Computer Aided Process and Product Engineering (CAPE)

CAPE Edited by Luis Puigianer and Georges Heyen

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ISBN 3-527-30831-8

Kai Sundmacher, Achim Kienle (Eds.)

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CAPE Computer Aided Process and Product Engineering Edited by Luis Puigjaner and Ceorges Heyen

WILEYVCH

WILEY-VCH Verlag CmbH & Co. KGaA

The Editors

Professor Dr. Luis Puigjaner Universitat Politechnica de Catalunya Chemical Engineering Department ESTEIB, Av. Diagonal 647 08028 Barcelona Spain Professor Dr. Georges Heyen Laboratoire d’Analyse et Synthese des Systemes Chimiques Universitk de Liege Sart Tilman B6A 4000 Liege Belgium

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the British Library. Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.

0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form - nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Typesetting Mittemeger & Partner, Plankstadt Printing betz-druck GmbH, Darmstadt Binding Litges & Dopf GmbH, Heppenheim Cover Design 4t Mattes + Traut, Werbeagentur

GmbH, Darmstadt

Printed in the Federal Republic of Germany Printed on acid-free paper ISBN-13

978-3-527-30804-0

ISBN-lo 3-527-30804-0

I"

Table of Contents Preface X I I I Foreword X X I List of Contributors XXV

Volume 1 1

Introduction 1

Section 1 Computer-aided Modeling and Simulation 1

Large-ScaleAlgebraic Systems

15

Cuido 5uzzi Ferraris and Davide Manca

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 2

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Introduction 15 Convergence Tests 17 Substitution Methods 20 Gradient Method (Steepest Descent) 20 Newton's Method 21 Modified Newton's Methods 24 Quasi-Newton Methods 27 Large and Sparse Systems 28 Stop Criteria 30 Bounds, Constraints, and Discontinuities 30 Continuation Methods 31 Distributed Dynamic Models and Computational Fluid Dynamics 35 Young-il Lim and Sten 5ayJmrgensen Introduction 35 Partial Differential Equations 35

Method of Lines 40 Fully Discretized Method 58 Advanced Numerical Methods 68 Applications 75 Process Model and Computational Fluid Dynamics 98 Discussion and Conclusion 102

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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Molecular Modeling for Physical Property Prediction Vincent Gerbaud and XavierJoulia

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Introduction 107 What is Molecular Modeling? 108 Statistical Thermodynamic Background 112 Numerical Sampling Techniques 175 Interaction Energy 121 Running the Simulations 124 Applications 125 Conclusions 132

4

Modeling Frameworks o f Complex Separation Systems 137 Michael C. Ceorgiadis, Eustathios 5. Kikkinides, and Margaritis Kostoglou

4.1 4.2

Introduction 137 A Modeling Framework for Adsorption-Diffusion-based Gas Separation Processes 138 Modeling of PSA Processes in gPROMS 148 Efficient Modeling of Crystallization Processes 149 Modeling of Grinding Processes 1GO Concluding Remarks 1GG

4.3 4.4 4.5 4.6 5

Model Tuning, Discrimination, and Verification Katalin M. Hangos and Rozalia Lakner

5.1 5.2 5.3

Introduction 171 The Components and Structure of Process Models Model Discrimination: Model Comparison and Model Transformations 174 Model Tuning 179 Model Verification 183

5.4 5.5

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Multiscale Process Modeling 189 Ian T: Cameron, Gordon D. Ingram, and Katalin M. Hangos

6.1 6.2 6.3 6.4 6.5

Introduction 189 Multiscale Nature of Process and Product Engineering 189 Modeling in Multiscale Systems 193 Multiscale Model Integration and Solution 203 Future Challenges 218

7

Towards Understandingthe Role and Function o f Regulatory Networks in Microorganisms 223 Krist V. Gernaey, Morten Lind, and Sten BayJmrgensen

7.1 7.2 7.3 7.4 7.5 7.6

Introduction 223 Central Dogma of Biology 228 Complexity of Regulatory Networks 229 Methods for Mapping the Complexity of Regulatory Networks 236 Towards Understanding the Complexity of Microbial Systems 247 Discussion and Conclusions 259

Section z Computer-aided Process and Product Design

1

Synthesis of Separation Processes 269 Petros Proios, Michael C. Georgiadis, and €$ratios

1.1 1.2 1.3 1.4 1.5

Introduction 269 Synthesis of Simple Distillation Column Sequences 272 Synthesis of Heat-integrated Distillation Column Sequences 279 Synthesis of Complex Distillation Column Sequences 285 Conclusions 292

2

Process Intensification 297 Patrick Linke, Antonis Kokossis, and Albert0 A h - A r g a e z

2.1 2.2 2.3 2.4

Introduction 297 Process Intensification Technologies 299 Computer-Aided Methods for Process Intensification 303 Concluding Remarks 324

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Computer-aided Integration of Utility Systems Franqois Marechal and Boris Kalituentzef

3.1 3.2 3.3 3.4 3.5

Introduction 327 Methodology for Designing Integrated Utility Systems 330 The Energy Conversion Technologies Database 334 Graphical Representations 339 Solving the Energy Conversion Problem Using Mathematical Programming 349 Solving Multiperiod Problems 367 Example 369 Conclusions 379

3.6 3.7 3.8

N. Pistikopoulos

327

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Equipment and Process Design 383 1. David, L. Bogle, and B. Eric Ydstie

4.1 4.2 4.3 4.4 4.5 4.6

Introduction 384 The Structure of Process Models 384 Model Development 390 Computer-aided Process Modeling and Design Tools 390 Introduction to the Case Studies 393 Conclusions 416

5

Product Development 419 Andrzej Kraslawski

5.1 5.2 5.3 5.4

Background 419 Definition Phase 424 Product Design 431 Summary 439

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Section 3 Computer-aided Process Operation 1

Resource Planning 447 Michael C. Georgiadis and Panagiotis Tsiakis

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

Introduction 447 Planning in the Process Industries 448 Planning for New Product Development 460 Tactical Planning 462 Resource Planning in the Power Market and Construction Projects 465 Solution Approaches to the Planning Problem 469 Software Tools €or the Resource Planning Problem 472 Conclusions 474

2

Production Scheduling 481 Nilay Shah

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12

Introduction 481 The Single-Site Production Scheduling Problem 483 HeuristicslMetaheuristics: Specific Processes 487 Heuristics/Metaheuristics: General Processes 488 Mathematical Programming: Specific Processes 489 Mathematical Programming: Multipurpose Plants 493 Hybrid Solution Approaches 500 Combined Scheduling and Process Operation 501 Uncertainty in Planning and Scheduling 502 Industrial Applications of Planning and Scheduling 506 New Application Domains 508 Conclusions and Future Challenges 509

3

Process Monitoring and Data Reconciliation 517 Ceorges Heyen and Boris Kalitventzef

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

Introduction 517 Introductory Concepts for Validation of Plant Data Formulation 520 Software Solution 527 Integration in the Process Decision Chain 527 Optimal Design of Measurement System 528 An Example 534 Conclusions 538

4

Model-based Control 541 Sebastian Engell, Cregor Fernholz, Weihua Cao, and Abdelaziz Toumi

4.1 4.2 4.3

Introduction 541 NMPC Applied to a Semibatch Reactive Distillation Process 543 Control of Batch Chromatography Using Online Model-based Optimization 552

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4.4 4.5 4.6

Control by Measurement-based Online Optimization 556 Nonlinear Model-based Control of a Reactive Simulated Moving Bed (SMB) Process 565 Conclusions 572

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Real Time Optimization 577 Vivek Dua, John D. Perkins, and Efstratios N. Pistikopoulos

5.1

Introduction 577 Parametric Programming 578 Parametric Control 581 Hybrid Systems 584 Concluding Remarks 589

5.2 5.3 5.4

5.5 6

6.1 6.2 6.3 6.4 6.5 6.6

Batch and Hybrid Processes 591 Luis Puigjaner andlavier Romero

Introduction 591

The Flexible Recipe Concept 597 The Flexible Recipe Model 601

Flexible Recipe Model for Recipe Initialization 602 Flexible Recipe Model for Recipe Correction 610 Final Considerations 617 621

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Supply Chain Management and Optimization Lazaros C. Papageorgiou

7.1 7.2 7.3 7.4 7.5 7.6 7.7

Introduction 621 Key Features of Supply Chain Management 623 Supply Chain Design and Planning 624 Analysis of Supply Chain Policies 630 Multienterprise Supply Chains 635 Software Tools for Supply Chain Management 637 Future Challenges 639

Section 4 Computer-integratedApproaches in CAPE 1

Integrated Chemical Product-Process Design: CAPE Perspectives Rafqul Can;

1.1 1.2 1.3 1.4 1.5

Introduction 647 Design Problem Formulations 648 Issues and Needs 654 Framework for Integrated Approach 658 Conclusion 663

2

Modeling in the Process Life Cycle 667 Ian T: Cameron and Robert 6.Newell

2.1 2.2

Cradle-to-the-GraveProcess and Product Engineering 667 Industrial Practice and Demands in Life-Cycle Modeling 675

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2.3 2.4

Applications of Modeling in the Process Life Cycle: Some Case Studies 681 Challenges in Modeling Through the Life Cycle 689 695

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Integration in Supply Chain Management Luis Puigjaner and Antonio Espuiia

3.1 3.2 3.3 3.4 3.5 3.6 3.7

Introduction 695 Current State of Supply Chain Management Integration 697 Agent-based Supply Chain Management Systems 702 Environmental Module 707 Financial Module 71 1 Multiagent Architecture Implementation and Demonstration 718 Concluding Remarks 727

4

Databases in the Field o f Thermophysical Properties in Chemical Engineering 731 Richard Sass

4.1 4.2

Introduction 731 Overview of the Thermophysical Properties Needed for CAPE Calculations 732 Sources of Thermophysical Data 733 Examples of Databases for Thermophysical Properties 733 Special Case and New Challenge: Data of Electrolyte Solutions 740 Examples of Databases with Properties of Electrolyte Solutions 741 A Glance at the Future of the Properties Databases 744

4.3 4.4 4.5 4.6 4.7 5

Emergent Standards 747 Jean-Pierre Belaud and Bertrand Braunschweig

5.1 5.2 5.3 5.4

Introduction 747 Current CAPE Standards 751 Emergent Information Technology Standards 755 Conclusion (Economic, Organizational, Technical, QA) 765

Section 5 Applications 1

Integrated Computer-aided Methods and Tools as Educational Modules 773 Rafiqul Cani andJens Abildskov

1.1 1.2 1.3

Introduction 773 Integrated Approach to CAPE Educational Modules 776 Conclusion 797

1.4

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Data Validation: a Technology for Intelligent Manufacturing Boris Kalitventzefi Ceorges H eyen, and Miguel Mateus

2.1 2.2 2.3 2.4 2.5 2.6

Introduction 799 Basic Aspects of Validation: Data Reconciliation 799 Specific Assets of Information Validation 806 Advanced Features of Validation Technology 815 Applications 821 Conclusion 826

3

Facing Uncertainty in Demand by Cost-effective Manufacturing Flexibility 827 Petra Heijnen andjohan Grievink

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

Introduction 827 The Production Planning Problem 829 Mathematical Description of the Planning Problem 830 Modeling the Profit of the Production Planning 832 Modeling the Objective Functions 836 Solving the Optimization Problem 840 Sensitivity Analysis of the Optimization 845 Implementation of the Optimization of the Production Planning Conclusions and Final Remarks 851 Authors’ Index 855 Subject Index 857

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1 Preface Computer Aided Process and Product Engineering (CAPE): Its Pivotal Role for the Future of Chemical and Process Engineering

Chemical and related industries are at the heart of the great number of scientific and technological challenges involving computer-aided processes and product engineering. Chemical and related industries including process industries such as petroleum, pharmaceutical and health, agriculture and food, environment, textile, iron and steel, bitumous, building materials, glass, surfactants, cosmetics and perfume, and electronics are evolving considerably due to unprecedented market demands and constraints stemming from public concern over environmental and safety issues. To respond to these demands, the following challenges faced by these process industries involve complex systems, both at the process-scale and at the productscale: 1. Processes are no longer selected on a basis of economic exploitation alone. Rather, compensation resulting from the increased selectivity and savings linked to the process itself is sought after. Innovative processes for the production of commodity and intermediate products need to be researched where patents usually do not concern the products but the processes. The problem becomes more and more complex as factors such as safety, health, environment aspects including nonpolluting technologies, reduction of raw materials and energy losses, and productlby-product recyclability are considered. The industry, with large plants, must supply bulk products in large volumes and the customer will buy a process that is nonpolluting and perfectly safe, requiring computer-aided process engineering (CAPE). 2. New specialities, active material chemistry, and related industries involve the chemistry/biology interface of agriculture, food, and health industries. Similarly, it involves upgrading and conversion of petroleum feedstock and intermediates, conversion of coal-derived chemicals or synthesis gas into fuels, hydrocarbons or oxygenates.This progression from traditional chemistry is driven by the new market objectives where sales and competitiveness are dominated by the end-use properties of a product as well as its quality. It is important to underline that today, 60 % of all products sold by chemical companies are crystalline,polymer, or ComputerAided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

amorphous solids. These complex and structured materials have a clearly defined physical shape in order to meet the designed and the desired quality standards. This also applies to plastics, ceramics, soft solids, paste-like products, and emulsions. New developments require increasingly specialized materials, active compounds, and special effects chemicals. The chemicals are much more complex in terms of molecular structure than traditional, industrial chemicals. Control of the end-use property (size, shape, color, aesthetics, chemical and biological stability, degradability, therapeutic activity, solubility, touch, handling, cohesion, rugosity, taste, succulence, sensory properties, etc.), expertise in the design of the process, continual adjustments to meet changing demands, and speed to react to market conditions are the dominant elements. For these specialities and active materials the client buys the product that is the most efficient and first on the market. He will have to pay high prices and expect a large benefit from these short life-time and high-margin products, requiring most often computer-aided process and product engineering. The triplet molecular processes-product-processengineering (3PE) approach requires the tools of CAPE. Today, chemical and process engineering are concerned with understanding and developing systematic procedures for the design and optimal operation of process systems, ranging from nano and microsystems to industrial-scale continuous and batch processes: this is illustrated by the chemical supply chain concept. In the supply chain, it should be emphasized that product quality is determined at the micro and nanolevel and that a product with a desired property must be investigated for both structure and function. A comprehension of the structure-property relationship at the molecular (e.g., surface physics and chemistry) and microscopic level is required. The key to success is to obtain the desired end-use property of a product, and thus control product quality by controlling complexity in the microstructure formation. This will help to make the leap from the nanolevel to the process level. Moreover, most chemical and biological processes are nonlinear, belonging to the socalled complex systems for which multiscale structure is common nature. Therefore, an integrated system approach for a multidisciplinary and multiscale modeling of complex, simultaneous, and often coupled momentum, heat and mass transfer processes is required: 0

0

Different time scales (10-15-108 s) are used from femto and picoseconds for the motion of atoms in a molecule during a chemical reaction, nanoseconds for molecular vibrations, hours for operating industrial processes, and centuries for the destruction of pollutants in the environment. Different length scales (10-'-lO6m) are used from nanoscale for molecular kinetic processes; microscale for bubbles, droplets, particles, and eddies: mesoscale for unit operations dealing with reactors, columns and exchangers: macroscale for production units; and megascale for environment and dispersion of emissions (see the following figure):

Preface

Therefore, organizing scales and complexity levels in process engineering is necessary in order to understand and describe the events at the nano and microscales, and to better convert molecules into useful products at the process scales. This multiscale approach is now also encountered in biotechnology, bioprocesses, and product engineering, to manufacture products and to better understand and control biological tools such as enzymes and micro-organisms. In such cases, it is necessary to organize the levels of increasing complexity from the gene with known properties and structures, up to the product-process relation, by modeling coupled mechanisms and processes at different length scales: the nanoscale is used for molecular and genomic processes and metabolic transformations; pic0 and microscales are used for enzyme and integrated enzymatic systems, and biocatalyst and active aggregates; mesoscale is used for bioreactors, exchangers, separators; and macro and megascales are used for production units and interactions with the biosphere. Thus, organizing levels of complexity at different length scales, associated with an integrated approach to phenomena and simultaneous and coupled processes, are the heart of the new view of biochemical engineering (see next figure). Indeed this capability offers the opportunity to apply genetic-level controls to make better biocatalysts, novel products, or developing new drugs, new therapies, and biomimetic devices. Understanding an enzyme at the molecular level means that it may be tailored to produce a particular end-product. Also, the ability to think across length scales makes chemical engineers particularly well poised to elucidate the mechanistic understanding of molecular and cell biology and its large-scale manifestation, i.e., decoding communications between cells in the immune systems.

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These examples are at the center of the new view of chemical and process engineering: organizing levels of complexity, by translating molecular processes into phenomenologicalmacroscopic laws to create and control the required end-use properties and functionality of products manufactured by a continuous or batch process. I have defined this approach as the triplet molecular processes-product-processengineering (3PE): an integrated system approach of complex pluridisciplinarynonlinear and nonequilibrium processes and phenomena occurring on different length and time scales, involving a strong multidisciplinary collaboration between physicists, chemists, biologists, mathematicians, computer-aided specialists, and instrumentation specialists. Today’s tools are wide-ranging for the success of chemical and process engineering for modeling, complex systems at different scales encountered in the process and product engineering. It’s possible to understand and describe events on the nano and microscale in order to convert molecules into useful products on process and unit scales thanks to significant simultaneous breakthroughs in three areas: molecular modeling (both theory and computer simulation), scientific instrumentation and noninvasive measurement techniques, and powerful computational tools and capabilities for information collection and processing. At the nanoscale, molecular modeling assists in maintaining better control of surface states of catalysts and activators, obtaining increased selectivity and facilitating asymmetrical synthesis, e.g., chiral technologies. Molecular modeling also assists in explaining the relationship between structure and activity at the molecular scale in order to control crystallisation,coating and agglomeration kinetics.

Preface

At the microscale, computational chemistry is very useful for understanding complex media and all systems whose properties are controlled by rheology and interfacial phenomena. At the meso and macroscales, computer fluid dynamics (CFD) is required for scaling up new equipment, or for the design of new operation modes for existing equipment such as reversed flow, cyclic processes, and unsteady operations. It is especially useful when rendering multifunctional processes with higher yields in chemical or biological reactions coupled with separation or heat transfer. It also provides a considerable economic benefit. At the production unit and multiproduct plant scale, dynamic simulation and computer tools for simulation of entire processes are needed more and more. These tools analyze the operating conditions of each piece of equipment in order to simulate the whole process in terms of time and energy costs. New performances (product quality and final cost) resulting from any change due to a blocking step or a bottleneck in the supply chain will be predicted in a few seconds. It is clear that such computer simulations enable the design of individual steps, the structure of the whole process at the megascale, and place individual processes in the overall context of production, emphasizing the role and the place of computer assistance in process and product engineering. The previous considerations on the necessary multidisciplinary and multiscale integrated approach for managing complex systems encountered by chemical and related process industries in order to meet market demands led to the proposal of four main parallel objectives involving the tools of CAPE. The first objective concerns a total multiscale control of the process to increase selectivity and productivity by the nanotailoring of materials. The nanotailoring can be produced with controlled structure, or by supplying the process with a local “informed” flux of energy and materials, or by increasing information transfer in the reverse direction, from process to man, requiring close computer control, relevant models, and arrays of local sensors and actuators. The second objective concerns the process intensification by the design of novel equipment based on scientific principles, new operating modes, and new methods of production. Process intensification with multifunctional equipment that couples or uncouples elementary processes (transfer-reaction-separation),involving the reduction in the number of equipment units leads to reduced investment costs and significant energy recovery or savings. Cost reduction between 10% and 20 % are obtained by optimizing the process. But the use of such hybrid technologies is limited by the resulting problems with control and simulation leading to interesting but challenging problems in dynamic modeling, design, operation and strong nonlinear control. Also, process intensification using microengineering and microtechnology will be used more and more for high-throughput and formulation screening. Indeed microengineered reactors have some unique characterictics that create the potential for high-performance chemicals and information processing on complex systems. Moreover, scale-up to production by replication of microreactor units used in the laboratory eliminates costly redesign and pilot plant experiments, thus accelerating the transfer from laboratory to commercial-scaleproduction.

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The third objective concerns the extension of chemical engineering methodology to product-focusseddesign and engineering in using the multiscale modeling of the above-mentionedapproach, 3PE. Indeed to be able to design and control the product quality of structured materials, and make the leap from the nanolevel to the process level, chemical and process scientists and engineers face many challenges in fundamental concepts (structure-activityrelationships on molecular level, interfacial phenomena, adhesive forces, molecular modeling, equilibria, kinetics, and product characterization techniques); in product design (nucleation growth, internal structure, stabilization, additive);in process integration (simulation and design tools based on population balance); and in process control (sensors and dynamic models). It should be underlined that much progress has been made in product-oriented engineering and in process control using the scientific methods of chemical engineering. The methods include examination of thermodynamic equilibrium states, analysis of transport processes and kinetics when they are separate and linked by means of models with or without the help of molecular simulation, and by means of computer tools of simulation, modeling and extrapolation at different scales for the whole supply chain up to the laboratory-scale. But how can operations be scaled up from laboratory to plant? Will the same product be obtained and will its properties be preserved?What is the role of the equipment design in determining product properties? This leads to the fourth main objective, which is to implement the multiscale application of computational chemical engineering modeling and simulation to reallife situations from the molecular scale to the overall production scale in order to understand how phenomena at a smaller length scale relate to properties and behavior at a longer length scale. The long-term challenge is to combine the thermodynamics and physics of local structure-forming processes like network formation, phase separation, agglomeration, nucleation, crystallization, sintering, etc., with multiphase computer fluid dynamics. Indeed through the interplay of molecular theory, simulation and experimentation measurements a better quantitative understanding of structure-property relations evolves, which, when coupled with macroscopic chemical engineering science, form the basis for new materials and process design (CAPE). Turning to the macroscopic scale, dynamic process modeling and process synthesis are also increasingly developed. Moreover, integration and opening of modeling and event-driven simulation environments in response to the current demand for diverse and more complex models in process engineering is currently taking a more important place. The aim is to promote the adoption of a standard of communication between simulation systems at any time and length-scale level (thermodynamic, unit operations, numerical utilities for dynamic, static, batch simulations, fluid dynamics, process synthesis, energy integration, process control) in order to simulate processes and allow the customers to integrate the information from any simulator into another one. Thus expanding and developing interface specification standards to ensure interoperabilityof CAPE software components justifies the creation of a standardization body (CAPE-OPENLaboratories Network, CO-LAN) to maintain and disseminate the software standards in the CAPE domain that have been developed in several international projects.

Preface

The CAPE Present Book a Vade Mecum in Process Systems Engineering

It is clear and I have shown that chemical and process industries have to overcome challenges linked to the complexity.They need to master phenomena in order to produce products “first on the market” with “zero pollution, zero accident, and zero defects” processes. Therefore, never before have enterprises invested so much in information processing and computer-controlled production, which proved in many cases that it was capable of reducing the costs and greatly increasing the flexibility than any other technology in past decades. Moreover, information and communication technology offered a great number of standardized but also specific possibilities of applications and solutions as never before. Therefore, a strategy aiming at the strengthening of competitiveness of production should obviously incorporate CAPE as a guideline for the reunion of the flexible production, the technical and administrative data processing, and the complete penetration of the enterprise activities with date processing. Within the European Federation of Chemical Engineering, the CAPE Working Party has been very active in this area since the end of the 19GOs, as shown by the success of the ESCAPE series of symposia. The activity of the Working Party is also shown by the publication of this book, which aims to present and review the state-ofthe-art and latest developments in process systems engineering. Its contents illustrates the modem day multidisciplinary and multiscale integrated approach for the integrated product-process design and decision support to the complex management of the entire enterprise. It also highlights the use of information technology tools in the development of new products and processes, in the optimal operation of complex and/or new equipment found in the chemical and process industries, and in the complex management of the supply chain. Actually, this book, based on the competences of scientists and engineers confronted with industrial practice, is a reference tool. Its ensuing and clear objectives in the topic of process systems engineering are: 0

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the necessary multidisciplinary bases required for understanding and modeling the phenomena occurring at the different scales from molecular range up to the global supply chain and extended enterprise; the experimental and knowledge-based methods and tools available to assist in the conception of new processes and products design, and in the design of plants able to manufacture the products in a competitive and sustainable way; the presentation of needed advances to fight ever-increasing complexity involved within the product-process life cycle; some tutorial examples and cases studies aiming to the state-of-the-artcomputeraided tools.

The theoretical and practical aspects of the computer-aided process engineering COVered in this book, involving computer-aided modeling and simulation, computeraided process and product design, computer-aided process operation, and computer integrated approaches in CAPE should find use in libraries and research facilities and make a direct impact in the chemical and related process industries.

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This book judiciously titled “Computer Aided Process and Product Engineering CAPE” is a vade mecum in process systems engineering. It is a valuable and indispensable reference to the scientific and industrial community and should be useful for engineers, scientists, professors and students engaged in the CAPE topic. Bravo and many congratulations to our collegues Prof. Puigjaner and Prof. Heyen for this publication and to the many authors involved in the CAPE Working Party of the European Federation of Chemical Engineering that have made this vade mecum a reality. Prof. Dr. Ing. Jean-Claude Charpentier President of the European Federation of Chemical Engineering

Foreword The European Working Party on Computer Aided Process Engineering has been an important and highly effective stimulus for and promoter of research and educational advances in process systems engineering for over 40 years. The 1991 redirection of the Working Party from the broad and all inclusive scope of embracing "the use of computers in chemical engineering", which was its theme for some thirty years, to its present emphasis on product and process engineering has had important consequences. It has reenergized the organization, sharpened its focus and promoted higher levels of technical achievement. Indeed over the past decade, the ESCAPE series of annual conferences sponsored by the Working Party has become a vital world forum for disseminating, discussing and analyzing progress in state-ofthe-art methodologies to support product and process design, development, operation and management. This volume represents a well-directed effort by the Working Party to capture the current status of developments in this field and thus to give that field its current definition. To be sure, the volume is an ambitious undertaking because the process systems engineering field has expanded enormously from its traditional primary focus on the design, control, and operations of continuously operated commodity chemical processes and its secondary concern with the design and control of batch unit operations. That expansion has included methodologies to support product design and development, increases in both scope and complexity of the processing systems under consideration, and approaches to quantify the risks resulting from technical and market uncertainties and incorporate risk-reward trade-offs in design and operational decisions. The scope of systems encompassed by process systems engineering now ranges from the molecular, biomolecular and nanoscale to the enterprise-wide arena. The levels of complexity include self-assemblyprocesses at the nanoscale, self regulating processes at the cellular level, the combination of mechanical, electrical and surface energetic phenomena in heterogeneous particulate systems, the interplay between thermodynamic, reaction and transport phenomena in integrated reactionlseparation operations, and even the decentralized and semiautonomous interactions of customers, suppliers, partners, competitors and government regulators at the enterprise level. Certainly, these developments have been greatly facilitated by remarkable advances in computing and information technologies. However, at least as important has been the expanded scope of the models that underpin design and operational decisions as well as key advances in the tools for creating, analyzing, solving and maintaining these models over the life cycle of the associate productlproComputer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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cess. The models of interest are now defined not just in terms of the traditional algebraic and differential equations, but also include systems of partial differential and integral equations, graphs/networks, logical relations/conditions, hybrids of logical conditionslrelations and continuous equations, and even object-orientedrepresentations of information, decision and work flows. Has this volume succeeded in addressing the expanded role of models, the thrusts in product design and development, the much enlarged scope and complexity of applications, and the innovative approaches to addressing uncertainty and risk? While it is impossible to address the full scope of these developments within the limited pages of a single volume, the editors and authors, all active contributors of the Working Party, have indeed done remarkably well in capturing and highlighting many of the most important developments. In Section 1, we find coverage of fundamental issues such as the development of modeling frameworks, model parameter estimation and verification methods, approaches to treatment of multiscale models, as well as numerical methods for solution of algebraic, differential and partial differential systems. The applications to particulate-basedprocesses such as crystallization, grinding, and granulation are of continuing special interest. Computational fluid dynamics and molecular modeling tools, which have become integrated into the process systems engineering toolbox are reviewed and the state of methods for the modeling and analysis of microorganisms are presented. The computational biology domain is receiving a high level of attention by the systems engineering community and will certainly receive even more extensive coverage in future reviews. The second section, which principally treats process design, reviews current developments in overall process synthesis as well as synthesis of reaction, separation and utility subsystems. The area of process intensification, which seeks to capture the potential synergies from exploiting the complex interactions of reaction-separationphenomena, is noted, discussed and recognized as an important direction for further research in process systems engineering. The third section on process operations covers important developments in the well-established hnctional levels of the process operations hierarchy: monitoring and data reconciliation, model based control, real-time optimization, scheduling, planning, and supply chain management. Additionally, issues related to the operation of flexible batch plants are reviewed. Key to progress in developments in scheduling, planning, supply chain and flexible batch plant operations have been advances in the formulation and solution of large-scale mixed integer optimization problems. The importance of these and need for continuing advances cannot be overemphasized. The fourth section treats three key integration issues as well as two supporting technology developments. While the basic features of product design are reviewed in Section 3, the progress in meeting the challenges of integrating product and process design are addressed in Section 4.As noted in that chapter, to date most of the progress has been in applications such as structured or formulated products in which the linkage between product and process is very close but hrther developments are on the horizon. The modeling technology required to support the product/process lifecycle raised in one of the chapters is a key issue facing many industry sectors. This

Foreword

issue is not yet as intensively addressed in the process systems community as it should be, given its importance in capturing product/process knowledge and managing corporate risk. The chapter on integrated supply chain management at roots deals with strategic and tactical enterprise-wide decisions. Uncertainty and risk are critical components of such decisions requiring more attention and intense future study. The sections on physical property estimation and databases, as well as open standards for CAPE software, discuss components that comprise an essential infrastructure for CAPE developments. The importance of tools for physical property prediction/estimation is evident in domains such as pharmaceutical products, in which the absence of such predictive tools has significantly retarded CAPE efforts in product and process design. The volume concludes with several enlightening case studies spanning the technologies reviewed in the preceding sections that are well chosen to make these technologies, their strengths and weaknesses more concrete. Given the limitations of a single volume, there necessarily are additional topics that will in the future require more intensive review and discussion. These include process intensification research at the micro and even nanoscales. While there have been research on microscale process design and control, the essential complexity of the phenomena that occurs at micro and nanoscales makes work in this area both challenging and of potential high impact. There has been progress in rigorous treatment of the full range of external and internal parameter uncertainties and promising computational methods for generating risk-reward frontiers that deserves notice, including the integration of discrete event simulation and discrete optimization methods. Algorithms and strategies for addressing multistage stochastic decision problems and incorporating the full valuation of the decision flexibility in multistage decision frameworks are receiving increased attention. Finally, large-scale optimization methods for attacking enterprise level decision problems of industrial scope are emerging and will become even more prominent in the near future. In summary, this volume is remarkably thorough in capturing the current state of development of the process systems engineering field and representing its broad scope. It will serve this field well in stimulating further research and in encouraging students to learn and contribute to a vital and growing body of knowledge that has important applications in broad sectors of the chemical, petrochemical, specialty, pharmaceuticals, materials, electronics and consumer products industries. The editors and authors are to be congratulated for a job well done. G. V. Reklaitis

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List of Contributors lens Abildskov

Bertrand Braunschweig

CAPEC Department of Chemical Engineering Splltofts Plads, Building 229 2800 Kgs. Lyngby Denmark

Institut Franiaise du Petrole Division Technologie, Informatique et Mathematiques Appliquees 1 and 4 avenue de Bois Preau 92852 Rued Malmaison CCdex France

Albert0 Alva-Argaez

Hankyong National University Department Chemical Engineering Kyonggi-do Anseong 456-749 Korea

/an T. Cameron

The University of Queensland School of Engineering Division of Chemical Engineering St Lucia QLD 4072 Australia

Jean-Pierre Belaud

National Polytechnic Institution of Higher Learning at Toulouse INPT Department of Process Systems Engineering 118, route de Narbonne 31077 Toulouse Cedex 4 France

Vivek Dua

University College London Department of Chemical Engineering Centre for Process Systems Engineering Torrington Place London WClE 7JE UK

1. David L. Bogle

University College London Centre for Process Systems Engineering Department of Chemical Engineering Torrington Place London WClE 7JE UK

Sebastian Engell

University of Dortmund Department of Biochemical and Chemical Engineering Process Control Laboratory Emil-Figge-Str.70 44221 Dortmund Germany

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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Antonio Esputia

Universitat PolitPcnica de Catalunya Chemical Engineering Department ESTEIB, Av. Diagonal 647 08028 Barcelona Spain Cregor Fernhob

Process Systems Enterprise Limited Merlostrasse 12 50668 Koln Germany Cuido Buzzi Ferraris

Politecnico di Milano CMIC Department Piazza Leonard0 da Vinci, 32 20133 Milano Italy Rafiqul Gani

CAPEC Department of Chemical Engineering Sdtofts Plads, Building 229 2800 Kgs. Lyngby Denmark Weihua Cao

GE Global Research Center Real Tirne/Power Controls Laboratory 1800 Cailun Road Zhangjiang High-tech Park, Pudong New Area 201203 Shanghai P. R. China Michael C. Ceorgiadis

Imperial College London Centre for Process Systems Department of Chemical Engineering, Engineering Roderic Hill Building South Kensington Campus London SW7 2AZ UK

Vincent Cerbaud

Laboratoire de Genie Chimique BP 1301 5 rue Paulin Talabot 31106 Toulouse, Cedex 1 France Krist Y. Cernaey

Technical University of Denmark Department of Chemical Engineering Sdtofts Plads, Building 229 2800 Kgs. Lyngby Denmark lohan Crievink

Delft University of Technology Faculty of Applied Sciences Department of Chemcial Technology Julianalaan 136 2628 BL Delft The Netherlands Katalin M. Hangos

Hungarian Academy of Sciences Computer and Automation Research Institute Process Control Research Group Kende u. 11-13, PO Box 63 1518 Budapest Hungary Petra Heijnen

Delft University of Technology Department of Technology, Policy and Management PO Box 5015 2600 GA Delft The Netherlands Ceorges Heyen

Laboratoire dAnalyse et SythPse des SystPmes Chimiques UniversitC de LiPge Alee de la Chimie 3-BG 4000 LiPge Belgium

List ofcontributors

Gordon D. lngram

Margaritis Kostoglou

CSIRO Land and Water Private Bag 5 Wembley WA 6913 Australia

Aristotle University of Thessaloniki Department of Chemical Technology, School of Chemistry Box 116 54124 Thessaloniki Greece

Sten Bay jirgensen

Technical University of Denmark Department of Chemical Engineering Sdtofts Plads, Building 229 2800 Kgs. Lyngby Denmark Xavier joulia ENSIACET -

Laboratoire de GCnie Chimique 117 Route de Narbonne 310077 Toulouse, Cedex 4 France

Andrey Kraslawski

Lappeenranta University of Technology Department of Chemical Technology PO Box 20 53851 Lappeenranta Finland Rozalia Lakner

Department of Computer Science Pannon University Egyetem Street 10, PO Box 158 8200 Veszprem Hungary

Boris Kalitventzd

BELSIM s.a. Rue Georges Berotte 29A 4470 Saint-Georges-sur-Meuse Belgium Eustathois S. Kikkinides

University of West Macedoinia School of Engineering and Management of Energy Resources Sialvera and Bakola Street 50100 Kozani Greece Antonis Kokossis

University of Surrey Centre for Process and Information Systems Engieering Guildford, Surrey, GU2 7XH UK

Young4 Lim

Natural Resources Canada CETC - Varennes Energy Technology and Programs Sector PO Box 27043 Calgary, Alberta T3L 2Y1 Canada Morton Lind

Technical University of Denmark 0rsted DTU, Automation Elektrovej, Building 326 2800 Kgs. Lyngby Denmark Patrick Linke

University of Surrey Centre for Process and Information Systems Engineering Guildford, Surrey, GU2 7XH UK

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Davide Manca

Politecnico di Milano CMIC Department Piazza Leonard0 da Vinci, 32 20133 Milano Italy Francois Marechal

Ecole Polytechnique FCderale de Lausanne Industrial Energy System Laboratory LENI-ISE-STI-EPFL Station 9 1015 Lausanne Switzerland Miguel Mateus

Belsim s.a. Rue Georges Berotte 29A 4470 Saint-Georges-sur-Meuse Belgium Robert 6. Newel1

Daesim Technologies Pty Ltd PO Box 309 Toowong QLD 4066 Australia Lazaros C. Papageorgiou

University College London Centre for Process Systems Engineering Department of Chemical Engineering Torrington Place London WC1E 7JE UK John D. Perkins

University of Manchester Institute of Science and Technology Sackville Street, PO Box 88 Manchester MGO IQD UK

Efstratios N. Pistikopoulos

Imperial College London Department of Chemical Engineering Centre for Process Systems Engineering Roderic Hill Building South Kensington Campus London SW7 2AZ UK Petros Proios

Imperial College London Department of Chemical Engineering Centre for Process Systems Engineering Roderic Hill Building South Kensington Campus London SW7 2AZ UK Luis Puigjaner

Universitat PolitScnica de Catalunya Chemical Engineering Department ESTEIB, Av. Diagonal 647 08028 Barcelona Spain Javier Romero

Universitat PolitPcnica de Catalunya Chemical Engineering Department ESTEIB, Av. Diagonal 647 08028 Barcelona Spain Richard Sass

DECHEMA e.V. Department of Information Systems and Databases Theodor-Heuss-Allee25 GO486 Frankfurt-am-Main Germany

Nilay Shah

Panagiotis Tsiakis

Imperial College London Department of Chemical Engineering Centre for Process Systems Engineering Roderic Hill Building South Kensington Campus London SW7 2AZ UK

Process Systems Enterprise Ltd. Bridge Studios, 107a Hammersmith Bridge Road London WG 9DA UK

Abdelaziz Toumi

Bayer Technology Services GmbH PMT-AMS-APC,Bld. E41 51368 Leverkusen Germany

B. Erik Ydstie

Carnegie Mellon University Department of Chemical Engineering Pittsburgh 5000 Forbes Avenue Pennsylvania 15213-3890 USA

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

I’

Introduction Since 1991 the working party (WP) of the European Federation of Chemical Engineering with the title “The Use of Computers in Chemical Engineering” adopted new term of reference and a new title-the Working Party on Computer Aided Process Engineering. This decision followed an internal debate on issues involving concepts like computer integrated manufacturing (CIM), computer-aided process operations (CAPE) and computer-aided process design (CAPD).The consensus reached in the new title naturally embraced computer-aided process operations as a subset of CIM, which is focused on the application of computing technology to integrate and facilitate the key technical decision processes which arise in chemical manufacture. Thus, CAPE focuses on algorithms, procedures and frameworks, which automate the operating/ design decisions for those functions which are automatable and support those operating decisions for which human intervention is necessary or desirable (Pekny et al. 1991). This re-structuring of the WP reflected the actual trends in the process industries. Never before had the enterprises so much invested in information processing. Computer-controlled production proved in many cases that it was capable of reducing the costs and increasing the flexibility far more greatly then any other technology in the past decades. Information and communication technology offered plenty of standardized but also specific possibilities of applications and solutions as never before. Therefore, a management strategy aiming at the strengthening of the competitiveness of production should obviously incorporate CAPE as a guideline for the reunion of the flexible production, the technical and administrative data processing and the complete penetration of all enterprise activities with data processing (Westkamper 1992). During this last decade these trends have consolidated and expanded. Thus, CAPE is a network with separate functions which are linked to each other and/or integrated by using common data and information. CAPE systems are used in the development and design, operations planning and production equipment planning departments. Otherwise, order processing is carried out by process control systems (materials resource planning). Both systems deliver data to an information system, which is the basis for the operation of the production with its flexible and control systems. Moreover, as the system boundaries have expanded, CAPE contribution and opportunities are present in the integrated product-process design and decision support to the complex management of the entire enterprise. Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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I Introduction

This book aims to present and review the state of the art and latest developments in process systems engineering. It seeks to highlight the use of information technology tools in the development of new products and processes, in the optimal operation of complex equipment found in the process industries, and in the complex management of the whole business. The book is intended as a valuable reference to the scientific and industrial community, and should contribute to the progress in computer-aided process and product engineering. This work should be also useful for teachers of postgraduate courses in these areas. Following this introduction, the book consists of 27 chapters organized into five major sections: Section 1 Section 2 Section 3 Section 4 Section 5

Computer-aided Modeling and Simulation, Computer-aided Process and Product Design, Computer-aided Process Operation, Computer-integrated Approaches in CAPE, Applications

Section 1 presents a review on actual trends and shows new advances in mathematical modeling and digital simulation techniques that permit practitioners to solve the complex scenario that describes real engineering systems. Basic techniques needed to develop and solve models are reviewed this extends from applied mathematics to model validation and tuning, model checking and initialization, and to the estimation of physical properties. In Chapter 1 steady state process simulation is introduced, which involves largescale algebraic systems. The most known solving algorithms are first presented. Alternative methods of the quasi-Newtonfamily are then described and some issues such as convergence, ill-conditioned and singular Jacobian matrices are also discussed. Then, it focuses on large and sparse algebraic systems, how to work with bounds, constraints and discontinuities as well as how to deal with the stopping criteria to be adopted. Finally, a short introduction to continuation methods is provided. Chapter 2 deals with distributed dynamic models, that is, partial differential equations (PDEs) or partial differential algebraic equations (PDAEs) incorporating convection, diffusion, reaction and/or thermodynamic property terms. Numerical methods for solving PDEs are reviewed in three sections treating first semidiscretized (method of lines) and fully discretized methods before discussing adaptive and moving mesh methods. Some applications are discussed, such as preparative chromatography, fured-bed reactors, slurry bubble columns, crystallizers and microbial cultivation processes. Finally, an approach for combining computational fluid dynamic (CFD)technology with process simulation is discussed. Process and product design studies rely on good knowledge of materials behavior and physical properties. Chapter 3 deals with estimation methods based on molecular modeling, describing the behavior of atomic and molecular systems subject to energetic interactions. It allows running numerical experiments and as any experiment, it can provide not only accurate physicochemical data but also increase the knowledge on the system studied. Molecular modeling concepts are presented so as

1 Introduction

to demystify them and stress their interests for chemical engineers. Mdtiscale approach including molecular modeling is not illustrated due to restricted space. Rather, routine examples on the use of several molecular techniques suitable to get accurate vapor-liquid equilibrium data when no data is available are provided. Chapter 4 presents a critical review of modeling frameworks for complex processing systems with emphasis not only on the models themselves but also on specialized techniques for the efficient solution of these models. More specifically, due to their increased industrial interest a general modeling framework for adsorptiondiffusion-based gas separation processes is presented in detail with focus on pressure-swing adsorption and membrane-based processes for gas separations. For subsequent sections of this chapter, a critical review of models and specialized solution techniques for crystallization and grinding processes is made. Finally, concluding remarks are drawn up and future research challenges are discussed. Process models are of increasing size and complexity, therefore the methods and tools for their tuning, discrimination and verification are of great importance. The widespread use of process models for design, simulation and optimization requires the proper documentation, re-use and retrofit of already existing models, which also need the above techniques. Thus, Chapter 5 deals with computer-aided approaches and methods of model tuning, discrimination and verification that are based on a formal structured description of process models. Besides the length and time scales, a detail scale could also be considered which seeks to develop models with varying degrees of fidelity in relation to the real world phenomena. This is the subject of Chapter 6, which presents coverage of multiscale modeling through a discussion of the origins of such phenomena in process and product engineering, as well as discussing the approaches to the modeling of systems that seek to capture multiscale phenomena. The chapter discusses the development of the partial models that make up the multiscale model particularly focusing on the characteristics of those models. The issue of partial model integration is also developed through the use of integrating frameworks. Those frameworks are analyzed to understand the important implications of model coupling and computational behavior. Throughout the chapter reference is made to granulation processing that helps to illustrate the concepts and challenges in this important area. Finally, Chapter 7 of Section 1 addresses one of the current challenges facing the modeling community: the description of regulatory networks in micro-organisms. Micro-organisms constitute examples of entire autonomous chemical plants, which are able to produce and reproduce despite shortage of raw materials and energy supplies. Understanding the intracellular regulatory networks of micro-organisms is important to process systems engineering for several reasons: microbial systems still constitute relatively simple biological systems, the study and understanding of which may enable better understanding of higher biological systems such as human beings. Furthermore, microbial systems are used, often following genetic manipulation, to produce relatively complex organic molecules in an energy efficient manner. Understanding how to couple the microbial regulatory functions and the higher level process and production control functions is a prerequisite for process engineering.

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7 Introduction

Section 2 of this book brings together process engineering and product design. One major use of models is the development and improvement of processes and products. This is a multidisciplinary approach, and it requires consideration of many aspects of the behavior of a production plant: equipment design, steady state and dynamic operation of integrated processes, raw materials and energy usage, economy, health and safety. Section 2 reviews the methods currently available to integrate knowledge from different disciplines, and presents tools available to assist in the conception of new products, and in the design of plants able to manufacture them in a competitive and sustainable way. Section 2 starts with a comprehensive review of the process separation synthesis problem with emphasis on complex distillation systems (Chapter 1). First, a critical overview of the synthesis of simple column sequences is presented with emphasis on the novel generalized modular representation framework developed at Imperial College London. Then, the synthesis problem of heat-integrated distillation trains is thoughtfully reviewed. Current state-of-the-art methodologies and algorithmic frameworks for the synthesis of complex distillation sequencing are also critically discussed. The term process intensification is associated mainly with more efficient and compact processing equipment that can potentially replace large and inefficient units commonly used in chemical processing but also includes methodologies, such as process synthesis methods, that enable the systematic development of efficient processing units. Chapter 2 provides an overview over current process intensification technologies and presents a number of recently developed systematic computeraided process intensification methods and tools. They enable the systematic screening and scoping of large numbers of alternative processing options and can identify novel options of phenomena exploitation that may lead to higher efficiencies. Such tools provide the basis for systematic approaches to novelty in process intensification and have the potential to identify processing options, which can easily be missed in design activities that rely on intuition and past experiences. Industrial processes require the use of energy, other utilities such as water and solvents, and produce wastes that need to be treated. The system performances rely not only on the efficiency of the process but also on the quality of its integration considering the energy conversion technologies, the possible combined heat and power production, the water usage and the waste treatment techniques. Chapter 3 presents computer-aided methods for solving the optimal integration of utility systems. Graphical representations support the engineer’s creativity; they are used to define the characteristics of a utility system, to analyze the potential of combined heat and power production and to analyze the quality of subsystems integration. From the requirement analysis, a utility system superstructure can be developed, to be later optimized using mathematical programming techniques. Several formulations are presented and discussed in order to integrate the different types of utility subsystems (e.g., combined heat and power, heat pumps and refrigeration) and optimize their integration with the processes. The problem of the water circuit integration can be addressed using similar concepts.

1 Introduction

The computational basis for equipment and process design in the chemical manufacturing industries is introduced in Chapter 4. Problems encountered are discussed through the use of case studies that range from modeling, simulation and optimization of existing and proposed processes. The work described in the case studies represents recent developments and trends in the industry in the area of Computer Aided Process Engineering (CAPE).The applications focus on the use of optimization techniques for obtaining optimal designs and better approaches for controlling the processes close to or at the optimal point of operation. Designs use rigorous models based on thermodynamics, conservation laws and accurate models of transport and fluid flow, with particular emphasis on dynamic behavior and uncertainty in market conditions. Product development and design starts to be a third paradigm in chemical engineering. This emerging field of research undergoes a phase of defining its scope and methods as well as the generalization of the existing industrial experience. Chapter 5 introduces the main phases of product development and the classes of the applicable methods. The special attention is given to the definition phase: methods for translation of the consumer requirements into the product parameters and approaches to generation of the product ideas. Also given is an introduction to the experimental and knowledge-based methods and tools for product design. Finally, the challenges that face CAPE in the field of product development and design are presented. Section 3 reviews the current problems facing process operations. It presents the state of relevant methods and technology, and needed advances to combat everincreasing complexity. The scope covers resource planning and production scheduling, extending to the analysis of supply chain. Process monitoring and measurement validation are described, as being preliminary steps for real-time process optimization and model-based process control. This section starts with a comprehensive review of state-of-the-art models, algorithms, methodologies and tools for the resource planning problem covering a wide range of manufacturing activities (Chapter 1). First, the long-range planning problem in the process industries is considered including a detailed critical discussion on the effect of uncertainty, the planning of refinery operations and offshore oilfields, the campaign planning problem and the integration of scheduling and planning. Then, the planning problem for new product development in pharmaceutical industries is discussed in some detail. Next, the tactical planning problem is briefly presented followed by a description of the resource planning problem in the power market and construction projects. Recent computational solution approaches to the planning problem are reviewed, while available software tools are outlined in the penultimate section of this chapter. Finally, concluding remarks are drawn and future challenges in this area are proposed. The complex problem of what to produce and where and how to produce it best is considered through an integrated hierarchical approach. Chapter 2 deals with production scheduling, focussing on the single site problem. Problem solution using heuristics is described, before presenting solution methods based on mathematical programming. Hybrid solutions are also mentioned, as well as the combined solution of scheduling and optimal operation. The state of the art for industrial applica-

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tions is described, before concluding with new application domains and future challenges. Measurements are needed to monitor process efficiency and equipment condition, but also to take care that operating conditions remain within acceptable ranges to ensure good product quality, avoid equipment failure and any hazardous conditions. However, measurements are never error free. Model-based data reconciliation techniques allow the detection and correction of random experimental errors, taking profit of redundant measurements. Chapter 3 deals with process monitoring and online estimation of performance indicators. This includes also fault detection capability, and is required as part of a model-based control system, since model tuning should be based on validated plant data. The design of effective redundant sensor network is also addressed. Operating a real plant at its optimal design conditions does not guarantee optimal operation. Some plant-model mismatch cannot be avoided, nor the effect of disturbances, this is why some sort of feedback control is needed. Chapter 4 deals with model-based control, i.e., the use of rigorous process models for feedback control by model-based on-line optimization. Several implementations with increasing level of complexity are discussed. Some plant inputs can be fixed by an off-line optimization while other inputs are controlled to keep some key process parameters on target. When nonlinear process models are available this leads to nonlinear model predictive control (NMPC)where the future values of the controlled variables are predicted over a finite horizon (the prediction horizon) using the model, and the future inputs are optimized over a certain horizon (the control horizon). As an extension of this concept, feedback control can be combined with model adaptation and re-optimization. Such a control scheme is presented for the example of batch chromatographic separations, including experimental results. Structural plant-model mismatch is a major problem also addressed. A solution is the use of optimization strategies that incorporate feedback directly; this idea is presented in detail and the application to batch chromatography is used to demonstrate its potential. To conclude, the problem of controlling quasicontinuous chromatographic separations is formulated as an on-line optimization problem where the measured outputs have to meet the constraints on the product purities but the optimization goal is not tracking of a pre-computed trajectory but optimal process operation. With the increasing fundamental understanding of the underlying physicochemical phenomena of various processes and strict environmental, safety and energy consumption constraints the need for efficient real time optimization tools has reached unprecedented levels. A better understanding of the processes is leading to highfidelity but complex mathematical models that can not always be solved efficiently in real time. The computation of the best operating or control strategy, given these models, is further complicated by the presence of constraints on control variables. In Chapter 5 a parametric programming approach is presented, which moves real time computational effort off-line. This is achieved by a priori computing the optimal control Variables as a set of explicit functions of the current state of the plant, where

7 Introduction

these functions are valid in certain polyhedral regions in the space of the state variables. This reduces real-time optimization to simple function evaluations. Actually, many production facilities constitute large hybrid systems, making it necessary to consider the continuous-discrete interactions taking place within an appropriate framework for plant and process simulation and optimization. The next chapter of Section 3 (Chapter 6) briefly discusses existing modeling frameworks for discrete/hybrid production systems embodying different approaches. A very recent framework for process recipe initialization that integrates a recipe model into the batch plant-wide model is introduced. The on-line and off-line recipe adaptation from real-time plant information is presented. Finally, a model-based integrated advisory system is described. This system gives on-line advice to operators on how to react in case of process disturbances. This way, an enhanced overall process flexibility and productivity is achieved. Application of this promising approach is illustrated through examples of increasing complexity. Process operation management and business competitiveness cannot be understood without considering supply chain activities. The main aim of Chapter 7 is to provide a comprehensive review of recent work on supply chain management and optimization mainly focused on the process industry. The first part describes the key decisions and performance metrics required for efficient supply chain management. The second part critically reviews research work on enhancing the decision-making for the development of the optimal infrastructure (assets and network) and planning. Next, different frameworks are presented, which capture the dynamic behavior of the supply chains by establishing efficient replenishment inventory management strategies. Finally, available software tools for supply chain management are outlined and future research needs for the process systems engineering community are identified. Section 4 focuses on recent developments aiming at the integration of different components in the CAPE world that offer a different degree of practical implementation. Supporting databases and a presentation of the necessary emergent standards in the CAPE domain are also included here. As chemical product design involves different disciplines, different types of data and tools, different solution strategies, etc., the need for a framework for integrated chemical product-process design becomes a subject of paramount importance. Moreover, there are chemical products where the reliability of the manufactured chemical product is more important than the cost of manufacture, while there are those where the cost of manufacture of the product is at least as important as the reliability of the product. Thus, product-centred process design is also very important. Identifying a feasible chemical product, however, is not enough; it needs to be produced through a sustainable process. The objective of Chapter 1 of Section 4 is first to define the general integrated chemical product-process design problem, then to identify the important issues and needs with respect to their solution and finally to illustrate through examples, the challenges and opportunities for CAPE/PSE methods and tools. Integrated product-process design where modeling and supply chain issues play an important role is also highlighted. Chapter 2 deals with the important issues of where, why and how models of various types are used throughout the life of an industrial or manufacturing process. The

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chapter does not deal specifically with the modeling of the life cycle process but concentrates on the use of models to address a plethora of important issues that arise during the many stages of a process' life, from the cradle to the grave. In this chapter, the life cycle concept is first discussed in relation to a "cradle to the grave" viewpoint, and then in subsequent sections consideration is made to specific issues related to the modeling goals and realizations. Some important issues are discussed which surround model development, reuse, integration, model documentation and archiving. Consideration is also made to the future needs of such modeling approaches and the important implications of life cycle modeling for corporations. Throughout this chapter the authors refer to several specific industrial case studies that help illustrate the importance of modeling throughout the life cycle as well as the challenges of doing so. What is evident in the following sections of this chapter is that there is a huge range of modeling used to help answer vital sociotechnical questions through the life cycle of the process or product. It is important to appreciate that process and product engineering have vital links to social and human factors within a holistic approach to modeling. Major infrastructure projects continually reinforce a more complete view than that which is often taken by process and product engineers. In this chapter the vision of modeling within the process or product life cycle is expanded to see just what has been achieved and where the challenges lie for the future. An introductory chapter (Section 3, Chapter 7) on the supply chain (SC) network has already presented the elementary principles and systematic methods of supply chain modeling and optimization. In Chapter 3 of Section 4, the need for and integrated management of the SC is further emphasized and novel challenging solutions are presented. As seen, supply chain management (SCM)comprises the entire range of activities related to the exchange of information and materials between costumers and suppliers involved in the execution of product and/or service orders in an extremely dynamic environment. A successful management of the supply chain management requires direct visibility of the global results of a planning decision in order to include this global perspective. This requires significant integration across multiple dimensions of the planning problem for nonconventional manufacturing networks and multi-site facilities over their entire supply chain. Objectives such as resources management, minimum environmental impact, financial issues, robust operation and high responsiveness to continuous needs must be simultaneously considered along with a number of operating and design constraints. All integrated applications needed to design and operate a plant during its whole life cycle need to access reliable physical properties for all chemicals and materials occurring in the process. Chapter 4 presents an overview of the thermophysical properties needed for CAPE calculations and describes the major sources of such data currently available. Several databases for pure component physical properties are described. Phase equilibrium data collections are also reviewed. The quality of data inside the data calculation modules is essential: inaccurate data may lead to very expensive misjudgements whether it is to proceed with a new process or modifica-

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tion of it. Inadequate or unavailable data may cause a promising and profitable process can be delayed or in the worst case be rejected, only for the reason that it was not properly modelled in a simulation. The text provides also up-to-date references to information sources available on the Internet. The lack of software standards in computer-aided process and product engineering has been a subject of concern for years, as a source of unnecessary costs, delays and inconsistencies between data produced and consumed by different nonintegrated systems using different bases, different calculation principles, different units of measurements, running on different computers under different operating systems and written in different languages. Chapter 5 introduces software standards intended to remove these problems by providing the desired interoperability between software tools, platforms and databases. With appropriate machine-to-machine interface standards, using the best available tools together becomes a matter of plug-and-play,supposedly as easy as connecting USB devices or hi-fi systems. Moreover, not only do these standards enable the putting together of several software pieces available on your local PC, but they allow interoperating heterogeneous software modules available on your organisations’ intranet, or on the Internet. The chapter starts with a discussion on the concepts of openness and of open standards; then some of the most significant operational standards in computer-aided process and product engineering are examined. Following this, the authors look at some of the current software interoperability technologies that will power future systems, namely web services, service-orientedarchitectures and ontologies for the Semantic Web. The chapter concludes with a brief look at the organisational and economic consequences of the trend towards interoperability and standards in CAPE. Section 5 presents tutorial examples and case studies aiming to illustrate typical problems that can be solved using state of the art computer-aided tools. The goal is not only to show the benefits of using CAPE methods, but also to indicate what are some current limitations and point out areas where future research and developments should be directed. Chapter 1 analyses the increased use of computers in chemical engineering education. The authors present a set of computer-aided educational modules that have been specially developed with the aim to avoid the dangers of misuse of the software. The motivation is to help the students to not only understand the concepts but also to appreciate how the theory can be applied to solve chemical engineering. The computer-aided educational modules presented here involve property prediction (suitable for a course on thermodynamics or product design), extractive distillation-based separation (suitable for courses on separation processes, distillation, or process design) and model derivation and solution (suitable for courses on modeling, simulation and/or numerical methods). The students are encouraged to first assemble modules for corresponding calculation steps into their own software for simple problems and then use specialized software for larger more complex problems. At this stage, an integrated computer-aided system also becomes very useful and data transfer between the various calculation steps and the corresponding software options take place automatically, thereby sav-

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I Introduction

ing considerable time, which can be spent instead to understand the problem better and to analyze the results. Chapter 2 describes industrial case studies in plant operation and process monitoring. The application and benefits of data validation is illustrated by several examples, taken in a range of industrial environments: oil and gas, chemicals, power plants. Besides plant monitoring and fault detection, the on-line evaluation of key performance indicators is also illustrated. It is shown how the use of more detailed models (e.g., starting with component mass balance, adding energy balances, and later equilibrium constraints) contributes to improving the result quality. Chapter 3 describes the application of a production planning method for a multiproduct manufacturing plant, which optimizes profit under uncertainties in product demands. Flexibility refers exclusively to the planning problem here and it is not coupled with a plant re-design. The development and the application of the method have been highlighted by means of a case study taken from a food additives plant. This method is considered practical for plant management, because the required input data for the demand and process models and the profit function is easy to get by the users of the method. The generated output facilitates an easy interpretation of sensitivities of the optimized production planning in terms of common economic and product demand specification parameters. Overall, the theoretical and practical aspects of the computer-aided process engineering covered in this book should find wide use in libraries and research facilities, and a direct impact in the chemical industry, particularly in production automation, utility networks, supply chain and business management with embedded computer integrated process engineering. The editors would like to acknowledge the many authors that have made this book a reality. We would also like to thank everyone who has assisted in producing the material for this book, and in particular Waltraud Wust at Wiley-VCH for her help in editing the final copy. Luis Puigjaner Georges Heyen

References 1 Pekny, /. Venkatasubramanian V. Reklaitis G. V. L. Prospects for Computer-Aided Process

Operations in the Process Industries, in Puigjaner, L., Espuiia A. (eds.) Computer Oriented Process Engineering, Elsevier, Amsterdam, (1991) pp. 427-434

2 Westkiimper E. Business Challenges in

Industrial Production, in Proceedings of Mdti Supplier Operations: Strategies, Management and Techniques for Improving the Performance of Supply and Distribution Chains, European Community Conference, Stuttgart, Germany 1992

Section I Computer-aided Modeling and Simulation

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

I

Section 1 presents a review on actual trends and shows new advances in mathematical modeling and digital simulation techniques that permit practitioners to solve the complex scenarios that describe real engineering systems. The material in this section is organized i n seven chapters covering basic methods and techniques needed to develop and solve models: these extend ffom large-scale algebraic systems found in steady-state process systems (Chapter 1 ) to partial differential equations (PDEs) or partial diferential algebraic equations (PDAEs) encountered i n distributed dynamic models (Chapter 2). In Chapter 1 a description of direct substitution gradient and Newton‘s basic methods isfollowed by the presentation of more elaborated alternative methods of the quasi-Newtonfamily and continuation methods. Distributed dynamic models are dealt with i n Chapter 2, which involve the solution of PDEs or PDAEs incorporating convection, dijksion, reaction and/or thermodynamic property terms. Since there only exist analytical solutions in few cases due to nonlinearity and complexity, computational methods (or numerical analyses) are i n general required to solve such distributed dynamic models. This chapter ends with a n approach for combining computational fluid dynamic (CFD) technology with process simulation, which is illustrated and discussed through motivating case studies. Chapter 3 presents molecular modeling concepts involved i n the multiscale modeling approach for process study i n a broader jarnework that promotes computer-aided integrated product and process design. Molecular modeling is presented as a n emerging discipline for the study of energetic interaction phenomena. A molecular simulation performs numerical experiments that obtain accurate physicochemical data provided sampling, and energyforcejeld issues are addressed carejhlly. Still, computer-demanding molecular modeling tools will likely not be used “online” or be incorporated in process simulators. But, rather like computerJuid dynamics tools, they should be used i n parallel with existing eficient simulation tools i n order to provide information at the molecular scale on energetic interaction phenomena and increase the knowledge of processes that must manufacture ever more demanding end products. Modeling jameworks for complex processing (specijcally separation) systems with emphasis not only on the models themselves but also on specialized techniques for the e&cient solution of these models are considered in Chapter 4. Specijcally, modelingjameworks on pressure-swing adsorption and membrane-based processes for gas separations, crystallisation, and grinding processes are presented due to their increased industrial interestThe increased complexity and size of process models requires appropriate methods and tools for their tuning, discrimination, and verijcation. An extension to model validation and tuning, model checking and initialization is made in Chapter 5,followed by a coverage of rnultiscale modeling through a discussion of the origins of such phenomena i n process

13

and product engineering, as well as discussing the approaches to the modeling of systems that seek to capture multiscale phenomena (Chapter 6). Finally, Chapter 7 of Section 1 addresses one of the current challenges facing the modeling community:the description of regulatory networks in micro-organismsas examples constituting entire autonomous chemical plants.

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

1 Large-Scale Algebraic Systems Cuido Buzzi-Ferraris and Davide M a m a

1.1 Introduction

In this section, we address the solution of a system of N nonlinear equations:

f(x) = 0

(1)

in N unknowns, x, with particular attention given to large systems. It is worth noting that the equations of system (1) must not necessarily be algebraic but may originate, for example, from the solution of a differential system with some initial conditions, or by the evaluation of the upper limit of an integral equation. The solution of nonlinear equations is therefore significant not only as a problem per se, but it is also connected to the solution of differential-algebraicequation (DAE) and ordinary differential equation (ODE) stiff problems. In the following, we will describe some iterative methods for the solution of system (1).With the term “iteration”we mean that given a previous point xi the following one is determined by the equation: Xi+l

= Xi

+ aipi

(2)

The numerical methods for the solution of Non Linear Systems, NLSs, are characterized by the selection of direction pi and by the amplitude of the movement (xi along pi. Some methods require the evaluation of the Jacobian matrix defined as:

In the following, fi represents f(xi)and Ji represents J(xi). As far as large systems are concerned, it is instinctive to try to reduce the dimensions of the problem. Using this idea, some previous numerical techniques, such as tearing and partitioning, were developed to automatically rearrange the system in order to minimize the Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

16

I

1 Large-Scale Algebraic Systems

number of equations to be solved simultaneously. Unfortunately,the following problems should not be underestimated 0

0

It is not certain that the solution of a small NLS requires less time then a larger one. In an NLS, the role of unknowns within an equation is not symmetric. In other words, a function can be easily solved with respect to a variable but it can be difficult to find the solution when another unknown is involved. In spite of the original NLS being well-conditioned, the reduced NLS obtained from the original one can be ill-conditioned.

The first problem arises from the fact that it is not possible to evaluate the nonlinearity of a system of equations. In other words, contrary to the linear case, it is not possible to determine a priori the time required to solve an NLS as a hndion of its dimension. For example, system (4)was shown to be easier to solve than the smaller system (5) by Powell (1970).

The second problem is once again bound to the nonlinearity of the system. An example is given by the conversion c in an adiabatic reactor as a function of the reaction temperature T. Often, it is possible to write the following energy balance: c =g m (6) Evidently, it is trivial to determine the conversion when T is assigned. Conversely, it may not be easy to evaluate the temperature that produces a specific conversion. The third problem is due to the fact that a rearrangement of the NLS can introduce an ill-conditioningthat was not originally present. Let us suppose we have to solve the following system: x1+ 1000x4 = 1001

+ x2 = 1001 + x3 = 1001 + + x3 + = 4

1000x1 1000x2 x1 xz

(7)

x4

whose solution is: x1 = x2 = x3 = x, System (7) can be rearranged into: XI

x2 x3

= 1001 - 1 0 0 0 ~ ~ = 1001 - 1000x1 = 1001 - 1000x2

f4 = x1+ x2 + + x4 X)

-4

=0

=

1.

1.2 Convergence Tests

The new problem (8), although being characterized by only one equation with unknown x4 has an extremely ill-conditionedform. As a matter of fact, if x4 is evaluated numerically as: x4 = 0.99999, then the following values are obtained: x1 = 1.010014, x2 = -9.013580, x3 = 10,014.58 andf(x,) = 10,003.58. It should be emphasized that system (8)is linear (therefore a simpler problem) and that it is reduced to a very simple equation in one unknown: x4. Quite often, it is better to avoid any manipulation of the system if the goal is to reduce its dimensions. Actually, it is advisable to leave the NLS in its original form since it comes from modeling a physical phenomenon. Doing so, there are more guarantees that the numerical system is well-posed because it describes a real problem. What should be done is something that is apparently similar to rearranging the system but it is conceptually quite different. It is advisable to try exploiting the structure of the system without manipulating it. A very simple example is represented by the solution of a steady-state distillation column. The liquid-vaporequilibria and the material balances of the unit should not be solved stage by stage, in a top-bottom sequence, while iterating towards convergence through the overall material balance of the column so to have the input/output flowrates consistent. By doing so, the physical structure of the problem would shift to obey to a sequential mathematical algorithm that would solve several apparently simplified subproblems. Such an approach would not respect the physical structure of the equilibrium stage in the sense that it would be equivalent to solving a flash problem starting from the known composition of one output stream to determine the compositions of the input and second output streams. On the contrary, the intrinsic structure of a distillation column brings tridiagonal organization to the correlated mathematical problem. Such a tridiagonal structure should be exploited to efficiently solve the numerical problem.

1.2 Convergence Tests

Working at the implementation of a numerical algorithm for the solution of NLSs, a quite important matter must be addressed. How do we determine if the new estimate, xi+l.is better or worse than the previous one, xi? The typical approach is to accept the new value, xi+,,if: (9)

Ilf(xi+l)ll2 < Ilf(xi)lll

or, equivalently, if there is a decrease in the merit function: 1

N

1 2

@(x) = - C 4 2 ( x ) = -fTf

j=1

18

I

I Large-Scale Algebraic Systems

The criterion represented by Eqs. (9) and (10) should be avoided within a generalpurpose program whenever the functions fare unbalanced and have significantlydifferent orders of magnitude. In those cases, the equations with lower orders of magnitude do not contribute to the merit function. As an example, we can report the evaluation of a flash, or the modeling of a distillation column. The stoichiometric equations (order of magnitude: 1) stay together with the enthalpy balance equations (order of magnitude: l.EG-l.E9) and significant differences in terms of orders of magnitude are present in the resulting NLS. An improvement of the previous criterion is given by weighting each equation with a suitable weight, wj.Consequently, the merit function becomes: . N

By introducing the diagonal matrix, W, which has elements equal to the weights, 9, the matrix notation follows: 1 1 @,(x) = -(Wf)T(Wf) = -fTW2f 2 2

(12)

More generally, the weights can vary with the iterations. Consequently, the weight matrix becomes Wi. A reasonable criterion for the definition of the weights is to make all equations have the same order of magnitude. To do so, it is sufficient to use weights equal to the inverse of the order of magnitude of the corresponding equations. This criterion can be implemented in the following ways: 0 0 0

The user directly writes the equations in an adimensionalized form. The user assigns the weights to be used by the numerical solver. The numerical solver evaluates the weights of Eq. (11).

Another approach is to consider whether vector, x, is sufficiently near the solution of the problem. Let us suppose we have the following linear system:

Ax=b

(13)

The distance of a point xi from one of the planes, j: ajlxl

+ aj2x2 + . . . +

ajNxN

= bj

(14)

is determined by calculating the point at which the orthogonal line passing through xi intersects the plane itself. The square of the distance between that point and xi is: dj

=

[ajl(xl)i

+ aj2(x2)i + . . . + ajN(xN)i - hi] 2 N

m=l

(15)

7.2 Convergence Tests 119

By adopting the following weights: 1

2

w.= J

N

m=l

every term of summation (11) evaluated at point x, represents the square of the distance between such a point and the planes of system (13). As far as NLSs are concerned, matrix A becomes an approximation of the Jacobian, J. Since the Jacobian matrix changes with the iterations, the weights should also be modified. This strategy may be adopted to automatically evaluate the weights in Eq. (11). Unfortunately, the aforementioned strategy does not benefit from the following property (Buzzi-Ferrarisand Tronconi, 1993): Given a merit function, F(x), applied to a linear system, it is assumed that if F(x,+,) < F(x,) then point x , + ~is closer to the solution than point x,. The criteria described so far do not benefit from this property except for the linear system (13) consisting of orthogonal planes. with reference to system (13),let us suppose we know the exact solution, x,, that makes the residuals null:

b-Axs=O

(17)

Given a point xi, other than x,, we have the residual:

b-Axi = f i

(18)

by subtracting Eq. (17) from Eq. (18) we obtain: A ( x ~- Xj) = f j

(19)

Formally, the Euclidean norm of the distance xi - x, is:

and the geometric interpretation of Eq. (20) is that the quantity IIA-'f,llz measures the distance of xi from the solution x,. With regards to NLSs, Eq. (20) is a measure of the distance of point xi from the solution of the linearized system, where A = Ji represents the Jacobian matrix evaluated using xi. Finally, the distance of a new point xi+, from the solution of the same system is:

Whenever a nonlinear system is concerned, the new point

must be accepted if

given that, in the case of linear systems, Eq. (22) means that xi+l is closer to the solution than xi is. It is worth highlighting that the Jacobian of Eq. (22) is kept constant while f, and f,+, are the residuals at points xi and xi+'.

20

I

I Large-Scale Algebraic Systems t

If Newton’s method is adopted to solve the NLS (see subsequent paragraphs) then the Jacobian matrix J i has already been factored to solve the linear system produced by the method itself. The evaluation of the merit function using the two points, xi and xi+l, is therefore straightforward and manageable. Often, besides normalizing the functions, it is also advisable to normalize the variables. A practical way to implement the normalization is to scale the variables by multiplying them for a coefficient so that all the variables have the same order of magnitude. By indicating with D a suitable diagonal matrix of multiplying coeficients, the proposed transformation is: z = DX

(23)

Consequently, the merit function with the new variables becomes: &D(z)

1 2

= -f(D-*z)

T

W2f(D-*z)

1.3 Substitution Methods

Before applying the substitution method to the solution of an NLS it is necessary to transform the equations into the following formulation:

h(x) = q(x)

(25)

where system h(x) should be easily solvable if the value of q(x) is known. The method consists of applying the iterative formula: h(xi+l) = q(xi)

(26)

where xi+l is obtained from xi. The easiest iterative formula is: x j = &(XI, x2, . . ., + l ,

xj+l,

. .., X N )

(27)

where each variable is obtained explicitly from the corresponding function. The procedure shown in (27) has the same shortcomings as the monodimensional case. Moreover, it is quite difficult to find a proper formulation that converges to the solution.

1.4 Gradient Method (Steepest Descent)

The gradient of a function is a vector. The function changes more rapidly in the direction of the gradient. With reference to the merit function (lo),the gradient in xi is given by:

Consequently, vector

P ( x ~= ) pi = -gi = - J T f i

(29)

describes the direction where the merit function (10) decreases more rapidly. Obviously, the direction of the gradient changes whenever a different merit function is adopted. When the merit function (11) is involved, the search direction becomes:

If the variables are also weighted and the merit function (24) is adopted, then the search direction becomes:

The evaluation of the space increment, ai,is performed by a monodimensional search. The procedures that adopt the gradient (steepest descent) method, as the search direction, have major limits if used alone. Actually, such methods are efficient only at the initial steps of the solving procedure. The gradient method may be efficiently coupled with Newton’s method since it is quite complementary to it. Newton’s method is rather efficient in the final steps of the search while the gradient method is efficient in the initial ones.

1.5 Newton’s Method

If the fi of the NLS can be expanded in terms of a Taylor series:

f(xi

+ di) = f i + Jidi + O( lldi 112)

(32)

and point xi is rather close to the solution, it is possible to stop the expansion to the first order terms. In this case, the correction vector, Di, to be summed with point xi comes from the solution of the system:

The following iterative procedure represents the elementary formulation of Newton’s method:

where di comes from the solution of the linear system (33):

J1. d1 .-- - f . 1

(35)

22

I

7 Large-Scale Algebraic Systems

Consequently, Newton's method has the following search direction: pi = di

(36)

and a,= 1 Whenever Newton's method converges, its convergence rate is quadratic. It is possible to identify one difference between the solution of nonlinear systems and multidimensional optimization. Usually, the Jacobian matrix of system (35) is not symmetric. Thus, it is not possible to either solve the linear system with the Cholesky algorithm or to halve the memory allocation. The most efficient methods adopted for the Jacobian factorization require twice as much time as the Cholesky algorithm. The correction, di, obtained from system (35) is independent from either a change of scale in the variables or the merit function. In fact, by introducing the scale change: y=cx+c

(37)

the new Jacobian, with respect to the variables y, becomes: Jy = JS1

(38)

and the Newton's method estimate for the x variables is: X;+I

= X; - Ji'fi

As a result, the Newton's method estimate is invariant with respect to a linear transformation using the variables x as well as the merit function (22). Vector di represents a direction where all the merit functions decrease. Actually:

g'd; = (JTfi>' (-JL'fi) T

= -fTJjJi'f; = -fTfi

gTd, w 1 -- (JTWtfi) (-Jr'fi)

= -fTWfJiJi'fi =

g%,di = (JTWtfiDF2)T (-JL1fi) =

i0

-fTWtfi < 0

-Di2fTWffi < 0

Such a property is valid if the following two conditions are satisfied: 1. the Jacobian matrix is not singular, i.e., the inverse matrix must exist; 2. the Jacobian in Eq. (41)must be a good approximation of the true Jacobian matrix and not a generic matrix Bi, otherwise:

1.5 Newton's Method

J,B;' # I (45) and the previous Eqs. (42-44) may not be true. It is also possible to outline another difference between the solution of nonlinear systems and multidimensional optimization. As far as multidimensional optimization problems are concerned, matrix Bi may also be a bad approximation of the Hessian (provided it is positive and definite) and at the same time be able to guarantee a reduction of the merit function. Conversely, matrix Bi involved in the solution of NLSs should be a good estimate of the Jacobian. Besides the previously mentioned advantages, Newton's method also presents some disadvantages that suggest not using it with the trivial iterative formulation of Eqs. (34) and (35). Three different categories for the classification of the problems related to Newton's method can be outlined: 1. Problems related to the Jacobian matrix 0 The method undergoes a critical point if the Jacobian is either singular or illconditioned. 2. Problems related to the convergence of the method 0 The method may not converge to the solution; 0 The new prediction may be worse than the previous one with respect to all merit functions. 3 . Problems related to the Jacobian evaluation and the linear system solution 0 Every new iteration requires the evaluation of the Jacobian matrix. If the Jacobian is evaluated numerically, this means that the nonlinear system (1)is called N times; 0 Each new iteration requires the solution of the linear system (35).

The algorithms derived by the original Newton's method may be divided into two classes depending on how the Jacobian matrix is evaluated. The first class comprises Newton's modified methods where the Jacobian is evaluated analyhcally or numerically approximated at point xi. The second class comprises the quasi-Newtonmethods that update the Jacobian by means of the information gathered during the iterative process. For both classes, as soon as the Jacobian matrix has been either evaluated or updated, it is recommended to immediately execute a Newton's iteration in order to exploit the efficiency of such a method. Consequently, both of the aforementioned classes first verify the point:

xi+l = xi

+ di = xi - Ji'fi

Such a point is accepted if it satisfies at least one of the following tests:

(46)

I

23

24

I

I Large-Scale Algebraic Systems

ffflW2fi+l < fTWZfi(1 - y )

(48)

The y parameter guarantees a satisfactory improvement of the merit functions.

1.6 Modified Newton's Methods

In these methods the Jacobian matrix is evaluated analytically or is approximated numerically. Since the Jacobian is recalculated at each iteration it is also necessary to solve the linear system (35). Several expedients and precautions are necessary to reduce the drawbacks of Newton's method.

1.6.1 Singular or Ill-conditioned Jacobian Matrix

The solution of system (35) is performed through the factorization of the Jacobian matrix. Whichever factorization is adopted, it is mandatory to evaluate the condition number of the system and to properly operate if such a number is too high. Actually, it is possible to introduce the auxiliary function:

The minimum of function (49) is:

which is equivalent to the prediction of Newton's method (35) applied to the solution of the nonlinear system. If the Jacobian is well-conditioned then the correction, Di, is achieved by solving system (35) instead of system (SO). Conversely, the use of function (49) becomes interesting when the Jacobian matrix is quite ill-conditioned or even singular. As a matter of fact, the system matrix, JTJi, is the Hessian of function (49) and it is symmetric. By using function (49) instead of the merit function (lo),there is the advantage of knowing the Hessian without having to evaluate the second derivatives. At the same time, it is possible to apply to matrix JTJi, all the expedients exploited when an ill-conditionedminimum problem is involved. Two algorithms implement the aforementioned idea: 0

The Levenberg-Marquardtmethod modifies system (50) in the following way:

1.G Modified Newton’s Methods

The ,u parameter may be chosen so to transform matrix (jTiji+ p ~ in) a wellconditioned matrix. Besides being an artifice to reduce the ill-conditioning of the Jacobian,the LevenbergMarquardt method is also an algorithm that couples Newton’s method to the gradient one. Actually, if the Jacobian is not singular, the solution of system ( S l ) , with p = 0, is equivalent to Newton’s estimate. Conversely, when high values of parameter p are involved, the search direction tends to the gradient of the merit function (10). The Gill-Murray criterion represents the second alternative. The idea is to make the diagonal coefficients of matrix J:Ji positive. If the Jacobian J is QR factored and matrix R is worked out in order to avoid any zeros in the main diagonal, then matrix JTJ = RTR is symmetric positive definite. Buzzi-Ferrarisand Tronconi (1986)showed a new methodology for the modification of the Jacobian matrix. If the Jacobian is ill-conditionedor singular then some equations in system (35) are linearly dependent. Consequently, it is possible to eliminate those linearly dependent rows. Since the resulting system becomes underdimensioned, it is appropriate to adopt the LQ factorization that produces the solution with minimum Euclidean norm for vector di. Thus, it is possible to avoid an excessively large correction on such a vector. The numerical solution satisfies not only the subsystem but also the equations that were removed, since, if compatible, they are almost a linear combination of the others. This criterion is often efficient and is preferable to the previous one since it is not influenced by the merit function. At the same time, it does not produce a false solution. By the term false we mean a solution of the minimum problem that is not the solution of the NLS. 1.6.2 The Convergence Problem

As mentioned, the Newton’s estimate is not satisfactory whenever point xi+ldoes not meet conditions (47) and (48).In such a case, it is possible to adopt the following strategies: 0

0 0

A monodimensional search is performed in the same direction as the Newton’s one. The region where the functions are linearized is reduced. An alternative algorithm to the Newton’s method is adopted.

Before addressing these points, the following feature should be emphasized: an NLS may not have a solution. Moreover, if a solution exists, we are not sure that it will be possible to determine it. A numerical program should warn the user about its incapability of solving the problem. 1.6.2.1 Monodimensional Search

Usually, since the monodimensional optimization is both not time-consuming and quite efficient, it is adopted in all-purpose solvers. Normally, the monodimensional

26

I

I Large-Scale Algebraic Systems

search algorithm is not pushed to the extreme. Actually, the optimization is intended to identify a new point where Newton’s method might easily converge. The merit function that is usually adopted is the weighted one (12).At the outset, the following data are known: 0 0

the value of Qw at point xi; the gradient g, at point xi and that in the direction di, g:di; the value of Qw at point xi + di.

Since there are three data in the direction di, the merit function Qw may be approximated by the parabola:

Y ( t ) = Y(0)+ tY’(0) + t2 [ Y ( U - y(0)

- Y’(O)]

(52)

Tne minimum of the parabola is:

In the following,we will assume to have a good estimate of the Jacobian matrix. Consequently, the following equation may be adopted:

and the minimum of the parabola becomes: U =

fTWffi f;+,Wff;+, fTW;fi

+

(55)

It is recommended to check that u is not too small by imposing: u > 0.1

(56)

Since point xi+l does not satisfy Eq. (47),an upper limit for u is automatically set. If the minimization is not successful then a new artifice should be exploited, otherwise the program must stop with a warning. 1.6.2.2 Reduction o f the Search Zone

The Levenberg-Marquardt method may be considered from three distinct perspectives: 0 0 0

as an artifice to avoid the ill-conditioned problem of the Jacobian matrix; as an algorithm that couples Newton’s method to the gradient one; as a method exploiting either a reduced step or a confidence region.

The third point is the most interesting when a reduction of the search zone is concerned. In this case, it is required to identify the correction di that minimizes the auxiliary function (49)with the constraint:

1.7 Quasi-Newton Methods

where 6 has a specified value. A valid alternative to the Levenberg-Marquardt method is represented by the dog leg method, also known as Powell’s hybrid method (1970). Once again, such a method couples Newton’s method to the gradient one. The original version of Powell’s method was close to the concept of either confidence region or reduced step. Powell proposed a strategy for the modification of parameter 6 subject to both the successes and failures of the procedure. 1.6.2.3 Alternative Methods

Whenever Newton’s method fails, it is necessary to switch to an alternative method. For this reason, the most commonly used method is the gradient of a merit function. There are several alternatives. It is possible to perform a monodimensional search along the gradient direction. Even better, the two methods may be coupled as it happens with the Levenberg-Marquardt algorithm or the dog leg method. Another choice is to perform a bidirectional optimization on the plane defined by both search directions. Unfortunately, there are no heuristic methods for the solution of NLSs. Only for very specific problems can a substitution method be expressly tailored and coupled to Newton’s method. As an example, in the field of chemical engineering, the boiling point (BP) method may be implemented and applied to distillation columns. In the following,we will introduce the continuation methods. Such methods transform the functions of the NLS and solve an equivalent and dynamically easier problem.

1.7 Quasi-Newton Methods

Let Bi be an approximation of the Jacobian matrix at point xi.As mentioned before, matrix Bi must be a good approximation of the Jacobian. Consequently, also in the case of quasi-Newton methods, it is necessary to evaluate either analytically or numerically the Jacobian matrix. If during the search of the solution the rate of convergence should decrease, reevaluating the Jacobian is recommended. Therefore, it is not possible to implement a quasi-Newton method without a modified Newton’s method. During the solution procedure the values of functions f, and f,+lare known in the points xiand xi+l. Such points must not necessarily correspond to previous Newton’s method estimates. Given:

AX;= ~ i + l xi

(58)

if the distance between the two points is not significant, it is possible to link the function values f, and fi+l through a Taylor expansion:

127

28

1

I Large-Scale Algebraic Systems

fi+l = fi

+ BAxi

(59)

where the Jacobian, B, is evaluated in a suitable point between xi and xi+l. Specifically, it is possible to impose that the Jacobian satisfies the following condition:

f i+l = f i

+ Bi+l AX;

(60)

Equation (GO) does not allow univocal evaluation of all components of the Jacobian when the number of equations N > 1. In this case, N - 1 more conditions are necessary. In 1965 Broyden proposed to choose the conditions to be added to Eq. (GO) in order to keep invariant the product between the Jacobian, evaluated in xi and in xi+l, and an orthogonal vector to Axi. Generally, for any given vector, qi, with: qTAxi = 0

(61)

it must result that:

This condition is reasonable ifwe consider Eq. (59). Actually, it is possible to modify the Jacobian in the direction Axi so as to satisfy condition (GO). On the contrary, in a direction orthogonal to the previous one, there is no additional information and the behavior of the Jacobian,with respect to a Taylor expansion in that direction, should be invariant. By coupling conditions (62) and (GO), it is possible to univocally identify the Jacobian in xi+l: Bi+l = Bi

+ (fi+l

-

fi -

B~AX~)AXT

AX:AX~

1.8 Large and Sparse Systems

When the number of equations and variables is quite large, often each equation depends on a reduced set of variables. As far as the Newton’s and quasi-Newton methods are concerned, it is necessary to exploit the sparsity of the Jacobian matrix so as to reduce the memory allocation while saving CPU time. In particular, the following expedients are essential: The solution of system (35) should be made by the method that best exploits the Jacobian sparsity and structure. If the Jacobian has no specific structure that can be directly exploited, it is worthwhile rearranging both the variables and equations so as to reduce the CPU effort and memory allocation required by the factorization of the Jacobian matrix. The null Jacobian components should not be evaluated. This happens automatically if the Jacobian is evaluated analytically. Conversely, whenever the Jacobian matrix is approximated numerically, the following computations:

1.8 arge and Sparse Systems

Jik =

J(Xi

+ hkek) -j(xi) hk

(64)

should be avoided if it is a pAoA known that: x ( x i + h&) =f;(xi) It is possible to exploit some formulas to update the Jacobian, which are able to preserve its sparsity. At the same time, if some elements are constant, they should not be updated by those formulas. Schubert (1970) proposed a modification of the Broyden formula (1965), while Buzzi-Ferraris and Mazzotti (1984) proposed a modification of the Barnes formula (1965). These formulas take into account the coefficientsthat are known and do not modify them. The update is performed only on the coefficients that are unknown. 0 If the Jacobian is evaluated numerically, it is not convenient to increment a variable one at a time and to perform a call to the nonlinear system. This point must be emphasized. If Eq. (64) is adopted to evaluate a Jacobian matrix that is supposed to be full, then vector ek is the null array except for position k, where the element is equal to 1. In this case, system (1) is called N times to evaluate the derivatives of the functions with respect to the N variables. Let us now consider the following sparse Jacobian matrix, where the symbol x represents a nonzero element (see Fig. 3.1). It can be observed that when the system is called to evaluate the derivatives with respect to variable xl, the only functions to be modified arefi and&. If at the same time variable x2 were modified, it could be possible to evaluate the derivatives with respect to this variable since it only influences functionsh andf7. Going on with the reasoning, it is possible to show that only three calls to the system of Fig. 3.1 are sufficient to evaluate the whole Jacobian matrix. In fact, with the first call it is possible to increment variables x1x2x3x4x6x9.With the second call we increment variables x5x8. Finally, with the third call we increment variables ~7x10.When the system is sparse, the total number of calls necessary for the evaluation of the Jacobian matrix can be drastically reduced. It is not easy to identify the sequence of variable groupings that minimizes the number of calls to the nonlinear system. Curtis, Powell and Reid (1972) proposed a heuristic algorithm that is often optimal and can be easily described. We start with the first variable and identify the functions that depend on it. We then check if the second variable does not interfere with the functions with which the first variable interacts. If this happens, we go on to the third variable. Any new variable introduced in the sequence also increases the number of functions involved. When no additional variables can be added to the list, this means that the first group has been identified and we can go on with the next group until all N variables of the system have been collected. It is evident that the matrix structure of the Jacobian must be known for this procedure to be applied. This means that the user must identify the Boolean of the Jacobian, i.e., the matrix that contains the dependencies of each function from the system variables (see Fig. 3.1).

29

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I Large-Scale Algebraic Systems Figure 3.1 The Boolean matrix describes the Jacobian structure and the function dependency from the variables of the nonlinear system.

1.9 Stop Criteria

When the problem is supposed to be solved or when there are insurmountable problems, there are some tests to bring the iterations to an e n d It is advisable to implement a limitation on the maximum number of iterations. If the weighted function (12) is lower than an assigned value, there is a good chance a solution has been reached. The procedure is stopped if the estimate of Newton’s method, di, has all components reasonably small. With multidimensional optimization it is not sufficient to check whether a norm of vector di is lower than an assigned value. On the contrary, it is advisable also to to check the following relative:

Even if a quasi-Newton method is used, a good approximation of the Jacobian is known. Consequently, this criterion is adequately reliable. Nonetheless, it should be emphasized that this test is correct only when the difference between two consecutive iterations, di = xicl - xi, comes from a Newton-like method and the Jacobian is not singular.

1.10 Bounds, Constraints, and Discontinuities

Some problems have solutions that are not acceptable since they belong to unfeasible regions. In these situations, it can be worthy assigning some bounds to the variables in order to avoid the solution from falling in those unfeasible regions. This issue requires the adoption of specifically tailored numerical algorithms that are able to

1 . 7 7 Continuation Methods

depart from the unfeasible attractor while moving towards the feasible region. Similar considerations apply when discontinuities are involved. In this case, the numerical algorithm should be able to work across the discontinuity while avoiding a crisis due to its presence. The discontinuity can be either in the function itself or in its derivatives (Sacham and Brauner 2002).

1.11 Continuation Methods

Let us suppose we have a nonlinear system of N equations whose solution is quite difficult. For some reason that will be explained in the following we suppose we have a vector of adjoint parameters z, of M elements, in the equations of the system. Therefore, the NLS can be rewritten as:

f(x, 2 ) = 0

(66)

The system must be solved with respect to the N unknowns, x, given a specific value, z = zF,of the parameter vector. Let us now suppose we know another system, q(x, z) = 0, in some way related to the previous one, whose solution, for a given value of parameters z, is quite easy. In this case it is possible to write a new system that is a linear combination of the previous two:

The parameter t in Eq. (67) is called the homotopy parameter. When the parameter t varies in the interval 0, ... 1, system h is solved for a value of x that satisfies both systems q and f. The parameters z can be a function of parameter t in any way, provided that for t = 1 we have z = zF. The most straightforward functional dependency between t and z is the linear one: z = ZO

+ (ZF

-

zo)t

(68)

where zo corresponds to the initial value of the parameters. Another functional dependency is the following one:

There are several alternatives for the auxiliary system q(x, z). The common characteristic is that for t = 0 the solution of system q ( q , zo) = 0 should be effortless. The following are some choices: 0

Fixed point homotopy: q(x, z)

=x -q

+ z - zo

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7 Large-Scale Algebraic Systems

h(x, Z, t ) = tf(x, Z) 0

+ (1 - t) [(x

ZO)

+ (1- t)J(%,

f ( q , zo) (71)

=

J(%. ZO) [(x - %) +

+

20) [(x - ~ g ) ( 2

Parametric continuation method: q(x, Z) h(x, Z, t ) = f(x, Z) = 0

-

(70)

=0

Homotopy with scale invariance: q(x, z) h(x, Z, t) = tf(x, Z)

0

- ZO)] = 0

Newton or global homotopy: q(x, z) = f(x, z) h(x, Z, t ) = f(x, Z) - (1 - t)f(Xg,

0

+

- ~ g ) (Z

- Z0)I = 0

(Z

- ZO)]

(72)

=0

(73)

The fourth criterion (73) deserves some explanation since one could think that the original problem has not been modified. In many practical cases, a problem may have a simple solution in correspondence to a value zo of the parameters, while there are numerical difficulties for zF. In this case the system is solved by setting t = 0 and z = zo. We then get a first solution ~0 that satisfies: h(xo, zo,O) = f h , 20) = 0

(74)

Successively, we change t from 0 to 1in order to modify continuously the parameters from zo to zF.By doing so, several intermediate problems are solved through a stepby-step procedure. It is worth highlighting two cases: 1. The parameters, z, correspond to some specifications that should be satisfied. Often, the problem can be easily solved if the specifications are mild, while it becomes hard when the requirements are tight. A typical example is represented by a distillation column. The continuation parameter can be the product purity. If the product purity is quite high, there can be some problems concerning the numerical solution. In this case, it is recommended to start with a lax specification. Once the solution has been evaluated, the problem is slightly modified by tightening the specification. A new solution is performed by adopting as a first guess the previous solution. By continuing the procedure, it is possible to reach the final product purity. 2. The problem can be solved easily by introducing some simplifications. The continuation method modifies continuously the simplified hypotheses, carrying the system towards the detailed model. In the case of separation units, one of the problems may be the evaluation of the liquid-vapor equilibrium constants, k. If the k vector strongly depends on the compositions then it can be difficult to identify the first guess values that make the Newton’s method converge. In this case, it is convenient to consider the system ideal. By solving the simplified problem under the hypothesis of ideal k values, a solution is easily obtained. Such a solution becomes the first guess for the continuation procedure that takes the system towards the hypothesis of nonideal liquid-vapor equilibria. The parameter vector z comprises the k values as follows:

7. 7 7 Continuation Methods

Initially, when t = 0, all parameters are equal to the ideal k values. The homotopy parameter, t , evolves from 0 to 1. By doing so the k values continuously change from the ideal to the real hypotheses. The same reasoning can be applied to the enthalpies of the mixture. The main advantage obtained by the continuation method is that the intermediate problems have a physical implication. Consequently, each intermediate problem has a solution where the variables take up reasonable values. Another approach to the solution of the continuation problem is to implement an ODE system that integrates the x variables and the z parameters from an initial condition (easy problem) to a final time (difficult problem). Seader and coauthors (Kuno and Seader 1988; Seader et al. 1990; Jalali and Seader 1999; Gritton et al. 2001) have worked extensively on this approach.

References 1 Barnes J. C. P. An Algorithm for Solving

2

3

4

5

6

7

8

9

Nonlinear Equations Based on the Secant Method. Comput. J. 8 (1965) p. 66 Broyden C. G. A Class of Methods for Solving Nonlinear Simultaneous Equations. Math. Comput. 21 (1965) p. 368 Broyden C. G. A New Method of Solving Nonlinear Simultaneous Equations. Comput. J. 12 (1969)p. 94 Buzzi-Ferraris G. Mazzotti M. Orthogonal Procedure for the Updating of Sparse Jacobian Matrices. Comput. Chem. Eng. 8 (1984) p. 389 Gritton K. S. Seader J. D. Lin W,]. Global Homotopy Continuation Procedures for Seeking all Roots of a Nonlinear Equation. Comput. Chem. Eng. 25 (2001) p. 1003 Buzzi-Ferraris G. Tronconi E. BUNLSI - A Fortran Program for Solution of Systems of Nonlinear Algebraic Equations. Comput. Chem. Eng. 10 (1986) p. 129 Buzzi-Ferraris G. Tronconi E. An Improved Convergence Criterion in the Solution of Nonlinear Algebraic Equations. Comput. Chem. Eng. 17 (1993) p. 419 Curtis A. R. Powell M./. D. Reid j . R On estimation of Sparse Jacobian Matrices. Report TP476 AERE Hanvell 1972 Jalali F. Seader J . D. Homotopy Continuation Method in Multi-phase Multi-reaction Equilibrium Systems. Comput. Chem. Eng. 23 (1999) p. 1319

10 Powell M . J. D. A Hybrid Method for Nonlin-

ear Equations. In: Numerical Methods for Nonlinear Algebraic Equations. Ed.: Rabinowitz G . Breach London, 1970 11 Schubert, L. K. Modification of a QuasiNewton Method for Nonlinear Equations with a Sparse Jacobian. Math. Comput. 24 (1970) p. 27

Further Reading 1

2

3

4

5

6

Allgower E. L. Georg K. Homotopy Method of Approximating Several Solutions to Nonlinear Systems of Equations. In: Numerical Solution of Highly Nonlinear Problems, Foster, Amsterdam, 1980 Davidenko D. On a New Method of Numerically Integrating a System of Nonlinear Equations, Doklady Akademii Nauk USSR 88 (1953) p. 601 Eberhan /. G.Solving Equations by Successive Substitution - The Problems of Divergence and Slow Convergence. J. Chem. Edu. 63 (1986) p. 576 Gupta Y. P. Bracketing Method for On-line Solution of Low-Dimensional Nonlinear Algebraic Equations. Ind. Eng. Chem. Res. 15 (1995) p. 239 Jalali F. Process Simulation Using Continuation Method in Complex Domain. Comput. Chem. Eng. 22 (1998) p. S943 /sun Y. W. Multiple-step Method for Solving Nonlinear Systems of Equations. Comput. Appl. Eng. Edu. 5 (1997) p. 121

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1 Large-Scale Algebraic Systems 7 Karr C. L. Weck B. Freeman L. M. Solutions

8

9

10

11

12 13

14

to Systems of Nonlinear Equations via a Genetic Algorithm. Eng. App. Artif. Intell. 11 (1998) p. 369 Kuno M. Seader]. D. Computing all Real Solutions to Systems of Nonlinear Equations with a Global Fixed-Point Homotopy. Ind. Eng. Chem. Res. 27 (1988)p. 1320 Neurnaier A. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge 1990 Paloschi]. R. Bounded Homotopies to Solve Systems of Algebraic Nonlinear Equations. Comput. Chem. Eng. 19 (1995) p. 1243 Paterson W. R. A New Method for Solving a Class of Nonlinear Equations. Chem. Eng. Sci. 41 (1986) p. 135 Rice R. J. Numerical Methods, Software and Analysis. Academic Press, London, 1993 Seader]. D. Kuno M. Lin W. J. Johnson S. A. Unsworth K. Wiskin]. W. Mapped Continuation Methods for Computing all Solutions to General Systems of Nonlinear Equations. Comput. Chem. Eng. 14 (1990)p. 71 Shacham M. Kehat E. Converging Interval Methods for the Iterative Solution of a Nonlinear Equation. Chem. Eng. Sci. 28 (1973) p. 2187

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Shacham M. Brauner N. Numerical Solution of Non-linear Algebraic Equations with Discontinuities. Comput. Chem. Eng. 26 (2002) p. 1449 Shacham M. Brauner N. Cutlip M. B. A Web-based Library for Testing Performance of Numerical Software for Solving Nonlinear Algebraic Equations. Comput. Chem. Eng. 26 (2002) p. 547 Schnepper C. A. Studthm M. A. Application of Parallel Interval Newton/Generalized Bisection Algorithm to Equation-Based Chemical Process Flowsheeting. Interval Comput. 4 (1993) p. 40 Sundar S. Bhagavan B. K. Prasad S. Newtonpreconditioned Krylov Subspace Solvers for System of Nonlinear Equations: a Numerical Experiment. Appl. Math. Lett. 14 (2001) p. 195 Wayburn T. L. Seaderj. D. Homotopy Continuation Methods for Computer-Aided Process Design. Comput. Chem. Eng. 11 (1987) P. 7 Wilhelm C.E. Swanq R. E. Robust Solution of Algebraic Process Modeling Equations. Comput. Chem. Eng 18 (1994) p. 511

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

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2.1 Introduction

Chemical and biotechnical processes are often described by distributed dynamic models, that is, partial differential equations (PDEs) or partial differential algebraic equations (PDAEs) incorporating convection, diffusion, reaction and/or thermodynamic property terms. The PDAE models represent temporal as well as spatial variation of state variables. Since analytical solutions only exist in few cases, due to nonlinearity and complexity, computational methods (or numerical analyses) are generally required to solve such distributed dynamic models. In this chapter numerical methods for solving PDEs are reviewed in the following three sections, first treating semidiscretized (method of lines) and fully discretized methods before discussing adaptive and moving mesh methods. Several applications of distributed models appearing in preparative chromatography, futed-bed reactors, slurry bubble columns, crystallizers and microbial cultivation processes are treated in section 2.6 as a means to introduce various relevant aspects for the solution of PDE/PDAE models for chemical and biotechnical processes. Finally in section 2.7 an approach for combining computational fluid dynamic (CFD) technology with process simulation is illustrated and discussed. 2.2 Partial Differential Equations

Chemical and biotechnical processes often take place in spatially distributed systems and are therefore most appropriately described by distributed dynamic models, that is, partial differential equations (PDEs)incorporating convection, diffusion, reaction and thermodynamic property terms (Heydweiller et al. 1977; Kohler et al. 2001). For example, the material, energy, and momentum balances on moving fluid phases result in PDEs with respect to time and one or more space dimensions. Partial time derivatives occur as a direct consequence of the transient operation, while convective Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 200G WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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2 Distributed Dynamic Models and Computational Fluid Dynamics

and diffusive (or dispersive) effects normally lead to first and second order partial space derivatives, respectively. Material and energy balances on stationary phases (e.g., the solid adsorbent in a packed-bed adsorberlreactor) may not involve any convective or diffusive terms and are therefore free of partial space derivatives.The properties of such a stationary phase at any single point obey ordinary differential equations (ODES).Algebraic equations (AEs) are often used to define chemical equilibria, physical properties (e.g., enthalpy in terms of temperature, pressure and composition), or other intermediate quantities appearing in the differential equations. Therefore, physical models are generally expressed as PDEs coupled with AEs, i.e., socalled partial differential algebraic equations (PDAEs) submitted to initial conditions and boundary conditions. For the purpose of this review, a PDAE system with one spatial coordinate can be expressed as follows:

where u(t, x ) is the state variable as a firnction of time (toIt Itf) and space (xo I x 5 xf),F(u)is the convection flux, D is the diffusion (or dispersion) coefficient, r(u, 8) is the reaction rate equation depending on state variables (u) and parameters (8), and g(u) is a nonlinear algebraic equation. On the right-hand side of Eq. (la), the first, second and third terms take into account convection, diffusion and reaction, respectively. The partial differential equations govern a family of solutions. A particular member of the family of solutions is specified by the auxiliary conditions like initial and boundary conditions. For a PDE containing a first-order time derivative, one initial condition (IC) is required at an initial time level, t = toalong the space ( x ) : U(t0,

x ) = uo

(2)

For a PDE containing a second-order spatial derivative like Eq. (la), two boundary conditions are required at the physical boundaries of the solution domain. For example, the well-known Danckwert’s boundary condition (BC) can be imposed for Eq. (la):

=0

at x = xf for all t

where f(u) 11 in is the inlet flux predescribed by the operating condition. In the literature, Eq. (3b) is called the Neumann BC and Eq. (3a)is a mixture of the Dirichlet BC and the Neumann BC. Proper specification of auxiliary conditions is a necessary condition to obtain a well-posed problem (Hoffman 1993).

2.2 Partial Differential Equations

Physical mathematical models like the partial differential equations (PDEs)have a continuous form, while theose for solution purposes have to be discretized into a semidiscrete form (e.g.,using only spatial discretization, Ax) or a fully discrete form (e.g., combining temporal and spatial discretization, At and Ax) in order to represent the models in the temporal and spatial (or computational) domain. Among the large number of numerical methods developed for the solution of PDE or PDAE systems, the following is a well-established classification: 0

0

0

Method of lines (MOL),including finite difference methods, finite element methods and finite volume methods (Finlayson 1980; Schiesser 1991; Leveque 1998; Lim et al. 2001a, Mantzaris et al. 2001a and 2001b). Fully discretized methods (Hoffmann 1993; Chang 1995 and 2002; Lim et al. 2004). Adaptive mesh refinement (AMR) or adaptive grid methods (Berger and Oliger 1984; Berger and LeVeque 1998; Vande Wouwer et al. 1998). Moving grid methods (Miller and Miller 1981; Dorfi and Drury 1987; Huang and Russell 1997; Li and Petzold 1997; Lim et al. 2001b).

The semidiscretized method is called MOL, where PDEs (or PDAEs) are converted into a system of ODES (or DAEs) with respect to time by spatial discretization (see Section 2.3 for details). The main advantage is that well-established time integrators, e.g., Runge-Kutta or backward differentiation formula (BDF) methods, can be used for solving a large set of ODES or DAEs. A main drawback is, however, that it is difficult to control and estimate the impact of the spatial discretization error (Oh 1995). For fully discretized methods (Section 2.4), a system of nonlinear algebraic equations is obtained after temporal and spatial discretization. Adaptive and moving grid methods seem to be most promising since the idea is to use a numerical method in which nodes are automatically positioned in order to follow or anticipate steep moving fronts (Section 2.5). The node positioning may be achieved by using two basic strategies, namely AMR (i.e., local mesh refinement) and moving mesh methods (i.e., continuous spatial redistribution of a futed number of mesh points). These two types of methods are appropriate for solving PDEs in the presence of steep moving fronts or discontinuities. One of the key challenges facing process modeling today is the need to describe the interactions between fluid flow and phenomena models such as chemical reactions, mass transfer and phase equilibrium (Bezzo et al. 2003). Process simulations taking convection, diffusion and reaction into account and using computational fluid dynamics (CFD)for fluid hydrodynamics are important tools for the design and optimization of chemical and biochemical processes. The two technologies are largely complementary, each being able to capture and analyze some of the important process characteristics (Bezzo et al. 2000). Their combined application can therefore lead to significant modeling and simulation benefits, as will be discussed in Section 2.7. Before proceeding with this review, several preliminary concepts are summarized to facilitate presentation of the numerical methods.

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2.2.1 ODE (or DAE) Integration

In the MOL framework, the numerical solution of PDEs (or PDAEs) is obtained by the time integration of the ODEs (or DAEs) resulting from spatial discretization. The general form of ODEs is expressed

(4)

M(t)u = h(t, U )

where u is the time derivative. When the matrix M(t) is singular, Eq. (4)represents a DAE system rather than an ODE system. Solving the DAE system is more complicated than solving the ODE system (see Section 2.2) because the DAE system only has a solution if the initial conditions ~0 are consistent in the sense that the equation M(to) uo = h(b,ug) has a solution, &, for the initial slope. Computations in a DAE integrator does not require M(t) to be nonsingular (Ascher and Petzold 1998). If the time dependent ODE has a condition number that is large, then the problem

a

is stiff. In other words, system (4)is stiff if the Jacobian J = - au (in the neighbor-

I

h

IL >>1. For the stiff ODE/DAE hood of the solution) has eigenvalues A,, where 3 lilminl

systems, implicit BDF time integrators, such as DASSL (Petzold 1983), LSODI (Hindmarsch 1980), and DISCO (Sargousse et al. 1999) and o d e l b in Matlab (The Mathworks Inc., MA, USA) are used for accurate evaluation of time derivatives.

2.2.2 Accuracy and Computational Performance

How close the numerical solution is to the true solution (or analytical solution, if that exists) at the finite temporal and spatial stepsizes (At and A x ) is assessed by evaluating the accuracy of the discretization. As At and A x converge to zero and as the approximation order of derivatives increases, the approximation error generally diminishes. However, one must also account for computational efficiency in terms of the computational time that increases as the accuracy rises. In this context, there is a tradeoff between accuracy and computational efficiency.Thus, to simultaneously minimize the approximation error and the computational time, it can be considered as a multiobjective problem (Lim et al. 2001a). The set of AEs or ODEs obtained after discretization of PDEs differs from the original PDE by the presence of the truncation error terms, which implicitly contribute to the numerical difision or dissipation. The truncation error related to accuracy is always present in the finite approximation of a PDE. An appropriate numerical method should be selected for a given PDE system in order to meet a tolerable numerical error within a reasonable computational time.

2.2 Partial Diferential Equations

2.2.3 Automatic Differentiation

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of some functions. Probably the best known are the gradient methods for optimization (e.g., successive quadratic programming, Powell 1971; see also Section 2.4), Newton’s method for the solution of nonlinear algebraic equations (see Section 2.1), and the numerical solution of ODEs and PDEs. Both the accuracy and computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical solution (Bischof et al. 1992). Taking a system of ODEs converted from a partial differential equation with MOL (see Section 2.1) as an example, the system is given as: du = h(t, AX, U )

(5)

dt

where the state variable u = [u1 ... u N and the nonlinear function h = [h, ... hNare represented (or approximated) on N discrete spatial mesh points (or finite elements). ODE solution methods, such as implicit Runge-Kutta and BDF methods, require a

(3

( N x N) Jacobian - , which is either provided by the user or approximated by a

difference quotient also called divided differences. In fully discretized methods (e.g., the conservation element and solution element (CE/SE) method, see Section 2.2) for the numerical solution of a PDAE, a nonlinear system is obtained as a function of time, spatial stepsizes, and state variables. 0 = h(At, AX, U)

(6) For a futed time and spatial stepsizes, Eq. (6) is solved by a Newton-type iteration dh requiring the Jacobian -. Therefore, the computation of derivatives (or JacodU

bian) is a crucial ingredient in the numerical solution of PDEs or PDAEs. Hand-coding is increasingly difficult and error prone, especially as the problem complexity increases. Numerical approximation by divided differences has the advantage that the function is only needed as a black box. For example, a central divide difference is expressed as:

The main drawback of divided differences is that their accuracy is difficult to assess. In addition, they are computationally expensive. The basic idea of automatic differentiation (AD) is to avoid not only numerical approximations, which are expensive and contain rounding errors, but also handcoded differentiation, which is error prone. Automatic differentiation techniques rely on the fact that every function, no matter how complicated, is evaluated on a com-

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puter as a sequence of elementary operations such as additions, multiplications and elementary functions (Bischof and Hovland 1991). By applying the chain rule

over and over again to the composition of those elementary operations, one can compute derivative information of h(u)exactly and in a completely mechanical fashion. Several AD packages such as Automatic Differentiation in FORTRAN (ADIFOR) (Bischof et al. 1998) are available from the AutoDiff organization Web site (http:/ /www.autodiff.org/)). 2.2.4 Fixed, Adaptive and Moving Grids

The numerical study of evolutionary PDEs with steep moving fronts has demonstrated the need for numerical solution procedures with time and space adaptation. Over recent years, a great deal of interest has developed in adaptive mesh methods (Vande Wouwer et al. 1998).The objective of such approaches is to obtain solutions as accurately as could be obtained if a fine mesh was used over the entire physical domain, but at significantly lower computing cost. One would normally like to concentrate a large proportion of the nodes in regions where the solution exhibits rapid variation with respect to space. In the solution of many chemical engineering problems, steep moving profiles also appear. Common examples are (1) concentration breakthrough curves in fixed-bed absorbers (Kaczmarski et al. 1997), (2) particle (or crystal) size distribution governed by a population balance equation (Kumar and Ramkrishna 1997),and (3) heat conduction problems with a phase change (Mackenzie and Robertson 2000). The futed grid method uses the constant spatial mesh size (Ax) during time integration, whereas the moving mesh method continuously moves a fued number of nodes to the regions of rapid solution variation over time. In the adaptive grid method (or AMR),meshes are locally added or removed at certain time levels according to solution steepness. In Section 2.3 adaptive and moving mesh methods are reviewed and compared. 2.3 Method of Lines

Time-dependent PDEs can be solved by means of the following two-stage procedures. First, the spatial variables are discretized on a selected spatial mesh so as to convert the original PDEs (or PDAEs) into a system of ODES (or DAEs) with time as an independent variable. Secondly, the discretization in time of the ODE/DAE system then yields the required fully discretized scheme, normally using an ODE/DAE solver. This two-stage approach is often referred to as the method of lines (MOL) in the literature.

2.3 Method of Lines

The spatial discretization means that the physical spatial domain (x E Rd, in d dimensions) is discretized, replacing the analytical domain by its discrete equivalent domain (computational domain, 5 E Rd) satisfylng the original PDE in a finite number of discrete points distributed over the physical domain. The discretization of PDEs on spatial domains normally leads to a Jacobian matrix whose elements lie within a narrow band (band Jacobian matrix). But, the bounded structure will be destroyed by the equations resulting from the boundary conditions, recycle streams or other nonlinear features. Hence, a sparse matrix would often be seen. In the ODE/DAE solver, the user will define the appropriate type of the Jacobian matrix to be evaluated by numerical difference, user-provided code or automatic differentiation, as discussed above. The discretization techniques are important since not satisfying local conservation equations will give meaningless results. The numerical scheme has to closely mimic the behavior of the original PDEs and guarantee local conservation of flow properties. To achieve this, it is necessary to not only use conservative formulation of the governing equations but also a conservative numerical scheme. The discretization of the spatial derivatives in Eq. (1) can be accomplished using three main categories: the finite difference method (FDM),the finite volume method (FVM) and the finite element method (FEM). The grid system may be a fixed grid, an adaptive grid or a moving grid. 2.3.1 Finite Difference Methods

The finite difference approximation of Eq. (la) can be expressed in a simple way on N mesh points as follows:

where the first-order spatial derivative is approximated by a first-order upwinding

af 2 0 (or positive convective flow) and the secondscheme under the condition I 3U order derivative by a central difference scheme. For i= 1 and N, boundary conditions such as Eq. (3) are applied. The spatial discretization of the parabolic PDE (1) may cause stiffness due to second-order spatial derivatives, while that of the convection-dominated PDE (i.e., large convection velocity relative to diffusion coefficient) may cause instability, which is associated with oscillatory behavior of their solution due to first-order spatial derivatives (Finlayson 1980).The instability is encountered in using central schemes and higher-order upwinding schemes. To improve the accuracy of the FDMs for the PDEs, numerous attempts have been focused on approximating the first-order spatial derivatives, x i n Eq. (la). Some guidance is provided in the selection of ax

upwind methods in the FDM solution (Saucez et al. 2001).

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In the traditional finite difference discretization (i.e., the fixed-stencil approach to be introduced later), the stencil (Si) used to approximate spatial derivatives is fixed in both size (number of grid points) and position of the stencil points over the discretization procedure. Fixed-stencil (FS) approximations may not be adequate near discontinuities or steep fronts where they may give rise to oscdlations. These problems have motivated the idea of an adaptive stencil (AS) (Shu and Osher 1989) and a weighted stencil (WS) (Jiangand Shu 1996). Namely, the left stencil shift (r) changes with the location xi (see Fig. 2.1), but retaining the total number of points in the stencil. We consider the cell-centered grid rather than vertex-centered grid, as shown in cell centers (xi), and stencils (Si) in one spatial dimension are Fig. 2.1. Cells (Ci), defined by Ci

= [xi-1/2,

+ xi+1/2),

xi = 0 . 5 ( x i - 1 / 2 Si[Ci-r,

(10)

xi+1/21,

. ., Ci, C i + l , . . . , Ci+sl =

Ci-r+l,.

Si[xi-r-1/2,

(11)

~i-r+1/2,

. . ., x i - 1 / 2 , 3 ~ i + 1 / 2 ,

. . .,~ i + s - 1 / 2 ,

(12)

xj+,+l/Z]

where rand s denote the left and right stencil shifts, respectively. The approximation order (k)is defined as: k-l=r+s Consequently, FS approximations can be classified according to the left stencil shift (r) at the given @-order accuracy (see Table 2.1). For the AS methods (e.g., essentially nonoscillatory (ENO) schemes, Shu and Osher 1989), the left stencil shift (r) changes with locations (xi) in order to avoid including a discontinuous (or steep front) cell (Ci)if possible. Just one stencil is selected out of some candidate stencils changed by r when doing the reconstruction, retaining the same order of accuracy.

i

Figure 2.1

;

I I

I

I'

I

fl-

i r=3 , s=3 -v '1 r

-

I

1

Right stencil shift (s)

Left stencil shift (r)

I

,-,'ci. ci+,.c

Si=[C,-,,Ck2,c

Stencil (5,) and cell (C,) structures in one dimensional problems

2.3 Method of Lines

As a result, there are no oscillations and peaks are sharpened. The weighted stencil (Jiang and Shu 199G), however, uses all candidate stencils, each being assigned a nonlinear weight that depends on the local smoothness of the numerical solution. For convective conservation laws, the one-dimensional hyperbolic PDE is expressed by, Ut

= -A

(14)

where the subscripts t and x indicate temporal and spatial partial derivatives (du/dt and df/dx), respectively. If a function h(x) satisfies at a discrete point xi,

then, its derivative with respect to x (i.e.,

fx) can be expressed as follows:

Therefore, if a numerical flux f;+1/2 approximates h ( ~ , + to ~ /a ~kth-order ) accuracy, the convection term can be discretized into k"-order accurate conservative forms:

where fi+llz and are numerical upflux and downflux, respectively, and the uniform mesh size (Ax)is used. Note that in the spatial direction, Eq. (17)can be considered as the finite volume discretization (see Section 2.3.3). The two numerical fluxes are exactly symmetrical with the one mesh distance. So, we only define the numerical upflux, in this text. 2.3.1.1 Fixed-Stencil Approach

In the FS approach, the stencil ( Si) is fixed both in number and position. The numerical flux is approximated in a conservative manner from the flux point values with constants to meet k*-order accuracy:

The constants ci are shown in Table 2.1 only for r 2 0 (Shu 1997). Note that the constants ci are obtained from the derivative of the Newtonian interpolation polynomial (see Eq. (25) for details). For instance, FS-upwind-1stands for a method of the futed stencil with the first-order accuracy (k = 1) in the upwind direction. When the convection velocity is 2 2 0 in Eq. (14), its numerical upfluxldownflux are given by dU

Eq. (18) and Table 2.1:

I

43

44

I

2 Distributed Dynamic Models and Computational Fluid Dynamics Table 2.1 Accuracy order

The constant ci up to fifth-order accuracy ( r 2 0)

Left stencil

(4 (3

j=i

=O

j=z

j=3

0

2

0 1

1I2 -112

112 312

0

113 -116 113

516 516 -716

-116 113 1116

2 3

114 -1112 1/12 -114

13/12 7/12 -5112 13/12

-5112 7/12 13/12 -23112

1/12 -1112 114 25/12

0 1 2 3 4

115 -1120 1/30 -1120 115

77/60 9/20 -13160 17/60 -21120

-43160 47/60 47/60 -43160 137160

17/60 -13160 9/20 77/60 -163160

4

5

1 2 0 1

fx= (J +AI x)

Reference name in this section

FS-upwind-1

1

3

j=4

I1

FS-central-2 FS-back-Z(TPB) FS-upwind-3

FS-central-4

-1112 1/30 -1120 115 137160

FS-upwind-5

af

for - > 0 au -

which was also introduced in Eq. (9). When the convection velocity is a f

+A;;;*

+ 0.5 (&2

-fi’lt1/2

-A:;;2)

(59)

For the explicit form of f(u), approximatingf”+1i+l/2 and fl+’i-1/2 to f ? + l p andf?-1,2, respectively, we can obtain a simple numerical form of the conservation law as follows,

which is a fully discrete formula for Eq. (49)where the convection term is discretized by the second-order central scheme (i.e., FS-central-2 in Section 2.3.1). Therefore, it seems that the explicit FVM for one-dimensional conservation law has almost the same formulation as the conservative FDM of Eq. (15). However, there are differences between the FVM and the FDM in accordance with the definition of the numerical f l w t e ~ f ? +In ~ ~Eq. ~ . (60),f?+l12is in fact an approximation to the average flux at x = along the finite volume Q::

and for the conservative FDM at t

= t,,

like Eq. (15):

Note that a complete FVM (namely the CE/SE method) in space and time domains is introduced in Section 2.4.3.

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2 Distributed Dynamic Models and Computational Fluid Dynamics

2.3.3.1 Spatial Finite Volume Method

Rather than attempting to discretize simultaneously in space and time, our attention is paid to discretization of spatial derivatives in the MOL using an adaptive time integrator, e.g., a BDF ODE solver. A naturally conservative spatial discretization procedure is provided by finite volume methods, where the discrete value viewed as an in Fig. 2.1, approximation to the average value of f(xi, P)over a cell Ci[xi-l,z, rather than as an approximation to a point-wise value of f(xi,t") (Leveque 1998).

where

The advantage of the semidiscretized approach is to achieve high accuracy in space. The cell average is simply the integration of f(x, t) over the cell divided by its area, so conservation can be maintained by updating this value based on fluxes through the cell edges. Although the derivation of such methods may be quite different from that of the conservative FDM,the resulting formulas are identical to Eq. (17). The flux function$+l,2 delivering high-order accuracy in space can be obtained by using higher-order interpolation polynomials like E N 0 schemes and WEN0 schemes (see Section 2.3.1).

2.4 Fully Discretized Method

The generic PDE with convection, diffusion and reaction terms can also be solved by temporal and spatial discretization of the original PDE. The time discretization procedure can be explicit or implicit. Several Mly discrete schemes are introduced in finite difference and finite volume approximations.

2.4.1 Explicit Time Discretization

In this section we consider a PDE with the flow velocity (a) and diffusivity (D) like in Eq. (la): ut = -au,

- Dux, - r(u)

(65)

The above equation is discretized by the forward-time methods. For example, the Leapfrog scheme can be expressed on equidistant At and A x as:

.;+" = UP ,-

where v

2.4 Fully Discretized Method

V

- (UP ,+I -

+P

u:-1)

-

2u:

+

+ Atr (ur)

(66)

a At = - is

called the Courant-Friedrichs-Lewy (CFL) number or convection Ax number and p = DAt is the diffusion number (Hoffman 1993). The partial time Ad derivative (u,) is approximated by a first-order forward difference and the partial space derivatives (u. and uxx)are approximated by a second-order central difference. Since the central scheme of the first-order spatial derivative is unconditionally unstable as mentioned in Section 2.3.1, an upwind scheme is given by the equation below when a 2 0:

The method is shown to be convergent but only conditionally stable. It introduces significant amounts of implicit numerical dissipation into the solution in the presence of steep fronts. The Lax-Wendroff scheme (1960)is a very popular explicit finite difference method for hyperbolic PDEs (i.e., D = 0 in Eq. (65)).To suppress numerical instability caused by the central discretization, an artificial diffusion term is introduced by a secondorder Taylor expansion in time:

ur'" x ur

1 + ( u t ) l A t + -(utt):At2 = u: 2

- a(ux)lAt

1 2 (u,,)lAt + -a 2

2

(68)

where the time derivatives ut and uttare determined directly from ut = -au,. Applying central discretization to Eq. (68),Lax-Wendroff scheme is given for Eq. (65):

+

(69) + u,?_,)+ Atr ( u r ) From a stability analysis, the method is stable only if1 ' 1 5 1. However, it is not V

un+" = UP - -

(UP 1+1 -

u:,)

V2

(uG1 - 24'

often used to solve convection-diffusion PDEs (Hoffman 1993). The Dufort-Frankel method (1953) proposed a modification of the Leapfrog scheme Eq. (GG), which yields a conditionally stable explicit method. In this modification, u? is replaced by the approximation u l =

+

At

U:fl

-

$1

2

(r(uf+l)

+ +-I))

Solving Eq. (70) for u:+' yields:

+

(1 2y)u;+l

=

-v

( U S " - U,P_")

+ (1

-

At +2 (r(uf+') + r@-1))

2y)uy-l

+2 p

-

(71)

I

59

60

I

2 Distributed Dynamic Models and Computational Fluid Dynamics

The scheme cannot be used for the first time step because of the term u7-l. The 5 1. However, large values of p result in inaccurate solumethod is stable only if tions and a starting method is required to obtain the solution of the first time step. The MacCormark method (1969)is based on the second-orderforward time Taylor series as Eq. (68).

(YI

u:+'

u:

1 + (ut):At + -(utt);At2 2

2:

u:

1

+ -2

((ut):

+ (u,):")

At

(72)

where (h); is obtained from the approximation (u)C= (-au? + D(u.)"&. The method is composed of a predictor and a corrector step. In the predictor step, ur+' is approximated by the first-order forward difference: ;;+I

= u: - v (u? 1+1 - ur)

+ p (u,?+'- 24' + u,?-,) + Atr(ur)

(73)

For the corrector step, u?' is given: l

=1

2

(.:+ q + 1 )

- "(;;+I

ui-')

- *n+l

+ ?p(":

- 26";

+ a;::) + Atr (uF)(74)

The two-sep method that shows second-orderaccuracy in both time and space is very popular for solving Eq. (65) and is conditionally stable. A numerical solution can be convergent only if its numerical domain of dependence contains the true domain of dependence of the PDE, at least in the limit as At and Ax go to zero. The necessary condition is called the CFL condition. All fully discrete explicit schemes require fulfillment of the CFL condition:

For stiff PDEs, implicit time discretization is usually preferred. The method of lines (see Section 2.3) using implicit time integrators is originally motivated to solve stiff PDEs, as mentioned above. In the next section, implicit methods fully discretized in both time and space are presented.

