widely used for flue gas desulfurization (FGD) processes. The main system adopted for FGD is the wet limestone scrubbing process in which the dissolution rate of limestone represents one of the essential kinetics (Diaz et al. 1985). Therefore an accurate evaluation of the dissolution of limestone is important for FGD process design and also plant operation. A mathematical model is needed with which it is possible to optimize the parameters involved in flue gas desulfurization. One way to test the reactivity of limestone is to use diluted strong acids like sulfuric or hydrochloric acid in a system that simulates a slurry solution (Ahlbeck et al.1995). Many studies on limestone dissolution have been done and the correlation between the pH value and limestone dissolution rate has been studied (Toprac and Rochelle, 1982). In addition, a model for FGD performance as a function of limestone reactivity was developed (Gage et al.,1990). Few studies have discussed the variation of the particle size distribution during dissolution. In this study a more general mathematical model has been developed; it takes into consideration the particle size distribution and transport phenomena as the main factors affecting the dissolution. The model represents a new tool for more accurate FGD performance evaluation. Future developments and tests will give a reasonable confidence in order to evaluate limestone reactivity and FGD performances.
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2. Mathematical modeling The mathematical model presented here takes into consideration a system in which the particles are not free to move under the gravity force and the mass transfer is due to turbulence in the surrounding fluid. Furthermore, the model takes into account the increase of mass transfer coefficient as a function of the power dissipation level (Calderbank and Moo-Young. 1961). The limiting factor is the diffusion of the reagents and products of reaction in the liquid film between the solid and the bulk. It is possible to divide the entire phenomenon in three main steps: 1. 2. 3. 4.
Diffusion of the reagents from the liquid bulk to the solid surface. Reaction of the reagents with the solid. Diffusion of the reaction products from the particle surface to the liquid bulk. Further dissolution of solid.
Table 1. Main reactions involved in BSTR system Fenomena
Reactions
Dissolution of limestone
CaCO3(s)ĺCa2+ + CO32-
Carbonate ions react with the hydronium ions according to:
H3O+ + CO32- ĺ HCO3- + H2O
Carbonic ions react with hydronium ions
HCO3- + H3O+ ĺ H2CO3 + H2O
Final products
H2CO3 ĺ CO2(g) + H2O
There are numerous factors affecting the resistance of the reagents motion through the liquid film to the solid surface, these factors are mainly the relative velocity between the fluid and the solid, the size of the particles and the fluid properties. The mechanism of reaction and the limestone dissolution have been studied and it has been demonstrated that the mass transfer is the limiting factor for the chemical reactions (Toprac and Rochelle, 1982). The correlation between volume Vp and time t is considered to be a function of the mass transfer coefficient related to the liquid film kL, for the particular case of limestone-acid system. (O. Levenspiel, 1999) and ( Jarl Ahlbeck,1995)
dV p dt
=
− πd p2 k L
ρm
⋅ Ch
(1)
Where ȡm is the molar density of the limestone and Ch is the concentration of hydronium ions and dp is the diameter of the particles. Calderbank gave a correlation for the mass transfer coefficient kL between fluid and solid particle (Calderbank and Moo-Young, 1961). A system was considered in which the above mentioned correlation is linked to heat and mass transfer in mixed vessels where the solid phase is in the form of a single submerged body. In this system the particles are considered not free to move under the force of gravity and the transfer is due to the turbulence in the surrounding fluid. Furthermore, the model proposed by Calderbank et al. takes into account the increase of mass transfer coefficient when the power dissipation level increases. The correlated equation is:
Mathematical Modeling of Limestone Dissolution in Batch Stirred Tank Reactors in Presence of a Diluted Strong Acid 2
§ υc · 3
§ ευ k L ¨ ¸ = 0.13¨¨ 2c ©D¹ © ρc
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1
·4 ¸¸ ¹
(2)
Where ȣc is the kinematic viscosity of fluid, İ is the agitation power per unit volume (W/l) and ȡc is the fluid density. If the fluid is not in motion the Sherwood number reduces to 2 (O. Levenspiel, 1999). Furthermore, we consider the equation (1) and (2) and taking into account at the same time the contribution of the turbulent and nonturbulent system we obtain: 1
1
ª
§ ευ · 4 § υ · πC h « § 6V p · 3 ¸¸ + 0.13¨¨ 2c ¸¸ ¨ c ¸ = −K 2 D¨¨ ρm « © π ¹ dt © ρc ¹ © D ¹ «
dV p
−
¬
2 3
§ 6V p ¨¨ © π
2 º ·3 » ¸¸ » ¹ » ¼
(3)
With: 1
πC § 6 ·3 A = − K ⋅ h 2 D¨ ¸ ρm ©π ¹
§ ευ πC h B = −K 0.13¨¨ 2c ρm © ρc
(4)
1
−
2
2
· 4 § υc · 3 § 6 · 3 ¸¸ ¨ ¸ ¨ ¸ ¹ © D ¹ ©π ¹
(5)
The variation rate of the particle volume becomes then:
dV p dt
1
2
= AV p3 + BV p3
(6)
Integrating and solving the equation (6) for a particle size range i we obtain: 1 ·½ § ¨ § ΔFi ⋅ mtot · 3 ¸ ° ° ¨ ¸ γ M 1 + ⋅ ¸ ¨ ° 1 1 ¨ ρ p ¸¹t ¸ °° ¨ © 0 3 °°§¨ ΔFi ⋅ mtot ·¸ 3 §¨ ΔFi ⋅ mtot ·¸ 3 1 ¹° = t − t ln © − γ + ¾ ®¨ γ 0 1 ¸ ¨ ¸ ρ p ¹t © ρ p ¹t M AM °© · § ¨ 0 § ΔFi ⋅ mtot · 3 ¸ ° ° ¸ ¸ ° ¨1 + M ¨¨ γ ° ρ p ¸¹t ¸ ° ¨ © °¯ ¹ °¿ ©
(7)
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Where ǻFi is the fraction in volume related to a particle size range, M is equal to B/A, Ȗ is the shape factor and mtot is the total limestone mass in the reactor.
3. Material The used limestone is from the Parainen quarry in SW Finland. The carbonate rock is a 1900 million-year-old limestone metamorphosed to marble during the Svecofennian orogeny 1830 million years ago (metamorphosed limestone). Mineralogically it is almost pure calcite and texturally an even grained marble.
4. Apparatus For particle size measurements the Malvern 2600 particle sizer system has been used. The equipment includes a batch stirred tank reactor with a volume of 0.75 liters and a laser-beam diffractometer where the sample particles are analyzed in order to get a particle size distribution. For each size range, the limestone fraction in volume was given. In this way, it has been possible to evaluate the change in the sample volume as a function of time. Much attention has been given in order to obtain less possible approximation to the particle size evaluation, for this purpose the limestone particles have been sieved between different size ranges and then the actual size was verified by diffractometry. Furthermore it was possible to control all the BSTR parameters by computer device. The pH vs time dependency was evaluated for each set of experiments. The two computer loggers were synchronized together. The system is described by the following picture:
Figure 1. The schematic shows the laboratory setup used for mineral reactivity measurement.
The pH and the particle size distribution in the reactor were measured simultaneously and several experiments have been done in order to have an optimized computerintegrated system. The limestone solution was agitated in order to create turbulence and to equally disperse the particle, the agitation power was estimated to be 20 W/liter. By means of a pump, the limestone slurry was conducted into a glass range lens where a laser beam was utilized in order to measure the particle size distribution. The acid
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solution was 0.1 molar and the particle size distribution was calculated by model independent analysis.
5. Results The carbonic acid concentration increases with time. Initially, the calcium carbonate is able to utilize all the hydronium ions in a fast way. But when the concentration of carbonic acid (weak acid) is reasonably high, the second step of reaction is slower. The experimental behavior of the hydronium concentration at different times is in agreement with this mechanism. The volume of the limestone particles is a function of time and pH. The following figures show the time vs volume function and the experimental pH vs time curve:
Figure 2. a (left): Time-pH relation for small limestone particles in BSTR. b (right): Volume-time dependency as a function of the hydronium concentration.