2.4.2 Implicit Time Discretization

The implicit Euler central difference method is: U!+1

p(

= UP - -

.?+I 1+1 - .?+I 1-1

) + p(uz:

Rearranging Eq. (76a)yields:

-(i v +

p ) u:

+ (1+ 2p)u:" +

-

2u7"

)::+7~

:':4.1

= ur

+ Atr (u:)

(76a)

+ Atr (ur)

(76b)

2.4 Fully Discretized Method

Eq. (76) cannot be solved explicitly for un+'i,because the two unknown neighboring ~ i ~ "++ ' ~i + also ~ appear in the equation. Due to the implicit feature, this values ~ ~ + and scheme, which has first-order accuracy in time and second-order accuracy in space, is unconditionally stable and convergent (Hoffman 1993). This implicit Euler method yields reasonable transient solutions for modest values of Y and p. The Crank-Nicolson central difference scheme is constructed by a second-order approximation in both time and space: .?+I

=

V un, - [(u::;'

-

- 2u;+l

+

At 2 [r(u;+l)

+

qy)+

(U>l

-

+ u;-+;) + (u;+l

.;-,)I

- 2u;

+ u;-l)]

(77)

I($)]

The Crank-Nicolson method is also unconditionally stable and convergent. The implicit nature of these methods yields a set of nonlinear algebraic equations, which must be solved simultaneously. Therefore, the iterative calculation requires substantial computational time, especially for multidimensional problems. Recently, an explicit fully discrete method called the CE/SE method has been developed as a finite volume approach to solve fluid dynamics problems. The CE/SE method enforces flux conservation in space and time, both locally and globally. The method is explicit and, therefore, computationallyefficient. Moreover, it is conceptually simple, easy to implement and readily extendable to higher dimensions. Despite its second-orderaccuracy in space, this method possesses low dispersion errors (Ayasoufi and Keith 2003).

2.4.3 Conservation Element/Solution Element Method

The CE/SE method has many nontraditional features, including a unified treatment of space and time, the introduction of conservation element (CE) and solution element (SE) and a novel shock capturing strategy without special techniques. Spacetime CE/SE methods have been used to obtain highly accurate numerical solutions for l D , 2D and 3D conservation laws involving shocks, boundary layers or contacting discontinuities (Chang 1995; Chang et al. 1999). The CFL number insensitive Scheme I1 (Chang 2002) has recently been proposed for the Euler equation (i.e., convection PDEs for mass, momentum and energy conservation). Stiff source term (e.g., a fast reaction) treatment for convection-reactionPDEs (Yu and Chang 1997) is also presented for the space-time CE/SE method. The extension to a PDAE system (Lim et al. 2004) derived from the original CE/SE method (Chang 1995) and Scheme I1 (Chang 2002) is presented in the following. Consider a PDE model like Eq. (65): Ut

=

-6 - p ( u )

(78)

I

62

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2 Distributed Dynamic Models and Computational Fluid Dynamics

where the flux (F, implying convection and difision is defined as

f = au - D U X

(79)

Thus, Eq. (78) is identical to Eq. (G5). By the divergence theorem the equation is equal to flux conservation as follows:

(80)

V.h=p

. By using Gauss's divergence theorem

(or Green's

theorem) in a space-time E,, it can be shown that Eq. (80) is the differential form of the integral conservation law:

where S (V) is the boundary of an arbitrary space-time region V in E2, and ds = d (a . n with d a and n,respectively, being the area and the outward normal vector of a surface element on S(V). Note that, because h . ds is the space-time flux of h leaving the region Vthrough the surface element ds, Eq. (81) simply states that the total space-time flux of h leaving Vthrough S (V) is equal to the integral of p over V. Also, since in E,, dais the length of a differential line segment on the simple closed curve S (V), the surface integral on the left-hand side of Eq. (81) can be converted into a line integral. In fact, Eq. (81)is equivalent to (Chang 1995):

i;?;

(-udz+fdt)

=

s,

pdv,

where the notation C.C. indicates that the line integral should be carried out in the counterclockwise direction. In Fig. 2.7, the mesh points (e.g., points A, C and E) are marked by circles. They are staggered in space-time. Any mesh point 0,n ) is associated with a solution element S E 0 , n) and two conservation elements CE-0, n) and CE+(I',n). By definition, SEO, n) is the interior of the shaded space-time region depicted in Fig. 2.7a. It includes a horizontal line segment, a vertical line segment, and their immediate neighborhood (Chang 1995).Also, by definition, (1) CE-(j, n) and CE+(j, n), respectively, are the rectangles ABCD and ADEF depicted in Fig. 2.7a and b; and (2) CE(j, n) is the union of CE_(j,n) and CE+(j, n),i.e., the rectangle BCEF. Let the coordinate of any mesh point (j,n) be (3,t") with xj = j A x and t" = nAt. Then, for any ( x , t ) E SE(j, n),u(x, t ) , f ( x , t ) and h(x, t ) , respectively, are approximated by a first-order Taylor expansion: .(xj, t " )

= uj" + (U.)j"(X

- Xj)

+ (ut)j"(t- t " )

(83)

2.4 Fully Discretized Method 1-112

1-1

I

1+1l2

l+1

Br

-

C

CE+W

Figure 2.7 Solution element (SE) and conservation element (CE) atPh position and nfhtime level (Chang 1995). (a) Space-time staggered grid near SE(j, n). (b) CE-(j, n) and CE+(j, n)

so that, q x j , t")

= (J'(Xj,

t"),

qzj, t")) .

(85)

Here u;, (ux);, (ut)T,J, (f")?and v;); are constants in SEG, n). In the CE/SE framework, (ut);,J, &); and, v;)) are considered as functions of (u); and (ux);.These functions will be defined as follows. According to Eq. (79),one has:

fJ " = QU; - D(U,);

(86)

Also, by neglecting the contribution from the second-order derivative, 6); may be obtained using the chain rule:

In order that (ut)? can be determined in terms of (ux);,it is assumed that for any (x, SEG, n),

t) E

v .q*j,

t") = 0

63

f-lF E

CEUA

I

(88)

Thus, within SE(j, n),the contribution of the source term (p) that appears in Eq. (80) is not modeled in Eq. (88).Note that (1)because it is the interior of a region that covers a horizontal line segment, a vertical segment and their immediate neighborhood, as shown in Fig. 2.7, SEO, n) is a space-time region with an infinitesimally small volume; and (2) as will be shown, the contribution of source terms will be modeled in a numerical analogue of Eq. (82). As a result, Eq. (88)implies:

Distributed Dynamic Models and Computational Fluid Dynamics

(J)Jn

=

(”In (y a. 25

- (f.);

. (f.); (&);

-a 2 (ux)jn

at

Note that, by using Eqs. (86), (87), (89) and (9O),J, V;)j”, (ut)j”and v;): can be determined explicitly in terms of uj” and (.&. 2.4.3.1 Iterative CE/SE Method

The approximated conservation flux,

Fn =

#

C.C.

S(CE(j,n))

in Eq. (82), is defined within CElj, n):

(-iidx+fdt)

With the aid of Eq. (83) and (84), the line integral in Eq. (91) results in:

The approximated source term flux (Pj”) is obtained within V(CE(j, n)) as:

?,‘f

~fv(p)jndV

The volume integral in Eq. (94) leads to: Ax

y=pjnl

d x l

At/2

dt=-

AxAt 2 Pj”

The numerical analogue of Eq. (82) becomes:

With the aid of Eqs. (92) and (95), Eq. (96) implies that:

Equation (97) is a nonlinear algebraic equation in terms of uy, which originates from a nonlinear source term (py), Since this system of equations should be solved iteratively (e.g., using a Newton’s iteration method), it is called the iterative CE/SE method, where Jacobian matricesf, and pu are required in Eq. (90) and (97). Here, A x and At are user-supplied parameters. How their values should be chosen is problem-dependent.A small spatial step size (Ax)should be chosen for a problem associated with steep moving fronts. Also, a small CFL number

2.4 fully Discretized Method

ferred for a problem that is stiff with respect to time. Note that the stability of a CE/ SE scheme requires that the CFL number IYI < 1 (Chang 1995), as mentioned for explicit schemes in Section 2.4.1. Without using special techniques that involve ad hoc parameters, the numerical dissipation associated with a CE/SE simulation with a fixed total marching time generally increases as the CFL number decreases. As a result, for a small CFL number (say J Y ~< O.l), a CE/SE scheme may become overly dissipative. To overcome this shortcoming, a new CFL number insensitive scheme, i.e., the so-called Scheme 11, was introduced in Chang (2002).The new scheme differs from other CE/SE schemes only in how (ux)Yis evaluated. Refer to Chang (2002) or Lim et al. (2004) for the detailed formulation. 2.4.3.2 Noniterative CE/SE Method

The noniterative CE/SE method is simply obtained from a first-order Taylor approximation of the source term (Molls and Molls 1998; Lim and Jarrgensen2004).

jP J =p"p"(X-xj)+p;(tJ xj

J

t")

(98)

Using the above equation, Eq. (95) is replaced by

where the time and space derivatives of source terms (p) are reformulated through the chain rule: p[

ZE

ap a u au at

- - =puU[

(100a)

(100b) With the aid of Eq. (99), Eq. (97) evaluated on CE(j, n) is replaced by:

At where w;;l)lzz= - (4p;;;%z+ AxpZ;'{h+ Atp$#$). (u,),!'is also evaluated by Scheme I1 8 proposed by Chang (2002). Thus, two unknowns (u5 u5) are obtained from four known values (u;!y: at the previous time level (tn-'I2).u; in Eq. (101) is obtained without nonlinear iteration procedure. This scheme is a noniterative CE/SE scheme, where Jacobian matrices fu and pu evaluated at the previous time level ( t = t"-'I2) are required in Eq. (101).

U;;Y,~)

I

65

66

I

2 Distributed Dynamic Models and Computational Fluid Dynamics

2.4.3.3 Boundary Conditions

Boundary conditions (atj = 1 and Nmesh)for state variables (u) and its spatial derivatives (u,.) are needed only at each integer-time level (n = 0, 1,2, 3, ...) because of the staggering mesh structure and the intrinsically space-time triangle computational elements (see Fig. 2.7). At each half-time level (n = 1/2, 1 + 1/2, 2 + 1/2, ...), the Values of u and u, for all mesh points (j = 1 + 1/2, 2 + 1/2, ..., NmeSh-1/2)are calculated on the basis of the values at the previous integer-time level without requiring boundary values. When the Danckwert boundary condition Eq. (3) is applied, conservative boundary conditions (BCs) at x = ~0 and x = xfcan be constructed within CE+(I, n) and CE-(Nmesh, n), respectively. Performing a line integral along CE+(l, n) and using Eq. (3a), the boundary condition at x = xo (i.e., j = 1) for the iterative CE/SE method is obtained: At 2 J

u? - - p ? + q ? J

J

= u n-112 . - n-112 J + ~ P 'j+1/2

(102a) (102b)

Ax At --fyj At2 andfk is the inlet flu predefined by the 4 A$' 4Ax operation condition. Eq. (102)leads to a nonlinear equation with respect to two variables, urand uz'when j = 1. The boundary condition at x = xf (i.e.,j= Nmesh) for the iterative CE/SE method is obtained in the same way but by performing a line integral along CE-(N-h, n):

where q;

=

-u

(103a) u,", = 0 J

(103b)

At Here, since q; can reduce to q;= - - with the aid of Eq. (90) and (103b), ur is A J computed from Eq. (103a)through a nonlinear iteration. For the noniterative CE/SE simulation, Eq. (102a) and (103a)are replaced, respectively, by:

When other boundary conditions are imposed, appropriate formulations can be derived in a conservative manner within the conservation elements (CE, (j, n)).

2.4 fully Discretized Method

2.4.3.4 Comparison of CE/SE Method with Other Methods

The iterative CE/SE method, at each time level, is associated with a block diagonal Jacobian matrix. Let the number of PDEs and spatial mesh points be N p D E and Nmesh, respectively. The maximum number of nonzero Jacobian elements for the CE/SE method, JgZLsE, is: = (NPDE x NPDE) x Nmesh

(106)

In the case of linear source terms or noniterative CE/SE simulations, the Jacobian matrix is further reduced to a diagonal form: CE/SE -

Jmi,

- (NPDE x 1) x Nrnesh

(107)

When an implicit ODE integrator is used in the MOL framework for Eq. (78),a band matrix is obtained. Let the length of the upper and lower band matrix be M U and M L dependent on the spatial discretization and nonlinearity of the PDE considered. The maximum number of nonzero band-Jacobian elements for the MOL is known as (Lim et al. 2004):

JEzL= NPDE

'

Nrnesh(ML

+ M U + 1) - -21M L ( M L + 1)

-

1

-MU(hfU 2

+ 1)

(108)

For example, in the simple case where the convection term is discretized by a firstorder backward scheme and the diffusion term by a central scheme like Eq. (9),ML = M U = N p D E . The smallest number of nonzero Jacobian elements in this case,Jip, can be approximated at each time step: (2NPDE X NPDE)X Nmesh

(109)

As a result, the following relation can be derived CE/SE

Jmi,


,

e

f

.I

Figure 2.8

A hierarchical block grid structure of AMR

I

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70

I

2 Distributed Dynamic Models and Computational Fluid Dynamics

Fig. 2.8 (Li 1998). Each refinement level consists of several blocks. A block is a logically rectangular grid. After each refinement, the refined cells are clustered into several blocks. Buffer zones and ghost boundaries may be added to each block. All the blocks are managed by a hierarchical data structure. The data structure in the AMR algorithm is complex due to the existence of several levels (m).If u(xi,t", m) were used to store the data, it would be a waste of memory, because at higher refined levels, only a small part of the grid is used. In order to efficiently manage all the discrete points at the same level, we need to cluster them into several disconnected segments, called patches, and treat the patch as the basic data unit (Li 1998). The patches are building blocks of the hierarchical grid structure. 2.5.1.3 Solution Interpolation

The regridding includes computing the physical locations for each fine grid and copying or injecting the solution from the old grid to the new grid. The physical mesh positions are easy to compute by linear interpolation. The solution needs more attention. Although the solution can be obtained from the coarse grid by injection or interpolation, a more accurate solution is obtained from the old grid at the same level, which partially overlays the new grid. One of the secrets behind the success of the AMR algorithm is that flow discontinuities always fall within the overlay regions between the new and old grid. Thus the adaptation process cannot introduce further errors in these problem regions by solution interpolation. The method used to interpolate the solution from the coarse grid needs to be chosen with care. Conservative interpolation is useful in regions near a discontinuity. The coarse grid solution is assumed to be piecewise linear. The slopes for each grid are found by applying a MinMod limiter function to the forward and backward slopes between cell centers (Li 1998). So, for a coarse cell i, ui+lp - ui-lp = MinMod(ui+l - ui, ui - ui-1) where MinMod(a, b) =

("

sign(a) . min(la1, Ibl),

ifab < 0 elsewhere

2.5.1.4 Boundary Conditions

There are two types of boundaries in an AMR system: external boundaries and internal boundaries. External boundaries are given by the problem definition and internal boundaries are generated by refinement. Each patch in one-dimension has two ends: the left and the right. The boundary values are often collected only at the backward time t"-' just before the integration from t"-' to t". This causes a problem when the time integration is performed by an implicit or higher-order MOL, because the boundary values at t" are usually required to compute the intermediate time derivatives of the boundary cells in an MOL approach. This problem can be solved by collecting the values for the internal boundaries from the parent coarse grid at the forward time t" before integrating the current time level.

2.5 Advanced Numerical Methods

2.5.2 Moving Mesh Methods

Although AMR or local mesh refinement is quite reliable and robust, Furzeland et al. (1990)stated that it is cumbersome in some cases to apply it because of the interpolation procedure, nonfxed number of grid points, restart of integration at certain time steps, etc. The moving grid methods (Miller and Miller 1981; Dorfi and Drury 1987; Huang and Russell 1997), where the number of mesh points is kept unchanged, could be very powerful due to the continuous grid adaptation with the evolution of the solution. In the MOL framework, Furzeland et al. (1990) consider the moving finite difference (MFD) approach (Do15 and Drury 1987; Huang and Russell 1997) as promising with respect to reliability, efficiency and robustness. The moving finite element (MFE) approach (Miller and Miller 1981; Kaczmarski et al. 1997; Liu and Jacobsen 2004) that enables one to handle more complicated physical domains may be considered difficult to use because of tuning parameters and to be computationally inefficient. Moving mesh methods have traditionally used a finite difference method (normally with a simple three point central difference) to discretize both the physical PDE and moving mesh PDE (MMPDE). The MFD approach using the central discretization proposed by Huang and Russell (1997) and Dorfi and Drury (1987) is still unstable in some cases because of the central discretization of first-order derivatives. The E N 0 and WEN0 methods (Shu and Osher 1989; Jiang and Shu 1996) are uniformly high-order accurate right up to the discontinuity. Moreover these methods may well be applied to the moving grid method due to the reliable numerical results of first-order derivatives. Li and Petzold (1997) presented a combination of the moving grid method of Dorfi and Drury (1987) with the E N 0 schemes (Shu and Osher 1989) in order to improve stability and accuracy in the discretization procedure. We are interested in the numerical solution ofwell-posed systems of PDEs, e.g., in Eq. (la). If meshes are moving continuously with time, i.e, xi= xi@),by the chain rule, the solution of Eq. (la) satisfies the following equation (Dorfi and Drury 1987):

where U and x denote the time derivatives of u and x , respectively,when nonuniform physical meshes (xi)are transformed into uniform computational meshes (5;).Mesh movement is governed by m(u, x, 3;). The PDE and the mesh equation are intrinsically coupled and are generally solved simultaneously. 2.5.2.1 Equidistribution Principle

The grid equation, m(u, x, X), is induced from the equidistribution principle (EP), which means that the grids are spaced in order to make each arc length of discrete solutions equally distributed at each grid step. Therefore, the nodes are concentrated

I

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I

2 Distributed Dynamic Models and Computational Fluid Dynamics Figure 2.9

of the solw

Arc length (ds =

tion a t a time level (t)

0

1

X

in steep regions. The one-dimensional EP can be expressed in its integral form with the computational coordinate (0 I 5 5 1)and the monitor function, M(x, t), as a metric of each arc length (see Fig. 2.9):

where M (x, t) is called the monitor function. For example, as shown in Fig. 2.9, the arc length monitor function is given: ds M ( x ,t ) = - = dx

d

m 1

Let the total arc length of a numerical solution at a time t be 0 ( t ( = J-M ( x , t ) dlj. 0 Therefore, Eq. (115) is replaced by:

where lji = i/Nmcshis the uniform computational coordinate mentioned above. O(t) is fmed at a given time regardless of 5 and is unknown. As it is difficult to treat this unknown term, O ( t ) , in the numerical procedure, it is eliminated by differentiating Eq. (117)with respect to once and twice. A quasistatic EP is so obtained

From equation (118)one can obtain various mesh equations involving node speeds (X), the so-called moving mesh PDE (MMPDE),which are employed to move a mesh having a fxed number of nodes in such a way that the nodes remain concentrated in regions of rapid variation of the solution (Huang and Russell 1997). For most discretization methods of Eq. (114),abrupt variations in the mesh will cause deterioration in the convergence rate and an increase in the error (Huang and Russell 1997). Moreover, most discrete approximations of spatial differential operators (e.g., u, in Eq. (114)) have much larger CFL condition numbers

2.5 Advanced Numerical Methods

(e.g., =

($+ k

73

) e in Eq. (114))on an abruptly varying mesh than they do on a

gradually varying one. The ill-conditioned approximations may result in stiffness in the time integration in the framework of MOL. Robust mesh equations spatially smoothed are proposed by Dorfi and Drury (1987) and Huang and Russell (1997). As an illustration, the well-known Burgers’ equation with a smooth initial condition is considered: U t = -uux U(X,

+ 10-~~,, o 5

0) = sin(2nx)

I 1

(119)

+ sin(rrx)/2

(120)

The boundary condition is given as u(0, t ) = 0.0 and u(1, t ) = 0.0. A uniform grid structure is used as the initial grid position. The solution is a wave that develops a very steep gradient and subsequently moves towards x = 1. Because of the zero boundary values, the wave amplitude diminishes with increasing time. This is quite a challenging problem for both fmed and moving mesh methods. Proper placement of the fine mesh is critical, and a moving grid method tends to generate spurious oscillation as soon as the mesh becomes slightly too coarse in the layer region, just like nonmoving mesh methods with a central difference (Lim et al. 2001b). Figure 2.10 shows numerical results of the Burgers’ equation solved by the MOL with the third-order W E N 0 scheme on 40 moving grid points (Lim et al. 2001b). The mesh points are well concentrated on the moving front and adapt to physical fluid flow. In Fig. 2.11, grid evolution with time is shown for this case. The mesh points move continuously according to variation of the solution. The moving grid method attains a resolution corresponding to 5000 equidistant grid points near the shock, and to 7.5 equidistant grid points near the smooth regions. 1.5 1 .o

a

2

0.5

Y

a 0.0 -0.5 -1.0 1

I

Figure 2.10 Numerical solutions of Burgers’ equation on 40 moving grid points

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2 Distributed Dynamic Models and Computational Fluid Dynamics

1.5

1.25

1

0.75 E .w

0.5

0.25

0

0.2

0.6

0.4

0.8

1

mesh, x Figure2.11 Grid evolution with time on 40 moving grid points

2.5.3

Comparison between AMR and Moving Mesh Method

In the numerical analysis of PDAEs, discretization methods on fixed mesh points are generally more robust and easy-to-use than those on adaptive mesh points. In the cases involving steep moving fronts, the adaptive mesh methods are efficient with respect to accuracy and computational time. AMR and moving mesh methods are two of the most successful adaptive mesh methods. However, some care is needed to successfully use them. AMR has been developed for explicit temporal integration, while the moving mesh method works efficiently for implicit temporal integration (e.g., MOL in Section 2.3) because of stiffness of the grid. Moving-grid methods use a fixed number of spatial grid points, without need for interpolation. Moving mesh methods implemented via implicit time integration take advantage of the fully automatic adaptation of temporal and spatial stepsize (At, and Ax,). However, simultaneous solution procedures of physical and mesh equations typically suffer from the large computation time due to highly nonlinear coupling between the two equations, often requiring an excessive Newton iteration at each time step. This problem is further exacerbated by the dense clustering of mesh points near discontinuities, which degrades the convergence of the iteration (Stockie et al. 2001). Moreover, the extension of moving mesh methods from one dimension to higher dimensions in not straightforward (Li 1998).The two-dimensional moving mesh equation is much more complicated, because it includes many factors such as temporal smoothness, orthogonality and skewness of the mesh (Huang and Russell

2.6 Applications

1999). Simplicity and efficiency for the extension from 1 D to 2D/3D motivate development of the local refinement method such as AMR (Li 1998). Data structure and algorithms in AMR for a one-dimensional grid can be extended to higher dimensions without difficulty. Adaptive mesh methods also introduce overhead. For the moving mesh, such overhead includes evaluation of the monitor function, regularization of the mesh function, computation of the mesh velocity and solving additional mesh equation for the node positions. Compared with the moving mesh method, the overhead for the AMR method is much less. The evaluation of the monitor function is much cheaper and there is no need for regularization of the mesh function. Most of the overhead comes from the refinement and management of the hierarchical data structure (Li 1998). Recently, the combination of the two adaptive mesh strategies was presented (Hyman et al. 2003) and the two methods are compared and reviewed.

2.6 Applications

This section illustrates applications of the introduced numerical methods for the solution of PDE or PDAE systems in several dynamic chemical/biochemical processes. In Table 2.6, the five examples to be presented are characterized according to the type of equations and physical dominant phenomena. Each of the five problems is described by a time-dependent process model within one-dimensional space. First, chromatography columns modeled by a PDAE system are presented in Section 2.6.1. Here, numerical performances of several MOL methods and the CE/SE method are compared for both linear and nonequilibrium adsorption. In the fmedTable 2.6

Classification o f application examples

Section

Type o f equations

Physical meanings related

Characteristics

2.6.1

Chromatography

PDAE with source term

Convection, diffusion, and adsorption

Steep moving fronts

2.6.2

Fixed-bed reactor

PDE with source term and recycle

Convection, diffusion, and reaction

Mass and heat recycle and oscillation profiles

2.6.3

Sluny bubble column reactor

PDE with source term

Convection, difFusion, and reaction

Chemical reaction related to three-phase hydrodynamics

2.6.4

Population balance equation

Integro-PDE with source terms

Growth, nucleation, agglomeration, and breakage

Dynamic behaviors of the particle size with discontinuous fronts

2.6.5

Cell population dynamics

Integro-PDE with source terms

Growth and cell division

Oscillatory behaviors of cell populations

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2 Distributed Dynamic Models and Computational Nuid Dynamics

bed reactor model (see Section 2.6.2), oscillatory behaviors of state variables caused by mass/energy recycling are examined and several numerical methods are compared. In Section 2.6.3, a slurry bubble column reactor for Fischer-Tropschsynthesis is considered, where three-phase hydrodynamics are modeled by empirical equations given by De Swart and Krishna. (2002). The dynamics of gaslliquid concentrations and temperature are predicted at the beginning of operation. A population balance equation modeling crystal growth, nucleation, agglomeration and breakage is solved in Section 2.6.4, where discontinuous moving fronts appear due to initial seed crystals. Finally, Section 2.6.5 considers cell population dynamics in microbial cultures described by cell population balance equation (PBE) coupled to metabolic reactions relevant to extracellular environment (Zhu et al. 2000).

2.6.1 Chromatography

Packed-bed chromatographic adsorption between the stationary and mobile phases leads, for each component, to a partial differential algebraic equation (PDAE) system involving one partial differential equation (PDE), one ordinary differential equation (ODE) and one nonlinear algebraic equation (AE) (Lim et al. 2004): (121a)

dn _ - k(n* - n)

(121b)

0 = g(C, n*)

(121c)

dt

where vLis the interstitial velocity, D,, is the axial dispersion coefficient, a is the volume ratio between the two phases, and k refers to the mass transfer coefficient. The liquid and solid concentrations for each component are referred to as C and n, respectively. n* is the equilibrium concentration (or adsorption isotherm). Since the Peclet number (ratio of convection to diffusion, Pe

=

YLL

Da,

where L, is the column

length) is often large in chromatographic processes (Poulain and Finlayson 1993), Eq. (121) is classified as a convection-dominatedparabolic PDAE system. The padted-bed chromatographic problem in Eq. (121), is solved for one component with the volume ratio a = 1.5, the fluid velocity v L = 0.1 m/s, the axial dispersion coefficient D, = 1.0 x lo-’ m’/s, and the adsorption rate coefficient k = 0.0129 s-’. A linear adsorption isotherm is used for the algebraic Eq. ( 1 2 1 ~ ) . n* = 0.85C

(122)

The column length is in the interval 0 5 z 5 1.5 and the integration time is 0 5 t 5 10 s. As the initial condition, C(0, z )= 0, n(0,z ) = 0 and n*(O, z ) = 0 for all z except z = 0 and z = 1.5.

2.G A p p h t i o n s

Suppose that the Danckwert's boundary condition for Eq. (121a) is imposed as below: aC At z = 0 and Vt, U L ( C- Cin) = D,, . (123a)

ac --

Atz=l.SandVt,

az

(123b)

az - 0

where Ci, is a known feed concentration just before entering to the column. Here, an inlet square concentration pulse is considered as follows: Ci, = 2.2, for 0 5 t 5 2.0s

( 124a)

Ci, = 0.0, for 2.0s 5 t 5 10.0s

(124b)

The numerical solutions are obtained on 201 equidistant spatial mesh points. The CFL number for the iterative CE/SE method (Lim et al. 2004; see also Section 2.4.3) is given at Y = 0.4. The reference solution is obtained on 401 equidistant mesh points through the iterative CE/SE method. The error is estimated using Eq. (36). Table 2.7 reports numerical performance on accuracy, computational efficiency and stability for the chromatographic adsorption problem with axial dispersion on 201 mesh points. The second-order central and fifth-order upwinding schemes give spurious oscillatory solutions near steep regions. Thus, the two methods seem to be inadequate for convection-dominatedproblems as mentioned in Lim et al. (2001a). The first-order upwinding scheme (called first-order upwind, or FS-upwind-1)is not accurate because of its low order of accuracy. The two WEN0 schemes (third-order and fifth-order) enhance accuracy and stability but at the cost of longer computation time. The CE/SE method gives, in this case study, the most accurate solution with very short calculation times in a stable manner. In Fig. 2.12 numerical solutions of the fluid concentration (C) are depicted near z = 0.9 at t = 10 s for the adsorption problem. The reference solution is a smeared square profile at z = 0.8 and 1. The CE/SE method shows the best solution without Table 2.7 Accuracy, temporal performance and stability evaluation for a chromatographic adsorption PDAE with axial dispersion and square input concentration on 201 mesh points Accuracy (LI error)**

MOL

FS-upwind-1 FS-central-2 FS-upwind-5 W S-upwind-3 WS-upwind-5

Iterative CE/SE

(CFL= 0.4)

**

Unstable numerical solution. L1 error at t = 10 s.

*t*

CPU time during 10-s integration time.

-L

CPU time (s)***

0.2075 0.0979" 0.0060" 0.0449 0.0168

1.6 1.9 2.9 11.3

0.0087

1.3

7.7

I

77

78

I

2 Distributed Dynamic Models and Computational Fluid Dynamics Reference Solution ..... .. FS-upwind-1 FScentral-2 W S-upwind-5

I

+

2.5 1

A

2.0 1.5

v

CFISE 0 . 4

C

.=0 1.0

e c 8 0.5

c.

0.0 0 -0.5

0

Axial

M

Figure 2.12 Fluid concentration (C) profiles for different numerical schemes around z = 0.9 at t = 10 s for the single component chromatographic adsorption problem with axial dispersion (Dax= 1.0 x lo-') and square input concentration on 201 mesh points

spurious oscillation of the six schemes tested. As expected, first-order upwind (or FSupwind-1) is not accurate and second-order central (or FS-central-2)is highly oscillatory. The MOL with fifih-order WENO (or WS-upwind-5)and the CE/SE with CFL = 0.4 exhibit similar resolution in steep regions. Figure 2.13 shows the propagation of steep waves with time. Note that the fifthorder WENO scheme (circles)and the CE/SE method (solid line) have a nondissipative

0

c'

.-

0

.I-

2

.I-

C 0,

2

8

o.:i1 0

0

0.5

1

0 r^ 0 ..a-

2

.a-

C

Q

0 C

8

1.5

axial direction, z

axial direction, z

I

2

0

c-

2

-

0

1.5

.-0 2 1 C

C

CI

0 .c.

w

4-

2 0)

8

E l C

a,

2

0.5

0

1.5

0

0.5

1

axial direction, z

1.5

8

0.5

0

0.5

0

1

axial direction, z

Figure 2.13 Fluid concentration (C) propagation with time for a chro. matographic adsorption problem with axial dispersion on 201 mesh points (dashed line: first-order upwind; circles: fifth-order WENO; solid lines: CE/SE with CFL = 0.4)

2.6 Applications

I

79

feature owing to conservative discretization, since the waves do not widen with time. In contrast, the peak of the first-order upwinding scheme (dashed line) broadens continually as time increases.

2.6.2 Fixed-Bed Reactor

Recycling is often used in industrial processes to reduce the costs of raw materials and energy. The nonlinear effects of introducing recycling on a futed-bed reactor are considered in plant-wide process control and bifurcation analysis (Recke and Jmgensen 1997). This nonlinearity has the most pronounced effect around bifurcation points, i.e., points where the system solutions change stability and/or number of possible solutions. The fEed-bed reactor we consider here is a packed-bed tubular reactor with a single irreversible exothermic reaction of hydrogen’s catalytic oxidation to form water (Hansen and Jnrrgensen 1976).

The reactor is mass- and heat-integrated, which means that unconverted reactants are recycled and the reactor effluent is used to preheat the reactor feed in an external heat-exchanger, as shown in Fig. 2.14. The reaction is assumed to be first order in oxygen concentration with Arrheniustype temperature dependence. The model describing the reactor with both mass and energy recycling is given by:

I

Fresh feed

Figure 2.14 Schematic drawing of the fixed-bed reactor with mass/ energy recycles

80

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2 Distributed Dynamic Models and Computational Fluid Dynamics

where the ratio of mass to thermal residence time x = 1/600, the dimensionless flow rate Y ) 1.0, the axial dispersion mass Peclet number Pe, = 270, the Damkohler number Da = 0.376, the Arrhenius number y = 9.0, the axial dispersion heat Peclet number PeH = 118, the Biot number Bi = 0.5, the dimensionless surrounding temperature 0, = 0.79, and the dimensionless heat reaction Be = 0.49 are used for simulation. The variables t, 6,y and O are the dimensionless time, axial direction, oxygen concentration and temperature, respectively. The mass and energy recycling are assumed to follow first-order dynamics:

where ,z and re denote mass and energy recycle time lag constants with the units [t-'1, respectively. The above two ordinary differential equations have analFc solutions as follows: Yrec

= ~ C =-I (Yrec,o

erec =

e,=l

- YO=I,O)

e

-rmt

- (&c,o - ec=l,o)ecTet

(130) (131)

where yreC,(,and y5=l,o are the initial conditions for yrc0 and ybl and Orec,Oand OE=~,Oare those for Ore, and E = ~Tqe . ~ e q w q h tipe s hay q o v m a v t a z, = 30 and teare used in this Simulation. The Danckwert boundary conditions at the inlet point (6= 0) are expressed as:

where the dimensionless feed oxygen concentration ( y f e d ) and temperature ( Ofeed) are given as y f d = 1.0 and Ofe, = 0.8 and the mass and energy recycle ratios are assumed to be cr, and ae. The boundary conditions at the outlet point (ij= 1)are given as:

The bed is initially set to no reactant (i.e., yo = 0 for all g at t = 0). The initial bed temperature is Oo = 0.79 for all 5. The model is solved by the MOL and the noniterative CE/SE method for solution comparison. In the framework of the MOL, the convection term is discretized on uniform 201-mesh points by the first-order upwinding scheme (FS-upwind-1)and

2. G Applications

the third-order WEN0 scheme (WS-upwind-3),and the diffusion term by the central scheme (see Section 2.3.1). The boundary conditions Eqs. (132)-(134) are converted into nonlinear algebraic equations (AEs) by spatial discretization. The band Jacobian structure is broken by mass and energy recycles. The resulting system is thus a set of DAEs with a sparse Jacobian matrix. Using the noniterative CE/SE method, the two coupled PDEs are fully discretized on uniform 201-mesh points at CFL = 0.6 The resulting system has 402 linear algebraic equations at each time level for uyand u respectively.

zj

-y

+y -y

x

*

0

02

04

(FS-upmd-1) (WS-up~d-3) (WSEmethod) theta (FS-upwmd-I) theta (WS-upwmd-3) theta (WSEmethod)

06

Reactor length

(u

04

06

08

I

08

I

2

? iu-

15

n =

A-

Y?!

@ a o e 1

0

c g 2kE

gg

05

0

0

02

Reactor length ( x ) Figure 2.15 Comparison o f numerical solutions for dimensionless oxygen concentration ( y ) and temperature (0) variations with respect to the reactor length (x) at (a) t = 3 and (b) t = 3 5

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2 Distributed Dynamic Models and Computational Fluid Dynamics

Figure 2.15 shows the spatial distribution of dimensionless oxygen concentrations (y) and temperatures (8) at two time levels, t = 3 and t = 3.5, for each of the three numerical methods. Even though smooth fronts move with time, the solution profiles depend highly on the numerical methods used due to mass/energy recycling. A different numerical method provides a different oscillatory frequency, phase degree, and/or amplitude. In Fig. 2.16, it is shown that a steady-statesolution is reached differently depending on the numerical method used.

2

-yy (FS-upwind-1) (WS-upwmd-3) U

-9-y

1

2

3

( W S E method)

5

4

6

time (t)

2

(b) 1 5 4 4 0

y (F'S-upwind-1) UY (WS-upwind-3)

d

y (WSEmethod) theta (FS-upwind-1) x theta (WS-upwind-3) o theta (WSEmethod)

___

0

15

16

17

18

19

time (t) Figure 2.16

Comparison o f numerical solutions for dimensionless oxygen concentration ( y ) and temperature (0) variations with respect to time, (a) 1 < t < 6 and (b) 1 5 < t < 20, at the reactor outlet point (5= 1)

20

2. G Applications

Liu and Jacobsen (2004)stated that some discretization methods such as finite differences and finite elements can result in spurious bifurcation and erroneous prediction of stability. To minimize discretization error, they proposed a moving mesh method (see Section 2.5.2), i.e., an orthogonal collocation method on moving finite elements, for solving a futed-bed reactor model with energy recycling. For the futed bed reactor system, there is clearly a need for checking the approximation error of spatial and temporal derivatives as the fronts move. This would mean for the CE/SE method that an adaptive mesh method is applied. In addition, it is questionable whether the exit boundary conditions Eq. (134) are physically reasonable, especially when steep fronts are moving out of the reactor.

2.6.3 Slurry Bubble Column Reactor

Slurry bed reactors are applied increasingly in the chemical industry. The specific example selected here focuses on Fischer-Tropsch (FT) synthesis. FT synthesis technology, such as fluidized bed, multitubular futed-bed, and three-phase slurry bed, forms the heart of many natural gas conversion processes that have been developed by various companies in recent years (e.g., SASOL, Shell, Exxon, etc.). The FT reaction converts the synthesis gas (H,+CO) into a mixture of mainly long straight chain paraffins. This example concerns the Fe-based (or Co-based)catalyk slurry bed reactor, as shown in Fig. 2.17. Unconverted gas

t

I+

Slurry

Model

-

I

-

Synthesis gas Figure 2.17 Hydrodynamic model of slurry bubble column reactor (SBCR) in the heterogeneous flow regime (Van der Laan et al. 1999)

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2 Distributed Dynamic Models and Computational Fluid Dynamics

A highly exothermic reaction takes place on the Fe-based catalytic surface at high temperature (about 250°C): 1 + (1 + E)H2 + -CnH, + H2O + 165kJ/mol n CO + H 2 O ++ C 0 2 + H 2 + 41 kJ/mol

CO

(135)

where n is the average length of the hydrocarbon chain and m is the number of hydrogen atoms per carbon. Since hydrogen is considered the limiting component, balance equations can be set up for hydrogen only (De Swart et al. 2002). The complex hydrodynamics of gas bubbles are simplified by gas holdups (&&big) of large bubbles (dg,big= 20-80 mm) and those ( E ~ , ~ , , , ~of U ) small bubbles (dg,smll= 1-6 mm), as shown in Fig. 2.18. The dimensionless mass and energy balances for hydrogen are described for the three phases: 0

gas phase

ay big & g , b i g F = -

0

liquid phase

0

solid phase

(1

1f

acont

+ acont . Ybig) 2

(usg

- udf) aYbig ugo

at

The dimensionless energy balance for the slurry phase is:

The dimensionless variables are denoted ybig = CH2,g,big/ CH2g07ysmall= C H ~ , ~ , ~ ~ xU / C H ~ , ~ ~ ~ = mCH,,L/CH,,g@8 = T/T,, = h/H and z = tugO/H,where the initial hydrogen concentration CHz,go = 0.38412 kmol/m3,the distribution coefficient of hydrogen between gas and liquid phases m = 5.095, the heat-exchanger wall temperature T, = 501 K, the slurry reactor height H = 30 m, and the inlet gas velocity ugo= 0.14 m/s are preliminarily given for simulation.

2. G Applications

For the gas phase mass balance, the gas holdup of large bubbles ( ~ ~ , can b ~ be ~ ) estimated by the following relation with the gas superficial velocity (usg= 0.14 m/s), the small bubble superficial rising velocity (u& the gas density (pg 7 kg/m3 at P 40 atm and T- 500 4, and the reference gas density (& 1.3 kg/m3 at P = 1 atm and

-

-

-

The gas holdup of the small bubbles is given where the transition from the homogeneous to the churn turbulent flow regime occurs (van der Lann et al. 1999):

where the small bubble holdup in solids-freeliquid is .&= 0.27 and the solid holdup is given as q,= 0.25. The gas contraction factor is assumed to be a,,,, -0.5 in Eq. (136). The gas phase Peclet numbers for large and small bubbles are assigned to be Peg,big 100 and Peg,small= u@G/EL 80, respectively. The Stanton numbers of the large bubbles (St,b, = kL,H2,bigabigH/m/ug0 4.51) and the small bubbles (St,,,lI = kL,Hl,smallClsmallH/m/upo 24.7) are calculated as an empirical correlation proposed by Calderbank and Moo-Young (1961).The superficial velocity of small bubbles, udf, is defined as:

-

-

-

-

-

Pa . s, surface tension u= 0.019 Pa . m, liquid density 7.0 kg/m3 and gravity g = 9.81 m/s2.

= 680

kg/tn3, gas density

=

For the liquid phase mass balance, the liquid hold up is determined by: &L =

- Ep -

(&g,big

+ Eg.small(1 - &g.big))

(144)

The liquid phase Peclet number (PEL = u@H/Er) is assumed to have the same value as the small bubble Peclet number. The liquid Stanton number for large bubbles and small bubbles are defined as Stg,big = ~,~~,bipa~,i~H/u@ (- 22.97) Stg,rmall = kL,H2,srnaiias. mallH/~gO (- 125.87), respectively. The superficial slurry velocity is equal to us,= 0.01 m/s in the simulation and the average catalyst concentration fraction is = 0.25. The Damkohler number as the dimensionless pre-exponential kinetic factor is defined as:

rs

Da = AmELH/ugo

(145)

where the preexponential kinetic factor (or collision frequency factor) is A = 5.202 X 10” s-’. The Arrhenius number is given from the kinetic data (De Swart et al. 2002):

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85

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2 Distributed Dynamic Models and Computational Fluid Dynamics

1.175 x lo5 J/mol = 28.209 8.314 J/mol/K. 501 K

E,

y=-=

RT,

For the liquid phase energy balance, the heat transfer Peclet number ugo H %ff a, (Pe, = -x 7Q)the heat transfer Stanton number ( S ~ H= EL

~

Ps cps ugo

x 7.0),

and the dimensionless heat reaction (Be = -AHRCH2’go x 0.0488) are from mpsCpsTc De Swart et al. (2002). The model described by the above set (i.e., Eqs. (136)-(140)) of partial differential equations (PDEs), which include convection, diffusion and reaction, is solved with initial conditions and Danckwert’sboundary conditions (see Eq. (3)). De Swart et al. (2002) solved the above model numerically using the MOL with finite difference method (FDM) and a BDF ODE integrator. We here use the noniterative CE/SE method (see Section 2.4.3) to solve the model. Figure 2.18 shows dynamic contours 0.4,

d C d

= -

J

0.3

’$ 6

8% 2 2 0.2

$n a

-P

C

a 0

5

35 a g

0.1

0 0

0.2

0.4

0.6

column height (5)

0.8

0.25 0.2

0.15

3

0.1

R(

0.05 0

0

1

0.2

0.4

0.6

column height (5)

0.8

250,

0

8

sf

Y

P 0

0.2

0.6 column height 0.4

(5)

0.8

1

1

I

245 240 235 230 225‘ 0

0.2

0.4

0.6

column height (5)

Figure 2.18 Unsteady-state concentration contour o f (a) large bubble gas concentration; (b) small bubble gas concentration; (c) liquid concentration; and (d) slurry temperature with respect to the reactor height, within 5 min

0.8

I

1

2.G Applications

of large bubbles, small bubbles and liquid concentrations of hydrogen, and bed temperatures along the reactor height. These profiles show how to reach steady state within 5 min. From the model-based dynamic simulation we can predict conversion ratio and temperature changes with feed composition, heat-exchanger temperature, feed flow rate, and catalyst types. The optimal operating conditions can be obtained for a given objective function (e.g., cost-benefit function) using the method of nonlinear programming (NLP, see also Section 2.4). The three-phase bubble column shows complex hydrodynamics of reactant gas bubbles at elevated pressures (e.g., 10-40 atm). Several recent publications have established the potential of computational fluid dynamics (CFD) for describing the hydrodynamics of bubble columns (Krishna and van Baten 2001). Using a commercial CFD code (CFX, AEA Tech., UK) to solve mass/momentum conservation equations in the three phases, fiishna and van Baten (2001)predict the gas holdup and the liquid velocity within a cylindrical two-dimensional reactor at different column dimensions, pressures, and superficial gas velocity. The empirical correlations of the gas holdups in Eqs. (141)and (142)can be verified or predicted for different column dimensions by the CFD simulation results (Krishna et al. 2000). In Section 2.7, we will present in detail a combination of process simulation and CFD.

2.6.4 Population Balance Equation

The population balance equation (PBE) has been demonstrated to describe the particle size distribution (PSD) in various chemical/biological engineering problems such as crystallization, polymerization, emulsion, and microbial cultures. Indeed, modeling with the PBE provides a good description for parameter identification, which may be used for determination of operating conditions, and for process design and control. In crystallization processes, the PBE, which governs the crystal size distribution (CSD), is solved together with mass/energy balances and crystallization kinetics such as nucleation, crystal growth, breakage, and agglomeration. The system, which often leads to hyperbolic-like integro-partial differential equations (IPDEs), is complex due to a lot of feedback relationships between the equations (Wey 1985). To determine the CSD, all equations (e.g., PBE, mass, and energy balances) must be solved simultaneously. An inaccurate solution of a PBE will affect particle nucleation and subsequently particle growth and results in an incorrect CSD. Therefore, a numerical procedure to obtain an accurate solution of PBEs is necessary (Lim et al. 2002). The crystal size distribution (CSD) is usually expressed as the crystal number (N, no.) or number density (n,no./m, or no./m3)with respect to the crystal size (L,m) or volume (v,m3).A simple relationship between the crystal number (N) and the crystal number density (n) is given as follows using the finite volume approach:

I

87

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2 Distributed Dynamic Models and Computational Fluid Dynamics

Ni =

Li

Li+l

ndL

n;(Li+l - Li)

or Ni =

Jci

"if1

ndu x ni(ui+l - ui)

(147)

Both bases (i.e., Nand n) can give a good description of the CSD. However, the CSD based on the number (N) is often preferred, for conservation of the mass and the number of crystals, in the cases involving agglomeration and breakage kinetics (Kumar and Ramkrishna 1997). A number-based PBE as a governing equation ofthe CSD is usually described in terms of the birth of nuclei, their growth, agglomeration, and breakage:

+ (-ddtNi )breakage

dt where

Nrnesh

yoAL.

(148)

La

2. N.J'

i=l

j=i+l Lj '

yo AL .

La Li

La

. N;

Nmesh

La

j=i+l

Lj

+ 2y0A L .

yoAL. 2 . Ni - yoLq . Ni, Li

. N j - y0Lq . Ni,

i = 2 . . . (Nmesh- 1) = Nrnesh

(152)

2.G Applications

2.6.4.1 Method of Characteristics

It is well known that for the scalar linear conservation law (e.g., PBE considered here) there usually exists a unique characteristic curve along which information propagates. If the solution moves along the path line of propagation, the convection term a(GN) in the PBE disappears. Hence, numerical error and instability caused by 8L approximation of the convection term is removed. Kumar and Ramkrishna (1997) derived a modified MOC formulation for the PBE:

!Lo-($) ,

dt

nucleation

+(%)

(153a)

agglomeration

dL; dt

(153b)

- = G;

where Eq. (153b)is the mesh movement equation. The MOC formulation is numerically solved by using the MOL. To overcome the nucleation problem, a new mesh of the nuclei size (Ll) is added at given time levels. The system size can be kept constant by deleting the last mesh at the same time levels. Since the number of crystal nuclei can vary with the number of mesh points added or deleted, a proper number of added mesh points should be selected according to stiffness of nucleation. Suppose that a stiff nucleation takes place only at a minimum crystal size ( L , = as a function of time: n(t, L1) = 100

+ lo6 exp (lOP4(t

- 0.215)2)

(154)

5 L 5 2.0, the nuclei grow and the crystals aggregate as Within the size range well as break for 0.0 5 t 5 0.5. A square initial condition as seeds is also given:

n(0, L ) = 100, for 0.4 5 L 5 O h n(0, L ) = 0.01, elsewhere

(155)

The kinetic parameters are given: G = 1 (linear growth rate), = 1.5 X (constant agglomeration kernel) and y = 1.0 x L2 (breakage kernel). See Lim et al. (2002) for details. The discretized PBE based on the crystal number (N,)or the crystal density (ni) is solved by using the implicit BDF O D E integrator in the framework of the MOL. 2.6.4.2 Nucleation and Growth

When the PBE with the nucleation and growth terms is considered on the basis of the crystal density (n),its analFc solution is derived from the MOC: n(t, L ) = 100

+ lo6 exp (-

2

104((Gt - L ) - 0.215) ), for 0.0 5 L p Gt,

n(t, L ) = 100, for 0.4 5 ( L - Gt) 5 O h ,

(156a)

(15Gb)

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2 Distributed Dynamic Models and Computational Fluid Dynamics

-Analytic solution WS-upwind-3 0 WS-~pwind-SA 0

1.E-02h 0.0 0.5

1 .o

MOC-5%

Crystal size ( L )

1.5

2.0

Figure 2.19 CSDs for the stiff nucleation case without agglomeration and breakage

n(t, L ) = 0.01, elsewhere

(156c)

In the solution, a discontinuous front (due to square seed) and a narrow wave (originating from nucleation) move along the propagation path line, L = LI+Gt. The numerical tests are carried out on the 200 fEed grids for both the numerical MOC and the WENO schemes. In Fig. 2.19, the numerical results of the WS-upwind-3/5A (see Lim et al. (2002) for details) and MOC-50p (i.e., numerical MOC with an additional 50 mesh points) are compared to the analybc solution Eq. (155) at the end time (t = 0.5). While moving fronts are smeared near discontinuities using the WENO schemes on the weighted stencil, the numerical MOC-50p shows a quite good resolution even at the discontinuous fronts. 2.6.4.3 Nucleation, Growth, Agglomeration, and Breakage

When the agglomeration and breakage kinetics are added to the previous PBE, the analytic solution can not be derived. The numerical solution of Eqs. (148) or (153) is obtained on 101 points of the uniform grid, using MOC-2Op or WS-upwind-5. Employing the MOC-2Op (insertingldeleting 20 mesh points), the following mesh equations are used dL1 -=O,

dt

d Li -=1 dt

f o r i = 2 . . . 101

(157)

In Fig. 2.20, CSD changes obtained from MOC-20p are depicted according to the kinetics used. The solid line is the analytic solution for the pure growth problem without agglomeration and breakage. Since numerical diffusion error is small, high resolution is observed at the corners of steep fronts. Due to the agglomeration term, the CSD spreads out and the population of large crystal sizes increases (see Fig.

2.6 Applications

(b) Grow th+Agglome ratio

c

.5 rn

5

-0

102

loo 10'

0.5

0 1o6

1

1

1.5

0

0.5

0

0.5

1

1.5

2

1.5

2

crystal size, L

(c) Growth+Breakagyl

I

0

2

crystal size, L

0.5

1

crystal size, L

1.5

1 2

1

crystal size, L

Figure 2.20 CSD changes obtained by the MOC-20p on 102 meshes according to the growth, agglomeration, and breakage terms (solid line: analytic solution for pure growth)

2.20b). In contrast, the breakage term increases the population of small crystal sizes (see Fig. 2.20~).The CSD of the PBE with four kinetics is dispersed more broadly, as shown in Fig. 2.20d. Using the fifth-order WENO scheme (WS-upwind-5),Fig. 2.21 also shows effects of the growth, agglomeration, and breakage terms on the CSD. Considerable numerical dissipation is found in steep regions (or discontinuities) in Fig. 2.21, and also shown in Fig. 2.19. However, comparing Fig. 2.20d with Fig. 2.21d, the two solutions are similar due to the effects of agglomeration and breakage on the CSD. Though the modified MOC gives more accurate numerical results than the WENO scheme, there are some limitations to using it such as the need for careful determination of addingldeleting time levels and a unique mesh velocity equation (or growth rate, see Eq. (153b)).Using the spatial discretization methods (e.g., MOL with WENO schemes) to circumvent these limitations, attention must be paid to discretization of the growth term (convection term), which can cause much numerical error and instability in the presence of steep fronts or discontinuities.

92

I

2 Distributed Dynamic Models and Computational Fluid Dynamics lo6

(a) Pure growth

,

h

I

'

(b) Growth+Agglomeratio

1o4

1o4 C

2 v)

C

W

U

1o2 1oo 10"

I

0

0.5

I

1

1.5

2

crystal size, L

I 0

0.5

0

0.5

I 1

1.5

2

1.5

2

crystal size, L

1o6

1 o6

(c) Growth+Ereakage

1o4 C

C

.25

.2;

u)

u)

C

C

W

W

U

U

1o2

1oo

10" I

0

0.5

I

1

1.5

crystal size, L

2

1

crystal size, L

Figure2.21 CSD changes obtained by the WS-upwind-5 scheme on 101 meshes according to the growth, agglomeration, and breakage terms (solid line: analytic solution for pure growth)

2.6.5

Cell Population Dynamics

Cell cultures are composed of discrete microorganisms whose population dynamics play an important role in bioreactor design and control. The cell cultures are known to exhibit autonomous oscillations that affect bioreactor stability and productivity. To increase the productivity and stability, it is therefore desirable to derive a dynamic model that describes the oscillatory behavior and to develop a control strategy that allows modification of such intrinsic reactor dynamics (Henson 2003). As a model example for cell culture dynamics, consider a segregatedlunstructured modeling based on the cell population balance equation (PBE) coupled to metabolic reactions that are relevant for the extracellular environment (Zhu et al. 2000; Mhaskar et al. 2002). The segregatedlunstructured model provides a realistic description of the cell cycle events that lead to sustained oscillation in cell cultures under the assumption that oscillations arise as a result of interactions between the cell population and the extracellular environment.

2.G Applications

The cell population dynamics including cell growth and cell division is described

X w , newborn-cell birth term (I 2 p r w d m ) , mother-cell division death term (-rW)and dilution loss by a partial differential equation including a convection term

(a,)

(-DW):

a w ( m , t ) - - a(v,(s’). ~ ( mt ),) at am +

I”

2p(m,m’)r(m’, S’) W(m’, t ) dm‘ - [ D + r ( m ) ] W(m, t )

(158)

where W(m, t) is the cell number concentration as a function of mass (m) and time ( t ) ,vS(S’is the overall single cell growth rate at the substrate concentration ( S ’ ) , p(m, m’) is the newborn-cell mass distribution function with newborn-cell mass m and mother-cell mass m’, r ( m ’ , S’), is the division intensity function, and D is the dilution rate. Detail models and their parameters are given below on the basis of Mhaskar et al. (2002) for a S. cerevisiae (or yeast) culture. For convenience, all of the g] and the cell number concentration ( W (m, t ) has masses have the units [ x the units [ X 10-l~no./g]. The division intensity function is introduced to account for the probability nature of cell division:

where m“, is the cell transition mass, mo = 1 is the minimum cell mass for division, and m“’d is the division mass. E = 5 and y = 200 are the constant parameters that determine the transition rate and the maximum intensity value, respectively. Sustained oscillations are generated through the introduction of a synchronization mechanism in which the transition and division masses are functions of the nutrient concentration. The following saturation functions are used (1GOa)

(1GOb)

where the substrate concentration is S’ = G’ + E , and the constants are given as Sl = 0.1 g/l, S ~ = ~ , O ~ , ~=, ,4.55, , ~ O mdo = 10.75, Kt = 0.01 . 1-l and & = 3.83 * 1-’.

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2 Distributed Dynamic Models and Computational Fluid Dynamics

The newborn cell probability function p (m,m’)has the form: p ( m , rn’) =

(y

. e-~(m-m;)2

lo.

+

. e-~(m--m’+m;)2 , m’> rn and rn’ > rn: elsewhere

+ mg

(161)

Here the constants are set to a = and p = 40. This function yields two Gaussian peaks in the cell number distribution, one centered at mgrtcorresponding to mother cells and one centered at m*,- m’corresponding to daughter cells. Oscillatory yeast dynamics are observed in glucose-limited growth environments. Under such conditions, both glucose and the excreted product ethanol can serve as substrates for cell growth. The following reaction sequence accounts for the relevant metabolic pathways, glucose fermentation, glucose oxidation, and ethanol oxidation:

where G’ and E represent intracellular glucose and ethanol concentrations, respectively, and 0 is the dissolved oxygen concentration. hgf= 30( x lo-’’ g/h),hgo = 3.25 ( x 10-13 g/h), and he,, = 7(x g/h) are maximum consumption rates, Km&= 40 g/l, KMgo= 2 g/l, Kmgd = 0.001 g/l, K,, = 1.3 g/l, and Kmed = 0.001 g/l are saturation constants, Kinhibit = 0.4 g/l is a constant that characterizes the inhibitory effect of glucose on ethanol oxidation. The overall single cell growth rate vg(g(s’)is the sum of the growth rates due to the three metabolic reactions. vg(S’) = Kgf(G’)

+ Kgo(G’, 0)+ Keo(G’, E’, 0)

(164)

For intracellular glucose and ethanol concentrations (GI, E ) and liquid oxygen concentrations (0)in Eq. (163),the mass balance equations of these substrates are d G’ dt

- = kg(G - G’)

d E’ dt

- = ke(E - E’)

do dt

-=

( 192 Kgo(G’) 180 Ygo

koa(O*- 0) - -~

96 Q,(E’)) +--46 Ye,

Ntotal

2.6 Applications

where G and E are extracellular concentrations, kg and k, = 20 h-1 are glucose and ethanol uptake rates, respectively, k,a = 1500 h-’ is the oxygen mass transfer rate, and Ygo= 0.65 g/g and Ye,= 0.5 g/g are the yield coefficients in the glucose oxidation and of microorganethanol oxidation reactions, respectively. The total cell number ( isms is defined by

The saturation oxygen concentration, 04, is obtained from the oxygen solubility, RT which is assumed to be governed by Henry’s law: 0” = H , -Ooul with the HenMW.02

ry’s rate constant (H, = 0.0404 g/l/atm), the gas constant ( R= 0.082057 1 . atm/mol/ K ) , the absolute temperature ( T = 298 K ) , the molecular weight of O2 (M,,o, = 32) and the oxygen concentration in the gas exhaust stream (Ooul). The gas phase oxygen balance is: V

* dt

= F(Oi, - Oout)- koa(O* - 0) . y

where Vg = 0.9 l and V, = 0.11 are the gas phase and liquid phase volumes, respectively, F = 90 l/h is the volumetric air-feed flow rate, and Oi, = 0.275 g/l (= 0.21 atm) is the oxygen concentration in the air-feed stream. For extracellular glucose and ethanol concentrations (G and E), the substrate mass balance equations are:

where D = 0.18 h-’ is the dilution rate, Gf= 30 g/l and Er= 0 g/l are the feed glucose and ethanol concentrations, respectively, and Yd= 0.15 g/g is the yield coefficient in the glucose fermentation reaction. The total cell number for microorganisms related to ethanol excretion is denoted in Eq. (171) as:

Experimental data suggests that key products, such as ethanol, are excreted primarily by budding cells. This behavior is modeled byf(m):

where ye = 1.25, E,

=

15 and me = 1.54 are constant parameters.

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2 Distributed Dynamic Models and Computational Fluid Dynamics

The liquid phase carbon dioxide balance (C) is

where k,a

=

1500 h-' is the C 0 2 mass transfer rate and C? is the saturation C02 con

centration modeled by c;' = H,RT C,, with the Henry's rate constant (H, = Mw,co* 1.48g/l/atm at pH = 5.0), the molecular weight of C02(Mw,co,= 44) and the COz concentration in the gas exhaust stream (C,,,,). The gas phase C02 balance is:

V

dt

= F( Ci, - Gout) - kca( C" - C) . Vl

(175)

where Ci, = 0.00054 g/l (= 0.0003 atm) is the carbon dioxide concentration in the airfeed stream. In summary, this cell PBE model is described by a PDAE system containing one PDE for the cell population (W(m, t ) )and eight ODES for eight substrate variations (G, E, G', E , 0, C, O,,,, and COu,).The single cell growth rate (vg(G',E , 0))is computed in Eq. (164). The initial condition of W(m, t) is set to W(m, 0) = 0.5 e-S.(m-G)', 1 5 m 5 11.The boundary condition of W(m, t ) is also given as W(11, t) = 0 for 0 5 t 5 6 hr. For the eight-substrate concentrations, their initial values are G' = G = 0.8, E = 0.01, E = 0.0001, 0 = 0.008, C = C,, = 0.003, and O,,, = 0.275. For the solution of cell PBE models, Zhu et al. (2000) and Mhaskar et al. (2002) used the orthogonal collocation FEM (Finlayson 1980). Motz et al. (2002) reported that the CE/SE method gives better performance in terms of accuracy and computational time than a flux limited finite volume method. Mantzaris et al. (2001a,b)compared several numerical methods such as finite difference methods (FDM) with explicit/implicit time integration and finite element methods (FEM) with explicit/ implicit time integration, where they suggested (i) the time-explicit scheme (e.g., Runge-Kutta method) is better for computational-efficiency than the implicit timeintegration scheme (e.g., BDF-types) and (ii) the finite difference method is preferred for multidimensional PBEs to the finite element method due to computational eficiency. Fortunately, this model can be solved by the modified MOC (see Eq. (153)),since there is a unique growth rate Eq. (164). The integration terms appearing in Eqs. (158), (168),and (172) are simply evaluated by the Trapezoidal rule:

where Nmsh is the number of mesh points. When the numerical MOC is used in the framework of the MOL, it is not easy to provide its Jacobian full matrix with hand-coding due to strong nonlinearity and it will be prohibitive to numerically evaluate the Jacobian because of the large system size (i.e., the number of equations is (2 X N,& + 8), and the Jacobian matrix is 2 X

2.6 Applications

N,& + S)2).The automatic differentiation technique is appreciated in this case for accuracy and computation efficiency. Figure 2.22 shows the dynamics of the cell population number density (W(rn,t ) ) is solved by the numerical MOC on 82 mesh points (N,,&,) where 135 mesh points are added at rn = 1 and also deleted at rn = 11. Due to cell division, the cell number density of small sizes tends to increase with time and the oscillatory behavior of the cell number density are regularized after about t = 6 hr. The oscillatory behaviors of the cell number (Ntotal) in Eq. (168) and the cell mass

(= c

Nrnesh-l

Ni

(mi

+ mi+l)

are shown in Figs. 2.23a and b. The cell number varia-

i=l

tion affects the extracellular glucose/ethanol (G and and oxygen/carbon dioxide (O,,, and C,,,) concentrations in the gas exhaust stream (see Figs. 2.23~-f,respectively). As ethanol is excreted, primarily by budding cells (see Eq. (173)),it is shown that the extracellular ethanol concentration ( E ) slowly reaches a regular oscillatory state in Fig. 2.23d. Figures 2.23g,h depict the dynamics of the consumed oxygen concentration ratio 100 x 100 x

(9)

and evolved carbon dioxide concentration ratio

, respectively.

800

-

600

m

2 D

z

7

z

400

v

200

0

12

5

6

13

mass, m (x10

Figure 2.22 Distribution of cell population concentration W(rn.t) over mass and time

g)

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2 Distributed Dynamic Models and Computational Fluid Dynamics

-

4.2

1

8

0

0.27361

,

2

4

6

8

W t ' hr

1

0 I

1

I

00001

2

1

0.0003

L - - . . . L r

0

2

4

I

6 time ( t l hr

8

10

12 I

'

I

0

0 0029

.

0 0028

8

00026

0 0025

s 6 3 N-

2 82 0

h

cu'

62 61 60

0

2

4

6 time (t),hr

8

10

12

Figure 2.23 Oscillatory behaviors in time of (a) cell number; (b) cell mass; (c) extracellular glucose (C); (d) extracellular ethanol (4; (e) oxygen in exhaust gas stream (Oout); (f) carbon dioxide in exhaust gas stream (&); (g) evolved oxygen ratio; and (h) evolved carbon dioxide ratio

All of the parameters used for this simulation need to be adjusted to experimental data, as shown in Mhaskar et al. (2002).

2.7 Process Model and Computational Fluid Dynamics

A multiscale model is a composite mathematical model formed by combining partial models that describe phenomena at different characteristic length and time scales. For example, modeling of a packed-bed catalytic reactor involves microscale chemical kinetics at the active sites on the catalyst, mesoscale transport processes through the pores of the catalyst pellets, and macroscale flow and heat exchange at the reactor vessel level. Computational tools such as molecular dynamics (MD), computational fluid dynamics (CFD), and process simulation have been used to help fill particular

22.7 Process Model and Computational Nuid Dynamics

length- and timescale gaps. In general, despite their obvious connection, phenomena at different characteristic scales have usually been studied in isolation (see Section 2.5). One of the key challenges facing process modeling today is the need to describe complex interactions between hydrodynamics and the other physical/chemical phenomena. This is particularly important in the case of complex systems (e.g.,polymerization, crystallization, and agitated bioreactors) in which the constitutive phenomena interacts with mixing and fluid flow behavior. Process simulation tools, which play an increasingly central role within most process engineering activities are able to represent (i)multicomponent, multiphase, and reactive systems, (ii) individual unit operations, multiple interconnected units, or entire plants, and (iii)thermodynamic properties. However, most of the models used by process simulation tools either ignore spatial variations of properties within each unit operation (invoking the well-mixed tank assumption) or are limited to simple idealized geometries. Moreover, the treatment of fluid mechanics is usually quite rudimentary (Bezzo et al. 2003). CFD techniques solve fundamental mass, momentum, and energy conservation equations (e.g., the Navier-Stokes equation) in complex three-dimensional geometries. From CFD simulation, some valuable information (e.g., mass flow rate, heat transfer coefficient, velocity, etc.) for process simulation can be obtained. However, CFD’s ability is still limited in application to complex reactive systems and multiphase processes with multicomponent phase equilibria. Furthermore, performing realistic dynamic simulation often requires excessive computational time. In view of the above, CFD and process simulation technologies are highly complementary (Bezzo et al. 2000). Combination of process simulation and CFD can therefore lead to significant advantages in accurate modeling of processes.

2.7.1 Computational Fluid Dynamics

The CFD technique has focused on the solution of PDEs representing conservation equations describing fluid flow over domains of often complex geometry. There are several commercial CFD packages such as Fluent (Fluent, Inc.), CFX (AEA Tech., Hanvell, UK) and FemLab (COMSOL). The CFD packages usually comprise three distinct elements, namely preprocessing (geometry specification, model selection, parameter specification, and grid generation), numerical solution procedure and post-processing (visualization and data treatment). In the solution procedure, mass/momentum/energy conservation equations are solved within the specified geometry. Generic conservation equations may be described by PDEs with advection, viscosity/diffusivity and source terms:

-a4 + - axa (~ 4 - ra ~ -- s 4 = o at a )l

(177)

I

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2 Distributed Dynamic Models and Computational Fluid Dynamics

where @ is a conserved quantity such as mass, energy or momentum, rQ the viscosity or difisivity, sg the source or sink and x the set of spatial dimension variables. The models are called the compressible (or incompressible) Navier-Stokesequation. When the viscosity/diffusivity terms can be neglected due to relatively small influence on the result, the inviscid Euler equation is obtained. Let p, u,p, and e be the mass density, velocity, pressure, and energy per unit volume, respectively. The inviscid Euler equation of a perfect gas can be expressed as:

where u = (p, p,e)' andf= (p, p + eu2,ue +

We may write e = @eint,,r

1 +-

2 p2, where eintemris the internal energy per unit mass. Therefore, this equation is the three-dimensional hyperbolic PDE. Most CFD packages do not use the MOL approach (see Section 2.3) of reducing PDEs into ODEs in time. Instead, they choose to discretize both temporal and the spatial dimensions (i.e., fully discrete methods, see Section 2.4), thereby reducing the PDEs into a set of nonlinear algebraic equations (Oh 1995). The process simulation models mentioned in Section 2.6 represent specific and simplified conservation equations related to the macroscopic process level. Here, complex fluid dynamics is lumped by parameters or simple empirical equations (e.g., the three phase bubble column model in Section 2.6.3). Microscopic chemical reactions are simplified by kinetic equations as a function of temperature, pressure, and concentrations. If we use a full CFD simulation including complex reactions, thermodynamics, population dynamics and hydrodynamics, it would be practically infeasible because of high computing load and lack of existing tools. To effectively take into account interactions between hydrodynamics and the other physicallchemical phenomena, a hybrid approach, namely, multizonal/CFD simulation (Bauer and Eigenberger 1999 and 2001; Bezzo et al. 2003),is proposed (see Fig. 2.24). Several zones, assumed to be well-mixed compartments, are described by process models (e.g., AEs, ODEs, PDEs or PBEs) with the exception of the fluid-flow ones, and CFD simulation provides each zone with the mass flow rate at interzonal interfaces and additional fluid dynamical properties such as mass transfer coefficient and turbulent energy dissipation rate (Bezzo et al. 2003).

2.7.2 Combination o f CDF and Process Simulation

Figure 2.24 shows a structure of the general multizonal/CFD model. The spatial domain of interest is divided into several zones (z1-z5).Each single zone (2)is considered to be well mixed and homogeneous. Two zones can interact with each other via an interface that connects a port (p) of one zone with a port of the other. The flow of material and/or energy across each interface is assumed to be bidirectional. The transient behavior of a zone is described by a set of algebraic equations (AEs),ordi-

22.7 Process Model and Computational Fluid Dynamics

Multizonal model (all phenomena except fluid dynamics)

physical properties

I

1

I

1

I

I

l

l

I

r

l

l

l

l

l

l

l

CFD model (total mass and momentum conservation only) Figure 2.24 al. 2003)

l

l

1

Structure of the general multizonal/CFD model (Bezzo et

nary differential equations (ODES),partial differential equations (PDEs) or population balance equations (PBEs).The multizonal model uses detailed dynamic modeling of all relevant physical phenomena, with the exception of fluid-flow, over a physical domain divided into a relatively small number of zones. Mixing parameters and interzonal mass flow rates are determined by solving a detailed CFD model over the same physical domain. The CFD model focuses solely on fluid-flow prediction, trylng to do this as accurately as possible by dividing the space into a relatively large number of cells and solving the total mass and momentum conservation equations. Thus, the CFD model does not attempt to characterize intensive properties such as composition, temperature or particle size distribution. The transient behavior is ignored, based on the assumption that fluid-flow phenomena operates on a much shorter time scale than all other phenomena. The solution of the CFD model will require knowledge of the distribution of physical properties (e.g., viscosity, density, compressibility factor, etc.) throughout the physical domain of interest. These properties are usually a function of the systemintensive properties and are computed within the multizonal model. The hybrid model is formed by the coupling of the multizonal model with the CFD mode, both representing the same spatial domain. The mapping between the zone and cell is achieved by means of appropriate disaggregation and aggregation procedure (Bezzo et al. 2003). The multizonal concept and CFD simulation is applied to bubble column reactors (Bauer and Eigenberger 1999, 2001) and to a bioreactor processing and mixing a highly viscous fluid (Bezzo et al. 2003).

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2 Distributed Dynamic Models and Computational Fluid Dynamics

2.8 Discussion and Conclusion

In many chemical and biotechnical processes, partial derivatives result from a consequence of dynamic behaviors of mass, energy and momentum in space. The derivative or algebraic terms describe fluid flow, physical phenomena and/or constitutive relations in the different phases. The description of convective and diffusive (dispersive) fluxes introduces first and second order spatial derivatives. Mass exchanges between the fluid and stationary phases (e.g., reactions and adsorptions) are described by time-dependent differential equations. Equilibrium relations and physical properties are described with algebraic equations (AEs).Thus process models are in general represented as partial differential equations (PDEs)coupled with algebraic equations (AEs),i.e., PDAEs with pertinent initial and boundary conditions. In this chapter, a large class of one-dimensional PDAE models is presented in Section 2.6 to introduce the most frequently applied numerical methods for their solution (Sections 2.3-2.5). Finally, the complementary relations between process simulation and computational fluid dynamics most often employed to solve models with fully developed flow field are demonstrated (Section 2.7). A very important element for a correct discretization is to ensure that the discretized formulation (or numerical approximation) indeed converges to the continuous formulation (or physical model), as the discretization (or spatial and/or temporal stepsize) is refined. However, this issue contains several subtleties and is not dealt with in detail in this chapter. To improve accuracy and efficiency of numerical solutions, it is desirable to select appropriate numerical methods according to the physical models considered. The method of lines (MOL),which includes time integration and spatial discretization, is adequate to solve stiff problems such as diffusion-dominated models and fast reaction problems (Section 2.3). In the presence of steep moving fronts, the MOL incorporating adaptive and moving mesh methods to capture large spatial variations provides efficient solutions (Section 2.5). When there is a unique solution propagation path line, the method of characteristics (MOC) can be formulated. The MOC formulation can be solved in the framework of the MOL (Section 2.6.4). Since the solution moves along the propagation path line, numerical error and instability caused by approximation of the convection term is avoided. In solving convection-dominatedmodels, the conservation element and solution element (CE/SE) method is appreciated for accuracy and efficiency due to a finite volume approach and explicit time integration (Section 2.4.3). The CE/SE method possesses low numerical dissipation error but a fine time stepsize is needed for stiff models. Most CFD packages use fully discrete methods (Section 2.4) rather than the MOL (Section 2.3) for solving conservation laws for fluid flow within an often complex multidimensional geometry. Combination of process simulation and CFD is useful to describe complex interactions between fluid hydrodynamics and other physical/ chemical phenomena (Section 2.7).

2.8 Discussion and Conclusion

Although many efficient methods have emerged for solving PDEs/PDAEs, several challenges remain. The numerical method of PDEs with stiff nonlinear source terms is one of the currently active research areas (Ahmad and Berzins 2001; Hyman et al. 2003), where mesh refinement by an efficient control of space-time errors is needed. Simulation methods for the processes considerably influenced by fluid hydrodynamics should be improved by combining CFD technologies. Hybrid dynamic systems that exhibit coupled continuous and discrete behaviors have also attracted much attention (Ma0 and Petzold 2002). When a reactant within a phase of a spatially distributed reactor disappears and appears, special considerations are required for the hybrid system to be properly handled by the numerical methods.

References 1 Ahmad 1. Berzins M . MOL solvers for hyper-

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bolic PDEs with source terms, Mathematics and Computers in Simulation 56 (2001)p. 115-125 Ascher U. M . Petzold L. R. Computer methods for ODES and DAEs, SIAM, Philadelphia 1998 Ayasouj A. Keith T. G. Application of the conservation element and solution element method in numerical modeling of heat conduction with melting and/or freezing 13(4) (2003) p. 448-471. Bauer M. Eigenberger G . A concept for multiscale modeling of bubble columns and loop reactors Chem. Eng. Sci. 54 (1999) p. 5109-5117 Bauer M. Eigenberger G. Multi-scale modeling of hydrodynamics, mass transfer and reaction in bubble column reactors Chem. Eng. Sci. 56 (2001) p. 1067-1074 Berger M. /. Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations J . Comp. Phy. 53 (1984) p. 484-512 Berger M . J. Leveque R. J. Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems, SIAM J . Numer. Anal. 35(6) (1998) p. 2298-2316 Bezzo F. Macchietto S. Pandelides C. C. A general framework for the integration of computational fluid dynamics and process simulation, Computers and Chemical Engineering 24 (2000) p. 653-658 Bezzo F. Macchietto S. Pandelides C. C. General hybrid multizonal/CFD approach for bioreactor modeling AlChE J. 49(8) (2003)p. 2133-2148 BischofC. Houland P. Using ADIFOR to compute dense and sparse Jacobians, Tech-

11

12

13

14

15

16

17

18

nical memorandum ANL/MCS-TM-159, Mathematics and computer science division, Argonne National Laboratory, USA 1991 Bischof C. Carle A. Corliss G. Griavank A. Hovland P. ADIFOR: Generating derivative codes from Fortran programs, Scientific Programming l(1)(1992) p. 11-29 Bischof C. Carle A. Khademi P. Mauer A. Hovland P. ADIFOR 2.0 user’s guide, Technical report ANL/MCS-TM-192, Mathematics and computer science division, Argonne National Laboratory, USA 1998 Calderbank P. H. Mooyoung M. B. The continuous phase heat and mass-transfer properties of dispersions Chem. Eng. Sci. 16 (1961) p. 39-54 Chang S. C. The method of space-time conservation element and solution element-A new approach for solving the Navier-Stokes and Euler equations J. Comput. Phys. 119 (1995) p. 295-324 Chang S. C. Courant number insensitive CE/ SE schemes, 38* AIAA joint propulsion conference, AIAA-2002-3890,Indianapolis, USA 2002 Chang S. C. Wang X. Y. To W. M . Application of the space-time conservation element and solution element method to onedimensional convection-diffusion problems J. Comput. Phys. 165 (2000) p. 189-215 Chang S. C. Wang X. Y . Chow C. Y.The space-time conservation element and solution element method: A new high-resolution and genuinely multidimensional paradigm for solving conservation laws J. Comput. Phys. 156 (1999)p. 89-136 De Swart S. W.A. Krishna R. Simulation of the transient and steady-state behavior of a bubble column slurry reactor for Fischer-

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19

20

21

22

23

24

25

26

27

28

29

30

31

Tropsch synthesis Chem. Eng. Processing 41 (2002)p. 35-47 Do@ E. A. Dmry L. O’C. Simple adaptive grids for 1-D initial value problems J. Comput. Phys. 69 (1987) p. 175-195 Dufort E. C. Frankel S. P. Stability conditions in the numerical treatment of parabolic differential equations, Mathematical Tables and Other Aids to Computation 7 (1953) p. 135-152 Finlayson B. A. Nonlinear analysis in chemical engineering, McGraw-Hill, NewYork 1980 Furzeland R. M . VemerJ. G. Zegeling P. A. A numerical study of three moving-grid methods for one-dimensional partial differential equations which are based on the method of lines J. Comput. Phys. 89 (1990) p. 349-388 Hansen K. ]orgensen S. B. Dynamic modeling of a gas phase catalytic futed-bed reactor 1-111, Chemical Engineering Science 31 (1976)p. 473-479,579-598 Harten A. Engquist B. Osher S. Chakravarthy S. Uniformly high order essentially nonoscillatory schemes I11 J. Comp. Phy. 71 (1987) p. 231-303 Henson M. A. Dynamic modeling of microbial cell populations, Current Opinion in Biotechnology 14 (2003)p. 460-467 Heydweiller]. C. Sincovec R. F. Fan L. T. Dynamic simulation of chemical processes described by distributed and lumped parameter models Comp. Chem. Eng. 1 (1977)p. 125-131 Hill P. /. Ng K. M. New discretization procedure for the breakage equation AIChE J. 41(5) (1995)p. 1204-1216 Hindmarsch A. C. LSODE and LSODI: two new initial value ordinary differential equation solvers, ACM SIGNUM newsletter, 15 (1980) p. 19-21 H o f i a n ] . D. Numerical methods for engineers and scientists, McGraw-Hill Inc., Mechanical engineering series Part 111. Partial differential equations (1993) p. 371-774 Huang W. Russell R. D. Analysis of moving mesh partial differential equations with spatial smoothing SIAM J. Num. Anal. 34 (1997) 1106-1 p. p. 126 Huang W. Russell R. D. Moving mesh strategy based on a gradient flow equation for two-dimensional problems SIAM Sci. Comput. 20(3) (1999)p. 998-1015

32 Hyman]. M. Li S. Petzold L. R. An adaptive

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40 41

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moving mesh method with static rezoning for partial differential equations Computers and Mathematics with Applications 46 (2003) p. 1511-1524 jiang G. Shu C. W. Efficient implementation of weighted E N 0 schemes J . Comp. Phy. 126 (1996) p. 202-228 Kaczmarski K. Mazzotti M . Storti G. Morbidelli M. Modeling fuced-bed adsorption columns through orthogonal collocations on moving finite elements Comp. Chem. Eng. 21 (1997) p. 641-660 Kohler R. Gerstlauer A. Zeitz M. Symbolic preprocessing for simulation of PDE models of chemical processes Mathematics and Computers in Simulation 56 (2001) p. 157-170 Krishna R. van Baten]. M . Eulerian simulations of bubble columns operating at elevated pressures in the churn turbulent flow regime Chemical Engineering Science 5G (2001) p. 6249-6258 Krishna R. van BatenJ. M. Urseanu M. I. Three-phase Eulerian simulations of bubble column reactors operating in the chumturbulent regime: a scale up strategy Chemical Engineering Science 55 (2000) p. 3275-3286 Kumar S. Ramkrishna D. On the solution by discretization balance equations by discretization-111. Nucleation, growth and aggregation of particles Chem. Eng. Sci. 52(24) (1997) p. 4659-4679 Lax P. D. Wendrof B. Systmes of conservation laws Comm. Pure and Appl. Math. 13 (1960) p. 217-237 Leveque R. 1.Finite difference methods for PDEs Lecture note Department of Mathematics University of Washington 1998 Li S. Adaptive mesh methods and software for time dependent PDEs PhD thesis University of Minnesota 1998 Li S. Petzold L. Moving mesh methods with upwinding schemes for time-dependent PDEs J. Comput. Phys. 131 (1997) p. 368-377 Lim Y. I. Jsrgensen S. B. A fast and accurate numerical method for solving simulated moving bed (SMB)chromatographic separation problems Chem. Eng. Sci. 59(10) (2004) p. 1931-1947 Lim Y. I . Chang C. S. ]srgensen S. B. A novel partial differential algebraic equation

2.8 Discussion and Conclusion

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(PDAE) solver: iterative conservation element/solution element (CE/SE) method Comput. Chem. Eng. .28(8) (2004) p. 1309- 1324 Lim Y. I. Le Lann]. M. ]oulia X.Accuracy, temporal performance and stability comparisons of discretization methods for the solution of Partial Differential Equations (PDEs) in the presence of steep moving fronts Comp. Chem. Eng. 25 (2001a)p. 1483-1492 Lim Y. I. Le Lann J . M. Joulia X. Moving mesh generation for tracking a shock or steep moving front Comp. Chem. Eng. 25 (2001b)p. 653-663 Lim Y. I. Le Lann J. M. Meyer X. M . Joulia X , Lee G.B. Yoon E. S. On the solution of Population Balance Equations (PBE) with accurate front tracking methods in practical crystallization processes Chem. Eng. Sci. 57 (2002) p. 177-194 Liu Y. Jacobsen E. W. On the use of reduced order models in bifurcation analysis of distributed parameter systems Computers and Chemical Engineering 28 (2004)p. 161-169 MacCortnark R. W. The effect of viscosity in hypervelocity impact cratering American Institute of Aeronautics and Astronautics paper (1969) p. 69-354 Mackenziej. A. Robertson M. L. The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method J. Compt. Phys. 161(2) (2000) p. 537-557 Mantzaris N. V. Daoutidis P. Srienc F. Numerical solution of multi-variable cell population balance models: I. Finite difference methods Computers and Chemical Engineering 25 (2001a)p. 1411-1440 Mantzaris N. V. Daoutidis P. Srienc F. Numerical solution of multi-variable cell population balance models: 111. Finite element methods Computers and Chemical Engineering 25 (2001b)p. 1463-1481 Ma0 G. Petzold L. R. Efficient integration over discontinuities for differential-algebraic systems Computers and Mathematics with Applications 43 (2002)p. 65-79 Mhaskar P. Hjorts0 M. A. Henson M. A. Cell population modeling and parameter estimation for continuous cultures of S. cerevisiae Biotechnol. Prog. 18 (2002) p. 1010-1026 Miller K. Miller R. N. Moving finite elements I SIAM J. Numer. Anal. 18 (1981) p. 1019-1032 Molls T. Molls F. Space-time conservation method applied to Saint Venant equa-

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tions J . Hydraulic Eng. 124(5) (1998) p. 501-508 Motz S. Mitrovic A. Gilles E.-D. Comparison of numerical methods for the simulation of dispersed phase systems Chem. Eng. Sci. 57 (2002) p. 4329-4344 Oh M. Modeling and simulation of combined lumped and distributed processes, PhD thesis, University of London 1995 Petzold L. R. A description of DASSL A differential/algebraic system solver in scientific computing , eds. R. S . Stepleman et al., North-Holland, Amsterdam (1983)p. 65-68 Poulain C. A. Finlayson B. A. A Comparison of Numerical Methods Applied to Nonlinear Adsorption Columns” Int. J. Num. Methods Fluids 17(10) (1993) p. 839-859 Powell M. J. D. On the convergence of the variable metric algorithm J. Inst. Math. Appl. 7 (1971)p. 21-36 Recke B. Jargensen S. B. Nonlinear dynamics and control of a recycle fmed bed reactor Proceedings of the 1997 American Control Conference vol4 (1997) p. 2218-2222 Sargousse A. Le Lann I. M. Joulia X. Jourdu L. DISCO:un nouvel environnement de simulation orient objet; Proceeding of MOSIM 1999 61-66, (1999) p. Nancy, France Saucez P. Schiesser W. E. van de Wouwer A. Upwinding in the method of lines Mathematics and Computers in Simulation 56 (2001) p. 171-185 Schiesser W. E. The numerical method of lines-integration of partial differential equations Academic press New York 1991 ShiJ. H u C. Shu C. W. A technique of treating negative weights in WEN0 schemes Brown University Scientific Computing Report Series BrownSC2000 (2000) p. 15 USA Shu C. W. Osher S. Efficient implementation of essentially non-oscillatory shockcapturing schemes J. Comp. Phy. 77 (1988) p. 439-471 Shu C. W.Osher S. Efficient implementation of essentially non-oscillatory shockcapturing schemes 11 J. Comp. Phy. 83 (1989) p. 32-78 Shu C. W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws ICASE Report No. (1997) p. 97-65 Stockiej. M. Mackenziej. A. Russell R. D. A moving mesh method for one-dimensional hyperbolic conservation laws SIAM J. Sci. Comput. 22(5) (2001) p. 1791-1813

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Van der Laan G. P. Beenackers A. Krishna R. Multicomponent reaction engineering model for Fe-catalyzed Fischer-Tropsch synthesis in commercial scale slurry bubble column reactors Chem. Eng. Sci. 54 (1999) p. 5013-5019 72 Vande Wouwer A. S a m z P. Schiesser W. E. Some user-oriented comparisons of adaptive grid methods for partial differential equations in one space dimension App. Num. Math. 26 (1998) p. 49-62 73 Villadsen J. Michelsen M. L. Solution of differential equation models by polynomial approximation. Prentice-Hall Englewood Cliffs New Jersey 1978 74 W q J .S. Analysis of batch crystallization processes Chem. Eng. Commun. 35 (1985) p. 231-252 71

Wu]. C. Fan L. T. Erickson L. E. Three-point backward finite-difference method for solving a system of mixed hyperbolic - parabolic partial differential equations Comp. Chem. Eng. 14 (1990) p. 679-685 76 Yu S. T. Chang S. C. Treatment of stiff source terms in conservation laws by the method of space-time CE/SE AIAA 97-0435 35" Aerospace Sciences Meeting, Reno, USA 1997 77 Zhu G.-Y. Zamamiri A. Henson M. A. Hjortse M. A. Model predictive control of continuous yeast bioreactors using cell population balance models Chem. Eng. Sci. 55 (2000) p. 6155-6167

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Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8 I107

3 Molecular Modeling for Physical Property Prediction Vincent Cerbaud and XavierJoulia

3.1 Introduction

Multiscale modeling is becoming the standard approach for process study in a broader framework that promotes computer-aided integrated product and process design. In addition to the usual purity requirements, end products must meet new constraints in terms of environmental impact, safety of goods and people, and specific properties. Engineering achievements can be startling from the user perspective like aqueous solvent paint that is still washable after drying! This can only be done by improving process knowledge and performance at all scales, right down to the atomic scale. Current experimental and modeling approaches assess with difficultly such submicronic scales. In experiments, there is the question of how to conceive experimental devices small enough and how to introduce them in molecular systems without irreversibly affecting the phenomena that they look at. In modeling and simulation, the questions are: which hypotheses are still relevant? How does one handle boundary effects? Numerical difficulties may arise along with the necessity of defining new parameters. They will be adjustable ones as no experiments can obtain them. This latter statement is particularly true for energetic interaction parameters like binary interaction parameters in current liquid-vapor equilibrium macroscopic thermodynamic models based on the activity coefficient approach or on the equation of state approach. The study of any process, phenomena attributed to energetic interactions has always been left for another time, but that time has come. Indeed, molecular modeling is a field of study that is interested in the behavior of atomic and molecular systems subject to energetic interactions. It is then a natural complement of experimental and modeling approaches to expand multiscale approaches towards smaller scales. Besides, process flows primarily concern molecules from raw materials to end products. Therefore, at any process development step, the challenge of knowing the physical properties and thermodynamical state of molecules is critical. However, the future of this challenge is dim when one thinks Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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about the millions of chemical compounds referenced in the chemical abstract series. Neither experimental approaches nor current themodynamic models can handle the combination of properties needed. In some cases experiments are not even practical because of material decomposition or safety issues. Universal group contribution methods are a pipe dream and existing ones are efficient but are restricted to specific areas like petrochemical and small molecular systems. As providers of accurate physicochemical data, molecular modeling methods offer an alternative to an intensive and expensive experimental campaign once molecular models are available, which is becoming increasingly the case (Case, Chaka, Friend et al. 2004). But the first goal is nothing compared to the main interest of molecular methods, that is, probing matter at the molecular level (Chen and Mathias 2002; De Pablo and Escobedo 2002; Sandler 2003). Indeed, molecular modeling can be seen as a “third way to explore real matter” (Allen and Tildesley 1987). Like a theoretical approach, it is based on a model system of the real one. But unlike theory, no hypothesis and no transcription of key phenomena into equations or correlations is performed. Rather, molecular modeling performs numerical experiments to simulate directly the behavior of the model system. The concept of numerical experiment is strong. First, the model system is made of a boundered molecular system and of an interaction model analogous to an experimental sensor that enables one to compute the internal energy of the model system. Second, think of the pseudoconstant thermometer temperature and of the Brownian motion of atoms in a liquid that generates a fluctuating temperature. More generally, any macroscopic property value measured by an experimental probe is a timeaverage over many instantaneous fluctuating values. Statistical thermodynamics postulates that this time-average equals an ensemble average over a statistically significant number of model system configurations. Molecular modeling generates them numerically using methods like molecular dynamics or Monte Carlo methods. Any property of interest is then derived using thermodynamical laws from instantaneous property value averages and correlation factors. Thirdly, numerical standard deviation associated to the ensemble average is the equivalent of experimental accuracy. This chapter presents molecular modeling concepts so as to demystify them and stress their interests for chemical engineers. Multiscale approach including molecular modeling are not illustrated due to restricted space. Rather, routine examples on the use of several molecular techniques suitable for acquiring accurate vapor-liquid equilibrium data when no data is available are provided. 3.2 What is Molecular Modeling?

Molecular modeling includes computer theoretical chemistry and molecular simulation. Computer theoretical chemistry calculations are carried out at 0 K and solve Schrodinger’s equation to obtain nuclear and electronic properties such as conformation, orbital, charge density, and electrostatic potential surface in fundamental or excited states. Computation time is huge, being proportional at best to N2.Selectrons,

3.2 What is Molecular Modeling?

which restricts its use to small systems. The precision of the results is significant because the only assumptions are linked to approximations carried out to solve Schrodinger’s equation. In particular, there are no adjustable parameters. Besides, it provides crucial information on the electronic distribution that enables one to evaluate electrostatic interactions in molecular simulation. Molecular simulation is a numerical technique used to acquire the physicochemical properties of macroscopic systems from the description, on an atomic scale, of the elementary interactions and from the application of statistical thermodynamics principles. It concerns the calculation of a model system internal energy at a positive temperature. Computation time is proportional to Nmolecules, which makes it a technique adapted to the study of real systems: phase properties, interfaces, reaction, transport phenomena, etc. Molecular simulation carries out dynamic modeling of the system subjected to realistic temperature and pressure conditions thanks to an adequate sampling of the system configurations. A configuration is a set of particle coordinates and connections. Inaccuracy may arise from the energetic models that contain fitted but physically meaningful parameters or from system configuration sampling techniques that must comply with statistical thermodynamic principles. Molecular simulation offers the most potential for process engineering. Wherever energetic-interaction-relatedphenomena have a prevalent place, molecular simulation deserves to be considered for use in studying and loolung further into the knowledge of the phenomena in the heart of the processes. In particular, it is suitable for the study of phase equilibrium, interfacial properties (specific adsorption on catalyst), transport coefficients, chemical reactivity, activity coefficients, etc.

3.2.1 Scientific Challenges of Molecular Modeling in Process Engineering

The use of molecular simulation in process engineering lies mainly in the difficulty of establishing the link between the macroscopic properties and their energetic description or that of significant parameters at mesoscopic or molecular scale. The micro-macro relation can be simple: in distillation, the knowledge of phase equilibrium data enables one to run an extensive study and design of the process. In tablet processing, the relation is more complex: the tablet properties (compactness, friability, dissolution) are related to the pellet’s cohesion and to the substrate’s solubility. Obviously, the energetic interaction is a key phenomenon and is taken into account through solubility parameters, which can be broken down into primary energy contributions (van der Waals repulsion-attraction, Coulombic interaction, etc.), precisely the applicability of molecular simulation. But particle size and solvent effects on the aggregate size and homogeneity are equally important, notwithstanding operational process parameters, and are still difficult to address at a molecular scale. So, identifying the limiting phenomena is a priority before any molecular simulation. The size of the model systems is not an unsolvable problem as periodic boundary conditions can be applied to replicate the original system box and mimic a homogeneous macroscopic phase. Rather, the scientific challenges concern issues often

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encountered in experiments, the sensor challenge, the sampling challenge, and the multiscale challenge. 3.2.1.1 The Sensor Challenge

For data-oriented simulations, accurate force fields/sensors are needed to evaluate precisely energetic interactions. The study of highly polar systems, reliable and relevant extrapolation of carefully set force field parameters, and the absence of temperature dependency of these parameters are key improvements of molecular simulation models over existing macroscopic models. The model system is usually a parallelepiped box filled with particles whose energetic interactions are described by a force field enabling one to compute the system internal energy. In order to mimic a homogeneous phase, the box is usually replicated in 3-D by applying periodic boundary conditions. The typical size ranges from 20 to 1000 8, and may vary during simulations. Edge effects are to be envisaged and can be attenuated by increasing the box size. The development of a force field requires a strong collaboration with theoretical chemists and physicists. Indeed, different lunds of force fields can arise: some based on quantum chemistry concepts and some based on molecular mechanics (Sander 2003). Quantum-based models are used in static modeling and naturally in computer theoretical chemistry calculations. Solving the Schrodinger equation, they provide the nuclear and electronic properties system and consequently the true energy of the system (e.g., the energy of ionization) that is physically measurable. Molecular mechanics models are used in molecular simulation to calculate intensive properties (T, P) and extensive properties, among which the internal energy of the system, which is not directly measurable by experiment, but enables one to calculate other thermodynamic properties by using thermodynamic laws. Properties like vaporization enthalpy connected to differences in internal energy are computed and can be compared to experiments. Quantum models (QM)are practical on a few tens of atoms at best and are being used more and more in combination with molecular mechanics models for some part of the system where accurate electronic distribution is needed, e.g., a reactive zone or to provide a description of the electronic distribution. Molecular mechanics (MM) models are the most used and are based on a springs and beads mechanistic description of the intermolecular interactions and of the intramolecular bonds. They allow calculations on several hundreds of particles, which enable one to model real systems in a satisfactory way. They contain physical parameters evaluated from quantum calculation but also empirical parameters, which must be regressed from experimental data. However, this empiricism is attenuated by some physical significance attributed to the parameters. Moreover, M M force fields show amazing properties. Valid over a large pressure and temperature range, they can be used to compute many properties and all molecules can be described from a small set of parameters if careful parameterization is conducted, which constitutes the first challenge.

3.2 What IS Molecular Modelmg?

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Figure 3.1

Process engineering and molecular modeling

3.2.1.2 The Sampling Challenge

The second challenge requires a strong involvement of process engineers. Novel and smart methods must be developed to sample specific states of the model system, which are of great interest for process engineering, for instance, transition states that set the reaction energetic barrier, azeotropes that affect strongly the distillation process feasibility and design, dew points, etc. Usually, existing molecular simulation methods sample nonspecific states like a vapor-liquid equilibrium point. Unlike measurement time, its experimental equivalent, numerical sampling can be advantageously biased to sample the specific state of interest but it requires expertise to comply with statistical thermodynamics principles, which permit a bridging of the microscopic and macroscopic scales. Furthermore, for existing methods based on molecular dynamic or Monte Carlo methods, sampling efficiency should be improved, in particular for complex molecules like macromolecules, even if the alternate solution of running more simulations is still the leading choice as computer power increases. With this second challenge, process engineering finds a new use for molecular modeling: it cannot be solely data-oriented, but also discovery-oriented and assumes its status of numerical experiment. 3.2.1.3 Molecular Modeling in a Multiscale Approach

The integration of molecular modeling in applicable models for the study of macroscopic systems and their properties is of the utmost importance for process engineering. Indeed, often considered as decisive, phenomena related to energetic interactions have often been left aside during a process study because of a lack of suitable tools or incorporated into parameters. Thermodynamic models used in phase equilibrium calculations are a good example: binary interaction parameters must be found empirically despite their solid physical meaning. The first illustrative example addresses the issue of calculating binary parameters by molecular modeling methods.

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Process engineering models are knowledge-based models. In most domains, process study requires a multiscale approach. As a technique of experimentation, molecular modeling makes it possible to visualize on a molecular scale physicochemical phenomena. It can thus be used to develop or revisit theories, models or parameters of models and therefore improve our knowledge of processes and increase the capacity of predictions and extrapolation of existing models.

3.3 Statistical Thermodynamic Background

Suggested Readings 1

2

McQuarry D. A. Statistical thermodynamics. Harper and Collins. New York, 1976. ISBN 0060443669 Allen M. P. Tildesley D. J. Computer Simdation of Liquids. Oxford University Press, Oxford, UK. 1987. ISBN 0198556454

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Frenkel D, Smit B Understanding Molecular Simulation. From Algorithms to Applications. Academic Press, San Diego, 1996. ISBN 0122673700

3.3.1 A Microscopic Description of Macroscopic Properties

Traditional thermodynamics and statistical thermodynamics address the same problems but differ in their approach: thermodynamics provides general relations without any consideration of the intrinsic constitution of the matter, while statistical thermodynamics supposes the existence of atoms, molecules, and particles to calculate and interpret thermodynamic properties at the molecular level. The objective of statistical thermodynamics is to describe the behavior of a macroscopic system in terms of microscopic properties of a system of molecular entities. The main idea is to evaluate an average property value and its standard deviation from a statistically significant number of configurations, much like a real experiment. Indeed, the temperature reading on a thermometer appears falsely constant. At the molecular level, a positive temperature is the result of atomic vibrations and collisions occurring on a time scale (e.g., IO-' s.) much lower than the sampling s.) (Fig. 3.2). Using statistical thermodyperiod of the experimental sensor (e.g., namic concepts, molecular simulation will do the same and perform a numerical experiment. Each instantaneous configuration (atomic positions and moments) of the system exists according to a probability distribution. The most probable will have the largest contribution to the computed average value. For the experimental system the macroscopic property X value is a time-average over a set of configurations r (t) sampled during the measurement time tmeas:

3.3 Statistical Thermodynamic Background

TO,

Measurement time (10-3s) >> fluctuations ( Figure 3.2

Measurement of a “mean” temperature and its relation with instantaneous temperature

s)

But knowing all configurations T(t)is impractical because the number of particles (6.023 x for a mole) and thus the number of positions and moments are incommensurable. Statistical thermodynamics was developed to solve this problem statistically. The first postulate of statistical thermodynamics is that “the value Ofany macroscopic property is equal to its average value over a sample of the model system conjgurations,” as shown here:

where ttotal is the number of sampled configurations. The notation ( )ensemble refers to a statistical ensemble. By definition it consists in a significant number of subensembles having the same macroscopic properties. The thermodynamic state of a macroscopic system is perfectly specified by a few parameters, for example the number of moles N,the pressure P, and the temperature T. From them, one can derive a great number of properties (density, chemical potential, heat capacity, difhsion coefficient, viscosity coefficient, etc.) through equations of state and other thermodynamic relations. Reproducing conditions occurring in experiments, the “canonical” NVT, and the “isobar-isothermal”NPTensembles are quite useful. The notations NVT and NPT mean, respectively, that the number of moles N + volume V + the temperature T and the number of moles N + the pressure P + the temperature T, are kept constant for each system configuration during simulations run in those ensembles. One considers that the postulate of statistical thermodynamics applies during simulations in a statistical ensemble on systems with a few thousands of particles replicated by periodic boundary conditions and that averages are made on a few million configurations. The sampling size and quality are often the Achilles’ heel of molecular simulations. 3.3.2 Probability Density

Equation 2 states that configurations have the same weight, on average, and the same probability of existence. This is the second postulate of statistical thermodynamics: “Allthe accessible and distinct quantum statesfrom a closed system offixed energy

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(‘microcanonic’NVE) are equiprobable.” Equation 2 is therefore rewritten: X(r(t))h,,

= (X)ensemble =

(x(r(r)) Pensernble(r(r))) ’

Second postulate

(3)

r(r)

where pensemble(I’)is the probability density, which is the probability of finding a configuration with positions and moments r(t).In the NVT ensemble, any configuration probability density is connected to its energy E and to the total partition function, namely the sum over all configurations, by the Boltzmann formula:

am,

Two points are noteworthy: 1. The knowledge of the partition function allows the calculation of all thermodynamic properties. But this can never be done fully but rather imperfectly through the generation of a statistically representative number of configurations. 2. A model is required to evaluate any configuration energy in order to calculate the partition function. This is done through a force field.

3.3.3 Average, Fluctuations, and Correlation Functions

Equation 2 is the usual mean formula to calculate an average value (molar fractions, etc.). Other properties (heat capacity, etc.) are calculated from the variance expressing the fluctuations around the mean:

( x ) Variance ~

(5)

Correlation coefficients give access to properties describing the dynamic state of the system. The nonnormalized form of the correlation coefficient over T configurations is:

C x(tO).x(to+~)Correlation coefficient

Ittotal

correlxx(r) = ( x ( T ) . x (=~~))

ro=l

(6)

The integration of the nonnormalized correlation coefficients enables one to directly calculate macroscopic transfer coefficients (diffusion,viscosity, or the thermal diffusivity coefficient). Their Fourier transform can be compared with experimental spectra.

3.4 Numericd Sarnp/ing Techniques

3.3.4 Statistical Error

Molecular simulation is a numerical experiment. Consequently, the results are prone to systematic and statistical errors. The systematic errors must be evaluated, and then eliminated. They are caused by size effects, bad random number generation, and insufficient equilibration period (see below). Statistical errors are inversely proportional to sampling and are thus zero for infinite sampling. On the assumption that the Gauss law applies, the statistical error is the variance (Eq. (5)). However, sampling a large but finite number of configurations induces a correlation between the Ttotd configurations that persist during a certain number of successive Configurations. A statistical factor of inefficiency s is introduced to evaluate the number of correlated successive configurations. The ttotal configurations are cut into nb blocks of ‘Gb configurations upon which the average ( 4 b and its variance ( S * ( a b ) are computed. By selecting several increasing values of o b , the statistical inefficiencys and the statistical error 02((X)total) is evaluated:

3.4 Numerical Sampling Techniques

The generation of a statisticallyrepresentative sample of the model system configurations is mainly done by two techniques: molecular dynamics and the Monte Carlo method. They obey the principles summarized in Fig. 3.3. Both methods differ in their applications. The Monte Carlo method is adapted for the study of static phenomena (equilibrium and static interface) while molecular dynamics is suitable for the study of dynamic phenomena (shear induced flow). A phase equilibrium easily computed using Monte Carlo methods would be difficult to reach in molecular dynamics because of the time needed and of boundary effects near the interface.

3.4.1 Molecular Dynamics

Molecular dynamics generates a trajectory by integrating the classical equation of motion over time steps 6t starting from an initial configuration whose particle positions and velocity are known (Fig. 3.3). The n* configuration can be traced down the initial one by reverse integration. In the equation of motion (Fig. 3.3), the forces Fi acting on the particle of mass mi are equal to the derivative of the Vi(r)potential describing the interactions of the particle i with its surroundings.

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3 Molecular Modelingfor Physical Property Prediction

Trajectory

C b-= m ddV, t

+

1 1 ?&

I

Figure 3.3

i

Molecular Dynamics

Monte Carlo

Random configurations

I _.

.:,

...

I ;j‘:.’

1

Basic concepts of the Monte Carlo method and molecular dynamics

The integration of the differential set of equations is carried out mainly by Verletlike algorithms rather than by Gear-like algorithms, which are widespread in process engineering. The Verlet algorithm calculates the new particle positions r(t) using a 3rdorder Taylor expansion and replacing the second derivative by the forces thanks to the equation of motion, one gets a formula with no velocity term: r(t

F ( t ) tit2 + tit) = 2r(t) - r(t - tit) + . - + o(tit4) m 2!

(9)

Velocities are computed afterwards: dr(t) dt

-

u ( t ) = --

r(t

+ tit) - r(t - tit) 26t

+ o(st2)

(10)

This algorithm shows several interesting characteristics: (1)It is symmetrical with regards to 6t, which makes the trajectory reversible over the time. (2) It preserves the total energy of the system over long periods of integration, a key point to get long trajectories and deduce with accuracy some correlation functions. In particular, it is more precise than the Gear-like algorithms for large 6 t (the reverse is true for small 6 t ) making it suitable to simulate long trajectories, which is our goal. (3) It requires less data storage than Gear-like algorithms. Transport coefficients (self-diffusion,thermal diffisivity, and viscosity) are computed from autocorrelation coefficients, the “Green-Kubo”formulas, for instance, the coefficient of self diffusion Diis related to the relative particle velocities:

Similarly, viscosity is obtained from the shear stress tensor autocorrelation coefficient related to the pressure exerted on the particle and the thermal diffusivity is obtained from the energy flow autocorrelation coefficient.

3.4 Numericd .Samp/ingTechniques

A challenge with molecular dynamics run in a statistical ensemble where the temperature is set constant, is keeping it constant when moving and interacting particles inevitably heat the system. A solution is to place the system in a large thermostated bath periodically set in contact with the model system through techniques like the Andersen or Nose-Hoover methods.

3.4.2 Monte Carlo Method

The Monte Carlo method generates system configurations randomly. The n* configuration is related to its preceding one but it is impossible to go back to the initial configuration. First of all, randomness is particularly critical and has given its name to the method in reference to the Monte Carlo casino. The advice is to always use a published robust random number generator and never try to build one or use the falsely random precompiled “Ran”function on a computer. Systematic deviation and repetitive sequences can be checked by running simple tests. The second key issue is sampling (Fig. 3.4). Uniform sampling allows a good estimate of the partition function needed to compute all macroscopic properties, but at the expense of sampling high energy and thus improbable configurations. Preferential sampling (or metropolis sampling) samples the configurations with the largest contribution in the calculation of the partition function and of averages. The disadvantage of metropolis sampling is that the partition function (equivalent to the surface under the curve) is no longer correctly evaluated. Thus, the question arises of finding how to generate the configurations with a correct probability distribution without having to calculate the function of partition that occurs in the definition of the probability density (Eq. (4)). The solution is to obey the microscopic law of reversibility. Given an old (0)and a new (n) configuration, their probability densities p are proportional to exp(-E(,,)/kBT)and exp(-E,,,/kBII) in the NVTensemble (Eq. (4)).Defining the transition probability M(o+n) of going from (0)to (n), the microscopic reversibility states that at equilibrium the number of transitions from (0)to (n) and from (n) to (0)corrected by the probability densities must be equal.

In addition, an acceptance criterion is introduced acc(o + n) along with a ( o-+ n) an (0)to (n),which is supposed to be symmetrical (a(o+ n) = a ( n + 0)):

a priori probability of trying to go from

M(o + n) = a(o + n) . acc(o -+ n)

(13)

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3 Molecular Modelingfor Physical Property Prediction

Then by exploiting the symmetry of a , Eq. (12) becomes:

(-(%

acc(o -+ n) - pg& acc(n -+ 0) = eXP

&

kbT

)

(14)

In this equation, the partition function that is so difficult to calculate no longer appears. The metropolis idea is to choose acc(o+n) asymmetrically. As indicated in Fig. 3.5:

If the new configuration energy is lower than the old one, the transition is always accepted If the new configuration energy is higher than the old one, one picks a random number between 0 and 1: o if = 5 exp(-(E(,) - E(,,))/keT), the transition is accepted, o if 5 = > exp(-(E(,, - E(o,)/kBTj,the transition is rejected.

c

Applied to Eq. (14), this acceptance criterion enables one to define the acceptance probability of a random displacement in general and in the NVT ensemble:

Last, a symmetrical a(o + n) is chosen to allow a sampling effective in terms of acceptance and efficient in terms of the configuration space. Usually one defines a maximum value associated with the transition, like a maximum displacement d,that is fxed in order to satisfy a rate of 50 % of accepted transitions. If several movements are possible (e.g., translation, rotation, and volume), the type of movement will be chosen randomly from a predetermined statistical distribution. Again, one insists on the randomness of the choices of particle and of the type of movement in order to respect the microscopic reversibility. In ensembles other than NVT, probability densities are corrected with respect of the microscopic reversibility law.

probability

1

r\

probability

ILAttt

Uniform sampling Figure 3.4 Uniform and preferential sampling

ttt

Preferential sampling

configurations

r.

0 Figure 3.5

E,,,-E,,

AE

Metropolis preferential sampling. Criterion of acceptance

3.4.3 Phase Equilibrium Calculations using Cibbs Ensemble Monte Carlo

The Gibbs ensemble was developed by Panagiotopoulos in 1987 to simulate vaporliquid equilibria. Simulations are carried out in a NVT ensemble on two microscopic boxes located within two homogeneous phases far from any interface. Each box is simulated with periodic boundary conditions. Constant total volume V and total N particles are divided between the two phases V,, N1 and V,, N2. The temperature is set constant in the simulations and random movements are performed to satisfy the phase equilibrium conditions as described in Fig. 3.6: 0

0

0

Displacements (translation, rotation) within each phase to ensure minimal internal energy; A change of volume proportional between the phases: AVl = -AV2 so that the total volume is constant. This should satisfy the pressure equality. Transfer of the particle from one box to the other to equalize the chemical potentials.

The acceptance probabilities of the various movements in the case of a single component system are given below. For the translation in each area:

For the change of volume, V, is being increased by A V and V2 is being decreased by just as much:

with A V chosen by generating a uniform random number 5 between 0 and 1 ; 6 V, being the change of maximum volume adjusted to obtain a fixed percentage (e.g., 50 %) of acceptance of the move: AV =

< . SVma, . min(V1, V2)

(18)

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For the transfer of a particle of area 2 to area 1:

One of the main difficulties of the Gibbs ensemble Monte Carlo method resides in the transfer of particles to satisfy the chemical potentials equality because of the difficulty to insert polyatomic molecules in the dense phase. An alternative is to seek open spaces where insertion is eased into the particle. This affects randomness and introduces a statistical bias like the configurational bias method, which consists of inserting segment by segment a molecule in a phase. The probability of acceptance of the transfer of the particle represented by Eq. (19)is then modified by introducing the energy differences A Ei into weighting factors Wi that represent the total energy of interaction with the surroundings of the inserted molecule. For an L segment molecule inserted in m possible directions:

More generally, the introduction of a bias consists of defining an a pliori probability a(o+n), which is no longer symmetrical. Equations 14 and 15 become:

Real bulk phases

Initial

Gibbs Ensemble Monte Carlo

state

Mavement type

Internal l.-placements

-.

Equilibrium conditions Figure 3.6 ensemble

AV, = -A&

............ .-

E, minimal

Principles of phase equilibrium simulations in the Gibbs

Partide lransfer .........

P, = P,

&,I = K,2

3.5 Interaction Energy I 1 2 1

To conclude this section, both molecular dynamics and Monte Carlo methods require the calculation of the interaction energy; for molecular dynamics to derive forces exerted on the system particles and for the Monte Carlo method to calculate the acceptance criterion. The following section reviews the main features of the force fields enabling to calculate intra and intermolecular interaction energies. 3.5 Interaction Energy Suggested Readings 1

Leach A. R. Molecular Modelling, Principles and Applications. Longmann, Harlow, UK, 1996

2

Karplus M. Porter R. N. Atoms and Molecules. Benjamin inc., New York, 1970

3.5.1 Quantum Chemistry Models

Quantum chemistry models are never used alone in molecular simulation because of the still prohibitive computation time. However, they must be considered as they can provide less-sophisticated molecular mechanics models with partial electronic charges and various dipoles useful for computing Coulombic and dipolar interactions. They can also provide accurate spring constant values describing the bonding intramolecular interactions associated with the various oscillatory modes within the molecules (stretching, bending, and torsion). In quantum chemistry, only atomic nuclei surrounded by revolving electrons are considered. Calculations provide the nuclear and electronic properties system and the true total energy of the system. Total energy is related to the general time dependent wave function Y (r, t) by means of the generalized Schrodinger equation: where H is the Hamiltonian, a mathematical operator with kinetic and potential energetic contributions. Apart from an analytical solution for the sole hydrogen atom, Schrodinger equation solutions are always approximate to some degree because a compromise must be made between computation time and accuracy. Three levels of approximation are considered, namely ab initio methods, mean field methods, like density functionnal theory (DFT),and semiempirical methods. Among ab initio methods, configuration interaction (CI) methods are the most accurate, but the slowest. Calculated energy values have a precision comparable with

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experimental ones (0.001 ev). CI solutions are obtained by minimizing a linear combination of the wave functions associated with the system fundamental state and all excited states. The self consistent field molecular orbital concept considers atomic orbitals that represent wave functions of electrons moving within a potential generated by the nucleus and by an average effective potential generated by the other electrons. The best such wave functions are Hartree-Fockwave functions and solve the Schrodinger equation for a given electronic configuration (e.g., the fundamental state) without any empirical parameter. They can be used for CI calculations. Atomic orbital wave functions are approximated using Gaussian functions, which leads to peculiar denominations like STO-3G Hartree-Fock calculations (use of a basis set of three Gaussian functions). The larger the basis set, the longer and the more accurate the calculation. The semiempirical methods are the most approximated quantum methods: Hiickel calculations can be done on a sheet of paper; finer semiempirical models enable one to obtain with good precision the ionization energy, optimal conformations, and electronic surface potential. However, they present the disadvantage of calculating the wave functions approximately by replacing various integrals by fitted empirical parameters. Between the two levels of approximation, one finds the mean field methods of the popular density functionnal theory. The idea is rather than to seek to solve the exact Hartree-Fock problem in an approximate way, one could seek to solve an approximate problem in an exact way. That consists of modifylng the Hamiltonian operator and replacing the term of exchange of correlation accounting for multiatomic orbital interactions by the electronic density pi. The results are obtained with satisfactory accuracy and much faster than Hartree-Fockcalculations, enabling one to even study periodic systems of interesting size. Nevertheless, all quantum mechanical calculations are performed for a static configuration of the system under 0 K conditions. But as a provider of key properties like electronic distribution, they should be systematically used in any molecular simulation aiming to be quantitative.

3.5.2 Molecular Mechanics Models

Molecular simulation uses molecular mechanics models to calculate the internal energy of the system. It considers that the molecules can be represented by centers of forces like beads and the bonds can be represented by springs (Fig. 3.7). As Fig. 3.7 shows, the total internal energy is the sum of intramolecular or bonding interactions and of intermolecular or nonbonding interactions. The set of molecular mechanics parameters is called a force field. Intramolecular energy takes into account vibration phenomena between bonded centers of forces. As the beads and spring model suggests, they are described by harmonic functions and handle stretching, bending, torsion as well as improper rotation

3.5

/flterOdOfl

Energy

if needed. Average parameters lo, +o and harmonic constants ki and are usually fitted to accurate vibration energy calculations made with quantum mechanical methods. Intermolecular energy takes into account the two-body interactions between the centers of forces. Three-body interactions are rarely included. Short range interactions can be described by a van der Waals potential modeled by a 12-6 Lennard-Jones function. The 1/rI2term represents the repulsive contribution, which becomes significant below 3 A. The 1/4term represents the attractive contribution related to the dispersive effect of induced dipoles. More rigorous forms may include 1/$ or l/rl’ terms or other functional forms (Buckingham potential, “exponential-6”potential, etc.). Electrostatic interactions are a major contribution to intermolecular energy as they are long-range interactions felt up to a distance of 25 A for multicharged ions. Permanent dipole and multipole are rarely included, but Coulombic interactions related to partial atomic charges qiand q, are a must. All electronic parameters (dipoles, partial charges) should be fitted to electronic surface potentials computed by quantum mechanics to improve quantitative predictions of molecular simulations. Hydrogen bonding interactions are either modeled explicitely by a 12-10LennardJones function or assumed to be implicitely taken into account in the van der Waals interaction. The functional form of the molecular mechanics energy shows that it is not a true energy that can be measured experimentally. Rather, for a single molecule, it is zero at its most stable conformation, whereas true zero energy corresponds to the protons, neutrons, and electrons infinitely split apart. Molecular mechanics predictions of conformations are in excellent agreement with experimental ones. Nevertheless, the practical use of molecular mechanics is great because for a system of several molecules, it computes the thermodynamic internal energy from which many interesting properties can be derived. Force fields can be of all-atoms (AA) type, as shown in Fig. 3.7, in which there is a center of force on each atom. Their names are Dreiding, Universal Force Field, Compass, OPLS, etc. But other types exist where atoms are grouped (e.g., -CH3) under a single center of force in order to reduce the computing time of short range interactions. This leads to united atoms (UA) force fields. In all cases, long-range electrostatic interaction is split in as many centers as possible, usually on all atoms and sometimes on virtual centers. A similar idea is at the origin of polarizable force field like the anisotropic united atoms (AUA), which intends to take into account the electronic cloud shift when two particles approach: the charged center is displaced along the resultant of the nearby bonds. Since all intramolecular parameters and electrostatic parameters are systematically derived from quantum mechanical calculations, molecular simulations using molecular mechanics force fields have greatly improved their accuracies. However, even if for a particle i, Lennard-Jones parameters ui and E~ are, respectively, associated with the collision diameter (the distance for which energy is null) and with the potential well. They must still be fitted to some extent, as will be shown later using experimental data (enthalpies, formation energies, densities, etc.).

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I-stretching

4,s;

Figure 3.7

2-bending

3-torsion

--

%Van der Waals 5-Coulomb

Typical molecular mechanics force field.

For multi component systems, the diameter ay and the energy parameter E Y are obtained from pure substances using traditional mixing rules like those of LorentzBerthelot:

These very simple rules have rarely been questioned, more proof of the strong physical basis of molecular simulation. Furthermore, they highlight that the study of a system with M different centers of forces only requires the knowledge of 2M parameters, whereas a traditional approach with a thermodynamic model with binary interaction parameters would require M(M+1)/2 such parameters. Even if the main functional forms of the potentials (stretching, bending, torsion, van der Waals and Coulomb) are present in all quoted force fields, the choice must be made by knowing the type of experimental data used to regress the Lennard-Jones parameters and the way electrostatic interaction are described. Mixing LennardJones parameters from several force fields without any confrontation to experimental data is acceptable only if qualitative results are sought. 3.6 Running the Simulations

How should one represent the behavior of macroscopic systems when the model system typically contains only a few thousand particles?The problem is solved by adopting periodic boundary conditions that duplicate in all directions identical images of the model system. In molecular dynamics, care should be taken that any particle moving through one wall of the main image will reenter at the opposite wall with the same velocity. Notice that the interaction energy of a particle must include interaction with all included replicated particles. However, for long-range interactions this would require too much computer effort and limiting techniques are implemented: rough ones, such as a “cutoff distance beyond which the interaction is supposed to be null, or more accurate ones like the Ewald summation. In the case of a cutoff, it is necessary to include long range corrections.

3.7 Applications

The initial particles in the box are usually set along a periodic network to avoid overlaps that would result in an infinite energy. Then, a statistical ensemble and a sampling technique are chosen. Force field parameters are associated with all force centers and for molecular dynamics simulations, a statistical distribution of initial velocities is set. Finally, the simulation is launched. It consists of a phase of equilibration and a phase of production. The purpose of the phase of equilibration is to bring the system from an initial configuration to a configuration representative of the system: random distribution of the molecules and the velocities within a system with imposed thermodynamic conditions (that of the chosen statistical ensemble). In molecular dynamics under fured temperature T,the system in gradually heated to the T set value. The phase of production starts when key properties like potential energy, pressure, and density fluctuate over mean values. Each configuration then generated is kept to calculate the macroscopic properties from averages of fluctuation to coefficients of correlation. As statistical error decreases when the number of configuration increases, at least 10' configurations should be generated. 3.7 Applications

Vapor-liquid equilibrium calculations are a major field of investigation because of the importance of processes like distillation. Too often, data are missing. We present two approaches that use molecular modeling to obtain such data. The first example aims at computing binary interaction parameters occurring in the UNIQUAC activity coefficient model. The second example directly computes the equilibrium compositions using a Gibbs ensemble Monte Carlo method.

3.7.1 Example I: Validation of the UNIQUAC Theory 3.7.1.1 Overview o f UNIQUAC Model

The practical calculation of vapor-liquid equilibrium (Eq. (26)) involves an activity coefficient (yi to describe the nonideality of the liquid phase due to energetic interactions.

By applying the thermodynamic relation of Gibbs-Duhem, one connects the individual coefficients of activity yi with the excess gibbs energy GE:

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The UNIQUAC model proposes an expression for the G Ewith two contributions: a combinatorial part that describes the dominant entropic contribution and a residual part that mainly occurs due to the intermolecular forces responsible for the mixing enthalpy. The combinatorial part is related to the composition xi and to the molecule shape and size. It requires only pure component data. The residual part depends, in addition, on the interaction forces embedded into two binary interaction parameters Ay and Aji. GE

RT

combinatorial

residual

Parameters ri, qi,and qi' are molecular constants for each pure component i, related respectively to its size, its external geometrical surface, and its interaction surface. q' can be different from q, in particular for polar molecules. The model system upon which the UNIQUAC theory was developped considers interacting molecules. Then, the two binary interaction parameters Ay and A,i can be expressed in terms of interaction energies Uvbetween dissimilar molecules i and j, and Uii between similar molecules i:

where NAis the Avogadro number. The Wilson activity coefficient model also proposes two binary interaction parameters. It is a simplification of the UNIQUAC model in which parameters r, q, and q' are all set to unity. Interaction surfaces are not taken into account and molar volumes are eliminated in the equation. The relationship between the Wilson and UNIQUAC parameters is as follows:

where V; and y a r e the molar volumes of components i and j. The traditional approach consists of regressing Av and A,i from experimental data, with all drawbacks associated with this approach: data specific parameters, poor extrapolation capacity, temperature and pressure dependency, and the need of experimental data. A few years ago, an attempt to directly calculate the binary interaction parameters was made and is reported below.

3.7 Applications

3.7.1.2 Calculation Using Molecular Mechanics UNIQUAC Binary Interaction Parameters

In 1994, Jonsdottir, Rasmussen and Fredenslund (1994) computed interaction energies between isolated couples of molecules. They used molecular mechanics models not in a molecular simulation perspective, but rather like a quantum mechanical approach. For a given orientation of the two molecules, an energy minimization was run to reach a stable conformation. Many orientations are selected and the mean interaction energy Ui,and U, is evaluated by weighting each value using its Boltzmann factor exp(- Uti/kBT). This corresponds to a rough sampling, obviously not statistically representative as only a few hundred couples are investigated. This questions the validity of the first statistical thermodynamic postulate that equals the ensemble average and macroscopic time-average value. Rightfully, the authors claim to perform a molecular static approach in between quantum mechanics and molecular simulation approaches. The consistent force field parameters are optimized for the alkanes and ketones that are the molecules of interest but no value in particular and no partial atomic charge values are provided. Alkane conformers are taken into account, however, which is an advantage of molecular modeling approaches over classical parameter fitting. The Uiiand U,interaction energies are computed as the difference between the molecules couple energy and the energy of each isolated molecule:

Simulation results are used with the UNIQUAC equation to predict vapor-liquid equilibrium data (Eq. (26)),which are compared with experimental ones: 0

0

For the alkane/alkane systems (n-butaneln-pentane; n-hexane/cyclohexane (Fig. 3.8) and n-pentane/n-hexane), the relative error ranges from 1.1 to 4% for the pressure and the absolute error tandis ranges from 0.011 to 0.042 for the molar fractions. For the alkanelketones (n-pentane/acetone; acetone/cyclohexane (Fig. 3.8); cyclohexane/cyclohexanone), the relative error ranges from 4.3 to 17.6 % for the pressure and the absolute error ranges from 0.016 to 0.042 for the molar fractions.

In conclusion, the error increases along with the molecule polarity. One may question the force field ability to handle electrostatic interaction in addition to likely insufficient sampling of the system configurations. Finally, the authors tested the Wilson model and found errors four times greater for the n-pentane/acetone system. They concluded that the UNIQUAC equation has a better physical basis than that of the Wilson equation. This result was foreseeable since the Wilson model is a simplified form of the UNIQUAC model.

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3 Molecular Modelingfor Physical Property Prediction

n-hexane I cyclohexane

12%!0

'

0:2

'

0:4

'

0:s

'

40.0

0:s

'

1jO

acetone I cyclohexane

XI

XI

1 .o I

- 30.0 sn m

20.0

10.0' 0.0

'

'

0.2

'

'

0.4

'

'

0.6

'

'

0.8

'

'

1.0

0.0 0.0

'

s

0.2

'

'

'

"

0.4

XI

"

0.6

0.8

1.0

XI

Bubble curve at 298.15 K for the n-hexane/cyclohexane (top) and acetone/cyclohexane (bottom) systems. Solid line: simulation. Stars: Figure 3.8

experimental data (reprinted from Jonsdottir, Rasmussen and Fredenslund (1994) with permission from Elsevier)

3.7.1.3

of UNIQUAC Binary Interaction Parameters Compared to Jonsdottir, Rasmussen and Fredenslunds (1994)work, Sum and Sandler (1999) used quantum mechanics models to improve the representation of electrostatic interactions. Often in such calculations, no rigorous sampling is performed, the emphasis being made on minimizing the total system energy. For each binary system, eight molecules are considered (four of each). A stable system conformation is found by minimization using semiempirical methods. Then the energy is minimized using ab initio methods (Hartree-Fock method with an extended basis set 6-3119> xR)and b(x) = xb ( x B first order exothermic reaction in tank

A simple process model example.

ters. The modeling assumptions can either be elementary assumptions consisting of just a single triplet or composite assumptions being the conjunction (logical and) of elementary assumptions. The model equations can be formally seen as a structured string obeying syntactical and semantic rules and the modeling assumptions can then be regarded asformal modeling transformations on these equations resulting in another set of model equations. The effect of an assumption on a given set of equations is computed following all of the implications ofthe assumption through the syntactical and semantic rules. Formally this is performed by substituting the assignment equations describing the assumption into all of the original model equations and then performing rearrangements using algebraic transformations. 5.3.2 Algebraic Transformations, Algebraically Equivalent Models

A set of functionally equivalent process models can be algebraically equivalent, when one can transform any member of the set to any other one using algebraic transformations. Algebraic transformations can be applied to model equations and to model variables (including both differential and algebraic ones). Examples of algebraic transformations on a set of process model equations are multiplying an equation by a constant number, adding two equations together, substituting one equation for another by expressing it as a variable and substituting that variable in every other equation. It is important to note that the variables do not change when applying algebraic transformations to the equations of a model, but the

5.3 Model Discrimination: Model Comparison and Model Transformations

CONSERVATION BALANCES Balance volume: tank - mass balance: M = const - energy balance: ._ dT v -=-(To dt V

- T ) + koe

RTCA(-AH)

p',

- component mass balances: dc, dt dcE

dt

-

v (cAo-cA)-k0e V

- 'c,+k,,e

Figure 5.2

V

Balance volume: cooler - mass balance: M-= const - energy balance: KA(T-T,)

dT,

V@,

dt

-

v,

V,

(TdJ-T )+

KA(T-T, I V c P$,'

__ E

R T ~ A

~-

'TcA

The substituted process model

model equations do. The formal description of algebraic transformations to a set of algebraic equations, together with a canonical set of primitive algebraic transformations and their effect on computational properties, can be found in Leitold and Hangos (1998).There it is shown that certain computational properties of DAE models, such as the differential index, does not change with algebraic transformations, but others, like the decomposition of the model may change quite drastically. Another type of transformation applicable to a model is when one applies a linear or nonlinear algebraic transformation to some of its variables and writes the model using these new transformed variables. This is analogous to coordinate transformation in geometry and is therefore called a coordinate transfornation. It is important to note, however, that the general locally invertible nonlinear transformations, which are useful and widely used in nonlinear system theory, are not well accepted in process systems engineering because they change the engineering meaning of the variables. The extensive-intensiveconstitutive algebraic equations, however, are widely used to transform a process model into its intensive variable form suitable for process control and diagnostic applications. Here we transform the set of differential variables in a balance volume originally equal to the set of conserved extensive quantities to be the set of overall masses (left unchanged) and the measurable intensive quantities (such as temperatures, compositions and pressures). Model classes. Algebraic transformations may change the mathematical form of a model, but an algebraicallytransformed model is the same from a process engineering point of view. Such algebraicallyequivalent models form a model class. Figure 5.2 shows an algebraically equivalent form of the simple process model of the jacketed tank reactor depicted in Fig. 5.1, where the constitutive equations have all been substituted into the differential ones.

5.3.3 Model Simplification and Model Building Transformations

Modeling assumptions can be regarded as representations of the engineering activity and decisions during the whole modeling process in constructing, simplifying and

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5 Model Tuning, Discrimination, and Verification

analyzing process models and they act as modeling transformations on the process models. Assumption-driven modeling works directly with modeling assumptions, thus enabling the definition and handling of process models as structured knowledge with defined syntax and semantics. Model building assumptions. The modeling assumptions applied in the model building phase determine the structure of the process model and the assumptions applied to an existing model modify the equations and may even change the structure of the model. The model building procedure is seen as a sequence of model building, specification assumptions, and their associated transformations, as well as algebraic transformations applied to a process model. This way of assumption-driven model building offers a systematic incremental way of constructing a process model in its canonical form. Model simplification assumptions. The model simplification assumptions, which can either be elementary (atomic) or composite, and are composed of a conjunction of elementary assumptions, can be formally described as model transformations. These transformations are projections in a mathematical sense and are often performed in two substeps :

1. adding the equality describing the assumption to the already existing set of model

equations and performing algebraic transformations (for example substitutions) to get a more simple form; 2. adjusting the set of differential, algebraic and design variables to satisfy the degree of freedom requirement. The effect of a simplification assumption on a given set of equations is computed following all of the implications of the assumption through syntactical and semantic rules. Formally this is performed by substituting the assignment equations describing the assumptions into all of the original model equations and then performing rearrangements using algebraic transformations. It is important to note that not every simplification transformation is applicable to a particular process model. Moreover, a transformation may influence only part of a process model and then this effect propagates through the relationships between the model elements. Forward reasoning can be applied to find all of the implications of a simplificationtransformation, and the effect of a composite transformation is computed by generating a sequence of simplified process models. It is important to note, however, that the resultant model may be different if the order of the assumptions is changed, because model simplificationtransformations may be related and noncommutative (Hangos and Cameron 2001a). In conclusion we can say that algebraic manipulations can be regarded as equivalence transformations, model simplification, and enrichment assumptions as general nonequivalence modeling transformations acting on process models that bring the process model out from its original model class.

5.4 Model Tuning

5.3.4 Model Discrimination and Model Comparison

Model discrimination aims to find an exact relationship between two given process models of the same process system. First, we have to determine if these models are developed for the same modeling goal, and if so, if they are algebraicallyequivalent. Unfortunately, there are no standard formal ways of performing the above two basic tasks, mainly because the lack of our knowledge in formal description and utilization of the modeling goal itself (see Lakner, Cameron and Hangos 2003). In the case of functionally equivalent models one should only perform model comparison to investigate if they are algebraically equivalent, and if not, give their relationship in terms of model simplification transformations that lead the more detailed model to a more simple one (see later Section 5.4.3). Canonical form. We have already seen in Section 5.3.1 that both functionally and

algebraically equivalent process models form a model class. It is then useful to define and use a canonicalform of a process model class, which is a member of the class having each model element in the form that has a clear engineering meaning (Hangos and Cameron 2001). The differential equations of a process model in canonical form are the conservation balance equations for the overall mass, total energy (or enthalpy) and all but one component masses in their extensive form containing terms for the convective, transfer and source transport. These are supplemented by constitutive algebraic equations of standard categories such as intensive-extensive relationships, reaction rate equations, thermodynamic state equations (such as the ideal gas law), etc. The simple process model shown in the left-hand side of Fig. 5.1 is in its canonical form. Comparison o f process models. In the case of algebraically different but functionally equivalent process models we aim at finding out if these models are from the same model class, or not. The general procedure of comparing these models is to first bring them into their canonical form and then compare them element-wise following the hierarchy of the model elements from top (balance volumes) to down (model variables and parameters). This approach requires that the models being compared are given with their entire model elements hierarchically arranged.

5.4 Model Tuning

Process models generated for a given modeling goal may often be over-simplifiedor over-complicated for another use, which is why there is usually a need to extend, to simplify, or to generate a new model in the worst case. In addition, process models usually contain unknown parameters to be estimated using measured data, when we need to calibrate the model to tune it to meet the modeling goal.

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In the model constructing step of the seven-step modeling procedure we may need to perform a model simplification phase for refinement of an already defined process model by additional simplifying modeling assumptions. These simplifylng assumptions can be described by triplets and are usually translated into additional mathematical relationships. The simplifying procedure itself consists of two main steps. These steps are the implication of the modeling assumptions on the model equations with the aid of syntactical and semantic rules, and the rearrangement of the resulting equations make use of formal algebraic transformations. Because the process model elements are related to each other by a well-defined syntax and semantic, a model element cannot be simplified independently of the others. In addition, the implications of a simplification assumption depend both on the assumption and the structure of the model. For example, when a modeling assumption is related to a balance volume, its implications can refer not only to the equations of the balance volume, but could modify other related balance equations in other balance volumes. The same way, a modeling assumption related to a term in a balance equation can imply modifications of other terms in other balance equations. Figure 5.3 shows how a modeling assumption on the mass convective term of a balance volume changes the energy and component mass convective terms when a simplification assumption is applied to the model of the jacketed tank reactor depicted in Fig. 5.1. The implications of an assumption on the model equations can be determined by forward reasoning where all of the implications of the assumption are computed by respecting syntactical and semantic rules. The set of resulting modeling equations at the end of the implication stage is rearranged to an easily-solvableform by using algebraic transformations (Lakner et al. 1999).

CONSERVATION BALANCES Balance volume: tank - mass balance: M = vp

- energy balance:

du= vpc,To dt

SIMPLIFICATION ASSUMPTION

- mass convective outlet in tank is negligible + Vr(

)-

Q

- component mass balances: dm

2= vcdo-Vr

dt dm,=Vr dt

Balance volume: cooler - mass balance: M, = const - energy balance: du, - vC~ , c , J ~ -v, o PF,T~ + Q

7

Figure 5.3

A simplified process model

CONSTITUTIVE EQUATIONS

Q=WT-T,J r = kc, E -_

k = k,e RT mA =Vc, mn

= VCB

U=Mc,T

u, =McccpTc M =Vp

M, = V,P,

5.4 Model Tuning

5.4.2 Model Extension

Model extension procedures are widely applied in process modeling in quite different contexts:

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At the end of a modeling cycle, in the model validation step, it may turn out that the developed model fails to fulfill the modeling goal. Then one has to extend the model by including additional model elements that were originally neglected, such as balance volumes, balances, mechanisms, etc. The incremental assumption-driven model building (Williams et al. 2002) uses model extension procedures, too. The incremental building of balance equations in the model equation constructing procedure can also be seen as model extension (see Section 5.2.2).

There are two questions of critical importance in model extension procedures: the selection of default values and the methods of ensuring incremental consistence. Default values set the value of model elements belonging to a model element (the “children elements” in the model element hierarchy) that is just being created. Incremental consistency is ensured by allowing one to add only such new model elements to an already existing consistent model that are not in conflict or contradiction to any already existing model element. Details about these questions can be found in the literature on computer-aided process modeling (CAPM)tools (see, e.g., Jensen-Krogh 1998; Modkit 2000). Empirical model building. This is a special method of model extension using empirical data and grey box models (Hangos and Cameron 2001). It is a top-down approach of model extension where the model element(s)to be changed or extended is (are)determined in a heuristic black box way by using sensitivity analysis. The submodel of the new element is also constructed in a heuristic black box way from some general approximating model class with its parameters estimated using measured data (see also model calibration in Section 5.4.4).

5.4.3

Model Comparison by Assumption Retrieval

In order to avoid any inconsistency during model simplification and extension, it is extremely useful to register explicitly all modeling assumptions applied in the construction and modification of the process model. The documentation of the model contains these modeling assumptions (Hangos and Cameron 20014 in the ideal case, but this documentation can often be incomplete or even missing. In order to complete the model documentation with all modeling assumptions, an assumption retrieval procedure could be used. The retrieval of modeling assumptions from a pair of process models for model analysis and comparison is an important but unusual problem where not only efi-

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cient algorithms but the engineering understanding is lacking. The reason for this is that assumption retrieval can be regarded as the inverse task of model transformations where modeling assumptions are determined from two related (one detailed and one simplified) process models of the same process system. As model transformations are projections in mathematical sense, it is not possible in general to retrieve fully the original model from the transformed one and from the transformations. Because of this, the result of assumption retrieval from the original and the transformed models may not be, and in general will not be, unique. Because of the nonuniqueness of the assumption retrieval task, an intelligent exhaustive search algorithm (Lakner et al. 2002) is needed for its solution. 5.4.4 Model Calibration (Model Parameter Estimation)

Process models developed from first engineering principles almost always contain model elements, model parameters and/or other elements like reaction rate expressions, the value of which is unknown. While the modeling approach futes the structure of the model, these unknown elements make the model “grey,”that is, partially unknown. Measured data from the real process system to be modeled is used along with model parameter and/or structure estimation methods to fine-tune the model for meeting the modeling goal. This fine-tuning of process models is called model calibration and is a standard step in the seven-step modeling procedure (Hangos and Cameron 2001). There are several key points to take special care of when performing model calibration: 0

0

Selection of model parameters to be estimated. Besides the real unknown model parameters, one often has parameters or model elements with large uncertainty associated to their values. If the model is sensitive with respect to the value of these uncertain parameters, then it is advisable to consider them as unknown and estimate their values using measured data (NCmeth et al. 2003). Nonlinear parameter estimation. In most of the cases the parameters to be estimated enter the model in a nonlinear way and the model itself is dynamic. This makes the parameter estimation problem especially difficult and can only be solved by numerical optimization techniques (Hangos and Cameron 2001 ; Ailer et. a1 2002). Quality of the data and the estimated parameters. The statistical nature of model parameter estimation requires one to check carefully the following key ingredients and properties of the parameter estimation method: - quality of the measured data (steady-state,no outliers and gross errors, etc.) and the presence of sufficient excitation; - quality of the prediction error sequence (if this is a realization of a white noise stochastic process); - quality of the estimated parameters considering their nonbiasness, variance, and covariance matrix.

5.5 Model Verijcation

5.5 Model Verification

Having completed the model equation constructing step of the seven-step modeling procedure (see Section 5.2.2), one needs to perform model verification, that is, to check the model against engineering insight and expectations, before attempting its solution. Model verification includes checks of syntax and semantics, as well as the well-posedness of the model from mathematical sense, and analysis of computational and dynamic properties.

5.5.1 Formal Methods for Checking Syntax and Semantics

Before a mathematical model is used for solvability analysis or is solved, it is useful to check and ensure its consistency. There are several methods for consistency checking that are applicable both in computer-aided modeling tools and in process systems engineering practices: 0

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Dimension analysis is a useful simple check for consistency of the model equations in terms of units of measure. This very useful but not widespread method is used in ASCEND (Evans et. a1 1979) and VeDa (Bogusch and Marquardt 1997) modeling languages, for example. Syntactical veriication methods (checking bracketing, vector operations, etc.) are especially important for computer-aided modeling tools in which the model equations can be directly defined by the users. An example for this is the ICAS/ModDev modeling system (Jensen-Krogh1998). Logical checking (hierarchical consistency, material characterization consistency, chemical reaction rate equation derivation, etc.) is used for examining the modeling assumptions’ consistency. This very important verification method, accomplished before generating the model equations, is used in the majority of computer-aided modeling tools.

It is important to note that the above-introduced model verification methods are applicable only for partial consistency checking and they cannot insure full model consistency.

5.5.2 Structural Analysis of Computational Properties of Process Models

The structural analysis of dynamic lumped process models form an important step in the seven-step modeling procedure and is used for the determination of the solvability and computational properties of the model. This analysis includes the determination of the degrees of freedom (DOF), the differential index and the structural components of the model.

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Analysis of DOF and differential index. In order to solve a mathematical model, a

sufficient number of variables have to be specified so that the number of unknown variables exactly equals the number of equations. The DOF, i.e., the difference between the number of unknown variables and the number of equations in the mathematical representation, is equal to the number of variables that must be specified for obtaining a solvable equation system. There are three possible values for DOF to obtain (Hangos and Cameron 2001): 0

0

DOF=O. This implies that the number of independent unknowns and independent equations is the same and a unique solution may exist. DOF>O. This implies that the number of independent variables is greater than the number of independent equations and the problem is underspecified. In this case some of the independent variables have to be specified by some external considerations in order for the DOF to be reduced to zero. DOF133-143. Kimj.-S., Ch.-G. Kim, Ch.-S. Hong (1999) Optimum design of composite structures with plv drop using genetic algorithm and exnert system shell. Composite S t r u t 46, 171-187. Kisefyoua N . N. (2000) Databases and semantic networks for the inorganic materials computer design. Eng Appl Artijcial Intell 13, 533-542. Konno K., D. Kamei, T. Yokosuka, S. Takami, M . Kubo, A. Miyamoto (2003) The development of computational chemistry approach to predict the viscosity of lubricants. Tribology Int 36, 455-458. Lakshminarayanan S., H . Fujii, B. Grosman, E. Dassau, D. R. Lewin (2000) New product design via analysis of historical databases. Comput Chem Eng 24, 671-676. Liu Y., Y . Liu, D. Liu, T. Cao, S. Han, G. Xu (2001) Design of CO" hydrogenation catalyst by an artificial neural network. Comput Chem Eng 25, 1711-1714. Mann D. L. (2003) Better technology forecasting using systematic innovation methods. Technol Forecasting Social Change 70, 779-795. McFarfand E. W. and W. H. Weinberg (1999) Combinatorial approaches to materials discovery. TibTech 17, 107-115. McLeod S., M.E. Johnston, L. F. Gladden (1997) Algorithm for molecular scale catalyst design.] Catalysis 167, 279-285. OrlofM. A. (2003) Inventive Thinking Through TRIZ. Springer, Berlin. Murphy V., A. F. Volpe, W. H . Weinberg (2003) High-throughput approaches to catalyst discovery. Curr Opinion Chem Biof 7, 427-433. Naes T., F. Bjerke, E. M. Faergestad (1999) A comparison of design and analysis techniques for mixtures. Food Qua1 PreflO, 209-217. Nakagawa T. (2004) USIT Case Study (2) Increase the Foam Ratio in Forming a Porous Sheet from Gas Solved Molten Polymer (1999),available at: http://www.osakagu.ac. jp/php/nakagawa/TRIZ/eTRIZ/epapers/eUSITCases990826/eUSITC2Polymer990826.html.

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EADOCS: conceptual design in three phases-an application to fibre reinforced composite panels. Eng Appl Artijicial Intell 10, 129-138. Petrick I. J. and A. E. Echols (2004) Technology roadmapping in review: a tool for making sustainable new product development decisions. Technol Forecasting Social Change 71,81-100. Phaal R., C. Farrukh. D. Probert (2004) Customizing Roadmapping, ReserarchTechnology-Management 26-37, March-April, 2004. Phillips F. and N. Kim (1996) Implications of chaos research for new product forecasting. Technol Forecasting Social Change 53, 239-261. ReVelle]. B., J. W . Moran; C. A. Cox (1998) The QFD Handbook. John Wiley & Sons, New York. Rodemerck U., M. Baems, M. Holenu, D. Wolf (2004) Application of a genetic algorithm and a neural network for the discovery and optimization of new solid catalytic materials. Appl Surface Sci 223, 168-174. Rowe R. C. and R. J. Roberts (1998a) Intelligent Softwarefor Product Formulation. Taylor & Francis, London. Rowe R. C. and R.]. Roberts (1998b) Artificial intelligence in pharmaceutical product formulation: knowledge-based and expert systems. PSTT4, 153-159. Sebastia M., 1. Femandez Olmo, A. Irabien (2003) Neural network prediction of unconfined compressive strength of coal fly ashcement mixtures. Cement Concrete Res 33, 1137-1146. Shi Z., H. Zhou, J. Wang (1997) Applying case-based reasoning to engine oil design. Artijcial Intell Eng 11, 167-172. Sdzen A., M . &alp, E. Arcaklioglu (2004) Investigation of thermodynamic properties of refrigerant/absorbent couples using artificial neural networks. Chem Eng Process, available online 25 March 2004. Sunada H., Y. Bi (2002) Preparation, evaluation and optimization of rapidly disintegrating tablets. Powder Technol 122, 188-198. Sundaram A., P. Ghosh, J . Caruthers, V. Venkatasubramanian (2001) Design of fuel additives using neural networks and evolutionary algorithms. AlChE] 47(6), 1387-1406. Takayama K., M. Fujikawa, Y. Obata, M. Morishita (2003) Neural network based

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optimization of dmg formulations. Adv Drug Delivery Rev 55, 121771231, Taskinen Y.,J . Yliruusi (2003) Prediction of physicochemical properties based on neural network modeling. Adv Drug Delivery Rev 55, 1163-1183. TechnologyFutures Analysis Methods Working Group (2004) Technology futures analysis: toward integration of the field and new methods. Technol Forecasting Social Change 71, 287-303. Tiirkoglu M., H. Varol, M. Celikok (2004) Tableting and stability evaluation of entericcoated omeprazole pellets. EurJ Pharm Biopharm 57,279-286. Venkatasubramanian V., A. Sundaram, K. Chan, J . M. Caruthers (1996) ComputerAided Molecular Design Using Neural Networks and Genetic Algorithms Polymers. in Delivers 1. (ed.) Genetic Algorithms in Molecular Modeling. Academic Press, New York. Venkatasubramanian V., K. Chan, and J. M . Caruthers (1995) Evolutionary design of molecules with desired properties using genetic algorithms. ] Chem Info Comput Sci 35, 188-195. Viaene J. and R. Januszewska (1999) Quality function deployment in the chocolate industry. Food Qual PreflO, 377-385. VilladsenJ. (1997) Putting structure into chemical engineering. Chem Eng Sci 52, 2857-2864. VojnovicD., B. Campisi, A. Mattei, L. Favretto (1995) Experimental mixture design to ameliorate the sensory quality evaluation of extra virgin olive oils. Chemometrics Intell Lab Syst 27, 205-210. Watson 1. (1997) Applying Case-Based Reasoning: Techniquesfor Enterprise Systems. Morgan Kaufmann, San Francisco. WesselingJ.A. (2001) Structuring of products and education of product engineers. Powder Technol 119, 2-8. Wibowo C. and K. M . Ng (2001) Productoriented process synthesis and cevelopment: creams and pastes. AIChE J 47, 2746-2767. Wiratunga N., S. Craw, R. Rowe (2002) Learning to Adapt for Case-Based Design, in Proceedings ofthe 6th European Conference on Case-based Reasoning, Springer-Verlag, Berlin, pp.421-435. Zhung Z., K. Friedrich (2003) Artificial neural networks applied to polymer composites: a review. Composites Sci Technol 63, 2029-2044.

Section 3 Cornputer-aided Process Operation

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

Section 3focuses on the application of computing technology to integrate and facilitate the key technical decision processes which arise in chemical manufacture. It comprises decision support systems at different levels of decision making. I t discusses the problem of coordinated planning and scheduling of distributed plants at the top level, product sequencing, and precise allocation over time of detailed process operations resource constrained, coordination between units, process monitoring and regulatory control in a real-time environment extended to contemplate hybrid systems. An introduction to modeling the entire supply chain is also presented, which isfirther elaborated in Section 4. Section 3 consists of seven chapters introducing the current problemsfacing process operations, the state ofrelevant methods and technology, and needed advances to combat everincreasing complexity of computer-aided process operations in a business-wide context. Chapter 2 presents a comprehensive review of state-of-the-art models, algorithms, methodologies, and toolsfor the resource planningproblem, covering a wide range of manufacturing activities and including a detailed critical discussion on the effect of uncertainty. The emerging trend in the area of short-term scheduling is the development of ejicient solution techniques and to render ever largerproblems tractable. Chapter 2deals with issues that must be resolved related mainly to problem scale. A sensible way forward is proposed by trying to capture the problem in all its complexity and then to explore rigorous or approximate solution procedures, rather than develop exact solutions to somewhat idealized problems. Afinal challenge relates to the seamless integration of the activities at different levels including data and finctional fiagtnentation, inconsistencies between activities and datasets, and different tools being used for different activities, which are the subjects of subsequent chapters and sections. The needfor quality measurements to monitor process operations, evaluation of their eflciency and the equipment condition, thus avoiding equipment failure and any subsequent hazardous conditions is treated in Chapter 3. Recent progress in automatic data collection and current developmentsaimingat combining online data acquisition with data reconciliation are presented in detail. The measurement information can also be used in the control scheme in various ways The weakestform offeedback is to use the measurements forparameter adaptation only, which requires a structurally correct model. Chapter 4 introduces modelbased control techniques and points out new trends. The techniques use the combination of first principles-based and black-box models the parameters of which are estimatedfiom operational data as a way to obtain suflciently accurate models without excessive effort. Online optimization using measurement information in many cases is an attractive alternative to the tracking of pre-computed references because the process can be

operated much closer to its real optimum, while still meeting hard bounds on the specifications. A rigorous treatment of real-time optimization problem is given i n Chapter 5. The last two chapters expand the concept of computer-aided process operations to also consider hybrid systems (Chapter 6) and the whole network of material procurement, material transformation to intermediates a n d j n a l products, and distribution of these products to customers (Chapter 7). The needfor integrated solutions will behrther explored in Section 4.

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

1 Resource Planning Michael C. Georgiadis and Panagiotis Tsiakis

1.1 Introduction

Until recently, resources planning exercises in many companies were based on quantitative, managerial judgements about the future directions of the firms and the markets in which they compete. Complex interactions between the different decision-making levels were often ignored. In the past few years however, important planning decisions, such as those relating to capacity expansion, new product introduction, oil and chemical product distribution and energy planning, have been formally addressed based on recent developments in mixed-integer optimization. Today, most process and energy industries have turned to the use of optimization models in seeking efficient long-term planning use of their resources (Shapiro 2004). In the last two decades, new techniques have developed to analyze large size planning models, while research in aggregation and decomposition techniques has multiplied. In addition, many managers have begun to recognize the major drawbacks of most current planning systems and the necessity for more intelligent and quantitative decisions tools instead of administrative routine procedures. This comes as a natural continuation of the pioneering work of F. W. Taylor and H. L. Gantt, who in the early 1900s identified the impact on productivity and other key performance indices, of general production planning systems based on scientific approaches (Wilson 2003). Today’scomputing offers more powerful techniques for modeling and solving planning problems, while Gantt charts still provide an excellent display tool for understanding and acceptance of plans in any type of environment, in addition to other available interfaces. During the last year, companies have realized that in order to achieve significant competitive advantage within their sector they need to understand the operations hierarchy and solve their problems in a unified framework, a fact that is resulting in the development of corresponding tools. Towards that, the interest in planning and scheduling capabilities has given rise to the providers of solution systems designing, developing and implementing planning systems as part of general supply-chain supComputer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim ISBN: 3-527-30804-0

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port systems or with open architecture to allow easy integration. Owing to the inherent complexity and the different scales of integration this has been accepted by the research community as a topic that needs urgent answers, since the planning software industry is in its infancy and under pressure to respond to the demand. The objective of this chapter is to present a comprehensive review of state-of-theart models, algorithms, methodologies and tools for the resource planning problem covering a wide range of manufacturing activities. For reasons of presentation, the remaining of this chapter is organized as follows. The long-range planning problem in the process industries is considered in Section 1.2 including a detailed discussion on the effect of uncertainty, the planning of refinery operations and offshore oilfields, the campaign planning problem and the integration of scheduling and planning. Section 1.3 describes the planning problem for new product development with emphasis on pharmaceutical industries. Section 1.4 presents briefly the tactical planning problem, followed by a description of the resource planning problem in the power market and construction projects in Section 1.5. Section 1.6 is a review of recent computational solution approaches to the planning problem are reviewed, while available software tools are outlined in the Section 1.7. Finally, Section 1.8 will make some conclusions and propose future challenges in this area.

1.2 Planning in the Process Industries 1.2.1 Introduction

New environmental regulations, new processing technologies, increasing competition and fluctuating prices and demands in process industries have led to an increasing need for quantitative techniques for planning the selection of new processes, the expansion and shut down of existing processes, and the production of new products. Further decisions also include creation of production, distribution, sales and inventory plans. (Kallrath 2002). It has been recently realized that in a competitive and changing environment the need to plan new output levels and production mixes is likely to arise much more frequently than the need to design new batch plants. Although the boundaries between planning and scheduling are not very clear we can distinguish the following basic features of the process planning problem: multipurpose equipment sequence-dependent set-up times and cleaning costs 0 combined divergent, convergent and cyclic material flows 0 multistage, batch and campaign production using shared intermediates 0 multicomponent flow and nonlinear blending for the refinery operations a finite intermediate storage, dedicated and variable tanks. 0 0

Structurally, these features often lead to allocation and sequencing problems and knapsack structures, or to the pooling problem for the petrochemical industries. In

7.2 Planning in the Process Industries

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production planning we usually consider material flow and balance equations connecting sources and sinks of a production network. Time-indexedmodels using a relative coarse discretization of time, e.g., a year, quarter, months or weeks are usually accurate enough. linear programming (LP), mixed-integer linear programming (MILP)and mixed-integer nonlinear programming (MINLP)technologies are often appropriate and successful for problems with a clear quantitative objective function, as will become clear in the following sections. Nowadays, it is possible to find the optimal way to meet business objectives and to fulfil all production, logistics, marketing, financial and customer constraints and especially: 0 0

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to accurately model single-site and multisite manufacturing networks; to perform capital planning and acquisition analysis, i.e., to have the possibility to change the structure of a manufacturing network through investment and to determine the best investment type, size and location based on user-defined rules related to business objectives and available resources; the results of such analysis can lead to nonintuitive solutions that provide management with scenarios that could dramatically increase profits; to produce integrated enterprise solutions and to enable a crossfunctional view of the planning process involving production, distribution and transport, sales, marketing and finance functions; to develop new product and introduction strategies along with capacity planning and investment strategies.

The following sections provide a comprehensive review of the above areas.

1.2.2 LongRange Planning in the Process Industries

Chemical process industries are increasingly concerned with the development of planning techniques for their process operations. The incentive for doing so derives from the interaction of several factors (Reklaitis 1991, 1992). Recognizing the potential benefits of new resources when these are used in conjunction with existing processes is the first. Another major factor is the dynamic nature of the economic environment. Companies must assess the potential impact on their business of important changes in the external environment. Included are changes in product demand, prices, technology, capital market and competition. Hence, due to technology obsolescence, increasing competition, and fluctuating prices of and demands for chemicals, there is an increasing need to develop quantities techniques for planning the selection of new processes, and the production of chemicals (Sahinidis et al. 1989) The long-range planning problem in process industries has received a lot of attention over the last 20 years and numerous sophisticated models exist in the literature. Sahinidis et al. (1989)consider the long-range planning problem for a chemical complex involving a network of chemical processes that are connected in a finite number of ways. The network also consists of chemicals: raw materials, intermediates and

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products that may be purchased from and/or sold to different markets. The objective function to be maximized is the net present value (NPV) of the planning problem over a long-range horizon of interest consisting of a number of NT time periods during which prices and demands of chemicals, and investment and operating costs of the processes can vary. The problem consists of determining the following items: 0 0

0 0

capacity expansion and shut down policy selection of new processes and their capacity expansion and shut down policy production profiles sales and purchase of chemicals at each time period.

It is assumed that the material balance and the operating cost in each process can be expressed linearly in terms of the operating level of the plant. The investment costs of the processes and their expansions are considered to be linear expressions of the capacities with a fmed charge cost to account for economies of scale. This is a multiproduct, multifacility, dynamic, location-allocation problem that has been formulated using MILP modes. Sahinidis and Grossmann (1991) extended the above model to account for production facilities that are flexible manufacturing systems operating in a continuous or in a batch mode. The suggested model provides a unified representation for the different types of processes. Norton and Grossmann (1994)extended the original model of Sahinidis and Grossmann (1991) for dedicated and flexible processes by incorporating raw materials flexibility in addition to product flexibility. In their model, raw material flexibility is characterized by different chemicals as raw materials or different sources of the same raw material. The model was able to handle any combination of raw material and process flexibility, thus providing a truly unified representation for all types of process flexibility in the long-range planning problem. The above industrial relevance of the chemical process planning problem motivated the need to develop more efficient solution techniques for large-scale problems. Liu and Sahinidis (1995)presented a comprehensive investigation of the effect of time discretization, data uncertainty and problem size, on the quality of the solution and computational requirements of the above MILP planning models. The importance of detailed time discretization was demonstrated and the effect of uncertainty was critically assessed. An exact branch-and-bound algorithm was also presented along with several heuristic approaches for the solution of larger problems. Extending this work, Liu and Sahinidis (199Ga) investigated separation algorithms and cutting plane approaches that were demonstrated to be more robust and faster than conventional solution approaches for large-scale problems with long timehorizons. Oxe (1997) considered a LP approach to choose an appropriate subset of existing production plants and lines and to optimize allocation, transportation paths and central stock profiles so that the overall costs are minimized while product delivery is ensured within some months (specified for each product) from the order. McDonald and Karimi (1997) developed production planning and scheduling models for the case of semicontinuous processes, which are assumed to comprise several facilities in distinct geographical locations, each potentially containing multi-

1.2 Planning in the Process Industries

ple parallel lines. The models developed are deterministic in nature and are formulated as mixed-integer linear programs. Oh and Karimi (2001a)presented a new methodology for determining the optimal campaign numbers for producing multiple products on a single machine with sequence-dependent set-ups. Their methodology is intended mainly for the purpose of capacity planning. In the second part of this work (Oh and Karimi 2001b) they addressed the problem of determining the sequence of these given product campaigns to obtained a detailed schedule of operation. Heuristic algorithms based on a decomposition scheme were investigated for the efficient solution of the underlying optimization problem.

1.2.3 Process Planning under Uncertainty

Decision making in the design and operation of industrial processes is frequently based on parameters of which the values are uncertain. Sources of uncertainty, which tend to imply the means for dealing with them, can be divided into: 0

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short-term uncertainties such as processing time variations, rush orders, failed batches, equipment breakdowns, etc.; long-term uncertainty such as market trends, technology changes, etc.

A detailed classification of different areas of uncertainty is suggested by Subrahmanyam et al. (1994)including uncertainty in prices and demand, equipment reliability and manufacturing uncertainty. An excellent review on the general subject of optimization under uncertainty has recently been presented by Sahinidis (2004). In the area of process planning, uncertainty is usually associated with product demand fluctuations, which may lead to either unsatisfied customer demands or loss of market share or excessive inventory costs. A number of approaches have been proposed in the process systems engineering literature for the quantitative treatment of uncertainty in the design, planning and scheduling of batch process plants with an emphasis on the design. The most popular one so far has been the scenario-based approach, which attempts to forecast and account for all possible future outcomes through the use of scenarios. The scenario approach was suggested by Shah and Pantelides (1992) for the design of flexible multipurpose batch plants under uncertain production requirements, and was also used by Subrahmanyam et al. (1994). Scenario-based approaches provide a straightfonvard way to implicitly account for uncertainty (a comprehensive discussion is presented by Liu and Sahinidis (199613)). Their main drawback is that they typically rely on either the a priori forecasting of all possible outcomes of the discretization of a continuous multivariable probability distribution, resulting in an exponential number of scenarios. Liu and Sahinidis (199Ga,b)and Iyer and Grossmann (1998) extended the MILP process and capacity planning model of Sahinidis and Grossmann (1991)to include multiple product demands in each period. They then propose efficient algorithms for the solution of the resulting stochastic programming problems (formulated as large

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deterministic equivalent models), either by projection (Liu and Sahinidis 199Ga) or by decomposition and iteration. However, as pointed out by Shah (1998) a major assumption in their formulation is that product inventories are not carried from one period to the next. This has the advantage in ensuring that the problem size is of, O(np x ns), where np is the number of periods and ns is the number of demand scenarios, rather than O(ns"J'+').However, if the periods are too short, this compromise the solution from two perspectives: 0

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All products must be produced in all periods if demand exists for them - this may be suboptimal. Plant capacity must be designed for a peak demand period.

Clay and Grossmann (1994)addressed this issue. They considered the structure of both the two-period and multiperiod problem for LP models and derived an approximate model based on successive repartitioning of the uncertain space, with expectations being applied over partitions. This has the potential to generate solutions to a high degree of accuracy in a much faster time than the full deterministic equivalent model. Liu and Sahinidis (1997)presented two different formulations for the planning in a fuzzy environment (the forecast model parameters are assumed to be fuzzy). The first considers uncertainty in demands and availabilities, whereas the second accounts for uncertainty of the right hand size of made constraints and objective function coefficient. The approaches above mainly focus on relatively simple planning models of plant capacity. Petkov and Maranas (1997)considered the multiperiod planning model for multiproduct plants under demand uncertainty. Their planning model embeds the planninglscheduling formulation of Birewar and Grossmann (1990) and therefore calculates accurately the plant capacity. They do use discrete demand scenarios, but assume normal distributions and directly manipulate the functional forms to generate a problem which maximizes the expected profit and meets certain probabilistic bounds on demand satisfaction without the need for numerical integration. Ierapetritou and Pistikopoulos (1994)proposed a two-stage stochastic programming formulation for the long-range planning problem including capacity expansion options. Based on the Gaussian quadrature method for approximating multiple probability integrals, Ierapetritou et al. (1996) considered the operational and production planning problem under varying conditions and changing economic circumstances. The effect of uncertainty on future plant operation was investigated via the incorporation of explicit future plan feasibility constraints into a two-stage stochastic programming formulation, with the objective of maximizing an expected profit over a time horizon, and the use of the value of perfect information. The main drawback of this approach is its high computation cost. To address this issue Bernard0 et al. (1999)investigated more efficient integration schemes for the solution of problems with many uncertain parameters. Recently, Ryu et al. (2004)addressed bilevel decision making problems under uncertainty in the context of enterprise-wide supply-chain optimization with one level corresponding to a plant planning problem, and the other to a distribution network problem. The bilevel problem was transformed into a family of single parametric optimization problems solved to global optimality.

1.2 Planning in the Process Industries

Rodera et al. (2002) presented a methodology for addressing investments planning in the process industry using a mixed-integer multiobjective optimization approach. Romero et al. (2003) proposed a modeling framework integrating cash flow and budgeting aspects with an advanced scheduling and planning model. It was illustrated that potential budget limitation can significantly affect scheduling and planning decisions. Recently, Barbaro and Bagajewicz (2004) proposed a new mathematical formulation for problems dealing with planning under design uncertainty that allows management of financial risk according to the decision-maker’s preferences. Sanmarti et al. (1995)define a robust schedule as one which has a high probability of being performed, and it is readily adaptable to plant variations. They define an index of reliability for a unit scheduled in a campaign through its intrinsic reliability, the probability that a standby unit is available during the campaign, and the speed with which it can be repaired. An overall schedule reliability is then the product of the reliabilities of units scheduled in it, and solutions to the planning problem can be driven to achieve a high value of this indicator. Ahmed and Sahinidis (1998)noted that the resulting two-stage stochastic optimization models in process planning under uncertainty minimize the sum of the costs of the first stage and the expected cost of the second stage. However, a limitation of this approach is that it does not account for the variability of the second-stage costs and might lead to solutions where the actual second-stage costs are unacceptably high. In order to resolve this difficulty they introduced a robustness measure that penalizes second-stage costs that are above the expected cost. Pistikopoulos et al. (2001) presented a systems effectiveness optimization framework for multipurpose plants that involves a novel preventive maintenance model coupled with a multiperiod planning model. This provides the basis for simultaneously identifying production and maintenance policies, a problem of significant industrial interest. This framework was then extended by Goel et al. (2003) to incorporate the reliability allocation problem at the design stage. Li et al. (2003) employed probabilistic programming approach to plan operations under uncertainty and to identify the impact on profits based on reliability analysis. Recently, Suryadi and Papageorgiou (2004) presented an integrated framework for simultaneous maintenance planning and crew allocation in multipurpose plants.

1.2.4 Integration of Production Planning and Scheduling

The decisions made by planning, scheduling, and control functions have a large economic impact on process industry operations - estimated to be as high as US $10 increased margin per ton of feed for many plants. The current process industry environment places even more of a premium on effective execution of these functions. In spite of these incentives, or perhaps because of them, there exists significant disagreement about the proper organization and integration of these functions, indeed even which decisions are properly considered by the planning, scheduling or control business processes. It has long been recognized that maintaining consistency among

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the decisions in most process companies continues to be difficult and the lack of consistency has real economic consequences. In their recent work Shobrys and White (2002) presented a critical and comprehensive analysis of several practical aspects that need to be carefully considered when challenges, associated with improving these functions and achieving integration, arise. The planning and scheduling levels of the operations hierarchy are natural candidates for integration because the structure of these two decision problems is very similar. However, the direct merging of these two levels requires embedding the details of the scheduling level into a super-scheduling-problem defined over the entire planning horizon. The result is a problem that is extremely difficult to solve. Thus, in recent years research has been increasingly interested in the issues around the integration of production and scheduling, in order to provide greater consistency. The most common approach for the simultaneous treatment of production planning and scheduling is a hierarchical decomposition scheme, where the overall production planning problem is decomposed into two levels (Bitran and Hax 1977).At the upper level, the planning problem, which usually involves a simplistic representation of the scheduling problem, is solved as a multiperiod LP problem in order to maximize the profit and set production targets. At the lower level, the scheduling problem is concerned with the sequencing of tasks that should meet the goals. An alternative integration approach is through the rolling schedule strategy (Hax 1978). Production planning and scheduling are closely related activities. Ideally these two should be linked, in order that the production goals set at the production plan level should be implementable at the scheduling level. Birewar and Grossmann (1990), based on their initial LP flow-shop scheduling model, proposed aggregate methods that allow tackling longer time-horizons by reducing the combinatorial nature of the problem. The model accounts for inventory costs, sequence-dependent clean-up times and costs, and penalties for not meeting predefined product demands. Using a graph enumeration method, the production goals predicted by the planning model are applied to the actual schedule, with the key point that both problems are solved simultaneously, since the sequencing constraints can be accounted for at the planning level with very little error. Bassett et al. (199Ga), working in the same direction of model-based integrated applications and focused on integrating planning decisions with the actual schedule, proposed an aggregation/disaggregation technique that can be used to provide solutions to otherwise intractable mid-term planning models. The initiative is the exploitation of available enterprise information within the process operational hierarchy tree. A more formal approach to integration of production and scheduling is described based on the previous work of Subrahmanyam et al. (1996), where the planning model, based on an aggregate formulation, is modified to be consistent with detailed scheduling decisions. Hierarchical production planning algorithms often make use of rolling horizon algorithms as a suboptimal to obtain feasible, but often good, solutions. The disadvantage of the method is reliance on the simplistic or rather poor representation of the scheduling problem within the aggregate part. Wilkinson (1996) derived an accurate aggregate formulation by applying formal aggregation operators to the resource-

7.2 Planning in the Process Industries

task network (RTN) formulation, and dividing the horizon into aggregate time periods (ATPs). This allows creating single MILP models that have varying time resolution. The first ATP is modeled in fine detail (scheduling) and the subsequent ATPs are modeled using the aggregate formulation (planning). The problem can then be solved as a single MILP, maintaining consistency between plan and schedule. Rodrigues et al. (2000) presented a two-level decomposition procedure for integrating scheduling and planning decisions. At the planning level, demands are adjusted, a raw material plan is defined and a capacity analysis is performed. At the scheduling level an MILP model is proposed. Geddes and Kubera (2000)described a practical integration between planning and online optimization with application in olefins production. Das et al. (2000) developed a prototype system by integrating two higher-level hierarchical production planning application programs (aggregated production plan and master production schedule) using a common data model integration approach into an existing planning system for short-term scheduling and supervisory management, which was originally developed by Rickard et al. (1999). Bose and Pekny (2000) presented a similar approach to model predictive control for integrated planning and scheduling problems. Van den Heever and Grossmann (2003) addressed the integration of production planning and reactive scheduling for the optimization of a hydrogen supply network consisting of 5 plants, 4 interconnected pipelines and 20 customers. A multiperiod MINLP model was proposed for both the planning and scheduling levels, along with heuristic solution methods based on Lagrangean decomposition. During the last Foundations on Computer Aided Process Operations (FOCAPO2003) event, several contributions presented were on the integration between planning and scheduling decisions. Harjunkoski et al. (2003) provided a comprehensive analysis of different aspects needed for the integration of the planning, scheduling and control levels in the light of ABB’s industrial initiative. They presented a framework introducing an approach to integrating all aspects relevant to decision making in a supportive way. An industrial case study was used to illustrate the benefits of the integrated framework. Yin and Liu (2003)developed a problem formulation and solution procedure for production planning and inventory management of systems under uncertainty. The production system is modeled by finite-event continuous-time Markov chains. Kabore (2003) presented a model predictive control formulation for the planning and scheduling problem in process industries. The main idea is to use moving-horizon techniques as well as a feedback control concept to continuously update production schedules. Wu and Ierapetritou (2003) proposed a method for simultaneously solving a planning and scheduling problem. The mathematical formulation of the planning problem involves scheduling decisions and results to a large MINLP problem, intractable to solve directly within reasonable computational time. A nonoptimal solution strategy is selected to provide near-optimal solutions within reasonable computational times. Tsiakis et al. (2003) applied the algorithm of Wilkinson (1996) to obtain an integrated plan and schedule of the operations of a complex specialty oil refinery, focusing on the downstream products of the oil supply-chain. Operating in an uncertain environment, the company needed to schedule the refinery operations in detail over the next month, while producing plans for the next year that were both reasonably accurate and consistent with the short-term schedule.

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1.2.5 Planning of Refinery Operations and Offshore Oilfields

The refinery industry is currently facing a rather difficult situation, typically characterized by decreasing profit margins, due to surplus refinery capacity, and increasing oil prices. Simultaneous market competition and stringent environmental regulations are forcing the industry to perform extensive modifications in its operations. As a result there is no refinery nowadays that does not use advanced process engineering tools to improve its business performance. Such tools range from advanced process control to long-range planning, passing through process optimization, scheduling and short-term planning. Despite their widespread use and the existence of quasi-standard technologies for these applications,their degree of commercial maturity varies greatly and there are many unresolved problems concerning their use. Moro (2003)presents a comprehensive discussion on current approaches to solving these problems and proposes directions for future development in this area. Traditionally, planning and scheduling decisions in refinery plants have been addressed using LP techniques and several tools exist such as the Integrated System for Production Planning (SIPP) and the Refinery and Petrochemical Modelling System (RPMS).An excellent review has recently been presented by Pinto et al. (2000). These tools allow the development of general production plans of the whole refinery. As pointed out by Pelham and Pharris (1996),the planning technology in the refinery operations can be considered well-developed and the margins for further improvement are very tight. The major advances in this area should be expected in the form of more detailed and accurate modeling of the underlying processes, notably through the use of nonlinear programming (NLP) as illustrated by Moro et al. (1998) using a real-world application. Ballintjin (1993) compared continuous and mixed-integer linear formulations and emphasized the low applicability of models based solely on continuous variables. In the literature, the first mathematical programming (MP) approaches utilizing advances in mixed-integer optimization are focused on specific applications such as gasoline blending (Rigby et al. 1995)and crude oil unloading. Shah (1996)presented a MP approach for scheduling the crude oil supply to a refinery, whereas Lee et al. (1996) developed a MILP model for short-term refinery scheduling of crude oil unloading with optimal inventory management decisions. Gothe-Lundgren (2002) proposed a planning and scheduling model which seems to be limited to the specific industrial problem to which it has been applied, whereas Jia and Ierapetritou (2004) addressed the optimal operation of gasoline blending and distribution, the transfer to product stock tanks and the delivery schedule to satisfy all of the orders. Recent work by Pinto et al. (2000) is a key contribution in this area. A nonlinear planning model for refinery production was developed that is able to represent a general refinery topology. The model relies on a general representation for refinery processing units in which nonlinear equations are considered. The unit modes are composed of blending relations and process equations. Certain constraints are imposed to ensure product specifications,maximum and minimum unit feed flow rates, and limits on operating variables. Real-world industrial case studies for the planning of

7.2 Planning in the Process industries

diesel production were used to illustrate the applicability and usefulness of the overall approach. In the second part of their work scheduling problems in oil refineries were studied in detail. Discrete time representations were employed to model scheduling decisions in important areas of the refinery such as crude oil inventory management and fuel oil, asphalt, and liquefied petroleum gas (LPG) production. Several real-world refinery problems were presented and solved using the developed models. Based on the above work, Neiro and Pinto (2004)proposed a general mathematical framework for modeling petroleum supply chains. A set of crude oil suppliers, refineries that can be interconnected by intermediate and final product streams and a set of distribution centres form the basis for this work. The scheduling of well and facility operations is a very relevant problem in offshore oil field development and represents a key subsystem of the petroleum supplychain. The problem is characterized by long planning horizons (typically 10 years) and a large number of choices of platforms, wells, and fields and their interconnecting pipeline infrastructure. Resource constraints such as availability of the drilling rings make the requirement for proper scheduling more imperative to utilize resources efficiency. The sequencing of installation of well and production platforms is essential to ensure their availability before drilling wells. The operational design of the well and production platforms and the time of installation are critical, as they involve significant investment costs, these decisions must be optimized to maximize the return on investment. Thus, oil field development represents a complex and expensive undertaking in the oil industry. The process systems engineering community has recently made several key contributions in this area based on advances in mixed-integer optimization. Iyer et al. (1998) developed a multiperiod MILP formulation for the planning and scheduling of investments and operations in offshore oil field facilities. For a given time-horizon, the decision variables in their model are the choice of reservoir to develop, selection from among candidate well sites, and the well-drilling and platform installation planning, the capacities of well and production platforms and the fluid production rates from wells for each time period. The nonlinear reservoir behavior is handled with piecewise linear approximation functions. Van den Heever and Grossmann (2000) presented a mixed-integer nonlinear model for oilfield infrastructure that involves design and planning decisions. The nonlinear reservoir behavior is directly incorporated into the formulation. For the solution of this model an iterative aggregationjdisaggregation algorithm is proposed according to which time periods are aggregated for the design problem, and subsequently disaggregated for the planning subproblem. Van den Heever et al. (2000) addressed the design and planning of offshore oilfield infrastructure focusing on business rules and complex economic objectives. A specialized heuristic algorithm that relies on the concept of Lagrangean decomposition was proposed by Van den Heever et al. (2001) for the efficient solution of this problem. Ierapetritou et al. (1999) studied the optimal location of vertical wells for a given reservoir property map. The problem is formulated as a large-scale MILP and solved by a decomposition technique that relies on quality cut constraints. Kosmidis et al. (2002) described a MILP formulation for the well allocation and operation of integrated gas-oil systems, whereas Barnes et al. (2002) focused on the production design of offshore plat-

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forms. Kosmidis (2003) presented a MINLP model for the daily well-scheduling, where the nonlinear reservoir behavior, the multiphase flow in the well, and constraints from the surface facilities are simultaneously considered. An efficient solution strategy is also proposed. Lin and Floudas (2003) presented a continuoustime modeling and optimization approach for the long-term planning problem for integrated gas-field development. They proposed a two-level formulation and solution framework taking into account complicated economic calculations. I.E. Goel, V. Grossmann Comput. Chem. Eng. 28 (2004), 1409 considered the optimal investment and operational planning of gas-field development under uncertainty in gas reserves. A novel stochastic programming model that incorporates the decisiondependence of the scenario was presented. Aseeri et al. (2004) discussed the financial risk management in the planning and scheduling of offshore oil infrastructures. They added budgeting constraints to the model of Iyer et al. (1998)by following the cash flow of the project, taking care of the distribution of proceeds and considering the possibility of taking loans.

1.2.6 The Campaign Planning Problem

The campaign planning problem has received rather limited attention in the past 20 years, yet it is considered a key problem in chemical batch production. If reliable long-term demand predictions are available, it is often preferable to partition the planning horizon into a smaller number of relatively long periods of time (“campaigns”),each dedicated to the production of single product. The campaign mode of operations may result in important benefits such as minimizing the number and costs of changeovers when switching production from one product to another. The complexity of management and control of the plant operation is further reduced by operating the plant in a more regular fashion, such as in a cyclic mode within each campaign, with the same pattern of operations being repeated at a constant frequency. Typical campaign lengths are from weeks to several months, with cycle times ranging from a few hours to a few days. The campaign mode of operations is often used for the manufacture of “generic” materials (e.g., base pharmaceuticals) which are produced in relatively large amounts and are then used as feedstocks for downstream processes producing various more specialized final products (Papageorgiou 1994, Grunow, et al. 2002). Mauderli and Rippin (1979)studied the combined production planning and scheduling problem, developing a hierarchical procedure suitable for serial processing networks operated in a zero-wait mode. First, they consider each product individually, generating alternative production lines of a single product by assembling the available processing equipment in groups in order to achieve maximum path capacity. A LP-based screening procedure is used to determine a set of dominant campaigns. Finally, the production plan is generated by solving a LP or MILP problem, allocating the available production time to the various dominant campaigns for a given set of production requirements.

7.2 Planning in the Process fndustries

The generation of alternative production lines in the Mauderli and Rippin (1979) algorithm is based on an exhaustive enumeration procedure. A more efficient generation procedure is described by Wellons and Reklaitis (1989a),who formulated the optimal scheduling of a single-product production line as a MINLP model. However, this approach has several limitations, including high degeneracy, as many path assignments result in equivalent schedules. The elimination of this degeneracy was considered by Wellons and Reklaitis (1989b)who identified a set of dominant unique path sequences and hence improved the solution efficiency of the original formulation. A further improvement from the single-product production line scheduling to the single-product campaign formulation problem has been presented by Wellons and Reklaitis (1991a),including the automatic assignment of different equipment items to groups, and also the assignment of these groups to production stages. This work was extended by Wellons and Reklaitis (1991b) to the multiproduct campaign formulation problem for multipurpose batch plants. Finally, a multiperiod planning model is proposed, allocating the production time among the dominant campaigns while considering simultaneously profit from sales, changeover, inventory costs and campaign set-ups. Papageorgiou and Pantelides (1993)presented a hierarchical approach attempting to exploit the inherent flexibility of multipurpose plants by removing various restrictions regarding the intermediate storage policies between successive processing steps, the utilization of multiple equipment items in parallel and also the use of the same item of equipment for more than one task within the same campaign. A threestep procedure was proposed. First, a feasible solution to the campaign planning problem is obtained to determine the number of campaigns and the active parts of the original processing network involved within each campaign. Secondly, the production rate in each campaign is improved by removing some assumptions and applying the cyclic scheduling algorithm of Shah et al. (1993).Finally, the timing of the campaigns is revised to take advantage of the improved production rates. An interesting feature of this approach is that any existing campaign planning algorithm can be used for its first step. However, this approach relies on several restricted assumptions, including limited flexibility in the utilization of processing equipment and limited operating modes, while multiple production routes or material recycles are not taken into account. The algorithms described above are hierarchical in nature, and therefore relatively easy to implement given the reduction in the size of the problem solved at each step. On the other hand it is difficult to relate the exact objective for each individual step in the hierarchy to the overall campaign and planning objective function, and therefore it is very difficult to assess the quality of the final solution obtained. Shah and Pantelides (1991)proposed a single-level mathematical (MILP) formulation for the simultaneous campaign formation and planning problem. Their algorithm simultaneously determines the number and the length of the campaigns and the products and/or stable intermediates manufactured within each campaign. They consider serial processing networks operating in a mixed Zero-Wait/Unlimited Intermediate Storage (ZW/UIS) mode, and nonidentical parallel equipment items operating in phase.

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Voudouris and Grossmann (1993)extended the work originally presented by Birewar and Grossmann (1989a,b, 1990) to campaign planning problems for multiproduct plants. They introduced cyclic scheduling, location and sizing of intermediate storage, and inventory considerations along with novel linearization schemes transforming the resulting MINLP formulation. Tsiroukis et al. (1993) considered the optimal operation of multipurpose plants operating in campaign mode to fulfil outstanding orders. Resource constraints are explicitly taken into account while the limited availability of resource levels affects the operation of the plant. To deal with the complexity,nonconvexity and nonlinearity of the MINLP formulation, more efficient formulations along with a problemspecific two-level decomposition strategy were proposed. Papageorgiou and Pantelides (199Ga)presented a general MP formulation for multiple campaigns planning/scheduling of multipurpose batch/semicontinuous plants. In contrast to hierarchical approaches presented above, a single-levelformulation was developed, encompassing both overall planning considerations pertaining to the campaign structure and scheduling constraints describing the detailed operating of the plant during each campaign. The problem involves the simultaneous determination of the campaigns (i.e., duration and constituent products) and for every campaign the unit-task allocations, the tasks’ timings and the flow of material through the plant. A cyclic operating schedule is repeated at a fxed frequency within each campaign, thus significantly simplifying the management and control of the plant operation. A rigorous decomposition approach to the solution of this problem is presented by Papageorgiou and Pantelides (199Gb) and its effectiveness was demonstrated by applying it to a number of examples. Ways in which the special structure of the constituent mathematical models of the decomposition scheme can be exploited to reduce the size and associated integrality gaps are also considered.

1.3 Planning for New Product Development

Pharmaceutical industries are undergoing major changes to cope with the new challenges of the modern economy. The internationalization of the business, the diversity and complexity of new drugs, and the diminishing protection provided by patents are some of the factors driving these challenges. Market pressures are also forcing pharmaceutical industries to take a more holistic view of their product portfolio. The typical life cycles of new drugs are becoming shorter making it harder to recover the investments, especially with the expiry of short-life patents and the arrival of generic substitutes that can later appear in the market, reducing its profitability. It becomes necessary that the industry protects itself against these pressures while considering the limited physical and financial resources available. Several important issues and strategies for the solution of problems concerning pharmaceutical supplychains are critically reviewed by Shah, (2004). A large number of candidate new products in the agricultural and pharmaceutical industry must undergo a set of steps related to safety, efficacy, and environmental

1.3 P h n i n g f o r New Product Development

impact prior to commercialization. If a product fails any of the tests then all the remaining work of that product is halted and the investment in the previous tests is wasted. Depending on the nature of the products, testing may last up to 10 years and the problem of scheduling of tests should be made with the goal of minimizing the time-to-market and the expected cost of the testing. Another important challenge that the pharmaceutical and agrochemical industry faces today is how, then, to configure its product portfolio in order to obtain the highest possible profit, including any capacity investments, in a rapid and reliable way. These decisions have to be taken in the face of considerable uncertainty as demands, sales prices, outcomes of clinical tests, etc. may not turn out as expected. These problems have recently received attention from the process systems engineering community utilizing advances from the process planning and scheduling area. The first approach appeared in the literature by Schmidt and Grossmann (199G),who considered the problem of optimal sequencing of testing tasks for new product development, assuming that unlimited resources are available. For a product involving a set of testing tasks with given costs, durations and probabilities of success, these authors formulated a MILP model based on a continuous-time representation to determine the sequence of those tasks. The objective of the model is to maximize the expected net present value (NPV)associated with a product, while a special case considers the minimization of cost, subject to a time completion constraint. Even though there may be a number of new products under consideration, the assumption of unlimited resources allows the problem, with either of the two objectives, to be decomposed by each product. Extending this work, Jain and Grossmann (1999) developed an MILP model that performs the sequencing and scheduling of testing tasks for new product development under resources constraints. It was shown that it is critical to incorporate resource constraints along with the sequencing of testing tasks to obtain a globally optimal solution. Blau et al. (2000) developed a simulation model for risk management in the new product development process andsubramanian et al. (2001) proposed a simulation-based framework for the management of the research and development (R&D)pipeline. The focus of these works, however, is the new products development processes and not the planning and design of manufacturing facilities. In most of these references it is assumed that there are no capacity limitations or that the production level of a new product is not affected by the production levels of other products. Furthermore, investments costs are not explicitly included in the calculation of the NPV of the projects. The problem of simultaneous new product development and planning of manufacturing facilities has received rather limited attention. Papageorgiou et al. (2001) developed a novel optimization-based approach to selecting a product development and introduction strategy, as well as capacity planning and investment strategies. The overall problem is formulated as a MILP model that takes account of both the particular features of pharmaceutical active ingredient manufacturing and the global trading structures. Maravelias and Grossmann (2001) considered the simultaneous optimization of resource-constrained scheduling of testing tasks in new product development and design/planning of batch manufacturing facilities. A multiperiod MILP model was proposed that takes into account multiple tradeoffs and predicts

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which products should be tested, the detailed test schedule that satisfy design decisions for the process network, and production profiles for the different scenarios defined by the various testing outcomes. A heuristic algorithm based on Lagrange decomposition was investigated for the solution of larger problem instances. Roger et al. (2002)have addressed a similar problem. In most of the above approaches it is assumed that the resources available for testing, such as laboratories and scientists, are constant throughout the testing horizon, and that all testing tasks have fured costs, duration and resources requirements. Another common assumption in all the above approaches is that the cost of one test does not depend on the amount of resources allocated to one test. However, as noted in the recent contribution by Maravelias and Grossmann (2004) a company may decide to hire more scientists or build more laboratories to handle more efficiently a great number of potential new products in the R&D pipeline. As another option the company may have to outsource the tests, often at a high cost. All these issues have been addressed by proposing a MILP model that is efficiently solved with a heuristic decomposition algorithm. In most of the above approaches uncertainty aspects have been neglected although clinical tests are highly uncertain in practice. The recent work by Gatica et al. (2003) explicitly considers uncertainty in clinical trial outcomes. A multistage, multiperiod stochastic problem was developed that was reformulated as a multiscenario MILP model. For this model, a performance measure that takes appropriate account of risk and potential returns has also been formulated. Levis and Papageorgiou (2004) extended the work of Papageorgiou et al. (2001) and proposed a two-stage multiscenario MILP model determining both the product portfolio and the multisite capacity planning in the face of uncertain clinical outcomes, while taking into account the trading structure of the company. They proposed a novel hierarchical algorithm to reduce the computational effort needed for the solution of the resulting large-scale MILP models.

1.4 Tactical Planning

Planning and scheduling is usually part of a company-wide logistics and supplychain management platform. However, to distinguish between those topics, or even to distinguish further between planning and scheduling is often an artificial rather than a pragmatic approach. In reality, the borderline between all these areas is diffuse, due to the strong overlaps between scheduling and planning in production, distribution or supply-chain management and strategic planning. Planning and scheduling considerations are very closely related and often confused. The most common distinction between the two concepts is based on the time horizon they consider. While scheduling considers problems that may be of some hours to a few weeks, planning problems may consider time horizons that are of a few weeks up to a few months, and in many applications can even be of years. Tacti-

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cal planning aims to set the targets for the scheduling applications that will follow in order to determine the operational policy of the plant in the short term. Owing to its nature of involving longer time horizons, planning decisions are often subject to uncertainty that might arise from many sources. The planning operation in the process industry is focused on analyzing the supplychain operations as they are defined by strategic planning (see Fig. 1.1).Competitive environment and technological advances have resulted in enterprise resource planning (ERP) systems to be widely used within the process sector; they are considered to be software suites that help organizations to integrate their information flow and business processes (Abdinour-Helm et al. 2003). The fundamental benefits of ERP systems do not in fact come from their planning capabilities but rather from their abilities to process transactions efficiently and to provide organized structured data bases (Jacobs 2003). Planning and decision support applications represent optional additions to this basic transactional, query and report capability. ERP has been designed to supersede the earlier concepts of material requirement planning (MRP) and manufacturing resource planning (MRP-11) that were designed to assist planners at a local level, by linking various pieces of information, especially in manufacturing. The advantage of a successful ERP implementation is the integration between different levels of the enterprise, such as financial, controlling, project management, human resources, plant maintenance and material flow logistics (Mandal and Gunasekaran 2003). The planning functions at a tactical level benefit from the existence in-place of an ERP system; the two systems do not replace each other but their relationship can be described as complementary. ERP systems play the role of an information highway that connects all planning levels and links various decision support systems to the same data. MRP systems were designed to work backwards from the sales orders to determine the raw material required for production (Orlicky 1975). MRP-I1 was introduced as a follow-up to resolve obvious operational problems usually associated with the absence of capacity considerations from MRP that resulted in poor schedules (Wight 1984).The weakness of both approaches is that they were targeting and develMulti-site planning

[~ _ Enterprise _ ~ _ _ _ _Resource _ - _ _ - _ Planning ___-

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Business transaction system Site planning

Scheduling & Execution

Scheduling & Execution systems

Fig. 1.1 Operations planning decision hierarchy.

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oped for the manufacturing environment, and very often ignored the complexities of the process world. ERP on the other hand, is not limited only to manufacturing companies, but is useful for any company with the need to integrate their information across many functional areas. Planning in the process industry is used to create production, distribution, order satisfaction and inventory plans, based on the information that can be extracted from ERP systems, while satisfying several constraints. In particular, operational plans have to be determined that are aimed to set targets for future production, plan the distribution of materials and allocate other related activities according to the business expectations. Business expectations are the product of strategic resource planning. A successful strategic resource planning, which can be performed either by activity-based cost (ABC), MP, resource-based view (RBV), or a combined approach, is sent to the ERP (Shapiro 1999).It is common practice that, based on these tactical plans, detailed schedules may be produced that define the exact sequence of operations, and determine the utilization of the available resources. Tactical planning is called on to address a number of decisions: the manufacturing policy (what shall we make?), the procurement policy (what do we need?), the inventory or stock policy (what stock already exists?),the resources utilization policy (what do I need to make it?). Tactical planning supports different short- to medium-term objectives for the business by using different objective functions. By using different objective functions we can create several operational plans to support the various strategic supply-chain decisions. Its differentiation from other planning approaches is that it requires a more detailed representation of the resources in a system. These resources are tied with a number of constraints that might need to be satisfied. A common approach to tactical planning in the process industry is to describe the problem using a MP model, and then to optimize towards a desired objective. The objective can be maximization of profit, customer order satisfaction,minimization of cost, minimization of tardiness, minimization of common resource utilization, etc. The production environment is a rather complex network and most standard heuristic production planning tools fail to address this complexity. This situation gave rise to the idea of employing MP-based models to provide planning systems with a higher degree of flexibility by considering both product demands as a function of the marketing and sales departments of an organization, and the plant capacity in terms of equipment, material, manpower and utility resources. The problem has been modeled using a number of approaches. Bassett et al. (1996b) proposed a higher level planning model based on formal aggregation techniques and using uniform time discretization. The model contains aggregate material balance constraints and equipment allocation constraints similar to those of the state-task network (STN) description of a process. This planning model forms part of a decomposition strategy where production is allocated to different time zones, thus creating a set of scheduling problems that can then be solved independently. Wilkinson (1995)presented a generic mathematical technique to derive aggregate planning models of high accuracy based on the resource-task network (RTN) repre-

7.5 Resource Planning in the Power Market and Construction Projects

sentation. The proposed formulations allow a large number of the complicating features of multipurpose, multiproduct plant operation to be taken into account in a unified manner. Sequence-dependent changeovers, task utility requirements and limited intermediate storage are some of the additional features included. Also the use of linking variables allows the planning model to take into account inventory levels more accurately. These two formulations are fairly generic and include most of the important features regarding the planning in process industries where fixed recipes are employed. Prior to them, most of the planning models contained complicated sets of constraints which had been tailored to a specific problem type. 1.5 Resource Planning in the Power Market and Construction Projects

The area of resources planning in the energy and power market and construction projects is worthy of a review in its own right; it will be considered somewhat briefly here, mainly due to its strong similarities with the process planning problem. 1.5.1 Resource Planning in the Power Market

In a traditional electric power system, a utility company is responsible for generating and delivering power to its industrial, commercial and residential customers in its service area. It owns generation facilities and transmission and distribution networks, and obtains necessary information for the economical and reliable operation of its system. For instance, an important problem faced daily by a traditional utility company is to determine which and when generating units should be committed, and how they should be dispatched to meet the system-wide demand and reserve requirements. The centralized resource planning problem involves discrete states (e.g., on/off of units) and continuous variables (e.g., units’ generation levels), with the objective being to minimize the total generation costs. A 1% reduction in costs can result in more than US$10 million dollars savings per year for a large utility company. Various methods have been presented in the literature and impressive results have been obtained (Wang et al. 1995, Guan et al. 1997, Li et al. 1997). Today, the deregulation and reconstruction of the electric power industry worldwide have raised many challenging issues for the economic and reliable operation of electric power systems. Traditional unit commitment of hydrothermal scheduling/ planning problems are integrated with resource bidding, and the development of optimization-based bidding strategies is a preliminary stage. Ordinal optimization approaches seek “good enough” binding strategies with high probabilities, and will turn out to be effective in handling market uncertainties with much reduced computational cost. Under this new structure, resource planning is intertwined with bidding in the market, and power suppliers and system operators are facing a new spectrum of issues and challenges (Guan and Luh 1999).

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Many approaches have been presented in the literature to address resources planning in the deregulated power markets. In this context, modeling and solving the bid selection problem has recently received significant attention. In Hao et al. (1998), bids are selected to minimize the total system cost, and the energy clearing price is determining as the highest accepted price for each hour. In Alvey et al. (1998),a bid clearing system in New Zealand is presented. Detailed models are used, including network constraints, reserve constraints, and ramp-rate constraints, and LP is used to solve the problem. Another very popular way to model the bidding process is to model the competitors’ behavior as uncertainties. Therefore, the bidding problem can be converted to a stochastic optimization problem. One of the widely used approaches in stochastic optimization to address this problem is stochastic dynamic programming (Contaxis 1990, Li et al. 1990).The basic idea is to extend the backward dynamic programming procedure by having probabilistic input and probabilities state transmissions in place of determining input and transitions and by using expected costs to calculate deterministic costs-to-go.The direct consequence is increased computational cost due to the significant increase in the input space and the number of possible transitions. For example, when stochastic dynamic programming is used to solve a hydroscheduling problem with uncertain inflows, one more dimension is needed to consider probable inflows in addition to reservoir levels, which significantly worsens the dimension of the problem. Another approach is scenario analysis (Carpentier et al. 1998, Takriti et al. 1996). Each scenario (or a possible realization of random events) is associated with a weight representing the probability of its occurrence. The objective is to minimize the expected costs over all possible scenarios. Since the number of possible scenarios and consequently the computational requirements increase drastically as the number of uncertain factors and the number of possibilities per factor increase, this approach can only handle problems with a limited number of uncertainties. Recently, stochastic dynamic programming has been embedded within the Lagrangean relaxation framework for energy scheduling problems, where stochastic dynamic programming is used to solve uncertain subproblems after system-widecoupling constraints are relaxed. Since dynamic programming for each subproblem can be effectively solved without encountering the curse of dimensionality, good schedules are obtained without a major increase in computational requirements (Luh et al. 1999). Among alternatives that are being investigated for the generation of electricity are a number of unconventional sources including solar energy and wind energy. In recent decades photovoltaic (PV) energy found its first commercial use in space. In many parts of the globe, PV systems are being considered as a viable alternative for generating electricity. Achieving this goal requires PV systems to enter the utility market, whereby electric utilities evaluate the potentials of each PV system corresponding to its impact on the electric utility expansion planning, and requirements for backup generating capacity to ensure a reliable supply of electricity. AbdulRahman (1996) presented a model for the short-term resource scheduling in power systems. An augmented Lagrangean relaxation was used to overcome difficulties with the solution convergence as realistic constraints were introduced (i.e.,transmis-

7.5

Resource Planning in the Power Market and Construction Projects

sion flows, fuel emissions, ramp-rate limits, etc.) in the formulation of unit commitment. Manvali et al. (1998) presented an efficient approach to short-term resource planning for an integrated thermal and PV battery generation. The proposed model incorporates battery storage for peak loads. Several constraints including battery capacity, minimum up/down time and ramp-rates for thermal units as well as natural PV capacity are considered in the proposed model.

1S . 2 Resource Planning in Construction Projects

Traditionally, resource planning problems in construction projects have been solved either as resources-leveling or as a resource-constrained scheduling problem. The resources-constrained scheduling problem constitutes one of the most challenging facing the construction industry, due to the limited availability of skilled labor, and the increasing need for productivity and cost-effectiveness. These challenges have been discussed by many practitioners and have led researchers to investigate various avenues. One of the most promising solutions to the problem of the shortage of skilled labor has been to develop methods that optimize or better utilize the skilled workers already in the industry (Burleson et al. 1998). The resource-leveling problem arises when there are sufficient resources available and it is necessary to reduce the fluctuations in the resource usage over the project duration. These resource fluctuations are undesirable because they often require a short-term hiring and firing policy. The short-term hiring and firing presents labor, utilization, and financial difficulties because (a) the clerical costs for employee processing are increased, (b) topnotch journeymen are reluctant to join a company with a reputation of doing this and (c) new, less experienced employees require long periods of training. The scheduling objective of the resource-leveling problem is to make the resource requirements as uniform as possible or to make them match a particular nonuniform resource distribution in order to meet the needs of a given project. Resource usage usually varies over the project duration because different types of resources are needed in varying amounts over the life of the project. In construction projects, for example, operators are needed in the beginning of the project to dig the foundations, but they are not needed at the end of the project for the interior finish work. In resource-leveling, the project duration of the original critical path remains unchanged. MILP models have been used to formulate the resource-constrained scheduling problem (Nutdtasomboon and Randhawa 1996). The efficiency of these models usually decreases due to the high combinatorial nature of the problem, and special algorithms have been developed as an attempt to reduce computational costs and improve the quality of the solution. Most of these algorithms rely on special branchand-bound and implicit enumeration approaches (Sung and Lim 1996, Demeulemeester and Herroelen 1997). An alternative approach to improving the computational efficiency is the use of heuristic methods that produce feasible, but not necessarily optimal, solutions (Padilla and Carr 1991, Seibert and Evans 1991).

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Savin et al. (1998) presented a neural network application for construction resource-levelingusing an augmented Lagrangian multiplier. The formulation objective is to make the resource requirements as uniform as possible. Thus, the formulation does not consider the case of nonuniform resource usage. Also, it only allows for one precedence relationship (finish-start) and one resource type, and does not perform cost optimization. Chan et al. (1996) proposed a resource scheduling method based on genetic algorithms (GAS). The method considers both resource-leveling and resourceconstrained scheduling. It can minimize the project duration, but it does not consider the case of nonuniform resource usage, neither does it minimize the construction cost. Adeli and Karim (1997)presented a general mathematical formulation for project scheduling. Multiple crew strategies, work continuity considerations, and the effect of varying job conditions on the crew performance could be modeled. They developed an optimization framework for minimizing the direct construction cost. However, the resource-leveling and resource-constrained scheduling problems were not addressed. Recently, Senousi and Adeli (2001) presented a new formulation including project scheduling characteristics such as precedence relationships, multiple crew strategies, and time-cost tradeoff. The formulation can handle minimization of the total construction cost or duration while resource-leveling and resourceconstrained scheduling are performed simultaneously. An important problem that has received rather limited attention in the literature is related to the optimal allocation of multiskilled labor resources in construction projects. This strategy is commonly found in the manufacturing and process industries where some of the labor force is trained to be multiskilled. Various studies have demonstrated the benefits of multiskilled resources. Nilikari (1995) presented a study involving Finnish shipbuilding facilities, based on a multiskilled work team strategy and found savings of up to SO % in production time. Burleson et al. (1998) explored several multiskill strategies such as a dual-skill strategy, a four-skill strategy and an unlimited-skill strategy. The study compared the economic benefits in a huge construction project to prove the benefits of multiskilling but did not develop a mechanism for selecting the best strategy for a given project. The work of Brusco and Johns (1998) presented an integer goal-programming model for investigating cross-training multiskilled resource policies to determine the number of employees in each skill category so as to satisfy the demand for labor while minimizing staff costs. The model was applied to the maintenance operations of a large paper mill in the USA. Hegazy et al. (2000)presented an approach for modifying existing resource scheduling heuristics that deal with limited resources, to incorporate the multiskills of available labor and accordingly to improve the schedule. The performance of the proposed approach was demonstrated using a case study and the solution is compared with that of a high-end software system that considers multiskilled resources.

7.6 Solution Approaches to the Planning Problem

1.6 Solution Approaches to the Planning Problem

Most of the planning problems in the process industry result in an LP/MILP or NLP/ MINLP model. Planning problems are usually NP-hard and data-driven;no standard solution techniques are therefore available,and in many cases we are actually searching for a feasible solution to the problem rather than an optimal one. The solution approaches found in the literature may be categorized as: 0

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exact and deterministic methods such as mathematical optimization including MILP and MINLP, graph theory (GT) or constraint programming (CP), or hybrid approaches in which MILP and CP are integrated; rnetaheuristics (evolutionarystrategies, tabu search, simulated annealing (SA),various decomposition schemes, etc.).

In this section we are going to focus on general solution approaches applied to planning problems, in addition to those that are mentioned in other sections and are problem-dependent. We are not going to describe extensively how these methods have been employed by a variety of authors, but we are going to describe the algorithms and the classes of problem to which they have been applied. Despite the extensive research work that exists for the solution of long-term planning and shortterm scheduling problems, the interest in medium-term planning problem is limited. While the benefits of integrating tactical planning into strategic planning and production scheduling are becoming clear, interest in research into more effective methods has increased. Applequist et al. (1997) provide an excellent review on planning technology and the approaches available for solving planning and scheduling problems. Despite substantial efforts over the last 40 years, no algorithm, either exact or heuristic, has been found that can provide a solution to all planning problems.

1.6.1 Exact and Deterministic Methods

In real life applications we rarely see any NLP/MINLP planning models, except in pooling or refinery planning. The rest of the models proposed, despite their complexity, in term of features they include and mathematical terms, they remain or are transformed to be linear regarding their variables and constraints. Therefore, using state-of-the-art commercial solvers, such as, XPRESS-MP (Dash Optimization, http://www.dashoptimization.com), CPLEX (ILOG, http://www.ilog.com), or OSL (IBM, http://www.ibm.com), LP/MILP problems can be solved efficiently and at a reasonable computational cost. In the case of NLP/MINLP, the solution efficiency depends strongly on the individual problem and the model formulation. Thus, in many cases the structure of the problem is exploited in order to provide valid cuts, or identify special structures in order to reduce computational times and increase the quality of the solution.

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However, as both MILP and MINLP are NP-hard problems, it is recommended that the full mathematical structure of a problem to be exploited. Software packages may also differ with respect to their ability in presolving techniques, default strategies for the branch-and-bound algorithm, cut generation within the branch-and-cut algorithm, and last but not least, diagnosing and tracing infeasibilities, which is an important issue in practice. Kallrath (2000) provides an extensive review of mixedinteger optimization in the process industry by describing solution methods, algorithms, and applications. Taking advantage of the special structure of mathematically formulated problems either as MILPs or MINLPs, several decomposition methods have been proposed and implemented in various types of problems. Bassett et al. (199Ga),focusing on chemical process industries, examined a number of time-based decomposition approaches along with their associated strengths and weaknesses. It is shown that the most promising of the approaches utilizes a reverse rolling window in conjunction with a disaggregation heuristic, applied to an aggregate production plan as part of their approach to integrate hierarchically related decisions. Resource- and task-based decompositions are also examined as possible approaches to reduce the problem to manageable proportions. To validate their proposed schemes a number of examples are presented. Gupta, A. Maranas, C. D. Ind. Eng. chem. Res. 38 (1999) 1937 utilized an efficient decomposition procedure to solve mid-term planning problems based on Lagrangean relaxation. Having tried commercial MILP solvers, they found that the employed solution strategy is more efficient. The basic idea of the proposed solution technique is the successive partitioning of the original problem into smaller, more computationally tractable subproblems by hierarchical relaxation of key complicating constraints. Alongside with the hierarchical Lagrangean relaxation they employ a heuristic algorithm to obtain valid upper bounds. Two examples are used to demonstrate the capabilities of the proposed algorithm. The size of the actual planning problem may be prohibitive for standard commercial solvers. Therefore, rigorous decomposition techniques that benefit from the special structure of MILP problems is exploited. Dimitriadis (2001), identified that block-diagonal MILP problems may be decomposed to simpler ones and introduced the concept of decomposable MILP (D-MILP). An algorithm based on the idea of “key variables”, which break the problem down into a number of smaller partial MILPs that can be solved independently and in parallel, was implemented based on a standard branch-and-bound scheme. The decomposition branch-and-bound (dBB) as the algorithm is called, achieves better performance by obtaining quick upper bounds to the problem and assisting the solver to find an optimal solution within reasonable computational time. One of the advantages of the approach is that is can guarantee the optimality of the solution. Tsiakis et al. (2000) improved the algorithm by providing an automated method to decompose the problem and implementing a more generic solution scheme applicable to all MILP problems that have a similar structure.

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1.6.2 Metaheuristics

In addition to the so called optimization methods we have techniques described as heuristics. These techniques differ in the sense that cannot guarantee an optimal solution; instead they aim to find reasonably good solutions in a relatively short time. Heuristics tend to be fairly generic and easily adaptable to a large variety of planning problems. There are a number of heuristic general-purpose approaches that can be applied to planning and scheduling problems (Pinedo 2003). SA and tabu searchare described as improvement algorithms. Algorithms of the improvement type are conceptually completely different from the constructive type algorithms. The algorithm starts by obtaining a complete plan that can be selected arbitrarily, and then tries to obtain a better plan by manipulating the current solution. The procedure is described as local search. A local search procedure does not guarantee an optimal solution, but aims to obtain a better solution in the neighborhood of the current one. They very often employ a probabilistic acceptance-rejection criterion with the hope it will lead to better solution. Reeves (1995) describes extensively the methods and applications in production planning systems. GAsare more general than SA and tabu search and they can be classified as a generalization of the previously mentioned techniques. In this case a number of feasible solutions are initially found. Then, local search based on an evolution criterion is employed to select the most promising solution for further exploitation. The rest of the solutions are fathomed (Reeves 1995). Heuristics are widely employed in industry to provide solutions to production planning problems. Stockton and Quinn (1995) describe how a GA based on aggregate planning techniques is used to develop a production plan that allows a strategic business objective to be implemented in short- and mid-term operational plans. LeBlanc et al. (1999) utilize an extension of the multiresource generalized assignment problem (MRGAP) in order to provide an implementable solution to production planning problems. The model considers splitting of individual batches across multiple machines, while considering the effect of set-up times and set-up costs, features that the standard assignment problem (AP) fails to capture. The proposed formulations are solved using adaptations of a GA and SA. A multiobjective GA (MOGA) approach was employed by Morad and Zalzada (1999) for the planning of multiple machines, taking into account their processing capabilities and the process costs incurred. The formulation is based on multiobjective weighted-sums optimization, which is to minimize makespan, to minimize total rejects produced and to minimize the total cost of production. Tabu search is employed by Baykasoglu (2001) to solve multiobjective aggregate production planning (APP) problems based on a mathematically formulated problem. The model by Masud and Hawng was selected as the basis due to its extensibility characteristics.

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1.7 Software Tools for the Resource Planning Problem

Enterprise resource planning (ERP) is a software-driven business management system which integrates all facets of the business, including planning, manufacturing, sales and marketing. Increasingly complex business environments require better and more accurate resource planning. Furthermore, management is under constant pressure to improve competitiveness by lowering operating costs and improving logistics, thus increasing the level of control within the operating environment. Organizations therefore have to be more responsive to the customer and competition. Resource planning as a business solution aims to help the management by setting up better business practices and equipping them with the right information to take timely decisions. Production planning as a later business function is considered to be part of the supply-chain planning and scheduling suite, alongside other functions such as demand forecasting, supply-chain planning, production scheduling, distribution and transportation planning. Tactical production planning includes those software modules responsible for production planning within a single manufacturing facility. These solutions normally address tactical activities, although they may also be used to support both strategic and operational decisions and are very often integrated with them.

1.7.1 Enterprise Resource Planning

A big share of the software and services provided worldwide is targeting the integration of ERP and supply-chainoperations. Most of the information needed by production planning software tools resides within ERP systems. Most of the ERP software providers already have developed their own fully integrated planning applications, have acquired smaller companies with production planning software or have been in partnership with such providers. The standard object-oriented approach to the implementation of ERP systems has contributed towards an easy integration. The leading suppliers and systems integrators to the worldwide ERP market across all industry sectors are alphabetically: Oracle (http://www.oracle.com), Manugistics (http://www.manugistics.com), Peoplesoft (http://www.peoplesoft.com), and SAP (http://www.sap.com)according to the latest market share studies. In small-medium enterprises (SMEs)the leading provider of ERP systems is Microsoft Business Solutions with its Navision system (http://www.microsoft.com/businessSolutions). 1.7.2 Production Planning

Production planning deals in medium-range time horizons, where decisions about incremental adjustments to the capacity or customer service levels are made.

1.7 Software Toolsfor the Resource Planning Problem

Changes to supplier delivery dates, swings in raw materials purchases, and outsourcing agreements may require 3-5 months. Thus, production planning deals with what will be done, and when, in a factory over longer time frames. Tactical plans are updated frequently based on the operational plan and the actual schedule. This section provides the profiles of production planning software suppliers with main focus on the process industry, again in alphabetical order. 1.7.2.1 Advanced Process Combinatorics (http://www.combination.com)

The company’s modular supply-chain product VirtECS contains a module, called Scheduler, with production planning capability. The package handles complex production planning models with multiple input/output bills of material, multiple routings, resource constraints and set-up times. Their algorithms used for production planning are based on a MILP formulation, with a number of techniques applied for their solution. Additionally, a set of Gantt-chart-based interactive tools provides the user with manipulating capabilities on the actual plan. A key strength of APC revolves around the research on optimization since the company was generated from an industrial research consortium at Purdue University. 1.7.2.2 Aspen Technologies (http://www.aspentech.com)

Aspen Technology’s supply-chain capabilities are based largely on the company’s acquisition of the Process Industry Modelling Systems (PIMS) from Bechtel and Manager for Interactive Modelling Interfaces (MIMI) of Chesapeake Decision Sciences. Aspen PIMS is a tactical level refinery planning package that is widely used in over 170 refineries worldwide. The Aspen MIMI production planner is focused on models that include material flows, set-up times, labor constraints and other resource restrictions. In addition to the standard heuristics and simulation employed for production planning and scheduling, the advanced planning offers LP-based optimization capabilities. Users can interact with the Gantt chart in order to develop “what-if”analysis cases and add constraints. Aspen has one of the larger installed bases of MIMI products for over 300 customers around the globe. 1.7.2.3 i2 Technologies (http://www.iz.com)

As part of its supply-chain platform, i2’s Factory Planner manages material and capacity constraints to develop feasible operating plans for production plants. The tool aims to be a decision support system in the areas of production planning and scheduling, taking into account material and capacity requirements. It utilizes a number of heuristic algorithms and basic optimization to obtain feasible plans, and to answer capable-to-promise delivery-date quoting.

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1.7.2.4 Manugistics (http://www.manugistics.com)

Manufacturing Planning and Scheduling, integrated within the Constraint-Based Master Planning supply-chain system of Manugistics, provides the detailed operational plan. It is based on a flow-oriented model, and uses the theory of constraints to solve the production planning problems. It takes into account throughput of equipment, determines the bill of materials, and allows what-if scenario analysis. 1.7.2.5 Process System Enterprise (PSE) (http://www.psenterprise.com)

PSE’s ModelEnterprise has been designed as a modular supply-chainmodeling platform that allows the construction and maintenance of complex enterprise models, and supports a wide range of tools applied to these models for solving different types of problem. The Optimal Single Site Planner and Scheduler (OSS Planner Scheduler) determines an optimal schedule for a plant producing multiple products. It is especially suited to multipurpose plant where products can be made on a selection of equipment units, via different routes and in different sizes. The plans produced are finite capacity and rigorously optimal. The objective of the optimization problem can be configured according to the economic requirements of the operation - for example, to deliver maximum profit, maximum output or on-time in-full. The OSS Planner Scheduler uses state-of-the-artMILP optimization algorithms that allow complex systems to be modeled. Utilizing comprehensive costing all costs may be accounted such as processing, storage, utilities, cleaning, supplies and penalties for late delivery. PSE originated at Imperial College, London, in the 1990s. and ModelEnterprise has been developed based on knowledge and research found there. 1.7.2.6 SAP AC (http://www.sap.com)

The APO Production Planning and Detailed Scheduling (PP/DS) tool comes under the umbrella of SAP APO supply-chainsolutions. The software can be used to generate production plans and sequence schedules. A variety of approaches is included in this solution for theory of constraints and mathematical optimization, but in principle it is a heuristics-based tool, where the user-developed rules are employed. Other features of the tool include forward and backwards scheduling, simultaneous capacity and material planning in detail, what-if analysis to simulate effects of changes in constraints, and interactive scheduling via a Gantt chart interface.

1.8 Conclusions

The impact of accurate resource planning on the productivity and performance of both manufacturing and service organizations are tremendous. Researchers have found that organizations that had no resource planning information technology

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infrastructure in place performed poorly most of the time compared to those who had a specific plan. The successful implementation of planning capabilities means reduction in cost, increased productivity and improved customer services. The importance of resource planning models and systems therefore becomes significant. Moreover, the solution to the problems associated with that poses further challenges. Despite many years of study in resource planning models, plus numerous examples of successful modeling systems implementations and industrial applications, there is still a great potential for applying them in a pervasive and enduring manner to a wider range of real-life industrial applications. Several researchers have tackled the resource planning problem under uncertainty using different approaches. However, in most cases they have skirted around the problem of multiperiod, multiscenario planning with detailed production capacity models (i.e., embedding some scheduling information). Here, issues that must be addressed mainly relate to problem scale. Combined mixed-integer programming and stochastic optimization techniques seem to offer a promising solution alternative to this problem. One of the major challenges will be to develop planning approaches that are consistent with detailed resource scheduling as part of the overall supply-chain integration. An obvious drawback is the problem size. This poses the need for rigorous decomposition algorithms and techniques that will enable handling problems of greater size without compromising the quality of the solution. Over the last few years a trend has developed bringing MP and constrained programming techniques closer to each other. This results in hybrid approaches (i.e., in algorithms combining elements from both areas) that may have a great impact on reducing computational requirements for solving large-scale planning problems. In addition to new techniques and solution approaches, advances in computational power in terms of hardware and software allow the exploitation of parallel algorithm optimization techniques. The tree structure in mixed-integer optimization, and the time- or scenario-dependent structures, indicates that more benefits are to be expected from parallelizing the combinatorial part. Dealing with large-scale NP-hard problems may lead to the implementation of distributed planning, where the computational effort and time is divided over a number of computers or clusters. Timebased or spatial decomposition methods will be exploited more and more. Resource planning is a fundamental business process that exists in every production environment. It has long been recognized that in the process industries there are very large financial incentives for planning, scheduling and control decisions to function in a coordinated fashion. Nevertheless, many companies have not achieved integration in spite of multiple initiatives. An important challenge thus relates to the development of efficient theoretical methodologies, algorithms and tools to achieve this integration in a formal way, allowing process industries to take steps to practically improve the integration activities at different levels. The planning problem of refinery operations and offshore oilfields has been recently attacked by several researchers. However, the practical implementation of most of the developed approaches is usually limited to subsystems of a plant with considerable simplifications. Here, the trend is to expand the planning process to

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include larger systems, such as a group of refineries instead of a single one. Another area that deserves further attention is the inclusion of scheduling decisions in planning processes. Furthermore, there is a lot of scope for developing commercial tools to serve refineries to cope with daily operational problems. In the area of product planning, the integration of development management and capacity and production planning seems to be very important. Currently, capacity issues are often not considered at the development stage. The development of integrated models of the life cycle, from the discovery through to consumption would greatly facilitate strategic decision making. Demand for advanced planning systems (APS) is expected to grow with the solutions being increasingly industry- and supply-chain-specific.The standards are specified by the large software suppliers, such as i2 and Manugistics. The scope for smaller suppliers is to have a more specific focus in segments of the industry. There is a clear trend for industry-specificsolutions, this being due to the different operating environments and the detail required in order to generate a meaningful plan. The development of resource planning systems very much depends on the industry segment (industrial or nonindustrial) and the manufacturing type (process or discrete industries). While segmentation based on the type of industry is common, it is important to be able to segment the operational environment based on the supplychain type. In this case we have distribution, manufacturing or source intensive supply chains, each one with their own needs. Many companies are competing as software providers for planning systems. However, they have realized that they need to be able to communicate with other libraries and software modules as part of supplychain solutions, and at minimum cost. Systems with open architecture and ease of integration are in demand. Initiatives such as CAPE-OPEN aim to define industrywide standards (CO-LaN 2001).

References 1 Abdinour-Helm S. Lengnick-Hall M. L. Lengnick-Hill C. A. Eur. 1. Oper. Res. 146 2

3 4

5

6 7

8

(2003) p. 258 Abdul-Rahman K. H. Shahidehpour S. M. Aganagic M. Mokhtari S. IEEE Trans. Power Syst. 11 (1996) p. 254 Adeli H. Karim A,]. Constr. Eng. Manage. 123 (1997) p. 450 Ahmed S. Sahinidis N. V. Ind. Eng. Chem. Res. 37 (1998) p. 1883 Aluey T. Goodwin D. Ma X . Streifeert D. Sun D. IEEE Trans. Power Syst. 13 (1998) p. 986 Applequist G. Samikoglu 0. Peknyj. Reklaitis G. ISA Trans. 36 (1997) p. 81 Aseeri A. Gorman P. Bagajewicz M. J. Ind. Eng. chem. Res. 43 2004, 3063 Ballingin K. 1993 In: Ciriani T. A. Leachman R. C. (eds.),Vol. 3, Wiley, New York

9 Barbaro A. Bagajewicz AICHJournal, 50

(2004) 963 10 Barnes R. Linke P. Kokossis A. 2002 In: Pro-

ceedings of ESCAPE-12, The Hague, The Netherlands, p 631 11 Bassett M. H. Dave P. Doyle F. J. Kudva G. K. Pekny J. F. Reklaitis G. V. Subrahmanyam S. Miller D. L. Zentner M. G. Comput. Chem. Eng. 20 (1996a) p 821 12 Bassett M. H . PeknyJ. F. Reklaitis G. V. AICHE 1.42 (1996b) p 3373 13 Bassett M. H. Peknyj. F. Reklaitis G. V. Comput. Chem. Eng. 21 (1997) p. S1203 14 Baykasoglou A. Int. 1. Prod. Res. 39 (2001) p. 3685 15 Bemardo F. P. Pistikopoulos E. N. Saraiva P. Ind. Eng. Chem. Res. 38 (1999) p. 3056 16 Birewar D. B. Grossmann I. E. Comput. ChemM. Eng. 13 (1989a) p. 141

References 1477 17 Birewar D. B. Grossmann I . E. Ind. Eng.

Chem. Process Des. Dev. 28 (1989b) p. 1333 18 Birewar D. B. Grossmann I. E. Ind. Eng. Chem. Res. 29 (1990) p. 570 19 Bitran G. R. Hax A. C. Decision Sci. 8 (1977) p. 28 20 Blau G. Metha B. Bose S. Pekny J. Sinclair C. Keunker K. Bunch P. Comput. Chem. Eng. 24 (2000) p. 659 21 Bose S. PeknyJ. F. Comput. Chem. Eng. 24 (2000) p. 329 22 Brusco M. J. Johns T. R. Decision Sci. J. 29 (1998) p. 499 23 Burleson R. C. Hass C. T. Tucher R. L. Stanley A. J. Constr. Eng. Manage. 124 (1998) p. 480 24 Carpentier P. Woodwin D. Ma X . Streiyeert D. Sun D. IEEE Trans. Power Syst. 13 (1998) p. 986 25 Chan W. T. Chua D. K. H. Kannan G. J. Constr. Eng. Manage. 122 (1996) p. 125 26 Clay R.L. Grossmann I. E. Chem. Eng. Res. Des. 72 (1994) p. 415 27 CO-LaN: The CAPE-OPEN Laboratories Network (http://zann.informatik.rwthaachen,de:808O/opencms/opencms/COLANgamma/index.html) 28 Contaxis G. Kavantza S. IEEE Trans. Power Syst. 5 (1990) p. 766 29 Das B. P. Rickard J. G. Shah N. Macchietto S. Comput. Chem. Eng. 24 (2000) p. 1625 30 Demeulemeester E. Herroelen W. Manage. Sci. 43 (1997) p. 1485 31 A. D. Dimitriadis 2001 PhD thesis Title: Algorithmsfor the solution of large-scale Scheduling problems. Imperial College of science, Technology and Medicine 32 Gatica C. Papageorgiou L. G. Shah N. Chem. Eng. Res. Des. 81 (2003) p. 665 33 Geddes D. Kubera T. Comput. Chem. Eng. 24 (2000) p. 1645 34 Goel H. D. Grieuink]. Welj'nen M. P. C. Comput. Chem. Eng. 27 (2003) p. 1543 35 Gothe-Lundgren M. Lundgren]. T. Persson J. A. Int. J. Prod. Econ. 78 (2002) p. 255 36 Grunow M. Gunther H. Lehmann M. OR Spectrum 24 (2002) p. 281 37 Guan X . . Luh P. B. Discrete Event Dyn. Syst. Theor Appl. 9 (1999) p. 331 38 Guan X , Ni E. Li R. Luh P. B. IEEE Trans. Power Syst. 12 (1997) p. 1775 39 Hao S.Angelidis G. A. Singh H. Papakxopoulos A. D. IEEE Trans. Power Syst. 13 (1998) p. 986 40 Harjunkoski I. Grossmann I. E. Friedrich M. Holmes R. 2003. FOCAPO 2003 p. 315 41 Ha% A. C. 1978 Handbook of Operations Research Models and Applications

42 Hegazy B. T. Shabeeb A. K. Elbeltagi E.

Cheema T. J. Constr. Eng. Manage. 126 (2000) p. 414 43 Ierapetritou M. C. Floudas C. A. Vasantharaj a n S. Cullick A. S. AIChE J. 45 (1999) p. 844 4.4 Ierapetritou M. G. Pistikopoulos E. N. Ind. Eng. Chem. Res. 33 (1994) p. 1930 45 Ierapetritou M. G. Pistikopoulos E. N. Floudas C. A. Comput. Chem. Eng. 20 (1996) p. 1499 46 Iyer R. R. Grossmann I. E. Ind. Eng. Chem. Res. 37 (1998) p. 474 47 lyer R. R. Grossmann I . E. Vasantharajan S. Cullick A. S. Ind. Eng. Chem. Res. 37 (1998) p. 1380 48 lacobs R. F. Bendoly E. Eur. J. Oper. Res. 146 (2003) p. 233 49 Jain V. Grossmann I. E. Ind. Eng. Chem. Res. 38 (1999) p. 3013 50 Jia 2. Ierapetritou M. C. Ind. Eng. Chem. Res. 43 (2004), p. 3782 5 1 Kabore P. FOCAPO 2003 p. 285 52 KallrathJ. Trans. IChemE 78 (2000) p. 809 53 Kallrath]. OR Spectrum 24 (2002) p. 219 54 Kosmidis V. D. 2003 Ph.D. Thesis University of London U.K 55 Kosmidis V. D. PerkinsJ. D. Pistikopoulos E. N. 2002 In: Proceedings of ESCAPE-12 The Hague The Netherlands p 327. 56 LeBlanc L. ]. Shtub A. Anandnalingham G. Eur. J. Oper. Res. 112 (1999) p. 54 57 Lee H. Pinto]. M. Grossmann I . E. Park S. Ind. Eng. Chem. Res. 35 (1996) p. 1630 58 Levis A. A. Papageorgiou L. G. 28 (2004), p. 707 Comput. Chem. Eng. 59 Li C. Johnson R. B. Svaboda A. J. IEEE Trans. Power Syst. 12 (1997) p. 1834 60 Li C. Yan R. Zhou]. IEEE Trans. Power Syst. 5 (1990) p. 1487 61 Li P. Wendt M. WoznyG. 2003 FOCAPO 2003 p. 289 62 Lin X. Floudas C. A. Optimisation Eng. 4 (2003) p. 65 63 Liu M.L. Sahinidis N. V. Ind. Eng. Chem. Res. 34 (1995) p. 1662 64 Liu M.L. Sahinidis N. V. Comput. Oper. Res. 23 (1996a) p. 237 65 Liu M.L. Sahinidis N. V. Ind. Eng. Chem. Res. 35 (199613) p.4154 66 Liu L. Sahinidis N. V. Eur. J. Oper. Res. 100 (1997) p. 142 67 Luh P. B. Chen D. Tahur L. S. IEEE Trans. Robot. Autom. 15 (1999) p. 328 68 Mandal P. Gunasekaran A. Eur. J. Oper. Res. 146 (2003) p. 274 69 Maravelias C. T. Grossmann I. E. Ind. Eng. Chem. Res. 40 (2001) p. 6147

478

I

I Resource Planning 70 Maravelias C. T. Grossmann I . E. 28 (2004),

p. 1921 Comput. Chem. Eng. in press 71 M a w a l i M. K. C. M a H. Shahidehpour S. M . Abdul-Rahman H . IEEE Trans. Power Syst. 13 (1998)p. 1057 72 Mauderli A. Rippin D. W. T. Comput. Chem. Eng. 3 (1979) p. 199 73 McDonald C. M . Karimi I . A. Ind. Eng. Chem. Res. 36 (1997)p. 2691 74 Morad N. Zalzada A. J. Intel1 Manuf. 10 (1999)p. 169 75 Moro L. F. L. Comput. Chem. Eng. 27 (2003) p. 1303 76 Moro L. F. L. Zanin A. C. Pinto]. M. Comput. Chem. Eng. S22 (1998)p. S1039 77 Neiro S. M . S. Pinto]. M. Comput. Chem. Eng. 28 (2004), p. 871 78 Nilikari M. J. Ship Prod. 11 (1995)p. 239 79 Norton L. C. Grossmann I. E. Ind. Eng. Chem. Res. 33 (1994) p. 69 80 Nutdtasomboon N. Randhawa S. Comput. Ind. Eng. 32 (1996)p. 227 81 O h H. Karimi I. A . Comput. Chem. Eng. 25 (2001a)p. 1021 82 O h H . Karimi 1. A. Comput. Chem. Eng. 25 (2001b)p. 1031 83 Orlicky ]. 1975 Material Requirements Planning. McGraw Hill. New York 84 Oxe G. Eur. J. Oper. Res. 97 (1997)p. 337 85 Padilla E. M . Carr R. L. J. Constr. Eng. Manage. 117 (1991)p. 279 86 Papageorgiou L. G. 1994; Ph.D. Thesis University of London 87 Papageorgiou L. G. Pantelides C. C. Comput. Chem. Eng. 17s (1993) p. S27 88 Papageorgiou L. G. Pantelides C. C. Ind. Eng. Chem. Res. 35 (1996a)p. 488 89 Papageorgiou L. G. Pantelides C. C. Ind. Eng. Chem. Res. 35 (1996b)p. 510 90 Papageorgiou L. G. Rotstein G. E. Shah N. Ind. Eng. Chem. Res. 40 (2001)p. 275 91 Pelham R. Phams C. Hydrocarb. Process. 75 (1996)p. 89 92 Petkou S. B. Maranas C. D. Ind. Eng. Chem. Res. 36 (1997) p. 4864 93 Pinedo M . 2003 Scheduling: Theory Algorithms and Systems 2nd Edn. Prentice Hall, New Jersey 94 Pinto]. M . joly M. Moro L. F. L. Comput. Chem. Eng. 24 (2000) p. 2259 95 Pistikopoulos E. N. Vassiliadis C. G. Arvela ]. A. Papageorgiou L. G. Ind. Eng. Chem. Res. 40 (2001)p. 3195 96 Reeves C. R. 1995 Modern Heuristic Techniques for Combinatorial Problems Wiley

97 Reklaitis G. V. 1991 Proceedings of the 4th

International Symposium on Process Systems Engineering Montebello Canada 98 Reklaitis G. V. 1992 NATO Advanced Study Institute on Batch Processing Systems Eng. Antalya Turkey 99 Rickard]. G. Macchietto S. Shah N. Comput. Chem. Eng. S23 (1999) p. S539 100 Rigby B. Lasdon L. S. Waren A. D. Interfaces 25 (1995) p. 64 101 Rodera H . Bagajewicz M . J . Tsafalis T. B. Ind. Eng. Chem. Res. 41 (2002) p. 4075 102 Rodrigues M . M . Latre L. G. Rodrigues L. A. Comput. Chem. Eng. 24 (2000)p. 2247 103 Roger M. ]. Gupta A. Maranas C. D.Ind. Eng. Chem. Res. 41 (2002) p. 6607 104 Romero J. Badell M. Bagajewicz M. Puigjaner L. Ind. Eng. Chem. Res. 42 (2003) p. 6125 105 RyuJ.-H. Dua V. Pistikopoulos E. N. Comput. Chem. Eng. 28 (2004),p. 1121 106 Sahinidis N. V. Comput. Chem. Eng. 28 (2004),p. 971 107 Sahinidis N. V. Grossmann I. E. Ind. Eng. Chem. Res. 30 (1991) p. 1165 108 Sahinidis N. V. Grossmann I. E. Fornari R. E. Chathrathi C. Comput. Chem. Eng. 13 (1989) p. 1049 109 Sunmarti E. Espuna A. Puigjaner L. Comput. Chem. Eng. S19 (1995)p. S565 110 Savin D. Alkass S. Fazio P. J. Comput. Civ. Eng. 12 (1998)p. 241 111 Schmidt C.W. Grossmann I. E. Ind. Eng. Chem. Res. 35 (1996)p. 3498 112 Seibert]. E. Evans G. W. J , Constr. Eng. Manage. 117 (1991)p. 503 113 Senousi A. B. Adeli H. J. Constr. Eng. Manage. 127 (2001) p. 28 114 Shah N. Comput. Chem. Eng. S20 (1996) p. S1227 115 Shah N. AIChE Symp Ser. 1998 No. 320 94 75 116 Shah N . Comput. Chem. Eng. 28 (2004),p. 929 117 Shah N. Pantelides C. C. Ind. Eng. Chem. Res. 30 (1991) p. 2308 118 Shah N. Pantelides C. C. Ind. Eng. Chem. Res. 31 (1992) p. 1325 119 Shah N. Pantelides C. C. Sargent R. W. H . Ann. Oper. Res. 42 (1993) p. 193 120 ShapiroJ.F. Eur. J. Oper. Res. 118 (1999) p. 295 121 Shapiro]. F. Comput. Chem. Eng. 28 (2004), p. 855 122 Shobrys D. E. White D. C. Comput. Chem. Eng. 26 (2002) p. 149

123 Stockton D. ]. Quinn L. Proc. Inst. Mech.

136 van den Heever S. A. Grossmann 1. E. Vasan-

Eng. 209(3) (1995) p. 201 124 Subrahmanyam S. Pekny]. F. Reklaitis G. V. Ind. Eng. Chem. Res. 33 (1994) p. 2668 125 Subrahmanyam S. Pekny ]. F. Reklaitis G. V. Ind. Eng. Chem. Res. 35 (1996) p. 1866 126 Subramanian D. Pekny]. F. Reklaitis G. V. AIChE J. 47 (2001) p. 2226 127 Sung C. S. Lim S. K. Comput. Ind. Eng. 1 2 (1996) p. 227 128 Suryadi H. Papageorgiou L. G. Int. J. Prod. Res. 42 (2004) p. 355 129 Takriti S. Birge]. Long E. IEEE Trans. Power Syst. 11 (1996) p. 1497 130 Tsiakis P. Rickard ]. G. Shah N. Pantelides C. C. 2003 AlChE Annual Conference San Francisco California USA 131 Tsiakis P. Dimitriadis A. D. Shah N. Pantelides C. C. 2000 AlChE Annual Conference Los Angeles California U S A 132 Tsiroukis A.G. Papageorgaki S. Reklaitis G. V. Eng. Chem. Res. 32 (1993) p. 3037 133 van den Heever S. A. Grossmann I. E. Ind. Eng. Chem. Res. 39 (2000) p. 1955 134 van den Heever S. A. Grossmann 1. E. Comput. Chem. Eng. 27 (2003) p. 1813 135 van den Heever S. A. Grossmann I. E. Vasantharajan S. Edwards K. Comput. Chem. Eng. 24 (2000) p. 1049

tharajan 5’. Edwards K. Ind. Eng. Chem. Res. 40 (2001) p. 2857 137 Voudouris T. V. Grossmann 1. E. Ind. Eng. Chem. Res. 32 (1993) p. 1962 138 Wang 5’. J. Shahidehpour S. M. Kirschem D. S. Mokhtari S. lrissari G. D. I E E E Trans. Power Syst. 10 (1995) p. 1294 139 Wdlons M. C. Reklaitis G. V. Comput. Chem. Eng. 13 (1989a) p. 201 140 Wellons M. C. Reklaitis G. V. Comput. Chem. Eng. 13 (1989b) p. 213 141 Weflons M. C. Reklaitis G. V. Ind. Eng. Chem. Res. 30 (1991a) p. 671 142 Wellons M. C. Reklaitis G. V. Ind. Eng. Chem. Res. 30 (1991b) p. 688 143 Wight 0. 1984 Manufacturing Resource Planning: MRP-I1 Wight Williston 144 Wilkinson S. ]. 1996 PhD Thesis University of London 145 Wilkinson S. /. Shah N. Pantelides C. C. Comput. Chem. Eng. 19 (1995) p. S583 146 Wilson]. M. Eur. J. Oper. Res. 149 (2003) p. 430 147 Wu D. Ierapetritou M. G. 2003. FOCAPO 2003 p. 257 148 Yin K. K. Liu H . 2003. FOCAPO 2003 p. 261

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

2 Production Scheduling Nihy Shah

2.1

Introduction

The theme of production planning and scheduling has been the subject of great attention in the recent past. Initially, especially from the early 1980s to the early 199Os, this was due to the resurgence in interest in flexible processing either as a means of ensuring responsiveness or of adapting to the trends in chemical processing towards lower volume, higher-value-addedmaterials in the developed economies (Reklaitis 1991, Rippin 1993, Hampel 1997). More recently, the topic has received a new impetus as enterprises attempt to optimize their overall supply chains in response to competitive pressures or to take advantage of recent relaxations in restrictions on global trade, as well as the information storage and retrieval capabilities provided by ERP systems. It is widely recognized that the complex problem of what to produce and where and how to produce it is best considered through an integrated, hierarchical approach that also acknowledges typical corporate structures and business processes. This type of structure is illustrated in Figure 2.1. In the most general case, the extended supply chain is taken to mean the multienterprise network of manufacturing facilities and distribution points that perform the functions of materials procurement, transformation into intermediate and finished materials and distribution of the finished products to customers. The most common context for planning at the supply-chain level is the coordination of manufacturing and distribution activities across multiple sites operated by a single enterprise (enterprise-wide or multisite planning). Here, the aim is to make the best use of geographically distributed resources over a certain time period. The result of the multisite planning problem is typically a set of production targets for each of the individual sites, and rough transportation plans for the network as a whole. The production scheduling activity at each individual site seeks to determine precisely how these targets can be met (or indeed how best to compromise them if they cannot be met in whole). This involves determining the precise details of resource allocation over time. Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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EnterpriweESupply chain manning

Process operations hierarchy

_ J * Single Site Production Plannmg

+

On-line Scheduling

.f

Supervisory ContraUMonitoring

1

Regulatory Control

I

Once a series of activities has been determined, these must be implemented in the plant. The role of the supervisory control system is to initiate the correct sequences of control logic with the correct parameters at the correct time, making sure that conflicts for plant resources are resolved in an orderly manner. It is also useful at this level to create a schedule of planned operations over a short future interval using a model detailed enough to ensure that there are no anticipated resource conflicts. This “online” scheduling allows current estimates of the starting and finishing times of each operation to be known at any time. Although this capability is not essential for the execution of operations in the plant, it is vital if the hierarchical levels are to be integrated so that production scheduling is performed in response to deviations in expected plant operation (“reactivescheduling”). Finally, the lowest levels of the hierarchy relate to execution of individual control phases and ensuring safe and economic operation of the plant.

2.1.1 Why Is Scheduling Important?

The planning function aims to optimize the economic performance of the enterprise as it matches production to demand in the best possible way. The production scheduling component is of vital importance as it is the layer which translates the economic imperatives of the plan into a sequence of actions to be executed on the plant, so as to deliver the optimized economic performance predicted by the higher-level plan.

2 2 The Single-Site Production Scheduling Problem

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2.1.2 Challenges in Scheduling

There is clearly a need for research and development in all the levels of the operations hierarchy. Four previous reviews in this area (Reklaitis 1991, Rippin 1993, Shah 1998, Kallrath 2002a) summarized some of the main challenges as: 0

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the development of efficient general-purpose solution methods for the mixedinteger optimization problems that arise in planning and scheduling; the design of tailored techniques for the solution of specific problem structures, which either arise out of specific types of scheduling problems or are embedded substructures in more general problems; the design of algorithms for efficient solution of general resource constrained problems, especially those based on a continuous representation of time; the development of hybrid methods based on optimization and constraint propagation methods; the development of commercially available software packages for optimizationbased scheduling (as distinct from planning); the systematic treatment of uncertainty; the advancement of online techniques for rapid adaptation of operations; the development of methods for the integrated planning and scheduling of multisite systems.

Multisite and supply-chain planning and scheduling is dealt with in section 5.7, and the focus here is on scheduling at a single site. Progress towards these challenges will be described. The remainder of this chapter is organized as follows: Section 2.2 describes the problem in more detail. Sections 2.3-2.9 review research into alternative solution methods for scheduling problems, both with deterministic and uncertain data, and Section 2.10 describes some successful industrial applications of advanced scheduling methods. The remaining sections list some new application domains and describe conclusions drawn.

2.2 The Single-Site Production Scheduling Problem

The scheduling problem at a single site is usually concerned with meeting fairly specific production requirements. Customer orders, stock imperatives or higher-level supply chain or long-term planning would usually set these requirements, as described in subsequent sections. It is concerned with the allocation over time of scarce resources between competing activities to meet these requirements in an efficient fashion. The data required to describe the scheduling problem typically include: 0

Production recipes: details of how each product is to be produced, including details of production of intermediates. This will include material balance information, resource requirements, processing times/rates of the process tasks, etc.

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Resource data: for process equipment, storage equipment, utilities (capacities, capabilities, availabilities, costs, etc.) Material data: stability, opening inventories, anticipated receipts of raw materials/ intermediates. Demand data: time horizon of interest, firm orders, forecasted demands, sales prices.

The key components of the scheduling problem are resources, tasks and time. The resources need not be limited to processing equipment items, but may include material storage equipment, transportation equipment (intra- and interplant), operators, utilities (e.g., steam, electricity, cooling water), auxiliary devices and so on. The tasks typically comprise processing operations (e.g., reaction, separation, blending, packaging) as well as other activities that change the nature of materials and other resources such as transportation, quality control, cleaning, changeovers, etc. There are both external and internal elements to the time component. The external element arises out of the need to coordinate manufacturing and inventory with expected product lifings or demands, as well as scheduled raw material receipts and even service outages. The internal element relates to executing the tasks in an appropriate sequence and at the right times, taking account of the external time events and resource availabilities. Overall, this arrangement of tasks over time and the assignment of appropriate resources to the tasks in a resource-constrained framework must be performed in an efficient fashion, which implies the optimization, as far as possible, of some objective. Typical objectives include the minimization of cost or maximization of profit, maximization of customer satisfaction,minimization of deviation from target performance, etc. Generally speaking, depending on raw material lead times, production lead times, forecast accuracy and other similar factors, production scheduling is driven either by firm customer orders (“make-to-order”)or forecasted demands (“make-to-stock”). As noted by Gabow (1983), all but the most trivial scheduling problems belong to the class of NP hard (Non-deterministic Polynomial-timehard) problems; there are no known solution algorithms that are of polynomial complexity in the problem size. This has posed a great challenge to the research community, and a large body of work aiming to develop either tailored algorithms for specific problem instances or efficient general-purpose methods has arisen. Solving the scheduling problem requires methods that search through the decision space of possible solutions. The search processes can be classified as follows: 0

0

Heuristic: a series of rules (e.g., the sequence of production should be based on order due-dates) are used to generate alternative schedules. Metaheuristic: higher level generic search algorithms (e.g., simulated annealing, genetic algorithms) are used to explore the decision space. Mathematical programming: the scheduling problem is posed as a formal mathematical optimization problem and solved using general-purpose or tailored methods (see section 4.2).

2.2 The Single-Site Production Scheduling Problem

The research into production scheduling techniques may be further subdivided into specific and general application domains. The latter division is intended to reflect the scope of the technique (in terms of plant structure and process recipes). Rippin (1993) classified different flexible plant structures as follows: 0

0

Multiproduct plants, where each product has the same processing network, i.e., each product requires the same sequence of processing tasks (often known as “stages”). Owing to the historic association between the work on batch plant scheduling and that on discrete parts manufacturing, these plants are sometimes called “flowshops”. Multipurpose plants (“jobshops”),where the products are manufactured via different processing networks, and there may be more than one way in which to manufacture the same product. In general, a number of products undergo manufacture at any given time.

In addition to the process structure, the storage policies for intermediate materials are critical in production scheduling, especially for batch plants. Any intermediate material can usually be classified as being subject to one of five intermediate storage policies: 0

0

0

0

0

Zero-wait (ZW): the material is not stable and must be processed further upon production. No intermediate storage (NIS): the material is stable, but no storage vessels are provided. However, it may reside temporarily in the processing equipment that produced it before being processed further. Shared intermediate storage (SIS): the material is stable, and may be stored in one or more storage vessels that may also be used to store other materials (though not at the same time). Finite intermediate storage (FIS): the material is stable, and one or more dedicated storage vessels are available. Unlimited intermediate storage (UIS): the material is stable, and one or more dedicated storage vessels are available, the total capacity of which is effectively unlimited.

The importance of these is clearly evident from the following example. Consider a process whereby a material C, is made from raw material A, via the following reactions: A -+ B (reaction 1, duration 3 h) B -+ C (reaction 2, duration 1 h)

Reaction 1takes place in reactor 1 (capacity 10.000 kg) and reaction 2 takes place in reactor 2 (capacity 5000 kg). The average production rate of C depends strongly on the storage policy for B. The rates for the ZW, NIS and UIS cases are calculated below.

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2.2.1 ZW Case

Here, only 5000 kg of A can be loaded into reactor 1,because once this batch is complete, it must be immediately transferred to reactor 2, which limits the size of the batch. A sample operating schedule is shown in Figure 2.2.

Figure 2.2

Sample schedule for the zero-wait (ZW) case

According to the schedule, 5000 kg of C is produced every 3 h, so the average production rate is 1667 kg h-'.

2.2.2 NIS Case

Here, 10.000 kg of A can be loaded into reactor 1. After the reaction is complete, 5000 kg of B can be transferred to reactor 2, and 5000 is held in reactor 1for an extra hour before being transferred to reactor 2. A sample operating schedule is shown in Figure 2.3.

Figure 2.3

Sample schedule for the no intermediate storage (NIS) case

In this case, 10.000 kg of C is produced every 4 h, so the average production rate is 2500 kg h-'.

2.2.3 UIS Case

In this case, there is sufficient storage (e.g., 10.000 kg) to decouple the operation of reactor 1 and reactor 2 completely. The production rate is then limited by the bottleneck stage; in this case reactor 1. A sample operating schedule is shown in Figure 2.4.

Figure 2.4 Sample schedule for the unlimited intermediate storage (UIS) case

2.3 Heuristics/Metaheuristics: Spec$% Processes

Here, 10.000 kg of C is produced every 3 h; the production rate is 3333 kg h-’. The above discussion serves to define categories for scheduling techniques and categories for process structures. The next sections review developments in the solution of scheduling problems and are organized along the categories listed above.

2.3 Heuristics/Metaheuristics: Specific Processes

Most scheduling heuristics are concerned with formulating rules for determining sequences of activities. They are therefore best suited to processes where the production of a product involves a prespecified sequence of tasks with fixed batch sizes; in other words, variants of multiproduct processes. Often, it is assumed that fixing the front-end product sequence will fuc the sequence of activities in the plant (the socalled permutation schedule assumption; see Figure 2.5). Generally, the processing of a product is broken down into a sequence of jobs that queue for machines, and the rules dictate the priority order of the jobs. Dannebring (1977), Kuriyan and Reklaitis (1985, 1989) and Pinedo (1995) give a good exposition on the kinds of heuristics (dispatching rules) that may be used for different plant structures. Typical rules involve ordering products (see, e.g., Hasebe et al. 1991) by processing time (either shortest or longest), due dates and so on. Most of the heuristic methods originated in the discrete manufacturing industries, and might be expected not to perform as well in process industry problems, because in the latter material is infinitely divisible and batch sizes are variable (unlike discrete “jobs”). Furthermore, batch splitting and mixing are allowed and are becoming increasingly popular as a means of effecting late product differentiation. Stochastic search approaches (“metaheuristics”)are based on continual improvement of trial solutions by the application of an evolutionary algorithm which modifies solutions and prioritizes solutions from a list for further consideration. The two main evolutionary algorithms applied to this area are simulated annealing and genetic algorithms. An early application of simulated annealing to batch process scheduling problems was undertaken by Ku and Karimi (1991), where they applied the algorithm to multiproduct plant scheduling. They concluded that such algorithms are easy to implement and tended to perform better than conventional heuristics, but often required significant computational effort. Xia and Macchietto (1997) described the application of simulated annealing and genetic algorithm techniques to the scheduling of multiproduct plants with complex material transfer policies. More recently, Murakami et al. (1997) described a repetitive simulated annealing procedure which avoids local minima by using many starting points with fewer evolutionary iterations per starting point. ._

Figure 2.5

Permutation schedule

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Sunol et al. (1992) described the application of a genetic algorithm approach to a simple flowshop sequencing problem, and found the technique to be superior to explicit enumeration. As noted by Hasebe et al. (1996),the performance of a genetic algorithm depends on the operators used to modify trial solutions. They applied a technique that selects appropriate operators during the solution procedure for the scheduling of a parallel-unit process. Overall, the stochastic search processes are best applied to problems of an entirely discrete nature, where an objective function can be evaluated quickly. The classic example is the sequencing and timing of batches in a multiproduct plant, where the decision variables are the sequence of product batches, and the completion time of any candidate solution is easily evaluated through recurrence relations or minimax algebra. The main disadvantages are that it is difficult to consider general processes, and inequality constraints and continuous decisions, although some recent work (e.g., Wang et al. 2000) aims at addressing this.

2.4 Heuristics/Metaheuristics: General Processes

The problem of scheduling in general multipurpose plants is complicated by the additional decisions (beyond the sequencing of product batches) of assignment of equipment items to processing tasks, task batch sizes and intermediate storage utilization. It is difficult to devise a series of rules to resolve these, and there are therefore few heuristic approaches reported for the solution of this problem. Kudva et al. (1994) consider the special case of “linear”multipurpose plants, where products flow through the plant in a similar fashion, but potentially using different stages and with no recycling of material. A rule-based constructive heuristic is used, which requires the maintenance of a status sheet on each unit and material type for each time instance on a discrete-time grid. The algorithm uses this status sheet with a sorted list of orders and develops a schedule for each order by backwards recursive propagation. The schedule derived depends strongly on the order sequence. Solutions were found to be within acceptable bounds of optimality when compared with those derived through formal optimization procedures. Graells et al. (1996) presented a heuristic strategy for the scheduling of multipurpose batch plants with mixed intermediate storage policies. A decomposition procedure is employed where subschedules are generated for the production of intermediate materials. Each subschedule consists of a mini production path determined through a branch-and-cut enumeration of possible unit-to-taskallocations. The minipaths are then combined to form the overall schedule. The overall schedule is checked for feasibility with respect to material balances and storage capacities. Improvements to the schedules may be effected manually through an electronic Gantt chart or through a simulated annealing procedure. Lee and Malone (2000) describe the application of a simulated annealing metaheuristic to a variety of batch process planning problems. Here, intermediate products, inventory costs and a variety of process flow networks can be represented.

2.5 Mathematical Programming: Specific Processes

As mentioned earlier, the application of heuristics to such problems is not straightforward. Although this effectively represents current industrial practice, most academic research has been directed towards the development of mathematical programming approaches for multipurpose plant scheduling. As will be described later, these approaches are capable of representing all the complex interactions present.

2.5 Mathematical Programming: Specific Processes

Here, we shall first outline some of the features of mathematical programming approaches in general, and then consider their application to processes other than the general multipurpose one. The latter will be considered in the Section 2.6. Mathematical programming approaches to production scheduling in the process industries have received a large amount of attention recently. This is because they bring the promise of generality (i.e., ability to deal with a wide variety of problems), rigor (the avoidance of approximations) and the possibility of achieving optimal or nearoptimal solutions. The application of mathematical programming approaches implies the development of a mathematical model and an optimization algorithm. Most approaches aim to develop models that are of a standard form (from linear programming (LP) models for refinery planning to mixed-integer nonlinear programming (MINLP) models for multipurpose batch plant scheduling). These may then be solved by standard software or specialized algorithms that take account of problem structure. The variables of the mathematical models will tend to include some or all of the following choices, depending on the complexity considered: 0 0 0 0 0

sequence of products or individual tasks timing of individual tasks in the process selection of resources to execute tasks at the appropriate times amounts processed in each task inventory levels of all materials over time.

The discrete nature of some of the variables (sequencing and resource selection) implies that binary or integer-valuedvariables will be required. The selection of values for all the variables will be subject to some or all of the following constraints: 0

0

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nonpreemptive processing: once started, processing activities must proceed until completion; resource constraints: at any time, the utilization of a resource must not exceed its availability; material balances; capacity constraints: processing and storage; orders being met in full by their due dates.

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Finally, optimization methods dictate that an objective function be defined. This is usually of an economic form, involving terms such as production, transition and inventory costs and possibly revenues from product sales. A very good review of mathematical programming techniques applied to scheduling and an associated classification of methods and models is provided by Pinto and Grossmann (1998). A critical feature of mathematical programming approaches is the representation of the time horizon. This is important because activities interact through the use of resources; therefore, the discontinuities in the overall resource utilization profiles must be tracked with time, to be compared with resource availabilities to ensure feasibility. The complexity arises because these discontinuities (unlike discontinuities in availabilities) are functions of any schedule proposed and are not known in advance. The two approaches for dealing with this are: 0

0

Discrete-time (or “uniform discretization”):the horizon is divided into a number of equally spaced intervals so that any event that introduces such discontinuities (e.g., the starting of a task or a due date for an order) can only take place at an interval boundary. This implies a relatively fine division of the time grid, so as to capture all the possible event times, and in the solution to the problem it is likely that many grid points will not actually exhibit resource utilization discontinuities. Continuous time (or “nonuniform discretization”): here, the horizon is divided into fewer intervals, the spacing of which will be determined as part of the solution to the problem. The number of intervals will correspond more closely to the number of resource utilization discontinuities in the solution.