For each pH value the volume-time correlation related to the limestone particles was plotted as reported in figure 3.a. in order to compare the experimental results with the theoretical ones. The actual pH and the related volume were reported with the theoretical curves obtained for different values of hydronium concentration. time ,sec
time ,sec 1
140 120 2
100 80 60 40 20
3 4 5 67
Vol. l 0.00001
0.00002
0.00003
0.00004
140 120 100 80 60 40 20 0 0
Volume, l 0.00001 0.00002 0.00003 0.00004
Figure 3. Results. a. (left): Volume-Time relation at different pH values and experimental data. B (right): Experimental values and theoretical curve
The previous figures show experiments that are made within 150 seconds. The relation between the numbered curves in figure 3.a and the pH values is reported in the following table:
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Table 2. PH values related to the parametric curves in figure 3a. Numbered curve
1
2
3
4
5
6
7
pH value
5.48
5.202
4.924
4.662
4.301
4.091
3.812
The experimental data were reported in figure 3.b with a two-dimensional function obtained considering the pH as a linear function of time. The mathematical model was sensitive to the pH variations: at small differences of hydronium concentration there was a sensible increase of the time needed to have the measured changes in volume. This behavior is perfectly in accordance with the model reported here. The K parameter is dimensionless and indicates the dissolution rate constant of limestone and it was found to be: K = 80000. Furthermore the dissolution rate parameter “A” was evaluated: A = 6.09384*10-12. This value is in good agreement with the dissolution rate parameter found by Toprac and Rochelle (Toprac and Rochelle 1982). Compared to the studies cited previously, the technique and the model presented in this work eliminate uncertainties and errors encountered when the pH of the solution is maintained unchanged. Constant pH is a condition difficult to obtain because limestone reacts quite quickly with strong acids. Furthermore the great congruence between experimental data and the obtained model suggest an additional degree of reliability with the introduction of the dimensionless parameter K.
6. Conclusions In the present work a mathematical model for the dissolution rate of limestone in presence of strong acid was studied considering BSTR design theory combined with the knowledge of stagnant and turbulent mass transport phenomena. The dissolution rate model gives results in good agreement with the experimental data and it takes into consideration all the most important parameters that have a significant role in limestone dissolution. According to this work, it is possible to evaluate the reactivity of high calcium limestone with specified particle size distribution and design the FGD process more accurately. The model and the experimental procedure provide a more complete tool for measuring the properties of the gas desulfurization chemicals.
References Jarl Ahlbeck, T. Engman, S.Fälten. (1995). Measuring the reactivity of limestone for wet fle gas desulfurization. Chem. Eng. Sci. Vol.50 NO.7, pp.1081-1089. Calderbank, P.H.; M.B. Moo-Young, (1961). The continuous phase heat and mass transfer properties of dispersions. Chem. Eng.Sci.,16,p.39. Levenspiel, Octave.(1999). Chemical reaction engineering. - 3rd ed. John Wiley & Sons. US. Rudin Walter. (1976). Principles of mathematical analysis.- 3rd ed. Mc.Graw Hill pag.132-133. Barton, P.; Vatanatham, T. (1076) Kinetics of limestone neutralization of acid waters. Environ. Sci. Technol. 10. 262-265. Lund K, Fogler HS, Mc Cune CC, Ault JW (1975). The dissolution of calcite in hydrochloric acid. Chem Eng. Sci 30:825-835 Mario Diaz, L. Fonseca, G. Coca. (1985). Kinetics of dissolution of limestone slurries in sulfuric acid. Chem. Eng. Technol. 57. Nr. 10, S.882-883. N. Makkinejad (1991). Reaktivitätstests zur Beurteilung von kalksteinmehlen fur den Einsatz in Rauchgasentschwefelungsanlagen. VGB Kraftwerkstechnik 71 Toprac, A.J. G.T. Rochelle (1982), Environ. Prog.1, p 52. Gage, C.L.,G.T. Rochelle (1990), SO2 control symposium, New Orleans, LA, May 8-10.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Biodiesel production from vegetable oils: Operational strategies for large scale systems Nívea de Lima da Silvaa, Elmer Ccopa Riverab, César Benedito Batistellaa, Danilo Ribeiro de Limaa, Rubens Maciel Filhob, Maria Regina Wolf Maciela a
Laboratoy of Separation Process Development and bLaboratory of Optimization, Design and Advanced Control, School of Chemical Engineering, State University of Campinas, P.O. Box 6066, 13081-970, Campinas, SP, Brazil
Abstract This work presents the transesterification process of vegetable oils with bioethanol in the presence of sodium hydroxide as catalyst, because it leads to better conversion and smaller reaction time. A computer-aided tool of this system to model the kinetic of biodiesel production was developed to explore the impact of each strategy on the process behaviour which is an important issue to lead the process to be operated at high level of performance. An analysis was made of the temperature effects on the reaction rates, and it was determined the reaction rate constants and the activation energies derived from experimental observation. The kinetic data showed to be satisfactory for a wide range of operating conditions. The assessment of possible implementation difficulties are carefully considered and discussed. Keywords: Biodiesel, ethanolysis, transesterification, modeling, optimization.
1. Introduction Biodiesel is a clean burning fuel derived from a renewable feedstock such as vegetable oil or animal fat. It is biodegradable, non-inflammable, non-toxic and produces lesser CO2, sulfur dioxide and unburned hydrocarbons than petroleum-based fuel. Biodiesel is a fuel made from fat. Either virgin vegetable oil or waste vegetable oil can be used to make quality fuel. Fats are converted to biodiesel through a chemical reaction involving alcohol and catalyst. Nowadays, due to the price of virgin oil such as canola, soybean oil, the use of low-cost feedstock, such as waste frying oils in an acid-catalyzed process, should help make biodiesel competitive in price with petroleum diesel, beyond being a suitable way to reuse waste materials. Alternatively, it is a good strategy to find out some vegetable oils that is not used in the food chain so that they tend to be a cheaper feedstock, as is the case for castor oil. Bioethanol (ethanol from biomass) is an alternative to methanol, because it allows production of entirely renewable fuel [1]. For both feedstocks, the transesterification reaction takes place in the biodiesel process production. This reaction can be carried out in the presence of alkaline, acid, and enzyme catalysts or using supercritical alcohol [2]. Another issue in transesterification processes is the influence of temperature on the kinetics. Thus, a description of the influence of temperature on kinetics of the biodiesel production is essential for a reliable mathematical modeling to be used in process design, optimization, control and operation. During the last years, several studies of the transesterification process mathematical modeling involving various types of vegetable oil have been carried out [3-5]. Hence, the difficulty in modeling transesterification
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N. De Lima da Silva et al.
processes is essentially on the precise description of the kinetics and robust modeling can only be achieved by incorporating reliable computer-aided procedures. Bearing this in mind, in this work the modeling of transesterification process of vegetable oils is studied with focus on developing a systematic method that can be used whenever an estimation of reaction rate constants is necessary.
2. Experimental Procedure 2.1. Materials The castor oil was obtained from Aboissa (São Paulo, Brazil) and the frying vegetable oil was colleted from a local Brazilian restaurant. The castor oil had 1.2 % of free fatty acid (FFA) and the frying oil had 3.2% of free fatty acids ( determined according to the AOCS official method Ca 5a-40 as oleic acid). The sodium hydroxide and the anhydrous ethanol were obtained from Synth (São Paulo, Brazil). All the standards were supplied by Sigma-Aldrish Chemical Company, Inc. (St. Louis, Mo). 2.2. Equipment The experiments were carried out in a batch stirred tank reaction (BSTR) of a 1 liter reactor, equipped with a reflux condenser, a mechanical stirred, and a stopper to remove samples. 2.3. Method of analysis Gel-permeation chromatography (Waters, USA) also called high-performance sizeexclusion chromatography (HPSEC) was used for the triglycerides, diglycerides, monoglycerides, ethyl esters and glycerol analysis according to Shoenfelder [6]. The mobile phase was HPLC-grade tetrahydrofuran (JT Baker, USA). The relative percentage of each component (xi) was give by HPSEC and it was determined by Eq. 1, where xi was calculated dividing the peak area of the ester by sum of the peak area of all components. § A EE x i = ¨¨ + + A A A DG MG + A EE + A GL © TG
· ¸ ¸ ¹
(1)
The molar concentration was calculated using Eq. 2. Mi was determined by dividing the product of the density (di) by the relative percentage xi by the molecular weight of each component (Mwi). § x × d i × 1000 · ¸¸ M i (mol/L) = ¨¨ i Mw i © ¹
(2)
2.4. Experimental conditions The system was maintained at atmospheric pressure and the experiments were carried out at constant temperature. The agitation was kept constant at 400 rpm. The reaction time was about 25 minutes. The experiments were carried out with 1% wt of sodium hydroxide, molar ratio ethanol: vegetable oil of 6:1. To examine the temperature dependency of the reaction rate constants, reactions at 30, 40 and 50°C were studied. 2.5. Procedures Initially, the reactor was loaded with 400g of either castor oil or frying oil, preheated to desired temperature and the agitation started. The sodium hydroxide was dissolved in ethanol and the reaction starts when the alcoholic solution was added to the vegetable oil. During the reaction, samples were prepared by dilution of 0,1g of the reaction in
Biodiesel Production from Vegetable Oils
1103
10ml of THF. After dilution the samples were filtered and analyzed in the HPSEC (high-performance size-exclusion chromatography). Twelve samples were collected during the course of each reaction.