In addition to the above, another attribute of time representation is whether the same grid is used for all major equipment items in the plant (the “common grid” approach) or whether each major equipment item operates on its own grid (the “individual resource grid”, only used with continuous-time models). Generally speaking, the former approach is more suitable for processes in which activities on the major equipment items also interact with common resources (materials, services, etc.) and the latter where activities on the major equipment items are quite independent in their interactions with common resources. These distinctions will become clearer when individual pieces of research are discussed. The distinctions between these representations are shown in Figures 2.6 and 2.7. The simplest specific scheduling process is probably a single production line which produces one product at time in a continuous fashion. Work in this area has been directed towards deriving cyclic schedules (where the production pattern is

1 unit2 1 unit3 1 unit4 1 unit1

1 1 1 1

Figure 2.6

Discrete-time representation

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2.5 Mathematical Programming: Specific Processes

1 - 1 unit2 1 - 1 unit3 1 - 1 unit1

4 - 1

unit4

individual resource grid Figure 2.7

Continuous-time representations

common grid

repeated at a fixed frequency) that balance inventory and transition costs by determining the best sequence of products and their associated run-lengths or lot-sizes.A review of this so-called economic lot scheduling problem is given by Elmaghraby (1978). Sahinidis and Grossmann (1991) consider the more general problem of the cyclic scheduling of a number of parallel multiproduct lines, where each product may in principle be produced on more than one line and production rates and costs vary between lines. They utilize a continuous-time individual resource grid model, which turns out to be a MINLP. This includes an objective function that includes combined production, product transition and inventory costs for a constant demand rate for all products. Their work was extended by Pinto and Grossmann (1994),who considered the case of multiple production lines, each consisting of a series of stages decoupled by intermediate storage and operating in a cyclic mode. Each product is processed through all stages, and each product is processed only once at each stage. The model again uses a continuous-time model, and it is possible to use the independent grid approach despite the fact that stages interact through material balances; this is due to the special structure of the problem. A number of mathematical programming approaches have been developed for the scheduling of multiproduct batch plants. All are based (either explicitly or implicitly) on a continuous representation of time. Pekny et al. (1988)considered the special case of a multiproduct plant with no storage (zero wait (ZW)) between operations. They show that the scheduling problem has the same structure as the asymmetric traveling salesman problem, and apply an exact parallel computation technique employing a tailored branch-and-bound procedure which uses an assignment problem to provide problem relaxations. The work was extended to cover the case of product transition costs, where the problem structure is equivalent to the prize-collecting traveling salesman problem (Pekny et al. 1990),and LP relaxations are used. For both cases, problems of very large magnitude were solved to optimality with modest computational effort. Gooding et al. (1994) augmented this work to cover the case of multiple units at each stage (the so-called “parallel flowshop” stage). A more complete overview of the development of algorithms for classes of problems (“algorithm engineering”) is given by Applequist et al. (1997)and a commercial development in this area is described by Bunch (1997). Birewar and Grossmann (1989) developed a mixed-integer programming model for a similar type of plant. They show that through careful modeling of slack times,

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and by exploiting the fact that relatively large numbers of batches of relatively few products will be produced (which allows end-effects to be ignored), a straightforward LP model can be used to minimize the makespan. The result is a family of schedules from which an individual schedule may be extracted. They extend the work to cover simultaneous long-term planning and scheduling, where the planning function takes account of scheduling limitations (Birewar and Grossmann 1990). Pinto and Grossmann (1995) describe a mixed-integer linear programming (MILP) model for the minimization of earliness of orders for a multiproduct plant with multiple equipment items at each stage. The only resources required for production are the processing units. Pinto and Grossmann (1997)then augmented the model to take account of interactions between processing stages and common resources (e.g., steam). Rather than utilize a common grid, they retained individual grids, and accounted for the resource discontinuities through complex mixed-integer constraints which weakened the model and resulted in large computational times. They therefore proposed a hybrid logic-based/MILP algorithm where the disjunctions relate to the relative timing of orders. This dramatically reduces the computational effort expended. Moon et al. (1996)also developed a MILP model for ZW multiproduct plants. The objective was to assign tasks to sequence positions so as to minimize the makespan, with nonzero transfer and set-up times being included. The extension of the work to more general intermediate storage policies was described by Kim et al. (199G),who proposed several MINLP formulations based on completion time relations. The case of single-stage processes with multiple units per stage has been considered by Cerda et al. (1997)and McDonald and Karimi (McDonald and Karimi, 1997; Karimi and McDonald, 1997). Both describe continuous-time-based MILP models. Cerda et al. focus on changeovers and order fulfilment, while Karimi and McDonald focus on semicontinuous processes and total cost (transition, shortage and inventory) with the complication of minimum run lengths. A characteristic of both approaches is that discrete demands must be captured on the continuous-time grid. Mkndez and Cerdi (2000) developed a MILP model for a process with a single production stage with parallel units followed by a storage stage with multiple units, with restricted connectivity between the stages. This was extended to the multistage case with general production resources by Mendez et al. (2001). In common with other models, there are no explicit time slots in the model; the key variables are allocations of activities to units and the relative orderings of activities. The work described above all relates to special process structures, which means that mathematical models can be designed specifically for the problem class. This ensures that, despite the typical concerns about computational complexity of discrete optimization problems, solutions are available with reasonable effort. The drawback of the work is its limited applicability. Nevertheless, several models appear to have been developed with specific industrial applications in mind (e.g., Sahinidis and Grossmann (1991a), Pinto and Grossmann (1995) and Karimi and McDonald (1997)).

2.G Mathernatica/ Programming: Multipurpose Plants

2.6 Mathematical Programming: Multipurpose Plants

A large portion of the most recent research in planning and scheduling undertaken by the process systems community relates to the development of mathematical programming approaches applied to multipurpose plants. As intimated earlier, in this case the application domain tends to imply the solution approach: mathematical models are the best way of representing the complex interactions between resource allocations, task timings, material flows and equipment capacities. Much of the recent work reported in the literature deals with this class of problem. The work in this are can be characterized by three different assumptions about plant operation: 0

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0

The unique assignment case: each task can only be performed by a unique piece of equipment, and there are no optional tasks in the process recipe and batch sizes are usually fured. The campaign mode of operation: the horizon is divided into relatively long campaigns, and each campaign is dedicated to one or a few products. Short-term operation: products are produced as required and no particular scheduling pattern may be assumed.

The first assumption is particularly restrictive. The second relates to a mode of operation that is becoming relatively scarce, as it implies a low level of responsiveness. One sector in which campaign operation is still prevalent is in the manufacture of active ingredients for pharmaceuticals and agrochemicals. The short-term mode of operation is tending to become the most prevalent elsewhere, as it best exploits operational flexibility to meet changing external circumstances. Mauderli and Rippin (1979) developed a procedure for campaign planning which attempts to optimize the allocation of equipment to tasks. An enumerative procedure (based on different equipment-to-task allocations) is used to generate possible singleproduct campaigns which are then screened by LP techniques to select the dominant ones. A production plan is then developed by the solution of a MILP that sequences the dominant campaigns and fixes their lengths. The disadvantages of this work are the inefficiency of the generation procedure and the lower level of resource utilization implied by single-product campaigns. Wellons and Reklaitis (1991a,b) addressed this through a formal MINLP method to generate campaigns and production plans in a two-stage procedure, as did Shah and Pantelides (1991) who solved a simultaneous campaign generation and production planning problem. An early application of mathematical programming techniques for short-term multipurpose plant scheduling was the MILP approach of Kondili et al. (1988). They used a discrete representation of time, and introduced the state-task network (STN) representation of the process (see Figure 2.8). The STN representation has three main advantages: 0

It distinguishes the process operations from the resources that may be used to execute them, and therefore provides a conceptual platform from which to relax the unique assignment assumption and optimize unit-to-task allocation.

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React

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Figure 2.8 Example of a state-task network. Circles: material states, rectangles: tasks

It avoids the use of task precedence relations, which become very complicated in multipurpose plants: a task can be scheduled to start if its input materials are available in the correct amounts and other resources (processing equipment and utilities) are also available, regardless of the plant history. It provides a means of describing very general process recipes, involving batch splitting and mixing and material recycles, and storage policies including ZW, NIS, SIS and so on.

The formulation of Kondili et al. (1988) (described in more detail in Kondili et al. (1993))is based on the definition of binary variables that indicate whether tasks start in specific pieces of equipment at the start of each time period, together with associated continuous batch sizes. Other key variables are the amount of material in each state held in dedicated storage over each time interval, and the amount of each utility required for processing tasks over each time interval. Their key constraints related to equipment and utility usage, material balances and capacity constraints. The common, discrete-time grid captures all the plant resource utilizations in a straightforward manner; discontinuities in these are forced to occur at the predefined interval boundaries. Their approach was hindered in its ability to handle large problems by the weakness of the allocation constraints and the general limitations of discrete-time approaches, such as the need for relatively large numbers of grid points to represent activities with significantly different durations. Their work formed the basis of several other pieces of research aiming to take advantage of the representational capabilities of the formulation while improving its numerical performance. Sahinidis and Grossmann (1991b)disaggregated the allocation constraints and also exploited the embedded lot-sizing nature of the model where relatively small demands are distributed throughout the horizon. They disag gregate the model in a fashion similar to that of Krarup and Bilde (1977),who were able to improve the solution efficiency despite the larger nature of the disaggregated model. This was due to a feature particular to mixed-integer problems: other things being equal, the computational effort for problem solution through standard procedures is dictated mainly by the difference between the optimal objective function and the value of the objective function obtained by solving the continuous relaxation where bound constraints rather than integrality restrictions are imposed on the integer variables (the so-called “integralitygap”).The formulation of Sahinidis and Grossmann (1991b) was demonstrated to have a much smaller integrality gap than the original. Shah et al. (1993a)modified the allocation constraints even further to generate the smallest possible integrality gap for the type of formulation. They also devised a tai-

2.6 Mathematical Programming: Multipurpose Plants

lored branch-and-boundsolution procedure which utilizes a much smaller LP relaxation and solution processing to improve integrality at each node. The same authors (Shah et al. 1993b) considered the extension to cyclic scheduling, where the same schedule is repeated at a frequency to be determined as part of the optimization. This was augmented by Papageorgiou and Pantelides (1996a,b) to cover the case of multiple campaigns, each with a cyclic schedule to be determined. Elkamel (1993) also proposed a number of measures to improve the performance of the STN-based discrete-time scheduling model. A heuristic decomposition method was proposed, which solves separate scheduling problems for parts of the overall scheduling problem. The decomposition may be based on the resources (“longitudinal decomposition”) or on time (“axial decomposition”). In the former, the recipes and suitable equipment for each task are examined for the possible formation of unique task-unit subgroups which can be scheduled separately. Axial decomposition is based on grouping products by due dates and decomposing the horizon into a series of smaller time periods, each concerned with the satisfaction of demands falling due within it. He also described a perturbation heuristic, which is a form of local search around the relaxation. Elkamel and Al-Enezi (1998) describe valid inequalities that tighten the MILP relaxations of this class of model. Yee and Shah (1997, 1998) and Yee (1998) also considered various manipulations to improve the performance of general discrete-time scheduling models. A major feature of their work is variable elimination. They recognize that in such models, only about 5-15 % of the variables reflecting task-to-unit allocations are active at the integer solution, and it would be beneficial to identify as far as possible inactive variables prior to solution. They describe a LP-based heuristic, a flexibility and sequence reduction technique and a formal branch-and-price method. They also recognize that some problem instances result in poor relaxations and propose valid inequalities and a disaggregation procedure similar to that of Sahinidis and Grossmann (1991b) for particular data instances (Romero and Puigjaner (2004)). Bassett et al. (1996) and Dimitriadis et al. (1997a, 1997b) describe decompostion-based approaches which solve the problems in stages, eventually generating a complete solution. Blomer and Giinther (1998)also introduced a series of LP-based heuristics that can reduce solution times considerably, without compromising the quality of the solution obtained. Grunow et al. (2002) show how the STN tasks can be aggregated into higher level processes for the purposes of longer-term campaign planning. Gooding (1994) considers a special case of the problem with firm demands and dedicated storage only. The scheduling model is described in a digraph form where nodes correspond to possible task-unit-time allocations and arcs the possible sequences of the activities. The explicit description of the sequence in this form addresses one of the weaknesses of the discrete-time formulation of Kondili et al. (1988, 1993),which was that it did not model sequence-dependent changeovers very well. Gooding’s (1994) model therefore performed relatively well in problems with a strong sequencing component, but suffers from model complexity in that all possible sequences must be accounted for directly.

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Pantelides et al. (1995)reported a STN-based approach to the scheduling of pipeless plants, where material is conveyed between processing stations in movable vessels. This requires the simultaneous scheduling of the movement and processing operations. Pantelides (1994)presented a critique of the STN and associated scheduling formulations. He argued that despite its advantages, it suffers from a number of drawbacks: 0

0

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The model of plant operation is somewhat restricted: each operation is assumed to use exactly one major item of equipment throughout its operation. Tasks are always assumed to be processing activities which change material states: changeovers or transportation activities have to be treated as special cases. Each item of equipment is treated as a distinct entity: this introduces solution degeneracy if multiple equivalent items exist. Different resources (materials, units, utilities) are treated differently, giving rise to many different types of constraints, each of which must be formulated carefully to avoid unnecessarily increasing the integrality gap.

He then proposed an alternative representation, the resource-task network (RTN), based on a uniform description of all resources (Figure 2.9). In contrast to the STN approach, where a task consumes and produces materials while using equipment and utilities during its execution, in this representation, a task is assumed only to consume and produce resources. Processing items are treated as though consumed at the start of a task and produced at the end. Furthermore, processing equipment in different conditions (e.g., “clean” or ”dirty“) can be treated as different resources, with different activities (e.g., ”processing”or “cleaning”)consuming and generating them this enables a simple representation of changeover activities. Pantelides (1994) also proposed a discrete-time scheduling formulation based on the RTN that, due to the uniform treatment of resources, only requires the description of three types of constraint, and does not distinguish between identical equipment items (which results in more compact and less degenerate optimization

-

*-.. \

.y / Resources

rc-3-4

-*% 1 -T

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.

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The resource-task network representation

*

Protluchon Cleanrn~changeover Transportation

A

Figure 2.9

l

Tasks

Feed\. products, intermediates Iftilities (\teain, operator\, etc ) Equipment (cleaddirty) Material at different locations

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2.6 Mathematical Programming: Multipurpose Plants

models). He illustrated that the integrality gap could not be worse than the most efficient form of STN formulation, but that the ability to capture additional problem features in a straightforward fashion made it an ideal framework for future research. The review above has mainly considered the development of discrete-time models. As argued by Schilling (1997),discrete-time models have been able to solve a large number of industrially relevant problems (see, e.g., Tahmassebi 1996), but suffer from a number of inherent drawbacks: 0

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0

The discretization interval must be fine enough to capture all significant events; this may result in a very large model. It is difficult to model operations where the processing time is dependent on the batch size. The modeling of continuous and semicontinuous operations must be approximated, and minimum run-lengths give rise to complicated constraints.

A number of researchers have therefore attempted to develop scheduling models for multipurpose plants which are based on a continuous representation of time, where fewer grid points are required as they will be placed at the appropriate resource utilization discontinuities during problem solution. Zentner and Reklaitis (1992)described a formulation based on the unique assignment case and futed batch sizes. The sequence of activities as well as any external effects can be used to infer the discontinuities and therefore the interval boundaries. A MILP optimization is then used to determine the exact task starting times. Reklaitis and Mockus (1995) detailed a continuous-time formulation based on the STN formulation, and exploiting its generality. A common resource grid is used, with the timing of the grid points (“event orders” in their terminology) determined by the optimization. The model is a MINLP, which may be simplified to a mixedinteger bilinear problem by linearizing terms involving binary variables. This is solved using an outer-approximationalgorithm. Only very preliminary findings were reported, but the promise of such models is evident. Mockus and Reklaitis (1996)then reported an alternative solution procedure. They introduce the concept of Bayesian heuristics, which are heuristics that can be described through parameterized functions. The Bayesian technique iteratively modifies the parameters to develop a heuristic that is expected to perform well across a class of problem parameters. They illustrate the procedure using a material requirements planning (MRP) backward-scheduling heuristic which outperforms a standard discrete-time MILP formulation solved using branch-and-bound. They extend this work (Mockus and Reklaitis 1999a,b)to the case where a variety of heuristics are used in combination with optimization). Zhang and Sargent (1994, 1996) presented a continuous-time formulation based on the RTN representation for both batch and continuous operations, with the possibility of batch-size-dependent processing times for batch operations. Again, the interval durations are determined as part of the optimization. A MINLP model ensues; this is solved using a local linearization procedure combined with what is effectively a column generation algorithm.

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A problem with continuous-time models of the form described above arises from the inclusion of products of binary variables and interval durations or absolute starting times in the constraints. The linearization of these products gives rise to terms involving products of binary variables and maximum predicted interval durations or starting times. The looser these upper bounds, the worse the integrality gap of the formulation and, in general, the more difficult it becomes to solve the scheduling problem. Furthermore, it is difficult to predict good duration bounds a priori. The poor relaxation performance of the continuous-time models is the main obstacle to their more widespread application. Schilling and Pantelides (1996)and Schilling (1997)attempted to address this deficiency. They developed a continuous-time scheduling model based on the RTN. They proposed a number ofmodifications to the formulation of Zhang and Sargent (1996) ,which simplify the model and improve its general solution characteristics. A global linearization gives rise to a MILP. They then developed a hybrid branch-and-bound solution procedure which branches in the space of the interval durations as well as in the space of the integer variables. For a given problem instance, this can be viewed as generating a number of problem instances, each with tighter interval duration bounds. The independence of these new instances was recognized by Schilling (1997),who implemented a parallel solution procedure based on a distributed computing environment. The combination of the hybrid and parallel aspects of the solution procedure resulted in a much improved computational performance on a wide class of problems. Their model and solution procedure was then extended to the cyclic scheduling case (Schilling and Pantelides 1999). Castro et al. (2001) made some adjustments to the model to account for stable materials that can be held temporarily in processing units; these improve the computational performance considerably. Ierapetritou and Floudas (1998a-c) and Ierapetritou et al. (1999)introduced a new continuous-time model where the task and unit events are not directly coordinated against the same grid, but have their own grids (i.e., individual resource grids). Sequencing and timing constraints are then introduced to ensure feasibility. This has the effect of reducing the model size and reducing the associated computational effort required to find a solution. Their model is able to deal with semicontinuous processes and products with due dates falling arbitrarily within the horizon. Lin and Floudas (2001) extended this work to cover simultaneous design and scheduling. Wu and Ierapetritou (2003) employed time-, recipe- and resource-based decomposition procedures to this class of model. They indicated that near-optimal solutions may be obtained with modest effort. The work was generalized further by Janak et al. (2004)who included mixed storage policies, batch-size-dependentprocessing times, general resource constraints and sequence-dependent changeover constraints. Lee et al. (2001)extended this body ofwork with a formulation that uses binary variables to represent the start, process and end components of a process task. The computational performance of their model is similar to that of Castro et al. (2001). Orcun et al. (2001)used the concept of operations through which batches flow to develop a continuous-time model. Each batch has a prespecified alternative set of recipes for its manufacture; each recipe defines the flow through the operations. One of

2.G Mathematical Programming: Multipurpose Plants

I

the major decisions is then the choice of recipe for each batch. The complicating constraints are those that ensure the timing and sequence of batches and operations are feasible. Majozi and Zhu (2001) modified the STN concept by removing tasks and units; thereby generating a state-sequence network (SSN); essentially a state-transition network. They developed a continuous-time model based on this, which relies on specialized sequencing constraints to ensure feasibility. Resources other than processing units cannot be treated. Giannelos and Georgiadis (2002)described a very straightforward continuous-time model for multipurpose plant scheduling based on the STN process representation. In their work, they introduced “buffer times”, which means that although all tasks must start at event points, they do not need to finish on event points. This reduced synchronization improves the computational performance considerably when compared to similar mathematical models. Giannelos and Georgiadis (2003) applied their continuous-time model to the scheduling of consumer goods factories. The latter are characterized by sequencedependent changeovers and flexible intermediate storage. By preprocessing the data, good upper bounds on the number of changeover tasks can be estimated and used to tighten the MILP model. Good solutions were found for the case of a medium-size industrial study. Maravelias and Grossmann (2003)used a mixed time representation, where tasks which produce ZW states must start and finish at slot boundaries, while others are only anchored at the start, as per Giannelos and Georgiadis (2002).A different set of binary variables and assignment constraints is used from other works in this area. General resource constraints, sequence-dependent cleaning, and variable processing times are also included. Good computational performance is observed. Castro et al. (2003) investigated both discrete- and continuous-time RTN models for periodic scheduling applied to a pulp and paper case study. A coarse and then a fine grid is used with the discrete-time model to optimize the cycle time, and an iterative search on the number of event points is used in the continuous-time model. The discrete-time model allowed more flexibility in the statement of the objective function and is easier to solve, while the continuous-time model in principle allows more accurate modeling of the operations. Castro et al. (2004) presented a simple model for both batch and continuous processes which has an improved LP relaxation compared to that of Castro et al. (2001), due to a different set of timing constraints; this model generally outperforms other continuous-time models proposed in the literature. Overall, considerable progress has been made towards the development of generalpurpose mathematical programming-based methods for process scheduling. At least two commercial packages ModelEnterprise (see http://www.psenterprise.com/products-me.htm1)and Verdict (see http://www.combination.com) have resulted from these academic endeavours.

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2.7

Hybrid Solution Approaches So far, we have described individual solution approaches. A new class of solution methods has arisen out of the recognition that mathematical programming approaches are very effective when the scheduling problems are dominated by flowtype decisions, but often struggle when sequencing decisions dominate. Hybrid approaches decompose the problem into flow and sequence-based components and then apply different algorithms to these components. An example of this is described by Neumann et al. (2002), who solve separate batching and scheduling problems. The batching problem is a mixed-integer optimization problem which determines the number of instances of each task on each unit. The scheduling problem then determines the sequence and timing of the batches. A tailored algorithm based on project scheduling concepts is used for the scheduling/sequencing problem (Schwindt and Trautmann 2000). Most of the other hybrid methods are based on the same decomposition principle, but recognize that constrained logic programming (CLP) (also called constraint programming) is a powerful technique for the solution of sequencing problems. It is based on the concept of domain reduction and constraint propagation (van Hentenryck 1989). Jain and Grossmann (2001)use a single, hybrid model where different degrees of freedom are determined by the two solvers. Effectively, this requires an iteration between MILP and CLP solvers which proceeds until an optimal and feasible solution is found. A specific (parallel flowshop),rather than general process is studied. Harjunkoski et al. (2000) extend this work by developing a solution procedure which starts with the relaxed MILP and then iterates through different CLP solutions, each with a different objective function target. This approach performed better on a trim-loss problem than a traditional jobshop scheduling problem as tackled by Jain and Grossmann (2001). Huang and Chung (2000) explained how CLP can be used on its own (along with some dispatching rules) for the scheduling of a simple pipeless batch plant. Maravelias and Grossmann (2004)and Roe et al. (2003, 2004) also recognized that mixed-integer optimization techniques are appropriate for the batching problem, and constrained logic programming (CLP) approaches may be appropriate for the scheduling problem. Roe et al. (2003,2005) developed an algorithm appropriate to all types of processes. A STN-based description is used. A “batching” optimization is solved to determine the number of allocations of STN tasks to units and the average batch sizes, and then a tailored algorithm based on the ECLiPse framework (Wallace et al. 1997) is used to derive the schedule which aims to ensure completion of all tasks in the minimum possible time. A series of constraints are introduced in the batching problem (as per Maravelias and Grossmann 2004) to try to ensure schedule feasibility. Their approach has a single pass, while that of Maravelias and Grossmann (2004) is more sophisticated in that the algorithm iterates between MILP and CLP levels, and the two solution methods deal with different parts of a single model (essentiallythat of

2.8 Combined Scheduling and Process Operation

Maravelias and Grossmann 2003), which allows for variable batch sizes. The CLP level, rather than just adding simple integer cuts, adds a more general type of cut that excludes similar permutations of the solution to be excluded. Romero et al. (2004) used a graph theoretical framework to tackle scheduling problems which involve complex shared intermediate storage systems. Their representation is based on two types of graph: the recipe graph which depicts possible material flow routes, and the schedule graph which shows a unique solution to the scheduling problem. A branch-and-bound algorithm is used to search for optimal solutions.

2.8 Combined Scheduling and Process Operation

A feature of scheduling problems is that the representation of the production process depends on the gross margin of the business. Businesses with reasonable to large gross margins (e.g., consumer goods, specialties) tend to use “recipe-based”representations, where processes are operated at fured conditions and to fixed recipes. Recipes may also be fuced by regulation (e.g., pharmaceuticals) or because of poor process knowledge (e.g., food processing). On the other hand, businesses with slimmer margins (e.g., refining, petrochemicals) are moving towards “property-based”representations, where process conditions and (crude) process models are used in the process representation, and stream properties are inferred from process conditions and mixing rules. Hence some degrees of freedom associated with process operation are optimized during production scheduling. Some examples of this type of process are described below. Castro et al. (2002) described the use of both dynamic simulation and scheduling for the improved operation of the digester part of a pulp mill. A dynamic model is used to determine task durations and an RTN-based model is used for scheduling. The schedule optimization indicated that steam availability limits throughput. Alternative task combinations based on different steam sharing options were generated through the detailed modeling, and these were made available to the scheduling model. This then (approximately) enables the scheduling model to optimize the details of process operation. Glismann and Gruhn (2001) describe a model which combines scheduling with nonlinear recipe blend optimization. Here, a long-range planning problem using nonlinear programming identifies products to be produced and different blending recipes to produce them. A short-term RTN-based scheduling model then schedules the blending activities in detail. Deviations between plan and schedule can then be reduced in a further step. Alle and Pinto (2002) developed a model for the cyclic scheduling of continuous plants including operational variables such as processing rates and yields. This enables the optimization procedure to trade off time and material efficiencies. A tailored algorithm is used to find the global optimum of this mixed-integer nonconvex optimization problem.

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A different type of operational consideration is performance degradation over time. Jain and Grossmann (1998)describe the cyclic scheduling of an ethylene cracking process. Here, the conversion falls with time, until a cleaning activity is undertaken to restore the cracker to peak performance. There is a tradeoff between frequent cleaning (and high downtime) and high average performance and infrequent cleaning (and lower downtime) and lower average performance. The problem is complicated by the presence of multiple furnaces and model nonlinearity. Joly and Pinto (2003)describe a discrete-time MINLP model for the scheduling of fuel oil and asphalt production at a large Brazilian refinery. The nonlinear operational component comes from the calculation of the viscosity through variable flow rates rather than through fixed recipes. Because the viscosity specifications are fixed, a linear model can be derived from the MINLP and solved to global optimality. Pinto et al. (2000) and Joly et al. (2002) described a refinery planning model with nonlinear process models and blending relations. They demonstrated that industrial scale problems can in principle be solved using commercially available MINLP solvers. Neiro and Pinto (2003)extended this work to a set of refinery complexes, and also added scenarios to account for uncertainty in product prices. To ensure a robust solution, the decision variables are chosen “here and now”. They demonstrate that nonlinear models reflecting process unit conditions and mixture property prediction can be used in multisite planning models. They also show that there are significant cost benefits in solving for the complex together rather than for the individual refineries separately. Moro (2003),in his review of technology in the refining industry, indicates that scheduling tools that include details of process operation are still not available, but their application should results in benefits of US$IO million per year for a typical refinery.

2.9 Uncertainty in Planning and Scheduling

As with any other industrially relevant optimization problem, production scheduling requires a considerable amount of data. This is often subject to uncertainty (e.g., task processing times, yields, market demands, etc.). Sources of uncertainty (which tend to imply the means for dealing with them) can crudely be divided into: 0

0

short-term uncertainties such as processing-time variations, rush orders, failed batches, equipment breakdowns, etc.; long-term uncertainties such as market trends, technology changes, etc.

Traditionally, short-term uncertainties have been treated through online or reactive scheduling, where schedules are adjusted to take account of new information. Longer-term uncertainties have been tackled through the solution of some form of stochastic programming problem. These two areas are considered below.

2.9 Uncertainty in Planning and Scheduling

2.9.1 Reactive Scheduling

A major requirement of reactive scheduling systems is the ability to generate feasible updated schedules relatively quickly. A secondary objective is often to minimize deviations from the original schedule. As plants become more automated, this may become less important. Cott (1989) presented some schedule modification algorithms to be used in conjunction with online monitoring, in particular to deal with processing-time variations and batch-size variations. Kanakamedala et al. (1994) presented a least-impact heuristic beam search for reactive schedule modification in the face of unexpected deviations in processing times and resource availability. This is based on evaluating possible product reroutings and selecting that which has least overall impact on the schedule. Rodrigues et al. (1996)modified the discrete-time STN formulation to take account of due-date changes and equipment unavailability. They use a rolling horizon (rolling out a predefined schedule) approach which aims to look ahead for a short time to resolve infeasibilities.This implies a very small problem size and fast solution times. Schilling (1997) adapted his RTN-based continuous-time formulation to create a hierarchical family of MILP-based reactive scheduling formulations. At the lowest level, the sequence of operations is futed as in the original schedule and only the timing can vary. At the topmost level, a full original scheduling problem is solved. The intermediate levels all trade off degrees-of-freedomwith computational effort. This allows the best solution in the time available to be implemented on the plant. Bael (1999)combined constraint satisfaction and iterative improvement (based on local perturbations) in his rescheduling strategy for jobshop environments. A tradeoff between computational time and solution quality was identified. Castillo and Roberts (2001) described a real-time scheduling approach for batch plants, based on model predictive control methods. The future allocation of orders to machines can be investigated using a fast tree-search algorithm, and robust solutions are generated in real time. This works due to the assumption of batch integrity throughout the process (i.e., there is no mixing or splitting of material). Wang et al. (2000) described a genetic algorithm for online scheduling of a complex multiproduct polymer plant with many conflicting constraints. They describe how this technique may be successfully applied to scheduling problems and give guidance on appropriate mutation and crossover operations. Henning and Cerda (2000)described a knowledge-based framework which aims to support a human scheduler performing both offline and reactive scheduling. They argue that purely automated scheduling is difficult because plant circumstances change regularly. An object-oriented,knowledge-based framework is used to capture problem information and a scheduling support system developed (within which a variety of scheduling algorithms can be encoded) that enhances the capabilities of the human domain expert via an interactive front end. Because schedules can be generated very quickly using this approach, it is suitable for reactive scheduling.

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One reason for reactive scheduling is the need to rework batches when quality criteria are not met. Flapper et al. (2002) provide a review of methods for planning and control of rework.

2.9.2 Planning and Scheduling under Uncertainty

Most of the work in this area is based on models in which product demands are assumed to be uncertain and to differ between a number of time periods. Usually, a simple representation of the plant capacity is assumed, and the sophistication of the work relates to the implementation of stochastic planning algorithms to select amounts for production in the first period (here and now) and potential production amounts in different possible demand realizations in different periods (see, e.g., Ierapetritou et al. (1996)). In relatively long-term planning, it is reasonable to introduce additional degrees of freedom associated with potential capacity expansions. Liu and Sahinidis (199Ga,b) and Iyer and Grossmann (1998) extended the MILP process and capacity planning model of Sahinidis and Grossmann (1991b)to include multiple product-demand scenarios in each period. They then proposed efficient algorithms for the solution of the resulting stochastic programming problems (formulated as large deterministic equivalent models), either by projection (Liu and Sahinidis 199Ga) or by decomposition and iteration (Iyer and Grossmann 1998).A major assumption in their formulation is that product inventories are not carried over from one period to the next. Clay and Grossmann (1994) also addressed this issue. They considered the structure of both the two-period and multiperiod problem for LP models and derived an approximation method based on successive repartitioning of the uncertain space with expectations being applied over partitions. This has the potential to generate solutions to a high degree of accuracy in a much faster time than the full-scale deterministic equivalent model. The approaches above are based on relatively simple models of plant capacity. Petkov and Maranas (1997) treat the multiperiod planning model for multiproduct plants under demand uncertainty. Their planning model embeds the planning/ scheduling formulation of Birewar and Grossmann (1990) and therefore accurately calculates the plant capacity. They do not use discrete demand scenarios but assume normal distributions and directly manipulate the functional forms to generate a problem which maximizes expected profit and meets certain probabilistic bounds on demand satisfaction without the need for numerical integration. They also make the no-inventory-carryoverassumption, but show how this can be remedied to a certain extent at the lower level scheduling stage. Sand and Engell (2004) use a rolling horizon, two-stage stochastic programming approach to schedule an expandable polystyrene plant that is subject to uncertainty in processing times, yields, capacities and demands. The former two sources of uncertainty are considered short-term and the latter two medium-term. A hierarchical scheduling technique is used where a master schedule deals with medium-term uncertainties and a detailed schedule with the

2.9 Uncertainty in Planning and Scheduling

short-term ones. The uncertainties are represented through discrete scenarios and the two-stage problem solved using a decomposition technique. Alternative approaches have attempted to characterize the effects of some sources of uncertainty on detailed schedules. Rotstein et al. (1994) defined flexibility and reliability indices for detailed schedules. These are based on data for equipment reliability and demand distributions. Given a schedule (described in network flow form),these indices can be calculated to assess its performance. Dedopoulos and Shah (1995) used a multistage stochastic programming formulation to solve short-term scheduling problems with possibilities of equipment failure at each discrete time instant. The technique can be used to assess the impact of different failure characteristics of the equipment on expected profit, but suffers from the very large computational effort required even for small problems. Sanmarti et al. (1995)define a robust schedule as one which has a high probability of being performed, and is readily adaptable to plant variations. They define an index of reliability for a unit scheduled in a campaign through its intrinsic reliability, the probability that a standby unit is available during the campaign, and the speed with which it can be repaired. An overall schedule reliability is then the product of the reliabilities of units scheduled in it, and solutions to the planning problem can be driven to achieve a high value of this indicator. Mignon et al. (1995)assess schedules obtained from deterministic data for performance under variability by Monte Carlo simulation. Although a number of parameters may be uncertain, they focus on processing time. Performance and robustness (predictability)metrics are defined and features of schedules with good indicators are summarized (e.g., introducing an element of conservatism when futing due dates). Honkomp et al. (1997)build on this to compare schedules generated by discretetime and continuous-time algorithms and two means of ensuring robustness in the face of processing time uncertainties, namely increasing the processing times of bottleneck stages and increasing all processing times at the deterministic scheduling level. They found that the latter heuristic was better, and that the rounding effect of the discrete-time model results in marginally better robustness. Robustness is defined with respect to variance in the objective function. Strictly speaking, penalizing the variance of a metric to ensure robustness assumes that the metric is twosided (i.e., “the closer to nominal the better” in the Taguchi sense). Since economic objective functions are one-sided (“themore the better”),robustness indicators such as these should be used with caution. This has been noted recently by Ahmed and Sahinidis (1998). Gonzalez and Realff (1998a) analyze MILP solutions for pipeless plants that generated by assuming lower level controls for detailed vehicle movements and futed, nominal transfer times. The analysis performed using stochastic simulation with variabilities in the transfer times. The system performance was found not to degrade considerably from its nominal value. They extended the work (Gonzalez and Realff 1998b) to consider the development of dispatching rules based on both general flexible manufacturing principles and properties of the MILP solutions. They found that rules abstracted from the MILP solutions were superior, and could be used in realtime.

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A similar “multimodel” technique that combines optimization, expert systems and discrete-eventsimulation is described by Artiba and Riane (1998), although their focus is on a robust package for an industrial environment rather than uncertainty per se. Bassett et al. (1997) contrasted aggregate planning and detailed scheduling under uncertainties in processing times and equipment failure. They argue that aggregate models that take these into account miss critical interactions due to the complex short-term interactions. They therefore propose the use of detailed scheduling to study the effects of such uncertainties on aggregate indicators such as average probabilities in meeting due dates and makespans. They also use Monte Carlo simulation, but use each set of sampled data to generate a detailed scheduling problem instance, solved using a reverse rolling horizon algorithm. Once enough instances have been solved for statistical significance, a number of comparisons can be made. For example, they conclude that long, infrequent breakdowns are more desirable, with obvious implications for maintenance policies. Lee and Malone (2001a, 2001b) developed a hybrid Monte Carlo simulationsimulated annealing approach to planning and scheduling under uncertainty. They treat uncertainties in demands, due dates, processing times, product prices and raw material costs. An expected NPV objective is chosen; this is calculated through simultaneous Monte Carlo simulation and simulated annealing. This can also be used to devise strategies to ensure flexibility and robustness, for example by including enforced idle times in the schedule to allow for adjustments or rush orders. Ivanescu et al. (2002) describe an approach for makespan estimation and order acceptance in multipurpose plants with uncertain task processing times (following an Erlang distribution). Instead of using a large mathematical model, regression analysis is used instead, based on a family of problem classes. Balasubramanian and Grossmann (2003) presented an alternative approach to scheduling under uncertainty, arguing that probabilistic data on the uncertainties (e.g., in processing times) are unlikely to be available, and instead proposing a fuzzy set and interval theory approach. A rigorous MILP that can provide bounds on the makespan is developed for the flowshop case, based on the evaluation of a fuzzy, rather than crisp, makespan, and rules for comparing alternative makespans in order to determine optimality. Kuroda et al. (2002)use the simple concept of due-date buffers to allow for flexibility in adjusting schedules in an operational environment. Here, orders further out in the horizon are allowed to move around within the buffer, while those near the current time remain futed. This facilitates responsiveness to unforeseen orders.

2.1 0

Industrial Applications of Planning and Scheduling

Honkomp et al. (2000) give a list of reasons why the practical implementation of scheduling tools based on optimization is fraught with difficulty. These include: 0

The large amount of user-defined input for testing purposes.

2.70 Industrial Applications ofplanning and Scheduling 0

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0 0 0 0

The difficulty in capturing all the different types of operational constraints within a general framework, and the associated difficulty in defining an appropriate objective function. The large amounts of data required; Book and Bhatnagar (2000) list some of the issues that must be faced if generic data models are to be developed for planning/ scheduling applications. Computational difficulties associated with the large problem sizes found in practice. Optimality gaps arising out of many shared resources. Intermediate storage and material stability constraints. Nonproductive activities (e.g., set-up times, cleaning, etc.) Effective treatment of uncertainties in demands and equipment effectiveness.

Nevertheless, there have been several success stories in the application of state-ofthe-art scheduling methods in industry. Schnelle (2000) applied MILP-based scheduling and design techniques to an agrochemical facility. The results indicated that sharing of equipment items between different products was a good idea, and the process reduced the number of alternatives to consider to a manageable number. Berning et al. (2002)describe a large-scale planning-scheduling application which uses genetic algorithms for detailed scheduling at each site and a collaborative planning tool to coordinate plans across sites. The plants all operate batchwise, and may supply each other with intermediates, creating interdependencies in the plan. The scale of the problem is large, involving on the order of GOO different process recipes, and 1000 resources. Kallrath (2002b)presented a successful application of MILP methods for planning and scheduling in BASF. He describes a tool for simultaneous strategic and operational planning in a multisite production network. The aim was to optimize the total net profit of a global network, where key decisions include: operating modes of equipment in each time period, production and supply of products, minor changes to the infrastructure (e.g., addition and removal of equipment from sites), and raw material purchases and contracts. A multiperiod model is formulated where equipment may undergo one mode change per period. The standard material balance equations are adjusted to account for the fact that transportation times are much shorter than the period durations. Counterintuitive but credible plans were developed that resulted in cost savings of several millions of dollars. Sensitivity analyses showed that the key decisions were not too sensitive to demand uncertainty. Keskinocak et al. (2002) describe the application of a combined agent- and optimization-based framework for the scheduling of paper products manufacturing. The framework solves the problems of order allocation, run formation, trimming and trim-loss minimization and load planning. The deployment of the system is claimed to save millions of dollars per year. The “asynchronous agent-based team” approach uses constructor and improver agents to generate candidate solutions that are evaluated against multiple criteria.

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2.1 1

New Application Domains

The scheduling techniques described above have in the main been applied to batch chemical production, particularly fine and specialty chemicals and pharmaceuticals. They are also appropriate to the wider and emerging process industries, and have started to find application in other domains, some of which are reviewed below. Kim et al. (2001)tackle the problem of semiconductor wafer fabrication scheduling involving multiple products with different due dates. A series of dispatching (“lot release”) and lot scheduling rules are evaluated. Bhushan and Karimi (2003) describe the application of scheduling techniques to the wet-etchingcomponent of a semiconductor manufacturing process. This process is complicated by its “re-entrant”nature, where a product revisits stages of manufacture, and therefore does not fit the classical flowshop structure. A MILP formulation combined with a heuristic is used to minimize the makespan required to complete an outstanding set of jobs. Pearn et al. (2004) describe the challenges associated with the scheduling of the final testing stage of integrated circuit manufacture and compare the performance of alternative heuristic algorithms. El-Halwagi et al. (2003) describe a system for efficient design and scheduling of recovery of nutrients from plant wastes and reuse of the nutrients, with a view to developing a strategy for future planetary habitation. Lee and Malone (2000b)show how planning can be useful in waste minimization. They combine scheduling with the main process and scheduling of the solvent recovery system. They show that such simultaneous scheduling can reduce waste disposal costs significantly. Pilot plant facilities can become very scarce resources in the modern chemical industry, with many more short-run processes. Mockus et al. (2002) describe the integrated planning and scheduling of such a facility. The long-term planning problem is primarily concerned with skilled human resource allocation while the shortterm scheduling problem deals with production operations. Roslof et al. (2001)describe the application of production scheduling techniques to the paper manufacturing industry. In this sector, large numbers of orders, some of which are for custom products, are the norm. Van den Heever and Grossmann (2003) describe the production planning and scheduling of a complex of plants producing hydrogen. This requires the description of the behavior of a pipeline and its associated compressors, which adds complexity and nonlinearity. The combination of longer-term planning and short-term reactive scheduling enables the decision-makers to deal effectively with uncertainty.

2.72 Conclusions and Future Challenges

2.12 Conclusions and Future Challenges

Production scheduling has been a fertile area for CAPE research and the development of technology. Revisiting the challenges posed by Reklaitis (1991), Rippin (1993), Shah (1998) and Kallrath (2002a),it is clear that considerable progress has been made towards meeting them. Overall, the emerging trend in the area of short-term scheduling is the development of techniques for the solution of the general, resource-constrained multipurpose plant scheduling problem. The recent research is all about solution efficiency and techniques to render ever-larger problems tractable. There remains work to be done on both model enhancements and improvements in solution algorithms if industrially relevant problems are to be tackled routinely, and software based on these are to be used on a regular basis by practitioners in the field. Many algorithms have been developed to exploit the tight relaxation characteristics of discrete-time formulations. There remains work to be done in this area, in particular to exploit the sparsity of the solutions. Direct intervention at the LP level during branch-and-bound procedures (e.g., column generation and branch-and-price) seems a promising way of solving very large problems without ever considering the full variable space. Decomposition techniques (e.g., rolling horizon methods) will also find application here. Much of the more recent research has focussed on continuous-time formulations, but little technology has been developed based on these. The main challenge here is in continual improvement in problem formulation and preprocessing to improve relaxation characteristics, and tailored solution procedures (e.g., branch-and-cut, and hybrid logic-continuous variable-integer variable branching) for problems with relatively large integrality gaps. Probably the most promising recent development is the implementation of hybrid MILP/CLP solution methods which recognize that different algorithms are suitable for different components of the scheduling problem. An important contrast between early and recent work is that the early algorithms tended to be tested on “motivating”examples (e.g.,to find the best sequence of a few products), while recent algorithms are almost always tested on (and often motivated by) industrial or industrially based studies. The multisite problem has received relatively little attention, and is likely to be a candidate for significant research in the near future. A major challenge is to develop planning approaches that are consistent with detailed production scheduling at each site and distribution scheduling across sites. An obvious stumbling block is problem size, and a resource-task-based decomposition based on identifying weak connections should find promise here as the problems tend to be highly structured. As scheduling and planning become integrated, the financial aspects will require more rigorous treatment. For example, Romero and Puigjaner (2004)describe the integration of cash flow modeling with production scheduling. This facilitates an accurate forward prediction of cash flow and even allows the enterprise to optimize treasury

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management simultaneously with decisions on purchasing, production and sales, and can be used to enforce upper and lower bounds on cash balances. Researchers have attacked the problem of planning and scheduling under uncertainty from a number of angles, but have tended to skirt around the fundamental problem of multiperiod, multiscenario planning with realistic production capacity models (i.e., embedding some scheduling information) in the case of longer-term uncertainties. Issues that must be resolved relate mainly to problem scale. A sensible way forward is to try to capture the problem in all its complexity and then to explore rigorous or approximate solution procedures, rather than develop exact solutions to somewhat idealized problems. Process industry models are complicated by having multiple stages (periods) and integer variables in the second and subsequent stages, so most of the classical algorithms devised for large scale stochastic planning problems are not readily applicable. The treatment of short-term uncertainties through the determination of characteristics of resilient schedules and then to use online monitoring and rescheduling seems eminently sensible. Further work is required in such characterization and in the design of rescheduling algorithms with guaranteed real-time performance. A final challenge relates to the seamless integration of the activities at different levels - this is of a much broader and more interdisciplinary nature. Shobrys and White (2002) describe some of the difficult challenges to be faced here, including data and functional fragmentation, inconsistencies between activities and datasets, different tools being used for different activities,time and material buffers at each function for protection, slow responses and information flow.

References 1 Ahmed S. Sahinidis N. V. Robust process

planning under uncertainty, Ind. Eng. Chem. Res. 37 (1998) p. 1883-1892 2 Alle A. Pinto J . M . A general framework for simultaneous cyclic scheduling and operational optimization of multiproduct continuous plants, Braz. J. Chem. Eng. 19:4 (2002) p. 457-466 3 Artiba A. Riane F. An application of a planning and scheduling multi-model approach in the chemical industry, Comput. Ind. 36 (1998) p. 209-229 4 Applequist G. 0. Sarnikoglu]. Pekny G. V. Reklaitis Issues in the use, design and evolution of process scheduling and planning systems, ISA Trans. 36 (1997) p. 81-121 5 Bael P. A study of rescheduling strategies and abstraction levels for a chemical process scheduling problem, Prod. Planning Control lO(4) (1999) p. 359-364 6 J . Balasubramanian Grossmann 1. E. Scheduling optimization under uncertainty - an

alternative approach, Comput. Chem. Eng. 27 (2003) 469-490 7 Bassett M. H . Peknyj. F. Reklaitis G. V. Decomposition techniques for the solution of large-scale scheduling problems, AIChE J. 42 (1996) p. 3373-3387 8 Bassett M . H Pekny]. F. Reklaitis G. V. Using detailed scheduling to obtain realistic operating policies for a batch processing facility, Ind. Eng. Chem. Res. 36 (1997) p. 1717-1726 9 Berning G. Brandenburg M. Gursoy K. Mehta V. Tolle F.-J. An integrated system for supply chain optimisation in the chemical process industry, OR Spectrum 24 (2002) p. 371-401 10 Bhushan S. Karimi I. A. An MILP approach to automated wet-etch station scheduling, Ind. Eng. Chem. Res. 42 (2003) p. 1391-1399 11 Birewar D. B. Grossmann I. E. Efficient optimi. zation algorithms for zero-wait scheduling of multiproduct batch plants, Ind. Eng. Chem. Process Des. Dev. 28 (1989) p. 1333-1345

References 12 Birewar D. B. Grossmann I. E. Simultaneous

production planning and scheduling in multiproduct batch plants, Ind. Eng. Chem. Res. 29 (1990) p. 570-580 13 Blomer F . Giinther H.-0. Scheduling of a multi-product batch process in the chemical industry, Comput. Ind. 36 (1998)p. 245-259 14 Book N . L. Bhatnagar V. Comput. Chem. Eng. 24 (2000) p. 1641-1644 15 Bunch P. A simplex-based primal-dual algorithm for the perfect B-matching problem a study in combinatorial optimisation, Phd Thesis, Purdue University (1997) 16 Castiflo I Roberts C. A. Real-time controll scheduling for multipurpose batch plants, Comp. Ind. Eng. 41 (2001)p. 211-225 17 Castro P. Barbosa-Pdvoa A. P. F. D. Matos H . An improved RTN continuous-timeformulation for the short-term scheduling of multipurpose batch plants, Ind. Eng. Chem. Res. 40 (2001) p. 2059-2068 18 Castro P. Barbosa-Pdvoa A. P. F. D. Matos H . Ind. Eng. Chem. Res. 43 (2004)p. 105-118 19 Castro P. M . Barbosa-Pdvoa A. P. Matos H . A. Optimal periodic scheduling of batch plants using RTN-Baseddiscrete and continuoustime formulations: a case study approach, Ind. Eng. Chem. Res. 42 (2003)p. 3346-3360 20 Castro P. M . Barbosa-Pdvoa A. P. Matos H . A . Novais A. Q. Ind. Eng. Chem. Res. 43 (2004) p. 105-118 21 Castro P. M . Matos H . Barbosa-Pdvoa A. P. F . D. Dynamic modelling and scheduling of an industrial batch system, Comput. Chem. Eng. 26 (2002) 671-686 22 Cerda 1.Henning G. P. Grossmann I. E. A mixed integer linear programming model for short-term scheduling of single-stage multiproduct batch plants with parallel lines, Ind. Eng. Chem. Res. 36 (1997) p. 1695-1707 23 Clay R. L. Grossmann I. E. Optimization of stochastic planning-models, Chem. Eng. Res. Des. 72 (1994) p. 415-419 24 Cott B. /. An integrated computer-aided production management system for batch chemical processes, PhD Thesis, University of London (1989) 25 Dannebring D. G. An evaluation of flowshop sequencing heuristics, Manage. Sci. 23 (1977) p. 1174-1182 26 Dedopoulos I. T. Shah N. Preventive maintenance policy optimisation for multipurpose plant equipment, Comput. Chem. Eng, S19 (1995)p. S693-S698 27 Dimitriadis A. D. Shah N. Pantelides C. C. RTN-based rolling horizon algorithms for

medium-term scheduling of multipurpose plants, Comput. Chem. Eng. S21 (1997a)p. S 1061- S 1066 28 Dimitriadis A. D. Shah N. Pantelides C. C. A rigorous decomposition algorithm for solution of large-scale planning and scheduling problems, paper presented at AlChE Annual Meeting, Nov. 16-21, Los Angeles (1997b) 29 El-Halwagi M . Williams L. Hall /. Aglan H . Mortley D. Trotman A. Mass integration and scheduling strategies for resource recovery in planetary habitation, Chem. Eng. Res. Des. 81 (2003) p. 243-250 30 Elkamel A. Scheduling of process operations using mathematical programming techniques, PhD Thesis, Purdue University (1993) 31 Elkamel A. AI-Enezi G. Structured valid inequalities and separation in optimal scheduling of the resource-constrained batch chemical plant, Math. Eng. Ind. 6 (1998) p. 291-318 32 Elmaghraby S. The economic lot scheduling problem. review and extensions, Manage. Sci. 24 (1978) p. 587-598 33 Flapper S. D. P. Fransooj. C. Broekmeulen R. A. C. M . Inderfurth K. Planning and control of rework in the process industries: a review, Prod. Planning Control, 13 (2002) p. 26-34 34 Gabow H . N. On the design and analysis of efficient algorithms for deterministic scheduling, Proceedings of the 2nd International Conference Foundations of Computer-Aided Process Design, Michigan, June 19-24, (1983) USA, Cache Publications, pp. 473-528 (1983) 35 Giannelos N . F. Georgiadis M . C. A simple new continuous time formulation for short tern scheduling of multipurpose batch processes, Ind. Eng. Chem. Res. 41 (2002) p. 2178-2184 36 Giannelos N . F . Georgiadis M . C. Efficient scheduling of consumer goods manufacturing processes in the continuous time domain Comput. Oper. Res. 30 (2003) p. 1367-1381 37 Glismann K. Gruhn G. Short-term scheduling and recipe optimization of blending processes, Comput. Chem. Eng. 25 (2001). p. 627-634 38 Gonzalez R. R e a l f M . /. Operation of pipeless batch plants - 1. MILP schedules, Comput. Chem. Eng. 22 (1998a)p. 841-855 39 Gonzalez R. R e a l f M . /. Operation of pipeless batch plants - 11. Vessel dispatch rules, Comput. Chem. Eng. 22 (199%) p. 857-866

I

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512

I

2 Production Scheduling 40 Gooding W. B. Specially structured formula-

tions and solution methods for optimisation problems important to process scheduling, PhD Thesis Purdue University (1994) 41 Gooding W. B. PeknyJ. F. McCroskey P. S. Enumerative approaches to parallel flowshop scheduling via problem transformation Comput. Chem. Eng. 18 (1994) p. 909-927 42 Graells M. Espuria A. Puiaaner L. Sequencing intermediate products: a practical solution for multipurpose production scheduling, Comput. Chem. Eng. S20 (1996)p. S1137-S1142 43 Gmnow M. Giinther H.-0. Lehmann M. Campaign planning for multistage batch processes in the chemical industry, OR Spectrum, 24 (2002)p. 281-314 44 Hampel R. Beyond the millenium, Chem. Ind. 10 (1997)p. 380-382 45 HajunkoskiJain V. Grossmann I. E. Hybrid mixed-integer/constrained logic programming strategies for solving scheduling and combinatroial optimization problems, Comput. Chem. Eng. 24 (2000)p. 337-343 46 Hasebe S. Hashimoto I. Ishikawa A. General reordering algorithm for scheduling of batch processes, J. Chem. Eng. Jpn. 24 (1991) p. 483-489 47 Hasebe S. Taniguchi S. Hashirnoto I. Automatic adjustment of crossover method in the scheduling using genetic algorithm, Kagaku Kogaku Ronbunshu, 22 (1996)p. 1039-1045 48 Henning G. P. Cerdli J . Knowledge based predictive and reactive scheduling in industrial environments, Comput. Chem. Eng. 24 (2000)p. 2315-2338 49 Honkomp S. J. Mockus L. Reklaitis G. V. Robust scheduling with processing time uncertainty, Comput. Chem. Eng. S21 (1997) p. S1055-S1060 50 Honkomp S. J . Lombardo S. Rosen 0. Pekny J. F. The curse of reality - why process scheduling optimisation problems are difficult in practice, Comput. Chem. Eng. 24 (2000) p. 323-328 51 Huang W. Chung P. W. H. Scheduling of pipeless batch plants using constraint satisfaction techniques, Comput. Chem. Eng. 24 (2000) p. 377-383 52 Ierapetritou M . G. Floudas C. A. Short-term scheduling: new mathematical models vs algorithmic improvements, Comput. Chem. Eng. 22 (1998a)p. S419-S426 53 Ierapetritou M. G. Floudas C. A. Effective continuous-time formulation for short-term

scheduling: I. Multipurpose batch processes, Ind. Eng. Chem. Res. 37 (199%) p. 4341-4359 54 Ierapetritou M. G. Floudas C. A. Effective continuous-time formulation for short-term scheduling: 11. Multipurpose/multiproduct continuous processes, Ind. Eng. Chem. Res. 37 (1998~) p. 4360-4374 55 Ierapetntou M. G. Hene T. S. Floudas C. A. Effective continuous-time formulation for short-term scheduling: 111. Multi intermediate due dates, Ind. Eng. Chem. Res. 38 (1999) p. 3446-3461 56 Ierapetntou M. G. Pistikopoulos E. N. Floudas C. A. Operational planning under uncertainty, Comput. Chem. Eng. 20 (1996) p. 1499- 1516 57 Ivanescu C. V. FransooJ. C. Bertrand]. W. M. Makespan Estimation And Order Acceptance In Batch Process Industries When Processing Times Are Uncertain, OR Spectrum, 24 (2002) p. 467-495 58 Iyer R. R. Grossmann I. E. Bilevel Decomposition A lgorithm For Long-Range Planning Of Process Networks, Ind. Eng. Chem. Res. 37 (1998) p. 474-481 59 l a i n V. Grossmann I. E. Cyclic scheudling of continuous paralle-process units with decaying performance, AIChE J. 44 (1998) p. 1623-1636 60 l a i n V. Grossmann I. E. Algorithms for hybrid MILP/CP models for a class of optimization problems, Informs J. Comput. 13 (2001) p. 258-276 61 Janak S. L. Lin X. Floudas C. A. Enhanced continuous-timeunit-specific event-based formulation for short-term scheduling of multipurpose batch processes: Resource constraints and mixed storage policies, Ind. Eng. Chem. Res. 43 (2004)p. 2516-2533 62 Joly M. Moro L. F. L. Pinto J. M. Planning and scheduling for petroleum refinerines using mathematical programming, Braz. J. Chem. Eng. 19(2) (2002)p. 207-228 63 Joly M . Pinto J . M. Mixed-integer programming techniques for the scheduling of fuel oil and asphalt production, Chem. Eng. Res. Des. 81 (2003) p. 427-447 64 Kallrath J . Planning and scheduling in the process industry, OR Spectrum, 24 (2002a) 219-250 65 Kallrath J . Combined strategic and operational planning - an MILP success story in chemical industry, OR Spectrum, 24 (2002b) p. 315-341

References 66 Kanakamedafa K. B. Rekfaitis G. V. Venkatasubramanian V. Reactive schedule modifica-

tion in multipurpose batch chemical plants, Ind. Eng. Chem. Res. 33 (1994)p. 77-90 67 Karimi I. A. McDonald C. M. Planning and scheduling of parallel semicontinuous processes. 2. Short-term Scheduling, Ind. Eng. Chem. Res. 36 (1997)p. 2701-2714 68 Keskinocak P. Wu F. Goodwin R. Murthy S. Akkiraju R. Kumaran S. Derebaif A. Scheduling solutions for the paper industry, Oper. Res. 50 (2002) p. 249-259 69 Kim M. Jung]. H . l e e I:B. Optimal scheduling of multiproduct batch processes for various intermediate storage policies, Ind. Eng. Chem. Res. 35 (1996) p. 4048-4066 70 Kim Y.-D. Kim].-G. Choi B. Kim H.-U. Production scheduling in a semiconductor wafer fabrication facility producing multiple product types with distinct due dates, IEEE Trans. Robot. Autom. 17 (2001) p. 589-598 71 Kondifi E. Pantelides C. C. Sargent R. W. H. A general algorithm for scheduling of batch operations, Proceedings of the 3rd International Symposium on Process Systems Engineering, Sydney, Australia, (1988) pp. 62-75 72 Kondifi E. Pantelides C. C. Sargent R. W. H . A general algorithm for short-term scheduling of batch operations - 1. Mixed integer linear programming formulation, Comput. Chem. Eng. 17 (1993) p. 211-227 73 Krarupj. B i l k 0. Plant location, set covering and economic lot size: an O(mn) algorithm for structured problems, Int Ser. Num. Math. 36 (1977) p. 155-180 74 Ku H . Karimi I. A . An evaluation of simulated annealing for batch process scheduling, Ind. Eng. Chem. Res. 30 (1991)p. 163-169 75 Kudva G . EfkamefA. Pekny]. F. Rekfaitis G. V. Heuristic algorithm for scheduling batch and semicontinuous plants with production deadlines, intermediate storage limitations and equipment changeover costs, Comput. Chem. Eng. 18 (1994) p. 859-875 76 Kuriyan K. Reklaitis G. V. Approximate scheduling algorithms for network flowshops, Chem. Eng. Symp. Ser. 92 (1985)p. 79-90 77 Kuriyan K. Rekfaitis G. V. Scheduling network flowshops so as to minimise makespan, Comput. Chem. Eng. 13 (1989) p. 187-200 78 Kuroda M . Shin H . Zinnohara A. Robust scheduling in an advanced planning and scheduling, Int. J. Prod. Res. 40 (2002) p. 3655-3668

79 l e e Y. G Malone M . F. Batch processes plan-

ning for waste minimization, Ind. Eng. Chem. Res. 39 (2000) p. 2035-2044 80 l e e Y. G Malone M. F. Flexible batch process planning, Ind. Eng. Chem. Res. 39 (2000b) p. 2045-2055 81 lee Y. G Malone M. F. Batch process schedule optimization under parameter volatility, Int. J. Prod. Res. 39 (2001a) p. 603-623 82 l e e Y. G. Malone M . F. A general treatment of uncertainties in batch process planning, Ind. Eng. Chem. Res. 40 (2001b)p. 1507-1515 83 Lee R-H. Park H . I. l e e 1. B. A novel nonuniform discrete time formulation for shortterm scheduling of batch and continuous processes, Ind. Eng. Chem. Res. 40 (2001a) p. 4902-4911 84 Lin X . Ffoudas C. A. Design, synthesis and scheduling of multipurpose batch plants via en effective continuous-time formulation, Comput. Chem. Eng. 25 (2001b) p. 665-674 85 l i u M. 1.Sahinidis N. V. Long-range planning in the process industries - a projection approach, Comput. Oper. Res. 3 (1996a)p. 237-253 86 l i u M. 1.Sahinidis N.V. Optimization in process planning under uncertainty, Ind. Eng. Chem. Res. 35 (1996b) p. 4154-4165 87 Majozi T. Zhu X . X . A novel continuloustime MILP formulation for multipurpose batch plants. 1. Short-term scheduling, Ind. Eng. Chem. Res. 40 (2001) p. 5935-5949 88 Maravefias C. T. Grossmann I . E. New general continuous-time statetask network formulation for short-term scheduling of multipurpose batch plants, Ind. Eng. Chem. Res. 42 (2003) p. 3056-3074 89 Maravefias C. T. Grossmann I . E. A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants, Comput. Chem. Eng. 28 (2004) p. 1921-1949 90 Mauderfi A. M . Rippin D. W. T. production planning and scheduling for multi-purpose batch chemical plants, Comput. Chem. Eng. 3 (1979) p. 199-206 91 McDonald C. M. Karimi 1. A. Planning and scheduling of parallel semicontinuous processes. 1. Production planning, Ind. Eng. Chem. Res. 36 (1997) p. 2691-2700 92 Mtndez C. A. Cerdd /. Optimal scheduling of a resource-constrained multiproduct batch plant supplying intermediates to nearby endproduct facilities, Comput. Chem. Eng. 24 (2000) p. 369-376

I

513

514

I

2 Production Scheduling 93 Mtndez C. A. Henning G . P. Cerdlt ]. An

MILP continuous-time approach to short-term scheduling of resourceconstrained multistage flowshop batch facilities, Comput. Chem. Eng. 25 (2001)p. 701-71 1 94 Mignon D. J . Honkomp S. J . Reklaitis G. V. A framework for investigating schedule robustness under uncertainty, Comput. Chem. Eng. S19 (1995) p. S615-S620 95 Mockus L. Reklaitis G . V. Continuous-Time Representation In Batch/Semicontinuous Process Scheduling - Randomized Heuristics Approach, Comput. Chem. Eng. S20 (1996) p. S1173-S1178 96 Mockus L. Reklaitis G. V. Continuous time representation approach to batch and continuous process scheduling. 1. MINLP formulation, Ind. Eng. Chem. Res. 38 (1999a)p. 197-203 97 Mockus L. Reklaitis G. V. Continuous time representation approach to batch and continuous process scheduling. 2. Computational issues, Ind. Eng. Chem. Res. 38 (1999b)p. 204-210 98 Mockus L. Vinsonj. M. Luo K. The integration of production plan and operating schedule in a pharmaceutical pilot plant, Comput. Chem. Eng. 26 (2002) p. 697-702 99 Moon S. Park S. Lee W. K. New MILP models for scheduling of multiproduct batch plants under zero-wait policy, Ind. Eng. Chem. Res. 35 (1996) p. 3458-3469 100 Moro L. F. L. Process technology in the petroleum refining industry - current situation and future trends, Comput. Chem. Eng. 27 (2003)p. 1303-1305 101 Murakami Y . Uchiyama H. Hasebe S. Hashimoto I. Application of repetitive SA method to scheduling problems of chemical processes, Comput. Chem. Eng. S21 (1997)p. S1087-S1092 102 Neiro S. M. S. Pinto]. M. Supply chain optimisation of petroleum refinery complexes, Proceedings of the 4th International Conference on Foundations of Computer-Aided Process Operations, Florida, USA, Jan (2003), Cache Corp, pp. 59-72 103 Neumann K. Schwindt C. Trautmann N. Advanced production scheduling for batch 104 Orcun S. Altinel I. K. Hortapu 6. General continuous time models for production planning and scheduling of batch processing plant, mixed integer linear program formulations and computational issues, Comput. Chem. Eng. 25 (2001) p. 371-38

plants in process industries, OR Spectrum, 24 (2002) p. 251-279 105 Pantelides C. C. Unified frameworks for optimal process planning and scheduling, Proceedings of the 2nd Conference on Foundations of Computer-Aided Process Operations, Snowmass, Colorado, USA, July 10-15 (1994) Cache. Corp., pp 253-274 106 Pantelides C. C. Real8 M.J. Shah N. Shortterm scheduling of pipeless batch plants Trans..IChemE A, 73 (1995) p. 431-444 107 Papageorgiou L. G. Pantelides C. C. Optimal campaign planning/scheduling of multipurpose batch/semicontinuous plants. 1. Mathematical formulation, Ind. Eng. Chem. Res. 35 (1996a)p. 488-509 108 Papageorgiou L. G. Pantelides C. C. Optimal campaign planninglscheduling of multipurpose batch/semicontinuous plants. 2. A mathematical decomposition approach, Ind. Eng. Chem. Res. 35 (199613) p. 510-529 109 Peam W. L. Chung S. H. Chen A. Y. Yang M. H. A case study on the multistage IC final testing scheduling problem with reentry, Int. J. Prod. Econ. 88 (2004)p. 257-267 110 Pekny J. F. Miller D. L. McCrae G. J. Application of a parallel travelling salesman problem to no-wait flowshop scheduling, paper presented at AIChE Annual Meeting, November 27 - December 2, Washington D.C. (1988) 111 Pekny J. F. Miller D. L. McCrae G. ]. An exact parallel algorithm for scheduling when production costs depend on consecutive system states, Comput. Chem. Eng. 14 (1990) p. 1009-1023 112 Petkov S. B. Maranas C. D. Multiperiod planning and scheduling of multiproduct batch plants under demand uncertainty, Ind. Eng. Chem. Res. 36 (1997)p. 4864-4881 113 Pinedo M.Scheduling. theory, algorithms and systems. Prentice Hall, New York (1995) 114 Pinto]. M. Grossmann I . E. Optimal cyclic scheduling of multistage continuous multiproduct plants, Comput. Chem. Eng. 18 (1994)p. 797-816 115 Pinto J . M. Grossmann I. E. A continuous time MILP model for short-term scheduling of multistage batch plants, Ind. Eng. Chem. Res. 34 (1995) p. 3037-3051 116 Pinto]. M. Grossmann I. E. A logic-based approach to scheduling problems with resource constraints, Comput. Chem. Eng. 21 (1997) p. 801-818 117 Pinto ]. M.Grossmann I. E. Assignment and sequencing models for the scheduling of

References chemical processes, Ann OR, 81 (1998) p. 433-466 118 Pintoj. M . Joly M . Moro L. F. L. Planning and scheduling models for refinery operations, Comput. Chem. Eng. 24 (2000) p. 2259-2276 119 Reklaitis G. V. Perspectives on scheduling and planning of process operations, Proceedings of the 4th International Symposium on Process Systems Engineering. Montebello, Canada, August 5-9 (1991) 120 Reklaitis G. V. Mockus L. Mathematical programming formulation for scheduling of batch operations based on non-uniform time discretization, Acta Chim. Slov. 42 (1995) p. 81-86 121 Rippin D. W. T. Batch process systems engineering: a retrospective and prospective review, Comput. Chem. Eng. S17 (1993) p. Sl-Sl3 122 Rodrigues M . T. M . Gimeno L. Passos C. A. S. Campos M . D. Reactive scheduling approach for multipurpose batch chemical plants, Comput. Chem. Eng. S20 (1996) p. S1215-Sl226 123 Roe B. Papageorgiou L. G. Shah N. A hybrid CLP and MILP approach to batch process scheduling, Proc. of 8th International Symposium on Process Systems Engineering, Kunming, China (2003) p. 582-587 124 Roe B. Papageorgiou L. G. Shah N. A hybrid MILP/CLP algorithm for multipurpose batch process scheduling, Comput. Chem. Eng. 29 (2005) p. 1277-129 125 Romero /. Puigjaner L. Joint financial and operating scheduling/planning in industry, Proceedings of 14th European Symposium on Computer-Aided Process Engineering, May (2004) Elsevier, p. 883-888 126 Romero /. Puigjaner L. Holczinger T. Friedler F . Scheduling intermediate storage multipurpose batch plants using the S-Graph, AIChE J. 50 (2004) p. 403-417 127 RoslbjJ. Hajunkoski I. Bjorkqvist /. Karlsson S. Westerfund T. An MILP-based reordering algorithm for complex industrial scheduling and rescheduling, Comput. Chem. Eng. 25 (2001) p. 821-828 128 Rotstein G. E. Lavie R. Lewin D. R. Synthesis of Flexible and Reliable Short-Term Batch Production Plans, Comput. Chem. Eng. 20 (1994) p. 201-215 129 Sahinidis N. V. Grossmann 1. E. Reformulation of multiperiod MILP models for planning and scheduling of chemical processes, Comput. Chem. Eng. 15 (1991) p. 255-272

E. Fomari R. E. Chathrathi M . Optimisation model for long-range planning in the chemical industry, Comput. Chem. Eng. 15 (1991a) 255-272 131 Sahinidis N. V. Grossmann I. E. MINLP model for cyclic multiproduct scheduling on continuous parallel lines, Comput. Chem. Eng. 15 (1991b) 85-103 132 Sand G. Engell S. Modelling and solving realtime scheduling problems by stochastic integer programming, Comput. Chem. Eng. 28 (2004) p. 1087-1103 133 Sanmarti E. Espuria A. Puigjaner L. Effects of equipment failure uncertainty in batch production scheduling, Comput. Chem. Eng. S19 (1995) p. S565-S570 134 Schilling G. Pantelides C. C. A simple continuous time process scheduling formulation and a novel solution algorithm, Comput. Chem. Eng. S20 (1996) p. S1221LS1226 135 Schilling G. H. Algorithms for short-term and periodic process scheduling and rescheduling, PhD Thesis, University of London (1997) 136 Schilling G. Pantelides C. C. Optimal periodic scheduling of multipurpose plants, Comput. Chem. Eng. 23 (1999) p. 635-655 137 Schnelle K. D. Preliminary design and scheduling of a batch agrochemical plant, Comput. Chem. Eng. 24 (2000) p. 1535-1541 138 Schwindt C. Trautmann N. Batch scheduling in process industries: an application of resource-constrained project scheduling, OR Spektmm, 22 (2000) p. 501-524 139 Shah N. Single- and multi-site planning and scheduling: Current status and future challenges, AIChE Ser. 94 (1998) p. 75-90 140 Shah N. Pantelides C. C. Optimal long-term campaign planning and design of batch plants, Ind. Eng. Chem. Res. 30 (1991) p. 2308-2321 141 Shah N. Pantelides C. C. Sargent R. W. H. A general algorithm for short-term scheduling of batch operations - 2. Computational issues, Comput. Chem. Eng. 17 (1993a) p. 229-244 142 Shah N. Pantelides C. C. Sargent R. W. H. Optimal periodic scheduling of multipurpose batch plants, Ann. Oper. Res. 42 (1993b) p. 193-228 143 Shobrys D. E. White D. C. Planning, scheduling and control systems: why cannot they work together, Comput. Chem. Eng. 26 (2002) p. 149-160 130 Sahinidis N. V. Grossmann I.

I

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I

2 Production Scheduling 144 Sunol, A. K. Kapanoglu M. Mogili P. Selected

topics in artificial intelligence for planning and scheduling problems, knowledge acquisition and machine learning, Proc NATO AS1 on Batch Processing Systems Engineering, Series F, Vol, 143 (1992) pp 595-630 145 Tahmassebi T. Industrial experience with a mathematical programming based system for factory systems planning/scheduling, Comput. Chem. Eng. S20 (1996)p. S1565-S1570 146 uan den Heever S. A. Grossmann 1. E. Comput. Chem. Eng. 27 (2003) p. 1813-1839 147 van Hentenryck P. Constraint satisfaction in Logic Programming, MIT Press (1989) 148 Wallace M. G. Novello S. Schimpfj. ECLiPSe: A platform for constraint logic programming, ICL Systems Journal 12 (1997)p. 137-158 149 Wang K. F. Lohl T. Stobbe M. Engell S. A genetic algorithm for online-scheduling of a multiproduct polymer batch plant, Comput. Chem. Eng. (2000)p. 393-400 150 Wellons M. C. Reklaitis G. V. Scheduling of multipurpose batch plants. 1. Formation of single-product campaigns, Ind. Eng. Chem. Res. 30 (1991a)p. 671-688 151 Wellons M. C. Reklaitis G. V. Scheduling of multipurpose batch plants. 2. Multipleproduct campaign formation and production planning, Ind. Eng. Chem. Res. 30 (1991b) p. 688-705 152 Wilkinson S. /. Shah N. Pantelides C. C. Aggregate modelling of multipurpose plant operation, Comput. Chem. Eng. S19 (1995) p. S583-SS88

153 Wilkinson S. /. Cortier A. Shah N. Pantelides C. C. Integrated production and distribution

scheduling on a Europe-widebasis, Comput. Chem. Eng. S20 (1996)p. S1275-S1280 154 Wu D. Ierapetritou M. G. Decomposition approaches for the efficient solution of short-term scheduling problems, Comput. Chem. Eng. 27 (2003) p. 1261-1276 155 Xia Q. Macchietto S. Routing, scheduling and product mix optimization by minimax algebra, Chem. Eng. Res. Des. 72 (1994) p. 408-414 156 Yee K. L. Efficient algorithms for multipurpose plant scheduling, PhD Thesis, University of London (1998) 157 Yee K. L. Shah N. Scheduling of fast-moving consumer goods plants, J. Oper. Res. SOC.48 (1997)p. 1201-1214 158 Yee K. L. Shah N. Improving the efficiency of discrete-time scheduling formulations, Comput. Chem. Eng. S22 (1998) p. S403-S410 159 Zentner M.G. Reklaitis G. V. An intervalbased mathematical model for the scheduling of resource-constrained batch chemical processes, Proc. NATO AS1 on Batch Processing Systems Engineering, Series F, Vol, 143 (1992) p. 779-807 160 ZhangX, Sargent R. W. H. The optimal operation of mixed production facilities-ageneral formulation and some approaches for the solution, Proceedings of the 5th International Symposium on Process Systems Engineering, Kyongju, Korea, June (1994)p. 171-178 161 Zhang X Sargent R. W. H. The optimal operation of mixed production facilitiesextensions and improvements, Comput. Chem. Eng. S20 (1996) p. S1287-S1292

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

3 Process Monitoring and Data Reconciliation Georges Heyen and Boris Kalitventzef

3.1

Introduction Measurements are needed to monitor process efficiency and equipment condition, but also to take care that operating conditions remain within an acceptable range to ensure good product quality and to avoid equipment failure and any hazardous conditions. Recent progress in automatic data collection and archiving has solved part of the problem, at least for modern, well-instrumented plants. Operators are now faced with a lot of data, but they have little means to extract and fully exploit the relevant information it contains. Furthermore, plant operators recognize that measurements and laboratory analysis are never error-free. Using these measurements without any correction yields inconsistencies when generating plant balances or estimating performance indicators. Even careful installation and maintenance of the hardware can not completely eliminate this problem. Model-based statistical methods, such as data reconciliation, have been developed to analyze and validate plant measurements. The objective of these techniques is to remove errors from available measurements and to yield complete estimates of all the process state variables as well as of unmeasured process parameters. This chapter constitutes a tutorial on process monitoring and data reconciliation. First, the key concepts and issues underlying a plant data validation, sources of error and redundancy considerations are introduced. Then, the data reconciliation problem is formulated for simple stready-state linear systems and extended further to consider nonlinear cases. The role of sensibility analysis is also introduced. Dynamic data reconciliation, which is still a subject of major research interest, is treated next. The chapter concludes with a section devoted to the optimal design of the measurement system. Detailed algorithms and supporting software are presented along with the solution of some motivating examples.

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 200G WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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3.2 Introductory Concepts for Validation o f Plant Data

Data validation makes use of a plant model in order to identify measurement errors and to reduce their average magnitude. It provides estimates of all process state variables, whether directly measured or not, with the lowest possible uncertainty. It allows one to assess the value of key performance indicators, which are target values for process operation, or is used as a soft sensor to provide estimates of some unmeasured variables, as in inferential control applications. Especially in a framework of real-time optimal control, where model fidelity is of paramount importance, data validation is a recommended step before fine-tuning model parameters: there is no incentive in seeking to optimize a model when it does not match the actual behavior of the real plant. Data validation can also help in gross error detection, meaning either process faults (such as leaks) or instrument faults (such as identification of instrument bias and automatic instrument recalibration). Long an academic research topic, data validation is currently attracting more and more interest, since the amount of measured data collected by Digital Control Systems (DCS) and archived in process information management systems,exceeds what can be handled by operators and plant managers. Real-time applications, such as optimal control, also require frequent parameter updates, in order to ensure fidelity of the plant model. The economic value of extracting consistent information from raw data is recognized. Data validation thus plays a key role in providing coherent and error-free information to decision makers.

3.2.1 Sources of Error

Some sources of errors in the balances depend on the sensors themselves: 0

0

0 0

Intrinsic sensor precision is limited, especially for online equipment, where robustness is usually considered more important than accuracy. Sensor calibration is seldom performed as often as desired, since this is a costly and time-consuming procedure requiring competent manpower. Signal converters and transmission add noise to the original measurement. Synchronization of measurements may also pose a problem, especially for chemical analysis, where a significant delay exists between sampling and result availability.

Other errors arise from the sensor location or the influence of external effects. For instance, the measurement of gas temperature at the exit of a furnace can be influenced by radiation from the hot wall in the furnace. Inhomogeneous flow can also cause sampling problems. A local measurement is not representative of an average bulk property. A second source of error when calculating plant balances is the small instabilities of the plant operation and the fact that samples and measurements are not taken at

3.2 Introductory Conceptsfor Validation ofPlant Data

exactly the same time. Using time averages for plant data partly reduces this problem.

3.2.2 Redundancy

Besides safety considerations, the ultimate goal in performing measurements is to assess the plant performance and to take actions in order to optimize the operating conditions. However, most performance indicators can not be directly measured and must be inferred from some measurements using a model. For instance, the extent of a reaction in a continuous reactor can be calculated from a flow rate and two composition measurements. In general terms, model equations that relate unmeasured variables to a sufficient number of available measurements are used. However, in some cases, more measurements are available than are strictly needed, and the same performance indicator can be calculated in several ways using different subsets of measurements. For instance, the conversion in an adiabatic reactor where a single reaction takes place is directly related to the temperature variation. Thus the extent of the reaction can be inferred from a flow rate and two temperature measurements using the energy balance equation. In practice, all estimates of performance indicators will be different, which makes life difficult and can lead to endless discussions about “best practice.” Measurement redundancy should not be viewed as a source of trouble, but as an opportunity to perform extensive checking. When redundant measurements are available,they allow one not only to detect and quantify errors, but also to reduce the uncertainty using procedures known as data validation.

3.2.3 Data Validation

The data validation procedure comprises several steps. The first is the measurement collection. Nowadays, in well-instrumented plants, this is performed routinely by automated equipment. The second step is conditioning and filtering: not all measurements are available simultaneously, and synchronization might be required. Some data are acquired at higher frequency and filtering or averaging can be justified. The third step is to verify the process condition and the adequacy of the model. For instance, if a steady-statemodel is to be used for data reconciliation, the time series of raw measurements should be analyzed to detect any significant transient behavior. The fourth step is gross error detection: the data reconciliation procedure to be applied later is meant to correct small random errors. Thus, large systematic errors that could result from complete sensor failure should be detected first. This is usually done by verifying that all raw data remain within the upper and lower bounds.

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More advanced statistical techniques, such as principal component analysis (PCA), can also be applied at this stage. Ad hoc procedures are applied in case some measured value is found inadequate or missing: it can be replaced by a default value or by the previous one available. The fifth step checks the feasibility of data reconciliation. The model equations are analyzed and the variables are sorted. Measured variables are redundant (and can thus be validated) or just determined; unmeasured variables are determinable or not. When all variables are either measured or observable, the data reconciliation problem can be solved to provide an estimate for all state variables. The sixth step is the solution of the data reconciliation problem. The mathematical formulation of this problem will be presented in more detail later. Each measurement is corrected as slightly as possible in such a way that the corrected measurements match all the constraints (or balances) of the process model. Unmeasured variables can be calculated from reconciled values using some model equations. In the seventh step the systems perform a result analysis. The magnitude of the correction for each measurement is compared to its standard deviation. Large corrections are flagged as suspected gross errors. In the final step, results are edited and may be archived in the plant information management system. Customized reports can be edited and forwarded to various users (e.g., list of suspect sensors sent to maintenance, performance indicators sent to the operators, daily balance and validated environmental figures to site management).

3.3 Formulation

Data reconciliation is based on measurement redundancy. This concept is not limited to the case where the same variable is measured simultaneously by several sensors. It is generalized with the concept of spatial redundancy, where a single variable can be estimated in several independent ways from separate sets of measurements. For instance, the outlet of a mixer can be directly measured or estimated by summing the measurements of all inlet flow rates. For dynamic systems, temporal redundancy is also available, by which repeated observations of the same variables are obtained. More generally, plant structure is additional information that can be exploited to correct measurements. Variables describing the state of a process are related by some constraints. The basic laws of nature must be verified: mass balance, energy balance, some equilibrium constraints. Data reconciliation uses information redundancy and conservation laws to correct measurements and convert them into accurate and reliable knowledge. Kuehn and Davidson (1961)were the first to explore the problem of data reconciliation in the process industry. Vaclavek (1968, 1969) also addressed the problem of variable classification, and the formulation of the reconciliation model. Mah et al.

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(1976) proposed a variable classification procedure based on graph theory, while Crowe (1989) based an analysis on a projection matrix approach to obtain a reduced system. Joris and Kalitventzeff (1987)proposed a classification algorithm for general nonlinear equation systems, comprising mass and energy balances, phase equilibrium and nonlinear link equations. A thorough review of classification methods is available in Veverka and Madron (1996) and in Romagnoli and Sanchez (2000). A historical perspective of the main contributions on data reconciliation can also be found in Narasimhan and Jordache (2000).

3.3.1 Steady-State Linear System

The simplest data reconciliation problem deals with steady state mass balances, assuming all variables are measured, and results in a linear problem. In this case x is the vector of n state variables, while y is the vector of measurements. We assume that random errors e=y-x follow a multivariate normal distribution with zero mean. The state variables are linked by a set of rn linear constraints:

Ax-d=O

(1)

min(y - xlTw(y- x)

(2)

The data reconciliation problem consists of identifying the state variables x that verify the set of constraints and are close to the measured values in the least square sense, which results in the following objective function: where W is a weight matrix. The method of Lagrange multipliers allows one to obtain an analytical solution:

i = y - W-'AT(AW-'AT)-'(Ay

-

d)

It is assumed that there are no linearly dependent constraints. In order to solve practical problems and obtain physically meaningful solutions, it may be necessary to take into account inequality constraints on some variables (e.g., flow rate should be positive). However, this makes the solution more complex, and the constrained problem can not be solved analytically. It can be shown that is the maximum likelihood estimate of the state variables if the measurement errors are normally distributed with zero mean, and if the weight matrix W corresponds to the inverse of the error covariance matrix C. Equation (3) then becomes:

x

i = y - CAT(ACAT)-'(Ay

i=My+e

-

d) = [I

-

CAT(ACAT)-'A]y

+ CAT(ACAT)-'d

(3b)

The estimates are thus related to the measured values by a linear transformation. They are therefore normally distributed with the average value and covariance matrix obtained by calculating the expected values:

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3 Process Monitoring and Data Reconciliation

E ( i ) = ME().) = x Cov(2) = E [ ( M Y ) ( M ~ )= ~ ]MCMT

(4)

This shows that the estimated state variables are unbiased. Furthermore, the accuracy of the estimates can easily be obtained from the measurement accuracy (covariance matrix C ) and from the model equations (matrix A). 3.3.2 Steady-State Nonlinear System

The data reconciliation problem can be extended to nonlinear steady-state models and to cases where some variables z are not measured. This is expressed by: min(y - xlTw(y - x) x,z

s.t. f (x, z) = 0 where the model equations are mass and component balance equations, energy balance, equilibrium conditions, and link equations relating measured values to state variables (e.g., conversion from mass fractions to partial molar flow rates). Usually the use of performance equations is not recommended, unless the performance parameters (such as compressor efficiency and overall heat transfer coefficients or fouling factors for heat exchangers) remain unmeasured and will thus be estimated by solving the data reconciliation problem. It would be difficult to justify correcting measurements using an empirical correlation, e.g., by correcting the outlet temperatures of a compressor by enforcing the value of the isentropic efficiency. The main purpose of data reconciliation is to allow monitoring of those efficiency parameters and to detect their degradation. Equation (5) takes the form of a nonlinear constrained minimization problem. It can be transformed into an unconstrained problem using Lagrange multipliers A and the augmented objective function L has to be minimized:

L(x, z, A) =

{1

(X - y)

T -1

C

(X - y)

+ AT . f (x, Z)

min L(x, y, A)

x,y.A

The solution must verify the necessary optimality conditions i.e., the first derivatives of the objective function with respect to all independent variables must vanish. Thus one has to solve the system of normal equations:

aL _ - f(x, z) = 0

aA

3.3 Formulation I 5 2 3

This last equation can be linearized as:

z+d=O

(7)

where A and B are partial Jacobian matrices of the model equation system: A=-

af ax

The system of normal equations in Eq. (6) is nonlinear and has to be solved iteratively. Initial guesses for measured values are straightforward to obtain. Process knowledge usually estimates good initial values for unmeasured variables. No obvious initial values exist for Lagrange multipliers, but solution algorithms are not too demanding in that respect (Kalitventzeffet al., 1978).The Newton-Raphson method is suitable for small problems and requires a solution of successive linearizations of the original problem Eq. (6):

where the Jacobian matrix J of the equation system has the following structure: C-'

0 AT

Numerical algorithms embedding a step size control, such as Powell's dogleg algorithm (Chen and Stadtherr 1981) are quite successful for larger problems. When solving very large problems, it is necessary to exploit the sparsity of the Jacobian matrix and use appropriate solution algorithms, such as those described by Chen and Stadtherr (1984a).It is common to assume that measurements are independent, which reduces the weight matrix C-' to a diagonal. Ideally, the elements of matrices A and B should be evaluated analytically. This is straightforward for the elements corresponding to mass balance equations, which are linear, but can be difficult when the equations involve physical properties obtained from an independent physical property package. The solution strategy exposed above does not allow one to handle inequality constraints. This justifies the use of alternative algorithms to solve directly the nonlinear programming (NLP) problem defined by Eq. (6). Sequential quadratic programming (SQP) is the method of choice (Chen and Stadtherr 1984a; Kyriakopoulou and Kalitventzeff 1996, 1997). At each iteration, an approximation of the original problem is solved: the original objective function being quadratic is retained and the model constraints are linearized around the current estimate of the solution.

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Before solving the NLP problem, some variable classification and preanalysis is needed to identify unobservable variables, parameters, and nonredundant measurements. Measured variables can be classified as redundant (if the measurement is absent or detected as a gross error, the variable can still be estimated from the model) or nonredundant. Likewise, unmeasured variables are classified as observable (estimated uniquely from the model) or unobservable. The reconciliation algorithm will correct only redundant variables. If some variables are not observable, the program will either request additional measurements (and possibly suggest a feasible set) or solve a smaller subproblem involving only observable variables. The preliminary analysis should also detect ouerspecijied variables (particularly those set to constants) and trivial redundancy, where the measured variable does not depend at all upon its measured value but is inferred directly from the model. Finally, it should also identify model equations that do not influence the reconciliation,but are merely used to calculate some unmeasured variables. Such preliminary tests are extremely important, especially when the data reconciliation runs as an automated process. In particular, if some measurements are eliminated as gross errors due to sensor failure, nonredundant measurements can lead to unobservable values and nonunique solutions, rendering the estimates and fitted values useless. As a result, these cases need to be detected in advance through variable classification. Moreover, under these conditions, the NLP may be harder to converge.

3.3.3 Sensitivity Analysis

Solving the data reconciliation problem provides more than validated measurements. A sensitivity analysis can also be carried out. It is based on the linearization of equation system in Eq. (9),possibly augmented to take into account active inequality constraints. Equation (9) shows that reconciled values of process variables x and z, and of Lagrange multipliers A are linear combinations of the measurements. Thus their covariance matrix is directly derived from the measurements covariance matrix (Heyen et al. 1996). Knowing the variance of validated variables allows one to detect the respective importance of all measurements in the state identification problem. In particular, some measurements might appear to have little effect on the result and might thus be discarded from analysis. Some measurements may appear to have a very high impact on key validated variables and on their variance: these measurements should be carried out with special caution, and it may prove wise to duplicate the corresponding sensors. The standard deviation of validated values can be compared to the standard deviation of the raw measurement. Their ratio measures the improvement in confidence brought by the validation procedure. A nonredundant measurement will not be improved by validation. The reliability of the estimates for unmeasured observable variables is also quantified.

The sensitivity analysis also allows one to identify all state variables dependent on a given measurement, as well as the contribution of the measurement variance to the variance of the reconciled value. This information helps locate critical sensors, whose failure may lead to troubles in monitoring the process. A similar analysis can be carried out for all state variables, whether measured or not. For each variable, a list of all measurements used to estimate its reconciled value is obtained. The standard deviation of the reconciled variable is calculated, but also its sensitivity with respect to the measurement's standard deviation. This allows one to locate sensors whose accuracy should be improved in order to reduce the uncertainty affecting the major process performance indicators.

3.3.4 Dynamic Data Reconciliation

The algorithm described above is suitable for analyzing steady-state processes. In practice it is also used to handle measurements obtained from processes operated close to steady state, with small disturbances. Measurements are collected over a period of time and average values are treated with the steady state algorithm. This approach is acceptable when the goal is to monitor some performance parameters that vary slowly with time, such as the fouling coefficient in heat exchangers. It is also useful when validated data are needed, to fine tune a steady-state simulation model, e.g., before optimizing set point values that are updated once every few hours. However, a different approach is required when the transient behavior needs to be monitored accurately. This is the case for regulatory control applications, where data validation has to treat data obtained with a much shorter sampling interval. Dynamic material and energy balance relationships must then be considered as a constraint. The earliest algorithm was proposed by Kalman (1960)for the linear time-invariant system model. The general nonlinear process model describes the evolution of the state variables x by a set of ordinary differential equations (ODE):

x = f ( t , x, u)

+ w(t)

(11)

where x are state variables, u are process inputs, and w(t) is white noise with zero mean and covariance matrix R(t). To model the measurement process, one usually considers sampling at discrete times t = kT, and measurements related to state variables by: Yk = h(xk)

+ "k

(12)

where measurement errors are normally distributed random variables with zero One usually considers that process noise wand meamean and covariance matrix Qk. surement noise v are not correlated. By linearizing Eqs. 11 and 1 2 at each time step around the current state estimates, an extended Kalrnanfilter can be built (see, for instance, Narasimhan and Jordache

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3 Process Monitoring and Data Reconciliation

2000). It allows one to propagate an initial estimate of the states and the associated error covariance, and to update them at discrete time intervals using the measurement innovation (the difference between the measured values and the predictions obtained by integrating the process model from the previous time step). An alternative approach relies on NLP techniques. As proposed by Liebman et al. (1992), the problem can be formulated as

subject to

f(F , x(t) h(x(t)) = 0

)

= 0;

x(t0)

=i o

(14)

(15)

In this formulation, we expect that all state variables can be measured. When some measurements are not available,this can be handled by introducing null elements in the weight matrix Q . Besides enforcing process specific constraints, the equalities in Eq. (15) can also be used to define nonlinear relationships between state variables and some measurements. All measurements pertaining to a given time horizon [to...tN] are reconciled simultaneously. Obviously, the calculation effort increases with the length of the time horizon, and thus with the number of measurements. A tradeoff exists between calculation effort and data consistency. If measurements are repeated N times in the horizon interval, each measured value will be reconciled N times with different neighboring measurements, as long as it is part of the moving horizon. Which set of reconciled values is the “best”and should be considered for archiving is an open question. The value corresponding to the latest time t N will probably be selected for online control application, while a value taken in the middle of the time window might be preferred for archiving or offline calculations. Two solution strategies can be considered. The sequential solution and optimization combines an optimization algorithm such as SQP with an ODE solver. Optimization variables are the initial conditions for the ODE system. Each time the optimizer sets a new value for the optimization variables, the differential equations are solved numerically and the objective function Eq. (13) is evaluated. This method is straightforward, but not very efficient: accurate solutions of the ODE system are required repeatedly and handling the constraints Eqs. (15) and (16) might require a lot of trial and error. An implementation of this approach in a MATLAB environment is described by Romagnoli and Sanchez (2000). Simultaneous solution and optimization is considered more efficient. The differential constraints are approximated by a set of algebraic equations using a weighted residuals method, such as orthogonal collocation. Predicted values of the state vari-

3.5 Integration in the Process Decision Chain

ables are thus obtained by solving the resulting set of algebraic equations, supplemented by the algebraic constraints of Eqs. (15) and (16). With this transformation, the distinction between dynamic data reconciliation and steady state data reconciliation vanishes. However this formulation requires solving a large NLP problem. This approach was first proposed by Liebman et al. (1992).

3.4 Software Solution

Data reconciliation is a functionality that is now embedded in many process analysis and simulation packages or is proposed as a standalone software solution. Bagajewicz and Rollins (2002) present a review of eight commercial and one academic data reconciliation packages. Most of them are limited to material and component balances. More advanced features are only available in a few packages: direct connectivity to DCS systems for online applications, access to an extensive physical property library, handling pseudocomponents (petroleum fractions), simultaneous data validation, and identification of process performance indicators, sensitivity analysis, automatic gross error detection and correction, a model library for major process unit modules, handling of rigorous energy balances and phase equilibrium constraints, evaluation of confidence limits for all estimates. The packages offering the larger sets of features are Datacon (Invensys) (2004) and Vali (Belsim) (2004). Dynamic data reconciliation is still an active research topic (Binder et al., 1998). It is used in combination with some real-time optimization applications, usually in the form of custom-developed extended Kalman Filters (see, for instance, Musch et al. (2004)),but dedicated commercial packages have yet to reach the market.

3.5 Integration in the Process Decision Chain

Data reconciliation is just one step - although an important step - in the data processing chain. Several operations, collectively known as data validation, are executed sequentially : 0 Raw measurements are filtered to eliminate some random noise. When data is collected at high frequency, a moving average might be calculated to reduce the signal variance. 0 If steady state data reconciliation is foreseen, the steady state has to be detected. 0 Measurements are screened in order to detect outliers, or truly abnormal values (out of feasible range, e.g., negative flow rate). 0 The state of the process might be identified when the plant can operate in different regimes or with a different set of operating units. Principal Component Analysis (PCA) analysis is typically used for that purpose, and allows one to select a reference case and to assign the right model structure to the available data set. This

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3 Process Monitoring and D a t a Reconciliation

0

0 0 0

0

0

step also allows some gross error detection (measurement set deviates significantly from all characterized normal sets). Variable classification takes place in order to verify that redundancy is present in the data set and that all state variables can be observed. The data reconciliation problem is solved. A global Chi-square test can detect the presence of gross errors. A posteriori uncertainty is calculated for all variables, and corrections are compared to the measurement standard deviation. In an attempt to identify gross errors, sequential elimination of suspect measurements (those with large corrections) can possibly identify suspect sensors. Alternatively, looking at subsystems of equations linking variables with large corrections allows one to pinpoint suspect units or operations in the plant. Key performance indicators and their confidence limits are evaluated and made available for reporting. Model parameters are tuned based on reconciled measurements and made available to process optimizers.

3.6 Optimal Design of Measurement System

The quality of validated data obviously depends on the quality of the measurement. Recent studies have paid more attention to this topic. The goal is to design measurement systems allowing one to achieve a prescribed accuracy in the estimates of some key process parameters, and to secure enough redundancy to make the monitoring process resilient with respect to sensor failures. Some preliminary results have been published, but no general solution can be found addressing large-scale nonlinear systems or dynamics. Madron (1972)solved the linear mass balance case using a graph-oriented method. Meyer et al. (1994)proposed an alternative minimum-cost design method based on a similar approach. Bagajewicz (1997) analyzed the problem for mass balance networks, where all constraint equations are linear. Bagajewicz and Sanchez (1999) also analyze reallocation of existing sensors. The design and retrofit of a sensor network was also analyzed by Benqlilou et al. (2004)who discussed both the strategy and tools structure.

3.6.1 Sensor Placement based on Genetic Algorithm

A model-based sensor location tool, making use of a genetic algorithm to minimize the investment cost of the measurement system has been proposed by Heyen et al. (2002)and further developed by Gerkens and Heyen (2004). They propose a general mathematical formulation of the sensor selection and location problem in order to reduce the cost of the measurement system while providing

3.G Optimal Design ofMeasurement System

estimates of all specified key process parameters within a prescribed accuracy. The goal is to extend the capability of previously published algorithms and to address a broader problem, not being restricted to flow measurements and linear constraints. The set of constraint equations is obtained by linearizing the process model at the nominal operating conditions, assuming steady state. The process model is complemented with link equations that relate the state variables to any accepted measurements, or to key process parameters whose values should be estimated from the set of measurements. In our case, the set of state variables for process streams comprises all stream temperatures, pressures and partial molar flow rates. In order to handle total flow rate measurements, the link equation describing the mass flow rate as the sum of all partial molar flow rates weighted by the component's molar mass has to be defined. Similarly, link equations relating the molar or mass fractions to the partial molar flow rates have also to be added for any stream where an analytical sensor can be located. Link equations also have also to be added to express key process parameters, such as heat transfer coefficients, reaction extents or compressor efficiencies. In the optimization problem formulation, the major contribution to the objective function is the annualized operating cost of the measurement system. In the proposed approach, we will assume that all variables are measured; those that are actually unmeasured will be handled as measured variables with a large standard deviation. Data reconciliation requires a solution of the optimization problem described by Eq. (5). The weight matrix W = C-' is limited to diagonal terms, which are the inverse of the measurement variance. The constrained problem is transformed into an unconstrained one using the Lagrange formulation as previously shown. Assuming all state variables are measured, the solution takes the following form:

The linear approximation of the constraints is easily obtained from the solution of the nonlinear model, since A is the Jacobian matrix of the nonlinear model evaluated at the solution. Thus matrix M can be easily built, knowing the variance of measured variables appearing in submatrix W and the model Jacobian matrix A (which is constant). This matrix will be modified when assigning sensors to variables. Any diagonal element of matrix W will remain zero (corresponding to infinite variance) as long as a sensor is not assigned to the corresponding process variable; it will be computed from the sensor precision and the variable value when a sensor is assigned in Section 3.6.2.3. Equation (17) need not be solved, since measured values Y are not known. However the variances of the reconciled values X depend only on the variance of measurements as shown in Heyen et al. (1996): var(xi) =

C ([M-11y)2 var (5)

j=1

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3 Process Monitoring and Data Reconciliation

The elements of M-' are obtained by calculating a lower and upper triangular (LU) factors of matrix M. In the case when matrix M is singular, we can conclude that the measurement set has to be rejected, since it does not allow observation of all variables. Row i of M-' is obtained by back substitution using the LU factors, using a right-hand-side vector whose components are 6 , (Kronecker factor: 6, = 1when i =j, 6 , = 0 otherwise). In the summation of Eq. (18),only the variables Yjthat have been assigned a sensor are considered, since the variance of unmeasured variables has been set to infinity.

3.6.2 Detailed Implementation of the Algorithm

Solution of the sensor network problem is carried out in seven steps: 1. process model formulation and definition of link equations; 2. model solution for the nominal operating conditions and model linearization; 3 . specification of the sensor database and related costs; 4. specification of the precision requirements for observed variables; 5. verification of problem feasibility; 6. optimization of the sensor network 7. report generation. Each of the steps is described in detail before presenting a test case. 3.6.2.1 Process Model Formulation and Definition of Link Equations

In the current implementation, the process model is generated using the model editor of the Vali 3 data validation software, which is used as the basis for this work (Belsim 2004). The model is formulated by drawing a flow sheet using icons representing the common unit operations, and linking them with material and energy streams. Physical and thermodynamic properties are selected from a range of physical property models. Any acceptable measurement of a quantity that is not a state variable (T, P,partial molar flow rate) requires the definition of an extra variable and the associated link equation, which is done automatically for standard measurement types (e.g., mass or volume flow rate, density, dew point, molar or mass fractions, etc.). Similarly, extra variables and link equations must be defined for any process parameter to be assessed from the plant measurements. A proper choice of extra variables is important, since we may note that many state variables can not be measured in practice (e.g., no device exists to directly measure a partial molar flow rate or an enthalpy flow). In order to allow the model solution, enough variables need to be set by assigning them values corresponding to the nominal operating conditions. The set of specified variables must at least match the degrees of freedom of the model, but overspecifications are allowed, since a least square solution will be obtained by the data reconciliation algorithm.

3.6 Optimal Design $Measurement System

3.6.2.2 Model Solution for the Nominal Operating Conditions and Model Linearization

The data reconciliation problem is solved either using a large-scale SQP solver, or the Lagrange multiplier approach. When the solution is found, the value of all state variables and extra variables is available, and the sensitivity analysis is carried out (Heyen et al. 1996). A dump file is generated, containing all variable values, and the nonzero coefficients of the Jacobian matrix of the model and link equations. All variables are identified by a unique tag name indicating its type (e.g., S32.T is the temperature of stream S32, E102.K is the overall heat transfer coefficient of heat exchanger E102, and S32.MFH20 is the molar fraction of component H 2 0 in stream S32). 3.6.2.3 Specification o f the Sensor Database and Related Costs

A data file must be prepared that defines for each acceptable sensor type the following parameters: 0 0 0

0

the sensor name; the annualized cost of operating such a sensor; parameters a, and bi of the equation allowing to estimate the sensor accuracy from the measured value y,, according to the relation: oi = a, + biy,; a character string pattern to match the name of any process variable that can be measured by the given sensor (e.g., a chromatograph will match any mole fraction, and will thus have the pattern MF", while an oxygen analyzer will be characterized by the pattern M F 0 2 ) .

3.6.2.4 Specification of the Precision Requirements for Observed Variables

A data file must be prepared that defines the precision requirements for the sensor network after processing the information using the validation procedure. The following information is to be provided for all specified key performance indicators or for any process variable to be assessed: 0 0

the composite variable name (stream or unit name + parameter name); the required standard deviation a;, either as an absolute value, or as a percentage of the measured value.

3.6.2.5 Verification of Problem Feasibility

Before attempting to optimize the sensor network, the program first checks for the existence of a solution. It solves the linearized data reconciliation problem assuming all possible sensors have been implemented. In the case where several sensors are available for a given variable, the most precise one is adopted. This also provides an , for the cost of the sensor network. upper limit,,C A feasible solution is found when two conditions are met: 0 0

the problem matrix M is not singular. the standard deviation oi of all selected reconciled variables is lower than the specified value oti.

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3 Process Monitoring and Data Reconciliation

When the second condition is not met, several options can be examined. One can extend the choice of sensors available in the sensor definition file by adding more precise instruments. One can also extend the choice of sensors by allowing measurement of other variable types. Finally, one can modify the process definition by adding extra variables and link equations, allowing more variables besides state variables to be measured. 3.6.2.6 Optimization of the Sensor Network

Knowing that a feasible solution exists, one can start a search for a lower cost configuration. The optimization problem as posed involves a large number of binary variables (in the order of number of streams X number of sensor types). The objective function is multimodal for most problems. However, identifylng sets of suboptimal solutions is of interest, since criteria besides cost might influence the selection process. Since the problem is highly combinatorial and not differentiable, we attempted to solve it using a genetic algorithm (Goldberg 1989). The implementation we adopted is based on the freeware code developed by Carroll (1998). The selection scheme used involves tournament selection with a shuffling technique for choosing random pairs for mating. The evolution algorithm includes jump mutation, creep mutation, and the option for single-point or uniform crossover. The sensor selection is represented by a long string (gene) of binary decision variables (chromosomes). In the problem analysis phase, all possible sensor allocations are identified by finding matches between variable names (see Section 3.6.2.2) and sensor definition strings (see Section 3.6.2.3). A decision variable is added each time a match is found. Multiple sensors with different performance and cost can be assigned to the same process variable. The initial gene population is generated randomly. Since we know from the number of variables and the number of constraint equations the number of degrees of freedom of the problem, we can bias the initial sensor population by fxing a rather high probability of selection (typically 80 %) for each sensor. We found however that this parameter is not critical. The initial population count does not appear to be critical either. Problems with a few hundred binary variables were solved by following the evolution of populations of 10-40 genes, 20 being our most frequent choice. Each time a population is generated, the fitness of its members must be evaluated. For each gene representing a sensor assignment, we can estimate the cost C of the network, by summing the individual costs of all selected sensors. We also have to build the corresponding matrix M (Eq. (3b))and factorize it, which is done using a code exploiting the sparsity of the matrix. The standard deviation ui of all process variables is then estimated using Eq. (18). This allows calculating a penalty function P that takes into account the uncertainty affecting all observed variables. This penalty function sums penalty terms for all rn target variables. m

P = p i i=l

3.G Optimal Design ofMeasurernent System

where Pi

=

ai when oi 5 o:

(Ji

The fitness function F of the population is then evaluated as follows: 0

0

if matrix M is singular, return F otherwise return F = - (C + P).

= -,,C ,

Penalty function Eq. (5) (slightly)increases the merit of a sensor network that performs better than specified. Penalty function Eq. (6) penalizes genes that do not meet the specified accuracy, but it does not reject them totally, since some of their chromosomes might code interesting sensor subnetworks. The population is submitted to evolution according to the mating, crossover, and mutation strategy. Care is taken that the current best gene is always kept in the population, and is duplicated in case it should be submitted to mutation. After a specified number of generations, the value of the best member of the population is monitored. When no improvement is detected for a number of generations, the current best gene is accepted as a solution. There is no guarantee that this solution is an optimal one, but it is feasible and (much) better than the initial one. 3.6.2.7 Report Generation

The program reports the best obtained configurations as a list of sensors assigned to process variables to be measured. The predicted standard deviation for all process variables is also reported, as well as a comparison between the achieved and target accuracies for all key process parameters.

3.6.3 Perspectives

The software prototype described here has been further improved by allowing more flexibility in the sensor definition (e.g., defining acceptable application ranges for each sensor type) and by addressing retrofit problems by specifylng an initial instrument layout. The capability of optimizing a network for several operating conditions has also been implemented. The solution time grows significantly with the number of potential sensors. In order to address this issue, the algorithm has been parallelized (Gerkens and Heyen 2004) and the efficiency of parallel processing remains good as long as the number of processors is a divisor of the chromosome population size. Full optimization of very complex processes remains a challenge, but suboptimal feasible solutions can be obtained by requiring observability for smaller subflowsheets. The proposed method can be easily adapted to different objective functions besides cost to account for different design objectives. Possible objectives could address the

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3 Process Monitoring and Data Reconciliation

resiliency of the sensor network to equipment failures, or the capability to detect gross errors, in the line proposed by Bagajewicz (2001). There is no guarantee that this solution found with the proposed method is an optimal one, but it is feasible and (much)better than the initial one.

3.7 An Example

A simplified ammonia synthesis loop illustrates the use of data validation, including sensitivity analysis and the design of sensor networks. The process model for this plant is shown in Figure 3.1. The process involves a five-componentmixture (N2, H2,NH3,CH4,Ar), 10 units, 14 process streams, and 4 utility streams (ammonia refrigerant, boiler feed water, and steam). Feed stream f0 is compressed before entering the synthesis loop, where it is mixed with the reactor product f14. The mixture enters the recycle compressor C-2 and is chilled in exchanger E-1 by vaporizing ammonia. Separator F-1 allows one to recover liquid ammonia in 0, separated from the uncondensed stream fb. A purge f7 leaves

F7-MFAR

Figure 3.1 Data validation, base case. Measured and reconciled values are shown in result boxes as well as key performance indicators

0 045 0046.

3.7 ~n Example

the synthesis loop, while f8 enters the effluent to feed preheater E-3. The reaction takes place in two adiabatic reactors R-1 and R-2, with intermediate cooling in E-2, where steam is generated. Energy balances and countercurrent heat transfer are considered in heat exchangers E-1, E-2, and E-3. Reactors R-1 and R-2 consider atomic balances and energy conservation. Compressors C-1 and C-2 take into account an isentropic efficiency factor (to be identified). Vapor-liquid equilibrium is verified in heat exchanger E-1 and in separator F-1. The model comprises 160 variables, 89 being unmeasured. Overall, 118 equations have been written: 70 are balance equations and 48 are link equations relating the state variables (pressure, enthalpy and partial molar flow rates) either to variables that can be measured (temperature, molar fraction, and mass flow rate) or to performance indicators to be identified. A set of measurements has been selected using engineering judgment. Values taken as measurements were obtained from a simulation model and disturbed by random errors. The standard deviation assigned to the measurements was: 0

0 0 0

0

1°C for temperatures below 1OO"C, 2°C for higher temperatures 1% of measured value for pressures 2 % of measured values for flow rates 0.001 for molar fractions below 0.1, 1% of measured value for higher compositions 3 % of the measured value for mechanical power.

Measured values are displayed in Figure 3.1, as are the validated results. The identified values of performance indicators are also displayed. These are the extent of the synthesis reaction in catalytic bed R-1 and R-2, the heat load and transfer coefficients in exchangers E-1, E-2 and E-3, and the isentropic efficiency of compressors C-1 and c-2. Result analysis shows that all process variables can be observed. All measurement corrections are below 20, except for methane in stream f 7. The value of objective function Eq. (5) is 19.83, compared to a x2 threshold equal to 42.56. Thus, no gross error is suspected from the global test. Sensitivity analysis reveals how the accuracy of some estimates could be improved. For instance, Table 3.1 shows the sensitivity analysis results for the heat transfer coefficient in unit E-1. The first line in the table reports the value, absolute accuracy and relative accuracy of this variable. The next rows in the table identify the measurements that have a significant influence on the validated value of the E-1 heat transfer coefficient. For instance, 77.57% of the uncertainty on U comes from the uncertainty of variable AMO1-T (temperature of stream amOl). The derivative of U with respect to AMO1-T is equal to 0.12784. Thus one can conclude that the uncertainty on the heat transfer coefficient could be reduced significantly if a more accurate measurement of a single temperature is available. Table 3.2 shows that the reaction extent in reactor R-2 can be evaluated without resorting to precise chemical analysis. The uncertainty for this variable is 4.35 % of

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3 Process Monitoring and Data Reconciliation Table 3.1

Sensitivity analysis for heat transfer coefficient in exchanger E-1

Variable

K

U E-1

Measurement

Tag Name

Value

Abs.Acc.

Computed

3.5950

Tag Name

Contrib.

ReLAcc.

Penal.

-

4.04 %

0.14515 Der.Val.

P.U.

Rel.Cain

Penal.

P.U.

1.21%

0.01

c

0.21%

0.00

C

34.29%

3.67

-

T

SAM01

AMO1-T

77.57%

T

SAM02

AMO2-T

5.75%

-0.34800E-01

MFNH3

R F6

F7-MFNH3

4.33 %

-30.216

MASSF

R AMOl

AMOI-MASSF

4.05%

0.16227E-01

46.50%

0.23

t/h

MASSF

R F12

F14-MASSF

1.75%

-0.27455E-02

33.79%

0.99

t/h

T

S F7

F7-T

1.50%

-0.177948-01

62.36%

1.16

C

T

S F6

F6-T

1.50%

-0.177948-01

62.36%

0.01

C

T

S F4

F4-T

1.50%

-0.177948-01

62.36%

1.16

C

Table 3.2

0.12784

Sensitivity analysis for reaction extent in reactor R-2

Variable

EXTENT1

U R-2

Measurement

Tag Name

Value

Abs.Acc.

Rel.Acc.

Penal.

Computed

7.6642

0.33372

4.35 %

Tag Name

Contrib.

Der.Val.

ReLCain

P.U. k m o l min-'

Penal.

P.U.

~~

T

S F11

F11-T

26.82%

-0.86410E-01

21.85%

0.00

C

T

S F12

F12-T

25.13%

0.836406-01

26.78%

0.22

C

T

S F9

F9-T

21.52%

0.77397E-01

27.69%

0.22

C

T

S F10

F1O-T

19.95%

-0.745328-01

22.02%

0.00

C

MASSF

R F5

FS-MASSF

1.56%

0.49680E-01

49.64%

0.23

t/h

~

~~

MASSF

R BFWOl

STMO1-MASSF 1.51%

0.465918-01

35.39%

0.01

t/h

MASSF

R AMOl

AMOI-MASSF

0.81 %

0.166478-01

46.50%

0.23

t/h

MASSF

RFO

FO-MASSF

0.77%

0.25907E-01

58.25%

0.14

t/h

MFNH3

RF12

F14-MFNH3

0.58%

18.215

29.41%

0.15

-

the estimated value and results mainly from the uncertainty in four temperature measurements. Better temperature sensors for streams f9, f10, f l l and f12 would allow one to better estimate the reaction extent. This sensor network provides acceptable estimates for all process variables. However the application of the sensor placement optimization using a genetic algorithm can identify a cheaper alternative.

3.7 ~n Example Table 3.3

Cost, accuracy, and range for available sensors

Measured Variable

Relative cost

Standard deviation D

Acceptable range

T

1

1“C

T < 150°C

T

1

2 “C

T > 15O’C

P

1

1%

1-300 bar

Flow rate

5

2%

1-100 kg SK’

Power

1

3%

1-10,000 kW

Molar composition (all components in stream)

20

0.001 1%

x, 0.1

A simplified sensor data base has been used for the example. Only six sensor types were defined, with accuracies and cost as defined in Table 3.3. Accuracy targets are specified for seven variables: 0

0 0

two compressor efficiencies, target u = 4 % of estimated value three heat transfer coefficients, target u = 5 % of estimated value two reaction extents, target o = 5 % of estimated value.

The program detects that up to 59 sensors could be installed. When all of them are selected, the cost is 196 units, compared to 42 sensors and 123 cost units for our initial guess shown in Figure 3.1. Thus the solution space involves 2 ” = 5.76 X 1017 solutions (most of them being unfeasible). We let the search algorithm operate with a population of 20 chromosomes, and iterate until no improvement is noticed for 200 consecutive generations. This requires a total of 507 generations and 10,161 evaluations of the fitness function, which runs in 90 s on a laptop PC (1 GHz Intel Pentium 111processor, program compiled with Compaq FORTRAN compiler, local optimization only). Figure 3.2 shows Fitness

Generations

0 100

-200

200

300

400

5 0

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3 Process Monitoring and Data Reconciliation

that the fitness function value varies sharply in the first generations and later improves only marginally. A solution with a cost similar to the final one is obtained after 40 % of the calculation time. The proposed solution involves only 26 sensors, for a total cost reduced to 53 cost units. The number of sensors is reduced from 16 to 11 for T, from 15 to 12 for P, from 6 to 2 for flow, and from 3 to 1 for composition. Thus the algorithm has been able to identify a solution satisfying all requirements with a considerable cost reduction.

3.8 Conclusions

Efficient and safe plant operation can only be achieved if the operators are able to monitor key process variables. These are the variables that either contribute to the process economy (e.g., yield of an operation) or are linked to the equipment quality (fouling in a heat exchanger, activity of a catalyst), to safety limits (departure from detonation limit), or to environmental considerations (amount of pollutant rejected). Most performance parameters are not directly measured and are evaluated by a calculation based on several experimental data. Random errors that always affect any measurement also propagate in the estimation of performance parameters. When redundant measurements are available, they allow one to estimate the performance parameters based on several data sets, leading to different estimates, which may lead to confusion. Data reconciliation allows one to address the state estimation and measurement correction problems in a global way by exploiting the measurement redundancy. Redundancy is no longer a problem, but an asset. The reconciled values exhibit a lower variance compared to original raw measurements; this allows process operation closer to limits (when this results in improved economy). Benefits from data reconciliation are numerous and include: improvement of measurement layout; 0 decrease of number of routine analyses; 0 reduced frequency of sensor calibration: only faulty sensors need to be calibrated; 0 removal of systematic measurement errors; 0 systematic improvement of process data; 0 clear picture of plant operating condition and reduced measurement noise in trends of key variables; 0 early detection of sensor deviation and of equipment performance degradation; actual plant balances for accounting and performance follow-up; 0 safe operation closer to the limits; 0 quality at process level. 0

Current developments aim at combining online data acquisition with data reconciliation. Reconciled data are displayed in control rooms in parallel with raw measurements. Departures between reconciled and measured data can trigger alarms. Analy-

sis of time variation of those corrections can draw attention to drifting sensors that need recalibration. Data reconciliation can also be viewed as a virtual instrument; this approach is particularly developed in biochemical processes, where direct measurement of the key process variables (population of microorganisms and yield in valuable by-products) is estimated from variables that are directly measured online, such as effluent gas composition. Current research aims at easing the development of data reconciliation models by employing libraries of predefined unit operations, automatic equation generation for typical measurement types, analyses of redundancy and observability, analyses of error distribution of reconciled values, interfaces to online data collection systems and archival data bases, and developing specific graphical user interfaces.

References

T.Data reconciliation and gross-error detection for dynamic systems. AlChE I. 42 (1996) p. 2841-2856 2 Bagajewicz M. J. Process Plant Inshumentation: Design and Upgrade. Chap. 6, Technomic Publishing Company, Lancaster PA (USA) (1997) 3 Bagajewicz M. J . Design and retrofit of sensor networks in process plants. AlChE I. 43(9) (2001) p. 2300-2306 4 Bagajewicz M. 1. Rollins D. R Data reconciliation. In.B.G. Liptak (ed.)Instrument Engineers’ Handbook (3rd edn.), Vol. 3: Process Software and Digital Networks. CRC, Taylor and Francis, Boca Raton, FL (USA) (2002). 5 Bagajewicz M. J . Sanchez M. C.Design and upgrade of nonredundant and redundant linear sensor networks. AlChE 1. 45(9) (1999) p. 1927-1938 6 Belsim, VAL1 4 User’s Guide. Belsim SaintGeorges-sur-Meuse. Belgium (2004). 7 Benqlilou C., Graells M. Puigjaner L. Decision-making strategy and tools for sensor networks design and retrofit. Ind. Eng. Chem. Res. 43 (2004) p. 1711-1722 8 Binder T.Blank L. Dahmen W. Marquardt W. Towards multiscale dynamic data reconciliation. In: R. Berber (ed.) Nonlinear ModelBased Process Control. NATO AS1 series, Kluwer, Dordrecht (1998) 9 Carroll D . L. FORTRAN Genetic Algorithm Driver, version 1.7, http://www.staff.uiuc. edu/carroll/ga.html (1998) accessed ruly 2001. 10 Chen H . S. Stadherr M. A. A modification of Powell’s dogleg algorithm for solving 1 AlbuquerqueJ . S. Biegler L.

systems of non-linear equations. Comput. Chem. Eng. S(3) (1981) p. 143-150 11 Chen H . S. Stadherr M. A. On solving large sparse nonlinear equation systems. Comput. Chem. Eng. 8(1) (1984a) p. 1-6 12 Chen H . S. Stadherr M. A. Enhancements of Han-Powell method for successive quadratic programming. Comput. Chem. Eng. 8(3/4) (1984b) p. 299-234 (198413) 13 Crowe C. M. Observability and redundancy of process data for steady state reconciliation. Chem. Eng. Sci. 44 (1989) p. 2909-2917 14 Crowe C. M. Data reconciliation - progress and challenges. I. Process Control. (6) (1996) p. 89-98 15 Datacon Invensys,http://www.simsci.com/products/datacon.stm, cited 3 May (2004) 16 Gerkens C.Heyen G. Use of Parallel Computers in Rational Design of Redundant Sensor Networks. 14th European Symposium on Computer Aided Process Engineering, Lisbon (2004) 17 Goldberg D. E. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA (USA) (1989) 18 Heyen G. Durnont M. N. KalitventzefB. Computer aided design of redundant sensor networks. In: Grievnik ]. Dumont M. N. Kalitventzeff B. 12th European symposium on Computer Aided Process Engineering The Hague, Elsevier Science, Amsterdam (2002) 19 Heyen G . Martkhal E. KalitventzefB. Sensitivity calculations and variance analysis in plant measurement reconciliation. Comput. Chem. Eng. 20s (1996) p. 539-544

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3 Process Monitoring and Data Reconciliation 20 Joris P. Kalitventzeff B. Process measure-

21

22

23

24

25

26

27

ments analysis and validation. In: Proceedings Chemical Engineering Fundamentals Conference (CEF’87):Use of Computers in Chemical Engineering, Italy, pp. 41-46 (1987) KalitventzeffB., Laud P. Gosset R. Heyen G. The validation of industrial measurements, a necessary step before the parameter identification of the simulation model for large chemical engineering systems. In: Proceedings of International Congress ”Contribution des calculateurs blectroniques au developpement du genie chimique,” Societe de Chimie Industrielle, Pans (1978) Kalman R. E. A new approach to linear filtering and prediction problems. Trans. ASME 1. Basic Eng. 82D (1960) p. 35-45 Kuehn D. R. Dauidson H . Computer control: mathematics of control. Chem. Eng. Prog. 57 (1961) p. 44-47 Kyriakopoulou D. /. Kalitventzeff B. Data reconciliation using an interior point sqp. ESCAPE-6, Rhodes, Greece, 26-29 May, Pergamon Press (1996) Kyriakopoulou D. /.Kalitventzeff B. Reduced Hessian interior point SQP for large-scale process optimization. First European Congress on Chemical Engineering, Florence, Italy, 4-7 May AlDIC Milano (1997) Liebman M . /. Edgar T. F. Lasdon L. S. Efficient data reconciliation and estimation for dynamic processes using nonlinear programming techniques. Comput. Chem. Eng. 16 (1992)p. 963-986 Madron F. Process Plant Performance: Measurement and Data Processing for Optimization and Retrofits. Ellis Honvood, London (1992)

28 M a h R. 5. H . Stanley G. M . Downing D. W.

Reconciliation and Rectification of Process Flow and Inventory Data. Ind. and Eng. Chem. Proc. Des. Dev. 15 (1976) p. 175-183 29 Meyer M . Le Lann]. M . L. Koeherf B. Enjalbert M . Optimal selection of sensor location on a complex plant using graph-oriented approach. In: Moser F. Schnitzer H. Bart H.-J. (eds.) European Symposium on Cumputer-Aided Process Engineering-3, Graz, Austria (1993). Suppl. to Computers and Chemical Engineering, Pergamon Press, Oxford (1993) 30 Musch H. List T. DempfD. Heyen G. On-line Estimation of Reactor Key Performance Indicators: an Industrial Case Study. (2004) 29 Narasimhan S.lordache C., Data Reconciliation and Gross Error Detection, an Intelligent use of Process Data. Gulf, Publishing Company, Houston, TX (USA) (2000) 30 RomagnoliJ. A. Sanchez M. C. Data Processing and Reconciliation for Chemical Process Operations. Academic Press, San Diego, CA (USA) (2000) 31 Vaclavek V . Studies on system engineering: on the application of the calculus of obsexvations in calculations of chemical engineering balances. Coll. Czech. Chem. Commun. 34 (1968) p. 3653-3660 32 Vaclavek V. Studies on System Engineering: Optimal Choice of the Balance Measurements in Complicated Chemical Engineering Systems. Chem. Eng. Sci. 24 (1969) p. 947-955 33 Vali Belsim http://w.belsim.com/Products-main.htm, cited 3 May 2004 34 Veverka V. V. Madron F. Material and energy balancing in the process industries. From microscopic balances to large plants, Computer-Aided Chemical Engineering. Elsevier Science, Amsterdam (1996)

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

4 Model-based Control Sebastian Engell, Cregor Fernholz, Weihua Cao, and Abdelaziz Toumi

4.1 Introduction

As explained in several chapters of this volume, rigorous process models can be used to optimize the design and the operating parameters of chemical processing plants. However, optimal settings of the parameters do not guarantee optimal operation of the real plant. The reasons for this are the inevitable plant-model mismatches, the effects of disturbances, changes in the plant behavior over time, etc. Usually not even the constraints on process or product parameters are met at the real plant if operating parameters that were obtained from offline optimization are applied. The only effective way to cope with the effect of plant-model mismatch, disturbances etc. is to use some sort of feedback control. Feedback control means that (some of) the degrees of freedom of the plant are modified based on the observation of measurable variables. These measurements may be performed quasicontinuously or with a certain sampling period, and accordingly the operation parameters (termed inputs in feedback control terminology) may be modified in a quasicontinuous fashion or intermittently. Often, key process parameters cannot be measured online at a reasonable cost. One important use of process models in process control is the model-based estimation of such parameters from the available measurements. This topic has been dealt with in the previous chapter. In this chapter, we focus on the use of rigorous process models for feedback control by model-based online optimization. Feedback control can be combined with model-based optimization in several different ways. The simplest, and most often used, approach is to perform an offline optimization and to divide the degrees of freedom into two groups. The variables in the first group are applied to the real process as they were computed by the offline optimization. The variables in the second group are used to control some other variables to the values which resulted from the offline optimization, e.g., requirements on purities are met by controlling the product concentration by manipulating the feed rate to a reactor or the reflux in a distillation column. In the design of these feedback controllers, dynamic plant models are used, in most cases obtained from a lineComputer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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arization of the rigorous model around the optimal operating regime or process trajectory. If nonlinear process models are available from the design stage, these models can be used directly in model-based control schemes. This leads to nonlinear model-predictive control (NMPC)where the future values of the controlled variables are predicted over a finite horizon (the prediction horizon) using the model, and the future inputs are optimized over a certain horizon (the control horizon). The first inputs’ values are applied to the plant. Thereafter, the procedure is repeated, taking new measurements into account. A major advantage of this approach is the ability to include process constraints in the optimization, thus exploiting the full potential of the plant and the available actuators (pumps, valves) and respecting operating limits of the equipment. In Section 4.2, NMPC around a precomputed trajectory of the process is presented in more detail and its application to a reactive semibatch distillation process is discussed. When closed-loop control is used to track a precomputed trajectory and the controllers perform satisfactorily, the process is kept near the operating point that was computed as the optimal one offline. Those variables which are under feedback control track their precomputed set-point even in the presence of disturbances and plant-model mismatch. However, the overall operation will in general no longer be optimal, because the precomputed operating regime is optimal for the nominal plant model, but not for the real plant. As an extension of this concept, feedback control can be combined with model adaptation and reoptimization. At a lower sampling rate than the one used for control, some model parameters are adapted based upon the available measurements. After the model has been updated, it is used for a reoptimization of the operating regime. The new settings can be implemented directly or be realized by feedback. In Section 4.3, such a control scheme is presented for the example of batch chromatographic separations, including experimental results. A serious problem in practice is structural plant-model mismatch. This means that an adaptation of the model parameters, even for an infinite number of noise-free measurements, will not give a model that accurately represents the real process. Therefore if the structurally incorrect model is used in optimization, the resulting operating parameters will not be optimal; often, not even the constraints will be met by the real process unless the constrained variables are under feedback control with some safety margin that reflects the attainable control performance, which again causes a suboptimal operation. A solution to the problem of plant-model mismatch is the use of optimization strategies that incorporate feedback directly, i.e., use the information gained by online measurements not only to update the model but also to modify the optimization problem. In Section 4.4,this idea is presented in detail and the application to batch chromatography is used to demonstrate its potential. NMPC involves online optimization on a finite horizon based upon a nonlinear plant model. This approach can be employed not only to keep some process variables at their precomputed values or make them track certain trajectories, but also to perform online predictive optimization of the plant performance. Bounds, e.g., on product specifications,can be included in the formulation as constraints rather than set-

4.2 NMfCApplied to a Semibatch Reactive Distillation Process

ting up a separate feedback control layer to meet the specifications at the real plant. In this spirit, the problem of controlling quasicontinuous (simulated moving bed) chromatographic separations is formulated in Section 4.5 as an online optimization problem, where the measured outputs have to meet the constraints on the product purities but the optimization goal is not tracking of a precomputed trajectory, but optimal process operation.

4.2 NMPC Applied to a Semibatch Reactive Distillation Process 4.2.1 Formulation of the Control Problem

In NMPC, a process model is used to predict the future process outputs 7 over a fmed prediction time horizon Hp for given sequences of H,changes of the manipulated variables u. The aim of the controller is to minimize a quadratic function of the deviation between the process outputs 7 and their desired trajectories yfas well as of the changes of the manipulated variables. The control move at the sampling point k + l is given by the optimization problem Eq. (1).The parameters ytrand k,, allow scaling the controlled and manipulated variables and shifting the weight either on good setpoint tracking or on smooth controller actions. Bounds on the manipulated variables can be enforced by using sufficiently large penalties I,, or by adding inequality constraints (Eq. (2)) to the optimization problem Eq. (1):

Umln

J

5 uk+j < - umax V j = 1 , .. . , H,.

If the control scheme is applied to a real plant, plant-model mismatch or disturbances will lead to differences between the predicted and the real process outputs. Therefore a time-varying disturbance model, as proposed by Draeger et al. (1995),is included in the process model. The formal representation of the complete model that is used by the model predictive controller is

where dk, denotes the estimated disturbances, ykmodeldenotes the model outputs given by the physical process model, and j$ the model prediction of the controller used in the optimization problem (1).The disturbances dk, are recalculated at every time k for each time step i. The process model is simulated from time k-i until time k taking into account the actual control actions giving the model outputs Yde'(klk-i). The errors ek, computed as the differences between the measurements ykmeasand the model outputs y d e ' ( k lk-i):

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F- ymodel( k I k - i ) .

(4)

ek,i - k

The new estimates of the disturbances are calculated by a first order filter:

dk,i= aek,i+ (1 - a)dk-l,i. 4.2.2 The Methyl Acetate Process

Methyl acetate is produced from acetic acid and methanol in an esterification reaction. The conventional process consists of a reactor and a complex distillation column configuration, while using reactive distillation, high purity methyl acetate can be produced in a single column (Agreda et al. 1990). The reaction can either by catalyzed homogeneously by sulfonic acid or heterogeneously using a solid catalyst. The latter avoids material problems caused by the sulfonic acid as well as the removal of the catalyst at the end of the batch. This process is investigated here. A scheme of the process is shown in Figure 4.1. The column consists of three parts. Two structured catalytic packings of 1 m height are located in the lower part of the column while the upper part contains a noncatal9c packing. Methanol is filled into the reboiler before the beginning of the batch and heated until the column is filled with methanol. Acetic acid is fed to the column above the reactive section. Since acetic acid is the highest boiling component, it is necessary to feed it above the catalpc packing in order to ensure that both raw materials are present in the catalytic area in sufficient concentrations. The upper section purifies the methyl acetate. The azeotropes of the mixture are overcome because water and acetic acid are present in the stream that enters the separation stages. The plant considered here is a pilot plant in the Department of Biochemical and Chemical Engineering at Universitat Dortmund. A batch run takes approximately 17 h. Condensor

Product Packing Catalytic Packing Catalytic Packing

f3 Reboiler

Figure 4.1

Scheme of the semibatch column

4.2 NMPCApplied to a Semibatch Reactive Distillation Process

A more detailed description of the process and a rate-based model and its validation are presented in Kreul et al. (1998)and Noeres (2003).The latter pointed out that for this process the accuracy of a rate-based model is not significantly higher than that of an equilibrium stage model, and thus the equilibrium stage model was used to determine the optimal operation of the process (Fernholz et al. 2000) and as a basis for controller design. Mass and energy balances for all parts of the plant result in a differential-algebraicequation system consisting of more than 2000 equations. The main assumptions in the model are: 0

0 0

0

0 0

0

0

0 0 0

The structured packings can be treated as a number of theoretical plates using the HETP-value (height equivalent to theoretical plate). The vapor and the liquid phase are in thermodynamic equilibrium. All chemical properties depend on the temperature and the composition. The phase equilibrium is calculated using the Wilson equations. The dimerization of acetic acid in the vapor phase is taken into consideration. The reaction kinetics are formulated by a quasihomogeneous correlation. The pressure drop of the packing is calculated by the equation of Mickowiak (1991). The hold-up of the packing is determined by an experimentally verified correlation. Negligible vapor hold-up. Ideal vapor behavior. Constant molar hold-up in the condenser. The dynamics of the tray hydraulics and the liquid enthalpy are taken into consideration.

The aim of the controller is to ensure the tracking of the optimal trajectory in the presence of model inaccuracies and disturbances acting on the process.

4.2.3 Simplified Solution of the Model Equations

Generally, any process model can be used to predict the future process outputs f k + l , as long as the model is sufficiently accurate. A straightforward approach would be to use the same model that was used to calculate the optimal operation. Unfortunately the integration of this differential algebraic model is too time-consuming to solve the optimization problem given by Eqs. (1)and (2) within one sampling interval. Thus, a different model had to be developed to make sure that the solution of Eqs. (1)and (2) is found between two sampling points. The physical process model is based on heat and mass balances resulting in a set of differential equations. A large number of algebraic equations is needed to calculate the physical properties, the phase equilibrium, the reaction kinetics and the tray hold-ups, as well as the connections between the different submodels. Various numerical packages are now available to solve large differential-algebraicequation (DAE) systems like gPROMS (1997) or the Aspen Custom Modeler (ACM). Even

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though they are designed to solve large and sparse DAEs in an efficient way, generalpurpose solvers do not take advantage of the mathematical structure of a special problem. Our aim was to find a way to reduce the numerical effort required to calculate the solution of the DAE system which describes the reactive distillation process. The main idea is to split up the equation system into a small section that is treated by the solver in the usual manner and a large subsystem containing mainly the algebraic equations. An independent solver that communicates with the DAE solver calculates the solution of this subsystem. Generally, this sequential approach may not be advantageous since the solution of the algebraic part must be provided in each step of the iteration of the DAE solver. It will only be superior if the solution of the second part is calculated in a highly efficient way. Therefore an analysis of the system equations for one separation tray is given in the sequel. Similar considerations can be easily made for the reactive trays as well as the other submodels of the process. The core of the model for each separation tray consists of the mass balances of the components (Eq. (6))the heat balance (Eq. (7)),and the constitutive equation for the liquid mole fractions (Eq. (8)):

In addition to the core Eqs. (6)-(8), empirical correlations are used to calculate the molar hold-ups of the trays (Eq. (9)),the liquid enthalpy (Eq. (lo)),the vapor enthalpy (Eq. (ll)),and the density (Eq. (12)):

Finally the phase equilibrium is calculated by using a four-parameter Wilson activity coefficient model for the liquid phase and a vapor-phasemodel which takes into consideration the dimerization of the acetic acid in the vapor phase (Noeres 2003). This phase equilibrium model (Eq. (13)) is an implicit set of equations in contrast to Eqs. (9)-(12) which are explicit functions of the composition and the temperature.

4.2 NMPC Applied t o a Semibatch Reactive Distillation Process

Even though the formal description of Eqs. (9)-(13) feigns that its size is similar to the core model Eqs. (6)-(8),the opposite is true. Owing to the necessity of introducing a lot of auxiliary variables, especially for the phase equilibrium, Eqs. (9)-(13) make up the largest part of the overall system. Thus the idea is to move as many algebraic equations as possible, especially the parts containing the auxiliary variables, from the part which is handled by the DAE solver to an additional solver that exploits the mostly explicit structure of the equations. The DAE solver used in this work is DASOLVE, a standard solver in gPROMS for stiff DAEs (gPROMS, 1997).The proposed architecture of the algorithm is shown in Figure 4.2. The main task of the external software is to solve the implicit phase equilibrium Eq. (13a,b)in an efficient manner. Solving Eq. (13a,b)for given pressure and liquid composition means to find the temperature T such that condition Eq. (13b) is fulfilled for the values calculated by Eq. (13a).Thus, the phase equilibrium calculation can be treated as solving a nonlinear equation with one unknown variable. Once Eq. (13a) and Eq. (13b) are solved, the remaining variables can be calculated straightforwardly by the explicit Eqs. (9)-(12). All values are passed back from the DAE solver via the foreign object interface. In order to minimize the number of equations handled by the DAE-solver, the dynamics of the tray hold-up N and the liquid enthalpy hli, were neglected. This causes deviations between the original model and the model with neglected dynamics. Several case studies were performed to check the differences between the original model and the model with neglected dynamics. In many cases the predictions of both models can hardly be distinguished. In some cases, however, noticeable differences in the dynamic behaviors result. These inaccuracies have to be handled by the disturbance estimation of Eqs. (3)-(5). By applying this scheme to the complete column model, the time required to calculate the solution for typical model predictive control scenarios could be reduced by a factor of 6-10. The use of a simplified model and the special solution algorithm enable the online solution of the optimal control problem of Eqs. (1)-(3). The optimization algorithm L-BFGS-B of Byrd et al. (1994) is used to solve the optimization problem. This code solves nonlinear optimization problems with simple bounds on the decision variables and ensures a decrease of the goal function in each iteration step. The user of this code has to supply the values of the goal function as well as its derivatives with respect to the decision variables. The value of the cost function is calculated by integrating the model, the derivatives are obtained by perturbation. Using perturbations offers the opportunity to parallelize the calculation. Within a sampling period of

Figure 4.2

Scheme of the algorithm

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6 min, about 100 function and gradient evaluations can be performed. The maximal number of function and gradient evaluations which were needed for the cases investigated was 33. Thus, the algorithm is able to find the optimal solution within the sampling time.

4.2.4 Controller Performance

The analysis of Fernholz et al. (1999a) showed that a suitable control structure for this process is to control the concentrations of methyl acetate and water in the product stream by the reflux ratio and the heat duty of the reboiler. At our pilot plant, NIR (near infrared spectroscopy) measurements of the product concentrations are available. The nonlinear model predictive controller was tested in several simulation cases. Here the original model is used as the simulated process, whereas the simplified model is used in the controller. In order to explore the benefits of the nonlinear controller, a linear controller was designed as well (Engell and Fernholz 2003). The linear controller was chosen based on an averaged linear model calculated from several linear models which were obtained by linearization of the nonlinear model at several points on the optimal trajectory. The controller design was done using the frequency response approximation technique (Engell and Muller 1993).The details of the linear controller design are beyond the scope of this book, they can be found in Fernholz et al. (19991-3). The parameters of the cost function in Eq. (1)were chosen such that deviations of both controlled variables give the same contribution to the objective functions. Additional bounds on the manipulated variables were added. The reflux ratio is physically bounded by the values 0 and 1, while the heat duty is bounded to a lower value of 1 kW and an upper one of 8 kW to ensure proper operation of the column. In order to avoid undesired abrupt changes of the manipulated variables, small penalties on these changes were added. The values of the penalty parameters )Lii were selected in a way that large changes are possible for large deviations of the controlled variables but are unfavorable if they are close to their set-points1. Preliminary work on the model predictive control of this process had shown that the choice of a control horizon of H, = 2 and of a prediction horizon of H, = 5 gave good results. The closed loop responses for a set-point change of the methyl acetate concentration from a mole fraction of 0.8 down to 0.6 and back to 0.8 are shown in Figure 4.3. The use of the nonlinear controller reduces the time required to decrease the methyl acetate concentration drastically. The price that has to be paid for this reduction is a larger deviation of the water concentration. For the set-point change back to the original value, the differences between the two controllers are small. Next, the performance of both controllers was checked for set-points of methyl acetate and water which force the process into a region where a sign change of the static gain occurs. If the set-points of the mole fractions of methyl acetate and water are of all A,,is 0.01, while y is set to one. The physical units of the controlled variables are mole mole-', the reflux ratio is dimensionless and the heat duty is given in kilowatts.

1 The value

4.2 N MPC Applied to a Semibatch Reactive Distillation Process

methyl acetate

1

0

100 200 300 reflux ratio

0

100 200 300 time [min]

water

0.151

1

0

100 200 300 heat duty

0

100 200 300 time [min]

Figure 4.3 Methyl acetate set-point tracking. Black: nonlinear controller; grey: linear controller

changed simultaneously to 0.97 and 0.02 respectively, both controllers drive the process in the correct direction (Figure 4.4), but only the nonlinear controller is able to track both concentrations accurately. If the set-points are set back to their original values, the linear controller becomes unstable while the nonlinear controller works properly.

c

I[_-..

O I K

-

0 .c

3 0.8 + L a,

f 0.6r

t

0

0.05

i?

--L-

.. 100 200 300 time [min]

'F-I 10

100

200

300

time [min]

Figure 4.4 Set-point tracking in a region o f a sign change of the static gain. Black: nonlinear controller; grey: linear controller

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4.2.4.1 Disturbance Rejection

The main goal of the controller is to track the optimal trajectory of the process in the case of disturbances and plant-model mismatch. In the case of an accurate model and the absence of disturbances, no feedback controller would be necessary. Thus, two disturbances are imposed on the process during the simulation to test the disturbance rejection capabilities of the controllers. First the influence of disturbances of the heat supply is considered. After 200 min the heat supply is decreased by 0.7 kW (which is about 20 % of the nominal value), set back to its nominal value at t = 300 min and increased by 0.7 kW at t = 550 min until it is again reset to the nominal value at t = 700 min. The simulation results for both controllers are depicted in Figure 4.5. The nonlinear controller rejects the disturbance much faster than the linear controller, especially for the product methyl acetate. The second disturbance investigated is a failure of the heating system of the column. In order to minimize heat losses across the column surface, the plant is equipped with a supplementary heating system. A malfunction of this system will change the heat loss across the surface. The heat loss is increased by SO W per stage, set back to 0 and decreased by SO W per stage at the same times at which the disturbances of the heat duty were imposed before. The simulation results in Figure 4.6 show that the nonlinear controller rejects this disturbance more efficiently than the linear controller. Thus, the disturbance rejection can be significantly improved by using the nonlinear predictive controller. methyl acetate I

200 0.641

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400 600 time [min]

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Figure 4.5 Rejection of a disturbance in the heat supply. Black: nonlinear controller: grey: linear controller; dashed optimal trajectory

4.2 NMPC Applied to a Semibatch Reactive Distillation Process

methyl acetate

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400 600 reflux ratio

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400 600 heat duty

800

200

400

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200

400 600 time [min]

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600 time [min]

Figure 4.6 Rejection of a disturbance in the heat loss. Black nonlinear controller; grey: linear controller; dashed optimal trajectory

4.2.5 Summary

In this section, we presented the principle of NMPC to track a precomputed trajectory of a complex process and discussed the application to a semibatch reactive distillation column. Neglecting the dynamics of the molar hold-ups and of the enthalpies enabled splitting up the original DAE system into a small DAE part, which is treated by the numerical simulator, and an algebraic part, which is solved by an external algorithm. This approach reduced the time needed to solve the model equations by a factor of 6-10, These reductions made the use of a process model that is based on heat and mass balances possible for a model predictive controller. The resulting nonlinear controller showed superior set-point tracking properties compared to a carefully designed linear controller. The nonlinear controller is able to track set-points that lie in regions where the process shows sign changes in the static gains and any linear controller becomes unstable. The nonlinear controller rejects disturbances faster than the linear controller. Moreover, since the nonlinear controller makes use of a model the range of validity of which is not restricted to a fNed operating region in contrast to the linear one, the nonlinear controller might be used for different trajectories giving more overall flexibility. The superior performance of the controller is due to the fact that a nonlinear process model is used. On the other hand, its stability and performance depend on the accuracy of the rigorous process model. If, e.g., the change of the gain of the process (which is caused by the fact that the product purity is maximized for certain values of reflux and heat duty) occurs for different values of the reflux and the heat duty than predicted by the model, the controller may fail to stabilize the process.

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4.3 Control of Batch Chromatography Using Online Model-based Optimization

4.3.1 Principle and Optimal Operation of Batch Chromatography

The chromatographic separation is based on the different adsorptivities of the components to a specific adsorbent which is futed in a chromatographic column. The most widespread process, batch chromatography, involves a single column which is charged periodically with pulses of the feed solution. These feed injections are carried through the column by pure desorbent. Owing to different adsorption affinities, the components in the mixture migrate at different velocities and therefore they are gradually separated. At the outlet of the column, the purified components are collected between cutting points, the locations of which are decided by the purity requirements on the products (Figure 4.7). For a chromatographic batch process with given design parameters (combination of packing and desorbent, column dimensions, maximum pump pressure), the determination of the optimal operating regime can be posed as follows: a given amount (or flow) of raw material has to be separated into the desired components at minimal cost while respecting constraints on the purities of the products. The operation cost may involve the investment into the plant and the packing, labor and solvent cost, the value of lost material (valuable product in the nonproduct fractions) and the cost of the further processing, e.g., removal of the solvent. The free operating parameters are: the throughput of solvent and feed material, represented by the flow rate Q or the interstitial velocity u, constrained to the maximum allowed throughput which in turn is limited by the efficiency of the adsorbent or the pressure drop; the injection period ti,(, representing the duration of the feed injection as a measure of the size of the feed charge; the cycle period tcyc.representing the duration from the beginning of one feed injection to the beginning of the next; the fractionating times.

0

0

0

The mathematical modeling of single chromatographic columns has been extensively described in the literature by several authors, and is in most cases based on differential mass balances (Guiochon 2002). The modeling approaches can be classified by the physical phenomena they include and thus by their level of complexity. Details

~~

injection

elution

7

column Figure 4.7

Principle of batch chromatography

,..

collection

tl

t2

b

trt

4.3 Control ofBatch Chromatography Using Online Model-based Optimization

on models and solution approaches can be found e.g., in (Diinnebier and Klatt 2000). The most general one-dimensional model (ignoring radial inhomogeneities) is the general rate model (GRM)

at

at

where also reaction terms in the liquid and in the solid phase were included. These two partial differential equations describe the concentrations in the mobile ) . adsorption isotherms relate phase (cb,i) and in the stationary phase (qi and c ~ , ~The the concentrations qi (substance i adsorbed by the solid) and cp,i(substance i in the stationary liquid phase). A commonly utilized isotherm functional form is biLangmuir isotherm: qi =

al%,i

1

+ C bIj5.i

+

a2cp,i 1+

j

C

b2jcp.j.

(16)

j

An efficient numerical solution for the GRM incorporating arbitrary nonlinear isotherms was proposed by Gu (1995).The mobile phase and the stationary phase are discretized using the finite element and the orthogonal collocation method. The resulting ordinary differential equation (ODE)system is solved using an ODE solver which is based on the Gear's method for stiff ODES. The numerical solution yields the concentrations of the components in the column at different locations and times. The concentration information at the outlet of the column is used to generate the chromatogram from which the production rate and the recovery yield can be computed. The requirements on the products can usually be formulated in terms of minimum purities, minimum recoveries or maximum losses. In the case of a binary separation without intermediate cuts, these constraints can be transformed into each other, so either the recovery yield or the product purity may be constrained. The production cost is determined by many factors, in particular the throughput, the solvent consumption and the cost of downstream processing. A simple objective function is the productivity Pr, i.e., the amount of product produced per amount of adsorbent. This formulation results in the following nonlinear dynamic optimization problem:

such that

Reci 1 Rec,in,i,

0 5 u i %ax> 0 5 Gnj, tcyc

i = 1, . . . , nsp

where Reci denotes the revovery yield of product i. This type of problem can be solved by standard optimization algorithms. In order to reduce the computation times to enable online optimization, Diinnebier et al. (2001) simplified the optimization problem and decomposed it in order to enable a more

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efficient solution. They exploited the fact that the recovery constraints are always active at the optimal solution and consider them as equalities. The resulting solution algorithm consists of two stages, the iterative solution of the recovery equality constraints, and the solution of the remaining unconstrained static nonlinear problem. 4.3.2 Model-based Control with Model Adaptation

In industrial practice, chromatographic separations are usually controlled manually. However, automatic feedback control leads to a uniform process operation closer to the economic optimum, and it can include online reoptimization. Dunnebier et al. (2001) proposed the model-based online optimization strategy shown in Figure 4.8.

7 t

Estimation of the Model Parameters

Control of the Fractionatink Valve

Independently &tmated

Parameters

7

Contraiatx

Purity, Recovery

mm.Pressure Drop Figure 4.8

Control scheme for chromatographic batch separations

4.3 Control ofBatch Chromatography Using Online Model-based Optimization

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Essentially, this scheme performs the above optimization of the operating parameters online. To improve the model accuracy and to track changes in the plant, an online parameter estimation is performed. A similar run-to-run technique has been proposed by Nagrath et al. (2003). Note that this scheme contains feedback only in the parameter estimation path. Therefore it will lead to good results only if the model is structurally correct so that the parameter estimation leads to a highly accurate model.

86 -

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,.A

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Figure 4.9 Product purities and operating parameters during an experimental run (set-point change for required purity at approximately 28 h from 80 to 85 %) (from Dunnebier et al., 2001)

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The scheme was tested successfully at the pilot scale for a sugar separation with linear adsorption isotherm by Diinnebier et al. (2001). The product concentrations were measured using a two-detector concept as first proposed by Altenhohner et al. (1997). A densimeter was used for the measurement of the total concentration of fructose and glucose and a polarimetric detector for the determination of the total rotation angle. Both devices were installed in series at the plant outlet. Figure 4.9 shows an experimental result. First the operating parameters are modified in order to meet the product purity and recovery of 80 % each. After about 28 h, the controlled operating parameters reach a stable steady state. At this point a setpoint change takes place in the product specifications: purity and recovery are now required to be 86 %. The control scheme reacts immediately, reducing the interstitial velocity and increasing the injection and cycle intervals. This leads to a better separation of the two peaks and to an increase in purity as desired. The controlled system quickly converges to a new steady state. 4.3.3 Summary

The key idea of the approach described in this section is to use model-based set-point optimization for model-based closed-loop control. Plant-model mismatch is tackled by adapting key model parameters to the available measurements so that the concentration profiles at the output which are predicted by the model match the observed ones. Experimental results showed that this approach works very well in the case of sugar separations where the model is structurally correct. The optimization algorithm was tailored to the structure of the problem so that convergence problems were avoided. Owing to the use of a tailored algorithm and the fact that the process is quite slow, computation times were not a problem. 4.4 Control by Measurement-based Online Optimization

In the two-step approach described in the previous section, the model parameters are updated by a parameter estimation procedure so that the model represents the plant at current operating conditions as accurately as possible. The updated model is used in the optimization procedure to generate a new set-point. This method works well for parametric mismatch between the model and the real plant. However, it does not guarantee an improvement of the set-point when structural errors in the model are present. In chromatographic separations, structural errors result e.g., from the approximation of the real isotherm by the Bi-Langmuir function. One important cause of plant-model mismatch can be the presence of small additional impurities in the mixture which may lead to considerable deviations of the observed concentration profiles at the output. The model-based optimization then generates a suboptimal operating point which in general does not satisfy the constraints on purity or recovery. The conventional solution is to introduce an additional control loop that regu-

4.4 Control by Measurement-based Online Optimization

lates the product purities, as proposed and tested by Hanisch (2002). However, the changes of the operating parameters caused by this control loop may conflict with the goal of optimizing performance. 4.4.1 The Principle of Iterative Optimization

To cope with structural plant-model mismatch, the available measurements can be used not only to update the model but also to modify the optimization problem in such a manner that the gradient of the (unknown) real process mapping is driven to zero, in contrast to satisfying the optimality conditions for the theoretical model. Such an iterative two-step method was proposed by Roberts (1979),termed integrated system optimization and parameter estimation (ISOPE). A gradient-modification term is added to the objective function of the optimization problem. ISOPE generates set-points which converge towards the true optimum despite parametric and structural model mismatch. Theoretical optimality and convergence of the method were proven by Brdys et al. (1987). From a practical point of view, the key element of ISOPE is the estimation of the gradient of the plant outputs with respect to the optimization variables. The general model-based set-point optimization problem can be stated as

min U

such that

J(u7i) g(u) 5 0 Urnin

5

5

Urnax

where J(u,y) is a scalar objective function, u is a vector of optimization variables (setpoints), y is a vector of output variables, and g(u)is a vector of constraint functions. The relationship between u and y is represented by a model

y = f (u, a )

(19)

where a is a vector of model parameters. ISOPE is an iterative algorithm, where at each step of the iteration measurement information (i.e., the plant output y$ 0, P 2 0, N y 1 Nu and the superwhere U P { ul, ... , u ~ + ~ , Q script Tdenotes the transpose of the corresponding vector or matrix. The problem (4) is solved repetitively at each time t for the current measurement x ( t ) and the vector of predicted state variables, ~ ~ +...~, Xt+I+ l ~ at, time t + 1, ... , t + k respectively and coris obtained. responding control actions ut, ... , In the following paragraphs, a parametric programming approach which avoids a repetitive solution of (4)is presented. First, we do some algebraic manipulations to recast (4) in a form suitable for using and developing some new parametric programming concepts. By making the following substitution in (4):

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Real Time Optimization

j=O

the objective J ( U, x(t))can be formulated as the following Quadratic Programming (QP) problem:

a

where U [u:, ..., u ~ + ~ E, -R',~ s] 4~ mN,, is the vector of optimization variables, H = HT > 0, and H , F, Y,G, W, E are obtained from Q R and (4)-(5). The QP problem (6) can now be formulated as the following Multi-parametric Quadratic Program (~P-QP): 1

p ( x ) = min - z T ~ z 2 2 s.t. G z 5 W Sx(t)

+

(7)

where z U + H-' FT x(t),z E R', represents the vector of optimization variables, S E + GH-' and x represents the vector of parameters. The main advantage of writing (4)in the form given in (7) is that z (and therefore v) can be obtained as an affhe function of x for the complete feasible space of x. To derive these results, we first state the following theorem. Theorem 1 For the problem in (7) let xo be a vector of parameter values and (zo,Lo) a KKT pair, where Lo = h(xo)is a vector of nonnegative Lagrange multipliers, h, and zo = z(xo)is feasible in (7). Also assume that (i) linear independence constraint qualification and (ii) strict complementary slackness conditions hold. Then,

where,

No

=

(Y,hlS1, . . .,

where Gi denotes the i* row of G, Sidenotes the ith row of S, Vi = Giza - Wi - Sixo, Wi denotes the i* row of Wand Y is a null matrix of dimension (s x n). See Pistikopoulos et al. (2002) for the proof. The space of x where this solution, (8), remains optimal is defined as the Critical Region (CRO)and can be obtained as follows. Let CRRrepresent the set of inequalities obtained (i) by substituting z ( x )into the inequalities in (7) and (ii) from the positivity of the Lagrange multipliers, as follows:

5.3 Parametric Control

CRR= ( G z ( x )5 W

+ S x ( t ) ,A(%) > 0 ) .

(9)

then CRo is obtained by removing the redundant constraints from C R Ras follows: CR' = A ( C R R }

where A is an operator which removes the redundant constraints - for a procedure to identify the redundant constraints, see Gal (1995). Since for a given space of statevariables, X , so far we have characterized only a subset of X i.e. CRo s X , in the next step the rest of the region CR"'', is obtained as follows (Pistikopoulos et al., 2002): CRreSt= X - CR".

(11)

The above steps, (8-11) are repeated and a set of z ( x ) , h(x)and corresponding CR's is obtained. The solution procedure terminates when no more regions can be obtained, i.e. when CR"' = @. For the regions which have the same solution and can be unified to give a convex region, such a unification is performed and a compact representation is obtained. The continuity and convexity properties of the optimal solution are summarized in the next theorem.

Theorem 2 For the mp-QP problem, (7), the set offeasible parameters Xfc Xis convex, the optimal solution, z(x): XJ+ R' is continuous and piecewise affine, and the optimal objective function p(x) : XJ+ R is continuous, convex and piecewise quadratic. See Pistikopoulos et al. (2002)for the proof. Based upon the above theoretical developments, an algorithm for the solution of an mp-QP of the form given in (7) to calculate U as an affine function of x and characterize X by a set of polyhedral regions, CRs, has been developed which is summarized in Table 5.4. This approach provides a significant advancement in the solution and real time implementation of model based control problems. Since its application results in a complete set of control variables as a function of state-variables (from (8))and the corresponding regions of validity (from (lo)),which are computed off-line. Therefore during on-line optimization, no optimizer needs to be called and instead for the current state of the plant, the region, CRO, where the value of the state variables is valid, can be identified by substituting the value of these state variables into the inequalities which define the regions. Then, the corresponding control variables can be computed by using a function evaluation of the corresponding affine function (see Figure 5.5). Figure 5.6 demonstrates how advanced controllers can be implemented on a simple hardware.

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5.4 Hybrid Systems

Hybrid systems can be defined as systems comprising a number of interconnected continuous subsystems where the interconnections are determined by logical or discrete switchings. Each subsystem is governed by a unique set of differential and/or algebraic equations. In this section we focus on piecewise afine (PWA) systems (Bemporad and Morari, 1999). PWA systems are defined by partitioning the state and input space into polyhedral regions and associating with each region a different linear state update equation x(t

+ 1) = Aix(t) + B'u(t) +fi

(14

where i = 1, ..., s, x E R"' x (0, l}"',u E R"' x (0, l}"',(Pi}tl is a polyhedral partition of the set of the state and input space P c R"+", n 4 n, + nl, rn & rn, rn,. P is assumed to be closed and bounded and x, E RnCand u, E R" denote the continuous components ofthe state and input vector, respectively;xi E (0, l}"' and uiE (0, l}"' similarly denote the binary components. Note that PWA models are not suitable for recasting analysislsynthesis problems into more compact optimization problems. For this purpose the Mixed Logical Dynamical (MLD) framework (Bemporad and Morari, 1999) is used. The general MLD form of a hybrid system is:

+ 1) = A x ( t ) + Blu(t) + B2S(t) + B3z(t) y ( t ) = Cx(t) + Diu(t) + D2S(t) + D3Z(t) E2S(t) + E 3 ~ ( t )i Eiu(t) + E d t ) + Es x(t

(13)

(14) (15)

SOLVER

d

2

Figure 5.5 Real time optimization via parametric programming

5.4 Hybrid Systems Table 5.4

Solution Steps o f the rnp-QP Algorithm

Step 1

For a given space of x solve (7) by treating x as a free variable and obtain [x,,]. xo and solve (7) to obtain [zn, Lo].

Step 2

In (7) fix x

Step 3

Obtain [ z ( x ) .A@)] from ( 8 ) .

Step 4

Define CRRas given in (9).

Step 5

From CRRremove redundant inequalities and define the region of optimality CR" as given in (10).

Step 6

Define the rest of the region, CR"", as given in (11).

Step 7

If no more regions to explore, go to the next step, othenvise go to Step 1

Step 8

Collect all the solutions and unify a convex combination of the regions having the same solution to obtain a compact representation.

=

Model Predictive Control Real Time Optimization Problem

1

Offline Parametric Optimization Problem Sensors measurements are Parameters Manipulated inputs are Optimization Variables

Optimal control action as

(1) Explicit functions of sensor measurements, and (2) Critical regions where these functions apply

State-of-the-art performance on the simplest of hardware

Figure 5.6

Achieving state-of-the-artcontrol performance on simple hardware

where x = [xz x:]' E RnGx (0, l}"'are the continuous and binary states, u = [uz uf]' E Rmc x (0, l}"' are the inputs, y = [y: y:]' E Rp' x (0, l} p ' the outputs, and 6 E (0, l}",z E R" represent auxiliary binary and continuous variables respectively. All constraints on the states, the inputs, the z and 6 variables are summarized in the inequalities (15). Note that, although the description (13)-(14)-(15) seems to be linear, nonlinearity is hidden in the integrality constraints over the binary variables. MLD systems are a versatile framework to model various classes of systems. For a detailed description of such capabilities we defer the reader to Morari et al. (2003).

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5.4.1 Predictive Control of MLD Systems

Let t be the current time, and x ( t ) the current state. Consider the following optimal control problem

k=O

where vi-' [vT(0), ..., vT (T- l)]', Q = QT > 0, Qz = 2 0, Q1 = @ 2 0, Q4= QT > 0 and Qs = 2 0. x(klt) x ( t + k, x(t), vi-') is the state predicted at time t + k resulting from the input u(t + k) = v(k) to (13-15) starting from x(Olt) = x(t). 6 ( k l t ) , z ( k l t ) and y(klt) are similarly defined. Assume for the moment that the optimal solution { v:(k)}~=O,...,T-l exists. According to the receding horizon philosophy mentioned above, set

ar

disregard the subsequent optimal inputs v: (l),... , v; (T- l),and repeat the whole optimization procedure at time t + 1. Note that (16-17) is a Mixed Integer Quadratic Program (MIQP).This problem can be formulated as a Mixed Integer Linear Program (MILP)if 1norm instead of the 2 norm is considered in the objective function. The repetitive somtion of the MIQP or MILP can be avoided by formulating (16-17) as a multiparametric program and solving it to obtain the control variables as a set of explicit functions of the current state of the system and the regions in the space of the state variables where the explicit functions remain valid (Bemporad et al., 2000; Sakizlis et al., 2002a). This is achieved by recasting (16-17) in a compact form as follows:

a,

where zcand z d are continuous and discrete variables of (16-17), GT, G,, Gd, S, F are constant matrices and vectors of appropriate dimensions and is symmetrie and positive definite. x(t) is the state at the current time t. The objective is to obtain ncand n d as a function of x(t) without exhaustively enumerating the entire space of x ( t ) .This can be achieved by using parametric programming. In the next section an algorithm for Multiparametric Mixed Integer Linear Programs (mp-MILP) is

5.4 Hybrid Systems

described. This reduces the real time hybrid system control problem to a function evaluation problem (Figure 5.7).

5.4.2 Multiparametric Mixed-Integer Linear Programming

Consider a multiparametric Mixed Integer Linear Programming (mp-MILP) problem of the following form: MULTl-PARAMETRIC MIXED-I NTEGER PROGRAM SOLVER

4 U

Y

X

i? 4

3

r

where

PARAMETRIC PROGRAMMING

and @* are constant vectors.

5.4.2.1 Initialization

An initial feasible nd is obtained by solving the following MILP:

where x ( t ) is treated as a vector of free variable to find a starting feasible integer solution. Let the solution of (21) be given by n d = Z d .

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5.4.2.2 Multiparametric LP Subproblem

Fix x d = z d (20) to obtain a multiparametric LP problem of the following form: s.t. GCT,4- Gdnd 5

s + Fx(t)

The solution of (22) is given by a set of linear parametric profiles, j ( x ( t ) ) ’ ,where j ( x ( t ) )is convex, and corresponding critical regions, CR’ (Gal, 1995).

The final solution of the multiparametric LP subproblem in (22) which represents a parametric upper bound on the final solution is given by (i)a set of parametric profiles, j(x(t))i,and the corresponding critical regions, CR’, and (ii) a set of infeasible regions wherej(x(t))’= m. 5.4.2.3 MILP Subproblem

For each critical region, CR’, obtained from the solution of the multiparametric LP subproblem in (22), an MILP subproblem is formulated as follows:

The integer solution, x d = zi, and the corresponding CRs, obtained from the solution of (23), are then recycled back to the multiparametric LP subproblem - to obtain another set of parametric profiles. Note that the integer cut, n d # z d , and the parametric cut, 4; xc+ & x d Ij ( x ( t ) ) ’are accumulated at every iteration. If there is no feasible solution to the MILP subproblem (23) in a CR’, that region is excluded from further consideration and the current upper bound in that region represents the final solution. Note also that the integer solution obtained from the solution of (23) is guaranteed to appear in the final solution, since it represents the minimum of the objective function at the point, in x(t), obtained from the solution of (23).The final solution of the MILP subproblem is given by a set of integer solutions and their corresponding CR’s. 5.4.2.4 Comparison of Parametric Solutions

The set of parametric solutions corresponding to an integer solution, x d = z d , which represents the current upper bound are then compared to the parametric solutions corresponding to another integer solution, ldd = z;, in the corresponding C Rs in order to obtain the lower of the two parametric solutions and update the upper bound. This is achieved by employing the procedure proposed by Acevedo and Pistikopoulos (1997b).

5.5 Concluding Remarks 1589

5.4.2.5 Multiparametric MILP Algorithm

Based upon the above theoretical developments, the steps of the algorithm can be stated as follows: Step 0 (Initialization) Define an initial region of x ( t ) , CR, with best upper bound j * ( x ( t ) ) = w , and an initial integer solution %d.

Step 1 (Multiparametric LP Problem) For each region with a new integer solution,

-

n d: 0

0

0

Solve multiparametric LP subproblem (22) to obtain a set of parametric upper bounds j ( x ( t ) )and corresponding critical regions, CR. !fj(x(t))< j " ( x ( t ) ) for some region of x(t),update the best upper bound function, J""(x(t)),and the corresponding integer solutions, ni, If an infeasibility is found in some region CR, go to Step 2.

Step 2 (Master Subproblem) For each region CR, formulate and solve the MILP master problem in (23) by (i) treating x(t) as a variable bounded in the region CR, (ii) introducing an integer cut, nd # %d and (iii) introducing a parametric cut, @: nc+ & nd< j ( x ( t ) ) ' .Return to Step 1 with new integer solutions and corresponding CRs. Step 3 (Convergence)The algorithm terminates in a region where the solution of the MILP subproblem is infeasible. The final solution is given by the current upper boundsp(x(t))in the corresponding CRs. The n,(x(t))and nd(x(t))corresponding to j " ( x ( t ) ) are then used to obtain u ( x ( t ) ) .

Note that the algorithms presented in this chapter have been implemented and tested on a number of real time optimization problems (PAROS, 2004).

5.5 Concluding Remarks

In this chapter it was shown how real time optimization problems can be recast as multiparametric programs. Linear discrete time optimization problems are recast as multiparametric quadratic programs and problem involving logical decisions as multiparametric mixed integer programs. Algorithms for solving the multiparametric programs were then presented to compute the optimal control actions as an explicit function of the state of the system. This reduces real time optimization problems to simple function evaluations.

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References 1 Acevedo J. Pistikopoulos E. N. A parametric

MINLP algorithm for process synthesis problems under uncertainty. Industrial and Engineering Chemistry Research 35 (1996) p. 147-158 2 Acevedoj. Pistikopoulos E. N. A multiparametric programming approach for linear process engineering problems under uncertainty. Industrial and Engineering Chemistry Research 36 (1997) p. 717-728 3 Acevedo J. Pistikopoulos E. N. An algorithm for multiparametric mixed integer linear programming problems. Operations Research Letters 24 (1999)p. 139-148 4 Bemporad A. Borrelli F. Morari M. Piecewise linear optimal controllers for hybrid systems, proceedings of the American Control Conference (2000) p. 1190-1194 5 Bemporad A. Morari M. Control of systems integrating logic, dynamics, and constraints. Automatica 35 (1999) p. 407-427 6 Dua V. Bozinis N. A. Pistikopoulos E. N. A multiparametric programming approach for mixed-integer quadratic engineering problems. Computers & Chemical Engineering 26 (2002)p. 715-733 7 Dua V. Papalexandri K. P. Pistikopoulos E. N. Global optimization issues in multiparametric continuous and mixed-integer optimization problems, accepted for publication in the Journal of Global Optimization, 30 (2004)p. 59 8 Dua V. Pistikopoulos E. N.Algorithms for the solution of multiparametric mixed-integer nonlinear optimization problems. Industrial and Engineering Chemistry Research 38 (1999) p. 3976-3987 9 Dua V. Pistikopoulos E. N. An algorithm for the solution of multiparametric mixed integer linear programming problems. Annals of Operations Research 99 (2000)p. 123-139 10 Edgar T. F. Himmelblau D. M. Optimization of chemical processes. McGraw Hill Book Co, Singapore 2000 11 Fiacco A. V. Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York 1983 12 Gal T. Postoptimal Analyses, Parametric Programming, and Related Topics. de Gruyter, New York 1995 13 Gal T. Nedomaj. Multiparametric linear programming. Management Science 18 (1972) p. 406-422

14 Marilin T. E. Hrymak A. N. Real-time

operations optimization of continuous processes. In: Kantor J. C. Garcia C. E. Carnahan B. (Eds.), 5th Int. Conf. Chem. Proc. Control. Vol. 93 of AIChE Symposium Series 1997 15 Morari M.Baotic M. Borrelli F. Hybrid systems modeling and control. European Journal of Control 9 (2003) p. 177-189 16 Morari M. Lee]. Model predictive control: past, present and future. Computers & Chemical Engineering 23 (1999)p. 667-682 17 Papalexandri K. P. Dimkou T. 1. A parametric mixed integer optimization algorithm for multi-objectiveengineering problems involving discrete decisions. Industrial and Engineering Chemistry Research 37 (5) (1998) p. 1866-1882 18 PAROS Parametric Optimization Solutions Ltd. http://www.parostech.com 2004 19 Perkins J. D. Plant-wide optimization: opportunities and challenges. In: Pekny J. Blau G. (Eds.), 3rd Int. Conf. Foundations of Computer Aided Process Operations. Vol. 94 of AIChE Symposium Series 1998 20 Pertsinidis A. Grossmann 1. E. McRae G. /. Parametric optimization of MILP programs and a framework for the parametric optimization of MINLPs. Computers & Chemical Engineering 22 (1998) p. S205 21 Pistikopoulos E. N. Dua V. Bozinis N.A. Bemporad A. Morari M. On-line optimization via off-line parametric optimization tools. Computers & Chemical Engineering 26 (2002)p. 175-185 22 Sakizlis V. Dua V. Perkins]. D. Pistikopoulos E. N.The explicit control law for hybrid systems via parametric programming, proceedings of the 2002 American Control Conference, Anchorage 2002a 23 Sakizlis V. Dua V. Perkins]. D. Pistikopoulos E. N. The explicit model-based control law for continuous time systems via parametric programming, proceedings of the 2002 American Control Conference, Anchorage 2002b 24 Sakizfis V. Kakalis N. Dua V. Perkins J. D. Pistikopoulos E. N. Design of robust model based controllers via parametric programming. Automatica 40 (2004) p. 189-201

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8 I591

6 Batch and Hybrid Processes Luis Puigianer andjavier Rornero

6.1 Introduction

Although historically, chemical engineers achieved their professional distinction with the design and operation of continuous processes [I],as we move into the new millennium, it comes somewhat as a surprise to realize that outside the petroleum and petrochemical industries, batch operation is still a common if not dominant mode of operation. Moreover, most batch processes are unlikely to be replaced by continuous processes [2, 31. The reason is that as the production of chemicals undergoes a continuous specialization, to address the diversif)ing needs of the marketplace, the continuous evolution of product recipes implies a much shorter life cycle for a growing number of chemicals, than has been traditionally the case, leading to a perpetual product/process evolution [4, 51. This situation has been matched and in part funded by a developing research interest in batch process systems engineering, batch production being the most suitable way of manufacturing the relatively large number of low-volume high-value-added products commonly found in the fine and specialty chemicals industry. Moreover, the coexistence of continuous and discrete parts in both strictly speaking batch processes and nominal continuous processes has motivated an increased research interest in further exploiting the inherent flexibility of batch procedures and the high productivity of continuous parts of the production system [GI.Thus, chemical plants constitute large hybrid systems, making it necessary to consider the continuous-discrete interactions taking place within an appropriate framework for plant and process simulation and optimization [7]. This chapter briefly discusses existing modeling frameworks for discrete/hybrid production systems embodying different approaches, before introducing a very recent framework for process recipe initialization that integrates a recipe model into the batch plant-wide model. Next, online and offline recipe adaptation from real-time plant information is presented, and finally, a model-based integrated advisory system Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright @ 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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is described. This system gives online advice to operators on how to react in case of process disturbances. In this way, an enhanced overall process flexibility and productivity is achieved. Application of this promising approach is illustrated through examples of increasing complexity. 6.1.1 Plant and Process Simulation

The discrete transitions occurring in chemical processing plants have only recently been addressed in a systematic manner. Barton and Pantelides [8] did pioneering work in this area. A new formal mathematical description of the combined discrete/ continuous simulation problem was introduced to enhance the understanding of the fundamental discrete changes required to model processing systems. The modeling task is decomposed into two distinct activities: modeling fundamental physical behavior, and modeling the external actions imposed on this physical system resulting from interaction of the process with its environment by disturbances, operation procedures, or other control actions. The physical behavior of the system can be described in terms of a set of integral and partial differential and algebraic equations (IPDAE). These equations may be continuous or discontinuous. In the latter case, the discontinuous equations are modeled using state-task networks (STNs) and resource-task networks (RTNs), which are based on discrete models. Otherwise, other frameworks based on a continuous representation of time have appeared more recently (event operation network among others). The detailed description of the different representation frameworks is the topic of the next section. 6.1.2 Process Representation Frameworks

The representation of a state-task network (STN) proposed by Kondili et al. [9] was originally intended to describe complex chemical processes arising in multiproduct/ multipurpose batch chemical plants. The established representation is similar to the flow sheet representation of continuous plants, but is intended to describe the process itself rather than a specific plant. The distinctive characteristic of the STN is that it has two types of nodes; mainly, the state nodes, representing the feeds, intermediates and final products and the task nodes, representing the processing operations which transform material from input states to output states (Fig. 6.1). This representation is free from the ambiguities associated with recipe networks where only processing operations are represented. Process equipment and its connectivity are not explicitly shown. Other available resources are not represented. The STN representation is equally suitable for networks of all types of processing tasks, continuous, semicontinuous or batch. The rules followed in its construction are:

6.1 Introduction

T10

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Figure 6.1 State-task network representation of chemical processes Circles: state nodes; rectangles: task nodes 0

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A task has as many input (output) states as different types of input (output) material. Two or more streams entering the same state are necessarily of the same material. If mixing of different streams is involved in the process, then this operation should form a separate task.

The STN representation assumes that an operation consumes material from input states at a fixed ratio and produces material for the output state also at a known fixed proportion. The processing time of each operation is known a priori and considered to be independent of the amount of material to be processed. Otherwise, the same operation may lead to different states (products) using different processing times. States may be associated to four main types of storage policy: 0 0 0 0

unlimited intermediate storage finite intermediate storage no intermediate storage zero wait (the product is unstable).

An alternative representation; the resource-task network (RTN)was proposed by Pantelides [lo]. In contrast to the STN approach, where a task consumes and produces materials while using equipment and utilities during its execution, in this representation, a task is assumed only to consume and produce resources. Processing items are treated as though consumed at the start of a task and produced at the end. Furthermore, processing equipment in different conditions can be treated as different resources, with different activities consuming and generating them; this enables a simple representation of changeover activities. Pantelides [lo] also proposed a discrete-time scheduling formulation based on the RTN, which, due to the uniform treatment of resources, only requires the description of three types of constraint, and does not distinguish between identical equipment items. He demonstrated that the integrality gap could not be worse than the most efficient form of STN formulation, but the ability to capture additional problem features in a straightforward fashion is attractive. Subsequent research has shown that these conveniences in formulation are overshadowed by the advantages offered by the STN formulation in allowing explicit exploitation of constraint structure through algorithm engineering. The STN and RTN representations use discrete-time models. Such models suffer from a number of inherent drawbacks [Ill: 0

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The discretization interval must be fine enough to capture all significant events, which may result in a very large model.

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It is difficult to model operations where the processing time is dependent on the batch size. The modeling of continuous operations must be approximated and minimum run-lengths give rise to complicated constraints.

Therefore, attempts have been made to develop frameworks based on a continuoustime representation. Reklaitis and Mockus [12] developed a continuous-time formulation based on the STN representation. A common resource grid is need, with the timing of the grid points (“eventorders” in their terminology) determined by optimization. The same authors introduced an alternative solution procedure based on Bayesian heuristics in a later work [13]. Zhang and Sargent [14] describe a continuous-time representation based on RNT representation for both batch and continuous operations. The poor relaxation performance of the continuous-time models is the main obstacle to their large scale application. To avoid this deficiency, Shilling and Pantelides [Ill modify the model by Zhang and Sargent (1996).A global linearization gives rise to a mixed-integer linear programming (MILP) which is solved by a hybrid branch-and-bound procedure. Recent reviews on these approaches can be found in Shah [15] and Silver et al. [16]. A realistic and flexible description of complex recipes has been recently improved using a flexible modeling environment [ 171 for the scheduling of batch chemical processes. The process structure (individual tasks, entire subtrains or complex structures of manufacturing activities) and related materials (raw, intermediate or final products) is characterized by means of a processing network which describes the material balance. In the most general case, the activity carried out in each process constitutes a general activity network. Manufacturing activities are considered at three different levels of abstraction: the process level, the stage level and the operation level. This hierarchical approach permits the consideration of material states (subject to material balance and precedence constraints) and temporal states (subject to time constraints) at different levels. At the process level, the process and materials network (PMN) provides a general description of production structures (such as synthesis and separation processes) and materials involved, including intermediates and recycled materials. An explicit material balance is specified for each of the processes in terms of a stoichiometriclike equation relating raw materials, intermediates and final products (Fig. 6.2). Each process may represent any kind of activity necessary to transform the input materials into the derived outputs. Between the process level and the detailed description of the activities involved at the operation level, there is the stage level. At this level, the block of operations to be executed in the same equipment is described. Hence, at the stage level each process is split into a set of the blocks (Fig. 6.3). Each stage implies the following constraints: 0 0

The sequence of operations involved requires a set of implicit constraints (links). Unit assignment is defined at this level. Thus, for all the operations of the same stage, the same unit assignment must be made.

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Figure 6.2 A process and materials network (PMN) describing the processing oftwo products. RM are row materials, IP are intermediate products, BP are by-products and FP are final products

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Figure 6.3 Stage level. Each stage involves different unit assignment opportunities 0

A common size factor is attributed to each stage. This size factor summarizes the

contribution of all the operations involved. The operation level contains the detailed description of the activities contemplated in the network (tasks and subtasks), while implicit time constraints (links) must be also met at this level. The detailed representation of the structure of activities defining the different processes is called the event operation network (EON). It is also at this level that the general utility requirements (renewable, nonrenewable, storage) are represented.

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The event operation network representation model describes the appropriate timing of process operations. A continuous-time representation of process activities is made using three basic elements: events, operations and links [18,191. Events designate those time instants where some change occurs. They are represented by nodes in the EON graph, and may be linked to operations or other events. Each event is associated to a time value and a lower bound. Operations comprise those time intervals between events (Fig. 6.4). Each operation rn is represented by a box linked with solid arrows to its associated nodes: initial NI m and final NF rn nodes. Operations establish the equality links between nodes (two) in terms of the characteristic properties of each operation: the operation time, TOP and the waiting time TW. The operation time will depend on the amount of materials to be processed; the unit model and product changeover. The waiting time is the lag time between operations, which is bounded.

Figure 6.4 The time description for operations. TOP Operation time, W w a i t i n g time, NI rn initial node of operation rn, N F rn final node of operation rn

Finally, links are established between events by precedence constraints. A dashed arrow represents each link K from its node of origin NOk to its destiny node NDk and an associated offset time A TK.

Figure 6.5 Event to event link and associated offset time representation. The dashed arrow represents each link K from its node of origin NOk to its destiny node NDk

Despite its simplicity, the EON representation is very general and flexible and it allows the handling of complex recipes (Fig. 6.6). The corresponding TOP, according to the batch size and material flow rate, also represents transfer operations between production stages. The necessary time overlapping of semicontinuous operations with batch units is also contemplated in this representation through appropriate links. Other resources required for each operation (utilities, storage, capacity, manpower, etc.) can also be considered associated to the respective operation and timing. Simulation of plant operation can be performed in terms of the EON representation from the following information contained in the process recipe and production structure characteristics: 0

0 0 0

A sequence of production runs or jobs associated to a process or recipe. A set of assignments associated to each job and consistent with the process p. A batch size associated to each job and consistent with the process. A set of shifting times for all the operations involved.

These decisions may be generated automatically by using diverse procedures for the determination of an initial feasible solution. Hence, simulation may be executed by

6.2 The Flexible Recipe Concept 1597 Figure 6.6 The recipe described as a structured set ofoperations The event operation network (EON) representation allows the handling o f complex synthesis problems The corresponding typical Gantt chart is given below

solving the corresponding EON to determine the timing of the operations and other resources requirements. The flexibility and potential of the EON representation has been further exploited by incorporating the flexible recipe concept, which is the subject of the next section.

6.2 The Flexible Recipe Concept

The simulation environments described in the previous section assume operating at nominal conditions following fixed recipes. Moreover, these nominal conditions are determined only once and sometimes considering only one stage of the process recipe. However, batch and hybrid manufacturing systems’ optimum performance require an integrated modeling environment capable of incorporating systematic information and of adapting to changing plant scenarios. Very recently, the flexible recipe concept has been introduced as an appropriate mechanism that permits the simultaneous optimization of recipe and plant operation [20, 211. This concept arose from the fact that batch processes normally do not operate at the plant-wide optimal nominal conditions of the fixed batch recipes, but the traditional fixed recipe does not allow for adjustment to plant resource availability or to variations in both quality of raw materials and in the actual process conditions. However, the industrial process is often subject to various disturbances and to constrained plant resources availability. Therefore, the fixed recipe is in practice approximately adapted, but in a rather unsystematic way depending on the experience and intuition of operators. As an alternative, the concept of flexible recipe operation is introduced, and a general framework is presented to systematically deal with the required adaptations at a plant-wide level. The flexible recipe concept was considered for the first time in the context of evolutionary operation [22].The main objective of that approach was to gain statistical insight into the problem behavior in order to gradually improve process efficiency

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through suggestions of minor recipe modifications in each batch-run. However, it was not until the work of Rijnsdorp appeared [20] that the concept of flexible recipes was adequately introduced. Here, the term recipe is understood in a more abstract way as referring to the selected set of adjustable elements that control the process output generating the flexible recipe. According to this concept, a flexible recipe philosophy to operate batch processes was described in the work of Venvater-Lukszo (211. This philosophy distinguishes two main levels in the flexible recipe: (a) the recipe initialization level, where different aspects of a master flexible recipe are adjusted to actual process conditions and availability of resources at the beginning of the batch, thus giving the initialized control recipe; and (b) the recipe correction level, where the initialized control recipe is adjusted to run-time process deviations, thus generating corrected control recipes. A flexible recipe improvement system tool (called COMBO) was developed by TNO TPD (Netherlands Organization for Applied Scientific Research) for application of the flexible recipes concept in industrial practice. However, in this approach, only one critical stage of the process is considered and hence, no interaction with plant-wide optimization is, in fact, attempted. More recently, the application of the flexible recipe concept to an entire batch train was attempted for the multistage case [23]. However, standard quality models were assumed for process operations, and hence, no insight into recipe behavior was obtained. A new framework for recipe initialization that integrates a recipe model into the batch plant-wide model has been recently introduced [24]. The aim of this approach is to optimize the entire batch process, from recipe set-point adjustment to product sequencing. For this purpose, a recipe model and a plant-wide production model are required to build the flexible recipe model. Moreover, fulfillment of present standards (ISA S88) should be a requirement for implementation in industrial practice. 6.2.1 The Flexible Recipe and the Framework of ISA S88

Batch-processes flexibility may be mainly exploited at the level of the recipe formulation. Here, the set of process parameters is adjusted to warrant process outputs as a function of uncertain process inputs. Each one of such parameters, whose value may be changed for each batch, is called a recipe item. These items can be quantitative or qualitative, time-dependent or time-independent. The equipment requirement level, as defined in I S A S 8 [25], is already a flexible category in itself. In fact, ISA-S88 defines this level as an equipment choice constraint. Finally, considering flexibility in the recipe procedure would only be contemplated when some unexpected event happens, which is out of the scope of the batch process flexibility enhancement sought here. In a company four types of recipes are typically found: 0

0

General recipe and site recipe; which basically describe the technique and are equipment independent. Master recipe, a recipe which is equipment-dependent and which provides specific and unique batch-execution information describing how a product is to be produced in a given set of process equipment.

6.2 The Flexible Recipe Concept

Control recipe, which starting as a copy of the master recipe, contains detailed information for minute-to-minute process operation of a single batch. The flexible recipe might be derived from a master recipe and subsequently used for generating and updating a control recipe. Venvater and Keesman [26] introduced the concept of different levels between these two stages defined at ISA-S88. With these new levels a better description of the different possible functionalities of the flexible recipe is obtained: 0

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Master control recipe, that is, a master recipe valid for a number of batches, but adjusted to the actual conditions (actual prices or quality requirements) from which the individual control recipes per batch are derived. Initialized control recipe, that is, the adjustment of the still-adjustable process conditions of a master control recipe to the actual process conditions at the beginning of the batch, i.e., the adjustment of variables such as temperature, pressure, catalyst addition and processing time in the face of deviations in the initial temperature of the batch, equipment fouling, available processing time and so on. Corrected control recipe, the result of adjusting the initialized control recipe to process deviations during the batch. And finally, for monitoring and archiving purposes, it is also useful to define the accomplished control recipe.

Therefore, on the basis of this basic philosophy, a novel flexible recipe approach [24] has been recently proposed that excerpts a flexible recipe model from a total master control recipe. This model describes the whole batch process train. However, it is only concerned with the critical batch process variables. Besides, it also considers the possible interactions between different batches because of scheduling purposes. Regarding the different levels between the master recipe and the initialized control recipe described, it can be concluded that four different flexible-recipe systems may be useful: 0

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A system for adjusting the master recipe to the actual prices and quality requirements, defining the master control recipe. A system for defining the initialized control recipe from the master control recipe as a function of the actual process conditions, availability of resources at the beginning of the batch and of the availability of the plant equipment. A model to generate the corrected control recipe in the face of deviations during each batch. A system for updating and improving the master control recipe as the database of accomplished control recipes increases. This model will also improve the preceding models.

The interaction of these systems in a real-plant environment is described in Fig. 6.7. These systems will have to be developed in laboratory experiments, pilot plant operation, during normal production by a systematic introduction of acceptable small changes in certain inputs and parameters, or by adjusting white models and simulating them under different operating conditions.

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Switching program regulatory control: Corrected Control Recipe

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On-line Process assessment and Evaluation of off-

1 Operational database management of accomplished control recipes Figure 6.7 Optimal flexible recipe environment information flow proposed

improvement and model development

6.3 The Flexible Recipe Model

6.3 The Flexible Recipe Model

The flexible recipe model is the tool that permits us to integrate a recipe optimization procedure with a batch plant optimization level. It represents the relationship that correlates a batch process output as a function of the selected input items of the recipes for different batch plant production scenarios. Therefore, it is a recipe description model that incorporates plant-wide variables. We identify four main components of the problem: quality or product specifications, process operating conditions, production costs and production due-dates. The flexible recipe model can be applied to a variety of scenarios. For instance, during batch process operation, processing times of some tasks may vary without setpoint adjustment, thus affecting the properties (quality) of the products obtained in such tasks. Then, to meet customer requirements, another batch of the same product might be able to compensate for these effects. For example, let’s assume a process in which A is converted into B; one batch with low conversion of A could be compensated for by another batch with a higher conversion, assuming that these two batches are going to be mixed afterwards, so that the final product quality corresponds to the customer and legal requirements. Otherwise, the processing time might be optimized without set-point adjustment by compensating for the quality within the same batch. For instance, a batch of product A that is first heated in one piece of equipment before reacting in another. A reduction in the processing time of the first task could be offset by a higher reaction time. Moreover, the processing time could be optimized with some set-point adjustment. In this situation, the properties of intermediates produced might be altered only at the expense of a higher operation cost. For instance, the reaction time could be reduced by increasing the reaction temperature, although this recipe modification would imply a higher operation cost. Which of the above-mentioned strategies should be applied in each case will depend on the specific process and on the available knowledge of the different tasks of the process. For example, such ways of operation might not be very suitable for highly restrictive processes, such as those found in the pharmaceutical industry, but they are probably convenient to specialty batch chemical production where customer requirements are defined simply by a set of product properties and not by the specific way the product has been produced. The preceding discussion leads to the basic concept upon which the modeling of scheduling problems considering the flexible recipe is built. 6.3.1 Proposed Concept for the Flexible Recipe Model

The flexible recipe model is regarded as a constraint on quality requirements and on production costs. In this approach, recipe items are classified into four groups: 0

The vector of process operating conditions, poc,, of stages i of a recipe. It includes parameters like temperature, pressure, type of catalyst, batch size, etc.

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The product specification vector, psi, at the end of each process stage iof a recipe. It might include parameters like conversion of a reactant, purity or quality aspects. Processing time, PTi, at each stage i of a recipe. Waiting time, TWi, that is, the time between the end of a stage and the next stage start time.

Then, the product specifications vector of a batch stage will in general be a function, Y, of processing time, waiting time, process set-points, and product specifications at different stages i"where the different inputs to stage i are produced. Moreover, within this model, product specifications, ps, and process operation conditions, poc, are subject to optimization within a flexibility region, a and A respectively. A general algorithm representation of the flexible recipe model for short term scheduling is presented in Eq. (1).This model contains the nominal recipe and its capacity to accept modifications. The model adjusts the different recipe parameters for each individual batch performed in a specific production plan 8,where 8 is the variable that permits integrating batch process scheduling with the recipe optimization procedure. Each specific production plan 8 is defined when the specific orders to be delivered at a specific set of due dates, S, is specified and when the specific set of different plant resources, A, is assigned to each order. Besides this, each production plan has to meet some physical plant constraints, T, such as the multistage flowshop or jobshop batch plant topology constraints, T,operating with a set ] of equipment units and a set R of process resources. Each production plan will be generated to meet the market constraints: set I of production orders in a given set DD of time horizon or due dates. A performance criterion @ is also included. This criterion may vary from batch to batch and it may contain economic as well as process variables. The flexible recipe model validity constraints are considered in IJ and A regions. Optimize @ (PTi, TWi,psi, poci, 0 ) subject to recipe constraints, psi = (mi,TWi, psi, poc;), Psi C g, pOCi C A , subject to production environment constraints, @ ( S A) , c Q(7, J , R,2,DD)

*

The model may interact with the short-term scheduling level either offline or online.

6.4 Flexible Recipe Model for Recipe Initialization

At the start of a batch the initial conditions may differ from those prescribed by the master recipe, even to the extent of making successful completion unlikely. Examples are deviations in catalyst activity, available heat, raw material quality and equip-

6.4 Flexible Recipe Modelfor Recipe Initialization

ment fouling, among others. In such cases, the flexible recipe concept makes it possible to alter the still-adjustableprocess conditions, so as to ensure the most successful completion of the run. Otherwise, because of scheduling requirements, it may be worthwhile modifying the processing time of a stage of the master recipe, by modifying some operating conditions, so as to debottleneck some piece of equipment or accomplish some product due-dates. The procedure of generating the initialized control recipe from the master recipe is called recipe initialization. This procedure also implies the need to specify in which specific equipment unit and in which product sequence will each stage of the recipe be carried out. In general, the objective is to generate the best control recipe for different production scenarios. Specifically, the proposed framework adjusts the different parameters of a master control recipe model to deviations in prices or quality of delivered raw materials and in expected initial process conditions. For instance, in such a case where available steam pressure is lower than the nominal value at the beginning of a batch, recipe items will have to be initially adapted to this fact. Another aim of this framework is to adjust the different recipe items to the availability of plant resources and equipment units. The inputs of the problem are the production master recipe for each product, that is, the different components that define each recipe, the available equipment units for each task, the list of common utilities, the market requirements expressed as specific amounts of products to be delivered at given instants, and others. The algorithm has to determine the optimal sequence of the tasks to be performed in each unit, the values of the different parameters that specify each recipe, that is, the initialized control recipe and the use of utilities as a function of time. Specifically, the optimal schedule in each case is efficiently reached using the Sgraph approach [27]. This approach implies a branch-and-bound algorithm. This algorithm proceeds from a root node corresponding to the nominal master control recipe. From this root, partial schedules (nodes of the tree) are built adding schedulearcs to the preceding nodes. At each node, a flexible recipe model is solved to calculate a relaxation of the algorithm. The solution of this model at the end of a leaf gives the optimal timing, considering the flexible recipe, of the schedule associated to that leaf. The optimal schedule corresponds to the leaf with best objective function value. Hence, a model for schedule timing integrated with a flexible recipe is necessary. The proposed model is linear, simply to permit a rapid convergence of the algorithm.

6.4.1

Flexible Recipe Model for Schedule Timing

In addition to timing restrictions, two sorts of flexible recipe constraint have to be considered: product specificationsand process operating conditions and their consequences on the production cost. The product specifications vector, ps, is a function, Y, of processing time, waiting time, process set-points, and other product specifications. The model adjusts these recipe parameters for each individual batch performed in a specific production plan, @, this plan being a function of orders to be

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satisfied, S, and of plant resources, A. Each production environment also has to meet some physical plant constraints, Q , such as the plant topology, T, operating with a set J of equipment units and a set R of production resources. Each production plan is generated to meet the market constraints (set of production orders in a given set DD of time horizons or due dates). A performance criterion Cp is also included. Hence, two sort of flexible recipe constraints have to be considered to define the flexible recipe model Y: product specifications (quality of the final products) and process operation conditions (set points) and their consequences on the production cost.

6.4.2 Quality and Production Cost Model

Product specifications,psi, might depend on processing time, waiting time, process operation conditions and product specifications at different stages i*where different inputs to stage i are processed. At the first stage of a batch, P will represent the raw materials. It will also be assumed that, within a time interval, a linear model can be adjusted to predict small deviations from process specifications,6psi, as a function of small deviations from the nominal values of PT;, TW;,poti and psi* (Eq. (2)).

where ai and bi, are the vectors that linearly correlate the effect of processing and waiting times of stage i on product specifications. C,i. is the matrix that linearly correlates the effect of the different product specificationinputs to stage i from stage i" on product specifications, and di the vector that correlates the effect of small deviations in process operation values on the product specifications. For instance, consider the production of one batch of product A. The stage i of this process consists in heating A in equipment unit 1. Stage i + 1 constitutes the reaction of A to give B in equipment unit 2. The main important product specification at stage i = 1 is the temperature reached in unit 1 and at the second stage, the conversion of reactant A and the temperature at the end of this stage. Therefore, the vector psl will only contain one element (temperature at the end of the stage 1).The vector ps2will have two elements, conversion of reactant and temperature. The vector al will consequently contain one element that will correlate the effect of small deviations in processing time of stage 1 on the temperature reached at stage 1. Similarly, a2 will have two elements, and each element will correlate the effect of processing time on each relevant product specificationj, psj, 2. If waiting time has no effect on product specifications, the vector bi is null. Otherwise, product specifications at stage 2 will clearly be affected by product specifications at stage 1. So, the matrix C2, will be { 1 x 2). Its elements correlate the effect of small deviations in the temperature reached at stage 1 on the conversion and temperature at the end of stage 2. Final products must meet some quality (product specifications)requirements. The model also considers the possibility of mixing different batches of the same product,

6.4 Flexible Recipe Modelfor Recipe Initialization

produced within a fixed horizon, to be sold or used together. Therefore, the properties of the last task of each batch, or, in the case of some batches being mixed, the properties of the final products mixed, must meet such requirements, 6ps,”. That is, only deviations up to a point will be permitted (Eq. ( 3 ) ) .

C BrnJpsrn i 6 ~ s C ; Bm m

m

Vp, Vrn

(3)

where B, is the batch size of product p at stage rn, and rn belongs to the set of last recipe stages of product p batches that are mixed. Process operation modification can have an influence on the operation cost. This fact is also considered in the flexible recipe model. Thus, within a time interval, the set-point modification is assumed to have a linear dependence with batch-stage cost (Eq. (4)). SCOSti =f;6poc,

(4)

6.4.3 Flexibility Regions

In Eq. (S), A and a define the flexibility regions for poci and psi respectively. The width of these regions will basically depend on the accuracy of the model presented in the previous section. That is, the regions are defined in which the model deviates from reality by only a predetermined percentage value, E. Assuming linearity, each of these regions can be described by a set of R” hyper planes (Eq. (5)) where n will be number of variables considered or degree of flexibility of the batch process considered.

where Li, l’; and l”i are the matrices that define the hyper planes bounding (Mi) the process flexibility to be considered within the linear model.

6.4.4 tntegration with the Scheduling Tool

Within the S-graph framework, a partial schedule is obtained at each node of the branch-and-bound algorithm. That is, at each node some equipment units may be already scheduled and some others not. The problem is relaxed by solving the linear flexible recipe model. Therefore, if a node has a relaxation higher than the best bound, the branch corresponding to that node is cut. Figure 6.8 shows the Linear Progamming (LP) model to be solved at each node of the branch-and-bound algorithm procedure where the objective function contemplates a trade off between production makespan and production costs. Thus, the recipe is optimized as well as the timing of the partial schedule. Here TIi and TFi are the starting and ending times of task i respectively, Siis the set of states that task i generates and Si” the set of states that feed task i*.

606

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6 Batch and Hybrid Processes

Timing of the schedule constraints,

Ti, o T F ~= TIi + T W ~ vi Tli = TFi Vi, i'/3s E Si n Si,

+

TWiiTWy" Vi M S 5 TFj V i

I-

I

Flexible recipe model, SpSj = ai6PTj

+ bjTWi + C C j , i * G p ~ j+* djSpoci

Flexibility region, LSpoc;

i*

+ /!SPTi + $"STWi 5 Mi

Vi

Performance criterion,

Figure 6.8 Formulation for recipe initialization and multipurpose batch process schedule timing

6.4.5 Motivating Example

The proposed framework for recipe initialization integrated to production scheduling has been tested in the batchwise production of benzyl alcohol from the reduction of benzaldehyde through a crossed Cannizarro reaction. This reaction has been extensively studied by Keesman [28]. In that work, an input-output kind of black box model is developed in order to describe the behavior of the reaction phase of the recipe. The model predicts the reaction yield, psi, as a function of the reaction temperature, poci, reaction time, PTi, amount of catalyst, poci,* and amount of one reactant in excess, poci, 3. Then, the model is used to optimize different recipe components analyzing the effects of model accuracy on the results. However, in that work only one batch phase of the recipe was considered. In the following study, the whole batch recipe train and a production environment are considered in order to fully exploit the potential of a more realistic batch process scenario. The flexible recipe model, Y, for this reaction phase and given the linearity required by the model proposed in Section 6.4.2, becomes,

C::::)

6.4 Flexible Recipe Modelfor Recipe Initialization

Gpsi,l = 4SPT;

+ (4.4,95,95)

Spoci,~

Vi

E

[Reaction phase)

(6)

The coefficients of Eq. (6) are the linear coefficients of the Keesman quadratic model. The flexibility of this batch stage, contained in A and u regions according to Eq. (5), is defined by the set of cutting planes (Eq. (7)) that bounds the deviation of opsi, predicted by Eq. (6) and that predicted by the quadratic model. For simplicity, it has been assumed that the hypervolume of @ containing A and u is a hypercube. Equation 7 represents the hypercube of maximum volume that bounds the flexibility region with a tolerance of less than 1.5 % for the reactant conversion. ‘ 1 0 0 0 - 1 0 0 0 0 1 0 0 0 0 0-1 0 0 1 0 0 0-1 0 0 0 0 1 , o 0 0-1

0.7 “C 8.5 g

(7)

27 g

7.5 g 9og 0.1 h

This reaction stage has been incorporated in the whole recipe. It is assumed that a preparation stage performed in equipment unit U 1 and two separation stages carried out in equipment units U3 and U4 are also necessary to produce the alcohol. The reaction stage takes place in equipment unit U2. Reaction temperature at the second stage, Gpoc;, depends on the temperature reached at the first one, Gpsi.,2 r as follows: SPOCi,J= SPSi’,2 (8) where i’ corresponds to any preparation stage and i to any reaction stage of the alcohol recipe. The temperature reached at the preparation stage depends on the processing time according to: 6psi1.2= lOSPTi/ (9) This recipe has been introduced into the production scenario given in Table 6.1. P1 represents the production of benzyl alcohol. The rest of products P2, P3, and P4 share equipment units and resources with product P1. Table 6.1 Products

Batch production environment

Number of batches

Equipment unit Processing Time (h)

“1 P1

u1 0.5

P2 P3 P4

u2 1.75

u1

u3

1.0 u7 2.0 u2 1.5

2.0 u4 1.0 u3 1.0

u3 2.0 u4 1.5 U6 1.0 u7 2.0

u4 0.5 U6 1.0 u5 1.0

us

1.5

3

1 2 1

608

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G Batch and Hybrid Processes

Figure 6.9 shows the Gantt charts corresponding to the optimum production scheduling for the proposed case study when the fixed recipe at nominal operation conditions is contemplated and when recipe adaptation is considered. The resultant production makespan is 10.75 h for the fxed recipe environment. When the proposed flexible recipe framework is considered, the production makespan diminishes to 10.45 h (2.8% makespan reduction). Also, a different sequence of batches is obtained when it is imposed that the mixing of the three batches of alcohol has to meet the nominal reaction yield (6pspO = 0). The optimal solution is obtained in 25.5 CPU seconds using an AMD-K7 Athlon 1 GHz. The resultant process operating conditions of the three alcohol batches for the flexible recipe scenario are summarized in Table 6.2. T r a d i t i o n a l F i x e d Reclpe

3

day 01

hour 0 0

day 01

hour 0 8

01/01/2001

F l e x i b l e Recipe

2 3 4 5

6 7 day I l l

hour f l O

day 01

hour 08

01/01/2001

Figure 6.9 Optimal Gantt chart of batch production environment of Table 6.1 when considering the fixed recipe and the recipe adaptation respectively. The case study recipe is represented in black

6.4 Nexible Recipe Modelfor Recipe Initialization Table 6.2 Formulation for recipe initialization and multipurpose batch process schedule timing Batch

1st 2nd 3rd

Temperature

Processing

(“C)

time (h)

64.5 64.5 63.8

1.2 1.2 1.2

Amount of

Amount of

Conversion

H*CO (g)

(“w

500 500 500

425 425 425

75 75 72

KOH (g)

To see the effect of initial process deviations on the recipe, Keesman [28] limited the reaction temperature to 63°C (6poq = -1). After optimizing the reaction stage alone, it is found that the reaction time has to be extended to 1.76 h so that the total amount of KOH reaches 528 g and the amount of formaldehyde goes to 475 g in order to keep the intended reaction yield. For these new nominal conditions, the resultant production makespan for the scenario described in Table 6.1 is 11.03 h, which means a reduction in productivity of 5.5 %. Otherwise, a better process performance can be achieved by applying the flexible recipe model to optimize the entire batch plant. The linear flexible recipe, Y, and the model validity constraints for these new nominal conditions are shown in Eqs. 10 and 11, respectively. Vi E {Reactionphase]

-10 0 1 0 - 1 0 0 0 0 0 0

0 0 0 1 - 1 0

‘-1°C 1“C

0 0 0 0 0 1

12g 23 g 13 g 28 g 0.57 h 0.4h

,

Now, the optimal production makespan becomes 10.61 h. Therefore, using the proposed framework, limiting the reaction temperature to 63 “C, only implies a 1.5 % reduction in process productivity. The new process conditions for the different batches of the alcohol production appear in Table 6.3. Table 6.3 Optimal process operation conditions for three batches of alcohol after limiting reaction temperature Batch

1st 2nd 3rd

(“C)

Processing

Amount of

time (h)

KOH (9)

63 63 63

1.55 1.36 1.36

512 512 512

Temperature

Amount of

Conversion

HSO (9)

(“A)

438 438 438

78.3 71.9 71.9

I

609

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G Batch and Hybrid Processes

Notice that in this case study the cost of modifying different process variables has been considered negligible. Usually, nominal values should correspond to an economic optimum. Thus, altering such nominal conditions should result in overrunning this economic optimum in spite of an eventual increase in plant productivity. Obviously, a more realistic scenario should also consider the costs associated to deviations in process operation conditions from nominal values.

6.5 Flexible Recipe Model for Recipe Correction

The recipe initialization is performed at the beginning of the batch phase, taking into account known initial deviations. But other run-time deviations may arise. However, under certain circumstances it is possible to compensate for the effects of these unknown disturbances during the batch run, provided that continuous or discrete measurements are available. The flexible recipe model is the relationship that correlates a batch process output as a function of the selected input items of the recipe. This model is regarded as a constraint on quality requirements and on production cost. Figure 6.7 shows the environment proposed here for real-time recipe correction. While a batch process takes place, different online continuous process variables and discrete variables values, sampled at different times, are taken. From this information, a process state assessment is performed. This assessment gives information about how the batch process is being carried out to the flexible recipe model for recipe correction. The time at which process state assessment is performed, and so at which actions take place, might be different from the moment at which a deviation is detected. Interaction or integration of the flexible recipe model with production scheduling algorithms is necessary to account for the ultimate effect of recipe correction on overall plant capacity. Three different kinds of models are identified: A prediction model that estimates the continuous and discrete sampled (at the sampling time) product specification variables, as a function of the actual control recipe that has already been established by the offline initialization tool. Then, the process state assessment consists of the evaluation of the batch-process run. The predicted product specification i, pvsi"',expected by the offline recipe initialization model, is compared with the actual variable observed at the wth process statement, psi'". If this deviation observed is greater than a fured permitted error, E, some actions will be taken in order to offset this perturbation. A correction model for control recipe adjustments, which describes the ultimate effect of the values measured at the time of the process state assessment as well as of those run-time corrections made during the remainder of the processing time. A rescheduling strategy to adjust the actual schedule to the recipe modifications.

6 5 Flexible Recipe Modelfor Recipe Correction

6.5.1 Rescheduling Strategy, 52

The output of the flexible recipe model for recipe correction might give variations in processing time or resource consumption, which would make the existing plant resources schedule suboptimal or even infeasible. Therefore, in order to accommodate for these deviations in the actual plant schedule, a rescheduling strategy is to be used. There are two basic alternatives to update a schedule when it becomes obsolete: to generate a new schedule or to alter the initial schedule to adapt it to the new conditions. The first alternative might in principle be better for maintaining optimal solutions, but these solutions are rarely achievable in practice and require prohibitive computation times. Hence, a retiming strategy is integrated into the flexible recipe model for recipe correction. At each deviation detected, optimization is required to find the best corrected control process recipe. From this, it is proposed to solve the LP shown in Eq. (12) along with a linear representation of the recipe correction model, to adjust the plant schedule to each recipe correction. In case of dealing with a multipurpose plant, it might happen that a given schedule becomes infeasible because of process disturbances. In such a situation further actions should be taken, like changing the order sequence or canceling a running batch: min (@(PTi,TWi, psi, poci, 0 ) )subject to, Tlij 2 0 Vi, j TFi,, = TIi,, PTi TWi,,?, j TIi,, = TFi,,,Vj, i , i ' / 3 s E { Si n Sit} TIi,, TFi,,-lVi,j TWi,j 5 TW,maxVi,j correction flexible recipe model constraints

+

+

,,

where TI,,,, TF, PT, and TWt,, are the initial, ending, processing and waiting times of each stage i of a batch corresponding to the specific sequence j of the schedule. The sequence is assumed to be fixed. S, is the set of stages that feed stage i. S,' is the set of stages fed by stage i'. Cp is the performance criterion of the flexible recipe model.

6.5.2 Batch Correction Procedure

Within each batch-run, the algorithm of Fig. 6.10 is applied. This algorithm first predicts the expected deviations in process variables from the nominal values as a function of the corrections already taken. Then, the process state assessment verifies if there exist significant discrepancies between the observed variables and the predicted. If so, it freezes process variables of all batch-stages already performed and of the batch-stages that are currently being performed and are not the actual batch-stage

I

611

612

I

,

4 7 1

6 Batch and Hybrid Processes

yes

assesment

I

POC~,TOPi, TFi,

I'

Tli,

to be optimized

I

I

'Flexible recipe correction model'

I IU

Figure 6.10

the batches I

Batch correction procedure algorithm

of assessment and reoptimizes the actual recipe taking into account the effect on the schedule timing.

6.5.3 Application: Model-Based Advisory System for Recipe Correction and Scheduling

In this section, an integrated model-based advisory system is designed to give online support for batch process operation. This application integrates recipe modifications as well as modifications in the actual plant schedule-timing, thus breaking the traditional approach to disassociate recipe correction from plant-wide adjustment. It is based on the flexible recipe concept. The application envisaged gives advice to plant operators and schedulers on how to react in the face of disturbances, so that different kinds of actions can be supported, for instance: correct recipe parameters to offset compensating disturbances to meet product specifications at the expense of processing time;

G. 5 Flexible Recipe Modelfor Recipe Correction 0

allow batches to end on time, that is, finishing the batch below expected product quality; reduce processing times in order to fit a rush order; modify process operating conditions and processing time to partly compensate for disturbances, finishing the batch below product specifications, but not as low as if no action would have been taken.

Different elements form the integrated model advisory system presented here; The recipe adaptation set, where recipe flexibility is defined, the plant adaptation set, where plant schedule adaptation is included using different kinds of rescheduling alternatives, and finally, an integrated criterion, where recipe items modifications, product due-dates accomplishment and product specification deviations costs are included. In this application, the flexible recipe concept is included in the recipe adaptation set. This set consists of a statistical process model optimized from historical process data and relevant model constraints. Variables in the process model may be classified into those that appear perturbed ( P ) ,those that may be tackled to compensate disturbances ( M )and those that define the output of the batch process in terms of quality or yield (0).Hence, the flexible recipe model (Y),included at the recipe adaptation set is as follows.

0 = q ( P T ,M, P) O c a

{M, PT) c S

(13)

where 6 is the flexibility region for process operating conditions and u is the flexibility region for product specifications. The plant adaptation set, the other key concept of the advisory system, describes the plant resources management, including the relevant equipment information for scheduling, and defines penalties for due-date violations for the accepted orders. In this application, sequence of products is predefined and is assumed not to change. Hence, the plant adaptation set is described by Eq. (13). When a deviation between the expected and the actual behavior during processing is observed, some advice on how to react is requested. The application presented here considers two different kind of perturbations: process disturbances on some input variable of the batch recipe stages, and rush orders, a new order to be satisfied at a specific due-date and to be fitted in the actual production plan. Figure 6.11 shows this advice system mechanism window. The application being presented here has been simplified to just consider a linear flexible recipe model at the recipe adaptation set. Then, an LP formulation is used to calculate process adaptation effects. As soon as a deviation is detected, the control recipe can be readjusted, and this readjustment may have an impact on the whole plant operation. A number of scenarios for recipe readjustment are considered, for instance;

I

613

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G Batch and Hybrid Processes

Figure 6.11 0

0

0

Integrated batch operation advice system results

The perturbation may be compensated for within the same batch stage, tackling manipulating variables with a consequence on operation cost. Other batches may have to be corrected, for instance reducing their processing time, to accommodate the impact of correcting a disturbance on a specific batchstage (i.e., on its processing time). The timing of the schedule may have to change, imposing a delay on product delivery.

An integrated optimization criterion computing consequences of different scenarios coordinates the recipe adaptation set actions with the plant adaptation set ones in order to maximize overall batch plant performance. This architecture has been implemented in MATLAB 6.0. When disturbances are encountered, the recipe adaptation set may decide to vary some processing times of some tasks of some recipes. This will have an impact on the actual production schedule, so some orders will have to be shifted forward (increased).The plant adaptation set is optimizing this order-shifting to minimize a function depending on delivery-datedelays. That is, not all order delays will have the same (for instance, economic) impact on the overall objective function, but the plant adaptation set, tries to shift orders so that the overall impact is minimized. This problem results in an LP formulation that is solved using MATLAB optimization toolbox.

G.5 Flexible Recipe Modelfor Recipe Correction

6.5.4

Advisory System Case Study

The case study corresponds to a multiproduct batch plant, over an advising-span of 1 week. During this week, the plant is producing three different products with a specific given sequence. The recipes and sequence of the case study are shown at Tables 6.4 and 6.5, respectively. Table 6.4 study

Master recipes of advisory system case

Recipes

Processing time of stages (h)

R1 R2 R3

10

Table 6.5

Master Schedule of advisory system case study

5 5 10

3 2

3 10 5

4

5 6

Master schedule Sequence Due dates

R3

R1 45

41

R2 58

R3 64

R1 68

R2 81

R3

87

R3 97

Recipe adaptation set (ras) variables are classified into a perturbed variable (P), manipulated variable (4, output variable (0)and processing time (P'T). For simplification, it is assumed that there is only one (critical) variable of each. Besides, the relationship among these variables is considered to be defined by a linear model and it is considered that there is only one flexible task for each product recipe. Table 6.6 summarizes the recipe adaptation set (ras) parameters. Table 6.6

Recipe adaptation set of case study

Flexible Recipe

R1 R2 R3

phase

Coefficients for

SM

61

6PT

2.5 1.0 2.0

2.0 0.5 1.o

1.5 0.5 0.5

A disturbance may be totally offset by modifying the manipulated variable and keeping the master processing time and master output (or quality). Or may be ignored, keeping the manipulated variable and processing time unmodified, so that the output variable (quality) will be affected, or, otherwise, a disturbance may be totally compensated by processing time, or partially by all variables. The integrated advisory criterion computes the effect of modifying manipulated and output variables from the nominal values. Table 6.7 show the costs associated

I

615

616

I

G Batch and Hybrid Processes

with modifying these variables. Also, the cost of delivery-datesdelay from due dates for each order is shown at Table 6.8. Table 6.7 Recipes

Integrated advisory criterion 1

Output deviation cost (u)

R1

1.o

R2 R3

2.0

Manipulated variable deviation cost (u)

0.1 0.5 0.7

0.5

Table 6.8

Integrated advisory criterion 2

Delivery-dates deviation cost (u)

0.2

0.1

0.02

0.5

0.0

0.2

0.1

0.1

0.2

0.03

Two types of disturbances are considered; process disturbances and rush orders. From plant operation, recipe perturbation input variable is retrieved. In this case study, disturbances follow an exponential increase. This would be the case, for instance, of a catalyst being used for all product recipes whose activity is decaying at each use along the production makespan. In the face of disturbances (process disturbances and rush order) the application gives advice on how to react following three policies: 0

0

0

Policy I. This policy ignores process disturbances, and therefore does not modify manipulated variables or processing times. This situation has a direct impact on the output variable, that is, quality of products. Policy 11. Here, process disturbances are totally compensated for by modifylng processing time (not modifymg manipulated variable and keeping output variables equal to nominal values).This situation has a direct impact on delivery dates of products. Policy 111 This policy modifies all recipe items: manipulated variable, processing time and output variable. Within this situation, disturbances may have an impact on delivery dates as well as on product quality, depending on their weight on the overall objective function.

In all policies, a rush order is always accepted. In the case study shown, disturbances have a negative impact of -14.7 u. for policy I, -11.3 u. for policy I1 and of -9.1 u. for policy 111. Policy 111 is the one containing more degrees of freedom to react in the face of disturbances, and therefore is showing the best performance. Figure 6.11 shows the application results window.

G. G final Considerations

6.6 Final Considerations

The increasing interest recently observed in rationalizing batchlhybrid process operations is well-justified. The great advantage offered by batch process stages resides in their inherent flexibility, which may give an adequate answer to present uncertain product demand, variable customer specifications, uncertain operating conditions, market prices variations and so on [29]. In batch plants, there is no reason why the same product must be made every batch; there is the possibility of tailoring a product recipe specifically for a particular customer. In this chapter firstly a review of relevant approaches to represent and exploit this potential flexibility of batchlhybrid process has been given. A novel framework (flexible recipe) has been presented that allows further exploration of flexible manufacturing capabilities of such types of processes. This framework proposes a new philosophy for recipe management in batch process industries that includes the possibility of recipe adaptation in a real-time optimization environment. Based on these novel concepts, a model-based integrated advisory system is presented. The system gives on-time advice to operators on how to react when process disturbances occur. This advice takes into account modification in recipe parameters (product quality, specifications, processing time, process variables) as well as modifications in the production schedule. A process state assessment module for evaluation of abnormal situations should advise when proper actions should be taken. The result is a user-friendly application for optimal batch process operation in industrial practice.

Acknowledgments

Financial support for this research received from the Generalitat de Catalunya", FI program and project GICASA-D (No 1-353) are fully appreciated. Also, support received in part by the European Community (project no G1RD-CT-2001-00466-04GG) is acknowledged. Funds were also received from Spanish MCyT (project no DPI200200806). Enlightening discussions and suggestions received from Prof. Antonio Espuiia and Prof. Verwater-Lukszo are thankfully appreciated. "

Nomenclature

A B, Ci, i+:

DD I 1

Assignment of different batch plant resources. Batch size of product p at stage m. Correlation matrix with the effect of product specifications inputs to stage i from stage i+:. Set of production horizon or due-dates. Observed perturbed variable. Set of production orders.

I

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G Batch and Hybrid Processes

Set of equipment units. Manipulable variable of advisory system. Output variable of batch process. Perturbed variable. Processing time of each stage i of a recipe. Process operation conditions vector as a function of time t of stage i. Observed product specification vector at the wth process state assessment moment of batch process stage i. Observed product specification vector at the end of batch process stage i*. Expected vector of product specification vector at the wth process state assessment moment of batch process stage i. Set of process Resources. Set of states generated by task i. Set of states that feed tasks i". Sequence of different batches. Multistage flowshop or jobshop batch plant topology. Starting time of task i. Ending time of task i. wth moment at which stage i of a batch is being assessed. Waiting time at stage i. Steam temperature condensation at pressure Pi. Flexibility region for process operation conditions. Steam enthalpy. Scheduling constraints. Performance criterion function of the Flexible Recipe model. Quality and production cost modelling function of prediction model. Quality and production cost modelling function of correction model of the wth process assessment moment. A specific production plan. Flexibility region for product specifications.

References 1 Reynold T. S. (1983) 75 years of Progress. A

History of the American Institute of Chemical Engineers 1908-1983. American Institute of Chemical Engineers, New York 2 Parakrarna R. Improving batch chemical processes. The Chem. Eng. 1985 p. 24-25 3 Rekfaitis G. V. (1985) Perspectives for computer-aided batch process engineering. Chem Eng Prog, 8 (1985) p. 9-16 4 Rekfaitis G. V. Sunof A. K. Rippin D. W. T. Hortacsu D. (1996) Batch Processing Systems Engineering. NATO AS1 Series 143, Spinger-Verlag,Berlin

Stephanopoulos G. Ali S. Linninger A. Safomon E. AIChE Symp. Ser. 323 (2000) p. 46-57 6 PuiPjaner L. Espuka A. Reklaitis G. V . (2002). Frameworks for discrete/hybrid production systems. In: Braunschwerg B. Gain R. (eds.) Software Architectures and Tools For Computer Aided Process Engineering. ComputerAided Chemical Engineering, 11. 88 (No. 9) (1985) Elsevier, Amsterdam, pp 663-700 7 Engell S. Kowalenski S. Sefmlz C Stursberg 0. Continuous-discrete interaction in chemical processing plants. Proc. IEEE 88 (2000) p. 5

1050-1068

References

8 Barton P. I. Pantelides C. C. Modeling of con9

10

11

12

13

14

15

16

17

18

tinued discrete/continuous processes. AIChE J. 40 (6) (1994) p. 966-979 Kondili E. Pantelides C. C. Sargent R. N. H. A general algorithm for short-term scheduling of batch operations - 1. Mixed integer linear programming formulation. Comput. Chem. Eng. 17 (1993) p. 211-227 Pantelides C. C. UnJixedJ?ameworks for optimal process planning and scheduling. Proceedings of the. 2nd Conference on Foundation of Computer-Aided Process. Operations. CACHE (1994) pp. 253-274, New York Schilling C. Pantelides C. C. A simple continuous time process scheduling fromulation and a novel solution algorithm. Comput. Chem. Eng. S20 (1996) p. S1221-SI226 Reklaitis G. V. Mockus L. Mathematical programming formulation for scheduling of batch operations based on non-uniform time discretization. Acta Chim. Esloven. 42 (1995) p. 81-86 Mockus L. Reklaitis C. V. Continuous time representation in batch/semicontinuous process scheduling-randomized heuristics approach. Comput. Chem. Eng. S20 (1996) p. S1173-Sl178 Zhang X. Sargent R. W. H. The optimal operation of mixed production facilities - extensions and improvements. Comput. Chem. Eng. S20 (1996) p. S1287-S1292 Shah N. Single and multi-site planning and scheduling: current status and future challenges. AlChE Symp. Ser 320 (1998) p. 75-90 Silver E. Ryke D. Peterson R. (1998) Inventory Management and Production Planning and Scheduling. John Wiley and Sons, New York Graells M. Canton J . Peschaud B. Puigjaner L. General approach and tool for the scheduling of complex production systems. Comput. Chem. Eng. 225 (1998) p. S395-S402 Puigjaner L. Handling the increasing complexity of detailed batch process simulation

19

20

21

22 23

24

25

26

27

28

29

and optimization. Comput. Chem. Eng. 23s (1999) p. S929-S943 Canton /. (2003) Integrated Support System for Planning and Scheduling of Batch Chemical Plants. PhD Thesis Universitat Polithcnica de Catalunya Rijnsdorp J. E. (1991) Integrated Process Control and Automation. Elsevier Amsterdam Venvater-Lukszo 2. (1997) A Practical Approach to Recipe Improvement and Optimization in the Batch Processing Industry. PhD Thesis. Eindhoven Technische Universiteit, Eindhoven, The Netherlands Box G. E. P. Draper N. R. (1969) Evolutionary Operation. Wiley, New York Graells M. Loberg E. Delgado A. Font E. Puigjaner L. Batch production scheduling with flexible recipes: the single product case. AIChE Symp. Ser. 320 (1998) p. 286-292 RomeroJ . Espuna A. Friedler F. Puigjaner L. A newframework for batch process optimization using the flexible recipe. Ind. Eng. Chem. Res. 42 (2003) p. 370-379 ANSl/lSA - S88.01 (1995) Batch Control. Part I : Models and Terminology. American National Standards Institute, Washington D.C. Venvater-Lukszo 2. Keesman K. J. Computeraided development of flexible batch production recipes. Prod. Planning Control 6 (1995) p. 320-330 Sanmarti E. Holczinger T. Puigjaner L. Friedler F. Combinatorial framework for effective scheduling of multipurpose batch plants. AlChE J. 48 (11) (2002) p. 2557-2570 Keesman K. J. Application of flexible recipes for model building batch process optimization and control. AIChE J. 39 (4) (1993) p. 581-588 Rippin D. W. T. Batch process systems engineering: a retrospective and prospective review. Comput. Chem. Eng. S17 (1993) p. S1-S13

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Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

7 Supply Chain Management and Optimization Lazaros C. Papageorgiou

7.1 Introduction

Modern industrial enterprises are typically multiproduct, multipurpose and multisite facilities operating in different regions and countries and dealing with a global international clientele. In such enterprise networks, the issues of global enterprise planning, coordination, cooperation and robust responsiveness to customer demands at the global as well as the local level are critical for ensuring effectiveness, competitiveness, business sustainability and growth. In this context, it has long been recognized that there is a need for efficient integrated approaches to reduce capital and operating costs, increase supply-chain productivity and improve business responsiveness that considers various levels of enterprise management, plant-wide coordination and plant operation, in a systematic way. A supply chain is a network of facilities and distribution mechanisms that performs the functions of material procurement, material transformation to intermediates and final products, and distribution of these products to customers. A definition provided by theSupplyChain.com (http://www.thesupplychain.com) is: “SCM is a strategy where business partners jointly commit to work closely together, to bring greater value to the consumer and/or their customersfor the least possible overall supply cost. This coordination includes that of order generation, order taking and order fulfilment/distribution ofproducts, services or information. €fictive supply-chain management enables business to make informed decisions along the entire supply chain, f r o m acquiring raw materials to manufacturing products to distributingfinished goods to the consumers. At each link, businesses need to make the best choices about what their customers need and how they can meet those requirements at the lowest possible cost.”

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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A similar definition has also been given by Beamon (1998) by defining a supply chain as an integrated process with a number of business entities (i.e., suppliers, manufactures, distributors, retailers). A key characteristic of a supply chain is a forward flow of material from suppliers to customers and a backward flow of information from customers towards suppliers. The supply-chainconcept has in recent years become one of the main approaches to achieving enterprise efficiency. The terminology implies that a system view is taken rather than a functional or hierarchical one. Enterprises cannot be competitive without considering supply-chain activities. This is partially due to the evolving higher specialization in a more differentiated market. Most importantly, competition drives companies toward reduced cost structures with lower inventories, more effective transportation systems, and transparent systems able to support information throughout the supply chain. A single company rarely controls the production of a commodity as well as sourcing, distribution, and retail. Many typical supply chains today have production that spans several countries and product markets are global. The opportunities for supply-chain improvements are large. Costs of keeping inventory throughout the supply chain to maintain high customer service levels (CSLs) are generally significant. There is wide scope to reduce the inventory while still maintaining the high service standards required. Furthermore, the manufacturing processes can be improved so as to employ current working capital and labor more efficiently. It has widely been recognized that enhanced performance of supply chains necessitates (a) appropriate design of supply-chain networks and its components and (b) effective allocation of available resources over the network (Shah 2004). In the last few years, there has been a multitude of efforts focused on providing improvements in supply-chain management and optimization. These efforts span a wide range of models, from commercial enterprise resource planning systems and so-called advanced planning systems to academic achievements (for example, linear and mixed-integer programming and multiagent systems). 0 0

There are three main areas in supply-chain modeling research: supply-chain design and planning simple inventory-replenishment dynamics “novel” applications (e.g., optimization of taxationltransfer prices, cross-chain planning etc.).

The main aim of this chapter is to provide a comprehensive review of recent work on supply-chain management and optimization, mainly focused on the process industry. The first part will describe the key decisions and performance metrics required for efficient supply-chain management, while the second will critically review research work on enhancing the decision-makingfor the development of the optimal infrastructure (assets and network) and planning. The presence of uncertainty within supply chains will also be considered, as this is an important issue for efficient capacity utilization and robust infrastructure decisions. Next, different frameworks are presented which capture the dynamic behavior of the supply chains by establishing efficient inventory-replenishment management strategies. The subse-

7.2 Key Features of Supply Chain Management

quent section of this chapter considers management and optimization of supply chains involving other novel aspects. Finally, available software tools for supplychain management will be outlined and future research needs for the process systems engineering community will be identified. 7.2 Key Features o f Supply Chain Management

Management of supply chains is a complex task, mainly due to the large size of the physical supply network and inherent uncertainties. In a highly competitive environment, improved decisions are required for efficient supply-chain management at both strategic and operational levels, with time horizons ranging from several years to a few days, respectively. Depending on the level, one or more of the following decisions are taken: 0

0 0

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number, size and location of manufacturing sites, warehouses and distribution centres; production decisions related to plant production planning and scheduling; network connectivity (e.g., allocation of suppliers to plants, warehouses to markets etc.); management of inventory levels and replenishment policies; transportation decisions concerning mode of transportation (e.g., road, rail etc.) and also material shipment size.

In general, the supply chains can be categorized as domestic and international, depending on whether they are based in a single country or multiple countries, respectively (Vidal and Goetschalckx 1997).The latter case is more complex, as more global aspects need to be considered such as: 0 0 0 0

different tax regimes and duties exchange rates transfer prices differences in operating costs.

It should be mentioned that effective application of suitable forecasting techniques are often critical to successful supply-chain management (see, for example, Makridakis and Wheelright (1989)).These quantitative forecasting techniques provide accurate forecasts (usually for product demands), which can then be used for planning purposes. The quality of the efficiency and effectiveness of the derived supply-chain networks can be assessed by establishing appropriate performance measures. These measures can then be used to compare alternative systems or design a system with an appropriate level of performance. Beamon (1998)has described suitable performance measures by categorizing them as qualitative and quantitative. Qualitative performance measures include: customer satisfaction, flexibility, information and material flow integration, effective risk management and supplier performance. Appropriate quantitative performance measures include:

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measures based on financial flow (cost minimization, sales maximization, profit maximization, inventory investment minimization and return on investment); measures based on customer responsiveness (fill rate maximization, product lateness minimization, customer response time minimization, lead-time minimization and function duplication minimization).

7.3 Supply Chain Design and Planning

Supply-chaindesign and planning determines the optimal infrastructure (assets and network) and also seeks to identify how best to use the production, distribution and storage resources in the chain to respond to orders and demand forecasts in an economically efficient manner. It is envisaged that large benefits will stem from coordinated planning across sites, in terms of costs and market effectiveness. Most business processes dictate that a degree of autonomy is required at each manufacturing and distribution site, but pressures to coordinate responses to global demand while minimizing costs imply that simultaneous planning of production and distribution across plants and warehouses should be undertaken. The need for such coordinated planning has long been recognized in the management science and operations research literature. A number of mathematical models have been presented with various features; steadystate, multiperiod, deterministic or stochastic. Early research in this field was mainly focused on location-allocation models. Geoffrion and Graves (1974)present a model to solve the problem of designing a distribution system with optimal location of the intermediate distribution facilities between plants and customers. In particular, they aim to determine which distribution centre (DC) sites to use, what size DC to have at each selected site, what customer zones to serve and the transportation flow for each commodity. The objective is to minimize the total distribution cost (transportation cost and investment cost) subject to a number of constraints such as supply constraints, demand constraints and specification constraints regarding the nature of the problem. The problem is formulated as a mixed-integerlinear programming (MILP) problem, which is solved using Benders decomposition. The model is applied to a case study for a supply chain comprising 17 commodity classes, 14 plants, 45 possible distribution centre sites and 121 customer demand zones. The risks arising from the use of heuristics in distribution planning were also identified and discussed early on by Geoffrion and van Roy (1979).Three examples were presented in the area of distribution planning demonstrating the failure of “common sense’’methods to come up with the best possible solution. This is due to the failure to enumerate all possible combinations, the use of local improvement procedures instead of global ones, and the failure to take into account the interactions in the system. Wesolowsky and Truscott (1975) present a mathematical formulation for the multiperiod location-allocation problem with relocation of facilities. They model a

7.3 Supply Chain Design and Planning

small distribution network comprising a set of fac es aiming to serve the demand at given points. The model incorporates two types of discrete decisions, one involving the assignment of customers to facilities and the other the location of the nodes. They consider both steady-stateand time-varying demands. Williams (1983) develops a dynamic programming algorithm for simultaneously determining the production and distribution batch sizes at each node within a supply-chain network. The average cost is minimized over an infinite horizon. Brown et al. (1987)present an optimization-baseddecision algorithm for a support system used to manage complex problems involving facility selection, equipment location and utilization, and the manufacture and distribution of products. They focus on operational issues such as where each product should be produced, how much should be produced in each plant, and from which plant product should be shipped to customer. Some strategic issues are also taken into account such as location of the plants and the number, kind and location of facilities (plants). The resulting MILP model is solved using a decomposition strategy. It is applied to a real case for the NABISCO Company. A two-phase approach was used by Newhart et al. (1993)to design an optimal supply chain. First, a combination of mathematical programming and heuristic models is used to minimize the number of product types held in inventory throughout the supply chain. In the second phase, a spreadsheet-based inventory model determines the minimum safety stock required to absorb demand and lead-time fluctuations. Pooley (1994) presents the results of a MILP formulation used by the Ault Foods company to restructure their supply chain. The model aims to minimize the total operating cost of a production and distribution network. Data are obtained from historical records; data collection is described as one of the most time-consuming parts of the project. Binary variables characterize the existence of plants and warehouses and the links between customers and warehouses. Wilkinson et al. (1996) describe a continent-wide industrial case study. This involved optimally planning the production and distribution of a system with 3 factories and 14 market warehouses and over 100 products. A great deal of flexibility existed in the network which, in principle, enables the production of products for each market at each manufacturing site. Voudouris (1996) develops a mathematical model designed to improve efficiency and responsiveness in a supply chain. The target is to improve the flexibility of the system. He identifies two types of manufacturing resources: activity resources (manpower, warehouse doors, packaging lines, etc.) and inventory resources (volume of intermediate storage, warehouse area). The activity resources are related to time while the inventory resources are related to space. The objective function aims at representing the flexibility of the plant to absorb unexpected demands. Pirkul and Jayaraman (199G) present a multicommodity system concerning production, transportation, and distribution planning. Single sourcing is forced for CUStomers but warehouses can receive products from several manufacturing plants. The objective is to minimize the combined costs of establishing and operating the plants and the warehouses to customers.

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Camm et al. (1997) present a methodology by combining integer programming, network optimization and geographical information systems (GIS) for Procter and Gamble’s North American supply chain. The overall problem is decomposed into a production (product-plant allocation) problem and a distribution network design problem. Significant benefits were reported with reconstruction of Procter and Gamble’s supply chain (reduction of 20% in production plants) and annual savings of $200m. McDonald and Karimi (1997) consider multiple facilities that effectively produce products on single-stagecontinuous lines for a number of geographically distributed customers. Their basic model is of a multiperiod linear programming (LP) form, and takes account of available processing time on all lines, transportation costs and shortage costs. An approximation is used for the inventory costs, and product transitions are not modeled. They include a number of additional supply-chain related constraints such as single sourcing, internal sourcing and transportation times. Other planning models of this type do not consider each product in isolation, but rather groups products that place similar demands on resources into families, and bases the higher level planning function on these families. More sophisticated models exist in the process systems literature. A model which selects processes to operate from an integrated network while ensuring that the network capacity constraints are not exceeded is described in Sahinidis et al. (1989).Means of improving the solution efficiency of this class of problems can be found in Sahinidis and Grossmann (1991) and Liu and Sahinidis (1995). Uncertainty in demands and prices are modeled in Liu and Sahinidis (1996) and Iyer and Grossmann (1998) by using a number of scenarios for each time period, thus resulting in multiscenario, multiperiod optimization models. Computational enhancements of the above large-scale model have been proposed by applying projection techniques (Liu and Sahinidis 1996)or bilevel decomposition (Iyer and Grossmannn 1998). A potential limitation of these approaches is that they use expectations rather than a variability metric of the second-stagecosts. Ahmed and Sahinidis (1998) resolved this difficulty by introducing a one-side robustness measure that penalizes second-stage costs that are above the expected cost. Similar measures based on expected downside risk have been developed by Eppen et al. (1989), and have recently been applied to capacity planning problems for pharmaceutical products at different stages in clinical trials (Gatica et al. 2003). Applequist et al. (2000) focus on risk management for chemical supply-chain investments. They introduce the risk premium approach in order to determine the right balance between expected value of investment performance and associated variance. An investment decision is approved provided that its expected return is better than those in the financial market with similar variance. An efficient polytope integration procedure is described to evaluate expected values and variances. Gupta and Maranas (2000) consider the problem of mid-term supply-chain planning under demand uncertainty. A two-stage stochastic programming approach is proposed with the first stage determining all production decisions (here-and-now) and all supply-chains decisions are optimized in the second stage (wait-and-see). This work is extended by Gupta et al. (2000) by integrating the previous two-stage

7.3 Supply Chain Design and Planning

framework with a chance constraint programming approach to capture the tradeoffs between customer demand satisfaction and production costs. The proposed approach was applied to the problem of McDonald and Karimi (1997). Sabri and Beamon (2000) develop a steady-state mathematical model for supplychain management by combining strategic and operational design and planning decisions using an iterative solution procedure. A multiobjective optimization procedure is used to account for multiple performance measures, while uncertainties in production, delivery and demands are also included. A MILP model is proposed by Timpe and Kallrath (2000) for the optimal planning of multisite production networks. The model is multiperiod, based on a time-indexed formulation allowing equipment items to operate in different modes. A novel feature of the model is that it can accommodate different timescales for production and distribution of variable length, thus facilitating finer resolution at the start of the planning horizon. The above model was applied to a production network of four plants located in three different regions. A larger example is briefly described in Kallrath (2000),which demonstrates the use of an optimization model involving 7 production sites with 27 production units operating in futed-batch mode. Bok et al. (2000)present a multiperiod optimization model for continuous process networks with main focus on operational decisions over short time horizons (one week to one month). Special features of the supply chain are taken into account such as sales, intermittent deliveries, production shortfalls, delivery delays, and inventory profiles and job changeovers. A bilevel decomposition solution procedure is proposed to reduce computational effort and deal with larger scale problems. Tsiakis et al. (2001) describe a multiperiod MILP model for the design of supplychain networks. The model determines production capacity allocation among different products, optimal layout and flow allocations of the distribution network by minimizing an annualized network cost. Demand uncertainty is also introduced in the multiperiod model using a scenario-based approach with each scenario representing a possible future outcome and having a given probability of occurrence. Papageorgiou et al. (2001) present an optimization-based approach for pharmaceutical supply chains to determine the optimal product portfolio and long-tem capacity planning at multiple sites. The problem is formulated as a MILP model, taking into account both the particular features of pharmaceutical active ingredient manufacturing and the global trading structures. Particular emphasis is placed upon modeling of financial flows between supply-chain components. A comprehensive review on pharmaceutical supply chains is given by Shah (2003). Kallrath (2002) describes a multiperiod mathematical model that combines operational planning with strategic aspects for multisite production networks. The model is similar to the one presented by Timpe and Kallrath (2000) but allows flexible production unit-site allocation (purchase, opening, shutdown), and raw material purchases and contracts. Sensitivity analyses were also performed, indicating that the optimal strategic decisions were stable up to a 20 % change in demand. Ahmed and Sahinidis (2003) propose a fast approximation scheme for solving multiscenario integer optimization problems, which is particularly relevant to capacity planning problems under discrete uncertainty.

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Jackson and Grossmann (2003) describe a multiperiod nonlinear programming model for the production planning and distribution of multisite continuous multiproduct plants where each production plant is represented by nonlinear process models. Spatial and temporal decomposition solution schemes based on Lagrangean decomposition are proposed, to enhance computational performance. Ryu and Pistikopoulos (2003)present a bilevel approach for the problem of supplychain network planning under uncertainty. The resulting optimization problem is then solved efficiently using parametric programming techniques. Levis and Papageorgiou (2004) extend the previous work of Papageorgiou et al. (2001)to consider the uncertainty of outcome of clinical trials. They propose a twostage, multiscenario MILP model to determine both the product portfolio and the multisite capacity planning, while taking into account the trading structure of the company. A hierarchical solution algorithm is proposed to reduce the computational effort needed for the solution of the resulting large-scaleoptimization models. Neiro and Pinto (2004) present an integrated mathematical framework for petroleum supply-chain planning by considering refineries, terminals and pipeline networks. The problem is formulated as a multiperiod, mixed-integer nonlinear programming model, and essentially extends previous work (Pinto et al. 2000) for single refinery operations with nonlinear process models and blending relations. The case study solved represents part of a real-world petroleum supply-chain planning problem in Brazil involving four refineries, five terminals and pipeline networks for crude oil supply and product distribution. 7.3.1 MultiSite Capacity Planning Example

Consider a multisite pharmaceutical capacity planning example (Levis and Papageorgiou 2004) with seven potential products (Pl-P7) subject to clinical trials, four alternative locations (A-D), where A and B are the sales regions, A is the intellectual property (IP) owner, and B, C and D are the candidate production sites. The entire time horizon of interest is 13 years. In the first 3 years, no production takes place and the outcomes of the clinical trials are not yet known. Initially, there are two suites already in place at production site B. Further decisions for investing in new manufacturing suites are to be determined by the optimization algorithm. It is assumed that the trading structure is given together with the internal pricing policies as shown in Fig. 7.1. Five out of seven potential products are selected in the product portfolio while the optimal enterprise-wide pharmaceutical supply chain is illustrated in Fig. 7.2 where location C is not chosen. The investment decision calendar is illustrated in Fig. 7.3. Note that investment decisions for additional manufacturing suites are taken in the early time periods while the clinical trials are still on going. The proposed investment plans take into account the construction lead-time (2 and 3 years for nonheader and header suites, respectively) and safeguard the availability of the newly invested equipment right after the end of the clinical trials phase.

7.3 Supply Chain Design and Planning .............................................

site B P1, P4, P5

i

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; IP centre

II

Site D ..........................................

:

c

;

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Figure 7.1 Trading structure o f the company. Pl-P7 Potential products subject to clinical trials, A-D four alternative locations where A and B

are the sales regions, A is the intellectual property and Dare the candidate production sites

(IP)owner, and

i - f

....................

............................................

Figure 7.2 Optimal business network

to

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Time (years) Figure 7.3 Investment decisions calendar. Black: site B; grey: site D

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120 100 80 m

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Product P I

Production m S a 4 e s +Demand Figure 7.4

+Inventory/

Characteristic profiles for the product P1

Operational variables (detailed production plans, inventory and sales profiles) for the selected products are also determined as illustrated in Fig. 7.4. In particular, the production of product P1 is taking place at both manufacturing sites B and D. Mainly due to the proposed investment plan and production policy, the total manufactured amount of P1 fully satisfies customer demand at all time periods.

7.4 Analysis of Supply Chain Policies

The operation of supply chains is a complex task, mainly due to the large physical production and distributions network flows, the inherent uncertainties and the dynamics associated with the internal information flow. At the operations level, it is crucial to ensure enhanced responsiveness to changing market conditions. In this section, different frameworks are presented which capture the dynamic behavior of the supply chains by establishing efficient inventory-replenishment management strategies. Beamon (1998)provides a comprehensive review of supply-chainmodels and classifies them as analytical and simulation. Analytical models usually use an aggregate description of supply chains and optimize high-level decisions involving unknown

-

7.4 Analysis ofSupply Chain Policies

configurations, while simulation models can be used to study the detailed dynamic operation of a futed configuration under operational uncertainty. In general, simulation is particularly useful in capturing the detailed dynamic performance of a supply chain as a function of different operating policies, Usually, these simulations are stochastic, thus deriving distributions of characteristic performance measures based on samples from distributions of uncertain parameters. Gjerdrum et al. (2000) describe a procedure for modeling of the physical and decision-making business process aspects of a supply chain. A specialty chemical process with international markets, secondary manufacturing plants and primary manufacturing plants illustrates the model. The above procedure proposes pragmatic, noninvasive policy and parameter modifications (e.g., safety stocks) that improve performance measures such as average inventory levels, probability of stock-outs and customer service levels (CSLs) are identified. A stochastic simulation approach is then proposed using the above procedure and sampling from the uncertain parameters to assess future performance of the supply chain. The above work has recently been extended by Hung et al. (2004) adopting an object-orientedapproach to model both physical processes (e.g., production, distribution) and business processes of the supply chain. An efficient sampling procedure is also developed which reduces significantly the number of simulations required. A model predictive control (MPC) framework for planning and scheduling problems is adopted by Bose and Pekny (2000). The framework consists of forecasting and optimization modules. The forecasting module calculates target inventories for future periods, while the optimization module attempts to meet these targets in order to ensure the desired CSL while minimizing inventory. Simulation runs are then performed to study the dynamics of a consumer goods supply chain focusing on promotional demand and lead time as the main control parameters. Different coordination structures of the supply chain are also investigated. Van der Vorst et al. (2000)present a method for modeling the dynamic behavior of food supply chains by applying discrete-event simulation based on time colored Petri-nets. Alternative designs of the supply-chain infrastructure and operational management and control are then evaluated with the main emphasis being placed upon distribution of food products. Perea-Lopez et al. (2001) describe a dynamic modeling approach for supply-chain management by considering the flow of material and information within the supply chain. The impact of different supply-chain control policies on the performance of supply chains is evaluated using a decentralized decision-making framework. This is demonstrated through a polymer case study with one manufacturing site, one distribution network and three customers. Perea et al. (2003) extend their previous work (Perea et al. 2001) by proposing a multiperiod MILP optimization model within an MPC strategy. A centralized approach is adopted where the corresponding MILP model considers the whole supply chain, involving suppliers, manufacturing, distribution and customers simultaneously. The benefits of centralized over decentralized management are then emphasized with a case study with profit increases of up to 15 %.

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Agent-basedtechniques have recently been reported in the process systems literature for the efficient management of supply-chain systems. Garcia-Flores et al. (2000) and Garcia-Flores and Wang (2002)present a multiagent modeling system for supply-chain management of process industries. Retailers, warehouses, plants and raw material suppliers are modeled as a network of cooperative agents. A commercial scheduling system is integrated in the multiagent framework, as plant scheduling usually dominates the supply-chain performance. A case study with a single multipurpose batch plant of paints and coatings is then used to illustrate capabilities of the system. A similar approach has also been reported by Gjerdrum et al. (2001a)to simulate and control a demand-driven supply-chain network system, with the manufacturing component being optimized through mathematical programming. A number of agents have been used, including warehouses, customers, plants, and logistics functions. The plant agent, which is responsible for production scheduling, is using optimization techniques while the other agents of the supply chain are mainly rulebased. The proposed system is then applied to a supply chain with two manufacturing plants by investigating the effect of different replenishment policies in the supply-chain performance. Julka et al. (2002a,b)propose an agent-based framework for modeling, monitoring and management of process supply chains. A refinery application is considered for the efficient management of crude oil procurement business process by investigating the impact of different procurement policies, demand fluctuation and changes in plant configuration.