3. CAPE tool for Biodiesel Production (Transesterification) Specifically, a step-by-step optimization procedure for the calculation of the reaction rate constants as a function of temperature used in this work is described below: 3.1. Determining the appropriate forms of rate expressions A system of differential equations based on kinetic model presented by Noureddini and Zhu [1] and Bambase et al. [2], shown in Eqs. 3-8, were used to model the stepwise transesterification reaction. d[TG] = −k1 [TG][A] + k 2 [DG][EE] − k 7 [TG][A]3 + k 8 [GL][EE]3 dt d[DG] = k1 [TG][A] - k 2 [DG][EE] − k 3 [DG][A] + k 4 [MG][EE] dt d[MG] = k 3 [DG][A] - k 4 [MG][EE] − k 5 [MG][A] + k 6 [GL][EE] dt d[GL] = k 5 [MG][A] - k 6 [GL][EE] + k 7 [TG][A]3 − k 8 [GL][EE]3 dt d[EE] = k1 [TG][A] - k 2 [DG][EE] + k 3 [DG][A] - k 4 [MG][EE] dt
(3) (4) (5) (6)
(7)
+ k 5 [MG][A] - k 6 [GL][EE] + k 7 [TG][A] - k 8 [GL][EE]3 d[A] d[EE] =− dt dt
(8)
where [TG], [DG], [MG], [EE], [A] and [GL] are the respective concentrations of triglyceride, diglyceride, monoglyceride, ethyl ester, alcohol, and glycerol expressed in mol/L. Kinetic rate constants have units L/mol⋅min. 3.2. Estimating a set of temperature dependent kinetic rate constants for each temperature considered in the experiments Temperature dependent kinetic rate constants of the three consecutive and reversible reactions were established based upon the kinetic scheme presented in Eqs. 3-8. Let θ specify the parameters vector, which contains all the kinetic rate constants. The objective of the mathematical estimation of model parameters is to find out θ by minimizing the objective function, min E(θ): np
E(θ ) =
ª ([TG] n − [TG]e n ) 2
¦ «¬« n =1
+
[TG]e 2max
([GL]n − [GL]e n ) 2 [GL]e 2max
+
([DG]n − [DG]e n ) 2 [DG]e 2max
([EE]n − [EE]e n ) 2 º + »= [EE]e 2max »¼
+
np
¦
([MG]n − [MG]e n ) 2 [MG]e 2max
(9)
İ 2n (θ )
n =1
where [TG]en, [DG]en, [MG]en, [GL]en and [EE]en are the molar concentrations of triglyceride, diglyceride, monoglyceride, glycerol and ethyl ester at the sampling time n. [TG]n, [DG]n, [MG]n, [GL]n and [EE]n are the concentrations computed by the model at the sampling time n. [TG]emax, [DG]emax, [MG]emax, [GL]emax and [EE]emax are the
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N. De Lima da Silva et al.
maximum measured concentrations and the term np is the number of sampling points. Here, εn(θ) is the error in the output due to the nth sample. The determination of the feasible region of the total search space in the multiparameter optimization of the deterministic model is complex. For that reason, in this work, the optimization procedure to minimize Eq. 9 is based on the combination of two optimization techniques. Initially, the potential of global searching of real-coded genetic algorithm (RGA) was explored for simultaneous estimation of the initial guesses for each kinetic rate constants in the model. Subsequently, the quasi-Newton algorithm (QN), which converges much more quickly than RGA to the optimal, was used to continue the optimization of the kinetic rate constants near to the global optimum region, as the initial values were already determined by the RGA global-searching algorithm. 3.3. Applying an equation based on Arrhenius form to describe the influence of temperature and fit it to the optimized values obtained for each temperature From the k-values obtained at different temperatures, the activation energy for each ethanolysis step was estimated using the integrated form of the Arrhenius equation: k = Ae
E − a RT
(10)
where k is the reaction rate constant, L/mol⋅min; A is the frequency factor; is the activation energy, cal/mol; R is the universal gas constant, R=1.9872 cal/mol⋅K and T is the absolute temperature, K.
4. Results and Discussion 4.1. Transesterification reaction The frying oil had a free fat acid (FFA) content higher than 1%; then the alkaline catalyst would be destroyed because the FFA reacted with the sodium hydroxide to produce soaps and water, hence, reducing the ester conversion. Figures 1 (A and B) show the effect of the time on the frying oil and on the castor oil transesterifications. The castor oil transesterification is very rapid because the ethyl ester concentration is 2 mol/L, (conversion of 72%) after 2 minutes, while that the higher conversion for frying oil (72%) is achieved after 20 minutes, at the same temperature (50oC). In the transesterification reaction, the reactants initially form a two-phase liquid system, because the TG and alcohol phases are not miscible [3]. This fact decreases the contact between the reactants and consequently, the reaction conversion. The castor oil and its derivatives are completely soluble in alcohols [7]. This fact leads to increase the mass transfer in the first stage of the reaction, and hence the ester conversion. Thus, the kinetic constant of the castor oil reaction (TG →DG) is higher than of other vegetable oils, for the same process temperature. 4.2. Reaction kinetic modeling Experimental observations at three temperatures (30, 40 and 50oC) are used to estimate the kinetic rate constants and its predictions at 50oC are shown in typical kinetic plots in Figures 1A and 2B for frying and castor oils, respectively. For the estimation of the kinetic rate constants, Eqs. 3-8 were solved using a Fortran program with integration by an algorithm based on the fourth-order Runge-Kutta method. The rate constants were determined by minimizing Eq. (9) using a hybrid approach, coupling RGA and QN algorithms, which intuitively made the prediction procedure to be significantly quicker.
Biodiesel Production from Vegetable Oils
1105 6 Concentration (mol/L)
Concentration (mol/L)
6 5 4 3 2 1 0
5 4 3 2 1 0
0
4
7
11
14
18
21
0
Reaction Time (min)
4
7
11
14
18
21
Reaction Time (min)
(A)
(B)
Fig. 1. Experimental data and kinetic modeling curves for the composition of the reaction mixture during (A) frying oil and (B) castor oil ethanolysis. Temperature=50oC, 1% of NaOH as catalyst, impeller speed=400rpm, molar ratio 6:1. (z, triglyceride; {, diglyceride; U, monoglyceride; S, glycerine; , ethyl ester;
, alcohol).
By considering the values optimized by RGA as initial guess estimates, the kinetic rate constants were re-estimated by QN. The procedure showed to have very good performance with a relatively lower computer burden. The rate constants for frying and castor oils ethanolysis are shown in Table 1. Figures 2A and 2B show the dependence of ln (k) on 1/T, confirming that the Arrhenius equation can be applied for determining the activation energies for the ethanolysis reactions. The values obtained are summarized in Table 2. 3.10
3.15
3.20
3.25
3.30
3.35
3.05 0.50
-0.90
-0.50
-1.80
-1.50
ln k
ln k
3.05 0.00
-2.70
-2.50
-3.60
-3.50
-4.50
3.15
3.20
3.25
3.30
3.35
-4.50 3
-1
1/T X 103 (K-1)
1/T X 10 (K )
(A)
3.10
(B)
Fig. 2. Arrhenius plot of (A) frying oil ethanolysis and (B) castor oil (, k1;
, k2; U, k3; S, k4; {, k5; z, k6).
The experimental results show that the second order models described adequately the reaction conditions. There is an increase in k with the temperature for both raw materials.
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N. De Lima da Silva et al. Table 1. Values for the kinetic rate constants for castor and frying oils ethanolysis
Castor oil Frying oil
Temperature (oC) 30 40 50 30 40 50
k1 0.2426 0.4110 0.4750 0.1811 0.2086 0.2215
Kinetic rate constants ( mol/L⋅min) k2 k3 k4 k5 0.0555 0.0561 0.0569 0.0257 0.0263 0.0280
0.9526 1.0949 1.3716 0.3216 0.3825 0.3939
0.6948 0.9920 1.1500 0.5317 0.5522 0.7000
0.0279 0.0300 0.0345 0.0751 0.0834 0.0860
k6 0.0180 0.0355 0.0420 0.0167 0.0200 0.0284
Table 2. Activation energies for the ethanolysis reactions Ea (cal/mol) Reaction TG →DG DG →TG DG →MG MG →DG MG →GL GL →MG
Castor oil 6570 245 3534 4921 2042 8309
Frying oil 1918 852 1927 2791 1297 5467
5. Concluding Remarks The performances of a reliable systematic procedure to describe the reaction kinetic of the transesterification process were assessed. The kinetic model presented acceptable fits, in comparison to experimental observations, using the proposed methodology. Values of activation energy for ethanolysis reaction indicated that higher temperatures favor the formation of DG (for the reaction TGļDG values of Ea for the forward reaction has a magnitude higher than the corresponding backward step), but also favor the consumption of MG and GL (for DGļMG and MGļGL values of Ea for the forward reaction has a magnitude lower than the Ea of the inverse reaction). With the proposed procedure, it was possible to predict the extent of the reaction at any time under particular conditions as well as to define process operating strategies in order to have high performance operation.
Acknowledgements The authors acknowledge FAPESP, CAPES and CNPq for financial support.
References 1. R. Fillières, B. Benjelloun-Mlayah and M. Delmas, J. Am. Oil Chem. Soc., 72, (1995), 427432. 2. N. De Lima de Silva, M.R. Wolf Maciel, C.B. Batistella and R. Maciel Filho, Appl. Biochem. Biotech, 130, (2006), 405-414. 3. H. Noureddini and D. Zhu, J. Am. Oil Chem. Soc., 74, (1997), 1457-1463. 4. M.E. Bambase, N. Nakamura, J. Tanaka, and M. Matsumura, J. Chem. Technol Biotechnol., 82, (2007), 273–280. 5. P.C. Narváes, S.M. Rincón and F.J. Sánchez, J. Am. Oil Chem. Soc., 84, (2007), 971-977. 6. W. Schoenfelder, Eur. J. Lipid Sci. Technol., 105, (2003), 45-48. 7. M.G. Kulkarni, S.B. Sawant, Eur. J. Lipid Sci. Technol., 105, (2003), 214-218.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Minimization of Life Cycle Greenhouse Emissions and Cost in the Operation of Steam and Power Plants Pablo E. Martinez and Ana Maria Elicechea Chem. Eng. Dept.,Universidad Nacional del Sur-CONICET, Camino La Carrindanga km 7, 8000 Bahía Blanca, Argentina.
Abstract The main objective of this work is to use environmental and economic objective functions to select the operating conditions of process plants. The operating conditions of a steam and power plant are selected to minimize greenhouse emissions and cost. The battery limits of the utility plant are extended to include the main greenhouse burdens of the imported electricity and its corresponding life cycle from raw material extraction, refining, transport, generation, transmission and waste disposal. Electricity generation by thermoelectric, hydroelectric and nuclear plants is considered. The reduction in CO2 equivalent emissions and its market price is included in the economic objective function. Significant reductions in greenhouse emissions and cost are achieved simultaneously, selecting the operating conditions such as temperature and pressure of high, medium and low pressure steam headers. The operating conditions include discrete decision for the selection of alternative drivers, between electrical motors and steam turbines, and equipment that are on or off, which are represented using binary variables in the mixed integer nonlinear programming problem. Significant reduction in greenhouse emissions and cost are achieved. Keywords: Life Cycle, Greenhouse emissions, Cost, Operation.
1. Introduction The International Panel on Climate Change has strongly recommended the reduction of greenhouse gases emissions as the only way to minimize potentially irreversible impacts on ecosystems and societies. The main source of greenhouse emissions is the combustion of fossil fuels although greenhouse emissions are also present in the entire life cycle of any product or service. CO2, N2O, CH4 are released from each stage in the supply chain of any product. The upstream processes consume raw materials and energy which have associated greenhouse emissions due to both fossil fuel consumption and fugitive emissions. The upstream processes include raw material extraction, processing and distribution. An exhaustive work on life cycle greenhouse emissions is presented by Weisser (2007) paying special attention to fossil fuel, nuclear and renewable energy technologies in the European Union and Japan. The life cycle approach has been traditionally used to quantify the environmental performance of a product. Azapagic and Clift (1999) have proposed the application of life cycle assessment for the selection of alternative technologies with the e-constraint multiobjective method applied to a mineral processing system. Multi-objective optimization applied to environmental and economic objectives has been treated by authors like Ciric and Huchette (1993) with two objectives, the amount of waste and the net profit of an ethylen glycol production plant. Dantus and High (1999) proposed a method to convert a biobjective optimization
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P.E. Martinez and A.M. Eliceche
into a single objective optimization problem; the method proposed is a variation of the utopia point distance minimization, including discrete variables to select the type of reactor to be used in the methyl chloride superstructure plant design. The steam and power generation system of a petrochemical plant is the sector where fossil fuels are burned to provide utilities to the process plant. This study focuses on the estimation and minimization of life cycle greenhouse emissions and cost of a steam and power plant selecting optimally the operating conditions, solving a multiobjective optimization problem. To assess greenhouse emissions in the life cycle context a key issue is the definition of the life cycle boundaries extending the battery limits of the steam and power sector in order to include the main sources of GHG emissions such as the corresponding to the imported electricity from thermoelectric, hydroelectric and nuclear generation. Typical operating conditions to be selected in utility systems are temperature and pressures of high, medium and low pressure steam headers, deareator pressure and letdowns flow rates. Binary operating variables are introduced to represent discrete decision such as equipment that can be on or off as boilers and their auxiliary equipment and the selection between optional drivers for pumps that can be either electrical motors or steam turbines. As a case study the steam and power sector of an ethylene plant in operation is analyzed.
2. Estimation of Greenhouse Emissions Greenhouse gases include CO2, N2O, CH4, SF6 and CFCs, each of them having different heat-trapping properties. To compare their effects on the atmosphere the Global Warming Potential, the gwp factors are used. Global Worming Potential is the ability of a greenhouse gas to trap heat in the atmosphere relative to an equal amount of carbon dioxide, thus gwp of CO2 has a value of 1. The next greenhouse gases of importance are CH4 and N2O which take values of 21 and 310, over a 100-year time span, Guinée et al (2002), respectively. The emissions of SF6 and CFCs are negligible in fossil fuel combustion and during electricity life cycle (Dones et al, 2004), thus these gases are not considered in the present work. Hence, to obtain the amount of greenhouse emissions CO2e (kilogram of carbon dioxide equivalent per time unit), the k flow rate is multiplied by its corresponding gwpk. In the following sections the evaluation of the greenhouse emissions for the utility plant and the imported electricity are presented. 2.1. Steam and power generation plant The utility sector of the ethylene plant, consume natural gas and a residual gas stream coming from the ethylene plant as fuel to produce high pressure steam. The greenhouse emissions come from the combustion in boilers and a waste heat boiler. The gases produced during combustion contain pollutants like CO2, CO, NOx, VOCs and trace metals. In this work only the greenhouse emissions are considered. The combustion emissions for the utility plant (UP) are calculated with the following equation: CO 2e UP
ª º l ¦ « Fng u ¦ e k Frg u e rg,k » u gwp k k ¬ l ¼
l
1,..., l ng
(1)
Where: Fng is the natural gas flow rate, Frg is the residual gas flow rate, both burned in boilers and waste heat boiler, erg,k is the residual gas emission factor for pollutant k;
Minimization of Life Cycle Greenhouse Emissions and Cost in the Operation of Steam and Power Plants
1109
e kl are the emission factor for greenhouse gas k in the life cycle stage l, lng is the total number of life cycle stages, including combustion in the utility plant and the natural gas fuel cycle, for natural gas fuel cycle the extraction and transportation stages are considered. The emission factors for different pollutants k during natural gas and residual gas combustion are estimated in the following way: stoichiometrically, according to the natural gas composition for CO2 and from AP-42 report (EPA, 1998) for CH4 and N2O. As the residual gas is produced in the ethylene plant, no life cycle stage has been considered for it.