7.4.1 A Pharmaceutical Supply Chain Example

A pharmaceutical supply chain example (Gjerdrum et al. 2000) is shown in Fig. 7.5. A primary manufacturing plant is situated in Europe. Secondary formulation sites in Asia and America receive A1 from this plant and produce final products for the main warehouses in Japan and the US. There are two main SKUs in the Japanese market: products A and B. Also, in the US market there are two principal products, C and D. Primary

Secondaw

Europe America

Figure 7.5

A supply chain example

Market

Products

7.4 Analysis ofsupply Chain Policies

There are also several other product SKUs that share secondary manufacturing resources (in Asia and America) which are handled by other (not explicitly modeled) warehouses e.g., in Europe. The CSL deemed sufficient for this supply chain by decision-makers (called the target CSL) is 97 %. The low figure is due to large inventories held at external warehouses downstream in the supply chain, which will buffer against any temporary stock-outs. Occasional SKU stock-outs are therefore not considered to be harmful since the end consumer is not affected. Therefore, the aim of this case study is to reduce inventory while maintaining the target CS L. The demand-management SKU data is presented in Table 7.1. Table 7.1

Demand management SKU base case data

Safety stock (weeks) MOQ (units) Deviation from forecast (%) Pack size (units) Initial stock (units)

Product A

Product B

Product C

Product D

6 10,000 25 12 15,000

6 5000 20 30 15,000

6 5000

6 20,000 25 30 60,000

25 30 60,000

The production data are given in Tab. 7.2. Table 7.2

Secondary manufacturing site base case

data

Safety stock (kg) A1 Order quantity (kg) Production capacity (h week-1) Production rate (units h-’) Flexibility of production (“A) Initial A1 stock (kg)

Asia

USA

50 30 60 650 40 80

150 130 60 1200 25 180

One of the most important supply-chain performance indicators is the amount of unutilized working capital in the chain. By closely tracking simulated inventory, substantial costs can be taken out of the supply chain. This must be done while maintaining required high CSLs, low probabilities of stock-outs and supply-chain efficiency in general. Therefore, we simulate the inventory levels as well as the more traditional customer-focused aspects of the supply-chain performance. Each simulation is repeated 100 times to ensure statistically trustworthy results. CSL is defined as part-fill on-time. When there is inventory enough at hand, the sales equal demand. When inventory runs out, it is assumed that inventory that is there can be sold while the rest of the demand is left unfulfilled. The probability of stock-out (PSO) is simply the number of times the inventory is zero divided by the total number of data points, i.e., the horizon length times the number of simulated simulation runs. Hence, this complete supply chain is dynamically simulated over a prespecified horizon of, e.g., 2 years. First, initialization of the

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model is performed with respect to fKed policy parameters, business processes and initial stock levels. At each time-step (e.g., each week) in the horizon, input parameters and model data from previous time steps are collected. Actual sales and machine breakdown are generated from stochastic distributions. Stock positions, current supply-chain orders and forecasts are then updated and evaluated. When any model variables violate the current procedures or policies (such as the safety stock) the model issues new directions of action (such as issuing new orders). To obtain statistically significant results of the stochastic process, the simulation is repeated over a number of runs. At each run, informative data are collected. Finally, all the supply-chain simulation results are extracted and evaluated. The experiments presented in Table 7.3 demonstrate the response of the supply chain to changes in internal and external parameters. These experiments are useful in that they provide information on whether current policies and external factors can be modified while maintaining strong supply-chain performance. INV is the horizon-average finished product (SKU) inventory. High demand variability represents a complex market to forecast. High order quantity shows what happens if a typical service level parameter is modified. Although these parameters obviously affect the performance levels, it seems that the demand management performance levels are not severely affected by the demand variability or the order quantity. The ramping and decreasing demands give conservative measures, since it is assumed that the forecast will not be updated during the horizon. The US market is able to handle a soaring demand better, due to fewer conflicting products. Table 7.3 Supply-chain experiments. CSL Customer service level, PSO probability of stock-out, INV horizon-average finished product inventory Experiment

Product A (Asia) CSL(%)

Base case H i g h demand variability H i g h order quantity Soaring demand Collapsing demand

98.33 98.05 97.94 95.52 99.83

PSO(%) 1.81 2.18 2.30 4.54 0.19

Product C (USA)

INV 48,074 48,678 58,688 43,997 54,645

CSL(%)

PSO (%)

98.81 97.76 98.21 98.73 99.51

1.33 2.31 1.96 1.22 0.75

INV ~

~

~~~~

105,041 107,315 109,049 112,554 111,789

In Fig. 7.6, the expected number of stock-outsfor various policies of safety stock is shown for product C in the US market. The value represents the risk of a stock-out occurring during the simulated period. In Fig. 7.7, the CSL defined as part-fill on-time is shown for different policies of weekly forward cover stock for product C. It can be seen that a policy of 4 weeks of forward cover will just about be sufficient to satisfy the target CSL of 97 %. In Fig. 7.8, the resulting mean average inventory values for various stock policies are shown for product C. The 4 weeks forward cover corresponds to an average inventory of about 70,000 units. This value can then be utilized to calculate the market inventory cost.

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7.5 Multienterprise Supply Chains

In recent years, the concept of multienterprises has gained increasing attention, since it promotes all the benefits of extended multienterprise collaboration. The determination of policies that optimize the performance of the entire supply chain as a whole, while ensuring adequate rewards for each participant is crucial and the relevant work is very limited. Conflicting interests in general extended multienterprise supply chains frequently lead to problems in how to distribute the overall value to each member of the supply

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chain. A simple approach to enhancing the performance of a multienterprise supply chain is to maximize the summed enterprise profits of the entire supply chain subject to various network constraints. When the overall system is optimized in this fashion, there is no automatic mechanism to allow profits to be fairly apportioned among participants. Solutions to this class of problems usually exhibit quite uneven profit distribution and are therefore impractical. They do however give an indication of the best possible total profit attainable in the supply chain as well as an indication of the best activities to carry out. van Hoek (1998)raises the question of how to divide supply-chainrevenues among the players in a supply-chain system when there is no leading player to determine how distribution of benefits should be handled. He states that supply-chain control is no longer based on direct ownership but rather on integration over interfaces of functions and enterprises. Traditional performance indicators limit the possibilities of optimizing the supply-chain network because the measures do not correctly address the wide opportunities for improvement. Cohen and Lee (1989) deliver a model for making resource deployment decisions in a global supply-chain network and solve different scenarios using an extensive mixed-integer nonlinear programming (MINLP) model. They also discuss several “policyoptions” for plant utilization, supply and distribution strategies. Pfeiffer (1999) describes transfer pricing in a supply chain consisting of procurement, manufacturing and selling units of one single company. His theoretical model handles one commodity at each node and does not include any capacity constraints. He proposes a transfer-price system governed by the headquarters, which fxes a specific transfer-price level. Each node optimizes its own decisions independently to maximize a given profit function, according to the price level fixed by the headquarters. After the decentralized optimization, headquarters evaluates and collects the overall results obtained and chooses a new transfer price that leads to a higher profitability. Alles and Datar (1998) claim that cost-based transfer prices of the companies are usually based in their competitive environment. The enterprise may cross-subsidize products in order to increase their ability to increase prices. Often, transfer prices for relatively lower cost products are decreased. The authors give evidence that transfer prices are determined based on strategic decisions rather than on internal cost systems. Jose and Ungar (2000) propose an approach to decentralized pricing optimization of interprocess streams in chemical industry companies. Their iterative auction method determines the prices of process streams so as to maximize an objective for a single chemical company, while each division within the company is constrained by its available resources. The approach is interesting in that each division conceals its private information from the other parties within the so-called micro supply chain. It normally takes several iterations for a model to converge, and the user has to define the limited amount of slack resources utilized. One of the main conceptual differences between their approach and the one presented in this paper is that they regard the channel members as adversarial and competitive for resources rather than cooperative. Also, they use a slack resource iterative auction approach, whereas in

7.6 Software Toolsfor Supply Chain Management

this paper the solution approach is to solve a noniterative separable MILP problem. Ballou et al. (2000) stress the importance of common objectives in the supply chain. Unattainable improvements for single companies in terms of cost savings and customer service enhancements can be obtained by cooperative companies. The authors point out that problems arise if some of the firms benefit at the expense of the others. The conflict resolution between supply-chain partners must be of focal interest, and to keep the coalitions intact, the rewards of cooperation must be redistributed. They identify three means to achieve this: 1. Metrics could be developed to capture the nature if interorganizational cooperation to simplify benefit analysis. 2. Information sharing mechanisms could transfer information about the benefits of cooperation among the members in the supply chain. 3. Allocation methods could be developed thatfairly distribute the rewards of cooperation between the members. According to Pashigian (1998), multiproduct industries form a new market structure characterized by novel market relationships among companies. Collusion takes place when the firms in an industry join together to set prices and outputs. Such an agreement is said to form a cartel. However, game theorists insist that there is an inherent incentive for each firm to cheat on such an agreement, in order to gain more profits for itself. Vidal and Goetschalckx (1997) present a nonconvex optimization model together with a heuristic solution algorithm for the management of a global supply by maximizing the after-tax profits of a multinational corporation. The model also considers transfer prices and the allocation of transportation costs as explicit decision variables. Gjerdrum et al. (2001b,2002) present a MINLP model including a nonlinear Nashtype objective function for fair profit optimization of an n-enterprise supply-chain network. The supply-chain planning model considers intercompany transfer prices, production and inventory levels, resource utilization, and flows of products between echelons. Efficient solution procedures for the above model are described by Gjerdrum et al. (2001b, 2002) based on separable programming and spatial branch-andbound respectively. Computational results indicate profits very close to those obtained by simple single-level optimization (e.g., maximization of total profit), but more equitably distributed among partners. Chen et al. (2003)propose a fuzzy decision-making approach for fair profit distribution for multienterprise supply-chain networks. The proposed framework can accommodate multiple objectives such as maximization of the profit of each participant enterprise, the CSL, and the safe inventory level. 7.6 Software Tools for Supply Chain Management

The coordination of operations on a global basis requires the implementation and use of software to support these decisions. State-of-the-artsoftware requires the ability to perform constraint-based, multisite planning that can become extremely com-

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plex. Modern software supply-chain tools aim to integrate traditionally fragmented views of operations, and to provide a holistic view of the problem, rather than linking separate planning operations.

7.6.1 Aspen Technologies (http://www.aspentech.com)

Aspen MIMI supply-chain suite includes the Aspen Strategic Analyzer that can be used to identify strategic and operational options such as capacity addition, production constraints and distribution modes. Aspen is the leading provider of supplychain solutions in the process industry, by market share.

7.6.2 i2 Technologies (http://www.i2.~om)

Supply-Chain Optimization is a holistic solution and framework to help companies create a macrolevel model for the entire supply chain that controls an integrated workflow environment. The user may select to extend the capabilities and study in depth specific areas of the supply-chain problem, such as logistics, production, demand fulfilment and profitlrevenue analysis.

7.6.3 Manugistics (http://www.manugistics.com)

Network Design and Optimization is a supply-chain design and operation package that is part of the Manugistics supply-chain suite. Among its capabilities is the design of a supplier, manufacturing site and distribution site network in the most effective way. The process considers inventory levels, production strategy, production and transportation costs, lead times and other user-specified constraints.

7.6.4 SAP AC (http://www.sap.com)

MySAP SCM (Supply-Chain Management) is designed to be a complete supplychain solution. The supply network planning and deployment tool assists planners to balance supply and demand while simultaneously considering purchasing, manufacturing, inventory and transportation constraints. Integrated with other support tools, it aims to provide a complete optimization framework.

7.7 Future Challenges

7.7 Future Challenges

It is clear that considerable research work has been done on process supply-chains especially in the areas of network design and planning. However, a number of issues provide interesting challenges for further research. As many modern supply chains are characterized by their international nature, optimization-based decisions are required for various features such as taxes, duties, transfer prices, etc. Systematic integration of business/financial and planning models should be considered for efficient supply-chain management (see, for example, Shapiro (2003),Romero et al. (2003),Badell et al. (2004),Badell M., Romero J., Huertas R., Puigjaner L. Comput. Chem. Eng. 28 (2004) p. 45-61). Significant effort has already been put into supply-chain modeling under uncertainty commonly related to product demands. The treatment of uncertainty still requires research effort to capture more aspects such as product prices, resource availabilities etc. In order to ensure that investment decisions are made optimally in terms of both reward and risk, suitable frameworks for the solution of supply-chain optimization problems under uncertainty are required. Most of the existing frameworks are suitable for two-stage problems, while there is a need for appropriate multistage, multiperiod optimization frameworks for supply-chain management. As most of the resulting optimization problems, and predominantly cases under uncertainty, will be of large scale, there is great scope for developing efficient solution procedures. Aggregation and decomposition techniques are envisaged as such promising solution alternatives. It should be mentioned that it is quite important to maintain industrial focus for the successful development of such solution methods. The analysis of supply-chain policies for process industries has recently emerged and this research area is expected to expand. Suitable frameworks seem to be the ones based on agents, MPC and object-oriented systems. A key issue here is the appropriate integration of business and process aspects (see, for example, Hung et al. (2004)). Another emerging research area is the systematic incorporation of sustainability aspects within supply-chain management systems, necessitating the development of multiobjective optimization frameworks (see, for example, Zhou et al. (2000), Hugo and Pistikopoulos (2003)). Finally, research opportunities are evident in the appearance of new types of supply chain, associated, for example, with hydrogen (fuel cells), energy supply, water provision/distribution, fast response therapeutics and biorefinenes.

Acknowledgments

The author is grateful to Nilay Shah, Jonatan Gjerdrum, Panagiotis Tsiakis, Gabriel Gatica and Aaron Levis for useful discussions and contributions to this work.

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Res. 37 (1998) p. 1883-1892 2 Ahmed S. Sahinidis N. V. Oper. Res. 51 (2003)p. 461-47 3 Alles M. Datar S. Manage. Sci. 44 (1998) p. 451-461 4 Applequist G. E. PeknyJ. F. Reklaitis G. V. Comput. Chem. Eng. 24 (2000) p. 2211-2222 5 Ballou R. H. Gilbert S. M. Mukherjee A. A. Ind. Market. Manage. 29 (2000) p. 7-18 6 Beamon B. M. Int. J. Prod. Econ. 55 (1998)p. 281-294 7 Bokj. K. Grossmann I. E. Park S. Ind. Eng. Chem. Res. 39 (2000) p. 1279-1290 8 Bose S. Peknyj. F. Comput. Chem. Eng. 24 (2000)p. 329-335 9 Brown G. G. Graves G. W. Honczarenko M. D. Manage. Sci. 33 (1987) p. 1469-1480 10 CammJ. D. Chorman T. E. Dill F. A. Evans]. R. Sweeney D.]. Wegryn G. W. Interfaces 27 (1997)p. 128-142 11 Chen C. L. Wang B. W. Lee W. C. Ind. Eng. Chem. Res. 42 (2003)p. 1879-1889 12 Cohen M. A. Lee H. L. j . Manuf. Oper. Manage. 2 (1989) p. 81-104 13 Eppen G. D. Marti R. K. Schrage L. Oper. Res. 37 (1989) p. 517-527 14 Garcf'a-Flores R. Wang X. 2.OR Spectrum 24 (2002)p. 343-370 15 Garcia-Flores R. Wang X. 2.Goltz G . E. Comput. Chem. Eng. 24 (2000) p. 1135-1141 16 Gatica G. Papageorgiou L. G. Shah N. Chem. Eng. Res. Des. 81 (2003) p. 665-678 17 G e o f i o n A. M. Graves G. W. Manage. Sci. 20 (1974) p. 822-844 18 Geofion A. M. van Roy T. J. Sloan Manage. Rev. Summer (1979)p. 31-42 19 Gjerdrum J . Jalisi Q. W. 2.Papageorgiou L. G. Shah N. 5th Annual International Conference of Industrial Engineering Theory Applications and Practice, Hsinchu, Taiwan, 2000 20 Gjerdrumj. Shah N. Papageorgiou L. G. Prod. Planning Control (2001a)p. 12 81-88 21 Gjerdrum J. Shah N. Papageorgiou L. G. Ind. Eng. Chem. Res. 40 (200117) p. 1650-1660 22 Gjerdrum]. Shah N. Papageorgiou L. G. Eur. J. Oper. Res. 143 (2002) p. 582-599 23 Gupta A. Maranas C. D. Ind. Eng. Chem. Res. 39 (2000)p. 3799-3813 24 Gupta A. Maranas C. D. McDonald C. M. Comput. Chem. Eng. 24 (2000) p. 2613-2621

25 Hugo A. Pistikopoulos E. N. Proceedings of

the 8th International Symposium on Process Systems Engineering, 2003, A and B ,214-219 26 Hung W. Y. Kucherenko S. Samsatli N. Shah N. J. Oper. Res. SOC.2004 55 (2004)p. 801-813 27 lyer R. R. Grossmann 1. E. Ind. Eng. Chem. Res. 37 (1998) p. 474-481 28 Jackson/. R. Grossmann I. E. Ind. Eng. Chem. Res. 42 (2003)p. 3045-3055 29 Jose R. A. Ungar L. H. AIChE J. 46 (2000) p. 575-587 30 Julka N. Srinivasan R. Karimi 1. Comput. Chem. Eng. 26 ( 2002a) 1755-1769 31 julka N. Srinivasan R. Karimi I. Comput. Chem. Eng. 26 (20024 1771-1781 32 Kallrathj. Chem. Eng. Res. Des. 78 (2000)p. 809-822 33 Kallrath J. OR Spectrum 24 (2002) p. 219-250 34 Levis A. A. Papageorgiou L. G. Comput. Chem. Eng. 28 (2004) p. 707-725 35 Liu M. L. Sahinidis N. V. Ind. Eng. Chem. Res. 34 (1995)p. 1662-1673 36 Liu M. L. Sahinidis N. V. Ind. Eng. Chem. Res. 35 (1996) p. 4154-4165 37 Makridakis S. Wheelright S. C. Forecasting methods for Management, 1989,Wiley, New York 38 McDonald C. M. Karimi I. A. Ind. Eng. Chem. Res. 36 (1997)p. 2691-2700 39 Neiro S. M. S. Pintoj. M. Comput. Chem. Eng. 2004 28 (2004) p. 871-896 40 Newhart D. D. Stott K. L. Vasko F. J . J. Oper. Res. SOC.44 (1993) p. 637-644 41 Papageorgiou L. G. Rotstein G. E. Shah N. Ind. Eng. Chem. Res. 2001 40 275-286 42 Pashigian B. P. Price Theory and Applications 1998 McGraw Hill Boston 43 Perea-Lopez E. Ydstie B. E. Grossmann I. E. Comput. Chem. Eng. 27 (2003)p. 1201-1218 44 Perea-Lopez E. Ydstie B. E. Grossmann I. E. Tahmassebi T. Ind. Eng. Chem. Res. 40 (2001) p. 3369-3383 45 Pfeifler T. Eur. J, Oper. Res. 116 (1999) p. 319-330 46 Pinto j . M. Joly M. Moro L. F. L. Comput. Chem. Eng. 24 (2000) p. 2259-2276 47 Dirkul H. Jayarama V. Transp. Sci. 30 (1996) p. 291-302 48 PooleyJ. Interfaces 24 (1994) p. 113-121 49 Romero j . Badell M. Bagajewicz M. P u i ~ a n e r L. Ind. Eng. Chem. Res. 42 (2003) p. 6125-6134

References 1641 50 Ryu J. H. Pistikopoulos E. N. Proceedings of

51 52

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56

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the 4th International Conference on Foundations of Computer-Aided Process Operations,( 2003) p. 297-300 Sabri E. H . Beamon B. M . Omega 28 (2000) p. 581-598 Sahindis N. V. Grossmann I. E. Comput. Chem. Eng. 15 (1991) p. 255-272 Sahindis N. V. Grossmann I. E. Fomari R. E. Chathranthi M. Comput. Chem. Eng. 13 (1989) p. 1049-1063 Shah N. Proceedings of the 4th International Conference on Foundations of ComputerAided Process Operations (2003) p. 73-85 Shah N. Escape-14 conference 2004 Shapiro J . Proceedings of the 4th International Conference Conference on Foundations of Computer-Aided Process Operations (2003) p. 27-34 Timpe C.H. Kallrath J . Eur. 1. Oper. Res. 126 (2000) p. 422-435

58 Tsiakis P. Shah N. Pantelides C. C. Ind. Eng.

Chem. Res. 40 (2001) p. 3585-3604

59 van der Vorst J. G. A. J. Beulens A. J . M . van

Beek P. Eur. I. Oper. Res. 122 (2000) p. 354-366 60 van Hoek R. I. Supply Chain Manage. 3 (1998) p. 187-192 61 Vidal C. J. Goetschalckx M. Eur. 1. Oper. Res. 98 (1997) p. 1-18 62 Voudouris V. T. Comput. Chem. Eng. 20s (1996) p. S1269-S1274 63 Wesolowsky G. 0.Tmscott W. G. Manage. Sci. 22 (1975) p. 57-65 64 Wilkinson S. J. Cortier A. Shah N. Pantelides C. C. Comput. Chem. Eng. 20s (1996) p. S1275-S1280 65 Williams J . F. Manage. Sci. 29 (1983) p. 77-92 66 Zhou 2 . Y . Cheng S. W. Hua B. Comput. Chem. Eng. 24 (2000) p. 1151-1158

Section 4 Computer-integrated Approaches in CAPE

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

Section 4presents a review on actual trends and shows new advances i n the integration of software tools and process data. The material in this section is organized infive chapters. Chapter 1 sets the goalsfor an integrated process and product design, possibly including the product application process in the analysis. Functions to be met by the product are the specijcations. However, identijjing afeasible chemical product is not enough, it needs to be produced through a sustainable process. Chapter 1 dejnes the general integrated chemical product-process design problem. The important issues and needs are identijed with respect to their solution and illustrated through examples. A n y CAPE method/tool needs to organize the scales and complexity levels so that the events at different scales can be described and understood:fiom property prediction at the nanoscale to phenomena occurring at the equipment scale. Integrated product-process design where modeling and supply chain issues play a n important role is also highlighted. Chapter 2 shows where, why, and how models of various types are used throughout the I+ of a n industrial or rnanufacturingprocess. Thisjustijes the need for tool and data integration across the process liji cycle. Modeling addresses a diversity of goals, and relies on a range of forms, approaches, and tools. Models differ widely i n the detail level, time, and length scale. Several industrial case studies help illustrate the challenges of modeling throughout the life cycle, since there is a huge range of models used to help answer vital sociotechnical questions through the I$ cycle ofthe process or product. The last chapter of Section 3 has already presented the elementary principles and systematic methods of supply chain modeling and optimization. Chapter 3 shows how the practical implementation of supply chain management software suffersfiom several deficiencies, due to a limited focus or a lack of integration. To overcome these deficiencies and respond better to industrial demands facing a more dynamic environment, there is a need to explore new strategies f o r supply chain management. Integrated solutions are required for the next generation of software tools given the number and complex interactions present among main components i n the global supply chain:financialJows, negotiation and environmental aspects need to be considered simultaneously along with a number of operating and design constraints. Agent-based systems are considered as a promising architecture for integration. Reliable and consistent thermophysical property data for pure components and mixtures are essential for CAPE calculations. Chapter 4 reviews the data needed and the quality requirements. Major sourcesfor physical properties and phase equilibrium data collections are compared. The text also provides up to date references to information sources available on the Internet. The major issue i n CAPE tools integration is to ensure software component interoperability and to allow seamless data exchange between tools. This issue is discussed i n Chapter 5

thatfocuses on operational standards in the domain of CAPE, namely the CAPE-OPEN. Promising software interoperability standards, leading to service-oriented architectures and the emerging Semantic Web are also described. The organizational and economic consequences of the trend towards interoperability and standards i n CAPE are also shortly described.

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

1 Integrated Chemical Product-Process Design: CAPE Perspectives Rafiqul Cam'

1.1 Introduction

Chemical process design typically starts with a general problem statement with respect to the chemical product that needs to be produced, its specifications that need to be matched, and the chemicals (raw materials) that may be used to produce it. Based on this information, a series of decisions and calculations are made at various stages of the design process to obtain first a conceptual process design, which is then further developed to obtain a final design, satisfying at the same time, a set of economic and process constraints. The important point to note here is that the identity of the chemical product and its desired qualities are known at the start but the process (flow sheet/operations) and its details are unknown. Chemical product design typically starts with a problem statement with respect to the desired product qualities, needs and properties. Based on this information, alternatives are generated, which are then tested and evaluated to identify the chemicals and/or their mixtures that satisfy the desired product specifications (qualities, needs and properties). The next step is to select one of the product alternatives and design a process that can manufacture the product. The final step involves the analysis and test of the product and its corresponding process. The important points to note here are that (1) the identity of the chemical product is not known at the start but the desired product specifications are known, and (2) process design can be considered as an internal subproblem of the total product design problem in the sense that once the identity of the chemical product has been established, the process and/or the sequence of operations that can produce it is determined. Note also that after a process that can manufacture the desired chemical product has been found, it may be necessary to evaluate not only the product but also the process in terms of environmental impact, life cycle assessment and/or sustainability. From the above descriptions of the product and process design problems, it is clear that an integration of the product and process design problems is possible and that such an integration could be beneficial in many ways. For example, in chemical Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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product design involving high value products where the reliability of the chemical product is more important than the cost of production, product specifications and process operations are very closely linked. In pharmaceutical products, there is a better chance to achieve success the first time with respect to their manufacture by considering the product-process relations. In the case of bulk chemicals or low-value products, the use of product-process relations may be able to help obtain economically feasible process designs. In all cases, issues related to sustainability and environmental constraints (life cycle assessment) may also be incorporated. As pointed out by Gani (2004a),integration of the product and process design problems can be achieved by broadening the typical process design problem to include at the beginning, a subproblem related to chemical product identification and to include at the end, subproblems related to product and process evaluation,including, lifecycle and/or sustainabilityassessments. Once the chemical product identity has been established, Harjo et al. (2004)proposes the use of a product-centricintegrated approach for process design. Giovanoglou et al. (2003),Linke and Kokossis (2002)and Hostrup et al. (1999) have developed simultaneous solution strategies for product-process design involving manufacture of bulk chemicals, while Muro-Sune et al. (2004) have highlighted the integration of chemical product identification and its performance evaluation. In all cases, integration is achieved by solving simultaneously some aspects of the individual product and process design problems. Recently, Cordiner (2004)and Hill (2004)have highlighted issues related to product-processdesign with respect to agrochemical products and structured products, respectively. Issues related to multiscale and chemical supply chain have been highlightedby Grossmann (2004)and Ng (2001). The objective of this chapter is to provide an overview of some of the important issues with respect to integrated product-process design, to highlight the need for a framework for integrated product-process design by employing computer-aided methods and tools, and to highlight the perspectives, challenges, issues, needs and future directions with respect to CAPE/PSE related research in this area.

1.2 Design Problem Formulations

In principle, many different chemical product-process design problems can be formulated. Some of the most common among these are described in this section together with a brief overview of how they can be solved.

1.2.1 Design of a Molecule or Mixture for a Desired Chemical Product

These design problems are typically formulated as, given the specifications of a desired product, determine the molecular structures of the chemicals that satisfy the desired product specifications, or, determine the mixtures that satisfy the desired product specifications (see Fig. 1.1).

7.2 Design Problem Formulations

In the case of molecules, techniques known as computer-aided molecular design (CAMD) can be employed, while in the case of mixtures, techniques known as computer aided mixture-blend design (CAM”) can be employed. More details on CAMD and CAMbD can be found in Achenie et al. (2002) and Gani (2004a,b).These two problems are also typically known as the reverse of property prediction as product specifications defined in terms of properties need to be evaluated and matched to identify the feasible alternatives (molecules and/or mixtures). This can be done in an iterative manner by generating an alternative molecule or mixture and testing (evaluating) its properties through property estimation. This problem (molecule design) is mainly employed in identifylng chemicals that are added to the process, such as solvents, refrigerants and lubricants that may be used by the process to manufacture a chemical product. In the case of mixture design, petroleum blends and solvent mixtures are two examples where the product is designed without process constraints. 1.2.1.1 Examples of Solvent Design

Consider the following process-product design problems where solvent design has an important role. The production of an active ingredient in the pharmaceutical industry needs the addition of a new solvent to an existing solvent-solute (reactant) mixture such that solubility is increased, and thereby the conversion is achieved. The new solvent must be totally miscible with the existing solvent (water) and must also be inert to the reactant. First determine all compounds that are totally miscible with water (use either a database or predict water miscibility).Next, screen out those that may react with the solute (this can be checked through the calculation of the chemical equilibrium constant). Next, identify those that will most likely dissolve the solute (this can be checked through the calculation of solubility).For this problem, alcohols, ketones, glycols are likely candidates. Consider also the following problem: it is necessary to designlselect an alternative solvent to remove oleic acid methyl ester, which is a fatty acid used in treatment of textile, rubber and waxes. The alternative solvent must be better than diethyl ether and chloroform in terms of safety and environmental impact while having solubility properties as good as the known solvents. Also, it must be liquid at temperatures between 270 K to 340 K. Searching of a compound that is acyclic (and containing only C, H and 0 atoms) that has a melting point below 270 K and boiling point above 340 K, has a Hildebrand solubility parameter that is * 16.95 MPa’12,and an octanol partition coefficient less than 2 generates the following candidates: 2-heptanone, 3-hexanone,methyl isobutyl ketone, isopryl acetate and many more. Interesting examples of application of CAMD in the agrochemicals, materials and pharmaceutical industries can be found in the edited monograph by Reynolds, Holloway and Cox (1995).

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1.2.2 Design of a Process

These design problems are typically formulated, given the identity of a chemical product plus its specifications in terms of purity and amount and the raw materials that should be used, and determine the process (flow sheet, condition of operations, etc.) that can produce the product (see Fig. 1.1). This is a typical process design problem, which now can be routinely solved (see for example, textbooks on chemical process design) with CAPE methods/tools when the chemical product is a low-value (in terms of price) bulk chemical. The optimal process design for these chemical products is usually obtained through optimization and process/operation integration (heat and mass integration) in terms of minimization of single or multiparametric performance function. For high-value chemical products, however, a more product-centric approach is beneficial, as pointed out by Harjo et al. (2004),Fung and Ng (2003) and Wibowo and Ng (2001). 1.2.2.1 Examples of Product-Centric Process Design

Harjo et al. (2004) have recently developed a systematic method for product-centric process design and illustrated the application of their method through the design of processes for the manufacturing of phytochemical (plant-derived chemical) products. Harjo et al. (2004)provide a general structure of phytochemical manufacturing processes (Fig. 1.2) and provide a list of heuristic rules for constructing flow sheet alternatives (see Appendix). As examples of application, Harjo et al. (2004)have considered the manufacturing of carnosic acid, which is known to have a powerful antioxidant activity and can be recovered from popular herbs such as rosemary and sage. One of the flow sheet alternatives generated and evaluated by the authors is presented in Fig. 1.3. The solution of the problem required a number of methods and tools, some of which needed to be developed (property and unit operation models) while others needed to be adopted (such as heuristics for flow sheet generation, flow sheet simulation and evaluation, etc.). Since solvents also play an important role in these processes, methods for solvent search are also needed.

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Differences between process design and molecule design problems. The question marks indicate what is unknown (needs to be determined) at the start of the design problem solution

Group properties

Molecule synthesis

7.2 Design Problem Formulations I 6 5 1

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Figure 1.2 The main processing steps for manufacture o f phytochemicals (from Harjo et al. 2004, reproduced with permission from IChemE)

1.2.3 Total Design of a New Chemical Product

In these design problems, given, the specifications (qualities, needs and properties) of a desired product, the objective is to identify the chemicals and/or mixtures that satisfy the given product specifications,the raw materials that can be converted to the identified chemicals and a process (flow sheet/operations) that can manufacture them sustainably, while satisfylng the economic, environmental and operational constraints. As illustrated in Fig. 1.4, solution of this problem could be broken down into three subproblems: a chemical product design problem that only identifies the chemicals (typically formulated as a molecule or mixture design problem), a process design part that determines a process that can manufacture the identified chemical or mixture (typically formulated as a process design problem) and a product-process evaluation part (typically formulated as product analysis and/or process analysis problems). In principle, mathematical programming problems can be formulated and solved to simultaneously identify the product and its corresponding optimal sustainable process. The solution of these problems are however not easy, even if the necessary

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Product Design Problem

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L l Product-Process Evaluation I Figure 1.4 Product design problem includes the molecule design and the process design problems

7.2 Design Problem Formulations I 6 5 3

models are available (Gani 2004a). Cordiner (2004) and Hill (2004) also provide examples of problems (formulations and structured products) of this type and the inability of current CAPE methods and tools to handle them. Numerous examples of new alternatives for the production of known chemical products can be found in the open literature and have been successfully addressed by the CAPE/PSE community. Examples of complete product-process design for new high-value chemical products may not be easy to find because of reasons of confidentiality. Interesting examples of some well known high-value chemical products from the pharmaceutical and specialty chemical industries can however be found, e.g., design and manufacturing of penicillin (Queener and Swartz 1979),and production of intracellular protein from recombinant yeast (Kalk and Langlykke 1985).

1.2.4 Chemical Product Evaluation

In these problems, given a list of feasible candidates, the objective is to identify/ select the most appropriate product based on a set of product-performance criteria. This problem is similar to CAMD or CAMbD except for the step for generation of feasible alternatives. Also, usually the product specifications (quality, needs, and properties) can be subdivided into those that can be used in the generation of feasible alternatives and those that can be used in the evaluation of performance. A typical example is the design of formulated products (also known as formulations) where a solvent (or a solvent mixture) is added to a chemical product to enhance its performance. Here, the feasible alternatives are generated using solvent properties while the final selection is made through the evaluation of the product performance during its application. Consider the following problem formulations: 0

0

0

0

Select the optimal solvent mixture and the paint to which it must be added by evaluating the evaporation rate of the solvent when a paint product is applied (Klein et al. 1992). Select the pesticide and the surfactants that may be added by evaluating the uptake of the pesticide when solution droplets are sprayed on a plant leaf (Munir 2005). Select the active ingredient (AI) or druglpesticide product and the microcapsule encapsulating it by evaluating the controlled release of the A1 (Muro-Sune et al. 2005). Select solvent mixtures for crystallization of a drug or active ingredient (Kanmanithi et al. 2004).

In all the above design problems, the manufacturing process is not included but instead, the application process is included and evaluated to identify the optimal product. Consider the following product evaluation problem from the agrochemical industry. A pesticide product consisting of an active ingredient and a surfactant and other additives need to be evaluated in terms of which surfactant can be added to the system to enhance the uptake of the A1 into the plant from the water droplets sprayed

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on the leaf surface. Solution of this problem requires property models that can predict the solubility of the A1 in the water plus surfactants mixture, the diffusion of the A1 through the leaf and into the plant, the evaporation of the water and many more. A modeling framework able to generate the necessary model for evaluation of the specified problem has been proposed recently by Muro-Sune et al. (2005).Through an integrated set of methods, models, and tools it is possible to not only evaluate the formulated product through its performance (in terms of uptake rate) but also find the best combination of AI, surfactant and plant that provides an improved product.

1.2.5 Chemical Process Evaluation

These problems are formulated typically, given the details of a chemical product and its corresponding process, to perform a process evaluation to improve its sustainability. To perform such analysis, it is necessary to have a complete design of the process (mass balance, energy balance, condition of operations, stream flows, etc.) as the starting point and new alternatives are considered only if the sustainability indices are improved. Here, the design (process evaluation)problem should also include retrofit design. Uerdignen (2003)and Jensen et al. (2003)provide examples ofhow such analysis can be incorporated into an integrated approach by exploiting productprocess relations. Note that the choice of the product and its specifications, the raw materials, the process fluids (for example, solvents and heatinglcooling fluids), the by-products, conditions of operation, etc., affect the sustainability indices.

1.3

Issues and Needs

Three issues and needs with respect to integrated product-process design are considered in this chapter, namely, the issue of models and the understanding of the associated product-process complexities, the issue of integration, and the issue of problem definition.

1.3.1 The Need for Models

According to Charpentier (2003), over fourteen million different molecular compounds have been synthesized and about one hundred thousand can be found on the market. Since however, only a small fraction of these compounds are found in nature, most of them will be deliberately conceived, designed, synthesized and manufactured to meet human needs, to test an idea or to satisfy our quest for knowledge. The issuelneed here is the availability of sufficient data to enable a systematic study

7.3 h u e s and Needs

leading to the development of appropriate mathematical models. This is particularly true in the case of structured products where the key to success could be to first identify the desired end-use properties of a product and then to control product quality by controlling microstructure formation. Another feature among product-process design problems is the question of systems with different scales of time and size. For integration of product-process design, it is necessary to organize scales and complexity levels in order to understand and describe the events at the nano- and microscales and to better convert molecules into useful products. The relation between length and time scales is very nicely illustrated through Fig. 1.5, which is adapted from Charpentier (2003). Figure 1.G highlights the relationship between scales (related to the product) and events (phenomena, operation, application, etc., related to the process). Examples of multiscale modeling for product-process design can be found in structured products and their manufacture, such as polymers by polymerization and solid crystals by crystallization. In polymerization, the nanoscale is used in kinetics, the microscale for mass and energy transport, the mesoscale for particle-particle and particle-wall interactions, the macroscale for global polymerization reactor behaviour, and the megascale for reactor runaway analysis and energy consumption analy-

Fluid Dynamics & Trans port

MolecularlElectronic

10-14

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Nano-scale

Molecular Process Active sites

Micro-scale

t-

Particles Droplets Bubbles Eddies

Biochemical products & processes Gene

Function

-

Micro organism enzyme Population cellular plant

Macro-scale

Meso-scale

+--

-

-

Reactors Exchangers Separators

*--

Production Units Plants

Pumps

Biocatalyst Enviroment

-

Reactors

__*

Environment

Athmosphere Oceans Soils

Units Plants Interaction

Active + -

aggregate

Bio

Mega-scale

Separators

*--

biosphere

Figure 1.6 Scales and complexity in chemical and biochemical product-process engineering

sis. For a biochemical process, the nanoscale may be used for molecular and genomic processes and metabolic transformations, the microscale is used for enzyme and integrated enzyme systems, the mesoscale is used for the biocatalyst and active aggregates, macroscale and megascales are used for bioreactors, units and plants involving interactions with the biosphere (Charpentier 2003).

1.3.2 The Need for Integration

According to IMTI (2000), integrated product/process development is the concurrent and collaborative process by which products are designed with appropriate consideration for all factors associated with producing the product. To make product right the first time and every time, product and process modeling must support, and be totally integrated with the design function, from requirements capture through prototyping, validation and verification, and translation to manufacture. Another issuelneed is the increasing complexity of new chemical products and their corresponding technologies, which provide opportunities for the CAPE community to develop/employ concurrent, multidisciplinary optimization of products and processes. Through these methods and tools, the necessary collaborative interaction between product designers and manufacturing process designers early in the product realization cycle can be accomplished. Few collaborative (design) tools are

1.3 hues and Needs

available to help turn ideas into marketable products, and those that are available are technology and product-specific. Optimizing a product design to meet a set of requirements or the needs of the different production disciplines remains a manually intensive, iterative process whose success is entirely dependent on the people involved.

1.3.3 Definition of Product Needs

Good understanding of the needs (target properties) of the product is essential to achieve "first product correct", even though it may be difficult to identify the product needs in sufficient details to provide the knowledge needed to design, evaluate and manufacture the product.

1.3.4 Challenges and Opportunities

Based on the above discussion, a number of opportunities have been identified by IMTI (2000),which are summarized below: Definition of Product-ProcessNeeds (Design Targets) 0

0

Provide knowledge management capability that captures stakeholder requirements in a complete and unambiguous manner. Provide modeling and simulation techniques to directly translate product goals to producibility requirements for application to product designs.

Methods/Tools for Product-ProcessSynthesis/Design 0

0

0

0

Provide a first principles understanding of materials and processes to assure that process designs will achieve intended results. Provide the capability to automatically create designs from the requirements data and from the characterization of manufacturing processes. Provide the capability to automatically build the process plan as the product is being designed, consistent with product attributes, processing capabilities, and enterprise resources. Create and extend product feasibility modeling techniques to include financial representations of the product as an integral part of the total product model.

Modeling Systems and Tools 0

Provide a standard modeling environment for integration of complex product models using components and designs from multiple sources/disciplines, where any model is completely interoperable and plug compatible with any other model.

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Integration 0

0

0

0

Provide the capability to create and manipulate product/process models by direct communication with the design workstation, enabling visualization and creation of virtual and real-time prototyped product. Provide simulation techniques and supporting processing technologies that enable complex simulations of product performance to run orders of magnitude faster and more cost-effectively than today. Provide the capability to simulate and evaluate many design alternatives in parallel to perform fast tradeoff evaluations, including automated background tradeoffs based on enterprise knowledge (i.e., enterprise experience base). Provide integrated, plug and play toolset for modeling and simulation of all life cycle factors for generic product types (e.g., mechanical, electrical, chemical).

1.4 Framework for Integrated Approach

The first step to addressing the issueslneeds listed above could be to define a framework through which the development of the needed methods and tools and their application in product-process design can be facilitated. Integration is achieved by incorporating the stages/steps of the two (product and process) design problems into one integrated design process through a framework for integration. This framework should be able to cover various product-process design problem formulations, be able to point to the needed stages/steps of the design process, identify the methods and tools needed for each stage/step of the design process and finally, provide efficient data storage and retrieval features. In an integrated system, data storage and retrieval are very important because one of the objectives for integration is to avoid duplication of data generation and storage. The design problems and their connec-

Product Design...--. v.

Property Models Product Models

..-. ._...-

,

_ _ A _ -

____..--

__._. __-. _._.-_..-_ _ - 1

Process SynthesislDesign Tools Simulation Engine

Figure 1.7 Integration of product-process design (see Table 1.1 for data flow details)

Product Application Model Process Analysis Tools

1.4 Framework for Integrated Approach

tions are illustrated through Fig. 1.3. The various types of design problems described above can be handled by this framework by plugging the necessary methods and tools into it. One of the principal objectives of the integration of product-process design is to enable the designer to make decisions and calculations that affect design issues related to the product as well as the process. The models and the types of models needed in integrated product-process design are also highlighted in Fig. 1.7. In the sections below, the issues of models and data flow and workflow in an integrated system are briefly discussed.

1.4.1 Models

-

One of the most important issues and needs related to the development of systematic computer-aided solution (design) methodologies are the models. For integrated product-process design, in addition to the traditional process and equipment model, product models and product-processperformance models are also needed. A product model characterizes all the attributes of the product while a product-performance model simulates the function of the product during a specific application. Figure 1.8 illustrates the contents and differences among the process, product and productperformance models. Constitutive (phenomena) models usually have a central role in all model types.

I

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Process Analvsis Tools

Process Models

Conceptual variablescannot be measured

Intensive

Balance Equations

Constraint Equations

dudt = f(x, Ys Pv d, t)

0 = g,(x, y, p, d)

Constitutive E uationsl Phenornena%odels

can be measured

T, P, x; N

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7 Integrated Chemical Product-Process Design: CAPE Perspectives

1.4.2 Data Flow and Workflow

The data flow related to the framework for integrated product-processdesign is highlighted through Table 1.1, where the input data and output data for each design (sub)problem is given. As highlighted in the problem formulation section, the workflow for various types of design problems is different and needs to be identified. In general terms, however, the following main steps can be considered (note that, as discussed above, some of these steps may be solved simultaneously): 0 0

0

Define product needs in terms of target (design) properties. Generate product (molecule, mixture, formulation, etc.) alternatives. Determine if process considerations are important. - If yes, define the process design problem and solve it. - If no, go directly to the product evaluation (analysis)step.

Table 1.1

Data flow for each design problem

Input data

Problem type

Output data

Building blocks for molecules, target Molecular design (CAMDj Feasible molecular structures properties and their upper/lower bounds and their corresponding propand/or goal values erties List of candidate compounds to be used Mixture design (CAMbD) List of feasible mixtures in the mixture, target properties and their (compoundsand their compoupper/lower bounds and/or goal values at sitions) and their correspondspecified conditions of temperature and/ ing properties or pressure Desired process specifications (input streams, product specifications, process constraints, etc.)

Process designlsynthesis (PD)

Process flow sheet (list of operations, equipments, their sequence and their design parameters)

Desired separation process specifications Process solvent design (input streams, product specifications, process constraints, etc.) and desired (target) solvent properties

Process flow sheet (list of operations, equipments, their sequence and their design parameters) plus list of candidate solvents

Details of the molecular or formulated product (molecular structure or list of molecules and their composition and their state) and their expected function

Product evaluation

Performance criteria

Details of the process flow sheet and the process (design) specifications

Process evaluation

Performance criteria, sustainability metrics

1.4 Frameworkfor lntegrated Approach Table 1.2

List of methods/algorithms and tools/software that may be used for each problem (design) type

1

Problem type

Method/Algorithm

Molecular and mixture design (CAMD)

Molecular structure generation Property prediction and database Screening and/or optimization

ProCAMD

Process design/synthesis (PD)

Process synthesis/design Process simulation/optimization Process analysis

ICAS (PDS, ICAS-sim, PA)

Process solvent design

CAMD methods/tools Process synthesisldesign Process simulation/optimization Process analysis

ICAS (ProPred, ProCAMD, PDS, ICAS-sim, PA)

Product evaluation

Property prediction and database Product-performance evaluation model Model equation solver

ICAS (ProPred, ICASutility, MOT)

Process evaluation

Process synthesisldesign Process simulation/optimization Process analysis

ICAS (ICAS-sim, ICASutility: MOT, PA)

0 0

Tools/Software

Analyze the process in terms of a defined set of performance criteria. Analyze the product in terms of a defined set of performance criteria.

In Table 1.2, the methods/algorithms and their corresponding tools/software are listed. Under tools/software, only tools developed by the author and coworkers have been listed (see the tools and tutorial pages at www.capec.kt.dtu.dk/Software/). Examples of application of the tools listed above are not given in this chapter but can be found in several of the referenced papers.

1.4.3 Simultaneous Molecular and Flow Sheet Design

Design of chemical products is often described as the design of molecules and their mixtures with desired (target) properties and specific performance, as drugs, pesticides, solvents or food products. Molecules likely to match the target properties and performance are identified, usually in experiment-based trial and error solution approaches. In product-centric process design, it is necessary to match a set of target performance criteria for the process, usually through process simulation. For process design, alternative process flow sheets can be generated through simulationbased synthesisldesign methods, where simulation is mainly used to evaluate and test alternatives. Systematic methods for generation of process alternatives are either rule-based or mathematical optimization-based.

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1 Integrated Chemical Product-Process Design: CAPE Penpectives

Group contribution methods, which provide the basis for molecule and mixture design, can also be applied in process design. That is, in the same way functional groups are defined to represent molecules and to estimate their properties, process groups are also defined to represent process flow sheets and to estimate their operational properties. Therefore, if a table of process groups representing a wide range of operations can be established, the technique of CAMD can be adapted to computer-

Problem formulation

Conversion into input and constraints

CAMD

CAFD

'I want aromatic compounds with double bounds, with a minimum Tm = 300K, minimum Tb = 400K and a minimum molecular weight of 300 g/mol and a maximum of 30 groups."

'I want to separate a mixture of 22-Dimethyl propane, iPentane, n-Pentane, 22Dimethyl butane, 23-Dimethyl butane, 2-Methyl pentane, nHexane and Benzene into pure streams."

A set of building blocks: CH=C, C=C, ACH, AC ACCH3, ACCH, ...

A set of building blocks: (NBCD), (ABICD), (NBCDEFG), (cyc GIH), ...

Set of property based numerical constraints

Set of property based numerical constraints

+

+

I

#IIABCDE

Generation of alternatives

E F

I

I

Post synthesis

Molecular simulation Experimentations

Reverse approach to get the complete design parameters Rigorous simulation

Figure 1.9 Common framework overview (from d'Anterroches et al. 2005, reproduced with permission from IChemE)

1.5 Conc/usion I663

aided flow sheet design (CAFD),so that CAMD and CAFD can both be used for modeling, synthesis and design. Also, since CAMD can generate and evaluate thousands of molecules within few seconds of computer time, CAFD would also be able to generate numerous process alternatives without any loss of accuracy or application range. d’Anterroches et al. (2005) has developed a group contribution-based method for simultaneous molecular and mixture design. Figure 1.9 illustrates the features of a common framework for CAMD and CAFD.

1.5

Conclusion

As pointed out by Cordiner (2004), Hill (2004), and the referenced papers by Ng, even though the primary economic driver for a successful chemical product is speed to market, this does not mean that process design is not strategically important to these products. The important questions to ask (to list a few) pertain to the chemical product, how they will be manufactured, how sensitive is product quality related to cost and production, where they will be used or applied, how their performance will be evaluated and, how long a period will they be sustainable? Obviously, the answers to these questions would be different for different products and consequently, the methods and tools to be used during problem solution will also be different. Many opportunities exist for the CAPE/PSE community to develop systematic model-based solution approaches that can be applied to a wide range of products and their corresponding processes. It is the study through these model-based solution approaches that will point out under what conditions the process or operational issues become important in the development, manufacture and use of a chemical product. Successful development of model-based approaches will be able to reduce the time to market for one type of products, reduce the cost of production for another type of product, reduce the time and cost to evaluate another type of product. The models, however, need to be developed through a systematic data collection and analysis effort, before any model-based integrated product-process tools of wide application range can be developed. Finally, it should be noted that to find the magic chemical product, these computer-aided model-based tools will need to be part of a multidisciplinary effort where experimental verification will have an important role and the methods/tools could be used to design the experiments.

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14 lensen N. Coll N. Gani R. An integrated com-

1 Achenie L. E. K. Gani R. Venkatasubramanian

2

3

4

5

6

7

8

9

10

11

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V. 2002 Computer-Aided Molecular Design: Theory and Practice, CACE-12, Elsevier Science, Amsterdam Charpentier]. C. The future of chemical engineering in the global market context: market demands versus technology offers, Kern Ind 52(9) (2003) p. 397-419 Cordiner]. L. Challenges for the PSE community in formulations, Comput Chem Eng 29(1) (2004) p. 83-92 d’Anterroches L. Gani R. Harper P. M . Hostrup M . 2005 CAMD and CAFD (computeraided flow sheet design), paper presented at World Chemical Engineering Conference, Glasgow, Scotland, July 2005 Fung K. Y. Ng K. M . Product centered processing: pharmaceutical tablets and capsules, AIChE J 49(5) (2003)p. 1193 Gani R. Chemical product design: challenges and opportunities, Comput Chem Eng 28(12) (2004a)p. 2441-2457 Gani R. Computer-aided methods and tools for chemical product design, Chem Eng Res Des 82(All) (2004b) p. 494-1504 Giovanoglou A. Barlatier]. Adjiman C. S. Pistikopoulos E. N. Cordiner]. L. Optimal solvent design for batch separation based on economic performance, AIChE J 49 (2003)p. 3095- 3109 Grossmunn I. E. Challenges in the new millennium: product discovery and design, enterprise and supply chain optimization, global life cycle assessment, Comput Chem Eng 29(1) (2004)p. 29-39 Haqo B. Wibowo C. Ng K. M . Development of natural product manufacturing processes: phytochemicals, Chem Eng Res Des 82(A8) (2004) p. 1010-1028 Hill M . Product and process design for structured products: perspectives, AIChE J 50 (2004) 1656-1661 Hostrup M. Harper P. M. Gani R. Design of environmentally benign processes: integration of solvent design and process synthesis, Comput Chem Eng 23 (1999) p. 1394-1405 ZMTZ First product correct: visions and goals for the 21st century manufacturing enterprise, Integrated Manufacturing Technology Initative Report USA 2000

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puter aided system for generation and evaluation of sustainable process alternatives, Clean Techno1 Environ Pol 5 (2003) p. 209-225. Kalk ]. Langlykke A. Cost estimation for biotechnology projects, ASM Manual of Industrial Microbiology and Biotechnology, ASM Press, Washington, D.C. 1986 Karunanithi A. Achenie L. E. K. Gani R. A computer-aided molecular design framework for crystallization solvent design, Chem Eng Sci 61 (2006) p. 1243-1256 Mein ]. A. Wu D. T. Gani R. Computer-aided mixture design with specified property constraints, Comput Chem Eng 1 G (1992)p. S229 Linke P. A. Kokossis Simultaneous synthesis and design of novel chemicals and chemical process flow sheets, in J. Grievink and J. van Schijndel (Eds.), ESCAPE-12, CACE-10, Elsevier Science, Amsterdam, (2002) pp. 115-120 Ng K. M . A multiscale-multifaceted approach to process synthesis and development, in R. Gani and S . B. Jmgensen (Eds.),ESCAPE11, CACE-9, Elsevier Science, Amsterdam (2001)pp. 41-54 Queener S. Swartz R. Penicillins; biosynthetic and semisynthetic, in Economic Microbiology 3, Academic Press, New York (1979)pp. 35-123 Reynolds C. H. Holloway M . K. Cox H. K. 1995 Computer-aided molecular design: applications in agrochemicals, materials and pharmaceuticals, ACS Symposium Series, 589, Washington, D.C., USA Munir A. Pesticide product and formulation design, Dissertation, CAPEC, Department of Chemical Engineering, DTU,Lyngby, Denmark 2005 Muro-Sune N . Gani R. Bell G. Shirley I. 2005 Model-based computer aided design for controlled release of pesticides, Comput Chem Eng, 30 (2005) p. 28-41 Uerdingen E. Gani R. Fischer U. Hungerbiihler K. A new screening methodology for the identification of economically beneficial retrofit options in chemical processes, AIChE J 49 (2003) p. 2400-2418 Wibowo C. Ng K. M. Product-oriented process synthesis and development: creams and pastes, AIChE J 47(2) (2001)p. 2746

1.5 Conclusion I665

Appendix

Heuristics for constructing flow sheet alternatives (from Harjo et al. 2004, reproduced with permission from IChemE). Feed Preparation

1. Consider reducing the size of the plant material to 2-5 mm to obtain good performance in industrial scale S-L extraction. 2. Consider using particle size bigger than 0.25 mm in S-L extraction to avoid clogging of the filter. 3 . If the plant material is hard and abrasive, consider using size reduction by ball mill, fluid jet mill, or hammer mill. 4. If the plant material is soft and tough or fibrous and woody, consider using size reduction by cutting mill, disk mill, or hammer mill. 5. If the plant material is brittle or crystalline, consider using size reduction by fluid jet mill, hammer mill, or roller crusher. 6. If the plant material is tough, fibrous, and very heat-sensitive, consider using cryogenic size reduction by cutting mill, disk mill, fluid jet mill, or hammer mill. 7. Consider reducing the moisture content of harvested plants to about 10% for a safe storage. Product Recovery

8. Consider using disk press for mechanical pressing of fibrous materials. 9. Consider using immersion type S-L extraction equipment if the target com-

pounds are in low concentrations, strongly bound, andlor slowly diffusing. 10. Consider using percolation type S-L extraction equipment ifthe target compounds are in high concentrations, loosely bound, or slightly soluble in the solvent. Product Purification

11. Whenever possible, consider using the same MSA as in the product recovery step. 12. For heat-sensitive materials, consider separations using L-L extraction, chromatography, or crystallization. 13. Consider using adsorption to separate natural pigments. 14. Consider using chromatography andlor crystallization for the separation of chiral molecules or when multiple single-compound products are desired. 15. Consider using pH swing crystallization for separation of compounds with acidic or basic groups. 16 Consider using large polarity differences between the mobile and stationary phases in reversed-phase chromatography to achieve high selectivity. 17. When handling liquid systems with little density difference, easily emulsified, or short contacting time is required, consider using centrifugal L-L extractors and separators. 18. When handling liquid systems containing suspended solids, easily emulsified, or large capacity, consider using reciprocating-plateL-L extractor columns.

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19. When handling liquid systems with high viscosity or large capacity, consider

using mixer-settler L-L extractors. 20. If the material has a very steep solubility curve (e.g., very sensitive to temperature), consider using cooling-type crystallizers. 21. If the material has a normal or moderate solubility curve, consider using evaporative-cooling,surface-cooling,or isothermal-evaporative crystallizer. 22. For batch and relatively low capacity processes, or feed with viscous solutions, consider using either plate-and-framefilter presses or leaf filters. 23. For continuous and large capacity processes, consider using either continuous rotary-vacuum-drumfilter or continuous rotary-disk filter. Product Finishing

24. If the feed to be dried is in liquid, suspension, or slurry solution forms, consider using either drum or spray dryers. 25. If the wet granular solids are to be dried, consider using either rotary or tray dryers. 26. Use freeze-drying only for heat-sensitive materials which may not be heated in the ordinary drying or when the loss of flavor and aroma must strictly be avoided.

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

2 Modeling in the Process Life Cycle /an T: Cameron and Robert 13. Newell

This chapter deals with the important issues of where, why and how models of various types are used throughout the life of an industrial or manufacturing process. The chapter does not deal specifically with the modeling of the life-cycle process but concentrates on the use of models to address a plethora of important issues that arise during the many stages of a process’ life, from the cradle to the grave. In this chapter we first discuss the life-cycle concept in relation to a cradle-to-thegrave viewpoint and then in subsequent sections consider specific issues related to the modeling goals and realizations. Some important issues are discussed which surround model development, reuse, integration, model documentation and archiving. We also consider the future needs of such modeling approaches and the important implications of life-cycle modeling for corporations. Throughout this chapter we refer to several specific industrial case studies that help illustrate the importance of modeling throughout the life cycle as well as the challenges of doing so. What is evident in the following sections is that there is a huge range of modeling used to help answer vital sociotechnical questions through the life cycle of the process or product. It is important to appreciate that process and product engineering have vital links to social and human factors within a holistic approach to modeling. Major infrastructure projects continually reinforce a more complete view than that which is often taken by process and product engineers. In this chapter we expand the vision of modeling within the process or product life cycle to see just what has been achieved and where the challenges lie for the future.

2.1 Cradle-to-the-Crave Process and Product Engineering

Cradle-to-the-graveis a concept that now pervades most industrial operations, driven by concerns for safety, health and the environment (SHE). Sustainability and global environmental issues also figure highly in the drive for life-cycle analysis. Those conComputer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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cerns have been heightened by community pressures on government and industry regarding the impact of process and manufacturing developments on ecosystems as well as associated social impacts. This is largely driven by past disastrous events that have had major impacts on local communities, either directly through such events as fires, explosions or toxic releases or through more sinister chronic impacts or severe land contamination. Much of the risk and environmental management legislation and regulations in Europe, the United States and Australasia have now focused on cradle-to-the-grave concepts to control industrial impacts and analyze economics over the complete life cycle of the process. These important concepts have been expressed in numerous international standards such as the IS014000 series and IS015288 [I].The life-cycle stages in these standards involve: 0 0

0 0 0 0

concept development production utilization support retirement.

Process and product related activities define similar stages to the generic standard as shown in Section 2.1.2. These holistic life-cycle concepts are particularly noticeable in such industries as vehicle manufacture, aluminum production and subsequent recycling, newspaper, glass production and recycling, plastic consumer articles and their reuse, to name just a few. The concepts are becoming increasingly common in the process and manufacturing industries, driven by tough environmental impact assessment regimes that demand in-depth analysis of the sociotechnical aspects of all major developments as well as facility expansions, well before any implementation. Life-cycle analysis is part of the responsible care program promoted by the International Council of Chemical Associations and in place since 1988 [2] after its initial start in Canada in 1985. The following sections outline in broad terms the key concepts that undergird the life-cycle modeling activities and put these into a broader sociotechnical context beyond the mere process perspective. In this way, the life-cycle concept is seen as a much more holistic activity.

2.1.1 The Life-Cycle Concept

The process life cycle is characterized by several chronological stages as illustrated in Fig. 2.1. Accompanying the process life-cycle phases are certain activities associated with each stage. Of prime importance throughout the life-cycle perspective will be the issues of raw materials, wastes and emissions as well as energy consumption, generation and reuse. These issues are necessarily part of an integrated framework [31.

2.7 Cradle-to-the-Grave Process and Product Engineering

These stages involve: strategic planning research and development activities 0 conceptual design of product and process 0 detailed engineering designs 0 installation and commissioning 0 operations and production 0 decommissioning of process 0 remediation of process related facilities. It is worth saying something about the phases of process life cycles to set the scene for a more in-depth analysis of the key issues from a modeling perspective. 0

0

Strategic Planning Phase

Here, the initial ideas of resource utilization or new product development have their genesis. This phase is driven by new business opportunities, perceived market needs or market push through the introduction of novel products, processes or markets. Modeling must incorporate uncertainty and is broad in scope and intent, as is to be expected in strategic and scenario planning. Research and Development Phase

Following an initial strategy phase is often a more focused phase of research and development for those options identified as having the best potential. From the product viewpoint this might involve the modeling of market responses to product ideas to gain understanding of acceptance. This is common in the food and consumer products sectors.

Remediation Decommissioning

Detailed Design

Conceptual Design Research and Development Strategic Planning

Figure 2.1

Life-cycle phases

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From the process perspective this phase can often involve very lengthy and intense research that covers such areas as product qualities, reaction kinetics, product yields and effects of operating conditions on product spectrums. In pharmaceutical developments it can involve significant computer-aided drug design and possibly the use of animal experimentation. This phase can also involve the analysis of environmental impacts through the treatment of process wastes such as solids, gases and liquids. Treatment options might be sought to eliminate or ameliorate impacts. Energy and utilities utilization for product creation will also be of importance. Here, the modeling can involve a wide range of time and length scales, using such tools as quantum chemistry, molecular simulations and specialized model development at one end of the scale, and producing partial models for use at macroscale levels that deal with equipment and plant design at the other end of the scale. Other efforts at this phase can concentrate on issues of risk management and the choice of particular processing paths which apply inherently safer design and operations concepts. An important issue at this phase is the development and validation of physicochemical prediction models for a range of phase equilibria applications. Conceptual Design Phase

For process technologies, conceptual design will lead to the development of inputoutput process models whereby overall economics can be better estimated. Flow sheeting in the traditional industries such as minerals, petroleum and chemicals is extensively used to generate these insights. Further, the use of these tools based on generic plant unit models leads to the development of the internal structure of the process system. Often the models are simply mixers, stream splitters, yield/stoichiometric reactors and component splitters. The aim will be to develop alternative flow sheet configurations to assess economics, product and by-product production plus environmental and risk impacts. The modeling is typically concerned with steadystate behavior. Structural optimization using simple process models may also take place in this phase in order to consider optimal processing structures. Of importance in this phase are the environmental impacts from air, noise, water and solid wastes. Extensive air-shed modeling is often required to assess potential impacts. Similar modeling may be required to assess impacts on groundwater and receiving waters such as rivers and bays. Particularly hazardous or noxious wastes may require modeling of their treatment options including destruction by incineration, landfill, chemical conversion or biological treatment. These can be significant modeling exercises in their scope and depth as well as time. Detailed Design Phase

The detailed design phase leads inevitably to such outputs as the definitive engineering flow sheet as well as the piping and instrumentation (engineering line) diagrams. It also covers such project outputs as detailed specifications for procurement. Modeling practice at this phase often involves the creation of equipment or unit specific models, which might take significant time to develop. The models might be

2. I Cradle-to-the-Grave Process and Product Engineering

integrated into larger software systems and dynamics can often be a significant issue driven by concerns for startup, shutdown, emergency response and regulatory control. As well, unit and plant-wide optimization modeling may take place at this point in order to consider best operational modes. Often, steady state assumptions move into continuous, dynamic considerations and then into hybrid (continuous-discrete) modeling environments. Installation and Commissioning

The installation phase of process and product plants is a key area involving project planning and related models. Here, critical path models, dynamic resource allocation and control models play a vital role in this life-cycle phase. Operations Phase

The operations phase includes such aspects as the construction and commissioning stages of process development. It clearly involves the day-to-day operations of the process under its intended operations policy over the useful life of the process or product. This operation period can vary widely depending on the industrial manufacturing sector being considered. Again it can be seen from the perspective of time and distance scales. Within the traditional process industries that make use of major natural resources such as oil, gas and mineral deposits, the time scale can be of the order of decades. In the consumer product area it can be of the order of months, where market forces demand quick time to market and flexibility of manufacture and delivery modes. The computer and electronics industries as well as the food sector provide well-known examples of these 'quick-to-market' sectors. Here, in the operations phase, modeling can focus on debottle-necking of existing processes for retrofit or incremental improvements. It can also address issues of effective supply chain design and operation under a dynamic market environment. It can also involve detailed risk modeling for improved design and operations as the external environment such as government regulations change. As well, the effect of changing resource characteristics can lead to significant process modeling that involves the assessment on the process of changing raw materials and product quality demands. Modeling of routine plant maintenance through techniques such as critical path procedures or risk-based inspection (RBI) or maintenance (RBM) strategies is a key area of production operations. They require modeling of the system in terms of predicted risk of failure and the need for preventative maintenance procedures on varying time scales. Decommissioning Phase

Most processes and products have a 'use by' date and inevitably come to a natural or in some cases, dramatic end. Decommissioning of the process or the product and product-line is now an important consideration in the life cycle. It can mean a very lengthy process of assessment and action. Much needs to be considered in the decommissioning phase, with a significant amount of work associated with the management of risk in achieving the outcomes.

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In particular the decontamination of plant for disposal may require specialized treatment and this can lead to in-depth modeling of the processes. In the case of defunct nuclear facilities the process of decommissioning can take decades as seen from recent activities within Europe and elsewhere. Remediation and Rehabilitation Phase

This is a phase of the life cycle which can involve significant financial resources, often in the past borne by government but now more likely by the operating companies if they remain financially viable. In many cases, specialized modeling and chemical experimentation is necessary to consider ways of achieving remediation of land and the environment. In many cases, where mining is carried out a remediation plan is activated, which is an integral part of the operations phase of the process. Modeling of mining operations and the remediation phase provides input to environmental management plans.

2.1.2 Process Modeling Within the Life Cycle

Modeling within the process life cycle is now an extremely important activity for all new industrial initiatives and expansions of existing facilities. However, what do we mean by the word ’modeling’?This seems an obvious question and for many there are simplistic answers. However, the modeling concept is far beyond the simple idea of a set of equations to be solved within a flow-sheetingpackage or numerical solver. In the context of life-cycle modeling, we do well to consider the generic definition of Minsky [4] who defined a model in the following terms: “A model (M) for a system (S) and an experiment (E) is anything to which E can be applied to answer questions about S.” As such, this definition captures a wide variety of models often used within the process life cycle, from physical models to mathematically-basedmodels. A nonexhaustive review of modeling applications and modeling forms or approaches is given in Table 2.1. This expands the life-cycle phases of Fig. 2.1 by introducing some intermediate activities often seen in industrial projects. Table 2.1 illustrates the diversity of modeling activities throughout the life cycle. There are many forms and approaches used in the phases, with significant reuse or integration of models - either directly or indirectly through data transfer from one model to another. The over-riding challenge in this area is unity of models, data and documentation. The principal characteristics can be summarized as: a diversity of modeling goals throughout the life cycle phases encompassing such purposes as: - assessing market potential or response; - generating basic data or property relations for use in later phases; - estimating economic potential;

2. I Cradle-to-the-Grave Process and Product Engineering Table 2.1

Model use and characteristics for process life cycle. Modeling forms or approaches

Basic economics Resource assessment

Purpose, goal, mission models Issue-based planning Scenario models Self-organizing models

Research and development

Resource characterization Basic chemistry Reaction kinetics Catalyst activity life Physicochemical behavior Pilot plant design and operation

Reaction systems models Catalyst deactivation models PFR, CSTR reactor models Elementary flow sheet packages Fluid-phase equilibria models Physical property models Molecular simulation Quantum chemistry models

Initial process feasibility

General mass and energy balances Alternate reaction routes Alternate process routes Input-output economic analysis Preliminary risk assessment

Flow-sheeting packages Semi-quantitative risk models Financial analysis models

Conceptual design

Mass and energy balances Plantlsite water balances Initial environmental impact Detailed risk assessment Economic modeling

Flow-sheeting packages Environmental impact (air, noise, water, solid wastes) Social impact assessment models Risk consequence and frequency models Computational fluid dynamics (CFD)

Detailed design

Detailed mass and energy balances Vessel design and specifications Sociotechnical risk assessment Risk management strategies Project management

Flow-sheeting packages Dynamic simulation for plant and units CFD modeling and simulation Mechanical simulation (finite element methods and variants) 3D plant layout models Fire, explosion, toxic release models Fault tree and event tree models Air-shed models for dispersion of gases and particulates Noise models

Commissioning

Startup procedures Shutdown procedures Emergency response

Grafcet and ladder logic models Safety instrumented assessment models Risk assessment models

Operations

Process optimization Process batch scheduling Supply chain design and optimization

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Table 2.1

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Process life-cycle phase Modeling applications Operations (continued)

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evaluating system dynamics; predicting environmental impacts; optimizing product and process performance; designing products and processes (structure and units); planning production cycles or routine maintenance; improving viability, process performance or risk management factors; - enhancing inherently safer designs and operations; a diversity of model forms and approaches to address the modeling goals such as: - social, economic, human factors and technical models; - mechanistic, empirical, stochastic and deterministic models; - physical and mathematical modeling approaches; a granularity in the model representations across the life cycle, typically increasing in detail as the life cycle phases progress chronologically; a diversity of time and length scales being captured in the models, representing the multiscale nature of product and process engineering; the current independence of much of the life-cycle modeling that is undertaken, typically by a range of external consultants, in-house company groups and government agencies; a diversity of tools to accomplish the modeling tasks including: - proprietary software products such as flow-sheeting packages; - purpose built models that are essentially standalone items in languages such as C, Fortran or Java; - specific models in commonly available software such as MS Excel or Matlab; a diversity of solution approaches to the models in the life cycle, for purposes of prediction, design, estimation or identification, spanning computation times of seconds to weeks for large-scale CFD computations. -

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2.2 lndustrial Practice and Demands in Life-Cycle Modeling

2.1.3 The Multiscale Nature of Modeling During the Life Cycle

In Section 2.1.2, there is a wide range of time and length scales involved in modeling across the life cycle. This applies across the life cycle phases as well as within the individual phases. The rise in interest in multiscale modeling approaches and the integration and solution of composite models built from several partial models is driven primarily by product engineering where the nano or microscale characteristics are seen as vital to 'designer' products. Combined with the meso and macroscales, typical of issues at the equipment and plant level, the emphasis on multiscale representations will continue to grow. The chapter in this current book on multiscale process modeling gives a comprehensive overview of this important area. Within the modeling practice across the life cycle, Marquardt et al. [ S ] have also mentioned its importance.

2.2 Industrial Practice and Demands in Life-Cycle Modeling

The following sections deal with some of the important issues facing those carrying out modeling at stages of the process life cycle. It emphasizes the fact that modeling is far more than just developing a set of equations to be solved by a simulation tool [6, 71.

2.2.1 Modeling Methodology and Workflow

One of the key underlying concepts is methodology within modeling. This is closely related to workflow concepts in carrying out any modeling activity. Figure 2.2 illustrates a particular modeling methodology [8] which possesses generic character and is applicable to many occasions when modeling is performed. It shows how various stages of the modeling cycle use and refine other stages. There are seven steps shown in this workflow scheme, each having an important part to play. It is an iterative process which demands clear understanding of each task and the need to specify conditions of modeling cycle termination. 0

Goal set dejnition and decomposition. This refers to the initial phase of asking: what is the purpose of the model? Here, the key goals are established with regard to model application area (control, design, optimization, etc.) and the desired outcomes from the modeling activity must be stated, leading to formal specifications. This includes a wide range of outcomes as mentioned in Section 2.1.3. This aspect of modeling is generally poorly done but is essential for establishing the termination conditions for the modeling cycle. It still remains a complex, difficult area with little guidance or techniques in how overall or canonical goals are decom-

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posed into subgoals as represented in a goal tree or goal graph and then subsequently to define the subsystems. Model conceptualization. Here, the model form or multiple forms have been chosen and the conceptualizationtakes place. In mechanistic models this is related to defining balance volumes for mass, energy, momentum or population conservation, together with convective and diffusive streams connecting the balance volumes. Other objects and attributes within balance volumes relate to reaction, physical properties, spatial distribution and the like. In the case of empirical model building, a selection of potential model forms is initially needed. The selection can be based on physical insight or through the use of information criteria which seeks to balance model complexity, usually the number of parameters, against the quality of the model fit to the data. This approach might cover completely black-box models with arbitrary structure or grey-box models that incorporate some predefined structure. Modeling data. This refers to both the type of data needed for calibration or parameter estimation and model validation as well as physicochemical data necessary for the building of mechanistic models. Here, experimental design can play an important role and cover classic factorial designs to such techniques as Latin hypercube sampling for Monte Carlo models. Model building and analysis. This brings us to the task of actually constructing the physical or mathematical representation based on the chosen approach. In most cases, significant use of computer-aidedtools can assist in this task. Nevertheless, the construction of mathematical models can be a time-consuming, error-prone task. Analysis of the resultant model set is absolutely necessary for reasons of degrees of freedom, model index and potentially observability,controllability and identifiability. Model ueiijcation. This relates to the systematic construction of solution code typically in the form of a computer program to solve the model. It requires such concepts as algorithm design, modular code construction and software verification tools. It seeks to ensure that the model solved is the model that was defined. Model solution. Solving the model can be a trivial task taking a few seconds of computer time to weeks of execution time on even the largest, distributed computing devices. Appropriate numerical methods are essential for minimizing computation time as well as ensuring solutions that are credible. Model calibration and validation. The final phase to be tackled in most industrial modeling is the need to calibrate the model against good plant or process data. This is nontrivial as 'good' data is often hard to obtain and requires significant effort and determination to get it. It leads to key parameter estimates being obtained. Model validation which asks: is the model prediction accuracy adequate for the task? This is another area that requires perseverance and in-depth statistical analysis - something often glossed over in industrial modeling.

2.2 industrial Practice and Demands in Lijk-Cycle Modeling

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2.2.2 Modeling Goals and Model Types

In Section 2.1.2 we discussed the various activity or application models commonly seen in industrial modeling practice. These were based on model outcomes in specific application areas. Such models as reaction kinetic models can have many forms, ranging from linear to nonlinear empirical models. Physical property models can have an enormous range of model forms. However, we can consider a more fundamental classification of process related models based on characteristicsof the models being developed and used in particular applications. Figure 2.3 provides a simple class diagram for a range of typical model forms, which include most of those seen in the life-cycle process. Other variants of these model types are possible. The basic classification relates to steady state and dynamic models with actual behavior being captured as continuous, discrete or hybrid (continuous-discrete).Further classifications lead to empirical, mechanistic, stochastic and deterministic models, with their various subclasses. Each of these models has a particular mathematical form that relates to the model type and which requires specific solution methods to be applied - in most cases this involves some form of numerical computation. Models are built for a purpose or 'goal' and that means they exist to answer questions about the reality they represent. As such, the idea of goal definition becomes an increasingly important idea that is not often explicitly stated or used in driving the modeling activities. There has been some work done in this area, using functional modeling approaches that are mainly driven by applications in fault diagnosis [9,10]. Recent work [ll]has been directed towards the concept of modeling goal development and evolution. This uses structured goal definitions to help drive the modeling with the intent of shortening the iterative nature of the modeling cycle and to improve modeling outcomes as shown in Fig. 2.2.

2.2.3 Model Ingredients

Industrial modeling requires a number of key ingredients to be effective. The following highlights some of these ingredients and comments on them. Assumptions

Key assumptions that relate to the conceptualization need to be recorded and then used to check consistency with the resultant model. It is vital that all assumptions relevant to the model development are available in the modeling life cycle. This will include such items as assumed balance volumes, mechanisms, details of species in the system or the lumping of species into larger classes for tractability of modeling. It will include issues related to key flows in the system, whether convective or diffusive as well as sources and sinks of energy and component masses.

2.2 industrial Practice and Demands in L@-Cycle Modeling

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Documentation Documentation still remains one of the biggest challenges in industrial modeling. The adequacy of documentation in most modeling exercises is usually very poor, leading to difficulties in model reuse and much repetition of effort by future generations of engineers that need to revisit historical work. Decision making and arguments concerning the positions taken on various modeling decisions can be documented in structured ways such as the IBIS system [12141.This consists of several elements such as issues to be addressed, positions to be taken in addressing those issues, arguments for and against the various positions. This is typically performed through hypertext and graphical descriptions. The generation of readable model descriptions and final reports as part of the modeling exercise is vital for future reuse. In general, reports are not stored as part of the modeling exercise but remain separate items. Better integration is necessary for reuse and utilization of efforts.

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Data

As mentioned in Section 2.2.1, modeling data - either physicochemical or plant data - is a vital ingredient for modeling. It requires careful analysis and archiving with the other inputs and outputs of the various phases of the modeling cycle. This aspect of modeling is one of the biggest challenges, with little if any facility in modern CAPE software tools to adequately store validation and other data together with the model.

2.2.4 Support Technologies

Modeling requires support technologies. This is a huge area and what follows is a brief mention of some of the key items often encountered in life-cycle modeling. Model Definition and Building

There is a plethora of model-building environments available for each life-cycle modeling phase. In the engineering area, many allow concepts and relationships to be defined at a higher conceptual level using GUIs. Such systems as ModeLLa, ModKit, ICAS-ModDev and SCHEMA are in this category [8].Other environments such as gPROMS, ASPEN Custom Modeler, Modelica and Daesim allow direct model descriptions in terms of equations in various forms that can be stored as model members. Matlab provides facilities for equation solution of ordinary differential equations (ODE)and differential-algebraicequations (DAE). There are also dedicated toolboxes that cover specialized areas such as neural network modeling, partial differential equation systems and finite element applications. Simulation

Again, simulators abound in most phases of the process life cycle. Process simulation systems such as ASPEN, PRO11 and HYSYS have dominated the petroleum and petrochemicals sectors with many other similar products available, that vary in their application areas and capabilities. Generic simulation tools such as gPROMS, ModKit, ICAS, Daesim Dynamics and other simulators are available for general solution of models in the form of differential-algebraicequations that may also be hybrid in nature. Several also handle partial differential equation systems and a few allow simulation of integro-differentialsystems. These tools need to be chosen carefully for the task being tackled. At the more fundamental chemistry level there is a wide range of tools for molecular simulation, quantum chemical calculations and the like. Other tools such as discrete element simulations can handle the dynamics of particulate systems and find wide use in minerals processing, bulk fertilizer and pharmaceutical applications. Environmental simulation tools are easily available for such applications as neutral, buoyant and heavy gas dispersion estimates as well as prediction of groundwater flows, river, estuarine and ocean impact assessments. Significant adaptation of finite element or finite volume methods has been applied to such application areas. Many are made available by national environmental protection agencies such as the US EPA.

2.3 Applications ofModeling in the Process Lfe Cycle: Some Case Studies

Data Analysis

Again, there are numerous tools for analyzing large data sets from process plant. The key issues here are good visualization facilities, ability to handle very large data sets (many millions or tens of millions of data points) and data reduction capabilities to handle multivariable data. The visualization of process data in real-time through the use of Web browser tools across the complete corporation is an increasingly important development. In many multinational corporations, the monitoring and analysis of real-time data from their world-wide operations is now commonplace. Typical of the systems in place for data capture is Honeywell’s Process History Database (PHD),which can be linked to other applications such as MS Excel to view archived data. Accompanying these issues is the ability to transform and manipulate data and to analyze its characteristics so that it is suitable for calibration and validation studies. Filtering, handling or reconstruction of missing data points, spectral analysis and time series analysis capabilities should be available to help tackle the data analysis problem.

2.2.5 Modeling Integration

Model integration is a major issue in industrial modeling practice. Model integration is poorly understood and practiced in the manufacturing and process industries. Much duplication of effort is required to integrate models across the process-product life cycle. In particular, the inputs and results from particular models are often transferred inefficiently between modeling applications. For example, the predictions of gaseous discharges from multiple sources in a process flow sheet are often required in area source dispersion models. The linked models are often not within the same corporation and even if they are much manual effort is often expended in data transfer. The initiative leading to pdxi data exchange protocols based on XML has not penetrated the process and related industries very well, if at all. Some progress has been made in integrating disparate process models into proprietary software simulation systems through the use of CAPE-OPEN and Global CAPE-OPEN standard interfaces. This also addressed physical property routines, numerical solvers and continues to be extended. The problem of data and model integration across the whole life cycle still remains as an unmet challenge.

2.3 Applications of Modeling in the Process Life Cycle: Some Case Studies

In this section we illustrate some aspects of life-cycle modeling on a recent, largescale industrial development of an alternative fuel source. This is based on oil shale. This section shows some of the extensive and diverse modeling that takes place dur-

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ing the life cycle of such a process, and comments on the importance and challenges in such modeling.

2.3.1 Shale Oil Processing

Shale oil has a long history around the world as an alternate source of hydrocarbonbased fuels. Plants have operated in many countries, either as demonstration plants or for commercial production. Countries such as China, Estonia and Brazil currently produce shale oil. Several demonstration plants operated in the US, mainly in Colorado. In Australia oil shale was processed in the early 1840s to produce 'kerosene' from the kerogen content of the shale. In the 1930s shale oil was produced in crude, batch retorts which pyrolized shale that had been suitably mined and crushed. It was an expensive and inefficient process but provided alternative fuels in a time when normal petroleum fuels were in short supply. Much research and development work was done around the work during the 1970s to 1990s to enhance processing and recoverability of products as well as understand the potential environmental impacts. Processing of oil shale into hydrocarbon products involves a combination of mining technologies, minerals processing and conventional hydrocarbon processing. Figure 2.4 shows a typical block diagram flow sheet representing a commercial operation located on the central coast of Queensland, near to the city of Gladstone [15]. This shows the complex nature of the process from mining and shale processing, which is heavily slanted towards solids processing technologies through to liquidvapor systems typical of petroleum processing. 2.3.1.1 Research Modeling

One of the key research issues in oil shale processing is the understanding of product yields under various conditions of pyrolysis. Other research issues relate to the drying characteristicsof crushed oil shale prior to the retorting of shale in the processor. Much academic and industrial research has sought to address these issues [16181.

In particular, models for the kinetics of oil shale pyrolysis, which were represented by nonlinear models were important for reactor design [19]. These were based on extracting rate constants through parameter estimation techniques. Other work related to understanding the effect of particle size on retorting and drying. 2.3.1.2 Conceptual Design

Some selected aspects of conceptual design are mentioned here. Preliminary Process Design

Modeling at the conceptual stage of the process was complemented by significant pilot plant studies that gave specific data from actual feedstock material, so that ini-

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tial mass and energy balances were possible through the use of minerals processing and petrochemical flow-sheetingpackages. Targetted modeling of key items such as the Alberta Taciuk Processor (ATP)were needed to ensure a good design basis for such a large piece of rotating equipment. Initial modeling used simplified multiple, lumped-parameter models to represent the distributed nature of the processor operations. The key parameters such as heat transfer coefficients and heats of combustion being obtained from pilot plant measurements. Environmental Aspects

Oil shale processing environmental issues continue to be one of the priority areas and as such a significant amount of modeling is required to answer questions related to environmental impacts. In particular the geographical location of such plants within complex air sheds poses particular challenges as to the impact of gaseous emissions. Complex dispersion models that can handle multiple sources such as the Industrial Source Complex version 3 (ISC3) [20] are needed to estimate such potential impacts of a wide range of gaseous species such as NO2 and SO2. Figure 2.5 shows the prediction of SOz levels (micrograms per cubic meter) from the planned stage 2 process. These showed that expected ground-level concentrations were well within accepted guidelines. It also showed potential areas of concern, which were very dependent on the geographical and atmospheric characteristics of the area. Other modeling involved such areas as: 0 Leaching models for spent shale to ascertain extraction rates of specific chemical substances from percolation of rain water. This involved the development of onedimensional partial differential equation models with appropriate constitutive relations for the extraction rates. permeation modeling of leachate into surrounding land and potentially into ground waters [21-231; Total site water management modeling to help design and develop 'zero discharge' operating policies. This covers water segregation, reuse and effects of atmospheric conditions such as cyclone conditions as well as sediment control issues close to the Great Barrier Reef Marine Park. premining and postmining flow modeling of principal creeks in the areas surrounding the operations. 2.3.1.3 Detailed Engineering

Detailed engineering inevitably involves the design of complex process equipment. In the case of oil shale processing, the ATP is a very complex device with four operational zones carrying out functions of shale preheating, spent shale cooling, retorting of dried shale and combustion of spent shale for energy recovery purposes. The zones are maintained at different pressures for operational reasons. Figure 2.6 shows a schematic of the ATP vessel and Fig. 2.7 shows the retort zone end of the demonstration pilot plant vessel, which is approximately SO m in length, 10 m in diameter and has a loaded weight of over 2500 tonnes.

2.3 App/ications ofModeling in the Process l$ Cycle: Some Case Studies

Figure 2.5 Predicted SO2 levels for stage 2 process from complex dispersion modeling

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Modeling aspects of detailed process design involved: Substantial flow-sheet modeling of the back-end process, which consists of fractionation, hydrogenation and product separation to produce a range of liquid and gaseous hydrocarbons products. Detailed process modeling of the ATP vessel using steady state models to compute the mass and energy balances. This involved the use of standalone programs to consider a range of scenarios for changing feed rates and pressure changes. Finite element stress modeling of the structural aspects of the ATP are used to ascertain adequacy of the internal mechanical design for vessel integrity.

Figure 2.7

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2.3 Applications ofModeling in the Process Lfe Cycle: Some Case Studies

2.3.1.4 Operations Modeling

Operational phase modeling considers the following issues:

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Initial modeling of the ATP dynamics to consider the effect of feed flow rate changes and moisture into the ATP vessel. This allowed the development of an initial tool for improving operator training and considering alternate control strategies for both set-point changes as well as disturbance rejection. This considered conventional PID loops as well as the potential for model-based control strategies. empirical modeling through planned step tests on the ATP to establish appropriate models for model-based control applications; improved flow-sheet modeling of the process to consider better operating policies for the hydrocarbon processing units of the plant; Development of a complex distributed parameter model of the preheat-cooling section of the ATP in order to answer questions about internal heat transfer design and potential hot gas bypassing. This involved the consideration of solids flow in rotating drums as a function of rotation speed and particle properties, the effect of particle size distributions on internal heat transfer and the effect of pressure driven flows in various flow zones within the device. A full distributed parameter model was developed to help answer the key questions.

2.3.1.5 Risk Modeling

Risk modeling that includes both financial and environmental risk is a crucial factor in modern process design and operations. In the case of shale oil production, there are a number of hazardous materials and conditions in the process. A full quantitative risk assessment was needed, which involved modeling all major events such as low and high pressure releases of gases and liquids, pool and jet fires as well as explosions. This led to estimates of iso-risk contours for potential fatalities as well as injury levels. Figure 2.8 shows predicted risk levels for radiation impacts at 4.7 and 23.0 kW m-2, which are key legislative limits for nearby residential and industrial land-uses. In this case, risk levels were well within acceptance levels, since nearby industrial sites were located hundreds of meters away and residential areas were several kilometers away. 2.3.1.6 Socioeconomic Impact Analysis

One of the key issues that is amenable to modeling is the impact that the proposed operations will have on social and economic aspects of the region. Regional economic impacts were measured using the Queensland Multi-Regional Input-Output Model that takes into account linkages between regions. This provides a tool to consider alternative strategies for regional development. This type of modeling can provide useful data on regional effects throughout the life cycle of the operation covering planning, conceptualization, construction and operational phases. The outputs can be linked to issues of employment levels, potential housing needs and the like.

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2.4 Challenges in Modeling Through the Life Cycle

2.3.2 Utility and Inventory Management Applications

Two applications that illustrate less traditional or less recognized modeling are utility management in a brewery and inventory management in a warehouse. Brewery Utility Management

Beer production is a deceptively simple process involving brewing (basically extraction of sugars from malted grain), fermentation (partial biological conversion of sugars to alcohol), filtration and packaging. It is complicated by the range of products generated by variations in ingredients and in the brewing and fermentation processes and by traditional processing in batches. A key economic driver to remain competitive is to reduce and manage the consumption of utility streams, about six in total. Utility management is based on the prediction of current consumption rates and the prediction of consumption over short periods into the hture. Utility consumption during individual steps in the batch processing is modeled empirically by a piecewise-linear profile based on processing time and sometimes batch size. The model needs to know what processing steps are active and when the steps commenced and then it simply performs interpolations and summations based on simple utility flow sheets to predict utility rates at various real and virtual sensor locations. This information is then used by operations and technical personnel for monitoring and diagnosis. Warehouse Inventory Management

Warehouses are also deceptively simple operations. The basic model is simply a dynamic mass balance that tracks inflows and outflows to predict inventories. A model validation is called a stocktake.Again there are many complicatingfactors: a large number ofproducts, discrete inflows and outflows in terms ofpacks, pallets and truck loads of various sizes, spatial factors governing the placement of material in the warehouse, product 'use by' dates, real-time orders and just-in-time delivery and manufacture. The economic drivers are minimizing inventories and wastage and increasing the ability to meet orders often with very small lead times. The model must not only predict current and future inventories but also advise the warehouse staff on where products are to be found to meet orders by careful tracking in the spatial domain as well as the time domain.

2.4 Challenges in Modeling Through the Life Cycle

This section outlines a number of challenges currently being addressed that help to tackle some of the more intractable aspects of life-cycle modeling for process and product systems. Most are to do with information management which is at the heart of these challenges.

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2.4.1 Model Management

It is clear that during the life cycle of a process or manufacturing plant there are a large range of models and associated data that have been gathered and developed by many different people with an often enormous associated cost over the life cycle. While there are well developed procedures for the life-cycle management of computer software, little is done to manage models, resulting in much loss of information and knowledge and much duplication of effort. This often occurs over relatively short periods in the operations phase largely due to changes in personnel and computer systems, let alone between life-cycle phases which frequently occur within different organizations. In many cases there is much process and operating knowledge in models developed in the strategic planning, research and development and design phases that is never utilized in the operations phase. Recent research into the tracking and representation of design information has led to several systems that seek to tackle this issue. The recording and utilization of modeling assumptions [7, 8, 331 and the transfer of software life-cycle management to modeling may one day address the model management issue more fully.

2.4.2 Model Repositories and Reuse

There have been efforts to address the issue of model repositories. It still remains a major challenge in process modeling and even more so in sociotechnical modeling, which presents a far greater challenge due to its diversity of applications and model forms. It is especially a problem when modeling over various life-cycle phases is carried out by a wide range of organizations not necessarily part of the corporation. Many model repositories are simply files within a directory that were used to run a specific simulation similar to those in current flow-sheeting packages. More sophisticated repositories that are ‘simulator neutral’ are not very common. Amongst the attempts to produce such repositories are languages such as system for chemical engineering model assembly (SCHEMA) [24, 251, that seek to store models and model families in a natural language form that includes the underlying assumptions in the model as well as a description that can be used to generate simulation code suitable for a specific simulation tool. In this case, the advantage of not being tied to a specific simulation package is clear when industrial companies make corporate decisions to change simulation platforms. This constitutes a major problem in maintaining process models. Other approaches have been proposed and prototyped. These include the repository of a modeling environment (ROME) system [26], which enables neutral models to be stored in terms of fundamental modeling objects. The ROME system provides import and export capabilities for various application software. It thus provides a means of storing, retrieving and using models over the life cycle. The wider problem of handling model storage across organizations is still largely unaddressed and

2.4 Challenges in Modeling Through the L$ Cycle

unsolved. It is often made more difficult by privacy and nondisclosure issues related to specific modeling systems or models that have significant commercial value. Along with this concept is the idea of exchanging models between different modeling environments such as gPROMS, Modelica or AspenPlus using a model exchange language like CapeML [27]. This provides a neutral exchange mechanism for model use across application packages. This was part of the larger program of CAPE-OPEN and Global CAPE-OPEN [28] that seeks to address mobility and exchange of modeling across diverse application platforms by setting open standard interfaces for computer-aided engineering applications. A number of major software vendors such as Aspen Technology, PS Enterprise, Fantoft Process and academic members support the Global CAPE-OPEN initiative.

2.4.3 Data Representation and Use

Data is at the heart of modeling and data representation is crucial to effective model development and use. In this context, significant work has been done to address the structuring of data across the design cycle. Development of the conceptual life-cycle model (CLiP) [29-311,has provided a framework in chemical engineering for design and model development and reuse. The CLiP development, in theory, covers sociotechnical systems but is yet to be expanded and developed to a point where it can adequately cover the range of industrial modeling activities common to major industrial developments. It includes some concepts covering technical, social and material systems that act as upper level metamodels to instances of these classes. One current development is the extension of the CLiP data model into an ontological representation called OntoCAPE [32], which seeks to put these concepts in the form of an ontology which can be used for reasoning about the domains covered by the concepts. This provides the possibility of building intelligent software agent systems that can help practitioners perform modeling and design tasks. Data exchange in the area of process engineering has also been of major concern leading to such initiatives as the Process Data Exchange Institute (pDXi) which was initiated in 1989 by the American Institute of Chemical Engineers and numerous organizations within the US and Europe. It is however difficult to assess the actual usage of the standard. More recently, initiatives such as the Standard for Exchange of Product Model Data (STEP) within the industrial automation and integration standard, I S 0 10303 will provide extensive specifications for chemical engineering related equipment, processes assembly and design [34].

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2.4.4 Documentation

Documentation in a corporation is a major challenge, given the enormous amounts of reports, figures, drawings, memos, letters, consulting documents and the like that are generated throughout the process or product life cycle. A number of large commercial systems exist to address this issue, such as Documentum [35], that provide enterprise content management (ECM). Recent developments provide collaborative workspaces that give facilities to share ideas and information within the corporation and beyond. Challenges still exist in being able to effectively link important documents to other technical systems such as hazard and risk registers or plant level systems, so that documents can be retrieved in a timely fashion for decision making purposes.

Acknowledgements

The authors would like to acknowledge the help given by Mr. Jim Schmidt, manag ing director (SPPD) and to Southern Pacific Petroleum (Development)for permission to quote details of the shale oil process referred to within this chapter. We also acknowledge permission from Unilever and CUB Limited to quote on warehouse and utility applications.

References 1 British Standards 2004

http://bsonline.techindex.co.uk

2 ICCA, 2004, International Council of Chemi-

cal Associations, www.icca-chem.org/ 3 Rosselot R S. Allen D. T. L$ Cycle Concepts, Product Stewardship, and Green Engineering, in D.T. Allen and D. Shonnard (eds.) Green Engineering: Environmentally Conscious Design of Chemical Processes, ch. 13, Prentice Hall PTR, Upper Saddle River, NJ 2002 4 Minsky M. Matter, Minds and Models in Semantic Information Processing, MIT Press, Boston, USA 1968 5 Marquardt W.uon Wedel L. Bayer B. Perspectives on Lifecycle Process Modeling, FOCAPD, 5th International Conference on Computer-Aided Process Design, AIChE Symposium Series 323 96 (200) p. 192-214 6 Virkki-Hatakka T. et al. Modeling at Different Stages of Process Life Cycle, European Symposium on Computer-Aided Process Engineering (ESCAPE)-13,Elsevier Science, Amsterdam (2003) pp. 977-982

7 Foss B. A. Lohmann B. Marquardt W.A Field

Study of the Industrial Modeling Process, J. Process Control, 8(5-6) (1988) p. 325-338 8 Hangos R M . Cameron I. T. Process Modeling and Model Analysis, Academic Press, London 2001 9 Lind M . Modeling Goals and Functions of Complex Industrial Plant, J. Appl. Artificial Intell. 8 (1994) p. 259-283 10 Modarres M. Cheon S. Function Centered Modeling of Engineering Systems Using the Goal Tree Success Tree Technique and Functional Primitives, Rehab. Eng. Syst. Safe. 64 (199) p. 181-200 11 Cameron I. T. Fraga E. S. Bogle I. D. L. Goal Set Development and Evolution in the Conceptualization of Process Models, CAPE Centre, University of Queensland, Internal Report 2004 12 Rittel H. Kunz W. Issues as Elements of Information Systems, Tech Report Working Paper 131, Institute of Urban and Regional Development, University of California, Berkeley, USA 1970

2.4 Challenges in Modeling Through t h e L@ Cycle 13 Batiares-Alcantara R. Lababidi H. M . S.

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Design Support Systems for Process Engineering, Comput. Chem. Eng. 19 (1995) p. 267-301 Batiares-Alcantard R. King J . M. P. Design Support Systems for Process Engineering, Comput. Chem. Eng. 21 (1997) p. 263-276 SPP-CPM Stuart Oil Shale Project, Draft Environmental Impact Statement, Southern Pacific Petroleum (Development) Pty Ltd, Sinclair Knight Merz, Australia 1999 Litster]. D. Bell P. R. F. Newell R. B. White E. T. The Role of Kinetics in Oil Shale Retorting, in Proceedings of CHEMECA 82, Sydney, Australia, August 1982, pp. 35-39 Do D. D. Litster]. D. Peshkof E. Newell R. B. Bell P. R. F. Pyrolysis of Queensland Oil Shale in a Fluidized Bed Modeling and Experimental Studies, in Proceedings 1st Aust. Workshop on Oil Shale, Lucas Heights, Australia, May 1983, pp. 131-134 Litster]. D. Rogers M. /. Newell R. B. Modeling Fluid Bed Drying and Retorting of Rundle Oil Shale, in Proceedings of 2nd Australian Workshop on Oil Shale, Brisbane, Australia, December 1984, pp. 206-211 Fincane D. George ]. H. H a m s H. G. Perturbation Analysis of Second Order Effects in Kinetics of Oil Shale Pyrolysis, Fuel 56(1) (1977) p. 65-69 United States Environmental Protection Agency [ USEPA) www.weblakes.com/lakeepal.html 2004 Connell L. D. Bell P. R. Modeling Moisture Movement in Revegetating Waste Heaps :I Finite Element Model for Liquid and Vapor Transport Water Resources Res. 29(5) (1993) p. 1435-1443 Connell L. D. Bell P. R. Hauerkamp R. Modeling Moisture Movement in Revegetating Waste Heaps: I1 Application to Oil Shale Wastes, Water Resources Res. 29(5) (1993) p. 1445-1455 Syamsiah S. Krol A. Sly L. Bell P. R. B. Adsorption and Microbial-Degradation of Organic Compounds in Oil-Shale Retort Water Fuel 72(6) (1993) p. 855-861 Williams R. P. B. Keays R. McCahey S . Cameron I. T. Hangos K. M. SCHEMA: an Object Oriented Modeling Language for Continuous and Hybrid Process Models, Asia Pacific Conference on Chemical Engineering (APCChE), Paper #922, 2002, Christchurch, New Zealand 2002

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McGahey S. Cameron I. T. Transformations in Model Families, ESCAPE12, Comp. Chem. Eng., The Hague, The Netherlands, 26-29 May 2002 Von Wedel L. Marquardt W. ROME: A Repository to Support the Integration of Models over the Lifecycle of Model-Based Engineering Processes, in s. Pierucci (ed.) European Symposium on Computer-Aided Process Engineering, 10, Elsevier, Amsterdam, (2000) pp. 535-540 Von Wedel L. CapeML A Model Exchange Language for Chemical Process Modeling Tech Report LPT-2002-16 Lehrstuhl fur Prozesstechnik, RWTH Aachen University, Germany 2002 http://zann.informatik.nvth-aachen.de:8080/ opencms/opencms/COLANgamma/ index.htm1 Bayer B. Conceptual Information Modeling for Computer-Aided Support of Chemical Process Design, Dissertation Nr. 787, Lehrstuhl fur Prozesstechnik, RWTH Aachen University, Germany 2003 Bayer B. Krobb C. Marquardt W. Data Model for Design Data in Chemical Engineering Information Models, Tech Report LPT-2001IS, Lehrstuhl fur Prozesstechnik, RWTH Aachen University, Germany 2002 Schneider R. Marquardt W. Information Technology Support in the Chemical Process Design Lifecycle, Chem. Eng. Sci. 57(10) (2002) p. 1763-1792 Yang A. et al. Principles and Informal Specification of OntoCAPE: COGENTS Project, Information Society Technologies (IST) Programme, 1ST-2001-34431,European Union 2003 Bogusch R. Lohmann B. Marquardt W. Computer-Aided Process Modeling with ModKit, Technical Report #8,RWTH Aachen University of Technology 1996 International Standards Organization [ISO) www.iso.org 2004 Documentum lnc. www.documentum.com 2004

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

3 Integration in Supply Chain Management Luis Puigjaner and Antonio Espuria

3.1 Introduction

An introductory chapter (SectionThree, Chapter 7) on the supply chain (SC)network has already presented the elementary principles and systematic methods of supply chain modeling and optimization. Here, the need for and integrated management of the SC is further emphasized and challenging solutions are presented. As seen, supply chain management (SCM) comprises the entire range of activities related to the exchange of information and materials between costumers and suppliers involved in the execution of product and/or service orders in an extremely dynamic environment (Fig. 3.1).

Rew Material Prcducer

Dowstream Matertal now Figure 3.1

Flow o f supply chain management information and materials

Computer Aided Process and Product Engmeenng Edited by Luis Puiglaner and Georges Heyen Copyright 02006 WILEY-VCH Verlag GmbH & Co KGaA, Weinhem ISBN 3-527-30804-0

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A successful management of the supply chain management requires direct visibility of the global results of a planning decision in order to include this global perspective. This requires significant integration across multiple dimensions of the planning problem for nonconventional manufacturing networks and multisite facilities over their entire supply chain [I]. Objectives such as resources management, minimum environmental impact, financial issues, robust operation and high responsiveness to continuous needs must be simultaneously considered along with a number of operating and design constraints [2, 31. Almost all the currently available SCM software suffers from several of the following demerits: product availability focus; reactive rather than proactive; long lead times; uncertainty treatment throughout; lack of flexibility in systems; performance measured functionally; poorly defined management process; no real partnership; insufficient performance measurement [4]. To overcome the above deficiencies and respond better to industrial demands facing a more dynamic environment (greater uncertainty of demand, shorter product life cycle, financial and environmental issues, fewer warehouses, new cost/service balance, globalization, channel integration and so on), there is a need to explore new strategies for supply chain management. Moreover, an integrated solution is required for the next generation of SCM given the number and complex interactions present among supply chain main components in the global supply chain (Fig. 3.2). This new scenario requires departing from current approaches that consider Supply chain optimization in a static way. Production-distribution-inventorysystems that are now being used in manufacturing companies are static information systems. Periodically (typically weekly or monthly), all data (demand forecasts, available machine capacity, current inventory levels, desired inventory levels, etc.) are collected and fed into a huge optimization system (typically some type of linear programming system). After hours of computation a company-wide plan is obtained: this plan repI

Forecast Demand

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resents next week’s (or month’s) production schedule, the inventory levels at the various facilities and the distribution of the final goods. However, due to demand fluctuations or other unpredictable situations, the plan does not exactly meet the company’s best course of action in length of changing conditions and data. So, production and plant managers adjust the plan to the best of their ability, given the frequent lack of data and their inability to compute the “best” course of action. Real-time adjustments in view of changing data are made manually and ad hoc. This situation is largely recognized and manifested in recent specialized forums of debate [S]. Therefore, new SCM solutions should be provided with the following main characteristics: interoperability, scalability, with open and flexible infrastructure; Weboriented interface; autonomous, capable of self-organization and reconfiguration, coordination and negotiation, with optimization and learning mechanisms, so to evolve and adapt to the dynamic market environment; adaptive process modeling, rapid prototyping; involving production planning and scheduling; capable of making forecasts accurately and to incorporate e-commerce and w-commerce. In this section, an open, modular-integrated solution is discussed that implements real-time supply chain optimization. The technology involved uses a network of cooperative and auto-associative software agents (smart agents) that constitute a decision support system for managing the whole supply chain in a real-time environment. This chapter is organized as follows: First, a review of recent approaches to SCM integration is presented and the requirements for next generation of SCM integrated solution are identified. Then, a specific environment is presented that encompasses the SCM characteristics identified above. Finally, the integration of negotiation, environmental, forecasting and financial decisions is reported as an example of the new technology that may lead to better, fully integrated, easier to use and more comprehensive tools for SCM. A brief description of the architecture and functionalities of the solution implemented is also given.

3.2 Current State of Supply Chain Management Integration

Supply chain management (SCM) has been extensively studied in recent years. Lee and Billington [7] consider inventory handling as the central part of supply chain management integration. This work considers three areas of potential conflict: 0 0 0

problems related to information and management of the SC; operational related problems; strategic and design problems.

Geoffrion and Powers [8]studied design aspects of the distribution network focusing on the storage location problem. The integration of production and distribution in the SC is examined in the work of Erengunc et al. [9]. The authors point out the necessary tradeoff between flexibility and quality on the one hand and product cost on the other in the SCM.

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As the level of integration in supply chain management increases, the complexity of the resulting model limits some approaches to contemplate small academic examples. Some representative methodologies to represent the supply chain are summarized.

3.2.1 Methods Based on Deterministic Analytical Models

Heuristics methods were used by Williams [lo] for planning and distribution of supply chain networks. The objective is to find the optimum production plan that satisfies the demand at minimum cost. Different models are used and compared with dynamic programming. In a later work, Williams [ll]developed a dynamic programming model to determine simultaneously production and distribution lot sizing for each echelon in the chain. Inventory and operation costs associated to each mode of the chain are minimized. A deterministic model was used by Ischii [12] to obtain the inventory levels and dead times associated to the solution of an integrated supply chain considering finite horizon and linear demand. Cohen and Lee [13] presented a mathematical programming formulation (mixedinteger nonlinear programming) that minimizes net profit of manufacturing and distribution centers under management constraints (production resources) and logistics constraints (flexibility,availability and demand limitations). This work was later extended [14] to minimize fixed and transport costs along the chain subject to supply, capacity, assignment, demand and raw material constraints. A combination of mathematical programming and heuristic models is used by Newhart et al. [15] to minimize the number of products in inventory through the network. A second step investigates the minimum inventory required to absorb demand delays and fluctuations. Arntzen et al. [16] develop a “global” model for the supply chain (GSCM) that implies a formulation of the type mixed-integer linear programming to determine: (1)the number and location of distribution centers, (2) client assignment to distribution centers, (3) number of echelons in the SC, and (4)product assignment to production plants. The objective is to minimize the weighted sum of total costs (production, inventory, transport and other fixed costs) and active days. The efficiency and response capacity of the SC can be improved by increasing its flexibility [17]. Here, flexibility is measured as the sum of the instantaneous difference between capacity and utilization of two types of resources: inventory and capacity resources. Given the necessary resources for manufacturing each product and bill of materials (BOM) information, the transport plan and delivery of each product is obtained and optimum inventory levels are achieved. Camm et al. [18] developed an integer mathematical programming (IP) model to determine the best location for distribution centers of Procter and Gamble and its proper assignment to clients grouped by zones. The model developed uses a simple transport model and the allocation problem does not consider capacity constrains.

3.2 Current State ofSupp/y Chain Management Integration

More recently, the design of multiechelon supply chain networks under demand uncertainty has been modeled mathematically as a mixed-integer linear programming optimization problem [191. The decisions to the determined include the number, location and capacity of warehouses and distribution centers to be set up, the transportation links that need to be established in the network and the flows and production rates of materials. The objective is the minimization of the total annualized cost of the network, taking into account both infrastructure and operating costs.

3.2.2 Methods Based on Stochastic Models

A detailed presentation of uncertainty sources present in the supply chain that affects its operation performance can be found in Davis [20]. In the same work a method is developed to treat the uncertainty associated to the supply chain of Hewlett-Packard. According to Davis [20], three different sources of uncertainty can be found in the SC: (1)suppliers, (2) production, and (3) clients. Chain suppliers are characterized by their performance and their response can be predicted. Uncertainty problems related to production can be solved by reliability analysis maintenance techniques. Finally, client demand uncertainty can be dealt with specialized forecasting methods. Stochastic models incorporate uncertain aspects of the supply chain and focus on certain parameters relative to its operation. For instance, in the work of Cohen et al. [21] a model is developed to establish a materials supply policy for each echelon in the SC. Four submodels are developed based on different costs for the control of materials, production, finished products storage and distribution. There are two probability distributions which are determined by the SC interactions, namely the materials’ demand in manufacturing plants and clients demand in distribution centers. Svoronos and Zipkin [22] consider a multiechelon SC distribution and estimate the average inventory level and the number of unfilled orders for a given base level of inventory. With these approximations, the authors build an optimization model to determine the inventory base level that implies minimum cost. A mathematical programming model for three echelons SC (one product, one factory, one distribution center and a retailer) is developed by Pyke and Cohen [23].The model minimizes the total cost subject to a service level constraint. A later work by Pyke and Cohen [24] considers the same network but with multiple types of products. Lee et al. [25] present a mathematical model that describes the “bullwhip” effect (variance distortion along SC upstream). Although it is often impossible to know exactly the probability distribution functions of products demand, it will always be possible to specify a set of demand scenarios with high probability of occurrence. Scenario-based planning permits the capture of uncertainly by defining a number of possible future scenarios [26]. Thus, the objective consists of finding solutions that behave satisfactorily under all scenarios. Mobasheri et al. [27] describe a number of

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scenarios as possible states from the actual state. The authors claim that this is avoided forecasting, which is less reliable. The same approach is used to formulate and solve operational problems, like environmental impact along the chain [28, 291. The midterm supply chain planning under demand uncertainly is addressed in a recent work with the objective to safeguard against inventory depletion at the production sites and excessive shortage for the customer [30]. A chance constraint programming approach in conjunction with a two-stage stochastic programming methodology is utilized for capturing the tradeoff between customer demand satisfaction and production costs. The design of multiproduct, multiechelon supply chain networks under demand uncertainty is considered by Tsiakis et al. [31]. Compared to previous models, the model integrates three distinct echelons of the supply chain within a single, mathematical-based formulation. Moreover, it takes into account the complexity introduced by the multiproduct nature of the production facilities, the economics of scale in transportation and the uncertainty inherent in the product demands. In a recent work [32], an optimization model is developed for the supply chain of a petrochemical company operating under uncertain demand and economic conditions. The proposed two-stage stochastic model succeeds in determining the optimum production volumes that maximize the volumes of products shipped for each scenario. However, the need for further investigation to study the dynamics of the petrochemical supply is recognized. A novel approach to increase the supply chain competitivenesshas been presented very recently [33]. The proposed strategy helps to coordinate the production/distribution tasks of the orders embedded in a SC by integrating the plant production scheduling with the transport scheduling to final markets. Uncertainty in the demand is considered and the problem is formulated as a two-stage stochastic optimization approach. The mathematical model looks for the detailed global schedule (production and transports) that maximizes the expected benefits.

3.2.3 Methods Based on Economic Models

The current trend of advanced planning and scheduling tools (APS) is to incorporate tools to model and change the current position of the financial and process managers during complex interconnected decision making in chemical process industries. Cash management models were considered in the supply chain following basically two stochastic approaches. Baumol’s model [34] had an inventory approach assuming certainty. Cash was treated similarly as holding inventory and payments were assumed at a constant rate. On the contrary, the Miller and Orr cash management model [35] was based on the fact that perfect forecasts of cash were virtually impossible because the tuning of inflows depend on payments to customers. In consequence, lower and upper bounds of cash were calculated to create a safety stock. In an attempt to model the client-provider behavior, Christy and Grout [36] develop a supply chain economic model based on games theory. The integration of budgeting

3.2 Current State ofSupp/y Chain Management lntegration

models into scheduling and planning models is also considered in a recent work [37]. A cash flow and budgeting model is coupled with an advance scheduling and planning procedure within the decision-making process for increased revenues across the supply chain. A further step in integrating levels of decision making in the SC is contemplated in the work of Badell et al. (381. This work considers business decisions and their impact in the SCM. It addresses the implementation of financial cross functional links with the SC operation and investment activities at the factory level when scheduling and budgeting in short term planning in batch processing industries. The target is to obtain tradeoff solutions preserving at most the profit and liquidity while satisfying customers.

3.2.4

Methods Based on Simulation Models

The fast development of new products and the increasing competitiveness of market agents have turned the SC system into a rapidly changing environment. Therefore, it becomes necessary to capture and characterize the dynamic behavior of enterprise systems and develop systematic procedures for decision-making support under these circumstances. Although the interest in integrated dynamic approaches for SCM is recent, some studies were clearly reported during the last four decades. Forrester [39] performs dynamic analysis and simulation of industrial systems by means of discrete dynamic mass balances and linear and nonlinear delays in the distribution channels and manufacturing sites. Although this work contemplated small academic examples, it permitted the identification of the aforementioned demand amplification problem. Later, Towhill [40] reported some effects to control SCs based on a transfer function analysis and classical feed-forward control. A changing environment is contemplated in the work of Back et al. [41].They propose a strategy to cater for the dynamics of the environment and the disturbances, as well as for the dynamics of operations of the business. The same approach is used in the work of Perea-Lopez et al. [42], but taking a step forward by considering a consumer-driven operation. They analyze the impact of heuristic control laws on the performance of the SC integrated by multiproduct multistage distribution networks and manufacturing sites. A more recent model, model predictive control (MPC), applied to the supply chain problem was reported by Brown et al. [43]. A comparison between these two control strategies can be found in Mele et al. [ a ] . A different approach is presented in the work of Mele et al. [45]. Here, a dynamic approach for SCM based on the development of a discrete event-drivensystem model of the SC contemplating several entities is reported. The interaction between these entities is explored through simulation techniques. The results obtained provide information about the tradeoff found in real systems and give valuable insight into SC dynamics. Thus, the proposed framework becomes a useful tool for decisionmaking support in real scenarios.

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Present analytic approaches to decision making have severe limitations when dealing with the amount of computations, probabilities and nonanalytic knowledge. Thus, there is an increasing interest in decision theory with artificial intelligence tools. It is used to address important tasks such as planning, diagnosis, learning, and serves as the basis for the new generation of “intelligent”software known as normative systems. An emerging area is the utilization of multiagent systems, since decision making is the central task of artificial agents [46]. This chapter focuses on a multiagent viewpoint for SCM and design. The proposed approach is to consider each possible configuration and action advice as an independent agent provided with autonomous, interactive, cooperative, adaptive and proactive capabilities. This approach permits new levels of integration and additional functionalities in SCM (environmental issues, human factors, financial decisions) as it will be unveiled in the next sections.

3.3 Agent-based Supply Chain Management Systems

Since SCM is essentially concerned with coherence among multiple, globallydistributed decision makers, a multiagent modeling framework based on explicit communication between constituent agents (such as manufacturers, suppliers retailers, and customers) seems very attractive. Agents can help to transform closed trading partner networks into open markets and extend such applications as production, distribution, and inventory management functions across the entire SC, spanning diverse organizations [46]. Agents are autonomous pieces of software that are designed to handle very specific tasks. In the case of SCs, where one has to deal with thousands of products, numerous requirements in production quality control, and many types of interactions, no single agent can be designed to handle this overall task therefore, we will have to design multiple specialized agents to guide the SC in its entirety. Multiagent systems may be regarded as a group of agents, interacting with one another to collectively achieve their goals. By drawing on other agents’ knowledge and capabilities, agents can overcome their own limits of intelligence. Otherwise, knowledge is distributed among several intelligent entities, the agents. Autonomous agents and multiagents represent a new way to designing, analyzing and implementing complex software systems [47]. A multiagent system uses cooperative agents towards a common goal. The agent is informed about the environment and/or can act on it. The agent has control of its own actions and internal state in a very flexible way, interacting when appropriate with other agents. Therefore, a multiagent system can emulate the behavior of distributed systems - like real world distributed supply chains - at a logical level, thus providing a resource for control of the real physical distributed systems.

3.3 Agent-based Supply Chain Management Systems

3.3.1 Multiagent System Architecture

A multiagent system (MASC) built on an open, distributed, flexible, collaborative, and self-organizing architecture has been recently proposed for SCM [48]. Retailers, warehouses, plants and raw material suppliers are modeled as a flexible network of cooperative agents, each performing one or more SC functions following a clientserver paradigm in an object-oriented fashion. An agent must use all its knowledge about the SC to determine the most convenient values of each attribute that must be negotiated. According to the resulting set of interests and capabilities of the network, the agent translates the value of each attribute into its value of satisfaction. Since it may be expected that not all attributes are equally important for the agent, each attribute has a different weight according to the agent’s scale of priorities. The total satisfaction that an agent obtains from a set of attributes is calculated taking into account the satisfaction given by each attribute and their respective weights. This final function, the utility function, gives an abstract value of the offers and counter-offers generated by both supplier and customer. Since objects of negotiation may be interdependent, the tradeoff between each pair of attributes considered is defined in a compensation matrix. This matrix is the element that enables the negotiation of all attributes at the same time, making the whole process faster and more similar to a human negotiation. The steps of the negotiation are: an agent receives a message of his opponent and evaluates how much this offer satisfies his expectations. From this initial vector of satisfaction, the agent generates an improved counter-offer using his compensation matrix. Then the agent can generate several counter-offers with the same utility using its weights. The opponent must do all the same steps after evaluating all the counter-offers and choosing the one with the highest applicable utility. The negotiation process finishes when an agent launches two consecutive offers that are nearly equal. Obviously, different negotiation policies can be considered and compared. Two types of agents are to be distinguished: the physical agent and management agent (Table 3.1). The physical agent represents the system’s physical entities (distribution center, warehouse, plant, etc.) and is capable of simulating the behavior and decision making of the corresponding entity, while information handling between entities is carried out by the management agents. A central agent, which is a management agent, is also responsible for the overall network management optimization. Table 3.1

Classification of the different entities in the MASC

Agents

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Users

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n

Figure 3.3 Communication types between entities

Module components (forecasting, scheduling, etc.) are information tools that act as servers to specific queries from other entity (agent, module, and user). These three types of entities define five types of communications as seen in Fig. 3.3 for illustration purposes. The proposed MASC which contemplates a central agent (CA) as management agent offers a flexible architecture allowing representing real SCs with different policies of information control and decentralized decision making. The simplified structure of the MASC can be seen in Fig. 3.4. The architecture proposed contemplates physical agents at each node of the supply chain network (client, warehouse, factory) while a central management agent communicates with all the other agents. Other management agents are also considered that may be subagents of these already enumerated. This flexible architecture should permit an easy adaptation to represent any real SC with its own level information sharing, from a centralized system to a wholly decentralized one. For instance, in a decentralized case every physical agent (manufacturer A and B, retailer) takes decisions on internal variables and negotiates with other physical agents within its own

Retarder

Manufacturer

Module Forecasting

Central Agent

Manufacturer Scheduling

Figure 3.4 Basic multiagent system showing constituent entities (phys ical and management agents, modules and user)

3.3 Agent-based Supply Chain Management Systems

SC. Here, the central agent plays the role of information handling without decisionmaking capacity. Otherwise, when a centralized control system is contemplated, the central agent is the only one to have the overall SC information and to make decisions, while every physical agent sends and receives information to and from him. In this case, the central agent is provided with improvement/optimization algorithms. A fundamental aspect of this architecture is the traceableness required for a proper SC operation. Namely, all transactions carried out through the SC must be clearly registered to facilitate reproduction of the results obtained by simulation of a particular scenario. The second important element of the framework is the agent modeling. A brief description of different physical and management agents contemplated is given below: Physical Agents

As mentioned previously, physical agents represent the system’s physical entities. Specifically, the following physical agents are considered:

Client agent. The client agent initiates the system’s information flow by placing an order to the central agent. Basically the information transmitted is related to the product type, the amount of it, the delivery date and acceptable price. The central agent receives this information and transmits it to potential suppliers (manufacturerlwarehouse agents). Following their own internal logic, the potential supplier makes an offer to the central agent which is transmitted to the client. The client internal logic (amount of product, delivery, date and price) negotiates the selected supplier through the central agent. Final confirmation of the order by the supplier is received though the CA (Fig. 3.5). Warehouse agent. This agent models the material-handling of different kinds (raw materials, intermediates, final products) to be distributed through the SC. Clients of the warehouse may be manufacturers, other warehouses and product endusers. This agent mechanism has already been described (client agent), The internal logic for making an offer obeys to the following issues: (1) delivery date depending on distance, transport and preparation time; (2) available amount of

loffer (amount

Figure 3.5

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product that will depend on the stock and eventual delivery time, and ( 3 ) the product selling price which is dependent on production and storage cost plus warehouse expected profit. The warehouse behaves similarly to the client. However, complex inventory policies must be modeled that have to include demand uncertainty. Moreover, since the inventory control policy will influence the cost of downstream echelons in the SC, optimum negotiation at this point become very essential. Manufacturer agent. This agent models the actual manufacturing facility behavior in the SC producing intermediate and/or final products. It receives orders from clients/warehouses and makes an offer in terms of products amount, due date and price, which is calculated by using a production scheduling module. Manufacturers also operate like clients regarding raw materials supply. Planning tools are used to determine the amount of raw material needed. Production scheduling models will have into account the process type (continuous, batch, hybrid). Information provided by these models will be used at upper levels of manufacturing decision making (MRP, financial modules).

Management Agents

This type of agents does not represent a physical entity of the SC, but it rather simulates the SC operation in these aspects that are not necessary related to a physical entity of the SC. They could optimize the overall performance of the SC by modeling specific parameters associated to the other agents. 0

0

Central agent. Coordination of the agent’s network is achieved by means of the central agent. It essentially supervises and analyses the information flow between the other agents. As a result of information analysis, they may also have an active role by modifylng adequate parameters looking for the optimum overall performance of the SC. Other agents. The architecture envisaged contemplates the existence of subagents operating within the agents already described. Namely, a manufacturerlwarehouse agent contains coordinated subagents to simulate its real behavior. Typical examples of subagents are the sales/buy agents that simulate the corresponding department in a factory. These subagents negotiate transactions between physical agents (client,warehouse, manufacturer agents) and perceive their consequences. They follow the client-supplier logic described before. The architecture developed may consider the “multiowner” case where one SC competes with other SC. In that case, each SC has a partial view of the whole situation and therefore cannot manipulate variables belonging to a SC of a different “owner”. Thus, negotiation between SCs is necessary; being the central agent of each SC the responsible for interchain negotiations mechanism to reach an agreement on multiple conditions (Fig. 3.6). Management agents are adaptive. Namely, they are able to learn from the operation of the SC. Otherwise, they must be provided with appropriate tools (modules) for internal optimization (vertical integration) and external optimum negotiation (horizontal integration).

3.4 Environmental Module

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Modules

Modules are not considered agents strictly speaking, but software tools needed to realize certain functionalities within the multiagent system. For instance, the warehouse physical agent model of inventory control may require demand forecasting tools to estimate the amount of future supply. Therefore, the warehouse agent will have to interact with the forecasting module to achieve proper inventory control. Available modules are: forecasting, negotiation, planning and scheduling, financial, optimization (multiobjective),environmental and diagnosis. Other plug-in modules can be added in the future to contemplate further functionalities. The next sections focus on three of them (environmental, financial, negotiation) that provide a challenging insight into the level of integration achieved for the whole SC performance optimization.

3.4 Environmental Module

Environmental considerations in the SC are necessary because industrial products most often reach the client through a variety of steps that are subject to strict environmental regulations. Moreover, these requirements migrate upwards through the SC and create a need for flow of environmental information. An adequate methodology to systematize this information and provide a vehicle for environmental impact minimization is the life-cycle assessment (LCA). The LCA approach has been adapted for the SC environmental assessment and improvement in this module [49]. The methodology used is summarized next. Let us consider the elementary SC shown in Fig. 3.7. It contains all the basic constituents of a generic SC in a simplified way, but although simple permits the representation of a variety of scenarios. The assumptions made in this base case study will

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Figure 3.7 Elementary supply chain representation utilized in the environmental module base case study

give an insight into the characteristics of the model contained in the environmental module. It should be observed that a high degree of aggregation is assumed in this SC representation so that energy and material streams are reduced to a minimum. This assumption implies that this SC representation is the result of a detailed modeling at the individual agent in the network, for instance, the manufacturer agent. Now let us consider Pml as the selected product of interest for LCA evaluation. This product leaves the factory as seen in Fig. 3.7. Then, the purpose of this study is to obtain an eco-label for this product in terms of environmental burden emissions associated to it following the LCA methodology guidelines (goal and scope, inventory analysis, impact assessment, integration phases) applied to the SC system. The first phase of LCA identifies the functional unit (product or process). This “functionality”can always be expressed as an equivalent product amount (in kg or MJ, according to the nature of the product) that will facilitate later calculations. The system boundaries are indicated in Fig. 3.7 (although in some cases it will be necessary to go deeper inside these boundaries to perform internal calculations to find environmental values for the global streams across the boundaries). Next, the inventory phase of manufacturing (the source block of product Pml) takes place, where the input streams Ps12 and Ps2 data, the emissions represented by Wm and data related to the products Pml and Pm2 are tabulated. Additionally, inputs and emissions downstream the manufacturing agent (Wo, Wu and Ww) are also considered. A key issue in inventory calculation is to establish the allocation policy for environment load associated to each product in each SC echelon. If causal relationship between inputs, outputs and emissions are known with certainty, inventory calculation can be easily done without need of an allocation procedure. Otherwise, the following general expression can be used for allocation at each SC echelon:

where Pk represents the stream of product k and vk is the corresponding eco-vector associated to product k. W . Y, is the waste stream weighted by its eco-vector, F, . vs is an input stream multiplied by its eco-vector and Pp . vpis the corresponding output stream weighted by its eco-vector vp.Finally, 6 and fop are allocation factors depending on the allocation policy (e.g.,mass allocation, energy allocation). Allocation to the chain left side of manufacturing (super supplier, supplier 1, supplier 2) is also analyzed in the same way as for the manufacturing case. This procedure is called forward allocation (Fig. 3.8) because environmental load is carried from left to right, that is in the same direction as the material flow in the SC. Following the LCA philosophy, the environmental module also considers a backward allocation (Fig. 3.9) that is in the opposite direction to the SC material flow. For instance, the manufacturer is also responsible for the environmental impact generated by this product after manufacturing, that is, along other processes in which it participates, during its use, and finally, during the waste management and treatment of the generated residues. Recycle processes and streams are treated by considering that the associated environmental load is included into the supplier LCA assessment. The model (Fig. 3.7) cuts the P, stream, thus P, and w,now include the inputs and the emissions for the

-------Figure 3.9

Backward allocation

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recycling process plus the inputs and emissions for the supplier 1, respectively.The environmental load associated to stream P, is considered to be zero.

3.4.1 Implementation Considerations

The user asks the system for an eco-label (ecological card). This eco-label can be expressed as a set of environmental loads as well as a set of environmental impacts. The system offers a table to enter data. These data belong to the following categories: inputs, emissions, products and functional unit, all referred to the main production process. This table would correspond to the manufacturing block in Fig. 3.7. Moreover, the system offers another table to introduce inputs and emissions associated to other processes such as those described as backward allocation. According to the data entered, the system generates additional input data tables to be filled-up by the user with inputs, emissions, products and calculation basis for each new table. These new tables would correspond to the blocks on the left to the manufacturing block in Fig. 3.7. Next, according to the kind of data entered in the tables, there are two types of calculation procedures. The tables whose inputs are all elementary flows must be calculated first. Otherwise, tables not having some elemental input have to be calculated afterwards. It is important to maintain the correct precedence in such a way that calculations follow the flow sheet from left to right. Finally, a table that contains all the information entered to the system is built. With the final table, the life cycle assessment calculations are made using data saved in an impact category table and a coefficients impact table. The Unified Modeling Language (UML) representation [SO]has been used to build the environmental module. The use case diagram shown in Fig. 3.10 summarizes the functionality of the module.

3.4.2 Industrial Testing

The environmental module has been tested in a real SC associated to automotive parts manufacturing. Specifically, the environmental impact associated to a certain component was evaluated and improvements were proposed to obtain the ecolabeling of the product. Once selected the functional unit for the product chosen, the inventory analysis was carried out from the information collected on raw material consumption, emissions and product(s). In the impact assessment phase, with the inventory analysis results some impact indexes were calculated for the following categories: 0 0

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eco-toxicological impact photochemical oxidant formation acidification eutrophication.

Then allocation of environmental load was carried out satisfactorily backwards and forwards the supply chain. This permitted the maintenance of registers (eco-labeling) for each product. This register may give the manufacturer a substantial increase of penetration in the market. Moreover, the manufacturer can reduce the environmental impact of its products by selecting the “most ecological”supplier and/or modifymg the process to reduce emissions, This could be done by incorporating other modules (planning, financial and optimization) in the final decision making.

3.5 Financial Module

The purpose of the financial module (FM) is to bridge the existing gap between supply chain financial decisions and production management by providing a common framework for integrated decision making that permits an optimum cash management thus avoiding “blind” financial/production disaggregated decision making occurring in industrial practice.

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The methodologies currently used in production planninglscheduling try to optimize some performance measure without consideration of cash availability. Then, the output solution of the scheduling-planning model tries to fit the finances in an iterative trial and error procedure [Sl]. This procedure (called sequential procedure) usually incurs in substantial debt and has to pledge receivables (financialtransaction of high cost to the manager). Moreover, the lack of synchronization between cash inflows and outflows results in cash balance fluctuations, which can be alleviated by considering the cash flows simultaneously with production decisions. To achieve integration, the budgeting variables of liabilities and exogenous cash are calculated as a function of production planning and scheduling variables. Namely liabilities at a specific time period are a function ofthe cost ofpurchasingraw materials,the cost of materials processing and the cost of having to purchase part of the final product from another supplier or another plant. Exogenous cash flow incurred in every time period is due to the sale of products. The detailed formulation can be found in Refs. [51,52]. In summary the proposed methodology contemplates:

0 0 0

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production expenses during the week consider an initial stock of raw materials and products, an initial working capital is considered, a short-tem financing source is represented by a constrained open line of credit, production liabilities incurred in every week period due to buy of raw materials, exogenous cash-flows due to sale of products, a portfolio of marketable securities is also considered.

3.5.1 Financial Module Interaction with the Multiagent System

The financial module constitutes the supporting tool for financial decisions within the multiagent system framework in a coordinated way with other decisions affecting the whole supply chain. This module permits coordination and integration of financial and operational decisions by exploiting the advantages offered by the multiagent system described previously. The structure proposed for the integration of the financial module with MASC is shown in Fig. 3.11. The FM will be used by the SC central agent to identify the best opportunities for investment and financing the SC, as well as to evaluate the impact of operational decisions in the manufacturer’s economy. The real supply chain is modeled and represented by the multi agent system. The central agent interacts with the FM in order to maximize the net profit for a given budget provided by the budgeting model that uses the specific information given by the scheduling and planning model module for two sets of time periods. The first time period set corresponds to the scheduling and planning period, while the second set goes beyond the end of the planning horizon up to one year budgeting (see Fig. 3.12). It is important to note that the model incorporates a number of subjective constraints to allow for different profiles in financial risk management.

3.5 Financial Module

3.5.2 Testing Results in Industrial Scenarios

The benefits obtained by incorporating the financial module in the SC decision making have been assessed at different levels. First, the use of an integrated model coordinating financial and operational decisions has been tested in a single manufacturer, specifically, a plant producing five different products and two different raw materials. Product switch-over basically

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depends on the nature of both substances involved in the precedent and following batch (precedence constraints). Cleaning times are constrained by the product sequence. Comparative results obtained from the application of a sequential approach and those achieved with the FM are shown in Fig. 3.13. It can be seen that the integrated solution incurs less debt and avoids having to pledge receivables which means a 20 % savings for the firm. The second case study deals with the SC of a large fruit cooperative made up of raw materials suppliers, manufacturing (fruit selection, clearing, and packaging), warehouses, distribution centers and clients. Here a deeper level of integration in the SC management was contemplated. Since this supply chain is driven by the raw materials arrival rather than by the customer demand, a main objective was to use the forecasting module (FOREST) to estimate the raw material arrival time thus reducing operational uncertainty. A second important objective was to integrate financial and production aspects linked to cash flow management across the supply chain. Both modules were used on-line through the Web, thus achieving high visibility (customer on-line information) and improved service (increased customer satisfaction). The net results were an increase of sales about 15 % and diminution of stocks about 20 % (saving of two million euro per campaign).

3.5 Financial Module

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3.5.3 Negotiation Module

When adopting an agent-oriented view of computation, it is readily apparent that most problems require or involve multiple agents as indicated before. Moreover, these agents will need to interact with one another, either to achieve their individual objectives or to manage the dependencies that follow from being situated in a common environment. These interactions can vary from simple information interchanges, to requests for particular actions to be performed and on to cooperation (working together to achieve a common objective) and coordination (arranging for related activities to be performed in a coherent manner). However, perhaps the most fundamental and powerful mechanism for managing interagent dependencies at run-time is negotiation - the process by which a group of agents come to a mutually acceptable agreement. Automated negotiation among autonomous agents is needed when agents have conflicting objectives and desire to cooperate. This typically occurs when agents have competitive claims on scarce resources, not all of which can be simultaneously satisfied. These resources can be commodities, services, time, money, etc. Specifically, the main objective of the negotiation module developed is to enhance profitable partnerships in SCs. This goal is divided into the following steps: 0

0 0

0

Identify the most profitable relationships and enhance them. Integrate supply contract negotiations into supply chain management. Evaluate different negotiation tactics according to the SC performance and partners behaviors. Develop learning techniques.

The proposed approach [53] takes into account the tradeoff between the quality of the offers made to customers, i.e., the level of satisfaction perceived by the client, and the expected profit to be achieved in the short term operation of the SC. Therefore, a twostage stochastic formulation is derived that considers the uncertainty associated with reactions to future demand, in order to compute a set of Pareto optimal solutions to the proposed problem. Each of these solutions comprises an SC schedule and a set of values for the parameters of the offers. Through comparison of the Pareto curve and the solution that would be obtained without negotiation, a set of offers representing contracts that are desirable from the supplier’s perspective is obtained. This set of values may be offered by the supplier in order to reach an agreement with the customer during the negotiation procedure. This approach facilitates a rational negotiation, in the sense that it enables the negotiator to simultaneously process much more data related to production and transport plans and customer preferences, thus avoiding having to rely exclusively on the negotiator’s beliefs and interests.

3.5 Financial Module

3.5.4 Motivating Example

Inspired in a real industrial case, a relatively simple linear SC is considered to illustrate the performance and results of the negotiation module. It entails a batch plant which produces three different products. The manufacturer has a warehouse (W) at which the products are stored when they leave the plant. As the plant has a limited capacity and is imagined to be next to the factory, no transport is necessary. There is also a distribution center (DC) from which customers are served. Three occasional orders are met if the DC has some amount of the product requested in stock, provided that it is not planning to use that stock to satisfy contractual requirements. If an order has only been partially met, there is no penalization but that particular sale will not be able to be carried out at a later point, when the merchandise reaches the DC. Moreover, the possibility of signing a contract with a customer is considered. The main objective of the proposed example is to observe how most of the activities executed by a SC can be integrated using the proposed negotiation model, rather than to study very complex structures involving many entities. The proposed approach provides a set of Pareto solutions to be used by the decision maker during the negotiation procedure (Fig. 3.14). There is a tradeoff between the expected profit and the quality of an offer sent to a customer, in this case the level of consumer satisfaction (CSat) attained by an offer, as well as the connection between customer relationship management (customer satisfaction) and production activities (schedules). For instance, for the stochastic Pareto solution the difference between the best-case and the worst-case values for CSat = 80 % is approximately 450 m.u. (20%), while the deterministic solution, shows, this difference equal to 1140 m.u. (55 %). Therefore, the stochastic treatment of the negotiation problem minimizes the impact of the uncertain environment by both increasing the expected profit and reducing the variability of the solution compared with the deterministic solution, which makes it very attractive from the perspective of the decision maker. Indeed more complex storage policies, plant flexibility, number of entities in the SC network and so on can be addressed using the same approach. In addition, since future predictions related to market behavior cannot be perfectly forecasted, a number of the parameters in the associated scheduling problem, such as product demands and prices, were considered to be uncertain parameters. The two-stage stochastic formula developed has allowed this situation, commonly found in practice, to be handled properly, which thus reduces the impact of the uncertainty on what profit is achieved in short-term planning. The usefulness of signing contracts as a way of reducing uncertainty has also been shown by means of the aforementioned stochastic formulation. The proposed strategy represents a method for facilitating rational negotiation, in the sense that it enables the negotiator to process a far greater amount of production, transport planning and customer preference data simultaneously and thus prevents beliefs and interests from being relied on exclusively.

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3.6 Multiagent Architecture Implementation and Demonstration

The multiagent system framework has been implemented as a Web service. Each agent receives and transmits relevant information for the optimization of the SC. All agents depend on a central agent that coordinates information handling and that may modify a particular agent's decision should it be necessary for the whole SC negotiation optimization. Web services (agents) are programmed in C# using the tools of Visual Studio.NET by Microsoft, while XML under the SOAP protocol is used for communication between them. Each agent may use distributed modules (forecasting, planning and scheduling, optimization, environmental, financial and diagnosis) to support his activities.

3.6.1 Manager Agent System

The manager agent system has a central agent that coordinates relevant information flow from/to the other agents in the network, and will eventually take decisions for

3.6 Multiagent Architecture Implementation and Demonstration

the whole SC optimization. This way, the SC behavior can be accommodated to a full range of scenarios from a decentralized operation to a fully centralized management where the director (central) agent has the control on every individual SC activity. In general, the central agent will perform the following functionalities: 0 0 0

0 0 0

decision support, real-time information on SC activities, SC performance optimization, simulation and performance indicators calculation, client/supplier selection, graphic representation (Pert, Gantt).

These and other functionalities (forecasting, environmental assessment, financial assessment, SC retrofit, etc.) will require the use of the appropriate module. Figure 3.15 shows the manager agent utility system. Main performance indicators and expected ratio are indicated on Table 3.2. Obviously, the expected ratio will depend on the SC original situation and the type of SC. The table should be continuously updated once intermediate objectives are achieved. A key component in the system architecture is the database that must be made available to each agent locally. For instance, the basic design of the database of the central agent is shown in Fig. 3.16 for the specific scenario contemplating retailers of four different items (computers, bakery, books, and furniture).

3.6.2 Graphic Interface

The graphic interface has a double objective. On the one hand a graphic user interface (GUI) is needed for the real client that requires interaction with the multiagent system (specific demand implementation, request of information). Otherwise, a graphic interface is needed for the SC manager. In this regard a client GUI is provided to perform the SC simulation. The SC client makes the command through the Web application shown in Fig. 3.17, which enables him to communicate with the central agent who consequently

Elementary indicator

Ratio expected (min. to max. %)

I1 Modeling time reduction 12 Forecast accuracy 13 Inventory reduction 14 Means of production capacity utilization increase I5 Cycle process time improvement I6 Supply chain costs reduction 17 Delivery performance improvement

60-80 % 15-65% 20-85 % 5-60% 15-70% 10-30% 15-45 %

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3.6 Multiagent Architecture Implementation and Demonstration

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will update the database. Once the client signs up in the Web service and provides the information requested (Fig. 3.18) he has access to the services and information offered (Fig. 3.19).

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demand generator supplied with different patterns (stochastic, probability distribution functions), connectivity with the central agent to receive/transmit messages, graphic user interface.

The interfaces created for the rest of the agents can be seen in the following figures. The central agent interface is shown in Fig. 3.20. It collects all information from the database (on products, transport, warehouses, factories, environmental impact, financial, etc.) and permits simulation (at the left panel) and optimization (at the right panel) of the SC: Multiobjective optimization is carried out using any of the solvers offered in the center panel. The forecasting module interface is shown in Figure 3.21 giving the demand forecast in terms of dates and amounts of specific products. The environmental module interface appears in Fig. 3.22. Here the left panel permits the input of raw materials needed for each specific product and the right panel has the commands to perform the life cycle analysis of the entire SC. Figure 3.23 shows the financial module interface. At the left initial assets, liability and equity can be introduced, which appear optimized at the right after optimization under the selected constraints at the center (minimum cash, debt, interest rate, etc). Finally, the negotiation agent interface can be observed in Fig. 3.24 for a certain product. It shows the evolution towards satisfaction for both, customer

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and supplier once the negotiation is initiated in terms of quantity, price and delivery time. The planning and scheduling module is not shown, since it is fully described elsewhere [54,55].The same can be said regarding the real-time monitoring and diagnosis module [5G]. 3.6.3 Demonstration

The multiagent system described has been tested in industrial scenarios. Some of the scenarios have been partially presented in previous sections of this chapter to show relevant components of the SC system. A global on-line through the Web demonstration took place recently at the CHEM Users Committee held in Lille, France [57]. Here operational tactical and strategic activities were shown to successfully cooperate in the SC, from demand forecasting to diagnosis, control and retrofit considerations. The demonstration contemplates the whole SC of a cosmetics manufacturing group of enterprises with the following characteristics:

3.7 Concluding Remarks

0 0 0

multiproduct manufacturing plants located in Europe (Oviedo, Tarragona in Spain and one in Italy), United States (California and Florida) and Mexico (Queretaro), warehouses for final products, distribution centers from which customers are served, transport system for distribution to retailers and clients.

The demonstration is initiated by forecasting from historical data the procurement needs of specific products at one of the warehouses in France. A robust demand is obtained using the forecasting module. Then, the following real-time sequence of decisions and activities is carried out by the multiagent system: 0

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The negotiation module is used to select and agree the most satisfactory provider (the factory situated in Tarragona) for the specific products and in the amounts, prices and due dates envisaged. The environmental impact is assessed for the complete life cycle of the products contemplated by means of the environmental module described before. Financial evaluation is carried out, taking into account budgeting, cash flow and additional considerations provided by the financial module. The central agent collects all the preceding information and requests additional manufacturing data from Tarragona plant. Simulation of the whole SC is then carried out checking for feasibility. Finally, multiobjective optimization (profit, cash flow, debt, environmental impact, due dates) is realized. Optimum values are transmitted over the Web to the plant in Tarragona for manufacturing. The production planning and scheduling module calculates the optimal production schedule for the forecasted demand, which is automatically performed in the plant. An incidence occurs during plant operation (the reactor heating system breaks down). The monitoring and diagnosis module detects and isolates the fault. An alarm is issued and diagnosed. As a consequence, a rescheduling procedure takes place to find an alternative production route which is implemented again in realtime. The operator repairs the reactor which comes back to operation. The monitoring system reacts sending a new plan, which coincides with the original since it was optimum, resuming the plant operation using the repaired reactor.

3.7 Concluding Remarks

The supply chain of a manufacturing enterprise is, nowadays, a world-wide network of suppliers, factories, warehouses, distribution centers and retailers through which raw materials are acquired, transformed and delivered to customers. In this sense, the whole supply chain can be considered as a dynamic virtual enterprise: by the adequate management of its supply chain, the manager can easily find adequate solutions to cope with the dynamics of its production scenario, which includes drastic

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and unexpected changes in materials or production resources availability, in the market conditions, or even in politics. This chapter has presented recent advancement on integrated solutions for on-line supply chain management. Specifically, an environment is presented that encompasses the SCM characteristics identified in a preliminary review of the state of the art. It reported the integration of negotiation, environmental, forecasting and financial decisions in a reactive mode as an example of a new technology that may lead to better, fully integrated, easier to use and more comprehensive tool for SCM. A brief description of the architecture and functionalities of the solution implemented has also been presented.

Acknowledgements

The authors wish to acknowledge support of this research work from the European Community (Contract No GIRD-CT-2001-004GG),the CICyT-MEC (project No DPI2003-0856),and the CIRIT-Generalitat de Catalunya (project No 1-353).Contribution from Fernando Mele, Gonzalo Guillen and Francisco Urbano, predoctoral students of the research group CEPIMA is also much appreciated (Chemical Engineering Department, Universitat Politecnica de Catalunya).

References

6 W u ] . Ulieru M. Cobzaru M. N o m c D. Agent-

1 Vidal C.]. Goetshalckx M . Strategic

2

3

4

5

Production-Distribution Models: A Critical Review with Emphasis on Supply Chain Models. Engineering Journal Operational Research 98 (1997)p. 1-18 Applequist G. E. Pekny]. F. Reklaitis G. V. Economic Risk Management for Design and Planning of Chemical Manufacturing Supply Chains. Computers and Chemical Engineering 24 (2000) p. 2211-2222 Badell M. Romero]. Huertas R. Puigjaner L. Planning, Scheduling and Budgeting ValueAdded Chains. Computers and Chemical Engineering 28 (2004) p. 45-61 W u ] . Cobzaru M. Ulieru M. Nome D. SCWeb-CS: Supply Chain Web-Centric Systems. Proceedings of the International Conference on Artificial Intelligence and SoftComputing, Bant, Canada (2000) pp. 501-507 Grossmann I . E. McDonald C. M. Foundations of Computer-Aided Process Operations: A View to the Future Integration or R&D Manufacturing and the Global Supply Chain, CACHE Cop., Austin, Texas 2003

7

8

9

10

11

Based Supply Chain Management System: State-of-the-Artand Implementation Issues, in Proceedings of European Symposium of Computer.Aided Process Engineering-14 (ESCAPE-14),Lisbon, Portugal, Elseiver, Amsterdam 2004 Lee H . L. Billington C. Managing Supply Chain Inventory: Pitfalls and Opportunities. Sloan Management Review, Spring (1992) p. 65-73 Geofion A. M . Powers R. F. Facility Location Analysis is Just the Beginning. Interfaces 10 (1980) p. 22-30 Erengunc S. S. Simpson N. C. Vakharia A,]. Integrated Production/Distribution Planning in Supply Chain: An Invited Review. European Journal of Operation Research 115 (1999) p. 219-236 Williams]. F. Heuristic Techniques for Simultaneous Scheduling of Production and Distribution in Multi-Echelon Structures: Theory and Empirical Comparisons. Management Science 27 (1981) p. 336-352 Williams]. F. A Hybrid Algorithm for Simultaneous Scheduling of Production and Distribution in Multi-Echelon Structures. Management Science 29 (1983)p. 77-92

References I 7 2 9 12 Ischii K. K. Takahashi Muramatsu R. Inte-

13

14

15

16

17

18

19

20

21

22

23

24

grated Production Inventory and Distribution Systems. International loumal of Production Research 26 (1988) p. 473-482 Cohen M. A. Lee H. L. Resource Deployment Analysis of Global Manufacturing and Distribution Networks. Journal of Manufacturing and Operations Management 2 (1989) p. 81-104 Cohen M. A. Moon S. Impact of Production Scale Economizes Manufacturing Complexity and Transportation Costs on Supply Chain Facility Networks. Journal of Manufacturing and Operations Management 3 (1990) p. 35-46 Newhart D. D. Stott K. L. Vasko F . J . Consolidating Product Sizes to Minimize Inventory Levels for a Multi-Stage Production and Distribution Systems, Journal of the Operational Research Society 44(7) (1993) p. 637-644 Arntzen B. C. Brown G. G. Harrison T. P. Trafton L. L. Global Supply Chain Management at Digital Equipment Corporation. Interfaces 25 (1995) p. 69-93 Voudouris V. T. Mathematical Programming Techniques to De-bottleneck the Supply Chain of Fine Chemical Industries. Computers and Chemical Engineering 2O(Suppl.) (1996) p. S1269-1275 Camm J. D. Chatman F. A. Evans]. R. Sweeney D. J. Wegryn G. W. Blending ORlMS Judgement and GIs: Restructuring P&G's Supply Chain. Research 27 (1997) p. 120-142 Papageorgiu L. Rotstein G. Shah N. Strategic Supply Chain Optimization for the Pharmaceutical Industries. Industrial and Engineering Chemistry Research 40 (2001) p. 275 Davis T.Effective Supply Chain Management. Sloan Management Review Summer (1993) p. 35-46 Cohen M. A. Lee H. L. Integrated Analysis of Global Manufacturing and Distribution Systems: Models and Methods. Operations Research 36 (1988) p. 216-228 Suoronos A. Zipkin P. Evaluation of One-forOne Replenishment Policies for MultiEchelon Inventory Systems. Management Sciences 37 (1991) p. 68-83 Pyke D. F. Cohen M. A. Performance Characteristics of Stochastic Integrated Production: Distribution Systems. European Journal of Operational Research 68 (1993) p. 23-48 Pyke D. F. Cohen M. A. Multi-Product Integrated Production-Distribution Systems. European Journal of Operational Research 74(1) (1994) p. 18-49

25

26

27

28

29

30

31

32

33

34

35

36

37

Lee H. L. Padmanabhan V. Whang S. Information Distortion in a Supply Chain: The Bullwhip Effect. Management Science 43 (1997) p. 546-558 Owen S. H . Daskin M. S. Strategic Facility Location: A Review. European journal of Operation and Research 111 (1998) p. 423-447 Mobasheri F. Orren L. H . Sioshansi F. P. Scenario Planning at Southern California Edison. Interfaces 19 (1984) p. 31-44 Mufueyj. M. Generation Scenarios for the Towers: Instrument System. Interfaces 26 (1996) p. 1-15 Jenkins L. Selecting Scenarios for Environmental Disaster Planning. European Journal of Operation and Research 121 (1999) p. 275-286 Gupta A. Maranas C. D. McDonald C.M. Mid-Term Supply Chain Planning Under Demand Uncertainty: Customer Demand Satisfaction and Inventory Management. Computers and Chemical Engineering 24 (2000) p. 2613-2621 Tsiakis P. Shah N. Pantelides C. C. Design of Multi-Echelon Supply Chain Networks Under Demand Uncertainty. Industrial and Engineering Chemistry Research 40 (2001) p. 3585-3604 Lababidi H . M. S. Ahmed M. A. Afatigi I. M. EL-Enzi A. F. Optimizing the Supply Chain of a Petrochemical Company Under Uncertain Operating and Economic Conditions. Industrial and Engineering Chemistry Research 43 (2004) p. 63-73 GuiflCn G. Bonfiff A. Esputia A. Puigjaner L. Integrating Production and Transport Scheduling for Supply Chain Management Under Market Uncertainty, in Proceedings of European Symposium of Computer-Aided Process Engineering-I4 (ESCAPE-14),Lisbon, Portugal, Elseiver, Amsterdam 2004 Baumof W. J. The Transactions Demand for Cash: An Inventory Theoretic Approach. The Quarterly lournal of Economics 66 (1952) p. 545-556 Miller M. H. Orr R. A. A Model of the Demand for Money by Firms. The Quarterly Joumal of Economics 80 (1966) p. 413-435 Christy D. P. Grout J. R. Safeguarding Supply Chain Relationships. International lournal of Production Economics 36 (1994) p. 233-242 Romero J. Badeff M. Bagajewicz M. Puigjaner L. Integrating Budgeting Models into Scheduling and Planning Models for the

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I

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38

39 40

41

42

43

44

45

46

Chemical Batch Industry. Industrial and Engineering Chemistry Research 42 (2003) p. 6125-6134 Badell M. Romero]. Puigjaner L. Joint Financial and Operating Scheduling/Planning in Industry, in Proceedings of European Symposium of Computer-Aided Process Engineering-14 (ESCAPE-14),Lisbon, Portugal, Elseiver, Amsterdam 2004 Forrester]. W. Industrial Dynamics. MIT Press, Cambridge, MA 1961 Towhill D. R. Industrial Dynamics Modeling of Supply Chains. Logistics Information Managment 9(4) (1996) p. 43-56 Backs T. Bosgra D. Marquardt W. Towards Intentional Dynamics in Supply Chains Conscious Process Operations in Pekny, J.F. and Blau G.E. (Eds.) Proceedings of Third International Conference on Foundations of Computer-Aided Process Operations, AIChE, New York, (1998) p. 5 Perea-Lopez E. Grossmann I. Ydstie B. E. Tcihmassebi T. Industrial and Engineering Chemistry Research 40 (2001) p. 3369-3383 Brown M. W. Rivera D. E. Carlyle W. M. et al. A Model Predictive Control Framework for Robust Management of Multi-Product, Multi-Echelon Demand Networks. In Droceedings of 15th IFAC world Congress, Barcelona, Spain, 2002 Mele F. D. Forquera F. Rosso E. Basualdo M. Puigjaner L. A Comparison Between Chemical and Model Predictive Control Over Supply Chain Dynamic Model, in Proceedings of 9th Mediterranean Congress of Chemical Engineering, Expoquimia, Barcelona, Spain 2002 Mele F. D., Esputia A., Puigjaner L. Supply chain management, through combined Simulation-Optimisation approach, in Proceedings ESCAPE-15 (L. Puigjaner, A. Espuna, Eds.), Elsevier, Amsterdam, (2005) p. 1405-1410. Garcia-Beltrdn C. and Feritil S. Multi-AgentBased Decision System for Process Reconfiguration, in Latino-American Control Conference, Guadalajara, Mexico, 2002

47 Lin J . You]. Smart Shopper: An Agent-

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49

50 51

52

53

54

55

56

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Based Web Approach to Internet Shopping. IEEE Trans Fuzzy Systems 11 (2003) p. 226-237 Report 02-2 Final Specifications of the Supply Chain Multi-Agent Architecture. Project 1-303 (GICASA-D) 2003 Report D19 Environmental Impact Considerations Based on Life Cycle Analysis. Project GlRD-CT-2000-00318 2003 Muller P. A. Modelado de Objetos con UML. Ediciones Gestion 2000 S.A. Barcelona 1997 Romero ]. Badell M. Bagajewicz M. Puigjaner L. Integrating Budgeting Models into Scheduling and Planning Models for the Chemical Industry. Industrial and Engineering Chemistry Research 42 (2003) p. 6125-6134 Badell M. Romero ]. Huertas R. Puigjaner L. Planning, Scheduling and Budgeting valueaided chains, Computers Chemical Engineering 28 (2004) p. 45-61 Guilltn G. Pina C. Espuria A. Puigjaner L. Optimal Offer Proposal Policy in an Integrated Supply Chain Management Environment. Industrial and Engineering Chemistry Research 44 (2005) p. 7405-7419 Puigjaner L. Handling the Increasing Complexity of Detailed Batch Process Simulation and Optimization. Computers and Chemical Engineering 23(Suppl.) (1999) p. S929-S943 Arbiza M. I. Cantdn Espuria]. A. Puigjaner L. Objective-Based Schedule Selector: a Rescheduling Tool for Short-term Plan Updating, in Barbosa-Povoa A. (Ed.) European Symposium on Computer-Aided Process Engineering-14, Lisbon, Portugal CDROM 2004 Ruiz D. Benqlilou C. Nougub]. M.Puigjaner L. Proposal to Speed Up the Implementation of an Abnormal Situation Management in the Chemical Process Industry. Industrial and Engineering Chemistry Research 41 (2002) p. 817-824 Puigjaner L. Real-Time, Optimization of Process Operations: An Integrated Solution Perspective. CHEM User's Committee Seminar, Lille, France, 2004

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8 I731

4 Databases in the Field of Thermophysical Properties in Chemical Engineering Richard Sass

4.1 Introduction

Process synthesis, design, and optimization, and also detail engineering for chemical plants and equipment depend heavily on availability and reliability of thermophysical property data of pure components and mixtures involved. To illustrate this fact we can analyze the needs for one of the essential process engineering processes, the separation of fluid mixtures. For the design of such a typical separation process, e.g., distillation, we require thermodynamic properties of mixture, in particular for a system that has two or more phases at a certain temperature or pressure. We require the equilibrium constants of all components in all phases. The quality of data inside the data calculation modules is essential and can have extensive effects. Inaccurate data may lead to very expensive misjudgements whether it is to proceed with a new process or modification of it or not to go ahead. Inadequate or unavailable data may cause a promising and profitable process to be delayed or in the worst case be rejected, only for the reason that it was not properly modelled in a simulation. Another potential danger, partially generated by the marketing statements of simulation software producers, is that the credibility of the results of a thermophysical model calculation generated by computer software is very high, even if the result is wrong. So the expert has the duty to prove that the most sophisticated software will not lead automatically to the most cost-effective solution in order to save effectively energy, if there is not a background with an accurate database of physical and thermodynamic data.

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA,Weinheim ISBN: 3-527-30804-0

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4 Databases in the Field of Thermophysical Properties in Chemical Engineering

4.2 Overview of the Thermophysical Properties Needed for CAPE Calculations

Without access to a numerical database and if the available literature and notes do not contain a value, the only possibility is to measure properties or to calculate them with a group contribution method or another estimation routine. The first alternative is expensive and time-consuming; the second one will produce data with unknown reliability in most cases, especially when molecules with two or more nonhydrocarbon functional groups in near proximity are involved. With the help of thermophysical databases with experimental values of pure component and mixtures, this problem can be solved. A description of what data are needed and which types of data are available follows. The properties required for the design of a thermal or chemical process depends upon the specific case and the temperature, pressure and concentration range. A short overview of the data needed in the simulation and design of processes is given in Table 4.1. Table 4.1

Important categories o f property data

Property type

I Specific properties

Phase equilibria

Boiling and melting points, vapor pressure, fugacity and activity coefficients, solubility (Henry’s constants, Ostwald or Bunsen coefficients)

PVT behavior

Density, volume, compressibility, critical constants

Caloric properties

Specific heat, enthalpy, entropy

Transport properties

Specific heat, latent heat, enthalpy, entropy, viscosity, thermal conductivity,ionic conductivity, diffusion coefficients

Boundary properties

Surface tension

Chemical equilibrium

Equilibrium constants, association/dissociation constants, enthalpies of formation, heat of reaction, Gibbs energy of formation, reaction rates

Acoustic

Velocity

Optical

Refractive index, polarization

Safety characteristics

Flash point, explosion limits, autoignition temperature, minimum ignition energy, toxicity, maximum working place concentration

Molecular properties

Virial coefficients, binary interaction parameters, ion radius and volume

~~

4.4 Examples of Databasesfor Jhermophysical Properties

4.3 Sources of Thermophysical Data

For years, the most popular way to find thermophysical property data was to take a look inside favorite book collections, starting with the Handbook of Chemistry and Physics up to data collection handbooks issued by data producers as DIPPR [I]and TRC [2], the Landolt-Bomstein [3] and the DECHEMA Chemistry Data Series [4]. Despite the inconvenience in using handbooks for data searches, a lot of users still appreciate the fast access to the data and, in comparison to the databases, relatively moderate price. An overview by Hochschule Merseburg University of Applied Science gives a list of available books and publications on thermophysical property data

(www.fh-merseburg.de/PhysChem).

Nowadays, mainly under the pressure of having data available in a short time for calculations and due to the full-time access to networks, the easiest way to find data is with access to databases, accessible or as in-house versions or on-line via hosts or via the World-Wide Web. Two types of collections and/or databases can be distinguished: bibliographical ones and numerical ones. A bibliographical collection or database is a literature source containing only references. Knowing the chemical species one needs data for, one can find literature references containing that data. Afterwards one has to go to the library and look up the different references to get the data. A numerical database or collection typically contains the literature references as well as measurement data. The numerical data could be accessed and used directly. In some cases this approach is combined with a critical review and selection of the available data, so that only thermodynamically consistent and proven data are contained in the collection. The approach could also be combined with model parameter fitting and recommendation, so that end-users only have to transfer the recommended parameters into their applications to implement a tested model with a defined reliability over all known measurement data points. In the following, a survey on the existing and still maintained collections and databases on solutions is given.

4.4 Examples of Databases for Thermophysical Properties

Due to the fact that dozens of sources for thermodynamic data are now available on the Web, only a few major providers will be mentioned in this chapter. To have access to a larger overview about what is available on the Web, a look at the pages, e.g., of the University of Illinois should be considered (http://tigger.uic.edu/-mansoori/Thermodynamic.Data.and.Property-htl) . A few examples for the largest and most famous databases are shown in Table 4.2. Three examples of databases are described as follows.

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4 Databases in the Field ofThermophysical Properties in Chemical Engineering Table 4.2

Provider list for thermophysical data

Producer

I

Database name

I

URL

~

DECHEMA

DETH E RM

www.dechema.de/detherm-lang-en. html

DDBST

DDB

www.ddbst.de/new/Default.htm

NIST

Properties of fluids

http://properties.nist.gov/ ~

NIST IUPAC-NIST K&K Associates

FIZ Chemie

I

Chemistry WebBook Solubility Database

~~

I http://srdata.nist.gov/solubility/

Thermal Resource Center www.tak2000.com/ INFOTHERM ties Database

MDL

~~

http://webbook.nist.gov/chemistryl

www.fiz-chemie.de

www.ceram.co.uk/thermet.html

Technical database

www.dnv.com/software/all/api/index.asp

CrossFire Beilstein

www.mdl.com/products/knowledge/crossfire-beilstein/

TPC, Academy of Science THERMAL Russia

www.chem.ac.m/Chemistry/Databases/ THERMAL.en.htm1

AIChE

DIPPR

http://dippr.byu.edu/

G&P Engineering Software

MIXPROPS

www.gpengineeringsoft.com/pages/pdtmixprops.htm1

G&P Engineering Software

PHYPROPS

www.gpengineeringsoft.com/pages/pdtphysprops.htm1 www.crct.polymtl.ca/fact/index.php

Ecole Polytechnique de Montreal S . Ohe

Fundamental Physical Properties

http://data-books.com/bussei-e/bs-index.1

Prode

Prode Properties

www.prode.com/en/ppp.htm

NEL

I PPDS

www.ppds.co.uk/Products/

http://thermodata.online.fr Science

Database

http://chinweb.ipe.ac.cn/

4.4 Examples ofDatabasesfor Thermophysical Properties

4.4.1 NIST Chemistry WebBook

The NIST Chemistry WebBook provides access to data compiled and distributed by NIST under the Standard Reference Data Program [5]. The NET Chemistry WebBook [GI contains: 0

0

0 0 0 0 0

0

0

thermochemical data for over 7000 organic and small inorganic compounds: - enthalpy of formation - enthalpy of combustion - heat capacity - entropy - phase transition enthalpies and temperatures - vapor pressure reaction thermochemistry data for over 8000 reactions: - enthalpy of reaction - free energy of reaction IR spectra for over 16,000 compounds; mass spectra for over 15,000 compounds; UV/V is spectra for over 1600 compounds; electronic and vibrational spectra for over 4500 compounds; constants of diatomic molecules (spectroscopic data) for over GOO compounds; ion energetics data for over 16,000 compounds: - ionization energy - appearance energy - electron affinity - proton affinity - gas basicity - cluster ion binding energies thermophysical property data for 34 fluids: - density, specific volume - heat capacity at constant pressure (C,) - heat capacity at constant volume (C,) - enthalpy - internal energy - entropy - viscosity - thermal conductivity - Joule-Thomson coefficient - surface tension (saturation curve only) - sound speed.

Data on specific compounds in the Chemistry WebBook based on name, chemical formula, CAS registry number, molecular weight, chemical structure, or selected ion energetics and spectral properties can be searched for.

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4 Databases in the Field OfThermophysical Properties in Chemical Engineering

4.4.2 DETHERM

The DETHERM [7] database provides thermophysical property data for about 24,000 pure compounds and 14G,OOO mixtures. DETHERM contains literature values, together with bibliographical information, descriptors and abstracts. At the time 5.2 million data sets are stored. DETHERM is a collection of data packages produced by well known providers of thermophysical packages, unified under a common graphical user interface. The database files in Table 4.3 are part of DETHERM. An example for the actual possibilities for presentation of the results is seen in Fig. 4.1. Table 4.3

Content of DETHERM ~

Dortmunder Datenbank DDB

'base equilibrium data

(ProJ Gmehling, University of Oldenburg)

1 I I

I

1 1 b

1 1

1

b 1 1 1 1

1

Vapor-liquid equilibria Liquid-liquidequilibria Vapor-liquid equilibria of low boiling substances Activity coefficients at infinite dilution Gas solubilities Solid-liquid equilibria Azeotropic data Excess properties Excess enthalpies Excess heat capacities Excess volume Pure component properties Transport properties Vapor pressures Critical cata Melting points Densities Caloric properties Others

Electrolyte data collection ELDAR (Prof: Barthel, University of Regensburg, LS Chemie IV)

Caloric data Electrochemical properties Phase equilibrium data PVT properties Transport properties

Thermophysical database INFOTHERM (FIZ CHEMIE)

PVT data Transport properties Surface properties Caloric properties Phase equilibrium data Vapor-liquid equilibria Gas-liquid equilibria Liquid-liquidequilibria Solid-liquidequilibria Pure component basic data

I 1 1 I

Dortrnunder Datenbank DDB

Phase equilibrium data

Thermophysical Parameter Database

Phase equilibria

COMDOR (Leuna GmbH in Cooperation with FIZ Chemie)

Excess enthalpies Transport and surface properties Caloric and acoustic data

Data Collection C-DATA (Institutfor Chemical Technic, Prag)

Twenty physicochemical properties for 593 pure components

Basic Database Bohlen BDBB (Sdchsische Olejnwerke AG Bohlen, now DOW Chemical)

Pure component database of the Sachsische Olefinwerke with chemical and physical basic data for 1126 pure substances (mainly for the fields of petroleum and coal chemishy)

Additional (DECHEMA e.V.)

Vapor pressures Transport properties 0 Thermal conductivities 0 Viscosities Caloric properties PVT data 0 PVT data 0 Critical data Eutectic data Solubilities Diffusion coefficients

4.4.3 DIPPR Database [i]

The major content of the database of the Design Institute for Physical Property Data (DIPPR), a subsidiary of the American Institute of Chemical Engineers (AIChE) [8], are mainly data collections of pure component properties but also data for selected properties of mixtures and the results of a project related to environmental, safety and health data. In total data of 1700 compounds in the database cover mainly the components of primary interest to the process industries. The special focus of the DIPPR database is to provide reliable data of thermophysical properties, including the temperature dependency of the properties, which are approved by technical committees, where industrial experts are involved in the design of the database and in the evaluation of the data. Table 4.4 gives an overview of the content of the DIPPR database. The use of these databases is meanwhile a standard option in the preparation of the process design. A bigger difficulty is the absence of thermophysical data for newer processes involving electrolytes and of solutions containing biomaterial. This specific topic will be explained in the next chapter.

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4 Databases in the Fieldof Jhermophysical Properties in Chemical Engineering

Figure4.1 Joint graphical display oftwo different LLE data sets in DETHERM for the system chlorobenzene/acetonitrile/water

Table 4.4

Properties in the DIPPR 801 Database [9]

Constant properties: property

Acentric factor

1 1.

Units

Auto ignition temperature

K

Dipole moment

Cm

Absolute entropy of ideal gas at 298.15 K and 1 bar

1 J (kmol K)-’

~

Lower flammability limit temperature

K

Upper flammability limit temperature

K

Lower flammability limit percent

1 V ~ %I in air

Upper flammability limit percent

Vol % in air

Flash point

K

Gibbs energy of formation for ideal gas at 298.15 K and 1 bar Standard state Gibbs energy of formation at 298.15 K and 1 bar

I J kmol-’ J kmol-’

4.4 Examples of Databasesfor Jhermophysical Properties Table4.4

Properties in the DlPPR 801 Database (9) (Fortsetzung)

Constant properties: property

Units

Net standard state enthalpy of combustion at 298.15 K

1 kmol-'

Enthalpy of formation for ideal gas at 298.15 K

J kmol-'

Enthalpy of fusion at melting point

1 kmol-'

Standard state enthalpy of formation at 298.15 K and 1 bar

J kmol-'

Heat of sublimation

J kmol-'

Liquid molar volume at 298.15 K

m' kmol-'

Melting point at 1 atm

IK

Molecular weight

kg krnol-'

Normal boiling point

K

Parachor

I-

Critical pressure

I

Radius of gyration

Im

Pa

Refractive index

-

Solubility parameter at 298.15 K

(1 t 1 - ~ ) 1 , 2

Standard state absolute entropy at 298.15 K and 1 bar

I J (kmol K)-'

Critical temperature

K

Triple point pressure

Pa

Triple point temperature

IK

Critical volume

m' kmol-'

van der Waals area

m2kmol-'

van der Wads reduced volume

m' kmol-'

Critical compressibility factor

-

Temperature-dependent properties: property

Units

Heat capacity of ideal gas

I

Heat capacity of liquid

1 (kmol K).'

Heat capacity of solid

1 (kmol K).'

Heat of vaporization

1 kmol-'

(kmol K).'

I

739

740

I

4 Databases in the Field of Thermophysical Properties in Chemical Engineering Table4.4

Properties in the DIPPR 801 Database [9] (Fortsetzung)

Temperature-dependentproperties: property

Liquid density

I Units

1 kmol m-'