2.2. Imported Electricity The electricity generation sector in Argentina has contributions from thermoelectric, hydroelectric and nuclear plants. The share of each is seasonal dependent. Thermoelectric power generation consumes coal, oil and natural gas as fuels, nuclear power generation consumes uranium fuel. The greenhouse emissions are estimated with data from National Greenhouse Gases Inventory (2005) including those values for the fossil fuels combustion which are the same values used by IPCC guidance for the country greenhouse emission inventory elaboration. The general equation for estimating the greenhouse emissions in electric power generation includes the following life cycle stages: extraction and processing of raw materials, transport, refining (where it is applicable) and electricity generation itself: CO 2e IE
l
j ¦ ¦ ¦ w j u e jk u gwp k
j k lj
(2)
Where the j subscripts is to accounting for the different way of electricity production, thermoelectric, nuclear and hydroelectric, lj superscript is to accounting for life cycle stage l in electricity generation option j and wj is the amount of electricity imported from each power source option j. A detailed analysis of each life cycle stages considered was presented in Eliceche et al (2007a). The methodology was updated with data from Weisser (2007), transmission loss equal to 6 % is also included (EIA, 2003) for all the electricity generation options.
3. Objective Functions to be minimized 3.1. Environmental Objective Function The life cycle greenhouse emissions are calculated as the sum of the utility plant greenhouse emissions (Eq. 1) and the imported electricity greenhouse emissions (Eq.2) as follows: CO 2e LC
CO 2e UP CO 2e IE
(3)
3.2. Economic Objective Function The economic objective function (C) consider: (i) the operating cost including costs of natural gas, freshwater, cooling water treatment and imported electricity as shown in Eliceche et al (2007b) and (ii) income due to greenhouse emissions reduction CO2eR traded in the market as shown in the following equation:
1110
C
P.E. Martinez and A.M. Eliceche R ¦ c i u Fi CO 2e u p i
(4)
Where the sub index i indicates each term of the operating cost, ci operating cost i, Fi represent flows rates and p is the market price of greenhouse emissions in the international emission trade market. A similar objective was used by Hashim et al. (2005) for the optimization of Ontario electricity system including the price of CO2e emissions, solving a linear programming problem. To select optimally the operating condition of the steam and power sector, both objectives greenhouse emissions and cost are minimized simultaneously as shown in the following section.
4. Selection of the operating conditions Considering the minimization of greenhouse emissions and cost the following multiobjective Mixed Integer Non Linear Programming (MINLP) problem can be formulated: Min x, y
s.t. :
C (x, y) , CO 2e LC (x, y) h(x, y) 0 g(x, y) d 0 x L d x d xU
(P1)
x Rn y {0.1} m
Where: C is the economic objective function (Eq. 4); CO2eLC are the life cycle greenhouse emissions (Eq. 3); x and y are continuous and binary variables; superscripts L and U indicates lower and upper bounds on the continuous variables. Pressures and temperatures of high, medium and low-pressure steam headers, deaerator pressure and letdowns flow rates are the continuous optimization variables, a subset of vector x. Binary variables y represent discrete decisions that allow the selection of alternative pumps drivers such as steam turbines and electrical motors and whether the boilers and their corresponding feed pumps and air fans are on or off. Equality constraints h(x,y) represent the steady state modeling of the utility plant, including mass, energy balances and steam properties prediction such as entropy and enthalpy. Inequality constraints g(x,y) represent minimum and maximum equipment capacities, logical constraints, operating and design constraints. The multiobjective (MO) optimization is a system analysis approach to problems with conflictive objectives, a key factor of MO optimization is that rarely exist a single solution that simultaneously optimizes all the objectives. In its place, there is a set of non-inferior solutions where one objective cannot be improved except at expense of another (Ciric et al, 1993). This set of compromise solution corresponds to a set of feasible solutions, generally referred as non-inferior or Pareto optimal solutions.
Minimization of Life Cycle Greenhouse Emissions and Cost in the Operation of Steam and Power Plants
1111
5. Improvements achieved in the operation of the steam and power plant A wide variety of multiple objectives techniques exist, a review can be seen in Alves et al (2007). The general approach consists in converting the multiple objectives into a single objective. The numerical results presented in this section have been calculated using as the objective function in problem P1 the sum of CO2eLC emissions (Eq. 3) and the economic objective (Eq. 4) as follows: EnvEco
CO 2e LC C
(5)
The greenhouse emissions evaluated are CO2, N2O and CH4. The numerical results correspond to the steam and power sector of an ethylene plant. The MINLP problem P1 is formulated and solved in GAMS (Brooke et al, 2003) using DICOPT as an outerapproximation algorithm, CONOPT algorithm to solve NLP sub problems and CEPLEX algorithm to solve MILP sub problems. Problem P1 was solved in three major iterations and a CPU time of 0.56 sec in a Pentium IV (1GHz). The main numerical results on each summand of the objective function EnvEco are reported in Table 1. The reductions achieved simultaneously are 13 % in CO2eLC emissions and 18% in operating cost. Due to an income in CO2eLC emission trade of 14 %, the total improvement in the economic performance reaches a 32 % with respect to the initial cost. Table 1. Improvements reached selecting the operating conditions.
Objectives CO2eLC Operating Cost CO2eLC Income Economic (C )
Units Kg CO2 eq./h U$S/hr U$S/hr U$S/hr
Initial point 33643.383 981.043 0.000 981.043
Solution point 29290.5500 803.0862 139.2906 663.7956
Improvement % 12.942 18.140 14.200 32.340
The improvements reported in Table 1 have been achieved selecting the continuous and binary operating conditions of the utility system. Most of the alternative drivers that were electrical motors at the initial point have been switched to steam turbines at the solution point. This is due to the fact that the ratio of CO2eLC emissions per KW and cost are much smaller in the utility plant than in the imported electricity. The solutions minimizing CO2eLC and cost separately are similar, having a difference in the order of 0.1 % in the respective objective functions. On the other hand minimizing CO2eUP (greenhouse emissions of the utility plant only) and cost separately, the solutions differ in the order of 10 %. These numerical results indicate that when life cycle boundaries are properly defined, environmental and economic objectives like CO2e emissions and operating cost are not necessarily conflictive ones, while if the battery limits are used these objectives are likely to render different results. Thus, a key issue when using simultaneously environmental and economic objectives is to define properly the system boundaries, as has been shown in the steam and power sector of an ethylene plant analyzed. The strategy presented can be applied to different steam and power plants. These utility plants are a very important sector of petrochemical plants basically due to the high consumption of non renewable fossil fuels and the combustion emissions generated in boilers.
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6. Conclusions An strategy to select the operating conditions of steam and power plants minimizing greenhouse emissions and cost simultaneously has been presented, solving a mixed integer nonlinear programming problem in GAMS. Significant reductions in the environomic objective can be achieved as shown in Table 1, reducing 13 % the greenhouse emissions, 18 % the operating cost and an additional 14 % due to CO2e emissions trade income that improves the economic objective in more than 30 %. Thus a significant improvement is achieved selecting the operating conditions of the utility sector. A proper definition of the life cycle limits is a relevant issue in process optimization when environomic objectives are considered. The numerical results show that objectives like the minimization of greenhouse emissions and cost are not necessarily conflictive ones when the life cycle limits are properly defined.
References A. Azapagic and R. Clift, 1999, The application of life cycle assessment to process optimization, Com. & Chem. Eng., 23, 1509-1526. A. Brooke, D. Kendrick, A. Meeraus, R. Raman (eds.), 2003, GAMS, A user guide, GAMS Development Corporation, Washington DC. A. Ciric and S. Huchette, 1993, Multiobjective Optimization Approach to Sensitivity Analysis: Waste Treatment Costs in Discrete process Synthesis and Optimization problems, Ind. Eng. Chem. Res., 32, 2636-2646. A. Eliceche and P. Martinez, 2007a, Minimization of life cycle CO2 emissions in the operation of a steam and power plant, ESCAPE17, V. Plesu and P.S. Agachi (Editors). A. Eliceche, S. Corvalan, P. Martinez, 2007b, Environmental life cycle impact as a tool for process optimization of a utility plant, Comp.& Chem. Eng., 31, 648-656. D. Weisser, 2007, A guide to life-cycle greenhouse gas (GHG) emissions from electric supply technologies, Energy, 32, 1553-1559. Energy Information Administration, 2003, Annual energy review. US Department of Energy. Washington, DC, USA. Available from http://www.eia.doe.gov/emeu/aer/contents.html. H. Hashim, P. Douglas, A. Elkamel and E. Croiset, 2005, Optimization Model for Energy planing with CO2 Emission Consideration, Ind. Eng. Chem. Res., 44, 879-890. J. Guinée, R. Heijungs, G. Huppes , R. Kleijn, A. Koning, L. van Oers, A. Sleeswijk, S. Suh, H. Udo de Haes (eds.), 2002, Handbook on Life Cycle Assessment. Operational Guide to the ISO Standards. Kluwer Academic Publishers, Dordrecht. M. Alves and J. Climaco, 2007, A review of interactive methods for multiobjective integer and mixed-integer programming, European J. of Operatinal Research, 180, 99-115. M. Dantus and K. High, 1999, Evaluation of waste minimization alternatives under uncertainty: a multiobjective optimization approach, Comp. and Chem. Eng., 23, 1493-1508. National Greenhouse Gases Inventory, 2005, Inventario Nacional de Gases de efecto Invernadero de la Republica Argentina, Fundacion Bariloche, Argentina. R. Dones, T. Heck and S. Hirschberg, 2004, Greenhouse gas emissions from energy systems, comparison and overview, Encyclopedia Energy, 3, 77-95. U.S. Environmental Protection Agency, 1998, AP-42, Compilation of air pollutant emission factors, fifth edition, North Carolina.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Developing A Lake Eutrophication Model And Determining Biogeochemical Parameters: A Large Scale Parameter Estimation Problem Vanina Estrada a, Elisa R. Parodi b, M. Soledad Diaza a
Planta Piloto de Ingeniería Química (PLAPIQUI), Universidad Nacional del SurCONICET b Instituto Argentino de Oceanografía ( IADO), Universidad Nacional del Sur-CONICET Camino La Carrindanga Km 7, Bahía Blanca 8000, Argentina.
Abstract This work addresses the dynamic parameter estimation problem for an eutrophication model, which is formulated within a simultaneous approach. Ecological processes are modeled through a set of complex nonlinear differential algebraic equations, with rate coefficients that must be estimated. Gradients of state variables are considered along the water column, rendering a partial differential equation problem, which is transformed into a differential algebraic (DAE) one by spatial discretization in several water layers. Within a simultaneous approach, the DAE constrained optimization problem is transformed into a large-scale nonlinear programming problem. Main biochemical and chemical parameters have been obtained, which allow a close representation of the lake dynamics. Keywords: Parameter estimation, eutrophication model, phytoplankton, nutrients. 1. Introduction The increasing download of nutrients into lakes, rivers and costal zones throughout the world, mainly due to agricultural and industrial activities, have intensified eutrophication of water bodies, which has in turn increased the need for predictive ecological water quality modeling. Eutrophication models provide a representation of major physical, chemical and biological processes that affect the biomass of phytoplankton and nutrients. They represent ecological processes through a set of complex nonlinear differential algebraic equations, with rate coefficients that require an estimation to suit site-specific environment. Therefore, the first step in the development of an eutrophication model is to solve a dynamic parameter estimation problem. This problem has been addressed through different approaches. Zhang et al. (2004) have proposed a sequential procedure to determine phytoplankton and zooplankton parameters using exergy as the objective function and calibrating both physical and chemical parameters by trial and error. Shen and Kuo (1998) used the variational method for estimating unknown kinetic parameters. More recently, Shen (2006) proposed a least-squares objective function and the resolution of the dynamic parameter estimation problem through the application of a modified Gauss-Newton method. In this work, we formulate a parameter estimation problem with a weighted leastsquares objective function subject to a large-scale partial differential algebraic equations model resulting from temporal and spatial dynamic mass balances in the major groups of phytoplankton community (cyanobacteria, diatoms and chlorophyta), key nutrients in
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the eutrophication, biochemical demand of oxigen and dissolved oxygen. Algebraic equations represent profiles for temperature, solar radiation and river inflows, in addition to the calculation of most factors that affect rate equations, such as effect of solar radiation, temperature, nutrients, etc. The PDE is transformed into an ordinary differential equation system by spatially discretizing it into sets of ordinary differentialalgebraic equations (DAE) (Rodriguez and Diaz, 2007). The DAE optimization problem is solved with a simultaneous approach. The present study has been performed on Paso de las Piedras Reservoir, which supplies drinking water for two cities in Argentina. The discretized NLP problem has been solved with a reduced Successive Quadratic Programming algorithm (Biegler et al., 2002). Numerical results show good agreement with values from the literature. The model is currently being validated with recently obtained additional data from the lake.
2. Study area and input data Paso de las Piedras Reservoir is located in the south of Buenos Aires Province (Argentina) at 38° 22´ S and 61° 12´ W. It was built to supply drinking water to Bahía Blanca and Punta Alta (cities whose population is above 400,000 inhabitants) and for industrial purposes at a petrochemical complex nearby. The lake has two tributaries: El Divisorio and Sauce Grande River. The lake has a coastline perimeter of 60 kilometers and a mean depth of 8.2meter. Biological and chemical data have been weekly collected from January to December 2004 at four sampling stations. Biological qualitative and quantitative determinations have been carried out, as well as physicochemical ones, that Secchi depth
3.E+05 2.E+05
Depth (m)
(cellml -1)
Concentration
Phytoplankton
2.E+05 1.E+05 5.E+04 0.E+00
0
100
200
300
400
3.5 3 2.5 2 1.5 1 0.5 0
2
Time (days)
46 84 125 231 280 327 365 Time (Days)
Figure 2. Measured Secchi disk depth (eutrophic state between 1 and 3 m)
1000
25
800
20
600
15
400
10
200
5
0
0 30
90
150
210
270
330
Time (Days)
Figure 3. Temperature (qC) and solar radiation (lyd-1) versus time.
Temperature (oC)
Solar radiation ( lyd-1)
Figure 1. Measured phytoplankton concentr. and eutrophication limit (5000 cell/ml)
Developing a Lake Eutrophication Model and Determining Biogeochemical Parameters: A Large Scale Parameter Estimation Problem
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include concentrations of nitrate, ammonium, organic nitrogen, phosphate, organic phosphorus, dissolved oxygen and biochemical demand of oxygen, water temperature, pH and depth of Secchi disk (depth at which the disk can be seen from outside the water body). The high content of phosphorus and nitrogen in Paso de las Piedras Reservoir is consequence of agricultural activities. The trophic level of this water body is currently eutrophic (Parodi et al., 2004), as it can be clearly seen in Figs. 1 and 2. These figures show measured concentration profiles for phytoplankton and Secchi disk depth as related to the levels beyond which the water body is considered eutrophic (horizontal lines that correspond to 5000 cells/ml and 3 m, for phytoplankton concentration and Secchi disk depth) Input requirements for the model are of four types. These are descriptive data for the lake itself, hydrodynamic forcing data (primarily meteorological, as temperature and solar radiation, and inflow and outflow profiles data), water quality known parameters, phytoplankton and nutrients profiles and initial conditions for all the modeled variables. High frequency sampling is required to properly describe the dynamics of the lake. The external forcing functions, such as temperature and solar radiation were approximated with polynomial functions (r2=0.98 and 0.94, respectively), as shown in Fig. 3. River inflows and associated nutrient loading., as well as outflow data have also been approximated with polynomials.
3. Dynamic Parameter Estimation Problem Eutrophication models comprise large sets of complex differential algebraic systems of equations (DAE). Therefore, the associated parameter estimation problem is formulated as a large-scale DAE-constrained optimization problem. Partial differential equations arise from dynamic mass balances for each state variable. Main simplifying hypothesis are: constant transversal area in the lake, constant water density, phosphorus as limiting nutrient and horizontally averaged concentrations. In this way, only gradients along the water column height are considered. To transform partial differential equations system into an ordinary differential equations one, the column height is discretized into two layers, according to the available data. Data at different depths are currently being collected to develop a model with a higher number of water layers. In most eutrophication models, the different types of phytoplankton are lumped within one state variable, however, we have considered three state variables corresponding to diatoms, chlorophytes and cyanobacteria, because it is important to know the proportion in which they are present in an algal bloom, to determine the potential damage they can produce in the water drinking resource. The remaining state variables correspond to concentrations of main nutrients (nitrate, nitrite, ammonium, organic nitrogen, phosphate, organic phosphorus), dissolved oxygen and biochemical demand of oxygen. Dynamic mass balances in each spatial layer include component inputs from tributaries, outputs for both potabilization and industrial purposes, generation and consumption, and transference between layers, also accounting for lake volume variability (through upper layer height variability). Estimated parameters are included within the generation/consumption terms. The three phytoplankton groups differ in their maximum growth rates, nitrogen and phosphorus kinetics and light requirements. Algebraic equations stand for profiles in temperature, solar radiation and river inflows. Additional equations have been written for the calculation of each component generation and consumption. The objective function is a weighted least squares one.