~~~

Second virial coefficient

m3 kmol-'

Solid density

kmol m-3

Surface tension ~~

~

Thermal conductivity of liquid Thermal conductivity of solid Thermal conductivity of vapor Vapor pressure of liquid Vapor pressure of solid or sublimation pressure

IN m-1 I w (m I w (m

I

~1-1

~1-1

pa

I Pa

Viscosity of liquid

Pa s

Viscosity of vapor

Pa s

4.5 Special Case and New Challenge: Data o f Electrolyte Solutions

A much bigger challenge than these normal solutions is the modeling of electrolyte containing solutions. The modeling of electrolyte solutions or, more generally speaking, liquids containing fractions of electrolytes is nowadays still an exhausting task. Chemical and process engineers for example are nowadays able to model or even predict a vapor-liquid equilibrium, the density or viscosity of a multicomponent mixture containing numerous different species with sufficient reliability. But if only traces of salt are contained in the mixture, nearly all models tend to fail. The modeling results however have a great impact on the design and construction of single chemical apparatus as well as whole plants or production lines. Proper functioning could only be guaranteed based on reliable results. Another area influenced greatly by electrolyte modeling is biochemical engineering. For example nobody knows how to predict quantitatively saltingout effect of proteins, crystallization processes of biomolecules, the influence of ions on nanoparticle formation, their size morphology and crystal structure, zeolite synthesis and so on. But the development of new production processes in this intensively growing area requires accurate macroscopic physical property models capturing accurately the underlying physics. In some cases there is a limited understanding of these mechanisms, but no real predictability. The chemical engineer developing new production processes as well as the physical chemist developing models are therefore having a pressing need to access reliable

4.6 Examples ofDatabases with Properties ofElectrolyte Solutions

thermophysical property data. Process as well as model development, either predicting or even only interpolating, requires multitudinous amounts of reliable thermophysical property data for electrolytes and electrolyte solutions. Among the most important property types are: 0 0

0 0 0 0

0 0

vapor-liquid equilibrium data activity coefficients osmotic coefficients electrolyte and ionic conductivities transference numbers viscosities densities frequency dependent permittivity data.

How does one find such data?

4.5.1 Reliable Data Sources

Thermophysical property data for electrolytes and electrolyte solutions are measured from numerous researchers and scientists and are published typically in a large number of journals and publications. But people requiring such data will not search the primary publications, because this is too time-consuming. And in most cases it is even impossible, because industrial users do not have access to all the required literature immediately. Instead the preferred way will be to check either a printed data collection or to search within an electronic database for the components, mixtures and properties one needs. Such printed data collections or databases are typically compiled and/or maintained by individuals or groups having a well known reputation in that field. Therefore they have an overview of the primary literature publishing physical property data and are able to continuously add new data to their collections. In most cases these groups also use their own collections for model development. In the following pages, a survey of maintained databases for electrolyte properties is given.

4.6 Examples of Databases with Properties of Electrolyte Solutions 4.6.1 The ELDAR Database [lo]

The Electrolyte Database Regensburg ELDAR is a numerical property database for electrolytes and electrolyte solutions. It contains data on pure substances and aqueous as well as organic solutions. The data collection for ELDAR started in 1976 within the framework of the DECHEMA study [ll]Research and Developmentfor Sau-

I

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4 Databases in the Field of Thermophysical Properties in Chemical Engineering

ing the Raw Material Supply which was supported by the German Ministry for Research and Technology (BMFT). The work of this study 1981 led to development of ELDAR. From the beginning up to now the ELDAR database development was headed by the Institute of Physical and Theoretical Chemistry of the University of Regensburg. The database was designed as a literature reference, numerical data and also model database for fundamental electrochemical research, applied research and also the design of production processes. The database is still maintained and has roughly doubled its size since beginning. It contains data of more than 2000 electrolytes in more than 750 different solvents. Nowadays ELDAR contains approximately: 0 0 0

7400 literature references 45,400 data tables 595,000 data points.

ELDAR contains data on physical properties like densities, dielectricity coefficients, thermal expansion, compressibility, PVT data, state diagrams, critical data, thermodynamic properties like solvation and dilution heats, phase transition values (enthalpies, entropies, Gibbs free energies), phase equilibrium data, solubility, vapor pressures, solvation data, standard and reference values, activities and activity coefficients , excess values, osmotic coefficients, specific heats, partial molar values, apparent partial molar values and transport properties like electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities and diffusion coefficients. ELDAR is distributed as part of DECHEMA’s numerical database for thermophysical property data, which is called DETHERM. To access ELDAR one could therefore use several options:

in-house client-serverinstallation as part of the DETHERM database [7]; Internet access using DETHERM ... on the WEB [7]; on-line access using host STN International [12]. To get an overview of the data available, the Internet access option could be recommended, because existence of data for a specific problem could be checked free of charge and even without registration. 4.6.2

The Electrolyte Data Collection

The Electrolyte Data Collection is a printed publication which is part of DECHEMA’s Chemistry Data Series. The Electrolyte Data Collection is published by Barthel and his coworkers from the University of Regensburg. The printed collection and the database ELDAR have complementary functions. The data books give a clear arrangement of selected recommended data for each property of an electrolyte solution. The electrolyte solutions are classified according to their solvents and solvent mixtures. All solution properties have been recalculated from the original measured

4.G Examples of Databases with Properties of Electrolyte Solutions

data with the help of compatible property equations. A typical page of the books contains the following for the described system: 0

0 0 0 0

general solute and solvent parameters fitted model parameter values measured data together with deviations against the fit a plot literature references.

The Electrolyte Data Collection has nowadays 18 volumes and consists of 9500 printed pages. Covered properties are: 0 0

0 0 0

conductivities transference numbers limiting ionic conductivities dielectric properties of water, aqueous and nonaqueous electrolyte solutions viscosities of aqueous and nonaqueous electrolyte solutions.

4.6.3 ICV-SEP Data Bank for Electrolyte Solutions

The Engineering Research Center Phase Equilibria and Separation Processes (ICVSEP) of the Technical University of Denmark (DTU) is operating a data bank for electrolyte solutions 1131. It is a collection of scientific papers containing experimental data for aqueous solutions of electrolytes and/or nonelectrolytes and also theoretical papers related to electrolyte solutions. The database is a mixture between a literature reference database and a numerical database. Currently references to more than 4000 papers are stored in the database. In addition experimental data from around 2000 of these papers are stored electronically as well. Most of the experimental data concern aqueous solutions. The access to the literature reference database is free of charge, but requires a registration. The access to the numerical database is restricted to members of an industrial consortium supporting the work of ICV-SEP.

4.6.4 The Dortmund Database DDB [14]

The Dortmund Database Software and Separation Technology from the University of Oldenburg is well known for its data collections in the areas of vapor-liquid equilibria and related properties. While the major part of the data collections is dealing with nonelectrolyte systems, two collections contain exclusively electrolyte data. They are focused on: 0 0

vapor-liquid equilibria gas solubilities.

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The two collections together currently contain 3250 data sets. Access to these collections is possible either on-line using the DETHERM on the Web or in-house using special software from DDBST or DECHEMA.

4.6.5 Closed Collections

In addition to the above-described publicly available and still maintained collections, do other old electrolyte data collections exist? Among them is for example the ELYS database, which was compiled by Lobo, Department of Chemistry, University of Coimbra, Portugal, or the DIPPR 861 Electrolyte Database Project. But these closed collections are typically not maintained any more and also not publicly available. It is likely the references and/or data published in these collections could also be found inside the aforementioned living collections.

4.7 A Glance at the Future of the Properties Databases

Most of the engineers in chemical companies trust in the power of their evaluation of the equations of state for the calculation of the optimal point of work. Nevertheless the opinion that databases have less importance these days is growing, mainly when budgetary elements come into consideration. The knowledge of the importance of a correct process design is run over by considerations that a saving of one euro per kg for a product which costs 50 euros per kg is not very relevant. That is not the case for basic chemicals, where saving of the same order of magnitude represents 25 % of the total costs and 10 % of the used energy. Unfortunately the production of these chemicals is today mainly transferred into low cost countries, i.e., not very relevant for research purposes. A lot of companies made the outsourcing of their measurements, so that only a limited amount of experts in companies maintain the knowledge for these activities. When we look at the constraints to find new methods for the design of biologic or polymer solutions, we must be sceptical to find enough people to manage future visions for models with the knowledge what was in the past. In the time of a rise in steel consumption in the Chinese industry, where in an unexpected way a demand of coal energy started again, it may be that the properties will rise in interest. From a governmental funding point of view, it is a good sign that new projects are coming up in order to find a new approach to build evaluated databases.

References 1745

References 1 Design Institute for Physical Properties (DIPPR): www.aiche.org/dippr/,2006 2 TRC Thermodynamic Tables: www.trc.nist.gov/tables/trctables.htm.2006 3 Landolt-Bornstein:www.springeronline.com/ sgw/cda/frontpage/02Cl18S5%2Cl-lOl13-295856-00?2COO.html,2006 4 DECHEMA Chemistry Data Series: www.dechema.de/CDS-lang-en.html, 2006 5 NIST Standard Reference Data Program: www.nist.gov/srd/,2006 6 NIST Chemistry WebBook http://webbook.nist.gov,2006 7 DECHEMA DETHERM database: www.dechema.de/detheim-lang-en.htm1, 2006

8 AIChE: www.aiche.org,2006 9 DIPPR Project 801: httpc//dippr.byu.edu,2006 10 University of Regensburg: www.uniregensburg.de/Fakultaeten/nat-Fak-IVIPhysikalische-Chemie/Kunz/,2006

11 DECHEMA, Forschung und Entwicklung

zur Sicherung der Rohstofiersorgung. Programmstudie Chemische Technik Rohstoffe, Prozesse, Produkte, Vol. 6 , DECHEMA Deutsche Gesellschaft fur Chemisches Apparatewesen e.V., Frankfurt am Main, 1976 l2 STN: www.stn-international.de/, 2006 13 ICV-SEP Data bank for electrolyte solutions: www.ivc-sep.kt.dtu.dk/databank/databank.asp, 2006 14 Dortmund Database DDB: www.ddbst.de, 2006

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8 I747

5 Emergent Standards Jean-Pierre Belaud and Bertrand Braunschweig

5.1 Introduction

Software standards in computer-aided process and product engineering are needed in order to facilitate application and software components interoperability. In the past, end-user organizations, software companies, governmental organizations and universities have spent hundreds of thousands, if not millions of euros, dollars and yens to develop bridges between software systems such as for transferring simulation data to an engineering database in order to provide the values for basic design: for integrating real time data coming from several process control systems into a common information network for the operators; for allowing a process simulation tool to use pure component data from a physical properties data bank for using a specialized unit operation simulation model within a commercial process simulation environment, etc. This question has been a subject of concern for years, as a source of unnecessary costs, delays and moreover of inconsistencies between data produced and consumed by different nonintegrated systems using different bases, different calculation principles, different units of measurements, running on different computers under different operating systems and written in different languages. This need in the domain of computer-aided process engineering has been described elsewhere; see, for example, Braunschweig and Gani (2002). Software standards remove this problem by providing the desired interoperability between software tools, platforms and databases. With appropriate machine-tomachine interface standards, using the best available tools together becomes a matter of plug-and-play,supposedly as easy as connecting USB devices or hi-fi systems’. Moreover, not only do these standards enable several software pieces available on your local PC to be put together, but they allow, thanks to the use of middleware, heterogeneous software modules available on your organizations’ intranet, or on the 1 Assuming that there is one commonly agreed stan-

dard and not several, e.g., see the problems of the

multiple standards for writable DVDs and the lack of interoperability that this multiplicity generates.

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 02006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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internet to interoperate, e.g., thanks to Web sewices technologies. Of course, such a facility has significant organizational, economic and technical consequences. We will briefly examine these consequences at the end of this chapter. However, our main focus will be on technologies,starting with a discussion on the concepts of openness and of open standards development. Then, we will examine some of the most significant operational standards in the domain of computer-aided process and product engineering, namely the CAPE-OPEN standard for process modeling tools, the OPC standard for process control systems. Following this, we will look at some of the current software interoperability technologies that we think will power future systems, i.e., XML and Web services technologies, leading to what is now called service-orientedarchitectures. Further on, we will shortly address standards for multiagent systems and the emerging Semantic Web standards, which should play a major role in the longer term, moving from syntactic to semantic interoperability of CAPE systems and services. We will conclude with a brief look at the organizational and economic consequences of the trend towards interoperability and standards. This chapter deals essentially with software-oriented standards, i.e., standards related to the use of one piece of software from within another piece of software. Data-oriented standards allowing to exchange data (from databases, files, etc.) between many software applications are only marginally addressed, e.g., in the POSC section.

5.1.1 Open Concepts

There is a clear fact that the emergence of the World-Wide Web was done with concepts of common development and usage. These concepts called here open concepts commonly encompass open standards, open computing, standardization processes and open software. In the first years of e-business, (open)standards were essential to the development of the Web, to e-commerce and to interlintra-organizational integration. Standardized information technologies such as TCP/IP, HTTP, HTML, XML, CORBA-HOP, Web services-SOAP,etc., achieve interaction and information exchange with external or internal, homogeneous or heterogeneous, and remote or nearby applications. These technologies are now core technologies of our networked environment. For the next generation of information systems and of computer technologies, open concepts should again play a key role for emergent information technologies (IT) standards introduced in Section 5.3. Heintzman (2003) gives a good introduction to open concepts for the domain of IT, through formal definitions, a brief history from the 1970s to the modern day battle of openness, and addresses commercial challenges of open projects from an IBM perspective. There is no reason why process engineering would escape from this trend, even if this field is a niche business and therefore more restricted and less global. Section 5.2 illustrates concrete technologies using open concepts in the field of CAPE. For example, CAPEOPEN (CO) is a significant technology for interoperabilityand integration of process

5.7 Introduction

engineering software components allowing engineering based on o$the-shelves components.

5.1.2 Open Standards and Standardization Process

In order to develop modem software applications and systems, technology selection involves many criteria. One main issue is to know if the technology is an (open) standard technology or a proprietary technology. Open standard technologies are freely distributed data models or software interfaces. They provide a basis for communication, common approaches and enable consistency (Fay 2003), resulting in improvements of developments, investments and maintenance. Clearly the common effort to develop an IT or a CAPE standard and its world-wideadoption by the community can be a source of cost reduction, because not only is the development cost shared but also the investment is expected to be more future-proof. Open standards are developed by software and/or business partners who collaborate within neutral organizations (such as W3C, OASIS, OMG, etc., for IT and COLaN, POSC, etc., for process engineering) in accordance with a standardization process. Such organizations represent a new kind of actor additional to more traditional actors, i.e., academics, software/hardware services suppliers and end-user companies. In the information and communication industry Warner (2003) calls this standardization process block-alliance in committee-based standard setting and examines it with block-alliancein market-based standard battle. The latter, which is beyond our scope, leads to defacto standards if the resulting technology successfully matches the market. However, both approaches are not so distinct since a standardization process can be a means in a business strategy. For example the Java platform and UML mix

Standard

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Timing o f standard

Responsive standards

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committee-based and market-based processes. If we consider the S-curve lifecycle of a simple technology, Sherif (2003) classifies the technological innovations in terms of market innovation and of technological competencies with radical, platform, incremental and architectural innovations. Weiss and Cargill (1992) show the ideal relationship between these types of innovation and the standardization process timing with the type of standards needed at each phase (Fig. 5.1). As an illustration we would say that the CO standard is in the second phase: initial products are commercialized; CO technology is now well disseminated; there is a well-establishedorganization releasing formal specifications;development tools, labeling process and promotion actions support the CO standard. 5.1.3 Open Computing, Open Systems, and Open/Free Software

By extension of the open standards paradigm, building modern software solutions can be based on an open computing paradigm. Open computing means that there is a standardization of information exchange. Then the resulting open system is a system whose characteristics comply with standards made available throughout the industry and therefore that can be connected to other systems complying with the same standards (IBM Glossary 2004). Open computing promises many benefits: flexibility/agility,integration capability, software editor independence, development cost and adoption of technological innovation. While always giving priority to the quality of business models available in a specific CAPE tool, process engineers can now privilege open CAPE systems, ensuring the exchange of information between CAPE solutions of distinct editors thus making it possible to benefit from various fields of expertise. This communication can be done statically with data models or dynamically with application programming interface (API). Open computing in CAPE is illustrated in Section 5.2. The tools for application engineering or for software development can be open source software tools or commercial software tools. Heintzman (2003)identifies several types of projects for the development and management of open source software: academic projects (especially viewed as a new media for collaboration, innovation promotion and dissemination), foundation projects (for base software such as Linux, Apache, Eclipse, Mozilla, etc.), middleware projects (advanced software such as JBoss, MySQL, etc.), niche projects (very specific software available on the Internet’). Open source software projects in the CAPE field are not significant at present but they could occur in academic or niche projects, the only known example at the time of writing being SIM42 project (Sim42 Foundation 2004), which develops an open source chemical engineering simulator. 2 For example SourceForge.net is the largest reposi-

tory of open source software projects with more

than 118000 projects at the beginning of 2006,

5.2 Current CAPE Standards

5.2 Current CAPE Standards

For several decades, experts and process engineers concentrated on the creation, evolution and improvement of models of thermodynamic and physical properties, unit operation, numerical methods, etc. Thus many CAPE software solutions allowing a more or less rigorous representation were developed. Each one is unique and dependent on the know-how of its author or editor. Particularly, in addition to the specific modeling activity, each one is characterized by selected computing technologies, i.e., supporting environment, implementation languages, persistence system, logical architecture, etc. This results in heterogeneity of available solutions and an impossibility of exchanging information between the different tools. Dual bridges between certain tools exist but this option remains proprietary and only operational for a limited number of associations of tools. Now the demand of users of CAPE tools turn to open systems, ensuring process, model and data exchange with third-party tools. In the same way, process engineers wish to be able to integrate their know-how easily and thus to deploy a final solution specific to their needs from best-in-classsoftware components. Open computing and its related IT and CAPE standards allow to build a user-centered modeling and simulation environment from enterprise internal components and selected off-the-shelfcomponents. Several initiatives that promote a standard for process information exchange can be identified, according to two types of techniques3, data models and API: 0

0

data models such as pdXML, energy estandards from POSC and Physical Property Data exchange from DECHEMA; APIs such as OPC from OPC Foundation, Physical Properties Package from IKCAPE and CAPE-OPEN from the CO-LaN.

Open software architectures can now be exploited by the new generations of CAPE software solutions in order to provide better enterprise process applications integration. As an illustration of interest, Fieg et al. (1995), Mahalec (1998),Braunschweig et al. (2000),White (2000), Braunschweig and Gani (2002) and Belaud et al. (2002) discuss open computing, its resulting and its expected benefits. The next sections introduce CAPE-OPEN, OPC and energy estandards. 5.2.1 CAPE-OPEN Standard for Modeling and Simulation

To solve problems, process engineers typically use a collection of in-house, commercial and/or academic software. Each user requires a broader access to available information and models to fit with the demand on the one hand, and has the constraint to match easily the old and the new, on the other hand. Information technologies play a predominant role to improve CAPE tools in supporting process engineers who 3 In some cases this distinction is not so obvious as some work both ways. Moreover, the XML technol-

ogy adopted by some standards does not really comply with this classification.

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face these new challenges of interoperability. It is quite obvious that work is needed to develop and establish open systems for CAPE related software. Development of open systems requires the establishment of open standards. The CAPE-OPEN standard, through which a host tool and any external tool can communicate, is the answer to this question, as it provides an open communication systemfor process simulation, allowing the final users to employ various elements within any other. Specifically, since 1995, an international group of operating companies, software suppliers and academics, developed, through the CAPE-OPEN initiative, an open communication system for key simulation elements, and demonstrated its effectiveness on numerous examples. Through this it also promoted the adoption of the open system by the major providers and users of process simulation. The CAPE-OPEN standard (Belaud and Pons 2002, present version 1.0) consists in a technical architecture, interface specifications and implementation specifications. The technical architecture relies on modern development tools and up-to-date information technologies such as object-orientedparadigm, component-based approach, Web-enabled distributed architecture, middleware technology and uses the Unified Modeling Language (UML) notation. The interface specifications identify a conceptual model and the implementation specifications give the corresponding platform specific model for COM and CORBA. The specifications cover major application areas, e.g., unit operation, thermodynamic and physical properties, numerical solvers, optimization, planning and scheduling, chemical reactions systems, etc. CAPE-

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OPEN compliant software environments and components are now available on the market. Belaud et al. (2003)deal with the unit operation interface and show an example for a fxed bed reactor for butane isomerization. The CAPE-OPEN standard is free of charge and is managed by the CO-LaN consortium (www.colan.org,and Pons et al. 2003), which gathers operating companies, software suppliers and academic institutes. In addition to publishing the standard specifications, CO-LaN provides tools for supporting the transition to CAPE-OPEN technology: 0

0

0 0

migration tools, that is, software that automate the migration of existing components to CAPE-OPEN compliance, code examples for re-use, software testers that check compliance with the standard, guidelines and other helpful documents.

Recent announcements from software suppliers, end-users and research institutions demonstrate that CAPE-OPEN is increasingly accepted by the CAPE community. Its main technological benefits are: 0

0

0

for suppliers: increased usage of CAPE tools and reduced development and integration costs, for users: “develop your expertise once, plug and run everywhere” and access to best-in-classsolutions, for academics: improved dissemination of research results and better matching with industrial needs.

Organizations who adopt the CAPE-OPEN standard, and possibly become members of the CO-LaN, will be the first ones to harvest the benefits of open standard interfaces in process modeling and simulation.

5.2.2 Extensions to the CAPE-OPEN Standard

The 1.0 version of the CAPE-OPEN standard offers the following interface specifications as shown in Fig. 5.2. Details on these specifications are available elsewhere and on CO-LaN’s Web site. Although addressing a broad range of applications of CAPE modeling and simulation, the specifications are subject to improvements and extensions. At the time of writing this chapter, two such projects are active: 0

0

Improvement and refactoring of the thermodynamic and physical properties specifications. This work will eventually deliver version 1.1 of the specification which should be restructured in a more logical way, better documented, and therefore easier to use. Extension of the unit operation (UO) specification. The UO CAPE-OPEN standard, in version 1.0, does only address steady state simulation; although several tests have shown that CAPE-OPEN unit operations could be used, with limitations, in

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dynamic simulation, work is going on to provide a specification fully compliant with all possible uses in dynamic simulation. A new version of the UO standard will be released after sufficient testing in a number of dynamic process modeling environments. The decision to launch a new improvement/extension project is taken by CO-LaN’s board of directors following proposals presented by special interest groups or by COLaN members. 5.2.3 OPC for Process Control and Automation

Since 1996 the OPC Foundation (OPC Foundation 1998) has been a nonprofit organization which ensures the definition and the use of interfaces for applications in control and automation of processes. It is dedicated to ensuring interoperability in automation by creating and maintaining open specifications that standardize the communication of acquired process data, alarm and event records, historical data, and batch data to multi-supplier enterprise systems and between production devices. The vision of OPC is to be the foundation for interoperability for moving information vertically from the factory floor through the enterprise of multi-vendor systems, as well as providing interoperabilitybetween devices on different industrial networks from different vendors. The foundation gathers more than 300 members, suppliers and users of control systems, instrumentation, and process control systems. It is worth noting that Microsoft is a member and acts as a technology advisor. The OPC-OLE for process control standard (Iwanitz and Lange 2002) is based on Microsoft OLE-ActiveX/(D)COMtechnology and standardizes the communication of OPC compliant data sources4 and OPC compliant applications’ through different connections (radio, serial, Ethernet and others) on different operating systems (Windows, Unix, VMS, DOS and others). Many specifications are available: 0 0

0

0

OPC Data Access provides access to real-time process data, OPC Historical Data access is used to retrieve process data for analysis, OPC Alarms and Events is used to exchange and acknowledge process alarms and events, OPC Data exchange defines how OPC servers exchange data with other OPC servers; OPC XML encapsulates process control data making it available across all operating systems.

As for CAPE-OPEN, the OPC foundation provides several tools and technologies supporting application and migration to the OPC standard, including self-testing software. 4 programmable logic controllers, distributed control

systems, databases and other devices

5 human machine interface, trending subsystems,

alarm subsystems, spreadsheet, historians, enterprise resource planning, etc.

5.3 Emergent Information Technology Standards

5.2.4 Energy estandards for Oil and Gas Processes

POSC is an international not-for-profit membership corporation. It unites industry people, issues and ideas to facilitate exploration and production information sharing and business process integration in the petroleum industry. Since 1990, membership has grown to over 100 companies. The membership includes world-wide representation of major and national oil companies, suppliers of petroleum exploration and production software and services, government agencies, computing and consulting companies, and research and academic institutions. POSC provides open specifications for information modeling, information management, and data and application integration over the life cycle. These specifications are gathered in the energy estandards project that relies principally on XML technologies (DTD, XML, Schema, etc.) for leveraging Internet technologies in the integration of oil and gas business processes. The set of standards are classified according to POSC areas: internet data exchange standards, practical exploration and production standards, data management standards, standards usability and application interoperability standards. For example, in the data management standards area the Epicentre standard provides a logical data model for upstream information. Also in the Internet data exchange standards area, ChemicalUsageML is a specification for the transfer of information about potential chemical hazards, and WellLogML is an XML DTD and a XML schema for well log data representation. These standards are not directly related to CAPE applications. However, the scope of POSC encompasses both underground applications (geology, geophysics, reservoir, drilling) and offshore applications (production, transportation). The second application area has many similarities with downstream areas such as petroleum refining, as it essentially involves the design, operation and monitoring of continuous processes. Some ofthe POSC projects such as POSC-CAESAR delivered technologies applicable to CAPE in general. Since these are data-oriented standards we do not address them in this chapter. Commonalities can also be found with a number of data modeling projects undertaken by the chemical engineering community such as PI-STEP, PDXI or pdXML (Teague 2002 and Teague 2002b).

5.3 Emergent Information Technology Standards

Although not yet fully exploited by the CAPE community, a number of emergent IT standards will become important for our applications in the near future. Complementing some of the technologies presented in the previous section, these new IT standards support Internet-based computing and take advantage of Web technologies. We will first look at Web services together with their newly developed business standards, leading to service-oriented architectures; then we will go a step further

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and introduce IT standards for multi-agents architectures and the recently published6 Semantic Web standards.

5.3.1 Web Services and Business Standards

Web technologies are being used more and more for application to application communication. Before the twenty-first century, software suppliers and IT experts promised this interconnected world thanks to the technology of Web services. Web services propose a new p a r a d i p f o r distributed computing (Bloomberg 2001) and are one of today’s most advanced application integration solutions (Linthicum 2003). They help business applications to contact a service broker, to find and to integrate the service from the selected service provider. For example, during a simulation, the simulation environment, in need of an external thermodynamic service, contacts a UDDI directory in order to take advantage of a particular thermodynamic model (yellow page function). Once the producer of such services (a company) is selected, the simulation environment recovers the signatures of all available services using the associated WSDL descriptions’. These phases of discovery and description can be carried out dynamically or statically during the development process. Then the simulation environment connects to the specific thermodynamic service and uses it with SOAP* communication protocol. This scenario can take place on the Internet or on company intranets or extranets; it uses a set of technologies: UDDI, WSDL and SOAP, proposed by the Web services community to ensure interworking and integration of Web services. However, even if the idea of Web services has generated too many promises’, Web services should be viewed for now as a part of a global enterprise software solution and not as a global technical solution. In a project, Web services can be used within a general architecture relying on Java EJB or on Microsoft’s .NET framework. Many projects already utilize Web services, sometimes with nonstandard technologies, particularly for noncritical intranet applications. Even if Web services miss advanced functionalities, many advantages like lower integration costs, the re-use of legacy applications, the associated standardization processes and Web connectivity can plead in favor of this new concept for software interoperability and integration (Manes 2003). 5.3.1.1 Definition

A Web service is a standardized concept of functions invocation relying on Web protocols, independent of any technological platform (operating system, application 6 at the time of writing this section (early 2004) 7 Web Service Description Language, somewhat equivalent to OMG’s CORBA and to Microsoft’s

COM IDL

8 simple object access protocol, known as the “pip-

ing” between Web services 9 Early standards, security, orchestration, transac-

tion, reliability, performance, ethic and economic models are the main concerns.

5.3 Emergent Information Technology Standards

server, programming language, database, and component model). Bearingpoint et al. (2003) focus on the evolution from software components to Web services and write: “a Web service is autonomous and modular application component, whose interfaces can be published, sought and called through Internet open standards.” We see the introduction of Web services as a move from component architectures towards internet awareness, this context implying the use of associated technologies, i.e., H T P and XML, and an e-business economic model. Current component technology based on EJB, .NET and CCM being not fully suitable, Web services provide a new middleware for providing functionality anywhere, anytime and to any device. 5.3.1.2 Key Principles IBM and Microsoft’s initial view of Web services, first published in 2000, identified

three kinds of roles (Fig. 5.3): 0

0

0

A service provider publishes the availability of its services and responds to requests to use its services. A service broker registers and categorizes published service providers and offers search capabilities. A service requester uses service brokers to find a needed service and then employs that service.

These three roles make use of proposed standard technologies: UDDI from the OASIS consortium, WSDL and SOAP from the World-Wide Web consortium (W3C).UDDI acts as a directory of available services and service providers; WSDL is an XML vocabulary to describe service interfaces. SOAP is an XML-based transfer protocol that allows you to send requests to services on through HTTP. Further domain-specific technologies related to Web services are being developed, e.g., the following proposed by the OASIS consortium, a consortium of companies interested in the development of e-business standards ebXML, supported by Sun Microsystems, is a global framework for e-business data exchange; BPEL (formerly called BPEL4WS), is a proposed standard for the management and execution of business processes based on Web services; SAML aims at exchanging authentication and authorization information; WS-Reliable Messaging is for ensuring reliable message delivery for Web services; WS-Securityaims at forming the necessary technical foundation for higher-levelsecurity services, etc. A recent glossary of technologies related to Web services, each one defined by only a few lines of text, is 16 pages long (Cutter Consortium 2003). Simply stated, the interface of a Web service is documented in a file written in WSDL and the data transmission is carried out through HTTP with SOAP. SOAP can also be used to query UDDI for services. The functions defined within the interface can be implemented with any programming language and be deployed on any platform. In fact any function can become a Web service if it can handle XML-based calls. The interoperability of Web services is similar to distributed architectures based on standard middleware such as CORBA, RMI or (D)COM but Web services offer a loose coupling, a nonintrusive link between the provider and the requester,

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Figure 5.3

Key principles of Web services

due to the loosely-coupledSOAP middleware. Bloomberg (2001)compares these different architectures. Oellermann (2002) discusses the creation of enterprise Web services with real business value. Basically he reminds that a Web service must provide the user with a service and needs to offer a business value. The technically faultless but closed .NET “my services”project from Microsoft demonstrates that this is always challenging to convince final users. With Google Web API beta (2004),software developers can query the Google search engine using Web services technology. Indeed Google search engine is available as a Web service since mid-2002. Search requests submit a query string and a set of parameters to the Google Web APIs service and receive in return a set of search results. A developer’skit provides documentation and example code (Java, C# and Visual Basic) for using this Web service from any platform that supports it. 5.3.1.3 SOAP a Loosely-coupled Middleware Technology

HTML-HTTP act as loosely-coupledmiddleware technology between the Web client (navigator)and the business logic layer (Web server). Around the year 2000 Microsoft and IBM proposed to use the XML data format over the Internet protocols: HTTP as transport layer and XML as encodingfomat now constitute the key underlying technologies for Web services. On top of these, SOAP (currently in version 1.2) was delivered in June 2003, as a lightweight protocol for exchange of information in a decentralized and distributed environment. SOAP can handle both the synchronous request/response pattern of RPC architectures and the asynchronous messages of messaging architectures. An example of SOAP request message in a synchronous manner can be found in Google Web APIs beta (2004).A SOAP request is sent as a HTTP POST. The XML content consists in three main parts: 0 0

0

The envelope defines the namespaces used. The header is an optional element for handling supplementary information such as authentification, transactions, etc. The body performs the RPC call, detailing the method name, its arguments and service target.

5.3 Emergent Information Technology Standards

Whereas OMG CORBA, Java RMI, Microsoft (D)COM and .NET Remoting try to adapt to the Web, SOAP middleware ensures a native connectivity with it since it builds on HTTP, SMTP and FTP and exploits the XML Web-friendly data format. The many reasons for the success of SOAP are its native Web architecture compliancy, its modular design, its simplicity and extensibility, its text-based model”, its error handling mechanism, its ability for being the common messaging layer of Web services, its standardization process and its support from major software editors. With so many advantages for integration and interoperability one could expect a massive adoption by software solutions architects. However the deployment of Web services still remains limited. In addition to technical issues, three main reasons can be noted 0

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Web services are associated to SOAP, WSDL and UDDI. The UDDI directory of Web services launched in 2000 by IBM, Microsoft, Ariba, HP, Oracle, BEA and SAP, was operational at the end of 2001 with three functions (white, yellow and green pages). However due to technical and commercial reasons this world-wide repository that meets an initial need (to allow occasional, interactive and direct interoperability) founded on the euphoria of e-business years does not match the requirements of enterprise systems. Entrusted to OASIS in 2002, UDDI version 3.0 proposes improvements in particular for intranet applications. The simplicity and interoperability claimed by Web services are not so obvious. Different versions of SOAP and incompatibilities of editors’ implementations are source of difficulties, to such a degree that editors created the WS-I consortium to check implementations of standards of Web services across platforms, applications, and programming languages. The concept was initially supported by a small group of editors (with Microsoft and IBM leading); now the “standards battle”” and the multiplication of proposed standards weaken the message of Web services (Koch 2003).

5.3.1.4 Service-oriented Architecture

In order to better integrate the concept of Web services in enterprise systems, IT editors now propose the service-oriented architecture (SOA) approach (Sprott and Wilkes 2004). Beyond the marketing hype, a consensus is established on the concept of service as an autonomous process, which communicates by message within an architecture that identifies applications as services. This design is based on coarsegrained, loosely-coupled services interconnected by asynchronous or synchronous communication and XML-based standards. The definition and elements of SOA are not well established yet. Sessions (2003)wonders whether a SOA is (1)a collection of components over the Internet, (2) the next release of CORBA or ( 3 ) an architecture for publishing and finding services. An SOA is only an evolution of Web-distributed component-based architectures to get applications integration easier, faster, cheaper and more flexible, improving 10 In contrast to binary and not self-describing

CORBA, RMI, (D)COM, .NET protocols.

11 with BEA, IBM and Microsoft on one side and lona, Oracle and Sun from the other side

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return on investment. In fact the main innovations are in the massive adoption of Web services’* by the industry and in the use of the XML language to describe services, processes, security and exchanges of messages. This promises more futureproof IT projects than in the past. Despite limitations of Web services, the technology now appears to be complementary to solutions based on classic middleware bus, as well as to enterprise application integration solutions. Its loose coupling brings increased flexibility and facilitates the re-use of legacy systems. Moreover Web services can be used like low-cost connectors between distinct technological platforms like COM, .NET and JZEE. The next release of Microsoft’s Windows Vista operating system will include Indigo, a new interoperabilitytechnology based on Web services, for unifylng Microsoft’s proprietary communication mode; Abitboul, research director at INRIA, estimates that Web services will represent, in the long run, the natural protocol for accessing information systems. Thus it seems that we are only at the start of Web services and SOA. Andrews (2004)predicts dramatic changes in the Web services market for 2006, and announces a new class of business applications called service-oriented business applications. The merging of Web, IT and object/component technologies to form SOA and Web services is announced as the next stage of evolution for e-business (knowing that grid computing and autonomic computing will add their contributions too, but this is another story). There is no doubt that the scientific field will get many benefits from this trend. As for CAPE, one can foresee several applications of SOA and Web services. However, it is sure that innovations will probably go beyond what is predictable at this stage of development. Here are a few examples:

0

Sama et al. (2003) presents a Web-based process engineering architecture where simulator components can be executed over the Web. Many front-end engineering companies share design data over communications network. Access to this design data could be made easier through an SOA. Physical properties databases can be made available through Web services; a good example of such a service is Dechema’s “DETHERM ... on the Web” on-line service (Westhaus 2004). This service is currently available through conventional technology (PhP requests on database) and could be made into a Web service, therefore directly interoperable with other programs. In the long run, process engineering software could interoperate with equipment manufacturers services not only to develop better simulation models by using the manufacturer’sspecific unit operation model, but as well to link into manufacturers’ supply chain when moving into detailed design, procurement and commissioning.

As can be seen from these examples, the advent of service-oriented architectures brings many opportunities to the CAPE professional. Now let us move even further and come to semantic interoperability. 12 Even if a SOA does not imply the use of web ser

vices technology and vice versa.

5.3 Emergent Information Technology Standards

5.3.2 WjC’s Semantic Web Standards

The current World-Wide Web is very rich in terms of content, but is essentially syntactic or even lexical. Looking for information on the Web, using search engines, is done by finding groups of terms in the pages and in the documents, without taking consideration of the meaning of those terms. For example, using the most popular search engine, Google, to look for information about the ESCAPE-15 conference, the first page brings the results seen in Table 5.1. Thanks to the referencing work done by the conference organizers, the first hit is the conference’s Web site. However, in the first page, together with the correct hit, Google reports a ski bag, a motor racing wheel, and a tour in New Zealand. One might wish to go to the “advanced search” page and specify that only Web sites about conferences should be returned. This is not possible, since Google does not allow this restriction. As a matter of fact, none of the most popular search engines currently used could restrict the search to a category of pages, as the semantics of the pages are unknown to them. Supported by the W3C, of which it is a priority action, many projects aim at developing the semantic level, where information is annotated by its meaning. A necessary stage is to define consensual representations of the terms and objects used in the applications-these consensual representations are called ontologies. These ontologies will be expressed in OWL (Ontology Web Language), which itself is based on XML and RDF (Resource Description Language), a specialization of XML. Programs in the whole world support this movement towards the semantization of informaTable 5.1

ESCAPE-15 search with Google on 18 July 2004

ESCAPE 15 The ESCAPE (European Symposium on Computer Aided Process Engineering) series brings the latest innovations and achievements ... www.ub.es/escape 15/escape15.htm Thule Escape 15 Cubic Foot Rooftop Cargo Bag Buy Thule Escape 15 Cubic Foot Rooftop Cargo Bag here, one of many top quality Ski Rooftop Storage products ... www.sportsensation.com/skiing/r/Ski-Rooftop-Storage/~ule-EscapeIS-Cubic-Foot-Rooftop-Cargo-Bag-1330418.htm Motegi Racing Escape, 15” Wheels 01-On info.product-fnder.net/motegi/Escape-. IS--Wheels-01-On154.html Grand Escape 15 Days Auckland to Christchurch This morning we journey across the Auckland Harbour Bridge traveling through small rural farming communities. Visit the Matakohe Pioneer Museum ... www.newzealandtours.net.nz/auckland/~ided/ak~id66x.html

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tion. In Europe, the EC strongly supports through the Information Society Technologies (IST) program. A few ontology development projects have taken chemical engineering as their application domain. A good definition of ontologies is provided in the Web Ontology Language Use Cases and Requirements document published by W3C (2004):

Ontology defines the terms used to describe and represent a n area of knowledge. Ontologies are used by people, databases, and applications that need to share domain infomation. Ontologies include computer-usable dejnitions of basic concepts in the domain and the relationships among them. They encode knowledge in a domain and also knowledge that spans domains. In this way, they make that knowledge reusable. The word ontology has been used to describe artijacts with diferent degrees ofstmcture. These rangeporn simple taxonomies to metadata schemes, to logical theories. The Semantic Web needs ontologies with a signijkant degree ofstructure. These need to specijjJdescriptionsfor the following kinds of concepts: classes (general things) in the many domains ofinterest, the relationships that can exist among things, the properties (or attributes) those things may have. The definition of ontologies is a multidisciplinarywork, which requires competence (1)in the application area: processes, chemistry, environment, etc., (2) in the modeling of knowledge into a form exploitable by machines. It is also an important stake for the actors of the field, who will use the standards defined to annotate and index their documents, their data, their codes, in order to facilitate the semantic retrieval. Applications of the Semantic Web are many. The last section of this chapter presents an example in intelligent reconfiguration of process simulations using software agents. Before this, it is worth listing the main use cases selected by the W3C working group on the definition of OWL that have guided its development before its official release as a standard: Web portals. A Web portal powered by ontologies will bring more relevant content by applying inferences on its content (e.g., a distillation column is a separation process, therefore information about distillation would be useful to readers interested in separation). Multimedia collections. Semantic annotation of large multimedia collections will help in the retrieval among these collections, e.g., a section of a video presentation about operating special equipment. Corporate Web site management. This is the same as above, with specific functionality for company personnel, such as finding competences among employee directories etc. Design documentation. The problem of documenting designs has been identified in the chemical engineering field as in other fields where design is a key phase; it is interesting to note that this problem has been outlined by the W3C as one which could most benefit of semantic annotations, allowing to retrieve design chunks in a structured manner.

5.3 Emergent Information Technology Standards 0

0

Agents and services. Ontologies will be used by software agents to discover and analyze service offers and select the most relevant one; the next section presents such a system developed in the COGents EC-funded project. Ubiquitous computing. New information and technical systems will be configured at runtime by appropriate selections of services in unchoreogruphed ways, that it, in configurations which were not predicted at the time of setting up the services; annotation of ubiquitous services by ontologies will help in interoperating such combinations.

5.3.3

Use of Ontologies by Software Agents

The IST COGents developed an agent-based architecture for numerical simulation, with a concrete implementation in the process simulation domain relying on the CAPE-OPEN interoperability standard. The project, which lasted two years (April 2002-March 2004), proposed and implemented a framework, designed the OntoCAPE domain ontology of modeling knowledge, and demonstrated its benefits through case studies. COGents was funded by the European Community under the Information Society Technologies program, contract IST-2001-34431. As before, the CAPE-OPEN standard facilitates process simulation software interoperability and can be the foundation for Web services in this domain. The COGents project pushed the technology further: we used cognitive agents to support the dynamic and opportunistic interoperability of CAPE-OPEN compliant process modeling components over the Internet. The result is an environment which provides automatic access to best-of-breedCAPE tools when required wherever situated. For this purpose the COGents project: 0

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defined a framework allowing simulation components to be distributed and referenced on the Internet and intranets, defined representations of requirements and services in form of an ontology of process modeling, “OntoCAPE”, designed facilities for supporting the dynamic matchmaking of modeling components, demonstrated the concepts through software prototypes and test cases.

The project was supported by case studies serving as examples: nylon-6 process modeling; HDA process synthesis and simulation. The nylon-6 process case study poses challenges to the component set-up and configuration: the choice on how a simulation shall be performed depends on the availability of solvers and discretization methods. The HDA process has been used as a case study in process design, process optimization and heat exchanger network synthesis. The availability of published results provides a benchmark for the agent-based design and optimization tools. The architecture of the COGents framework is illustrated in Fig. 5.4. The extended functionality of COGents is provided by a multi-agent system (MAS), represented by the DIMA block in the above figure. MAS aims to model com-

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D M A Agent Platform

onrvChPE oritolpy

DTMA Agent Platform

CO interfaces

Figure 5.4

The COCents framework

plex systems as collections of interactive entities called agents. Each agent is autonomous and proactive and can interact with others and act upon its environment, applying its individual knowledge, skills, and other resources to accomplish goals. In COGents the key role of the MAS is to conduct negotiation mechanisms for composing the simulation during the design phase, as well as providing runtime facilities such as diagnostics and guidance to the users. The communication between individual agents is done with messages exchanged using an Agent Communication Language (ACL), whose content is expressed using the OntoCAPE ontology. DIMA is complemented with DARX, which provides a global naming and location service on a network. COGents integrates a security layer based on SSH, which provides strong authentication and secure communications over the Internet. The advantages of agent-oriented approach are as follows: 0 0

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Openness. New Agentscan can be dynamically and easily added and/or removed. Heterogeneity. The various components can be developed with different programming languages, they can be executed on different platforms. Flexibility. Interactions between the various entities are not rigidly defined. Distribution/Mobility. The agents can be executed on a set of distributed machines and can move from one machine to another.

In COGents, agents are used to improve the dynamic of simulations and to facilitate the design and development of distributed large-scale simulations. These distributed interactive simulations are built from a set of independent simulation components linked together by a network. They provide rich adaptive simulations with agents that can interact with humans and each other. As any application where domain knowledge has to be explicitly represented, COGents calls for an ontology to support the knowledge representation and interagent communication. More specifically, this ontology of the process modeling

5.4 Conclusion (Economic, Organizational, Technical, QA)

domain defines concepts indispensable for describing process modeling tasks, modeling strategies as well as software resources, and is the foundation of a matchmaking between requirements of users (i.e., process engineers) and suitable software components. OntoCAPE supports reasoning for mapping user’s requests into modeling strategies and for locating software resources to implement the identified modeling strategies. OntoCAPE was developed in DAML + OIL, a predecessor of the OWL language. More details on the COGents project, including full access to OntoCAPE, can be obtained from COGents (2004).

5.4 Conclusion (Economic, Organizational, Technical, QA)

Interoperability standards such as CAPE-OPEN, OPC, Web Services and the Semantic Web’s OWL supporting reference ontologies, open new opportunities for the process industries. Once these ideas gain wide acceptance by the process engineering community, we will find ourselves facing some very major changes in the ways process engineering software are designed, developed, marketed, distributed and used, for the mutual benefit of users and vendors. The market now has access to robust, reliable, commercial simulators that have standard software component interfaces. Process industries will be able to enjoy the lower cost and lower maintenance of commercial software, but this will be combined with an abundant flexibility. This combination will allow those companies to predict and manage process performance as never before. The number of potentially affected products is in the hundreds, due to the numerous application areas, components and suppliers. We will see many innovative combinations of process modeling components and services from large and small suppliers, used in opportunistic and changing ways depending on the modeling task at hand. This new collaboration framework is called “co-opetition”as defined by Brandenburger and Nalebuff (1996):“Business is cooperation when it comes to creating a pie and competition when it comes to dividing it up.” Plug-and-play capacity stimulates the market and creates new opportunities that could never have happened before. New value nets will be created with one supplier being another supplier’s competitor, and at the same time the supplier’s complement, as assembling components (or Web services in SOA) from several sources will provide more than just summing up the parts by operating them separately. Be prepared for further innovations and business benefits in process and product engineering thanks to the increasing role of interoperability standards and to emerging information technologies.

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American Institute of Chemical Engineering Application Programming Interface Business Process Execution Language Business Process Execution Language for Web Services Business Process Markup Language Business Process Management Initiative Computer-aided process engineering CORBA Component Model CAPE-OPEN co CO-LaN CAPE-OPEN Laboratory Network CORBA Common Object Request Broker Architecture (D)COM (Distributed) Component Object Model Document type definition DTD Enterprise Application Integration EAI Electronic business XML ebXML Hyper Text Markup Language HTML Hyper Text Transfer Protocol HTTP Interface Description Language IDL Internet Interorb Protocol IIOP Information system IS Information technologies IT Java 2 Platform Enterprise edition J2EE Multi-agent system MAS Organization for the Advancement of Structured Information Standards OASIS Object linking and embedding OLE OLE for process control OPC Ontology Web Language OWL Process Data Exchange Institute Pa1 PlantData XML pdXML Object Management group OMG Resource description framework RDF RPC Remote procedure call Security Assertions Markup Language SAML Structured Query Language SQL Service-oriented architecture SOA Simple Object Access Protocol SOAP Universal Description, Discovery, Integration UDDI Unified Modeling Language UML uo Unit operation Web Services Description Language WSDL Web Services Interoperability Association ws-I World-Wide Web Consortium w3c Extensible Markup Language XML

AIChE API BPEL BPEL4WS BPML BPMI CAPE CCM

References I 7 6 7

Acknowledgements

The authors wish to express their thanks to colleagues of the CAPE-OPEN, Global CAPE-OPEN and COGents projects.

References 1 Andrews W. (2004) Predicts 2004, Gartner’s

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predictions, www3.gartner.com/research/ spotlight/asset-55117-895.jsp Bearingpoint, SAP and Sun Microsystems (2003), Livre blanc, Les services Web, Pourquoi? www.bearingpoint.fr/content/library/ 138-731.htm Bfoombergj. Web services: A New Paradigm for Distributed Computing, The Rational Edge, September 2001, www-106.ibm.com/ developenvorks/rational/library/content/ RationalEdge/archives/sepOl.html Befaud j . P. Pons M . Open Software Architecture for Process Simulation, ComputerAided Chemical Engineering, 10, May 2002, Elsevier, Amsterdam, pp 847-852 Befaud J . P. Braunschweig B. L. Hafforan M . Irons K. Pi-nof D. Von Wedef L. Processus de standardisation pour l’interoperabilite des composants logiciels de l’industrie des procCdCs, Systeme d’information modelisation, optimisation commande en genie des procCdes, October Toulouse, France 2002 Belaudj. P. Roux P. Pons M . Opening Unit Operations for Process Engineering Software Solutions, AIDIC Conference Series, Val. 6, AIDIC & Reed Business Information S.p.A. (2003) pp 35-44 Brandenburger A. N a f e b u f B. Co-opetition, Currency Doubleday, New York 1996 Braunschweig B. L. Britt H . Pantefides C. C. Sama S. Process Modeling: the Promise of Open Software Architectures, Chemical Engineering Progress, September (2000) pp. 65-76 Braunschweig B. L. Gani R. (eds.) Software Architectures and Tools for Computer-Aided Process Engineering, Elsevier, Amsterdam 2002 COGents (2004), COGents project Web site, www.cogents.org Cutter (2003) Consortium Web Services Terminology, Web Services Strategies, Vol. 2, No. 12. December 2003

12 Fay S. (2003), Standards and Re-Use, The

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Rational Edge, May 2003, www106.ibm.com/developerworks/rational/ library/2277.html Fieg G. Gutermuth W . Kothe W. Mayer H . H . Nagef S. Wendeler H . Wozny G. A Standard Interface for Use of Thermodynamics in Process Simulation, Computers and Chemical Engineering, Val. 19, Suppl., (2002) pp. S317-S320 Google Web APIs Beta (2004), www.google.fr/apis/index.html Heintzman D. (2003), An Introduction to Open Computing, Open Standards, and Open Source, The Rational Edge, July 2003, www-lO6.ibm.com/developerworks/rational/ library/content/RationalEdge/archives/ julyO3 .html IBM Glossary (2004), Glossary of Computing Terms, www-306.ibm.com/ibm/ terminology/goc/gocmain.htm Koch C. (2003),The Battle for Web Services, CIO magazine, October 2003, www.cio.com/ archive/l00103/standards.html Iwanitz F. Lange /. OPC-Fundamentals, Implementation and Application, Huthig Fachverlag 2002 Linthicum D. S. Next Generation Application Integration: From Simple Information to Web services, September 2003, Addison Wesley, Boston 2003 Mahalec V. Open System Architectures for Process Simulation and Optimization, AspenTech Speech, ESCAPE’8 Conf., Belgium, 25 May 1998 Manes A. T. Web Services: a Manager’s Guide, September 2003, Addison Wesley, Boston 2003 Oellermann W. Create Web Services with Business Value, .NET Magazine, November 2002, Val. 2, Number 10, www.ftponline.com/wss/2002-1l/magazine/features/ wollermann/default.aspx OPC foundation (1998).OPC Technical Overview, www.opcfoundation.org/Ol-about/ 0PCOverview.pdf

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Pons M. Belaud]. P. Banks P. Irons K. Merk W. Missions of the CAPE-OPEN Laboratories Network, Proceedings of Foundations of Computer-Aided Process Operations, 2003, Coral Springs, Florida 2003 Sama S. PiiTol D. Serra M. Web-based Process Engineering, Petroleum Technology Quarterly, 2003 Sessions R. What is a Service-OrientedArchitecture (SOA)?Objectwatch Newsletter, Number 45, October 2003, www.objectwatch.com/issue-45.htm Shenf M. H. When is Standardization Slow ?, International Journal of IT Standards and Standardization Research, Vol. 1, Number 1, March 2003 Sim42 Foundation Simulator 42 Open Source Chemical Engineering Process Simulator, 2004 www.virtualmaterials.com/sim42 Sprott D. Wilkes L. Understanding ServiceOriented Architecture, Microsoft Architects Journal, EMEA edition, January 2004, www.thearchitectjournal.com/Journal/ issue I /article2.html Teague T. L. Electronic Data Exchange Using PlantData XML, AIChE Spring National Meeting, 10-14 March 2002, New Orleans Riverside, New Orleans 2002

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Teague T. L. PlantData XML, Section 4.3 of Software Architectures and Tools for Computer-Aided Process Engineering, Elsevier, Amsterdam 2002b W3C (2004)W3C, World-Wide Web Consortium, Web Ontology Language Use Cases and Requirements, www.w3.org/TR/2004/ REC-webont-req-20040210/ Warner A. G. Block Alliances in Formal Standard Setting Environments, International Journal of IT Standards and Standardization Research, Vol. 1, Number 1, March 2003 Weiss M. Cargill C. Consortia in the Standards Development Process, Journal of the American Society for Information Science, Vol. 43, Number 8 (1992)pp. 559-565 Westhaus U.DETHERM ... on the Web, an On-line Service from DECHEMA, http://isystems.dechema.de/detherm/ 2004 White M. Working Together: Collaborative Competition Creates New Markets, Cap Gemini Ernst & Young Center for Business Innovation E-journal, Issue 5 (2000) pp. 33-35, www.cbi.cgey.com/journal/issueS/ index.hhnl

Section 5 Applications

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

The previous sections ofthis book have shown how process systems engineering has developed methods and tools to address the increasing complexity of the process industries; it seeks tofoster the development of new products and processes, to achieve optimal operation of complex equipment, and to help in the complex management ofthe global enterprises. Section 5 illustrates some applications of CAPE techniques, and aims to demonstrate what their benefits are, their current limits, and their short and long-term perspectives. Thefirst chapter illustrates the issue of education and training: how to teach the students to eficiently use very powerjd tools, in order to better understand the concepts, to appreciate how the theory can be put into practice, while avoiding the dangers of misusing the software by merely pushing buttons to generate results. The applications covered deal mainly with process and product design, and illustrate also the concept of tool integration, since results must be carried o u t f i o m one calculation step to the next. The second chapter concentrates on model-based process operation. It illustrates various industrial applications of data validation, and shows how the use of more detailed models can improve the accuracy of estimating plant parameters. Use of thermodynamic constraints besides component and overall mass balances is illustrated. Examples are taken f i o m a range of industries: oil refineries, chemicals, fertilizers, nuclear power plants. The main benefits are more reliable plant monitoring, capability to operate closer to limits with a better eficiency, early detection offaults, and reduction of analytical and instrumentation cost. The last chapter illustrates CAPE techniques applied to solving production-planning problems for a multiproduct plant. The goal is to optimize revenue by reacting sw$y to changes in product demand, market prices and feed stocks availability. The uncertainty aspect is modeled by means of a stochastic approach. Multiple objectives are considered: either maximizing the expected value of thefinal profit over the planningperiod, or maximisation of thefirst quartile of the profit (robust solution). All steps i n the application ofthe method are illustrated by means of a case study takenfiom afood additives plant. Thus, Section 5 illustrates the diversity ofCAPE tools and methods, and shows examples ofcurrent practice i n areas rangingfiom process design to plant operation and production planning under uncertainty.

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8 I773

1 Integrated Computer-aided Methods and Tools as Educational Modules Rafiqul Gani andJens Abildskov

1.1 Introduction

The CAPE community has been developing computer-aided methods and tools for several decades and these days it is common practice in teaching as well as in industrial problem solving to use one or more pieces of currently available software. Students are trained to solve process-product engineering problems with state-of-the-art software, which they also later use during their professional career. Process simulators and their use in process design education has become a standard tool for process design courses everywhere. While these tools are able to provide excellent training in analysis of problems that are well-defined and have sufficient information to completely solve the problem, it is questionable if they are also suitable for solving open-ended problems (Dohertyet al. 2000), such as those related to process-product design. Also, use of these tools in process-product design encourages the use of the inefficient trial and error solution approach as opposed to a systematic generate and test approach where additional tools for synthesis and design may be used together with process simulators. As computer-aided design becomes more prevalent in the process industry, according to Finlayson and Rosendall (2000),it is essential that graduating engineers know the capabilities of the computer-aided systems that are available as well as the scepticism to interpret the results wisely. At the same time, advances in computeraided design and simulation tools and reduced computing costs have allowed new uses of computing in chemical engineering education. Indeed, chemical process industries remain one of the strongest segments of the world-wide economy due to the cost effectiveness of well-designed chemical processes as well as to innovative chemistry (Doherty et al. 2000). Process simulators (ASPEN+,PRO-11, gPROMS, ChemCad, ProSim, etc.) together with modeling and simulation software (Mathematica, Maple, MATLAB, etc.) have become standard computer-aided tools in chemical process design, process control Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCHVerlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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and, chemical process-operationmodeling. As industries face major new challenges because of increased global competition, greater regulatory measures, uncertainties in prices for energy, raw materials and products, etc., it becomes more and more important to consider integrated solution approaches. Similar to process integration, tools and/or problem integration imply the solution of more than one problem simultaneously or use of more than one tool in the solution of the problem. Also, the introduction of new courses such as product design has led to new challenges in fields such as applied thermodynamics (Abildskov and Kontogeorgis 2004), which also requires new software. This chapter highlights the use of a system viewpoint within an integrated approach to the solution of chemical engineering problems. As noted by Edgar and Rawlings (2004),the chemical engineer leverages knowledge of molecular processes across multiple length scales to synthesize and manipulate complex systems that encompass both processes and products. Several computer-aided educational modules that encourage the development of this viewpoint, are presented in this chapter. First, a brief overview of the integrated approach to CAPE is given, followed by a short presentation of an integrated computer-aided system that has been used as a basis for the development of a number of computer-aided education modules. Three examples of these educational modules are presented together with references of where other modules can be found. In conclusion, uses of these modules in courses are discussed.

1.2

Integrated Approach to CAPE

An integrated approach to CAPE, also known as concurrent engineering, simply means the solution of two or more problems in a single step, for example, make decisions in the early stages of design that also select the control structure and guarantee acceptable environmental impact. In this way, it is similar to process integration where two or more operations are performed through a single operation, for example, a heat exchanger combining a cooling operation with a heating operation. Application of the integrated approach, however, also needs an integration of tools. As illustrated through Fig. 1.1, most CAPE problems (synthesis, design, and analysis) are multitask by nature and require a number of different tools. To achieve integration of tools, it is necessary to establish the workflow and data flow with respect to the solution steps and the tools that would be needed in each of the steps. Tools integration, therefore, avoids duplication of work while providing efficient data transfer from one tool to another. Through a computer-aided framework that includes a collection of tools (and their associated subtools such as databases, models, solvers, etc.) and allows access of the tools according to specific workflow and data flow, typical chemical engineering problems can be solved in an integrated manner. More details on tools integration can be found in Fraga et al. (2002).

7.2 Integrated Approach to CAPE

Develop methods for process integration and algorithms for tools integration

Figure 1.1

Multidisciplinary

tools for nature processproduct design problems

1.2.1 Integrated Computer-aided System

An integrated computer-aided system (ICAS) (Gani 2001) combines computational tools for modeling, simulation (including property prediction), synthesis/design, control and analysis in a single integrated system. These computational tools are presented as toolboxes. During the solution of a problem, the student moves from one toolbox to another in order to solve problems, which require tools from more than one toolbox. Typically, problems in process synthesis, process design, and process control require the use of more than one tool. For example, in process design/synthesis, one option is to define the system input stream, to analyze the mixture (use of analysis tools), to generate flow sheet alternatives (synthesis/design tools), to evaluate the alternatives (simulation and analysis tools), and finally, to optimize the flow sheet (design tools). Each toolbox has a number of tools associated with it and are connected to the necessary tools from other toolboxes. Figure 1.2 illustrates the architecture of ICAS. ICAS has been developed specifically to solve problems in an integrated manner, which can be used to develop educational modules for different types of productprocess engineering problems. It is currently used to solve industrial problems as well as research and teaching. In this chapter, only the teaching related features will be highlighted. As shown in Fig. 1.2, ICAS consists of a simulator (with steady state and dynamic simulation engines) having the same features as other process simulators. ICAS, however, also has tools that “add to the system” and “toolboxes”that help to solve some of the tasks typically found in different CAPE related problems (for example, designselection of solvents, synthesis of process flow sheets, environmental impact analysis, model parameter estimation, etc.). The “add to the system” helps to introduce new compounds into the database, new unit operation models into the simulation model library, and new property models into the property model library in an integrated manner and requiring no additional programming. Once all these additions are introduced to the system, all tools within ICAS will be able to use them. In this way, the “add to the system” and “toolboxes” help to define the problem

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ICAS

An ahT1u

L

1

J

1

F

Kmetic hlodel

Adaptation

I

solved together Figure 1.2 problems

Multidisciplinary tools for nature process-product design

where most of the time is spent in software-based solution of problems. Often, the problems are not defined correctly or consistently, resulting in failure of the numerical solver. The different features of ICAS help to guide the students into defining/ formulating the problem correctly so that the numerical solver does fail, if a solution for the formulated problem exists.

1.3 Educational Modules

Three computer-aided educational modules involving property prediction (suitable for a course on thermodynamics or product design), extractive distillation-basedseparation (suitable for courses on separation processes, distillation, or process design), and model derivation and solution (suitable for courses on modeling, simulation and/or numerical methods) are presented. The objective of these educational modules is to highlight the solution strategies for typical chemical engineering problems (traditional as well as new) where software may be used (with clearly defined objectives) in some or all the solution steps (tasks).At the same time, it is emphasized that

7.3 Educational Modules I 7 7 7

the software is just an efficient calculator (that is, it provides answers when asked) but it does not work as an engineer. Also, in addition to the above calculator service, the software plus the workflow and data flow provide insights to improve the solution efficiency (of the overall problem) and therefore, the productivity of the user (student). 1.3.1 Computer-aided Property Estimation

This computer-aided teaching module introduces the students to the workflow, data flow and the tools needed to perform phase equilibrium calculations (saturation point calculation and generation of various types of phase diagrams: vapor-liquid, liquid-liquid or solid-liquid). The students learn the importance of the property model selection, the need for property databases, the need for additional property models, the model equations, and finally, the important calculation steps for solving the problem. In this way, the students are able to appreciate not only the property related calculations but also understand their influence in other problems, such as process simulation and design. Two problems are presented here: 0

0

Analyze the properties of a chemical called chemical fentanyl. Evaluate the binary mixture of ethanol-water.

The first problem could easily come from the product analysis step of a chemical product design problem, while the second problem could come from a bioprocess (downstream separation of a fermentation product or solvent based separation by distillation or even a solvent based crystallization process). In order to progress further in the process-product design problem, the pure component properties as well as the mixture properties need to be evaluated. 1.3.1.1 Analysis of Fentanyl

Here, we wish to analyze the properties of fentanyl (CAS number 000437-38-7) in terms of its state at the normal conditions of temperature and pressure, if it is toxic and its solubility properties in water and other solvents. The pure component properties that would be needed are: normal boiling point (Tb),normal melting point (Tm), the heat of fusion (AHf),the heat of vaporization (AHvap), the vapor pressure (Pat), the Hildebrand solubility parameter (as),the octanol-water partition coefficient (log &,) and a measure of toxicity (LCsO). The following steps (workflow) could be performed: 1. Check databases to find properties of fentanyl (properties such as Tb, Tm, A&, (Hvap, Pat, a s , log &,and Lcso). 2. If the properties cannot be found in the databases, use a property estimation package. a. Generate the needed properties through a property model by giving the molecular structural information.

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3. Analyze the properties (estimated or retrieved from database). a. What is the state (solid, liquid or gas) at the normal condition of temperature and pressure? b. Is it a hazardous compound? c. Are there known solvents for fentanyl? d. How can solubility of fentanyl in solvents be quickly checked?

The methods and tools that are needed to perform the workflow shown above are the following: a fairly large database of pure component properties, a software package for prediction of pure component properties (with its resident model parameter tables), a software package for solvent search, a software package for solubility calculations (requires property models for mixture properties as well as algorithms for saturation point calculations).ICAS provides all the above in a single integrated system. Uses of ICAS (Gani 2001) for each of the above steps are highlighted below (information on all the ICAS tools can be found at www.capec.kt.dtu.dk/Software/ICAS-andits-Tools/or in Gani (2001)): Step 1: Search of the CAPEC database (Nielsenet al. 2001) in ICAS finds fentanyl but having only the molecular weight (336.48) and the normal melting point (360.65 K). This means all other properties need to be estimated. Databases in most process simulators will not have this compound or its properties. Step 2 To generate the properties, the ProPred toolbox within ICAS is used. ProPred needs the molecular structure of the molecule (as a 2D drawing, as a 2D/3D mol.file or as a SMILES string). The CAPEC database has the SMILES string, from which ProPred is able to draw the molecule, identify the needed groups and estimate the properties (in the case of fentanyl, since all the group parameters were not available, it also needed to create the groups, which is an option available in ProPred). Table 1.1 gives the SMILES string for fentanyl, the 2D drawing of the molecule and the properties estimated by ProPred. Step 3: Analyze fentanyl in terms of the generated properties. Step 3a: At the normal condition of 300 K and 1 atm, fentanyl is solid. Step 3b: It is hazardous as indicated by the -log (LC50) value. A high value (higher than 3) indicates a highly toxic compound. LC50 is the aqueous concentration causing 50 % mortality in fathead minnow after 96 hours. Step 3c: The CAPEC database does not list any known solvents for fentanyl. However, as the Hildebrand solubility parameter is known (6, at 298 K), it can be used to obtain some idea of which compounds could be good solvents. A search of the database for compounds having similar & (at 298 K) shows that hydrocarbons are likely to be good solvents while fentanyl will have very low solubility in water. Step 3d: To estimate the solubility, the needed properties can be seen from the following equation (condition for solid-liquid equilibrium where only one compound exists in the solid phase): 1 = X S Y S exp [AHfI(RTm)I(T - Tm)l]

(1)

SMILES string

CCC(=O)N(C~CCCCC~)C~CCN(CCC~CCCCC~)CC~

Tb

703.47 K (estimated with created groups[’])

T,

360.65 K

AHf

44.66 kJ mol-’ (estimated with created groups)

AH,,,at 298 K

42.16 kJ mol-’

6s at 298 K

20.78 MPa”* (estimated with created groups)

Log K,

3.85

-Log (LCSO)

7.32

P”‘ at 300 K

Fentanyl is solid at this ternperatwe

where x, is the saturation composition of solid s in solution, y s is the liquid activity coefficient of the solid compound in solution, R is the universal gas constant and T is the temperature at which solubility is to be calculated. From Eq. (l),it becomes dear that to estimate the solubility of fentanyl in a solvent,we need to estimate its liquid activity coefficient in the solvent (for which a property model is necessary) as well as the heats of fusion and melting point of fentanyl. A quick estimate may be obtained by setting y, = 1 (assuming ideal liquid). Note that if a liquid activity coefficient model such as UNIFAC (Hansen et al. 1991; Kang et al. 2002) is used, it will require the corresponding group interaction parameters, which for fentanyl are not available. Also, since ys is dependent on composition as well as temperature, an iterative solution technique would be necessary. The SoluCalc toolbox in ICAS, which has been specially developed for estimating solid solubility in solvents, can be used for this purpose. Figure 1.3 shows the calculated fentanyl saturation curve in hexane (solvent).Note that the students have the option to directly calculate the temperature versus composition diagram through ICAS utility toolbox, or, develop their own binary SLE phase diagram software using the property model (as a model object) from ICAS through modeling/simulation software (such as EXCEL, MATLAB, etc.).

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Figure 1.3

x,

Estimated saturation solubility curve for fentanyl in hexane

The above workflow could be repeated for any new chemical being considered as a product, provided the needed property variables can be identified and their values measured or estimated through appropriate property models. Solving this type of problems with process simulators is not efficient and in most cases probably not also possible. Having all the necessary tools available in an integrated manner saves time and provides valuable insights to the problem and its solution. 1.3.1.2 Evaluation of Ethanol-Water Mixture

Here, we wish to evaluate the ethanol-water mixture with respect to its separation from a biofermentation reactor. Depending on the mixture characteristics, different separation schemes may be generated. Here, however, we will first look at the vapor-liquid equilibrium and confirm that it is indeed a minimum boiling azeotrope. Then we will introduce a solvent, for example benzene or ethylene glycol, to the system and evaluate the ternary mixture (in terms of ternary azeotrope and liquid-liquid miscibility).The methods and tools needed to perform these tasks (calculations) are available in most commercial simulators but they are not necessarily organized for an integrated approach. In this example, however, we will break down the problem into multiple tasks in order to understand the problem, to highlight the importance of property model selection, the need for accurate pure component properties (in this case, vapor pressure) as well as the associated workflow (calculation steps or tasks) and data flow. Since ethanol-water is a nonideal mixture for which vapor-liquid (and possibly vapor-liquid-liquid when a ternary system is considered), equilibrium needs to be calculated, the properties, calculation methods and tools that are needed, are linked to the equilibrium model used. That is, if we select the equilibrium model as a twomodel gamma-phi type, we may select an activity coefficient model for the liquid

1.3 Educational Modules

phase and the ideal gas model (equation of state) for the vapor phase. Neglecting the Poynting correction factor, the vapor-liquid equilibrium is represented by:

In the above equation, yl is the vapor phase composition of component i, x, is the corresponding equilibrium liquid phase composition, y ,is the liquid phase activity coefficient of component i, F' is the vapor pressure of component i at the equilibrium temperature and P is the corresponding system pressure. Since y bis a function of composition and temperature and is a function of temperature, an iterative solution scheme needs to be devised to obtain the equilibrium temperature and the corresponding vapor composition for given liquid composition and pressure. Repeating the calculations for different values of liquid composition within the limit zero to one and keeping the pressure fxed at the original value, generates the entire so-called PT-xy diagram. Now consider the following three options:

rt

0

0

0

Given models for yl (for example, UNIFAC) and PFt (for example, the Antoine correlation), develop a computer program to generate the phase diagram. In principle, any modeling software (EXCEL, MATLAB, etc.) can be used to develop the software with the ICAS supplied property model object. Given a program to calculate the saturation temperature and vapor composition for specified liquid composition and pressure (and for a selected set of property models), repeat the calculations to generate the phase diagram. In principle, any modeling software (EXCEL, MATLAB, etc.) can be used to develop the software with the ICAS supplied property-utility object. Given software with built-in models and calculation options, select the appropriate model and calculation option to generate the needed phase diagram. In principle, any process simulator and/or ICAS utility toolbox may be used. If, however, the compounds are not ethanol and water, then the available options in the software need to be checked.

All three options will give the required solution, while the first option will be timeconsuming, the student will gain more insight on the needed workflow and data flow than the last option, which will be efficient in terms of problem solution but will provide little insight. An interesting approach could be to get the students to use all options, that is, use the first option at the beginning and use the last option when they are experienced in phase equilibrium calculations. This example also provides insights on property model selection (assuming an ideal system, which is usually the default selection for many software, the azeotrope will not be found) and accuracy of the needed properties (that is, the predicted azeotrope location may be highly sensitive to the accuracy of the vapor pressure model). Also, the parameters of the liquid activity coefficient model are important as they may give different values of the location of the azeotrope. Having analyzed the binary system, the next step is to analyze the mixture when a third component (for example, a solvent) is introduced. What happens to the azeotrope? Are there still a vapor and a liquid phase in equilibrium? If not, is there an

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additional liquid phase? If yes, how to calculate the phase compositions and is there also a ternary azeotrope? As in the case of the binary mixture calculations, most commercial simulators also provide options to perform the calculations so that the above questions can be answered. The important points, however, are the following: Have the correct property model selections been made? What are the workflow and data flow? Are the results acceptable?Again, by breaking down the problem into multiple tasks, the students will gain more insights to the solution of the problem. In terms of calculations, in addition to the vapor-liquid equilibrium, the liquid-liquid equilibrium also needs to be computed: X l i Y l i = X2iY2i

(3)

The subscript 1 and 2 in the above equation indicates liquid phase 1 and liquid phase 2, respectively. The same liquid phase activity coefficient model will now be used in Eq. (2) and ( 3 ) .However, the liquid composition from Eq. (2) needs to be checked for phase stability and if found unstable, Eqs. (2) and (3) will need to be solved simultaneously. The following calculation steps (workflow) could be used 0

0

Use Eq. ( 3 ) to identify any binary pair (there are 3 binary pairs in the ternary mixture), which splits into two liquid phases: - Check also if this is the vapor-liquid azeotrope point (for a vapor-liquid-liquid system, one pair will satisfy this condition). - For the binary system showing both an azeotrope as well as liquid-liquid phase split, add incremental amounts of the third component and perform the vaporliquid-liquid calculations until there is only one liquid phase (note that for each calculation, the pressure is fixed at a constant value but the temperature is also calculated).The ethanol-water system with benzene as the solvent will show a vapor-liquid-liquid ternary system with the benzene-water pair showing the binary liquid-liquid phase split. If none of the binary pairs split into two liquid phases, there will only be a vapor in equilibrium with liquid and the calculations for the binary mixture can be repeated in the same way as before. The ethanol-water system with ethylene glycol as the solvent will show only a vapor-liquid system.

The three options listed above for the binary mixture calculations can also be repeated now for the ternary mixture calculations. Again, initially, it is better for the students to develop their own calculation program but later, they can use standard software (process simulator and/or ICAS utility toolbox). Further extension to this problem could be considered by adding an inorganic salt to the ethanol-water mixture (to study the salting-in or salting-out effect). Here, again the workflow will basically remain the same but the data flow will be significantly different because of the different property models and their corresponding property parameters. The above modules will prepare the students to solve all types of phase equilibrium problems in a systematic way, even when not all data and/or property model parameters are available. One advantage of allowing the students to develop their

7.3 Educational Modules

own software is that in the case of new compounds or systems, they will be better prepared to perform the necessary tasks. Note that since developing their software will not need much programming effort, they will actually concentrate on learning the calculations involved in each task.

1.3.2 Separation of Azeotropic Mixtures

The second computer-aided educational module introduces the students to aspects of design and simulation of solvent-based extractive distillation. The students use the phase diagrams that they have learned to generate. The main feature of this module is that it encourages the students to make the design decisions based on simple thermodynamic calculations rather than use the simulator on a trial and error basis to find the solution. That is, all the important design decisions are made through the generated phase diagrams and thermodynamic insights (for example, sequencing of distillation columns, selection of solvents, design of individual columns, etc.), which also generates an initial estimate for a detailed simulation of the process. In the final step, the initial estimate is passed to the simulator and the solution is obtained without too many iterations (by the rigorous model solver). Therefore, the student spends less time with the simulator and more time generating information (knowledge) that can be used for problem solution. 1.3.2.1 Problem Description

The problem which we will consider is the separation of a binary mixture of acetone and chloroform into high purity products. As this binary mixture forms an azeotrope (to be verified), solvent-based extractive distillation is an option. Benzene is a well known solvent that has been reported as a suitable solvent. Benzene, however, is not acceptable for environmental, health and safety (EHS) reasons and an alternative solvent needs to be found and verified. 1.3.2.2 Problem Solution

The following steps provide a solution to this binary mixture problem. Step 1: Perform a mixture analysis and verify that an azeotrope exists and check for its dependence on pressure. Make decisions/choice of property model and calculation steps. An ideal system cannot be assumed since the binary mixture forms an azeotrope. A VLE-based phase diagram (using Eq. (2)) needs to be generated. Figures 1.4a and 1.413 show the binary azeotropes as a function of pressure (ICAS utility toolbox is used to generate these diagrams). Step 2 Find solvents that perform as well as benzene but without the negative EHS properties of benzene. Using the ProCAMD tool in ICAS, a large number of candidate solvents are generated. The problem definition is as follows: find solvents that

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Figure 1.4 Acetone-chloroform VLE calculated at 5 bar (a). Acetone chloroform VLE calculated at 1 bar (b)

are acyclic organic compounds having 320 K < Tb < 420 K, T, < 250 K, that is more selective to chloroform than acetone (selectivity > 1.7), is totally miscible with acetone-chloroform (therefore a vapor-liquid system) and does not form azeotrope with either acetone or chloroform. The solution statistics from ProCAMD is shown in Fig. 1.5. It can be noted that 5614 candidate molecules were generated, out of which 59 satisfied all constraints. From these 59 molecular structures, 133 isomers were generated and a more refined property estimation was made to identify 111 compounds that satisfied all constraints. Note that to identify the solvents, pure component properties ( Tb, T,) as well

: I _I-

_I.--^ Number d

m q o u n d s designed 5614 Number ot m g p u n d s d e c t e d 59 Number 01 itmers deslped 133 Numbn of is0mt.l selected 111 Tolal tm wed to hesign 0 32 s

I'ScreenedOM'Statistics In1 Prnnery Calculatms F ~ m c I i mpwp I m w m q 5755 of 5614 Nmmal Bdinp point 36 d 259 Molecular wlghE 92 of 223 Solvent lox 7 of 131

_I

Figure 1.5 Solution statistics from ProCamd for the solvent selection/design task

7.3 Educational Modules

1

785

CHLOROFORM (61 1) Azeotrope Feed from ICAS

*I

0

A

__

0 ACETONE (56.1)

100

0

2-METHYLHEPTANE (1 17.6)

Figure 1.6 Calculated distillation boundaries for the acetonechloroform solvent

as phase equilibrium calculations (selectivity,azeotrope calculation and liquid miscibility) needed to be performed. Therefore, an integrated system capable of doing these steps automatically for the user is very useful for this type of problems. Two of the alternatives found are methyl-n-pentyl-etherand 2-methylheptane. Step 3: Analyze the alternative solvent candidates in terms of distillation boundaries. For this step, the PDS tool in ICAS is used. PDS performs, among others calculations of distillation boundaries, residue curves and distillation column design for a specified ternary system (reacting or nonreacting). This problem is nonreacting and the distillation boundaries calculated through PDS are shown in Fig. 1.6

Step 4 Generate the process flow sheet and design the corresponding distillation columns. This can be done interactively. Design the first distillation column with the feed mixture and the fresh solvent added. The combination of the feed mixture and solvent places the total feed in the region where acetone can be obtained as the top product, and a mixture of mainly solvent and chloroform will be obtained as the bot-

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All temperatures are displayed in Celcius

CHLOROFORM

-+-

Liquid on top trays Vapor on top trays -t Liquid on bottom tray -AVapor on bottom tray

+-

0 ACETONE

100 n 2-METHYLHEPTANE

Figure 1.7 Design of the distillation column that is consistent with the distillation boundaries

tom product. This feed will then be sent to a second column, from where the chloroform will be obtained as a top product and the solvent will be recovered and recycled. PDS and ICAS-SIM (steady state simulation engine) can be used interactively to design the first column (number of stages, feed location, product purity, reflux ratio, etc.) and verified through steady state simulation. Then the second column is added and the procedure repeated, which also generates the total flow sheet. Figure 1.7 shows an output from PDS, highlighting the design calculations for the distillation column. Step 5: Perform simulation and optimization to determine the optimal design of the separation process. In this case, all solvents can also be included in the same calculations and the optimization problem will find the optimal flow rate for each of the solvents. The flow sheet used in problem formulation and the sample simulation of the flow sheet are shown in Figs. 1.8a and 1.8b. This last step can be performed with the steady state simulation engine of ICAS or with any process simulator. ICAS has a

1.3 Educational Modules

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787

S Q d y colmn connection stream nurnbprs ; .

I c

Feedsham1

FeedPtream2

Top prohfucl

EWnrtl product

1 :

Plole T b top product 6 hnuld a l w y h.we tee lowett stream w~rnher, cornparad to the bottom plrdlJCt Stlmv

7

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Figure 1.8a Generation of flow sheet (synthesis and design) with PDS-ICAS (a).

direct interface for the PRO-I1 steady state simulator. This means that any flow sheet synthesized and designed can be directly simulated in PRO-I1 without adding any further information in PRO-11. Several variations of the problem are possible. For example, provide a binary azeotropic mixture that has significant pressure dependence so that the solvent-based separation can be compared with pressure-swing distillation. If a solvent that introduces a phase split is selected or specified, then at least one distillation column will have vapor-liquid-liquid phase equilibrium and the design calculations will have to be consistent with the resulting distillation boundaries. Also, a reacting system may be introduced. Basically, the tasks (steps in workflow) shown above would be similar in all cases but the data flow would be different because of specific choices of the models used to perform the tasks. If the student is given the calculation steps (workflow) and a corresponding set of integrated tools, the students will not only be able to solve these problems without too much difficulties but also gain valuable insights with each solution step.

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b ) S T R E A M NUHBER

_____-----

_________--______-

TEMPERATURE (K) PRESSURE (atm) ENTHALPY ( K/ Kmo l e ) ENTROPY (l/Kmole) U-ENERGY (K/Kmo l e ) DENS. ( K m o l e / m " 3 ) VAPOUR FRACTION L I Q U I D FRACTION -- - -- ( K m o l e / h r ) ACETONE CHLOROFORM 2 -ME THYL HE P T W E

_

__

-

STREAM NUMBER

___ _

.

----_ __ _ -_ _ 10.00039 10.98840 89.89447

373.15131 332.04270 1.00000 1.00000 -24505.51626 -26910.01571 44.693 63 35.62 145 .24532.76285 -2 6910.18654 5.85403 0.03 670 0.00000 1.00000 1.00000 0.00000 9.05476 0.85620 0.06853

__________ 9.97949 ________-_ __________

5

6

389.00747 1.00000 -27545.64659 47.80138 -27545.83081 5.42829 0 .ooooo 1 .ooooo

350.00000 1.00000 -19114.10880 3 6.69383 -19142.82893 0.03482 1.00000

0.00039 0.98811 88.89475

10.00000 10.00000 1.00000

4

3

__________

_ _ _ - _ _ --_ _ _ _ _

.

0.94563 10.13220 89.82593

342.63881 1.00000 -14287.60495 37.41181 -143 15.72 103 0.03557 1.00000 0.00000 0.94524 9.14408 0.93118

_____-___11.02051 __________ __--_-_-_-

_-_-_-_-_- __________

_________________TEMPERATURE ( K ) PRESSURE (atm) ENTHALPY ( K / K m o l e ) ENTROPY(l/Kmole) U-ENERGY ( K / K m o l e ) DENS. (Kmol e / m * 3 ) VAPOUR FRACTION L I Q U I D FRACTION - -- - ( K m o l e / h r ) ACETONE CHLOROFORM 2 -ME THYL HEP TANE

350.00000 1.00000 -27615.86917 41.50294 -2 76 16.02 699 6.33 628 0.00000 1.00000

2

-

0.00000

__________ 2 1.00000 _---_--____ _________ __________ __________ -------_-_ 89.88325

Figure 1.8b sheet (b)

Verification by simulation o f the generated process flow

1.3.3 Integrated Computer-aided Modeling

The third educational module deals with modeling issues. Here, the importance of model analysis before attempting to solve the model equations is emphasized together with model reuse in an external modeling/sirnulation environment. The degrees of freedom, the ordering of equations, the method of solution are all interrelated and through a computer-aided modeling toolbox, the students are encouraged to use these features whenever they have to solve problems represented by a set of equations. As shown in Fig. 1.9, the objective is to transform the model equations into a program code that can be used by other simulation engines and/or solvers. At the same time, the programming effort should be a minimum. But, before going to the solution phase, the model equations must be thoroughly analyzed. Although the modeling/simulation problems in most cases can be solved through a number of existing programs (MATLAB, Maple, Mathematica, etc.), in the current example, the use of ICAS-MOTis highlighted for the reasons given above.