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The resulting DAE constrained optimization problem is formulated within a simultaneous dynamic optimization approach, in which the DAE system is transformed into a large nonlinear programming (NLP) problem by representing state variables profiles by polynomial functions over finite elements in time. The NLP is then solved with an efficient reduced successive quadratic programming (rSQP) algorithm within program IPOPT (Biegler et al., 2002). Mass balances for horizontal layers Upper layer
dCUj
NIN QIN U,k
¦
dt
k 1 VU
C NOUT QOUT U C r - kdA (C C ) Uj dhU Uj Uj Uj Lj V ǻhU hU hU dt U m 1
CIN Ujk ¦
Lower layer
dC Lj
NOUT QOUTL
¦
dt
m 1
VL
C Lj rLj
C Lj dh L kdA (C Lj CU,j ) Lower layer ǻh L h L h L dt
Rate equations for phytoplankton (rij; i=upper, lower layer: j= cyanobacteria, diatoms, cyanophytas)
rij
Rij,growth-Rij,resp-Rij,death-Rij,sedim
Rij,growth
f(T)
k j,growth*f(T)*f(I)*f(N)* Cij
Temp Temp exp( 1 ) Tempj Tempj
Rij,resp
k j,resp*Cij Rij,death
I Ii exp (1 ) Ij Ij
f(I)
k j,death*Cij
f(N )
CiPO 4 CiPO 4 kpj
Rij,sedim
k j,sedim*
Rate equations for phosphate (rij; i=upper, lower layer: j=phosphate)
rij
Rij,death Rij,miner -Rij,uptake
Rij,death
3
¦ m 1
(apc * k m,death * (1 f po ) * C im ) 3
Rij,miner
k miner * T miner * exp(Temp - 20) *
¦ Cim * CiOP
m 1
3
km pc ¦ C im j 1
Rij,uptake
3
¦ (Rim ,growth * a pc * Cim )
m 1
Rate equations for nitrate (rij; i=upper, lower layer: j=nitrate)
rij
Rij,nitri Rij,uptake - Rij,denitr
1 *C hi ij
Developing a Lake Eutrophication Model and Determining Biogeochemical Parameters: A Large Scale Parameter Estimation Problem
Rij,nitri
Rij,denitr Rij,uptake
1117
CiNH4 * CiDO k nio CiDO C * kno 3 k denitr * T denitr * exp( Temp 20 ) iNO 3 kno 3 C iDO 3 ¦ ( anc * Rim,growth * ( 1 PNH 4 )*Cim ))
k nitri * T nitri * exp( Temp 20 ) *
m 1
Additional rate equations have been written for the remaining components. Parameters of the model are of three types: kinetic, stoichiometric and physical.
4. Discussion of Results The resulting parameter estimation problem to determine the values of nine parameters in the Paso de las Piedras eutrophication model has twenty differential equations and fifty algebraic ones, after spatial discretization in two layers. Currently available weekly measurements of concentrations at two water levels (water surface and outflow level, at six meters depth) have rendered this discretization. A time horizon of 365 days has been considered to account for a complete annual cycle. The resulting nonlinear programming (NLP) problem for forty elements and three collocation points has 10432 nonlinear equations. It has been solved with an Interior Point method with reduced Successive Quadratic Programming (rSQP) techniques within program IPOPT (Biegler et al., 2002; Raghunathan et al., 2004), in which successive parametric NLP subproblems are solved for decreasing values of the barrier parameter. Initial barrier parameter value has been 0.01. Estimated parameters are shown in Table 3. Their values give state variables profiles which are in agreement with data from the lake. Figure 3 shows cyanobacteria, diatoms, nitrate and phosphate profiles as compared to experimental data for an entire cycle of 365 days. Table 3. Optimal parameter set for eutrophication model Symbol Description kC,growth Max growth of cyanobacteria (d-1) IC Optimal growth radiation of cyano (lyd-1) Max growth of diatoms (d-1) kD,growth Optimal growth radiation of diatoms (lyd-1) ID Max growth of chlorophytes (d-1) KG,growth Optimal growth radiation chlorophytes (lyd-1) IG Rate coeff. mineralization ON(d-1) kON,miner Rate coeff. mineralization OP(d-1) kOP,miner Half-sat. conc. for oxygen lim. of nitrification (mgl-1) knio
Calibrated value 0.210 109.9 0.405 24.52 0.654 89.74 0.0922 0.0149 0.3430
5. Conclusions The parameter estimation problem for an eutrophication model has been solved with a simultaneous dynamic approach. To our knowledge, these rigorous models have not been solved with advanced dynamic optimization techniques. A large number of biological parameters has been determined, based on weekly measurements throughout 2004. No data reconciliation has been required at this stage. Currently, more detailed data are being obtained at different water levels to formulate a more detailed model.
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Once validated, the dynamic optimization model will be run to determine optimal profiles for nutrient inputs to establish remediation policies.
2 1.5 1 0.5 0 0
100
200
300
400
Concentration (mgCl -1)
Diatoms
-1
Concentration (mgCl )
Cyanobacteria
1.5 1 0.5 0 0
100
Time (days)
2.5 2 1.5 1 0.5 0 100
200 Time (days)
300
400
300
400
Phosphate Concentration (mgCl-1)
Concentration (mgCl -1)
Nitrate
0
200 Time (days)
300
0.6 0.5 0.4 0.3 0.2 0.1 0 0
100
200 Time (days)
Figure 3. Experimental data and simulated profiles (continuous line) with estimated parameters
References Biegler, L.T., A. Cervantes, A.Waechter , 2002; Advances in simultaneous strategies for dynamic process optimization. Chem. Eng. Sci. 57: 575-593. Estrada, V., E.R. Parodi, M.S. Diaz, Ecological studies and dynamic parameter estimation for eutrophication models, ECCE-6, Denmark, September 2007. Parodi, E.R., V. Estrada, N. Trobbiani, G. Argañaraz Bonini, 2004, Análisis del estado trófico del Embalse Paso de las Piedras (Buenos Aires, Argentina). Ecología en tiempos de Cambio. 178. Raghunathan, A., M.S. Diaz, L.T. Biegler, 2004, An MPEC formulation for dynamic optimization of distillation operations, Comp. & Chem. Eng., 28, 2037. Rodriguez, M., M.S. Diaz, 2007, Dynamic modelling and optimisation of cryogenic systems, Applied Thermal Engineering, 27, 1182-1190. Shen, J., Kuo, A.Y., 1998, Application of inverse model to calibrate estuarine eutrophication model. J. Environ. Eng. 124 (5), 409–418. Shen, J., 2006, Optimal estimation of parameters for aestuarine eutrophication model, Ecol. Model. 191, 521–537. Zhang, J.J., S.E. Jorgensen, H. Mahler, 2004, Examination of structurally dynamic eutrophication model. Ecol. Model. 173, 313–333.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Computer Aided Design of Occupationally Healthier Processes Mimi H. Hassim, Markku Hurme Helsinki University of Technology, P.O. Box 6100, FIN-02015 TKK, Finland
Abstract Computer aided approaches for assessing inherent occupational health hazards and ranking process concepts based on their health properties were developed for the first stages of a process lifecycle; the process development, preliminary design, and basic engineering steps. The methods are tailored to the process design lifecycle steps in terms of their principle and information requirement. The methods can be integrated with existing computer aided design tools as described. A case study is given to illustrate the approach. Keywords: occupational health evaluation, CAPE, process development and design.
1. Introduction Occupational health concerns with the two-way relationship between work and health. Each year, more people die from diseases caused by work than are killed in industrial accidents. Still unlike in process safety, there are only a very limited number of methods available for evaluating occupational health hazards during the chemical process design (Hassim and Edwards, 2006). Such computer aided methods are clearly needed as most of design work is done by using CAPE tools now.
2. Assessment stages Although inherent occupational health concept can be applied throughout the process lifecycle, the opportunity of implementation decreases as the design proceeds. Basic engineering is the last step to make the changes at a moderate cost. The aim of this research has been to develop a set of occupational health assessment methods for the three early stages of a process lifecycle; 1) process research and development (R&D), 2) preliminary process design and 3) basic engineering. These stages differ in terms of the type and extent of information available (see Table 1). This will eventually affect the assessment procedure as well as the accuracy of the results. At later stages, a more comprehensive assessment is possible due to the better availability of process information.
3. Approaches to Occupational Health Assessment The methods developed for evaluating occupational health properties of process alternatives are described in the following. 3.1. Process R&D Stage For process R&D a qualitative index-based method, called the Inherent Occupational Health Index (IOHI) was developed (Hassim, et al., 2006). The method is reaction steporiented. Therefore a whole reaction step is considered as one entity (see Fig.1). Only chemical and health properties and reaction operating conditions are used in the index, because of their availability and their ability to represent the inherent occupational
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health hazards in the R&D stage. The main objective of the method is to rank alternative chemical process routes for the production of the desired product. The required information are the chemicals present, their chemical properties (boiling point (Iv), toxicity, corrosiveness (IC) and phase (IMS)), the pressure (IP), temperature (IT) and the mode (IPM), e.g. batch mode of the main process item (typically reactor). The IOHI consists of two parts; the Index for Physical and Process Hazards (IPPH) and the Index for Health Hazards (IHH). The IPPH represents process related physical hazards. The IHH is evaluating acute and chronic toxicity hazards by considering the exposure limits (IEL) and R-phrases (IR) of the compounds present. The eight evaluation factors were selected based upon their availability in this phase of design. In the method each factor is assigned with a set of penalty; a higher penalty indicates a higher hazard posed by the factor. The sum of the two scores is the IOHI index value (Hassim, et al., 2006). Table 1. Information Availability at Different Process Design Stages Stage:
R&D
Process predesign
Basic engineering
Information available:
Reaction steps Type of chemicals Physical/chemical/ toxicity properties
All in Stage 1 Flowsheet Mass/energy balances
Process conditions Product yield
Unit operations
All in Stage 1 and 2 P&I diagram Equipment, instrumentation, piping details Process layout Manual working procedures
3.2. Flowsheet Stage A more detailed method, called the Health Index (HI), is proposed for assessment in the predesign phase. This semi-quantitative method is capable of both ranking process options and indicating the presence of chronic health risks due to chemical exposures from fugitive airborne emissions. The fugitive emissions are mainly due to leaks in process components such as valves, flanges and pump seals. Since the mechanical details of the process in this design stage are still unknown, the index utilizes precalculated standard process modules for fugitive emissions. The standard process modules represent typical operations in chemical plants such as distillation, flash, reactors, absorption etc. systems (see Fig. 1). The fugitive emission rates for the modules were created by evaluating the number of leak sources in these operations by studying typical piping and instrumentation diagrams (PID) of the sub processes. To implement the HI method, the information needed are process flow diagrams (PFDs), chemical exposure limits, vapor pressures, phases and concentrations of the compounds present in the process. The main task in HI method is to estimate the chemical exposure concentrations. It involves two steps: The fugitive emission rates (FE) are calculated from the standard process modules present. This is then combined with data on typical process layout dimensions and typical wind speed to evaluate the air volume flow rate (Q) and concentrations (C) of the most hazardous chemicals in air (see Section 4.2). The concentrations are then compared to acceptable exposure limits (EL) such as threshold limit values both as individual chemicals and a chemicals mixture. The higher the estimated exposure value is compared to the limit value, the greater the risk from chemical exposure. HI evaluates only the risks from chronic exposures of airborne emissions. It is a non additive-type index unlike the IOHI.
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3.3. PID Stage The Occupational Health Index (OHI) method developed for the PID stage is an extension of the HI method presented earlier for the flowsheet stage. OHI covers both chronic and acute exposures, whereas HI assessed only chronic inhalation based exposures. In OHI chronic exposures, the non-carcinogenic and carcinogenic risks are assessed separately. The assessment of acute and dermal exposures from manual operations is also done. Consequently there are four different sub indices in the method. One of the subindices is the HI for chronic airborne exposures but it is evaluated in more exact way than in flowsheeting stage. It is now based on the calculation of fugitive emissions by considering pipe and equipment details from PID's and 3D plans (Fig. 1). OHI can be used as a more quantitative health risk assessment tool during detailed process design phase. It aims to assess the occupational health hazards of process concepts rather than only to rank process options by their risk level as the Stage 1 and 2 methods. The aim is also to highlight the main health hazards of each process concept. Therefore by using OHI the process design can be improved based on the index values evaluated. d
CH2 = CH2
propionaldehyde
CO, H2
1) R&D stage 2) PFD stage 3) PID stage a
c b
heavy ends Figure 1. Utilization of Evaluation Levels on the Different Stage Methods in the Case Study Process; 1) process step at R&D stage, 2) standard modules of the predesign stage, 3) piping details at basic engineering stage (a=reactor, b=flash, c=distillation system, d=compressor)
4. Case Study To depict the method, a case study is presented. The case study selected is the first sub process in the ethylene via propionaldehyde based route for methyl methacrylate (MMA) production (Fig. 1). Ethylene, carbon monoxide and hydrogen are reacted to produce propionaldehyde (Eq. 1). The reaction takes place at 100 °C and 15 bar. CH2 = CH2 + CO + H2 Æ CH3CH2CHO
(1)
4.1. Process R&D Stage The IOHI is calculated based on the properties of chemicals, process conditions and a process block diagram. The process is divided into main, typically reaction steps (see Fig. 1). The reaction operating conditions determine the process mode, temperature and pressure sub indices. Sub indices values for the other factors (such as volatility etc.) are
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taken as the worst values in the reaction step. The sub index evaluation tables are presented by Hassim et al. (2006). The results below show that the sub process falls under 'moderate risk' category: IPPH = IPM + IP + IT + Max(IMS) + Max(IV) + Max(IC) = 1 + 1 + 1 + 2 + 3 + 0 = 8
(2)
IHH = Max(IEL) + Max(IR) = 2 + 4 = 6
(3)
IOHI = IPPH + IHH = 8 + 6 = 14
(4)
4.2. Flowsheet Stage In the Health Index method the fugitive emissions are evaluated based on sub process module data. Therefore the process is represented as standard process modules (see Section 3.2 and Fig. 1). Based on the chemical composition and vapor pressure data, service type of each module stream is classified as light liquid, heavy liquid or gas service. If the stream is in liquid phase and it contains mostly highly volatile chemicals, it is light liquid service. Other liquids fall under the category of heavy liquid service. The fugitive emissions of the streams are then estimated based on EPA average emission factors. The most hazardous chemical in each stream is determined; that is the major component that has the lowest emission limit value. The emission stream rates which have the same dominant chemical are totaled up. Then, the volumetric wind rate within the sub process is estimated based on average wind speed, a typical floor area and height of the each module. The emission concentrations in air are calculated from emission rates and volumetric air rate. Finally; the HI for individual chemical (HIi) is estimated by comparing the concentration in air to the respective exposure limit value, EL (Table 2). The HI for chemical mixture (HImix) is also calculated, assuming that the chemicals have additive effects (worst-case scenario). Since the HI index value in Table 2 < 1, the risk from chronic airborne emissions is absent. 4.3. PID Stage The main principle of estimating the risk of chronic inhalative exposures is similar as in the flowsheet stage. However, real emission source data, e.g. number of flanges from PID (see Fig.1) and 3D plans are used instead of typical module values. Also knowledge on the type of leak source (e.g. pump shaft with single mechanical seal) is used instead of the average values (e.g. 'typical' pump seal) due to the more detailed information available at this stage. In the case study, there is no carcinogen present so only non-carcinogenic risk is assessed. To analyze acute inhalation and dermal exposures the manual operations are identified. In the sub process, a manual sampling point exists in the top product stream of the distillation column. It may pose a source of acute inhalative or dermal exposure during sampling. The risk of acute inhalation exposure is estimated based on the comparison between the chemical’s vapor equilibrium concentration at 20 oC (Ceq) with its shortterm (15 min) exposure limit value (EL). The index can be calculated both for individual chemicals and mixture of chemicals (Table 4). Index value greater than 5000 indicates a dangerous condition (Lipton and Lynch, 1994). Eye and dermal exposures are also evaluated. In the acute exposure source (sampling point), only propionaldehyde may cause irritation to eye and skin, as indicated by its Rphrases (R36 and R38). R36 and R38 fall under the group of low toxicity. Based on a qualitative assessment using a matrix concept, risk of dermal and eye exposure to propionaldehyde in this sub process is minor but present.
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As a summary the calculations reveal that the results in PID stage (Table 3) are somewhat lower than those obtained by using the average emission factors in the flowsheeting stage (Table 2). It can be seen that chronic non-carcinogenic risks are absent (Table 3). There is neither carcinogenic risk. The risk of acute inhalation is present (Table 4) due to propionaldehyde, as well as the minor but existing risk to eye and dermal exposures. Table 2. Calculating the HI for Flowsheet Stage Chemical Carbon monoxide Propionaldehyde
FE mg/s 148 399
Q m3/s 621
C mg/m3 0.24 0.64
EL mg/m3 35 46
HIi
HImix
Risks present?
0.007 0.014
0.021
Absent (