7.3 Educational Modules

Figure 1.9 Import o f model equations to MOTand after transformation and analysis, export to a process modeling component (or external simulation engine)

The use of MOT, a tool in ICAS, as an educational tool will be highlighted through a simple reactor modeling exercise. 1.3.3.1 Modeling Problem Description

The series reactions:

are catalyzed by H2SO4. All reactions are first order in the reactant concentration. The reactions are carried out in a semi-batch reactor that has a heat exchanger inside with UA = 35 000 cal h-' K and ambient temperature of 298 K (see Fig. 1.10). Pure A enters at a concentration of 4 mol dm-3,a volumetric flow rate of 240 dm3h-', and a temperature of 305 K. Initially there is a total of 100 dm3 in the reactor, which contains 1.0 mol dm-3 of A and 1.0 mol dm-3 of the catalyst H2S04.The reaction rate is independent of the catalyst concentration. The initial temperature of the reactor is 290 K. The objective of this exercise is to highlight the basic features of ICAS-MOTand at the same time, the modeling steps needed to obtain the dynamic evolution of all concentrations in the semi-batch reactor for the given operating conditions.

vO

Figure 1.10 Semi-batch reactor scheme

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1.3.3.2 Description of the Mathematical Model Mole Balances

dcA dt

-==A+

d CEI dt

- = rg

dCC dt

(CAO - CA) VO V CB V

- -VO

CC V

- = rc - -vo

(7)

and the kinetic constants are Arrenhius-type

The relative rates are obtained using the stoichiometry (liquid phase) for the reaction series (Eq. (4)):

So that the net rates are as follows:

rA = r1A = -klACA

4 mol dm3 mol FA,, = -x 240 - 19GO dm3 h h

7.3 Educational Modules

Energy Balance NC

_-

NR

i=l

i=l

dt

NC

is equivalent to dT _ -

uA(Ta - T ) - FAoCPA(T- TO)+ [(AHRxlA)(hA) 4- (AHR~~,)(QB)]V

dt

+ CBCpB + c C c p C ] v f N H z S O ~ C ~ H ~ S O ~

[CACpA

(22)

Summarizing, the process model is given by: four ordinary differential equations (Eqs. (4-6, 22)) and fourteen algebraic equations (Eqs. (8-20); note that Eq. (14)is actually two equations). This differential-algebraic system can be solved simultaneously using ICAS-MOT.The data for this problem can be found in Table 1.2. Table 1.2

Data for the differential-algebraic system

Variable

Value

Units

Description

MoT-variable

CAO

4.0

mol dm-'

Initial concentration of compound A

CAO

CHiSOdI

1.0

mol dm-3

Initial catalyst concentration

CH2S040

vo

240.0

dm' h-'

Initial flow rate

vo

vo

100.0

dm'

Initial reactor volume

vo

UA

35^000.0

cal h-' K

Heat transfer coefficient

UA

T,

298.0

K

Ambient temperature

Ta

To

305.0

K

Inlet Temperature

TO

TI A

320

K

Reaction temperature (reaction 1)

TlAO

K

Reaction temperature (reaction 2)

T2BO

Kinetic reaction constant(reaction 1)

klAO

TZB

~~~

300 ~~~

~

~

~

~ I A

1.25

h-'

kzB

0.08

h-'

Kinetic reaction constant (reaction 2)

k2BO

EIA

9500.0

cal mol-'

Activation energy (reaction 1)

E1A

EZB

7000.0

cal mol-'

Activation energy (reaction 2)

E2B

cPA

30.0

cal mol-' K

Thermal heat capacity of compound A

CpA

cPB

60.0

cal mol-' K

Thermal heat capacity of compound B

CpB

CPC

20.0

cal mol-' K

Thermal heat capacity of compound C

CpC

35.0

cal mol-' K

Thermal heat capacity of catalyst

CpH2S04

-6500.00

cal mol-'

Reaction enthalpy (reaction 1)

DHRxlA

A HRAB

+8000.00

cal mol-'

Reaction enthalpy (reaction 2)

DHRx2B

R-

1.987

cal mol-' K

Universal gas constant

R

CPHSO~

AHR~IA ~~~~~

I

791

792

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1 Integrated Computer-aided Methods and Tools as Educational Modules

1.3.3.3 Modeling Steps in MOT

The model developer does not need to write any programming codes to enter the model equations. Models are entered (imported) as text files or XML files, which are then internally translated. Step 1:Type the model equations in MOTor transfer a text file or an XML file. In Fig. 1.11,the model (Eqs. (4-22)) has been typed into MOT.

............................................ #*Nonisothermal Multiple Reaction * * #* #*CAPEC, Department of Chemical Engineering* #*Technical University of Denmark * #*MSC, April, 2004 *

............................................ #The series reactions: # k 1A K2B B - _ _ _ _ > 3c 274 -----> # # (1) (2)

#************* #Solution

*

#************* #Kinetic klA = klAO*exp( (ElA/R)* (l/TlAO - 1 / T ) k2B = k2BO*exp ( (E2B/R)* (1/T2BO - 1 / T )

) )

#Rate Laws rlA = -klA*CA r2B = -k2B*CB rA = rlA rB = klA*CA/2-k2B*CB rC = 3*k2B*CB #Reactor volume v = vo + vo*t FA0 = CAO*vo Cpmix = CA*CpA + CB*CpB + CC*CpC #Mol balances

dCA dCB dCC

=

= =

rA t (CAO - CA)*vo/V rB - CB*vo/V rC - CC*vo/V

#Energy Balance dT = (UA*(Ta-T) - FAO*CpA*(T-TO) + (DHRxlA*rlA + DHRx2B*rZB)*V)/(Cpmix*V + CHZS04O*VO*CpH2S04) Figure 1.11

MOTmodel

7.3 Educational Modules Figure 1.12a Incidence matrix (a). Equation parttioning and incidence matrix comparison (b)

Step 2: Model translation. MOTtranslates the imported model, lists all the equations and variables found in the translated model. It has built-in knowledge to distinguish between algebraic equations (explicit and implicit), ordinary differential equations and partial differential equations. The variables are classified as parameters, known, unknown (implicit), unknown (explicit), dependent and dependent prime (used for differential equations only). MOT automatically identifies the unknown (implicit), unknown (explicit) and dependent equations. The user needs to classify the known variables as either parameters (which could then be selected for model parameter estimation) or known variables (which could be used as design variables for optimization). Also, the user needs to link the dependent variables to the dependent prime (that is, in dyldt, y is the dependent variable and dy is the dependent prime).

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7 Integrated Computer-aided Methods and Tools as Educational Modules

Step 3: Incidence matrix analysis. As the variables are assigned, MOT is able to generate a corresponding incidence matrix (equations are placed in rows and variables in columns) and order the equations as near as possible to a lower tridiagonal form. Also, unless the degrees of freedom are matched (that is, a square matrix of equations and unknown variables and the known variables equal the degrees of freedom), MOT does not allow the solver to be called. A sample of the incidence matrix is shown in Figs. 1.12a and 1.12b. Step 5: Define the independent variable. In this case, the independent variable is time t. MOT is now able to find the 14 algebraic equations and 4 ordinary differential equations and is therefore ready to start the solver. However, before the solver is called, the initial values for the dependent variables need to be specified together with the parameters and the known variables. Step 6: Set variable values. Figure 1.13 shows the specified values for the variables. Model Solution

Step 7 Select variables for output. The user may select the variables whose values can be stored and visualized as the numerical solver progresses towards the solution.

1

0 0

0 0

a 0 0

h 0

Figure 1.13

Initial condition and values of known variables

1.3 Educational Modules I 7 9 5

Imbendent Vanable

. . -- ..... - .... Figure 1.14 Component A: dynamic concentration motion. Component 8:dynamic concentration motion

.--

Step 8: Select the solver. In this case, dynamic option and forward integration with the BDF method is chosen and an end-time of 1.5 hours may be specified. Step 9: Simulation results. As the numerical solver integrates, the selected variables values from Step 7 will be shown in dynamic plots and their values will be stored in files for later use. Figures 1.14a and 1.14b shows two samples of the dynamic plots.

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1 Integrated Computer-aided Methods and Tools as Educational Modules

Step 10: Saving the MOTfile for reuse as well as export to other simulation engines. When the user is satisfied with the model and its solution, the MOTfile can be saved for use within the ICAS simulation engine, for use from EXCEL or for use from any external simulation engine (with or without the CAPE-OPEN interface). Further expansion of the exercise includes providing experimental data and regressing the kinetic model parameters and process optimization. Other exercises may also be developed where the generated model object is used to simulate the reactor, which is part of a process flow sheet. The same procedure can also be repeated to generate model objects for new property models, kinetic models and unit operation models. Using these model objects and a simulation environment such as EXCEL, the student can develop their own process simulator. For process design tasks involving new chemical products, this option is very practical and useful as the available process simulators do not have the chemicals and/or the models to handle them.

1.3.4 Other Educational Modules

A number of ICAS-based educational modules have been developed and can be downloaded from the following address: www.capec.kt.dtu.dk/Software/ICASTutorials/ICAS-Tutorials-Workshops. These tutorials cover problems related to: 0 0 0

0 0 0

computer-aided property estimation computer-aided modeling computer-aided product design computer-aided separation process design computer-aided batch process modeling integrated computer-aided process engineering.

The objective of all these exercises is to highlight a systematic solution procedure and the use of an integrated set of methods and tools. Other useful information can be found in the document from CACHE Corporation (2004) on Computing through the curriculum: an integrated approach for chemical engineering (www.che.utexas.edu/cache/newsletters/fa112003~computing.pdf). See also Strategiesfor creative problem solving by Fogler and LeBlanc (www.che.utexas.edu/ cache/strategies.html); The fiontiers in chemical engineering education (web.mit.edu/ che-curriculum/); the EURECHA Web site at (www.capec.kt.dtu.dk/eurecha/);the EFCE working party on Education (www.efce.org/wpe.html).

Reference 1797

1.4 Conclusion

The educational modules are documents containing the problem definition together with a detailed step by step solution strategy where the calculations for each step are highlighted with possible use of specific software (data flow and workflow).They can be used by the teacher to highlight an algorithm or methodology or technique (theory). They can also be used by the student to learn how to apply the theory (algorithmslmethods) to solve problems. Through the education modules, some of the important issues (including the danger of misuse) related to the use of computers in chemical engineering education have been highlighted. They have been prepared such that the user is in charge of the navigation and decisions while the computer does the calculations, data transfer, code generation, etc., which it is supposed to perform very efficiently. One of the principal experiences from the use of the presented educational modules has been that once the students understood the main ideas and got familiar with the workflow and data flow, they are able to tackle a wide range of similar problems without much help and in a very short time. In this way, they also learn to appreciate that the computer-aided tools are there to help them but they are the ones who need to make the right decisions and drive the use of the software in the appropriate direction. Finally, it was found that the students were able to appreciate the concepts better, were able to solve more challenging problems in a shorter time, resulting, thereby, an increase in productivity. They were able to use the same methods and tools also for problem solution in other courses. The feedbacks from the students have also helped to improve the software as well as the workflow and data flow of the educational modules. Finally, we would like to emphasize that software should not be used as a replacement of the process-product engineer; it should be used to do what it was designed for, with the user always in charge of directing it.

References Abildskov]. Kontogeorgis G. M. Chemical product design: a new challenge of applied thermodynamics. Chemical Engineering Research and Design 82(All) (2004) p. 1494-1504 Doherty M. F. Mafone M . F. Huss R. S. Decision-making by design: experience with computer-aided active learning. AIChE Symposium Series 323(19) (2000) p. 163-175 Edgar T. F. Rawlings]. B. Frontiers of chemical engineering: The systems approach. DYCOPS Conference. Paper No. 206, Boston, MA, July 2004 Finlayson B. A. Rosendalf B. M . Reactor transport models for design: how to teach

5

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students and practitioners to use the computer wisely. AIChE Symposium Series 323 (96) (2000) p. 176-191 Fraga E. S. Gani R. Ponton J . W.Andrews R. Tools integration for computer-aided process engineering applications, in B. Braunschweig and R. Gani (eds.) Software Architectures and Tools for Computer-aided Process Engineering. CACE-11, Elsevier Science, Amsterdam, (2002) pp. 485-514 Gani R. ICAS Documentations CAPEC Internal Report, Technical University of Denmark, Lyngby, Denmark 2001 Hansen H. R Rasmussen P. Fredenslund A. Schifler M. Gmehling J . Vapor-liquid-. equilibria by UNIFAC group contribution

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8

Revision and extension. Industrial Engineering Chemistry Research 30 (1991) p. 2352-2355 Kang]. W. Abildskov]. Gani R. Cobas]. Estimation of mixture properties from first and second-order group contributions with UNI-

9

FAC models. Industrial Engineering Chemical Research 41(13) (2002) p. 3260-3273 Nielsen T. L. Abildskov J. Harper P. M. Papaeconomou I. Gani R. The CAPEC Database, Journal of Chemical Engineering Data 46 (2001)p. 1041-1044

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

2 Data Validation: a Technology for Intelligent Manufacturing Boris Kalitventzefi Ceorges Heyen, and Miguel Mateus

2.1 Introduction

This document is intended to progressively demonstrate the technical assets of the data validation technology. Most of the technical features of the technology will be enlightened by specific process systems. However, validation technology can be and is implemented in various industrial sectors. Namely, it covers chemical, petrochemical and refining process plants, thermal and nuclear power plants, upstream oil and gas exploitation fields. Data validation is an extension of data reconciliation. Before demonstrating the technical assets of the validation, the reconciliation concept will be reviewed.

2.2 Basic Aspects of Validation: Data Reconciliation

Data reconciliation (DR) is the first mathematical method that addressed the concept of data validation for linear problems. It exploits information redundancy and (linear) conservation laws to extract accurate and reliable information from measurement data and from the process knowledge. It allows for the production of a single consistent set of data representing actual process operations, assuming the plant is operated in a steady state. To understand the basic principles of data reconciliation, one must first recognize that plant measurements (including lab analyses) are not 100% error free. When using these measurements without correction to generate plant balances, one usually gets incoherence in these balances. Some sources of errors in the balances directly depend on sensors themselves: 0 0 0

intrinsic sensor accuracy, sensor calibration, sensor location.

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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2 Data Validation: a Technologyfor Intelligent Manufacturing

A second source of error when calculating plant balances is the small variations in the plant operating conditions and the fact that samples and measurements are not exactly taken at the same time. Using time averages for plant data partly reduces this problem. However, lab analyses are usually carried out at a low frequency, and thus can seldom be averaged. Finally, one must also realize that in some parts of a plant too many measurements are available, whereas in other parts some measurements are missing and must be back-calculated from other measurements. As shown in detail in Section 3, Chapter 3 of this book, data reconciliation can be expressed mathematically as:

subject to where where

F(x ,y*) = 0 G(x ,y") 1 0

pi

Yi

3 oi

F(x,Y") = 0 G(x,y*) 2 0

is the reconciled value of measurement i, is the measured value of measurement i, is the unmeasured variablej, is the standard deviation of measurement i defining its confidence interval. corresponds to the process equality constraints. corresponds to the process inequality constraints. is called the penalty of measurement i.

In early publications on DR, equality constraints were considered linear. Thus, one obtains a quadratic formulation, where the Jacobian matrix of F is constant. It is a Gaussian regression problem: given a set (y, oY), the algorithm provides x and y* vectors together with their standard deviation ay*(when computed). When inequality constraints were not considered, some values y or x could be negative, what had no physical meaning in chemical or mechanical processes, where most variables must be positive (e.g., pressure, flow rate, mole fraction). It was considered as a source of information because one had to find which measurement was responsible for that negative value. Later on, simple inequalities (y 2 0, x 2 0 ) were considered. When F or G is nonlinear, the DR problem can be solved by sequential linearization. The minimization problem is solved iteratively, using algorithms such as SQP (sequentialquadratic programming). It is now possible in some commercial codes to calculate not only the reconciled values of measurements (y?;, oy*) but also unmeasured state variables ( x , ox)and some key performance indicators (KPIs) related to measured and unmeasured state variables (yq, x),as well as their uncertainty aKpI:

measurements Y a priori accuracy *' first principle modeling statistical laws

VALIDAJION

' ' O

x

y*

*X

I

OKPI

Kpl

2.2.1 Redundancy Analyses: Local/Overall

The level of redundancy is the number of measurements, which are available beyond the absolute minimum needed to calculate the system. Three different cases can be encountered: 0

0 0

If a system's redundancy is negative then there is not enough information to determine the state of the system. Additional measurements need to be introduced. A redundancy equal to zero means that the system is globally just calculable. And finally, if a system has a positive redundancy, DR can use it as a source of information to correct the measurements and increase their accuracy. In fact, each measurement is corrected as slightly as possible but in such a way that the reconciled measurements match all the constraints of the process model.

However, overall redundancy is not enough. It must also be achieved at the local scale. Indeed, redundancy can be positive at the global scale, but negative locally; consequently, information is lacking to completely describe the whole process. This point is illustrated with Fig. 2.1, based on a typical synthesis loop. Components A and B are introduced into the process feed, and converted into component C in the reactor unit SYNTHES (2C = 3A + B). Afterwards, the product ABC is separated in three distinct streams. One is recycled upstream in the process, another represents a purge, and finally an outlet stream contains only the compound C. Let us consider a process model restricted to mass balances. Measured variables are shown on Fig. 2.1. This simple process model presents a global redundancy level of 2 (20 equations for 18 unmeasured variables). However, local redundancy of unit SEP-2 is equal to zero. If one of the measurements around this unit was missing then global redundancy of the model would still be 1 but local redundancy of unit SEP-2 would be -1. Therefore, the system would not be reconcilable until a supplementary measurement around the mentioned unit has been provided.

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2 Data Validation: a Jechnologyfor intelligent Manufacturing

I RECYCLED I AB-OUT I I FLOWtld I 300300 I 109109 1

del measured

Figure 2.1

reconciled

Process flow diagram (PFD) of a synthesis loop

2.2.2 If Complementary Measurement(s) are Needed: Which One(s)?

If the available measurement set is not enough to calculate all required process performance parameters, how do you propose an extra set from which complementary measurements can be chosen? Thus, the system becomes either just calculable or locally redundant, but necessarily globally redundant, as illustrated before. Consider the previous example, but here we would remove the total flow rate measurement of stream “purge”.Reconciliation software would then propose a set of variables from which possible complementary measurements ought to be chosen. Namely, the software would purpose in this case a choice between partial flow rates of compounds A and B in either stream “abc”or “purge”,or compound C partial flow rates in either stream “abc”or “c-prod. If it is not possible to add any measurement to the system (because of economical constraints for example), another way of avoiding negative redundancy is to aggregate some units in the model as a more global “black box” (that simply ensures global balances to be satisfied). Less information will be obtained locally, but this may allow estimating the required KPIs.

2.2.3 Increased Accuracy on Measured Data: Why?

As explained before, data reconciliation is based on measurement redundancy. This

concept is not limited to replicate measurements of the same variable by separate sensors; it includes the concept of topological redundancy, where a single variable can be estimated in several independent ways, from separate sets of measurements. Therefore, a posteriori accuracy of validated data will be better than a priori accuracy of measured data. A priori and a posteriori means before and after consistency treatment, or in other words before and after validation and reconciliation.

2.2 Basic Aspects of Validation: Data Reconciliation Table 2.1

DR back corrects measurements and increases their accuracy

AB-1

Flowrate Partial Flowrate (A) Partial Flowrate (B)

RECYCLED

Flowrate

AB-2

Partial Flowrate (A) A-3”B

ton/d tonid ton/d

Meas.

Meas. Acc.

Reconc.

Reconc. Acc.

1016,O 181.0 885,O

3,00% 3,00% 3,00%

1042,8 180,l 862,s

1,64% 2,98% ZOO%

30,O

3,00%

30,O

3,00%

190,O

3,00% O,OO%

190,s 0,o

O,OO%

0,o

1,60%

In the previous example, unit MIX-2 presented a level 2 redundancy. Indeed, for 5 equations and 9 variables (and thus 4 degrees of freedom) we have G measurements (G - 4 = 2). Table 2.1 shows the a priori and the a posteriori accuracy of those measurements around unit MIX-2. Reconciled measurements are more accurate than raw data when measurement redundancy is available. But when no redundancy is available locally, no improvement can be expected. This is the case for the estimation of the recycled flow rate: the measured value is not corrected, and its accuracy is not improved. When some measurement is not corrected that does not imply it can be trusted; this would only be the case if the standard deviation would decrease.

2.2.4 DR Avoids Error Propagation

Progress in automatic data collection has presented plant operators with a flood of data. Tools are needed to extract and fully exploit the relevant information it contains. Furthermore, most performance parameters are often not directly measured, but calculated from measured values. Thus, random errors on measurements also propagate in the estimation of KPIs. Data reconciliation, on the contrary, allows state estimation and measurement correction problems to be addressed in a global way. As a result, validation technology avoids error propagation, and provides the most likely estimate of the actual operating point of the process. Thus, the plant can be safely operated closer to its limits. Illustration of error propagation is addressed in Table 2.2 for the example considered in Fig. 2.1. The goal is to estimate the flow of component C in the process output. Because raw measurements are not error free, mass balance equation around mixer MIX-1 is not respected (fourth row of Table 2.2). Cases 1 to 3 show what happen when each of the three (process inlet) flow rates are manually corrected to close the mass balance, the flow rate of stream C being computed afterwards. In the last case DR is used to provide a consistent and accurate set of reconciled measurements. Indeed, Table 2.2 shows a balance value equal to zero. Note that measurements may be considered as correct since reconciled values are inside their confidence limits.

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2 Data Validation: a Technologyfor Intelligent Manufacturing Table 2.2

Error propagation

Measured

ton/d 181.0 A in B in ton/d 885.0 t o n l d 1016.0 AB in Balance in ton/d -50.0

ABC Purge ton/d Cout ton/d

72.0

1

Accuracy

3.00% 3.00% 3.00%

/

3.00%

I

Case z

Case 3

Reconcilied

Accuracy

131 885 1016

180.1 862.8 1042.8

2.98% 2.00% 1.64%

0

181 835 1016 0

0

o

72 994

72 994

72 944

72.0 959.9

Case 1

181 885

1066

/ 3.00 % 1.80%

Knowing that the standard deviation of flow measurements is 3 % of the measured value, one obtains for outlet compound C the flow rate: 0 0

with DR: a standard deviation equal to 1.80 % with an estimate of 960 ton/d; with manual correction: a spread of estimates equal to 5.03 % (from944 to 994 tonld).

Thus, DR avoids error propagation and so provides more accurate computed parameters than those calculated by less rigorous or ad hoc correction modes. Plant engineers have to solve that type of problem regardless of if they have the appropriate tools or not. 2.2.5 Process Measurements to be Exploited

Key performance indicators (KPIs)can be determined accurately by validation of process measurement data. They are very useful for many purposes, e.g., revamping, energy integration, improved follow-up of the plant, possibility of working closer to specifications, detecting degradation of equipment performance, etc. A hydrogen plant process is used to illustrate the determination of accurate and reliable KPI. Namely, this example concerns the steam to carbon ratio (S/C) in the steam reformer feed, that is, one of the key control parameters in such plants. It allows controlling the conversion of methane to carbon oxide and hydrogen while avoiding carbon deposition on the catalyst. Two different cases were studied to compute this ratio: 0

0

First, DR was not considered. Ratio S/C was calculated from raw measurements of flow rates and compositions of process inlets (steam and natural gas) and reforming gas recycled. Afterwards, the same KPI was determined by means of DR.

Each of these two cases were reassessed, considering a measurement error on the steam flow rate (e.g., due to a leak). Namely, the steam flow rate is measured at either 72 ton/h or 78 ton/h. Results shown in Table 2.3 demonstrate that the uncertainty on the S/C ratio is reduced when data reconciliation is performed. Also, reconciled S/C ratio is less sensitive to the flow rate measurement error, which is detected and corrected by data

2.2 Basic Aspects ofValidation: Data Reconciliation

reconciliation. Thus, reconciliation detects errors in available measurements and yields accurately consistent and complete estimates of measured as well as unmeasured process parameters. Furthermore, in industrial practice one must take a safety margin for the S/C ratio to avoid carbon deposition in the catalyst. With DR, safety margins can be thinner, steam consumption is reduced and therefore plant operation costs less. Table 2.3

KPI computation

Without rneas. errors

With meas. errors

SIC ratio

rel. error

SIC ratio

rel. error

without D R

3.545

4.24 %

3.840

4.24 %

with D R

3.514

3.52 %

3.673

3.53 %

Here a real industrial case encountered in a hydrogen plant is described, for which validation technology was applied. In a hydrogen plant (operated by ERE company), the feed gas composition was not monitored accurately; measurement errors were leading to an approximate knowledge of the steam/carbon ratio [2], uncertainty being on the order of 30%. However, the hydrogen production efficiency and cost are strongly related to this ratio. Indeed a low S/C ratio decreases energy consumption. Therefore, a potential return of 500,000 euro per year had been identified. On the other side, a low S/C ratio could lead to carbon deposition (see Fig. 2.2) entailing a risk of catalyst damage (shut down for replacement costs five million euro). With on-line validation software the steamlcarbon ratio is determined nowadays with a precision of 1 %. This allows operating at the optimal point where energy costs are mastered and carbon deposition is avoided. This example shows how validation software allows for operation closer to the limits, taking care of safety constraints.

Fraction down wfoniler tuhr Figure 2.2

Profile of reformer reactor (courtesy of BP-ERE [3])

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2 Data Validation: a Technologyfor Intelligent Manufacturing

2.3 Specific Assets o f Information Validation

Data validation is an extension of DR. In that case the set of corrected measurements and other calculated data respect linear and nonlinear constraints (mass, components and energy balances, reaction constraints as well as physical and chemical thermodynamic equilibrium constraints). Furthermore the technology includes data filtering, gross error detection/elimination, and it also provides the a posteriori accuracy of all the calculated data. Therefore, accurate and reliable KPIs are determined, as well as their accuracy. Moreover, validation software detects faulty sensors and pinpoints degradation of equipment performance (heat rate, compressor efficiency, etc.).

2.3.1 Accuracy of Nonmeasured but Calculated Data

Unmeasured variables of the system are calculated and their accuracy is quantified on basis of the measurements that are related to them. Therefore, in addition to providing substitution values for failed instruments, data validation software also calculates values that are not directly measured. Validation acts as a set of “soft sensors” that are robust and accurate because they are based on the reconciled values of all the measurements. Typically, validation technology provides three times more calculated data (and their accuracy),than the number of effectively measured data. Benefits are undeniable, costly lab analyses can be avoided. For instance, on the chemical site of Wacker Chemie (Germany)an on-line implementation of validation software reduced the number of routine analyses up to 40% (see Fig. 2.3) [3]. Wacker considered validation as a revolutionary way for quality follow-up of their plants: fobj, the sum of weighted squares of measurement corrections were checked for three years (see Fig. 2.4) [3]. They showed a reduction of the objective function (fobi) from 30,000 to 1000, demonstrating a better quality of sensors tuning. Any increase of that validation criterion alerts operators on possible plant upset.

Initial situaiioii 140

120 100

80 60 40

20 ~1ilrp

Figure 2.3 Reduction of lab analysis cost (courtesy o f Wacker Chemie [3])

2.3 .Spec+c Assets oflnformation Validation

30 OM

Source: Wacker Chemie

25 MI

20 nw 1s OM oidirre doily +

lOo(H1

5wn I

7

0 4 Figure 2.4 Sum of weighted squares of measurement corrections (courtesy of Wacker Chemie [3])

Furthermore, Wacker also follows the ratio -,J based on the chi-square statistical fob,

test (2). The chi-square test value depends on the number of redundancies of the system and on the statistical threshold of the test, typically 95 %. Active bounds are considered as adding new levels of redundancy. Two different cases are possible, whether the ratio is higher or lower than 1: 0

If-J > 1: no presence of gross errors in the set of measurements can be fobi expected.

0

If-J 5 1: presence of at least one gross error in the set of measurements is expected.

A data reconciliation result can only be exploited if the chi-square test is satisfied. Gross error detection and elimination is a feature of validation software that will be detailed next. 2.3.2 Key Performance Indicators and Their Accuracy

Key performance indicators (KPIs) are identified in the same way as nonmeasured state variables. Because measurement errors have been withdrawn from the set of reconciled data, the best possible estimate of the plant performance is delivered. Thus, KPIs can be accurately determined. Typical KPIs include: 0 0

global plant efficiency yields

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2 Data Validation: a Technologyfor Intelligent Manufacturing 0 0 0 0 0

steam/carbon ratio, oxygenlcarbon ratio, H2/N2ratio, etc. specific energy consumption specific energy cost equipment duty and efficiency catalyst activity, etc.

Table 2.4 shows S/C ratio values and accuracy using data validation technology. In the third case, thermodynamic constraints were taken into account. KPI accuracy is more improved with data validation than with data reconciliation. This is due to the fact that data validation considers all available process information (temperatures, pressures, chemical reactions, equilibrium constraints, etc.), the redundancy level being thus higher. Moreover, S/C ratio is much less sensitive to measurement bias, as demonstrated with the introduction of a measurement error on the steam flow rate entering the reformer (see Table 2.4). The additional assets of data validation are described here after. Table 2.4

S/C ratio Without rneas. errors SIC ratio rel. error

With rneas. errors SIC ratio rel. error

without DR

3.545

4.24%

3.840

4.24 %

with DR

3.514

3.52 %

3.673

3.53 %

with data validation

3.423

0.63 %

3.432

0.63 %

2.3.3 Nonlinear Thermodynamic-based Data Validation 2.3.3.1 The Limitation of (Linear) Mass Balance-based Reconciliation

Most commercial data reconciliation packages are based on a linear solver and reconcile measurements on the basis of overall mass balances. Moreover, bounds on variables are seldom considered, meaning that negative flow rates or negative inventories can appear in the results. Additionally, mass balance-based systems only offer a low level of redundancy: at the most one gets one level of redundancy around each node where all incoming and outgoing rates are measured. As a consequence, the improvement in data quality is low and the results are very sensitive to gross errors in the measurements. On the contrary, thermodynamic-based data validation software provides additional equations increasing consequently the redundancy of the system, making it more accurate and less sensitive to measurement errors. At the same time, key performance indicators can be directly derived with a high level of accuracy and reliability. Of course, using thermodynamic properties has its drawback: most of the equations become nonlinear making linear solvers useless. Therefore, one must then use a nonlinear algorithm as large scale SQP-IP (sequential quadratic programming-

2.3 Specific Assets oflnformation Validation

v

p

Case I Design Data

A

‘-“-u.. A-STYRENE-RECOVERY A-EBZ-RECOMRY

n

Case 2 Compound Balance

‘-=-ljc.2

B f 98 97 B8 f $761 87 61

C-STYRENE-RECOMRY C-EBZ-RECOMRY

1500 1493 zocl 2 18 700 fie0 390 3 8 3

t O Q O 10 51 DO0 0 0 0

0uo

DO0

2430 1441 71 60 71 64 0 02 0 02

Measured

/ \

Case 3 Mass Balance

P M-STYREHE-RECOWRY M-EBZ-REC O M R Y

Measured Figure 2.5

0430 192 ?; 9852 4 8 9 %

/ \

Vahdated

Compound balances influence on accuracy

n

97 gQ 0 08 4. 87 85 0 41 %

030

000 000

030

go 70 Pa TO

ooo o m

Validated

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2 Data Validation: a Technologyfor Intelligent Manufacturing

interior point), which has been implemented to solve complex nonlinear data reconciliation problems. 2.3.3.2 Example: Reconciliation of Two Distillation Columns

Two consecutive distillation columns are used to separate styrene (the final product) from unreacted ethylbenzene (EB), which is recycled to the reaction section (see Fig. 2.5). Case 1presents the design mass (and compound) balance of the plant. Case 2 presents typical measured values with a significant bias on the flow rate of recycled EB (stream c4) as reconciled in a compound-based data reconciliation system. The bias is clearly identified (3.70) and corrected (3.32) so that the styrene and EB recovery are accurately determined (87.86 * 0.41 %). Case 3 then presents the same flow rates reconciled using a simple mass balance system, which is unable to detect the measurement error and therefore calculates a wrong recovery of EB and styrene. One can see that the accuracy of the computed recoveries is considerably better when performing a compound balance than with a simple mass balance (in this case, more than ten times better).

2.3.4 Exploiting LV and LLV Equilibria as Source of Information

Variables describing the state of a process must be reconciled to verify consistency constraints representing basic laws of physics: dew point and boiling point constraints in condensers, evaporators, or distillation columns are a source of information exploited by thermodynamic-based validation software. The process of industrial ammonia production may be subdivided into three distinct parts: synthesis gas production, compression section and ammonia synthesis loop. Process natural gas (PNG) and steam enter the primary reformer reactor, after sulfur removal of PNG. High temperature and low temperature shift sections follow the secondary reforming, where compressed air is also introduced. After the methanator section, synthesis gas is partially recycled upstream in the process and partially introduced in the hyper compressor section. Finally, gas enters the ammonia synthesis loop. Figure 2.6 represents an ammonia synthesis loop process flow diagram (PFD), which can be considered as having an 8-digit structure with a heat exchanger in the middle. The synthesis gas enters the hyper compressor as well as the recycle gas, then the outlet (process gas) is cooled and partially condensed (106F) to recover ammonia. Afterwards, gas is heated through a counter-current heat exchanger, goes to the reactor section, then again to the same heat exchanger (at lower pressure than the cold process gas) before closing the synthesis loop. Condenser temperature (see Table 2.5) reflects a compromise between ammonia content and flow rate of the gas entering the reactor section. Considering condenser pressure as constant (158 bar) to simplify the following illustration, and condenser

2.3 Specific Assets oflnforrnation Validation Table 2.5

Condenser lO6F measurements Raw measurements

Validated measurements

Condenser lO6F

T Vapor flow rate (Nm’ h-’)

-14°C 456,890

-16.50“C 455,040

Reactor

PI, TI,

165 barg 185 “C 2.4 11.2

165 barg 181 C 2.829 11.07

%mol NH, %mol inerts

inlet composition and vapor flow rate specified, three different “what if‘ cases were studied (see Table 2.6). First, temperature was assumed equal to measured temperature -14°C. In the second column, temperature was considered the same as validated value -16.5”C. Finally, temperature is computed for ammonia content in vapor phase identical to raw measurement 2.40 %. Thus, a large amount of information can be extracted from the results: 0 0

0 0

At 158 bar, hydrogen solubility rises slightly with temperature. If temperature is considered equal to the raw measurement (-14”C), ammonia vapor composition estimated is considerably different from measurement (3.1 % instead of 2.4%). This proves inconsistence in the measurement set. On the contrary, vapor flow rate computed seems closer to that of the measurement value. In the second “what if” case, we reproduce validated data. To reach specified reactor inlet ammonia content (2.4%), temperature should be -20.8”C, instead of the -14°C measured. Therefore, vapor flow rate decreases.

This illustration shows the limitations of any partial “manual” validation. Why is validated data so important in this particular case? The “what if‘ computations show the size of uncertainty of different data. The more NH3 you condense in the condenser the better, but this has a direct cost, the energy spent in the cooling loop. How do you optimize any compromise if only nonvalidated data are available? Does it make sense? Table 2.6

LV equilibrium calculation results

T (“C)

-14

-16.5

-20.8

Vapor fraction

0.9586

0.9558

0.9517

3.10

2.83

2.40

Vapor flow rate (Nm3h-’)

456,330

455,039

453,049

%mol HI in liquid phase

0.38

0.36

0.33

Liquid flow rate

14.95

15.93

17.44

%ma1 NH3 in vapor phase ~~~~~

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2.3.5 Exploiting Reactions and Chemical Equilibria as Source of Information

This point can be illustrated with the same ammonia process described previously (see Fig. 2.6), in particular its reactor section. Ammonia is produced in a two adiabatic catalytic stages reactor. Reactants are nitrogen and hydrogen, entering the reactor in a stoichiometric mixture. Ammonia formation reaction is exothermic and reversible; therefore, gas leaving the first adiabatic stage is cooled before entering the second stage. Furthermore, the model considers a performance equation, consisting in the introduction for both adiabatic stages of a A Teqparameter, which takes into account deviation from chemical equilibrium. Because reaction is exothermic, A Teq will be positive. Thus, important information that can be extracted from data validation, considering reactions and chemical equilibrium, are performance parameters A Teq(see Table 2.7). Results pinpoint a closer approach to equilibrium in the first catalyst bed. In addition, it is possible to visualize validated ammonia concentration profile together with equilibrium curve and plant measurements (see Fig. 2.7). The two vertical lines represent measured inlet and outlet temperatures of the heat exchanger between the two catalyst beds. One cannot accept a measurement point above the equilibrium curve. This erroneous measurement set could not have been noticed any other way than exploiting reactions and chemical equilibria as an information source. Table 2.7

Performance parameters

AT- (‘C) First catalytic bed

6

Second catalytic bed

14

2.3.6 Exploiting Process Information

As explained before, data validation is based on measurement redundancy. The plant structure yields additional information, which is exploited to correct measurements. Consequently, considering a process at a global scale brings more accuracy to validated data than only taking into account a local section of the process. It is the same for the accuracy evolution of key performance indicators. Considering the same ammonia process as before, the H2/N2ratio in the synthesis loop was estimated in several ways. First, only a local section of the process was considered (the synthesis loop). Then, additional information of the plant was successively added until the whole process was taken into account. Results pinpoint a substantial reduction of the KPI inaccuracy when more and more process information is considered (see Fig. 2.8).

2.3 Specific Assets oflnforrnation Validation

........................ ...........................

813

c 30%

-

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Y

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20%

8

15%

8

10%

c

5%

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0%

-.

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Raw measurements +Validated

data

Synthesis reactor equilibrium curve

Evolution of loop H2/N2ratio accuracy 3,06 3,04

T

3,02

-

3,OO

z"

2,ga

0

c

e

-a I

2,96 2,94 2,92 2,90

Figure 2.8 Evolution o f a KPI imprecision according to process information taken into account

It was previously demonstrated that validation technology avoids error propagation. In fact, data validation software propagates accuracy. This technology combines process information and raw measurement data. The more information of the process taken into account, the more nonmeasured data (and so KPIs) will be accurate and reliable.

2.4 Advanced Features ofvalidation Technology

2.3.7 Detection of Leaks

Validation technology points out process performance degradation sources and helps to operate the plant closer to its ultimate performance. In particular, validation allows the detection of leaks. This can be illustrated by a practical case study related to a previous ammonia plant, where a leak in a NH3 synthesis loop was discovered. It would have been hardly detected by tools other than validation technology. A Carbochim plant operated in Belgium at 90 % of nominal capacity; a retrofit was studied to restore the expected capacity. Validation conveyed a leak in the heat exchanger in the middle of the 8-shucture synthesis loop (see Fig. 2.6). Thus, part of the process gas was cycling around from the compressor and condenser section, to the heat exchanger and again to the compressor. That leak had not been suspected. It probably developed and increased smoothly, but the question is, how could it have been discovered in the absence of the appropriate tool? Plant was shut down for isolating leaking tubes in the exchanger and was reopened to easily achieve the expected production rate without any costly additional investment. 2.4 Advanced Features of Validation Technology 2.4.1 Trivial Redundancy

Trivial redundancy cases are met when the validated value of a measured variable does not depend at all upon its measured value but is inferred directly from the model. This can occur in particular in L/V equilibrium drums, where complementary thermodynamic constraints must be respected. Indeed if, e.g., temperature, pressure, flow rate and composition of a condenser inlet stream were known together with the unit pressure drop, any complementary measurement (e.g., outlet temperature) would be considered as a trivial redundancy. Proper validation software detects trivial measurements, which then are no longer considered as measured. As a consequence, their measurement accuracy will not affect the accuracy of the respective validated variable. 2.4.2 Gross Error Detedion/Elimination

Gross errors are detected by means of a chi-square (2)statistical test, which has been previously explained at Section 2.3.1. 2.4.2.1 Detecting Gross Errors

The 2 statistical test enables the detection of gross errors in the sets of measurements. The 2 value depends on the total number of redundancies of the system, active bounds being considered as adding new levels of redundancy, and on the sta-

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tistical threshold of the test, typically 95 %. If the weighted sum of penalties is higher than the 2 threshold value, then there is a significant suspicion that gross errors exist. In such a case, all results obtained with that model are to be used with caution: validated values, identified performance factors and their reconciled accuracy. 2.4.2.2 Eliminating Gross Errors: The Highest Impact Method

Identifymg the actual source of the gross errors is not always trivial and requires a careful analysis of the results. The conventional technique (highest penalty method) is to ignore the measurements for which the highest corrections are made. This method is known to be inadequate in detecting some gross errors, for example, when the corresponding measurement is specified with a high level of accuracy as compared to the other measurements. On the contrary, the highest impact method detects the impact on the total sum of penalties by removing each of the measurements. This approach is in principle highly time-consuming and is therefore not used by most data validation packages. However, by means of specific algorithm, one can apply this technique in a calculation time of the same order of magnitude as a single validation run.

2.4.3 How to Validate with Petroleum Fractions

The modeling of a refinery process or a part of it is always confronted by the complexity of the petroleum and its products. Indeed, crudes and petroleum cuts are mixtures of a large number of chemical compounds, thus making it very difficult to model their properties without accurately knowing their composition. Therefore, it is common practice to model such streams by the well known pseudo-componentconcept. 2.4.3.1 Concept

A pseudo-component is a hypothetical molecule characterized by its density and its boiling temperature. Those parameters are then used to estimate the other thermodynamic properties (like critical properties or specific heat capacity) using empirical correlations as proposed for example by American Petroleum Institute (API). According to the crude type and origin, different pseudo-components must be used to get an accurate representation.The usual way of characterizing petroleum fractions is to generate a defined mixture of pseudo-components,with given boiling point, having the same properties as the Petroleum fraction. Namely, their composition and their density are identified in order to match all stream distillation curves and densities. Most common standards for distillation curves are true boiling point (TBP)and ASTM; each of them can be expressed on a weight basis or on a volume basis (see Fig. 2.9). Several petroleum cuts involved in a distillation process can be modelled as a data validation system involving:

2.4 Advanced Features ofvalidation Technology

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200 T@ 100

0

20

0

40

Vol Yo

60

80

100

Figure 2.9 Decomposition in pseudo-components based on a TBP curve of a gas oil 0

0

0

as variables, the pseudo-compounds densities and their measured volume fractions in each stream; as equations, the mass balances of the distillation column for each pseudocomponent; as measurements, the densities and TBP or ASTM curves of all connected streams.

On this basis, data validation will generate calculated distillation curves from measured TBP or ASTM data, as it identifies the density of each pseudo-compound; this involves minimization of weighted deviation between measured and calculated distillation points, under density constraints, mass and thermal balance constraints. The other thermodynamic properties of the pseudo-compounds are also estimated. 2.4.3.2 Crude Oil Atmospheric Distillation Example

Following example concerns the modeling of a crude oil distillation unit (CDU), preThe crude oil is separated into six ceded by the preheating train (see Fig. 2.10) [4]. Petroleum cuts: naphtha, jet, kerosene, gasoline, diesel and residue. Gasoil

+P 4

4J

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Diesel

4 I

NaDhta

Kero

Figure 2.10

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Measurements available to perform the modeling are: 0 0 0

density and distillation curves (ASTM-DSG)of the petroleum cuts, temperature, pressure and flow rates of the streams, design data of the exchangers.

These measurements are validated and the other thermodynamic properties of pseudo-compounds are subsequently computed. Furthermore, with several sets of measurements taken in one year it was also possible to confirm fouling problems for the exchangers at the end of the preheating train. Indeed, their heat transfer coefficient decreased by a factor of two after one year of operation. Thus, data validation uses a rigorous method integrating robustly complex distillation systems. This forms a sound basis for the analysis of refinery performance, and for instance, of a retrofit potential.

2.4.4 Advanced Process Control Benefits from Working with Data Validation

Nowadays plants face a market where margins are under pressure due to global competition, more stringent environmental regulations, a higher demand for flexible operation and more severe safety requirements. Control techniques are required to increase those margins. Advanced process control (APC) systems can help optimize control to deal with those challenges [S]. Data validation technique enhances the quality of information allowing APC systems to work more efficiently.

Plant

Figure 2.11

tnput a output "

+[ream meac

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KP'

+

%;ll

outpui

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Dynamic

2.4 Advanced Features ofvalidation Technology

king raw information reliability and coherency. Some measurements could be erroneous and balances not be closed. Data validation software uses input and output streams of raw measurements in order to provide one coherent and accurate data set. With data validation, APC systems are allowed to take actions on the process based on coherent and reliable measured and nonmeasured data. Validated data contains measurements, equipment parameters, KPIs, and many other nonmeasured but validated data. The a posteriori accuracy of measurements and KPIs is provided. When a dynamic model is tuned according to validated data, benefits are generated as early as at the model design stage. 2.4.4.2 Benefits at Model Design Stage

Reduced dynamic model must be certified: dynamic model parameters are chosen and adjusted in order to produce results identical to measurements (A = 0 on Fig. 2.1 1).Benefits using validation techniques are double: 0

0

Measurements, to which dynamic model results are compared, are checked and corrected by data validation techniques. Measurements are much more reliable (they represent the actual process operation) and thus the model will be more reliable as well. Data validation technology reduces the number of principal directions needed to represent process variability, allowing the reduced dynamic model to represent the same level of variability using a model with a lower number of principal directions (see Fig. 2.12) [GI.

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KPI validated (%) KPI based on raw measurement (%)

103 102 101 100 99

98 97

96 95 M-l 0

5

10

15

20

Run Figure 2.13

25

-

30

35

40

45

KPI follow-up and control

Figure 2.12 illustrates the number of principal directions (or components) necessary to represent the variability of a given system when the latter is based on validated data or on raw measurement data. Taking into account more principal components allows for the explanation of a higher fraction of the total process variability: 0

0

When using raw measurements, a large number of components are needed to explain most of the process variability (upper limit is the number of original variables, 186). When using the validated data sets, the number of significant principal components tends to a much lower number than the number of variables (upper limit is the number of degrees of freedom of the data validation model).

This reduction in the problem size allows the dynamic model to be more reduced, when based on validated data (accuracyincreased and noise reduced). Control of the process is made easier and the computing demand is decreased. Furthermore, since data validation technique enforces the strict verification of all mass and energy balance constraints, use of this technology ensures that the principal components represent the proper process behavior. 2.4.4.3

Benefits at Operation Stage Process control behavior can be very different whether APC is working together with data validation or not. Figure 2.13 presents the evolution of a process yield (KPI) versus time (run) whether data validation software is used or not: 0

Without data validation, APC detects a KPI variation and tries to stabilize the process operation. Based on raw data with embedded errors, APC takes actions risking being unusefd, resources-expensive, and even process-disturbing.

2.5 Applications I821 0

With data validation, APC considers actual process operation (validated,measured and nonmeasured, data are used as inputs to APC). APC can now use all of its resources on optimization of the process rather than on more stable operations.

2.5 Applications 2.5.1 On-line Process Performance Monitoring

The goal is to deliver on a periodic basis (typically each 10 to GO minutes) a coherent heat and mass balance of a production unit. In addition to the compound balances, the laws of energy conservation are introduced in the form of heat balances. This more detailed modeling of the production unit allows validation software to work as an advanced process soft sensor and to determine reliable and accurate KPIs. Typical benefits are: 0 0

0

0

0

access to unmeasured data, which is quantified and related accuracy determined; early detection of problems: sensor’s deviation and degradation of equipment performance are pinpointed; quality at process level: anticipate off-spec products by carefully monitoring the process; work closer to specifications: as the accuracy of measurement data improves, the process can be safely operated closer to the limits. This feature is reported as being financially the most productive. decreased number of routine analyses (up to 40 % in chemical applications); reduced frequency of sensor calibration (only faulty sensors need to be calibrated).

improvement of Product Selectivity in a BASF Plant

This example shows how the operation of a production unit at a BASF operating division of performance chemicals can be improved using data reconciliation 171. The product C is produced by conversion of component A with component B using 2 reactors. Several undesired by-products are generated, thus selectivity has to be maximized. Process model generated took into account only component mass and atomic balances. Several data sets at different process conditions were validated and from those the selectivity of product C was calculated. The diagram Fig. 2.14a (courtesy of BASF) shows this selectivity as a function of residence time in the first reactor, calculated from measured values; Fig. 2.1413 shows the results from validated data. The selectivity, calculated from crude data, is spread widely and in some cases selectivity values of more than 100 % were obtained, which is meaningless. The corresponding unfeasible area is marked on the charts. One could estimate in this case that a residence time of about 45 minutes is enough to maximize selectivity. However the selectivity based on reconciled data shows a clearer trend and does not

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Figure2.14 Nitrile selectivity as a function of residence time in the reactor: raw data versus reconciled data (courtesy of BASF [7])

exceed the 100% boundary. One realizes that residence time should be larger than the one estimated without data validation, in order to achieve the product optimal selectivity (residence time of about 48 minutes). This example (considering only a restricted part of a process) shows that the evaluation of selectivity is meaningful only on the basis of validated operational data. These lead to a safe interpretation of measurements. By doing so, a selectivity close to 99% can be obtained systematically, which is 2 % higher than the average figure obtained without data validation.

2.5 Applications I823

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reconciled data

mI I

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rate of back-reaction

molar ratio water I methyl-formate

Figure 2.15 Evolution o f t h e specific energy consumption as a function o f the rate o f back-reaction and parameters that influence this rate: crude data versus reconciled data (courtesy o f BASF (71)

Reducing Energy Consumption in a Formic Acid Plant of BASF

A main problem at the formic acid production is the undesired back-reaction of formic acid during distillation, which increases the specific energy consumption [7]. This is shown in the left diagram of Fig. 2.15, on the basis of measured values within a time interval of G days. BASF looked for process parameters, which may influence the back-reaction, in order to decrease operation costs (specific energy consumption). One of them is the molar ratio of water to methyl formate, both educts of the formic acid synthesis. The diagram on the right shows the influence of the mentioned molar ratio to the rate of the unwanted back-reaction: 0

0

Without data validation (raw data , black symbols), no influence is visible but only a cloud of data. Using validated values (grey symbols) a clear trend is visible, which means that reducing the molar ratio decreases the rate of back-reaction.

Both parameters could be correlated only by data validation. Due to these results the specific energy consumption can be reduced by 5 %. Data validation allows the most effective command variables for the control of a process to be determined. This study led to the discovery of which control variable had a dominant effect on the said rate of back-reaction, and consequently on the specific energy consumption. Performance Monitoring at KKL Nuclear Power Plant

On-line implementation of validation software in the nuclear power plant (NPP) of Leibstadt - Switzerland (KKL) generated substantial benefits (two million USD per year) over the past 10 years. The priority of NPP operators is to run their plant as close as possible to the licensed reactor power in order to maximize the generator power. To meet this objective, plant operators must have the most reliable evaluation of the reactor power. The definition of this power is based on a heat balance using several

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Rcconcilcd Vnlue

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/

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0

Sfi

1 on

150

200

250

300

Days in Operation Figure 2.16 Operating closer to the limits: site feed water flow of the NPP Leibstadt (courtesy o f Kernkraftwerk Leibstadt [8])

measured process parameters, among which the total feed water flow rate is the most critical value. On-line implementation of validation software in the NPP of Leibstadt - Switzerland (KKL) has quantified the deviation between the actual and the measured feed water flow rate (see Fig. 2.16). In Fig. 2.16, only one recalibration is illustrated. This was used to convince the legal authorities about the reliability of the implemented validation technique. Validation results were also compared to test runs. In agreement with the authorities in charge of safety of NPP, KKL nowadays recalibrates the measured flow rate based on the validated value, as soon as a deviation becomes significant. This enables the power plant to work close to its maximum capacity throughout the whole year (1145 MW). Prevention of losses due to heat balance errors increased the plant output by 5 MW. In addition, the use of this technology also made the annual heat cycle testing obsolete and significantly reduced the cost for mechanical and instrumentation maintenance [8]. Performance Monitoring of Refinery Units at LOR (Lindsey Oil Refinery), U.K.

On-line validation software is used at LOR for the performance monitoring of refinery units for several years. One set of applications is about the follow-up of fouling of the heat exchangers of several preheat trains. The main goal of the application is to determine the appropriate amount of anti-fouling product in order to maintain an adequate operation of the preheat trains and thus energy efficiency of the plant.

2.5 Applications

Another set of applications concerns the follow-up of furnaces and power plant boilers. The goal here is to determine with sufficient reliability and accuracy their energy efficiency. Any inappropriate operation can easily be detected and corrected when necessary. Performance Monitoring of PE Plant at Confreville, France

The application enables any deviation within the instrumentation to be detected and provides guidance to the operators for the recalibration of the on-line analyzers. In addition, it ensures that the on-line soft sensors remain valid by counter-checking the quality of the instrumentation on which they rely.

2.5.2 On-line Production Accounting 2.5.2.1 Description and Benefits

This solution aims at providing a clear view of the production accounting, on a daily basis, of a whole industrial site: rigorous and automatic procedure for production accounting based on closed material balances. These material balances can be performed either: 0

0

On a global mass balance basis: mass flow rates, in terms of tons entering and tons going out of each production unit, are reconciled to generate a coherent mass balance of the whole site. This approach is typically applied in refineries and covers the whole site including the tank farm. On a chemical compound basis: additional information is then required on the composition of the various streams and the reactions schemes. This approach is typically applied in chemical and petrochemical production plants.

Typical benefits are: 0

0

Actual plant balances: closed balances are key elements as much for effective production accounting as for efficient performance monitoring. Decrease of unidentified losses and surpluses: abnormal conditions leading to losses and/or apparent surpluses are identified and can be corrected before they impact the economics of the plant.

Several real cases can be referred to, namely an adiponitrile plant and two refineries. Production Accounting at ERE and Holborn Refineries

On-line validation software establishes the daily mass balance of the whole ERE refinery (BP refinery located at Lingen, Germany), covering about 150 tanks and about 50 production or blending units. Only a global mass balance (in tons) is made around each unit. The person in charge of the use (and maintenance) of the system spends about 30 minutes per day to generate all the validated reports and inputs for the production accounting. More recently the Holborn refinery in Germany has

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installed a similar system, which also automatically detects abrupt changes in measured data identifying possible changes in operation or instrumentation failure. Production Accounting at Butachimie, France

In this application the modeling includes compound balances of each main piece of equipment of an adiponitrile production facility. Reconciled compound balances are provided on a daily basis. All main chemical compounds as well as the catalysts used in the system are rigorously tracked all over the process unit.

2.6 Conclusion

Data reconciliation and validation is nowadays a mature technology. However it is often confused with flow sheeting and process simulation. Still, much has to be done to inform engineers and managers who have not learned about this technology during their studies. We have tried to convey the importance of this technology, and the very high diversity of applications and benefits that it can provide for the process industry.

References 1

2

3 4

Belsim VAL1 4 User’s Guide, Belsim, Belgium, 2005 BP-ERE, AN-ERE-Ol.pdf,available at: www.belsim.com, 2004 WACKER AN-Wacker-Ol.pdf, available at: www.belsim.com, 2002 Delava P. Maricchal E. Vrielynck B. Kalitventzef B. Modeling of a Crude Oil Distillation Unit in Terms of Data Reconciliation with ASTM or TBP Curves as Direct Input. Application: Crude Oil Preheating Train, Proceedings of ESCAPE-9 conference, Budapest, May 31-June 2 1999, Computers and Chemical Engineering Suppl., (1999) pp. 17-20

5 6

7 8

APC Systems www.ipcos.be, 2005 Amand T. Heyen G. KalitventzefB. Plant Monitoring and Fault Detection: Synergy between Data Reconciliation and Principal Component Analysis. Computers and Chemical Engineering 25 (2001) p. 501-507 BASF, AN-BASF-OZ.pdf, available at: www.belsim.com, 2002 Kernkraftwerk Leibstadt, AN-KKL-Ol.pdf, available at: www.belsim.com, 1995

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8 I827

3 Facing Uncertainty in Demand by Cost-effective Manufacturing Flexibility Petra Heijnen andjohan Grievink

3.1 Introduction

This chapter deals with a case of flexible production planning for a multiproduct plant to optimize expected proceeds from product sales when facing uncertainty in the demands for existing and emerging new products over the planning period. The manufacturing capacities of the plant (that is, the nominal production rates) for the existing and new products are futed by its design and these are not subject to adaptations by making changes to the plant. Hence, the flexibility refers exclusively to the planning problem and it is not coupled with a plant redesign. As the inherent uncertainty in customers’ demand forecasts is hard to defeat by a company, the industry’s specific capabilities with respect to responding rapidly to new and changing orders must be improved. New technologies are required, including tools that can swiftly convert customer orders into actual production and delivery actions. On the production side, this may require new planning technologies or new types of equipment that are, for example, dedicated to product families, rather than to individual products. Many companies need to use medium term planning in their product development and manufacturing processes in order to sustain the reliability of supply and the responsiveness to changing customer requirements. Flexibility is often referred to in operations and manufacturing research as the solution for dealing with swift changes in customer demands and requests for intime delivery (Bengtsson 2001). The concept has received even more attention with the upcoming of e-business in the chemical industry. The actual meaning, interpretation and consequences of “operating flexibility” are, however, not instantly clear for a particular case or company (Berry and Cooper 1999). A number of uncertainties may induce organisations to seek more flexible manufacturing systems. Common sources of uncertainties are depicted in Fig. 3.1.

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright @ 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

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I Product Demands

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:;?ability Figure 3.1

Types of uncertainties

On the input side, manufacturing systems have to deal with suppliers’ reliability with respect to feed stock supply, involving quantities (v), quality (q), cost (C), and with uncertainties in time (t). Secondly, process inherent uncertainties exist, concerning equipment availability (Tj, and modeling uncertainties. On the product demand side, the same types of uncertainties can be found for each product, involving demand (d), quality ( q ) ,and cost (C), and time (t). For the products a distinction is made regarding two different sales conditions. At the beginning of the planning period some sales contracts can be secured, under which the amounts ( y ) that can be manufactured and sold. The excess manufacturing capacity of the plant can be used to make the amounts (z),which will capture market opportunities during the planning period. It is noticed that the number of products (n) can change over time. This change reflects a trend towards diversification in many production markets. To achieve this diversification and to cope with shorter product life span, it seems preferable for manufacturing systems to have flexible resources. Extensive research has been done into the flexibility of (chemical) processes that are subject to uncertainties on the input side and with respect to the availability of the processing equipment, possibly influencing the feasible operating region of the plant (Bansal et al. 1998; Swaney and Grossmann 1985). Less research has been done, however, into flexibility that is characterized by the possibility to cope with changes in demand or product mix. The right way to respond to change is always system specific, and dependent on the system’s flexibility. Many approaches for dealing with uncertainties exist (CorrEa 1994). As this study concerns product mix variations and demand variations, the monitoring and forecasting technique was selected. The uncertainty aspect is modeled by means of a stochastic approach. In the development of a planning technique its applicability requires careful consideration. Firstly, the technique should be compatible with the work processes and the associated level of technical competence. Among others, this requires that the input and the output can be well understood and interpreted by those who will use it. Secondly, the cost of using the technique (time and money wise) should remain low. It would be very helpful to use input data that can be obtained without excessive efforts, while the results of the planning can be easily (re)producedwith small computational effort.

3.2 The Production Planning Problem

3.2 The Production Planning Problem

A case study was developed based on experiences at a company that makes various

types of food additives in a multiproduct batch plant. In this plant several groups of products are produced on a number of reactors. At the beginning of every new production period of one year, planning management agrees with the customers about the amount and price of products that will be produced to meet customer demands in the coming period. These agreements between company and customers are laid down in annual contracts. The demand for products that could be sold in these annual contracts is in general very large and the total capacity of the plant could have been sold out. However, planning management has strong indications that the demand for a new and very profitable product will increase during the coming production period and it could be very attractive to keep some of the capacity free for this newcomer on the market. Not only that, but also for the current products it could be quite profitable to not sell all capacity beforehand, since the price for which the products can be sold during the production period is in general significantly higher than before by contract price. Unfortunately, the demand for the products during the production period cannot be assured. Planning management would like to establish in the production planning how much of the current products they should sell in annual contracts and how much capacity they should leave open for every individual current product and for the new one in such a way that the final profit achieved at the end of the production period is as high as possible. The plant production capacity acts as a restriction on the total amount that can be produced. The next sections will introduce a simple probabilistic model for the product demands as well as a manufacturing capacity constraint (Section 3.3). The realised product sales are related to the corresponding profit over the planning period (Section 3.4). In order to optimize the manufacturing performance, two objective functions are chosen that take into account the distributive nature of the demands and product sales (Section 3.5). The first objective is the expected value of the final profit over the planning period. The second objective is a measure for the robustness of the planning; it involves maximization of the first quartile of the profit. The outcome of the modeling is a multiobjective, piecewise linear optimization problem (Section 3.6). Due to the discontinuities the problem is solved by means of a direct search method, the Nelder and Mead algorithm. The multiobjective problem is turned into two single objective problems. The solutions to these problems define the full range between maximum expected profit (with a high risk) and the robust profit (for a low risk scenario). This approach allows a production manager to take a preferred position between these two extremes. The result is a production planning and the associated profit. Each step in the model development is illustrated by its application to the case study of the food additives plant, taking base case values for model parameters. To be able to make a good evaluation of the risks, the sensitivity of the profit and the optimal planning are studied for small changes from the nominal model parameters

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3 Facing Uncertainty in Demand by Cost-efective Manufacturing Flexibility

(Section 3.7). Finally, the implementation aspects of the proposed planning method are discussed (Section 3.8).

3.3 Mathematical Description o f the Planning Problem

To solve this production planning problem we need to formulate it in a more formal way. Assume that the current product portfolio consists of n products that can be produced on several exchangeable units. The decision about on which specific unit a product will be made is established in the production schedule and is considered to be outside the scope of the production planning. In the production planning, the planners take the overall production capacity into consideration without allocating products to specific units. In the production planning the following decisions variables should be established: 0

the amount of the current products sold in annual contracts in ton per year:

yi, i 0

E (1, 2 ,

..., n} ;

the capacity left open for the current products and for the new one in ton per year: xi,

i E { 1, 2, ..., n, n + I} .

The information that is needed to make these decisions consists of the following parameters: the profit that can be made with the production of one ton of a certain product, depending on the retail price and on the production costs, divided into: - the profit made on the current products sold in annual contracts in dollars per ton: q,i E (1, 2, ..., n} ; - the profit made on sold amounts of the current products and of the new one

during the production period in dollars per ton:

,pi,i E { 1, 2, ..., n, n + I} ; the total production time available in hours per year: T; the production time needed to make the products in hours per ton: z i , i E { 1 , 2,..., n , n + l } ;

the demand for the current products that can be sold in the annual contracts:

Si,i E (1, 2, ..., n} ;

3.3 Mathematical Description ofthe Planning Problem

Since the total amount of product made during the production period cannot exceed the total available production time, the decision variables are restricted by:

i=I

i=l

The assumption is made that the planners have enough and correct information to make a good estimation of the values of these parameters. Therefore, these parameters are assumed to be the deterministic factors in the planning problem. the demand for the current products and for the new one during the production period in ton per year: di, i E (1, 2, ..., n, n + 1) . The uncertainty of the demand during the production period is quite large and therefore these factors are assumed to have a stochastic nature. The assumption is made that the planners have enough information to indicate the minimum and maximum demand that can be expected and the mode of the demand, that is, the demand for which the probability density function is maximized. The demand for the products will therefore be modeled by a triangular distribution with the probability density function given in Eq. (2). This triangular form (see Fig. 3.2) corresponds with the shape used in fuzzy modeling.

in which aiis the minimum, p, the mode and a certain product i.

ffjl A, a;

P,

3:

the maximum of the demand di for

d,

The expected demand for product i will then be: E(di) =

~ r +, Pi

3

+

Yi , E { 1 , 2,..., n , n + l } .

The probability distribution of the demand di reads:

Figure 3.2 The triangular probability density function o f the demand

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In Section 3.4 the mathematical description of the planning problem will be continued, but the generic problem will first be applied to a case study in a plant where various types of food additives were made.

3.3.1 Case Study in a Food Additives Plant

In a multiproduct multipurpose batch plant different food additives are produced on two reactors. The present portfolio consists of two product groups A and B. Having strong indications about a growing demand for a new product C, operations management wants to reevaluate the current product portfolio and the production planning for the coming year. The product groups A and B are manufactured on two exchangeable reactors. Planning management has estimated the production times based on the current annual operation plan. The total amount of available operating time for the reactors is determined by the available time in a year minus 15 % down and changeover time, resulting in 4625 hours for reactor 1 and 4390 hours for reactor 2. Together this results in a total production time for the coming year of T = 9015 hours. Table 3.1 shows the estimated values for all parameters in the planning problem. From the figures it is clear that the total production capacity could have been sold out in the annual contracts, since the demand for the product groups A and B is high enough. The new product C however is expected to be very profitable and it would very likely be an unwise decision to sell out the total production capacity. Unfortunately the demand for the new product C is not very certain. Table 3.1

Estimated values for the planning parameters

Production time in hours per ton Contract profit in $ per ton Demand for contracts in ton per year Profit in production period in $ per ton Minimum demand in ton per year Mode of demand in ton per year Maximum demand in ton per year

Product group A

Product group B

0.24 1478 6, = 20 000 eA= 1534 a, = 16 040 PA= 17550 '/A = 19 900

ZB = 0.47

tA =

UA =

897 6 B = 11000 eB= 953 aB= 8350 bs = 8900 '/B = 9150 UB=

Product C tc = 1.4

-

ec = 3350 Q=O Pc = 850

yc

=

1600

This case study will be continued in Section 3.4.1.

3.4 Modeling the Profit of the Production Planning

The criterion on which planning will be assessed is the total profit that is achieved after the production period when the production is executed in accordance with the production planning. For that, not only is the expected profit important, but also the

3.4 Modeling the Profit ofthe Production Planning

certainty that this profit will be achieved should be taken into account in the final decision. If a small deviation of the expected demand results in a much lower profit than expected, it could be safer to choose a more robust planning with a lower, but more certain profit. Let zi, i E { 1, 2, ... n, n + l} be the sold amount of products when the production period is finished. Together with the products that are sold before the production period in annual contracts, the final profit that will be made in this period equals: n

n+ 1

i=l

i=l

The amount of products sold during the production period will depend on the demand for these products and the available production time. If the demand is lower than the amount that can be produced in the available production time, then the total demand can be satisfied. However, if the demand is larger than the available capacity then only that amount of product can be made and sold. Therefore, the total amount of product sold during the production period will equal zi = min(di,xi),i E (1, 2, ... n, n + I}. The same holds for the amounts sold in annual contracts. The overall profit will then be P(yi,. . . , yn, x i , . . . , xn, xn+i) =

n+l

n

Cai min(&, + C p i min(di, xi). yi)

i=l

i=l

(5)

For fned values of the decision variables, the maximum and minimum total profit that can be achieved depends on the planned amounts of the products on the production planning, and on the maximum, respectively minimum demand for the products:

C

n+ 1

n

max P(y1, . . . , yn, ~ 1. .,. , x n , xn+l) = minP(y1,. . . , yn, xi,.. . , xn,xn+i) =

i=l

(Ti

min(yi, si)

+ C pi min(xi, vi) i=l

n

n+l

i=l

i=l

Cgi min(yi, hi) + Cpi min(xi, ail.

(6)

For fured values of the decision variables the probability density of the final profit can now be derived from the probability density of the demand for the products during the production period, under the assumption that the demands for these products are mutually independent. In general for a linear combination w = ax + by, where the stochastic variables x and y are independent, the density function of w reads (Papoulis 1965):

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3 Facing Uncertainty in Demand by Cost-eflective Manufacturing Flexibility

The final profit was defined by P(yl, ..., yn, xl, ..., x,,,

=

”

n+l

i=l

i-l

10,min(di,yi) + 1pi min(di, xi).

Let p i , i E { 1,2, ..., n, n + I} be the profit made by selling the amount zi of product i during the production period, then pi = pizi,with a minimum of 0 and a maximum of pixi. Applying the general proposition (Eq. (1))on the final profit P, the probability density function of P reads:

i=l

i=l

If the actual demand di, i E (1, 2, ..., n, n + 1) is smaller than the planned capacity xi then the sold amount of product zi will equal the demand di. In that case, the probability density of zi will follow the probability density of the demand di. However, if

the actual demand di is larger than the planned capacity xi then only the amount zi = xi will be produced and sold. The probability that this will happen is the probability of a demand larger than the planned capacity, that is, di 2 xi (see Fig. 3.3).

Figure 3.3

The probability density function o f the sold amount o f product

By this observation, the probability densityfi,(zi), i E (1, 2, ..., n, a + I} of the sold amount of product zi satisfies: 0 < 2; < xi , i E [1,2,.

. . , n, n +

1)

(9)

Unfortunately, by the local discontinuities in the probability density function of the final profit, the integrals cannot be solved analytically. The derived theoretical results will now be applied on the case study described in Section 3.3.1.

3.4 Modeling the Profit ofthe Production Planning Figure 3.4

Simulation of the final profit for one possible production planning

profit (in million 9)

3.4.1

Modeling the Profit for the Food Additives Plant

In the aforementioned case study the production planning should be made for two current product groups A and B and one new product C. For reasons of comprehensibility, the assumption is made that no products were sold before the production period, that is yA = y B = 0. The total profit that can be made will now depend on the demand for the products during the production period and on the planned amounts of the different products, that is, P(xA,x g . xc) = 1534 min(dA,x A ) + 953 min(dB,x B )+ 3350 min(dc, xc), under the restriction that the total production time will not be exceeded, 0.24 xA+ 0.47 X B + 1.4 X C = 9015. The probability density function of the profit satisfies:

Although this probability density cannot be solved analytically, it can be simulated for fned values of xA,x9, xc by randomly picking a certain demand for the products A, B and C from their individual probability density functions. Figure 3.4 shows a probability histogram of the simulated profit for a production planning with xA= 17 000, xB= 9588, xc = 950 ton per year. The sample size taken is 1000. The unequal distribution in the left tail is caused by the sample size and would not be present in the theoretical distribution. This histogram shows a very skewed

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3 Facing Uncertainty in Demand by Cost-effective Manufacturing Flexibility

distribution to the left. This skewness is caused by the discontinuities in the function P(xA,xB,xc). In Section 3.5.1 this case study will be continued.

3.5 Modeling the Objective Functions

The quality of a certain production planning will be assessed on the expected value of the profit that can be achieved with the planning. The expected value of the final profit satisfies: EP(Y1,. . . , yn, X I , .

. . , xn, x n + l )

=

withyi 5 di, i E (1,2,. . . , n)

n

n+l

i=l

i=l

Cci min(di, yi) + C PiEzi(xi)

(11)

From the probability density functionfi,(zi), i E (1, 2, ..., n, n + l}of the amount of sold products, the expected value of the amount zi can be determined by:

There are four possibilities for the planned amount x,in comparison to the expected demand d,, i E (1, 2 , ..., n, n + l}. Remember that d, was expected to lie between al and y, with a mode 8.Elaboration of Eq. (12) yields: 1. If x,5 a, then Ez, (x,)= x,.

2. If a,5 x,5 p, then

4. If xi > yi then Ezi (xi) =

a+S+y

3

Unfortunately, the expected value of the profit that can be achieved with a certain production planning, does not guarantee that this profit will be achieved in reality. Due to the skewed density function, for most choices of the production planning, the median of the profit will be higher than the expected value of the profit. This

3.5 Modeling the Objective Functions

means that with a probability of more than 50% the real profit will be higher than the expected value. And with a probability of less than 50 % the real profit will be lower than the expected value. As a consequence, the average deviation below the expected profit will be larger than the average deviation above the expected profit. As a measure for the robustness of the planning the first quartile Qo(y,, x,)of the profit is chosen. The probability that the real profit will be lower than this first quartile equals 25 %. Under the assumption that the demands for the different products are mutually independent, the first quartile of the total profit will be a linear combination of the first quartiles of the sold amounts of products z,, i E { 1,2, ..., n, n + l} and can be written as:

The first quartile of the sold product, Qz,(xJ,will equal the first quartile of the demand d, if the planned amount x, is larger than this demand, otherwise it will equal x,: Qz,(xi) = min(Qo,(di), xi), i

E

(1,2,.. . , n, n + 1)

As long as the first quartile Q,(di) is smaller than the mode

(14)

PLof the demand, i.e.,

If the first quartile Q,(d,) is larger than the mode PI of the demand, i.e., PI > 0.75 a, yL,then

i0.25

3.5.1 Modeling the Objective Functions of the Food Additives Plant

For the case study described in Section 3.4.1, the objective functions can now be modeled. The expected value of the final profit satisfies:

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3 Facing Uncertainty in Demand by Cost-efectiue Manufacturing Flexibility

180001 16000

14000 12000

7 10000

fi

8000 6000

4000 2000

X20000 P

t

200 0

30000

1000

2000 3 M O 4000 5000 6000

x-c

Figure 3.5 The expected amount of sold products A, B and C for a certain production planning

3.5 Modeling the Objective Functions

C

'=c

e

Q

Figure 3.6 planning

The expected profit for different choices o f the production

Figure 3.5 shows the functions of Ez,(xA),Ezs(xB)and Ezc(xc).respectively. The vertical lines indicate the different parts of the piecewise functions, that is, x,< a,, a, I x,5 b,, PI < x,5 Y,,x,> y,, i E {A, B, C}. Figure 3.6 shows the three-dimensional plot and the contour plot of EP(xA,xB,xc) with the restriction that the total production time is filled, but not exceeded, that is, ~ ~1 . 4 ~ ~ 9015 - 0 . 2 4 0.47 The figures show that there is one production planning that leads to a maximum value for the expected profit E p ( x A , xB,xC).A rough estimation can already be made from the contour plot that in this production planning around 18,200 tons will be planned of product A, around 500 tons will be planned for product C, which will leave capacity for about 8400 tons of product B. The second objective function is the first quartile of the total profit, that is, xB =

Q p ( x ~X, B , xc) = 1534 min(17247, xA)+953 min(8682, x ~ ) + 3 3 5 0min(583, xc).

Figure 3.7 shows the three-dimensional plot and the contour plot of Qp(xA,xB,xc) again with the restriction that the total production time is filled, but not exceeded (%I. (18)).

Also these figures show that there is one production planning that leads to a maximum value for the first quartile Qp(xA,xB,xc)of the final profit. Again a rough estimation can be made from the contour plot. In this production planning around 17,200 tons will be planned of product A, around GOO tons will be planned for product C, which will leave capacity for about 8600 tons of product B.

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3 Facing Uncertainty in Demand by Cost-efectiue Manufacturing Flexibility

136.5

Figure 3.7 The first quartile o f the profit for different choices o f the production planning

3.6 Solving the Optimization Problem

The production planning problem is translated into a multicriteria piecewise linear optimization problem. The problem, however, will not be solved as a multicriteria problem, since the objectives are the extremes of one scale, from an uncertain but high profit to a more certain but low profit. For planning management willing to run a higher risk for a higher expected profit, the most profitable planning, corresponding with the maximum expected profit, may be the right choice. For planning management not willing to run any risk the most robust planning, that is, the one with the highest first quartile will be a more certain choice, although the expected profit will be much lower in that case. For every nuance of profitableness at a certain risk, a production planning in between those two extremes can be found. The optimization problem is as follows: determine y1, ..., yn, X I , ..., x,, x,,~ for which EP(Y1,.

..

I

Yn, X I , .

n

n+l

i=l

i=l

. . , xn, xn+1) = Caiyi + C P i E z i ( X i )

or

n

is maximized, subject to

T=

C +c n

i=l

tiyi

n+l i=l

tixi.

3.6 Solving the Optimization Problem

Due to the piecewise character of the objective functions, common gradient methods for optimization cannot be used. Therefore a choice is made to use a direct-search method, the simplex method of Nelder and Mead (Nelder 1965). The Nelder-Mead algorithm is mentioned in many textbooks, but very seldom explained in detail. That is why a short description of the working method is given here (Fig. 3.8). If there are n decision variables in the optimization problem, the Nelder-Mead algorithm will start by choosing n + 1 points arbitrarily. For reason of simplicity, assume that there are two decision variables. Then there will be 3 starting points (PI, P2, P3), which together form a triangle. This triangle is called the simplex. If the objective function is to be maximised then the point with the smallest value ( P l ) is reflected into the middle of the opposite side, in the supposition that this will lead to a better value for the objective function. There are four different possibilities on how the search will continue. 1. If the objective value of the new point (P4) lies between the best and the worst values of the other points (P2, P3), then P4 is accepted as a new starting point and the new simplex is (P2, P3, P4) (Fig. 3.8a). 2. If the objective value of the new point (P4) is better than all others then the point is even further drawn out, twice as far from the reflecting point as P4. Therefore, P5 will form the new simplex with P2 and P3 (Fig. 3.8b). 3. If the objective value of the new point (P4)is worse than all others but better than the original (PI), then a new point PG is evaluated half as far from the reflecting point as P4 (Fig. 3.8~).Again there are two possibilities: a. If P6 is worse than all others then the whole simplex is decreased by half towards the best point in the simplex. The new simplex is then (P2, P3’, PG’) (Fig. 3.8d). b. Otherwise, the new simplex is (P2, P3, PG). 4. If the objective value of the new point (P4) is worse than P1 then a new point P7 is defined halfway between the reflecting point and P1 itself. The new simplex will then be (P2, P3, P7) (Fig. 3.8e).

The new simplex is now used as starting point and the same procedure is performed until the best point and the second best point differ less than a fxed value E. For both objective functions the Nelder-Mead algorithm could be used to find the production planning with the highest expected profit and the production planning with the highest first quartile, that is, the most robust planning. The planners will be provided with information about the robustness and the expected profit of different possibilities of the planning, on which they can base their final choice. In the next paragraph, the Nelder-Mead algorithm will be applied on the objective functions in the case study.

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Figure 3.8

Nelder-Mead algorithm

3.6.1 Solving the Optimization Problem in the Case Study

For the case study the production planning problem is translated into the following optimization problem: Determine xA, x g , xcfor which Ep (%a, xg, xC)

=

1534 EzA( x A )

+ 953 Ez,

(xg)

+ 3350 Ez,

(xc)

or Qp (xA,xg, xc) = 1534 min(17247, xa) + 953 min(8682, x g ) + 3350 min(583, xc) is maximized, subject to xg =

9015 - 0.24 X A - 1.4 xc 0.47

3.6 Solving the Optimization Problem Figure 3.9 The Nelder-Mead algorithm to determine the maximum expected profit

Figure 3.9 shows for the decision variables X, and xc, the contour plot of the expected profit Ep(xA,xB,xc) with the simplices resulting from the Nelder-Mead algorithm. The optimal planning found is the planning in which 18,221 tons for product A, 8445 tons for product B and 481 tons for product C are planned (Table 3.2). The expected profit for this planning equals: Ep(18221,8445, 481) = 3.67 . lo7 dollars. The first quartile for this planning, that is, the robustness of the planning, equals Qp (18221, 8445, 481) = 3.61 . lo7 dollars. The most robust planning, that is, the one with the highest first quartile, is found by applying the Nelder-Mead algorithm to: Qp (xA, x f l ,xc) = 1534 min(17247, xA) + 953 min(8682, x B )+ 3350 min(583, x,-) 9015 - 0.24 X A - 1.4 xc subject to x f l = 0.47

The company itself should now decide if they will speculate on a higher expected profit or if they will prefer a lower but more certain profit. The diagram in Fig. 3.10 below can serve as an informative tool for the decision making.

Results of the optimization

Table 3.2

Optimization ~

~

~~

Ep(XA, XB! xc) (million dollars)

XA

XB

xc

(million dollars)

(ton)

(ton)

(ton)

36.1 36.6

18221 17248

8445 8647

48 1 579

Qp(xAr

XB! XC)

~~

Max. expected profit 36.7 Max. robustness 36.3

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3 Facing Uncertainty in Demand by Cost-efective Manufacturing Flexibility

planned new product C (in tons] Figure 3.10

The profit levels for planned amounts of product C

In the planning with the maximum expected profit 481 tons were planned for product C. In the planning with the maximum 25 % limit of the profit 579 tons were planned for product C. Figure 3.10 shows for the interesting region for the planned amounts of product C, that is, between 400 and 700 tons, four different profit levels: Profit level 1 is the maximum expected profit that can be achieved with the planned amount of product C, assuming that the remaining capacity is optimally divided over the product groups A and B. Profit level 2 is the 25 % profit limit if the planning with the maximum expected profit (see profit level 1) is implemented. Profit level 3 is the maximum 25% profit limit that can be achieved with the planned amount of product C, assuming that the remaining capacity is optimally divided over the product groups A and B. Profit level 4 is the expected profit if the planning with the maximum 25 % profit limit (see profit level 3) is implemented. Assume that the company, based on the information from Fig. 3.10, decides to plan 579 tons of product C. This seems to be a profitable but not too risky choice. Compared to the planning with for example xc = 481, the maximum expected profit is a bit lower, but all other profit levels are very high. It will now depend on the choice for the planned amounts of products in the groups A and B, if they can expect a higher profit with more uncertainty or a lower profit with less uncertainty. However, the 25 % profit limit gives no information about how the profit is distributed below this limit. To have more information on how low the profit could be, Fig. 3.11 shows, for 579 tons planned for product C, the probability distribution of the profit for different amounts planned for product groups A and B.

3.7 Sensitivity Analysis ofthe Optimization

From Fig. 3.11 it is clear that the more product A is planned for, the more profit can be expected, but the more uncertainty exists whether this profit will be achieved. For instance, if the company decides to plan 18,000 tons for products from product group A, then the maximum profit they can achieve is about US $37.5 million and there is a probability of GO% that this profit will not be achieved. There even is a probability of 25 % that the profit will be lower than US $36.3 million.

3.7 Sensitivity Analysis of the Optimization

The planners settle several parameters on which the determination of the optimal planning is based. Some deviation from the expected values will lead, after completion of the production period, to profit results that differ from what was expected. To be able to make a good evaluation of the risks, the sensitivity of the profit and the optimal planning will be studied for small deviations from the expected values of the following parameters in the objective functions: 1. the profit ei, i E (1, 2, ..., n, n + I} made on the sold amounts of the current products and the new one during the production period; 2. the minimum ai, the mode 6,and the maximum y, of the demand di,i E { 1 , 2 , ..., n, n + I} of all products during the production period. XA=

38 f 37.6:

18500 ton

.....

37.2 7

xA=I7500 ton

c36.80s

xA=1725Oton

-

xA=l7000 ton

4 36.41 S

.-0 E

E

36:

...,

m . , ,

. . . . I . . .

6 0.7 0.8 0.9

cumulative probability Figure 3.11 of product A

Probability distributions of the profit for different amounts

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Also the sensitivity of the solution to the parameters in the production time constraint will be studied: 3. the total production time T available per year; 4.the production time ti,i E (1, 2, ..., n, n + 1} that is needed to make one ton of product. Let (yypT,xYPT)be the optimal planning with respect to the maximum expected profit. Let E$'PT= Ep crypT,_xYpT) be the maximum value of the expected profit. The effect on the optimal value E$'" of a small change in for example the para-

meter

el is now given by aE$'PT, the absolute sensitivity coefficient of el.The same a PI --

can be done for all other parameters and for both objective functions. The stepwise character of the objective functions is in this case for the differentiation not a problem, since the discontinuities of the function are only found in the decision variables, not in the parameters. For the parameters, the objective functions are continuous and therefore differentiable. The size of the absolute sensitivity coefficients depends on the scale on which the parameters are measured. To make them comparable they are scaled by

-.

de1

- , which form the relative sensitivity coefficients, for example, for the

GPT

parameter el. The other uncertain parameters influence the only constraint in the problem: n

n+1

i=l

i-1

Cziyi + C

tixi =

T. Changes in the parameters tior in Twill cause the optimal plan-

ning to be no longer feasible. In practice a decrease in comparison to the expected values of ti,i E {1,2, ..., n, n + 1} or an increase in comparison to the expected value of Twill not cause any problem. The planned amounts of products can still be made and it will be possible to make an even higher amount of product than was planned, although it is not guaranteed that this extra amount can be sold as well. Information is needed to determine for which product the extra production time should be used to make as much profit as possible. An increase, however, ofthe values of t i , i E { 1,2, ..., n, n + 1} or a decrease of the overall production time T will cause the optimal planning to be unachievable, and information is needed at the expense of which product the reduction of production time should be found to keep the profit as high as possible. In general Lagrange multipliers can be used to investigate the influence of changes in the right hand side of the constraint parameters, but due to the piecewise character of the objective functions the Lagrange multiplier cannot analytically be calculated for an arbitrary T. The sensitivity analysis will be illustrated on the basis of the case study from Section 3.6.1.

3.7 Sensitivity Analysis ofthe Optimization

3.7.1 Sensitivity Analysis in the Case Study

Assume that the company, based on the information given in Figs. 3.10 and 3.11, has decided to plan 18,000 tons for product group A, 8265 tons for product group B and 579 tons of product C. The expected profit for this planning equals US $36.6 million and there is a probability of 25 % that the real profit is lower than US $36.3 million. To study the sensitivity of the results for small changes in the profit parameters @A, @B, @cand the demand parameters aA,PA,y ~ aB, . PB,yB,%, Pc, yc, the relative sensitivity coeffkients are calculated in the neighbourhood of the expected values of these parameters, presented in Table 3.3. Table 3.3 Parameter

Sensitivity o f the profit for different planning parameters Expected value

25 % Probability limit

Expected profit Absolute sensitivity

Relative sensitivity

Absolute sensitivity

Relative sensitivity

~~~

@A

ee Qc aA P A

YA aB P B

Ye

ac PC

Yc

1534 $ per ton 953 $ per ton 3350 $ per t o n 16,040 t o n 17,550 t o n 19,900 ton 8350 t o n 8900 ton 9150 t o n 0 ton

850 ton 1600 ton

17,578 8265 531 41 1 347 166 0 0 0 539 188 100

0.74 0.22 0.05 0.18 0.17 0.09 0 0 0 0

0.00 0.00

117,247 8265 579 0 0 0 0 0 0 0 0 0

0.73 0.22 0.05 0 0

0 0

0 0 0

0 0

The expected profit and the first quartile of the profit are most sensitive for the profit that can be made with the current product A, due to the high amounts of this product planned to be made and sold, according to expectations. Furthermore, the profit is sensitive to changes with respect to the profit that can be made with one ton of product B, and for changes in the demand of product A. Small changes in the other parameters have hardly any influence on the profit that can be made with the chosen planning. A change in the total production time will also influence the profit that could be achieved with the implementation of the chosen planning. Figure 3.12 shows the change in expected profit, respectively 25 % profit limit, if the increase or decrease in production time T is totally covered by an increase, i.e., a decrease in planned amounts of product group A, B or product C. Figure 3.12 shows clearly that a decrease in the total production time should never be covered at the expense of product group A, but should be found in a smaller amount of product group B or product C. On the other hand, when the production time is higher than expected, the extra time should be used to produce more of product C, although the differences are not so large. The robustness of the planning for

I

847

848

I

3 Facing Uncertainty in Demand by Cost-efective Manufacturing Flexibility

34.5

-400-300-200-100 0 100 200 300 400

...... change in T (hours) Figure 3.12

-400-300-200-100 0 100 200 300 400 change in T (hours) m . . . . .

The changes in profit for smaller or large production time

a small decrease in total production time will not change if less of product A is made. However, a large decrease should go at the expense of the other products. An increase of the production time should as well be used to make more of the product group B or product C. Figure 3.13 shows the change in expected profit, respectively 25 % profit limit, if the increase or decrease in the time ta needed to produce one ton of product A is totally covered by an increase, i.e., a decrease in the planned amounts of product group A, B or product C. Figure 3.13 shows that an increase of the production time needed to make one ton of product A can best be covered by making less of product group B or product C, although to keep the same robustness it is better to make less of product A. For a decrease, it is best to make more of product C. An increase or decrease of the production time needed to make one ton of product group B or of product C, gives more or less the same results as for product group A.

3.8 Implementation ofthe Optimization ofthe Production Planning

I

849

I

35.84 -0.012 -0.008 -0.004 0

0.004 0.008 0.012

-0.012 -0.008 -0.004

0

" l ,

,

change in t[A] (hourdton)

change in t[A] (hourdton) . r n . . D .

t.....

Figure 3.13 product A

The changes in profit for a smaller or larger time/ton for

3.8 Implementation of the Optimization of the Production Planning

In the development of the method the focus was on the practical use for the planners in a multiproduct plant. The users of the method should not be bothered with the mathematical background of the method, which from their point of view can be considered as a black box. The emphasis should be on the information that should be acquired from them as an input for the method and on the results obtained from this information to be presented in a comprehensible and useful way. Knowledge of the transformation from the input into the output can increase the confidence in the results, but is not required to be able to use the planning method (see Fig. 3.14). The informationjom the planners, needed as an input for the method, should consist of:

-tnformatron from

planners

Figure 3.14

Implementation of the planning method

,

0.004 0.008 0.012

850

I

3 Facing Uncertainty in Demand by Cost-efectiue Manufacturing Flexibility 0

0

0 0 0

0

the profits made on the current products sold in annual contracts in dollars per ton; the profits made on sold amounts of the current products and of new ones during the production period in dollars per ton; the total production time available in hours per year; the production times needed to make the products in hours per ton; the demand for the current products that can be sold in the annual contracts; the demand for the current products and for the new ones during the production period in ton per year described by: - the minimum demand in ton per year; - the mode of the demand in ton per year; - the maximum demand in ton per year.

Table 3.1 is an example of such input information. The results for the planners, produced by the planning method, consist oE 0

0

0 0

results of the optimization showing the optimal planning with respect to the maximum expected profit and the optimal planning with respect to the maximum 25 % profit limit (Table 3.2); the profit levels for planned amounts of new products showing the maximum expected profit and its corresponding 25 % profit limit and the maximum 25 % limit and its corresponding expected profit for different choices of free capacity for the new product(s). If more than one new product is taken into consideration, then the aggregate free capacity for these new products will be showed on the xaxis (Fig. 3.10). probability distributions of the profit for different planned amounts of the products showing the total probability distribution of a certain planning. For practical use, it should be easy to change the chosen amounts for all products to assess the effect of the changes on the profit distribution (Fig. 3.11). sensitivity of the profit for different planning parameters showing for a chosen planning which parameters are really influencing the profit, and by that require a good estimation of the expected value (Table 3.3); the changes in profit for smaller or larger production time (Fig. 3.12); the changes in profit for a smaller or larger time per ton for the products showing which adaptation to the planning should be made if the real values of production times differ from the expected ones (Fig. 3.13).

When the results are presented in such a way that the planners have full insight into the consequences of a chosen planning, the method will serve as a valuable decision support tool.

Reference I 8 5 1

3.9 Conclusions and Final Remarks

A production planning method has been presented for a multiproduct manufacturing plant, which optimizes the profit under uncertainties in product demands. In the method these uncertainties are modeled by means of a simple triangular probability distribution, which is easy to specify. The optimization goal can be formulated as either a maximum expected profit or a robust profit (first quartile of the profit) to lower the risk. Due to discontinuities in the probabilistic distribution function of sold products a direct search optimization technique, Nelder-Mead, must be applied rather than a gradient-based optimization. The development and the application of the method have been highlighted by means of a case study taken from a food additives plant. This method is considered practical because the required input data for the demand and process models and the profit function is easy to get by the users of the method, while the output information facilitates the interpretation of sensitivities of the optimized production planning in terms of common economic and product demand specification parameters. The method should be accessible to plant production management rather than to operations research specialized planning experts.

References Bansal V. Perkins /. D. Pistikopoulos E. N . Flexibility analysis and design of dynamic processes with stochastic parameters. Comp. Chem. Eng. 22(Suppl.) (1998) p. S817-S820 Bengtsson /. Manufacturing flexibility and real options: a review. Int. J. Prod. Ec. 74 (2001) p. 213-224 Berry W. L. Cooper M . C. Manufacturing flexibility: methods for measuring the impact of product variety on performance in process industries. J. Op. Mgmt. 17 (1999) p. 163-178

Corrka H . L. Managing unplanned change in the automotive industry. Dissertation University of Sao Paulo Wanvick Business School, Avebury. Aldershot 1994 Nelder /. A. Mead R. A simplex method for function minimization. Comput. J. 7 (1965) p. 308-313 Papoulis A. Probability, Random Variables, and Stochastic Processes. McGraw-Hill, Boston 1965 Swaney R. E. Grossmann I. E. An index for operational flexibility in chemical process design. AIChE J. 31(4) (1985) p. 621-641

Indices

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8

Authon's Index I 8 5 5

Authors' Index Abildskov, Jens V-1" Alva-Argaez, Alberta 11-2 Belaud, Jean-Pierre IV-5 Bogle, I. David L. 11-4 Braunschweig, Bertrand IV-5 Cameron, Ian T. 1-6, IV-2 Dua, Vivek 111-5 Engell. Sebastian 111-4 Espuria, Antonio IV-3 Fernholz, Gregor 111-4 Buzzi-Ferraris, Guido 1-1 Gani, Rafiqul IV-1, V-1 Gao, Weihua 111-4 Georgiadis, Michael C. 1-4, 11-1, 111-1 Gerbaud, Vincent 1-3 Gemaey, Krist V. 1-7 Grievink, johan V-3 Hangos, Katalin M. 1-5, 1-6 Heijnen, Petra V-3 Heyen, Georges 111-3, V-2 Ingram, Gordon D. 1-6 Jmgensen, Sten Bay 1-2, 1-7 joulia, Xavier 1-3 Kalitventzeff, Boris 11-3, 111-3, V-2 Kikkinides, Eustathois S. 1-4

Kokossis, Antonis 11-2 Kostoglou, Margaritis 1-4 Kraslawski, Andrey 11-5 Lakner, Rozalia 1-5 Lim, Young-il 1-2 Lind, Morton 1-7 Linke, Patrick 11-2 Manca, Davide 1-1 Marechal, Francois 11-3 Mateus, Miguel V-2 Newell, Robert B. IV-2 Papageorgiou, Lazaros G. 111-7 Perkins, john D. 111-5 Pistikopoulos, Efstratios N. 11-1, 111-5 Proios, Petros 11-1 Puigjaner, Luis 111-6, IV-3 Romero, javier 111-6 Sass, Richard IV-4 Shah, Nilay 111-2 Toumi, Abdelaziz 111-4 Tsiakis, Panagiotis 111-1 Ydstie, B. Erik 11-4 "( Section-Chapter)

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

Computer Aided Process and Product Engineering Luis Puigianer and Georges Heyen . Co. KGaA, Weinhein Copyright 02006 WILEY-VCH Verlag GmbH 8 Subject Index I 8 5 7

Subject Index a abstraction 226 f acceptance criterion 117 f f accuracy - data validation 801 ff, 808 f - distributed dynamic models 38 ff - simultaneous integration 207 - stencil methods 43, 47 acetic acidlmethyl acetate process 544 acetone-chloroform mixtures 785 ff acetone-cyclohexane system 127 acetone-water system 129 achieve relation 255 acidification 71 1 acoustic databases 734 action-instrumental artisan model 249 active pharmaceutical ingredients (API) 405, 434, 649f

active tablet components 435 activity coefficients 125 ff, 781 activity-based costs (ABC) 464 adaptive grids method 40 adaptive mesh refinement (AMR) 35 ff, 68 ff, 74 ff

adaptive stencil methods 42,45 ff adaptive supply chains capabilities 702 adsorption - batch chromatography 552 - distributed dynamic models 75 - gas separation 3, 11, 138-147 - model-based control 567 - separation systems 137 ff advanced numerical methods 68 advanced planning and scheduling systems (APS) 476, 622, 700 advanced process combinatorics 473 Advanced Process Control (APC) 820 advection 99 advisory system 612, 615 f aeroderivative duty gas turbines 336 affine functions 583 f agent-based supply chain management 632, 697 K 702 ff

agglomeration 75, 87, 90ff aggregate time period (ATP) 455 aggregation - decomposition techniques 447,454 f f - distillation 278, 287 - granulation process 191 agitated reactors 307 agrochemicals 649 air conditioning 328 ff air preheating 355 Alberta Taciuk Processor (ATP) 684 alcohols 649 algebraic systems 2, 15-34, 175, 201 algorithm implementation 530 alkane groups 127ff allocation - product scheduling 488 ff - resource planning 448, 457, 460 - supply-chain management 624, 637, 708 allolactose, lac operon 231 Altshuller method (TRIZ) 428 aluminum process, carbothermic 399 amino acid chains 228 ammonia synthesis 534 ff, 812 ff analogies methods 428 Anderson molecular modeling 117 Andrecovich- Westerberg model 273 anisotropic united atoms force fields 123 Apache standards 752 application programming interface (API) standards 752 applications 174, 485, 771 -854 - chemical product-process design 659 - distributed dynamic models 75 ff - embedded integration framework 210 - flexible recipe model 612 - frameworks 209 - 214 - life cycle modeling 681 ff - molecular modeling 125 ff - multiscale processes 203 - product scheduling 506 ff - simultaneous integration 207 r-arabinose ( A M ) regulatory networks 242

Computer Aided Process and Product Engineering. Edited by Luis Puigjaner and Georges Heyen Copyright 0 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 3-527-30804-0

858

I

Subject Index

arc length 72 ARMAX package 679 aromatics groups 130 Arrhenius temperature dependence 79 ff, 85 Arrhenius-type kinetic constants 792 artisan model of instrumental action 249 ARXmodel 567 Aspen Custom Modeler (ACM) 545 Aspen packages 473, 638 AspenPlus - educational modules 775 - equipment design 390 - life cycle modeling 680, 691 - multiscale process modeling 214 asphalt production 457 assumption retrieval 181, 678 asymmetric traveling salesman problem 490 asymptotic solutions 162 asynchronous agent-based team 507 atmospheric distillation unit (CDU) 323 attainable region method 306 AUA4 force fields group 131f auction method, iterative 636 augmented Lagrangean relaxation 466 ff, 470 auto-associated software agents 697 autocorrelation coefficients 116 automatic differentiation 39 f automation OPC standards 755 autonomic chemical plants 223 autonomous agents 702 auxiliary functions 24, 31, 159 average values - data reconciliation 521 f - molecular modeling 112 ff - supply-chain inventory 634f Avogadro number 126 azeotropes - distillation 278ff - educational modules 782 ff - methyl acetate process 544

b backdiffusion effects 142 backward allocation 709 backward differentiation formula (BDF) 36 ff, 57 ff balance composite curves 345 f balance equations 172- 182 - chemical product-process design 659 - educational modules 778 - equipment design 388 - multiscale process modeling 198 - process monitoring 520 balance volumes 172 ff, 180ff - multiscale process modeling 198 - partial models 201

Bardenpho process 314 batch chromatography 552 ff, 562-568 batch correction procedure 611 batch crystallization 159 batch processes 498, 591 -620 batch production 448,458ff batch reactor model equations 406 batch scheduling 673 batch splitting 487 Bayesian networks 238, 594 beads model 122 benzene 388, 785 benzyl alcohol production 606 beta-factor 566 beta-galactoside permease 231, 256 f bibliographical therrnophysical databases 735 bid selection problem 466 bifurcations 237 bi-Iangmuir function 556ff bill of materials (BOM) 698 binary interaction parameters 127 binder - granulation 196 - tablet formulation 435 biochemical processes (BioPro) 75 ff, 408 biochemical product-process design 656 biogas outlet temperatures 355 biological regulatory framework 250 biological systems/biomolecules 224ff Biot number 80 biotransformation processes 224 ff black-box model - flexible recipes 606 - life cycles 676 - multiscale processes 199 blending - data validation 827+ - product development 432 - product scheduling 484 - resource planning 448, 456 block grid structures 69 blow-down steps 140, 148 boilers 337, 370ff boiling point 649, 734 Boltzmann factor 114, 127 bond molecular models 122 Boolean matrix 29 f Boolean networks 238 Boolean variables 277, 290f bottom-up approaches 194, 197f boundary conditions 172 ff - distillation 281 - distributed dynamic models 36, 54, 66 ff, 77 - gas separation 147 - meshrefinement 70 - molecular modeling 108 ff

Subject Index I 8 5 9

- mdtiscale processes 198 - partial models 201 - separation systems 139 f - thermophysical databases 734 bounds 30 bovine somatropin (BST) 409 Box- Jenkins model 679 brainstorming product development 427 branch and bound technique - distillation 282 - hybrid processes 594 - product scheduling 495 ff - resource planning 467 ff - supply-chain management 637 branch-and-cut enumeration 488 Brdyi model 557 ff breakage - crystallization processes 162 - distributed dynamic models 75, 87, 90 ff brewery utility management 689 bromopropyl compound amination 405 Brownian motion 108 Broyden condition 28 f, 559 bubble columns 307 bubble curve, hexane/cyclohexane system 128 Buckingham potential 123 budgetinghorizons 714 buffer times 499 building blocks - chemical product-processes 660 - distillation 277 building transformations 177 bulk chemicals 648 bullwhip effect 699 Burger’s equation 73 business strategies 421 butanoic acid chlorination 308 butyronitrile 131 Buzzi-Ferraris property 19, 25, 29 bypassing strategies 305 byproducts 297, 327

C

Caballero-Grossmann model 277 Calderbanl- Moo-Young correlation 85 calibration 182 ff calibration - data validation 801 - equipment design 391 - life cycle modeling 676 - multiscale process modeling 194 caloric databases 734 campaign production 448,458ff, 493 f Cannizarro reaction 606 canonical models 179 canonical NVT 113

capacities - chemical product-processes 657 - cost-effectivemanufacturing 831 ff - planning 541 - product scheduling 489, 504 - resource planning 450 CAPEC database 780 CAPE-OPEN - standards 750ff - life cycle modeling 680 f, 691 - multiscale process modeling 214 - resource planning 476 carbon catabolite repression 233 f, 256 ff carbon dioxide balance 96 ff carbon ratio 806 ff carbothermic reactors 399 f carboxyl groups 130 carnosic acid manufacture 652 Carnot efficiency 342 cascade model 331 case studies - equipment design 393 ff - life cycle modeling 681 ff - cost-effective manufacturing 834 ff, 844 ff case-based reasoning systems (CBR) 423,434 ff cash flow 695, 712 catabolite repression 233 ff, 256 ff catalysts - ammonia formation 814 - design 434, 655 - educational modules 791 - flexible recipe model 601 - intensification 300 - life cycle modeling 673 - utility systems 328 catalytic slurry bed 84 cause effect analysis 199 cell compartments 237 ff cell division 75 cell number variation 97 cell population - biochemical process design 409 - distributed dynamic models 75, 92 ff cell state control 224, 244 central agents 705 f, 727 central dogma of biology 228 f centrifuges 411 f chain rule, distributed dynamic models 40, 63 Chang method 61 ff, 65 ff chaos properties, regulatory networks 237 character string pattern 531 charge conservation 384 ChemCad modules 775 Chemical Abstracts Service (CAS) 419 chemical engineering, thermophysical databases 733 - 748

860

I

Subject Index

chemical engineering plant cost index (CEPCI) 335 f chemical equilibria 36, 649, 814 chemical industrial plants 327 ff chemical phenomena 301 f, 422 chemical potential 384 chemical product-process design, integrated 75ff, 647-668 chemical vapor deposition (CVD) 195, 203 chemistry - computer-theoretical 108ff - intensification 302 - quantum models 121 ff chemistry WebBook, thermophysical databases 736 ff CHEMKIN software 214 chi-square test 528, 809 f, 817 f chlorination, butanoic acid 308 chloroform 649 chloroform-acetone mixture separation 785 ff chocolate couverture, house of quality 426 Cholesky algorithm 22 CHP schemes 349 chromatographic separation 6, 552 chromatography 35,75 ff chromosomes 532 classification - integration methods 204 - life cycles 679 - linking frameworks 205 f - multiscale process modeling 199 - partial models 198ff cleaning 328 client agents 705, 722 clinical trial outcomes 462 closed-loopcontrol 542 coagulation 150 ff,155 ff coal outlet temperatures 355 coalescence 196 concurrent beds 307 COGents standards 766 COLaN standards 751 ff cold streams 329 ff,334 ff, 370 collision frequency 153 collocation method - crystallization processes 155 - distributed dynamic models 52 - intensification 315 columns - batch chromatography 552 - distillation 270-295 - intensification 307 - methyl acetate process 544 COM standards 754, 758 COMBO system 598 combustion 328, 351 ff, 686

commissioning 669 ff common grid approach 490 communicative actions 250 compensated disturbances 612, 616 complementary slackness 582 complex column sequences 285-296 complex multiphase reactor 393 ff complex separation systems 137- 170 complexity - batch chromatography 552 - chemical product-process design 656 - product scheduling 489 - regulatory networks 229ff, 236ff component integration 7 component-based hierarchical explorative pro. cess simulator (CHEOPS) 214 components 171 ff composite curves 331 compositions 171 compositions - multiscale process modeling 197 - utility systems 345 f, 371 ff, 375 compound balances 811 ff, 827 compound selection 660 compressed gases 328 compression - ammonia synthesis 536 - refrigeration cycles 359 computer theoretical chemistry 108 ff computer-aided educational modules 9 computer-aided equipment/process design 383-418 computer-aided flow sheet design (CAFD) 662 computer-aided integration, utility systems 327-382 computer-aided intensification methods 297- 326 computer-aided mixture-blend design (CAMbD) 649 ff, 653 ff computer-aided modeling/simulation 11-264 computer-aided molecular design (CAMD) 422, 649 ff, 653 ff computer-aided process modeling (CAPM) 1ff, 181 computer-aided process operation 443 -642 computer-aided process/product design 1ff, 265-442 computer-aided production engineering (CAPE) 1, 5, 643-770 - see also: CAPE, CAPE-OPEN computer-integrated manufacturing (CIM) 1ff computational fluid dynamics (CFD) 11, 35, 98-106 - equipment design 383 - life cycle modeling 673 - parallel integration framework 212 - simultaneous integration 207

Subject Index I861

concentration dynamics, regulatory networks 233 concentration profiles - ammonia formation 815 - model-based control 568 conceptual design - life cydes (Clip) 669, 676 ff, 691 - multiscale process modeling 203 - shale oil processing 682 condensers - complex multiphase reactor 394 - data validation 812 - distillation 283, 291 condition number 24 conditioning 519 conductive media simulation 401 configuration - interaction methods 121 ff - nonazeotropic mixtures 286 conjoint analysis 424 connection relation 255 conservation balances 176ff conservation element/solution element (CE/SE) method 39, 57, 61 ff conservation laws - distributed dynamic models 43, 62 - equipment design 384, 388 ff consistency 183 constitutive equations 173-182 - multiscale process modeling 191ff, 202 ff constraint logic programming (CLP) - product scheduling 500 ff - resource planning 469 - supply-chain management 627 constraint propagation methods 30 - chemical product-process design 659 - cost-effective manufacturing 831 f - data validation 802 - educational modules 778 - flexible recipe model 613 - hybrid processes 594, 601 ff - model-based control 558ff - process monitoring 520ff, 529ff - product scheduling 483, 489f, 496f - real-time optimization 581 ff - resource planning 456 - supply chain management 714 - utility systems 350, 365 f construction projects 465 ff consumer requirements 5, 424 contaminant profiles 322ff, 375 ff continuation methods 31 f continuity, boundaries 54 continuous multiscale process modeling 199 continuous time discretization 490, 497 continuous time representation 594

control hybrid processes 599 - model-based 541 -576 - multiscale process modeling 194 - resource planning 453 - transcriptional regulation 235 f controllability - complex multiphase reactor 397 - dynamical properties 185 - life cycles 676 - product development 431 convection - cell population dynamics 93 - complex multiphase reactor 401 - distributed dynamic models 35, 43, 59, 75 convergence 17 f, 25 - material flows 448 - real-time optimization 589 - separation systems 142 conversion systems 329 ff convex hull disjunction formulation 277, 284 f cooling requirements 330, 370 coordinate transformation 177 CORBA-IIOP standards 750, 754f Corporate Web site management 764 correction model - distributed dynamic models 60 - flexible recipes 610 correlations - molecular modeling 114 ff - multiscale process modeling 204 - utility systems 335 cosmetics 438 costs - chemical product-process design 648 f - correlations 335 - data validation 810 - effective manufacturing 829-854 - flexible recipe model 603 ff - model-based control 548, 566 - nonlinear functions 361 - process monitoring 537 - real-time optimization 580 - resource planning 450 - supply-chain management 623 - utility systems 334ff Coulombic interactions 109, 121 f, 124f counter currents - carbothermic aluminum process 400 - utility systems 330 - intensification 307 - separation systems 142 coupling - multiscale processmodeling 189 - regulatory networks 244 Courant- Friedrichs - L e y (CFL) number 59

-

862

I

Subject lndex

covariance matrix 521 CPLEX solver 469 CPU conditions 28 CPU time - distributed dynamic models 51 - water systems 324 cradle-to-the-graveprocess 667 Crank- Nicolson central difference scheme 61 creative templates 430 critical region 579 ff, 588 ff crude desalting 323 crude oil distillation - datavalidation 819 - inventory management 457 - real-time optimization 580 crystal fragmentation 150ff crystal growth - distributed dynamic models 75, 87 ff - separation systems 150 ff crystal size distribution (CSD) 87, 152 crystallization 13, 159 - chemical product-process design 653 - distributed dynamic models 35 - separation systems 149ff customers demands - cost-effective manufacturing 829 - product development 430 - supply-chain management 621, 630f customers service level (CSL) 622, 631, 635 cutoff distance 124 cycle periods, batch chromatography 552 cyclic adenosine monophosphate (CAMP) 234 cyclic material flows 448 cyclic steady state (CSS) - model-based control 565, 570 - separation systems 139

d Daesim dynamics 680 Damkohler number 80,85, 387 Danckwert's boundary condition 36ff, 66, 77, 86 D AM standards 766 data analysis - chemical product-process design 660 - life cycle modeling 681 - multiscale process modeling 194 - product development 423,438 ff data handbooks 735 ff data quality 182 data reconciliation 6, 517-540, 802ff, 81Off data validation 801-828 data validation - computer-aided integration 329 - process monitoring 519 ff, 524 f - utility systems 330

databases - educational modules 779 - thermophysical properlies 733- 748 Datacon package 527 debottle-necking 303,674 decay rates, regulatory networks 240 decentralized decision making 704 DECHEMA databases 735 ff, 744ff, 753 decommissioning 669 ff decomposition techniques - fluid bed reactor 414 - life cycle modeling 675 - product scheduling 495 ff - resource planning 447, 454 ff, 469 ff - structural 184 decoupling frameworks 205 f default values 181 definition phase, product development 421 ff deformation rate, granulation 196 degradation 502, 816 delay differential equations (DDEs) 231 f delta function 164 demand data 451 - cost-effective manufacturing 829-854 - expected 833 - manager agent system 723 - product scheduling 484 - supply-chain management 621, 626 - water usage 376 demonstration, multiagent system 726 dense overlapping regions (DOR) 243 densities, thermophysical databases 734 density functional theory (DFT) 121ff, 130f desalter 323 design - chemical product-processes 648, 657 - complex multiphase reactor 399 f - documentation standards 764 - equipment 390 - life cycle modeling 669 - product development 421,424ff, 431 - supply-chain management 624 - utility systems 367f design institute for physical property data (DIPPR) 735, 739ff desorption 139147 deterministic methods - life cycle modeling 674, 679 - multiscale process modeling 199 - product scheduling 505 - resource planning 469 - supply chain management 698 f DETHERM thermophysical databases 736, 762 diabatic distillation column 394 DICOPT MINLP solver 276 Diesel engines 336, 343

Subject lndex I863

diethyl ether 649 difference schemes 60 differential equations - partial models 201 - regulatory networks 239 ff differential index 177, 184 f differential-algebraicequation (DAE) 2, 13- 34, 171ff - educational modules 778 - life cycle modeling 680 - model-based control 545 ff diffusion - computational fluid dynamics 80, 99 - distributed dynamic models 35 f, 75 - gas separation 145 - intensification 311 diffusion coefficients - distributed dynamic models 59 - molecular modeling 114 - thermophysical databases 734 dilution loss 93 DIMA block standards 765 dimension analysis 183 dipolar interactions 121 Dirac delta function 164 Dirichlet’s boundary condition 36 discontinuities 30 discretization - crystallization processes 156ff - distributed dynamic models 35 ff - fixed-bed reactors 83 - hybrid processes 591 ff - multiscale process modeling 199 - partial differential equations 55 - time grids 488, 490 ff, 494 ff discrimination process models 171- 188 disintegrant 435 disjunctions 277 dispersion - crystallization processes 155, 161 - distributed dynamic models 36 - shale oil processing 684 displacements 119 dissipation 59 distance, linear systems 18 distillation 4, 17, 27, 32 - chloroform-acetone mixture 787 ff - columns 17f, 27, 32 - data validation 811, 818f - equipment design 388 ff, 393 ff - intensification 297, 310 - model-based control 543 ff - molecular modeling 109 - process synthesis 269- 296 - separation systems 138ff - solvents 787

distributed dynamic models 35- 106 distributed parameter multiscale process modeling 199 distribution centres 623 f, 696ff, 717 disturbances - feed compositions 397 - flexible recipe corrections 610ff, 616 - methyl acetate process 550 - model-based control 543 f divergent material flows 448 divided differences method 45 dividing wall column 286 DNA replication 224, 228 ff Documentum package 679, 692 domain relationship 206 Dorfi-Drury method 71 Dortmunder database (DDB) 736ff, 745 drum design 196 Dufort-Frankel method 59,67 duty gas turbines 336 dyes 437 dynamic data reconciliation 517, 524ff dynamic models - environment 696 - life cycles 678 - plants 541ff dynamic population balance 75, 87, 92 dynamic simulation - equipment design 390 - process operation scheduling 501 dynamical properties 185

e Eastman process 297 f echelons supply chain 699 ff, 708 f Eclipse standards 500, 752 eco-label (ecological card) 710 e-commerce 697. 750 economic lot scheduling 491 economic models - life cycle modeling 672 - supply chain management 700 eco-toxicological impact 711 edge effects 110 educational modules 9, 775 -800 effect modeling and optimization (EMO) 349 ff efficiency - data validation 809 - utility systems 335, 362 effluents 328 eigenvalues 38 ELDAR, thermophysical databases 738, 743 ff electrode heating 403 electrodeposition 203 electrolyte solution data bases 742 ff electrostatic interactions 123, 131

864

I

Subject Index

elementary functions, regulatory networks 251 f embedded integration framework 210 embedding relations 252 emergency response 673 emissions - utility systems 328 - water use 374 empirical model building 181, 199, 674 encapsulation 653 energetic-interaction-relatedphenomena 109 energy balances 173, 180ff energy balances - chemical product-process design 654 - distributed dynamic models 36 - educational modules 793 - equipment design 384 - process monitoring 535 energy consumption - datavalidation 810 - distillation 270 - formic acid plant 825 - utility systems 328-382 energy dissipation 150 f energy estandards 753, 757 ff energy recovery 330 energy recycling 80 engineering - life cycle modeling 669 ff - shale oil processing 684 enterprise content management (ECM) 692 enterprise resource planning (ERP) 463 ff, 472 ff enthalpy - balance equations 18 - thermophysical databases 734 - utility systems 340 ff entrainer selection 281 entropy - complex multiphase reactor 395 - equipment design 384 ff - thermophysical databases 734 enumeration - distillation 271 - product scheduling 488 f - resource planning 459, 467ff environmental impact - chemical product-process design 649 - life cycles 668, 672, 680 - manager agent module 707, 725 - shale oil processing 684 - supply chain management 696, 710, 727 environment-health -safety (EHS) 785 enzyme activity 568 equation construction procedure 172 equation partitioning 795

equation weights 18 f equation-oriented packages 392 equidistribution principle 71 equilibrium - adsorption 144 - chemical product-process design 649 - data validation 814 - ethanol-water mixture 782 - thermodynamics 384ff equipartition of entropy production (EDF) 389, 395 f equipment - costs 335ff - design 383-418 - failure 505, 517 - process intensification 299 ff errors - adaptive mesh refinement 68 - covariancematrix 521 - data validation 801 ff, 805 ff - distributed dynamic models 37, 51 - model-based control 560, 564f - molecular modeling 115 - multiscale process modeling 216 - process monitoring 518 ff - UNIQUACmodel 131 Escherichia coli - biochemical process design 409 - regulatory networks 224-235, 242ff essentially nonoscillatory (ENO) schemes 42-47, 57ff, 71ff esterification, methyl acetate process 544 ethanol oxidation 94 ethanol-water system 129, 782 ethylbenzene separation 811 ethylene dichloride (EDC) fraction 398 ethylene glycol production 312 Euclidean norm 19, 25 eukaryotes 237 Euler central difference method 60 ff Euler discretization 156f Euler equation 100 EURECHA Web site 798 European Symposium on Computer-Aided Process Engineering (ESCAPE) 763 eutrophication 711 event operation network (EON) 595 ff event tree 673, 679 evolutionary algorithms 487, 597 Ewald summation 124 exact solution approaches 469 exchange rates 623 exergy analysis 341 ff exergy losses 362 ff, 395 exhaust gas flow 98 exothermic behavior 146

Subject Index I865

experimental design - model-based control 569 - product development 422, 432 ff experts systems 778 explicit time discretization 58, 60 f extended Kalman filter 525 extensible markup language (XML) 750, 757 extension conditions 181 extensive quantitives 174, 387 extracellular glucose 229 extracts, separation systems 140 f

f Factory Planner software 473 FACT thermophysical databases 736 factorization 24 failure - methyl acetate process 550 - process monitoring 517 - product scheduling 505 fault diagnostics 251, 673, 678f feasibility studies 520, 531 feed compositions 270, 397, 680 feed flow rates 275, 282 feedback control 541 - 576 feedforward loop 243 feeding strategies 305 FEMLAB multiphysics module 401 Fenske-Gilliland- Underwood short cut model 283f fentanyl analysis 779 ff fermentation 318, 408 field molecular orbital concept 122 fill rate maximization 624 fillers 435 filtering 519 financial analysis models 673, 69G financial module 711, 725 finishing 651 finite difference methods (FDM) - batch chromatography 563 - distributed dynamic models 41, 54, 86 finite element methods (FEM) - complex multiphase reactor 401 - crystallization processes 154 - distributed dynamic models 41, 51 ff - life cycles 680 - stress modeling 686 finite intermediate storage (FIS) - hybrid processes 593 - product scheduling 485 finite volume method (FVM) 41, 55 ff first principals model 234 Fischer-Tropsch synthesis 83 fitness function 533 fixed-bed gas separation 143f

fixed-bed reactors 35, 75, 79ff fixed-grid method 40 fied-point homotopy 31 fixed-stencil approximation 42 ff flexible cost-effectivemanufacturing 829-854 flexible environment modeling 594 ff flexible recipe model 597-613 Floudas optimization 274, 305 f flow rates - batch chromatography 552 - complex multiphase reactor 396 - distributed dynamic models 49 - real-time optimization 580 - refrigeration cycles 359 - regulatory networks 256 - resource planning 448 - utility systems 340ff flow sheets - chemical product-process design 651, 661 - distillation 284 - educational modules 778 - life cycle modeling 672 - shale oil processing 683 fluctuations, molecular 108, 113 ff flue-gas flow 352 FLUENT software 214 fluid bed reactor 413 ff fluid concentration propagation 78 flux terms, gas separation 145 food additives plant 834 ff force equipartition 389 force fields l l O f f , 114ff, 123ff forecast management 696, 703 ff forecasting module (FOREST) 714 forecasting techniques 830 formalization, regulatory networks 251 formic acid plant 825 formulation - process monitoring 520 - product development 432 forward allocation 709 Fourier transform 114 fractionation 686 fragmentation lSOff, 160 ff frameworks - integrated chemical product-process design 658 - multiscale process modeling 205 ff, 215 f - regulatory networks 249 free software standards 752 freedom degrees 157, 183 f frequency response approximation 548 freshwater consumption 320 fmit cooperative 714 fuel additives 436 fuel cells 338

866

I

Subject

Index

fuel consumption 334 ff,352 f fuel oil production 457 fuel outlet temperatures 355 fully discretized methods 35 ff, 58 fully thermally coupled column sequences 288 functional analysis 251 f functional B-splines 163 functional equivalence 172 functional genomics 224, 236f functionalities 599 function- property-composition relations 420 ff Furzeland method 71 fuzzy modeling - cost-effective manufacturing 833 - resource planning 452 - supply-chain management 637

g

gain matrix 558, 562 galactoside permease 231 Galerkin residuals 155 ff, 163 gamma distribution 165 gamma-phi equilibrium model 782 Gantt charts 447, 608 gas concentration factor 85 gas constant 95 gas engines 336 gas permeation 314 gas phase, Fischer-Tropsch synthesis 84 gas processes, eStandards 757 f gas separation 3, 11, 138-148 gas turbines 336, 351, 373 gas-liquid-liquid reactors 311 gas-oil systems 457 gasoline blending 456 gasoline data 580 Gauss divergence 62 Gauss integration 166 Gauss law 115 Gaussian waves 50 Gear-like algorithms 116 Gebhard- Seinfeld collocation 155 gene interactions 224 gene population 532 gene transcription 228, 233ff general flexible recipe algorithm 602 f general purpose solutions 483 general rate model (GRM) 553 generalized disjunctive programming (GDP) 277 generalized Maxwell- Stefan (GMS) equation 145 generic activity-based product development 421 ff generic algorithms - investment cost function 361 - life cycle modeling 680

-

process monitoring

528, 532

- product development 423 ff, 438 - product scheduling 487, 503 - resource planning 468 ff generic manipulation 223 ff genericity tests 131 genetic code, lac operon 229 genome sequencing 224 genome wide molecular interactions 246 geographical information system (GIS) 626 Gibbs ensemble Monte Carlo 119ff, 125f Gibbs model 386 Gibbs-Duhem relation 125 f Gilliland-Fenske- Undemood method 276, 283 ff Gill-Murray criterion 25 global supply chain management (GSCM) 696 ff global warming 710 glucose - fermentation/oxidation 94 - regulatory networks 229 f, 258 glycols 649 Goffman framework 249 gPROMS package - educational modules 775 - equipment design 392 - gas separation 148 - life cycle modeling 680, 691 - model-based control 545 f - multiscale process modeling 214 gradient methods 20 ff, 26, 39, 557 ff gradual model enrichment 197 grafcet logic models 673 grand composite curves 331 - 346, 375 granulation 3, 189-197, 408 graphic user interface (GUI) 719ff, 724ff graphical representations - intensification 305, 310f - resource planning 469 - utility systems 333 ff, 339 ff - water usage 377 - water-pinch concept 320 ff Green’s theorem 56, 62 green-kubo formulas 116 grey-box model - life cycles 676 - multiscale process modeling 199 grid methods - crystallization processes 156 - distributed dynamic models 40, 52, 69 - hybrid point timing 594 grinding processes 13, 151ff,160ff gross errors 809f, 817 - data validation 803, 809 - process monitoring S18ff, 528

Subject Index Grossmann model 277 Grossmann- Pinto method 490 ff group contribution methods 662 growth, crystallization Isoff, 155 ff

h Habermas approach 249 f HAD process standards 765 Hamiltonian operator 121 f Hangos-Cameron model 172 ff, 390 hardware, process intensification 299 ff Hartree-Fock method 128 heat balances - educational modules 792 - gas separation 146 - utility systems 330f, 335 f heat cascades 331 heat exchange - ammonia synthesis 536 - distillation 270 - educational modules 791 - granulation process 191 - intensification 297, 300 f heat exchange network (HEN) 276, 328 f, 349 ff heat integrated column sequences 279 ff heat pumps 337, 360, 372 heat recovery boilers 337 heating requirements 370 heating system failure 550 heat-power combination 329 heavy duty gas turbines 336 height equivalent to theoretical plate (HETP) value 545 Hendry- Hughes technique 274 Henry coefficients 569, 734 Henry’s law 95 heptanone 649 Hermite polynomials 155 f, 165 Hessian matrix 23 f heuristic methods - distribution planning 624 - product scheduling 484, 487 ff - supply chain management 698 f hexanone 649 hidden components 174 hierarchical approaches - hybrid processes 594 - product scheduling 481 - resource planning 459 high-temperature reaction zone 400 high-throughout experimentation (HTE) 433 Hildebrandt solubility 649, 779 Hill coefficient 240 Hill-Ng procedure 163 f Hoffmann’s number 59 ff homogeneous azeotropic separation 281 f

homotopy 31 Honeywell‘s database 681 horizon methods - data reconciliation 526 - flexible recipe model 605 - model-based control 542 - real-time optimization 586 - resource planning 454, 457 - supply-chain management 628, 633 f, 714 horizon-averaged finished product (SKU) inventory 634 hot streams 329& 334ff, 352& 370 house of quality 425 Huang-Russell approach 71 Huckel calculations 121 human factors - life cycles 674 - supply chains 702 hybrid methods 7, 16, 27 ff hybrid methods - embedded integration framework 211 - life cycle modeling 671 - multiscale processes 199 - product development 438 - product scheduling 483,498 ff,506 f - real-time optimization 584 - resource planning 469 - see also: Powell method hybrid multizonal/CFD modeling 160 hybrid processes 591 -620 hybrid separation 137, 297, 301, 314-321 hydrocarbon-based fuels 682, 686 hydrocarbons 323 hydrogen bonding interactions 123 hydrogen catalytic oxidation 79 hydrogen energy balances 84 hydrogen plant process 806 f hydrogen production 414 hydrogen recovery 316 hydrogen sulfide 323 hydrogenation 686 hydrotreating system (HDS) 323 hydroxyl groups 130 hyperplanes 386 hypertext markup language (HTML) standards 750 hypertext transfer protocol (HTTP) standards 750 HYSIS package 680

i i2 packages 473, 638 - factory Planner 473 IBIS system 679 ICAS package 680 ICV-SEV electrolyte solution data

745

I

867

868

I

Subject Index ideal adsorption solution theory (IAST) 144f ideal gas law 143, 545 ideality product development 429 identification problem 248,676 ill-conditioned approximations 16, 24, 73 ILOG solver 469 implementation - cost-effective manufacturing 851 - supply chain management 710 implicit constraints 594 implicit enumeration approaches 467 implicit time discretization 60 improvement algorithms 471 incidence matrix 795 inclusion body (IB) 408, 410ff incorporation techniques 280 incremental assumption-driven models 29, 181 independence constraint quality 582 individual resource grid 490 inducer exclusion 233 ff,258 ff industrial applications - process intensification 302 - product scheduling 506 ff - supply chain management 710ff industrial source complex version 3 (ISC3) 684 inequality constraints 174 information flows, multiscale processes 204 ff Information Society Technologies (IST) standards 764 information technology standards 758 INFOTHERM thermophysical databases 736ff infrastructure - life cycle modeling 667 - supply chains 697 initial conditions 171ff - cell population dynamics 96 - distributed dynamic models 36 f, 49 f - educational modules 796 - partial models 201 - regulatory networks 255 initialization - flexible recipe model 602 f - mixed-integer linear program 587 ff injection period 552 inlet temperatures 332 integer cut 360 integral/partial differential/algebraic equations (IPDAE) 161f, 592 integrality gap 494 integrated chemical product-process design 647-668 integrated composite curves 345 f integrated computer-aided system (ICAS) 777-800 integrated supply chains management 695-732

integrated system optimization and parameter estimation (ISOPE) 557ff integrated system production planning (SIPP) 456 integration methods - crystallization processes 158 - flexible recipe model 605 - multiscale process modeling 196, 202 - ODE 38 - production/resource planning 453 - supply chain management 695 - 732 - utility systems 327-382 integropartial differential equations (IPDEs) 87 intelligent manufacturing, data validation 801-828 intensive variables 384 ff interactions, molecular 108, 121ff, 127 interactive multiscale frameworks 205 f interface - environmental module 725 - financial module 725 - negotiation agent 727 intermediates 448 ff,485 interoperability, supply chains 697 interpolation - crystallization processes 165 - distributed dynamic models 43, 53, 70 interpretation frameworks, regulatory networks 248 ff introduction strategy 461 inventory-replenishing dynamics 622, 630 f, 710 investment costs - generic function 361 - resource planning 450 - utility systems 334 investment decision calendar G28 ISA S88 framework 598 Ising method 132 IS010303 691 IS014000/15288 668 isobaric/thermal distillation 274 isobar-isothermal NPT 113 isopryl acetate 649 iso-risk contours 687 iterative methods 20 ff, 64 iterative methods - model-based control 557 ff - multiscale process modeling 197 - supply-chain management 636 IUPS software 214 jacobian matrices 2, 15, 19-31 - data reconciliation 523 ff, 529 ff, 802 - distributed dynamic models 38 ff, 64 f, 96

Subject Index I869

i

Jacob-Monad model 229ff Java platform standards 751 ]boss standards 752 jobshops 485 ff Jonsdottir - Rasmussen - Fredenslund method 128

k

Kalman filter 525 Keesman quadratic model 606 kernel functions 197 kerosene data 580 ketones 649 ketones/alkanes system 127 key assumptions 678 key performance indicators (KPI) 802-827 kinetic cell population rates 94 kinetic constants 792 knowledge-based methods 422,434 ff, 503 Kotler concept 419 ff Kronecker factor 530 Kumar-Ramkrishna discretization 156 ff, l64ff k--E turbulence model 401

I lac operon (lactose) 225-235, 256ff

ladder logic models 673 Lagrange decomposition 455 ff, 466 ff 470 ff Lagrange multipliers - cost-effective manufacturing 848 - crystallization processes 155 f - data reconciliation 521 ff, 529 ff - distributed dynamic models 53 - model-based control 558 ff - real-time optimization 582 f Laguerre polynomials 155 f, 165 Langmuir isotherm 144 ff, 553 ff large-scale algebraic systems 2, 15-34 large-scale process modeling 190 large-scale simultaneous integration 207 Lax-Wendroff scheme 59, 67 LCA evaluation 708 leaching models 684 leaks detection 816 ff lean burn configurations 336 Leapfrog scheme 58 f, 67 least-impact heuristic schedules 503 Legendre polynomials 52 Lengeler model 244, 256 length scale models 190c 203 length scale models - chemical product-processes 655 - life cycle modeling 674

Lennard-Jones functions 123, 130f Levenberg- Marquardt method 24 ff life cycle modeling 8, 667-694 - chemical product-process design 647 - product development 420 - supply chain management 707 f lignite 355 Lim - Jorgenson method 65 linear data reconciliation 810 linear discrete time system 577 ff h e a r driving force approximation (LDF) 146 linear independence constraint quality 582 linear multiscale process modeling 199 h e a r programming 489, 531 linearization, piecewise 361, 842 Iinks - hybrid processes 594 f - process monitoring 528 ff - see also: constraints Linux standards 752 liquefied petroleum production 457 liquid phase, Fischer-Tropsch synthesis 84 liquid streams 270, 328 ff liquid-liquid mass exchanger 311 liquid-vapor equilibria 812 list splitting technique 274 location-allocation problem 450, 624 logical checking 183 lognormal distribution 165 long-term planning 207, 502 ff, 449 ff Lorentz-Berthelot rule 124 LQ factorization 25 LU factorization 530 lubricants 435 Ludzack- Ettinger process 314 lumped parameter multiscale processes 199

rn MacCormark method 60, 67 macroscale multiscale process modeling 204 ff maintenance costs 334f make-to-order/stock 484 management agent system 703, 706ff, 718 manufacturing process - life cydes 667-694 - supply chains 696 manufacturing resource planning (MRP-11) 463 ff Manugistics packages 474, 638 mapping regulatory networks 236 ff market potentials 672 Markov chain 679 Marshall Swift index tables 335 mass balances - chemical product-process design 654 - crystallization processes 154, 159ff

870

I

Subject Index

data validation 810, 827 distillation 274 - equipment design 384 - gas separation 143 f - utility systems 335 mass exchange network (MEN) 276, 311, 321 mass recycling 80 mass transfer - granulation 191, 196 - intensification 304, 311 - model-based control 569 master recipes - flexible 615 - hybrid processes 598 - real-time optimization 589 material balances - distributed dynamic models 36 - product scheduling 483,489 f - resource planning 450 material data - hybrid processes 597 - product scheduling 484, 493 - resource planning 448 material requirement planning (MRP) 463 ff, 497 mathematical educational modules 775 mathematical models - batch chromatography 552 - cost-effective manufacturing 832 - equipment design 384 - life cycle modeling 672 ff mathematical programming - product scheduling 484-500 - resource planning 456 - utility systems 349 f MATLAB - educational modules 775, 781 ff - flexible recipe model 614 - life cycle modeling 674 maximum product yield 405 Maxwell- Stefan surface diffusivities 145 mean variance 407 means-end analysis 227 ff,251 ff, 255 ff measurement system 5, SlSf, 528, 556 measurements optimization 801, 808 mechanical simulation 673 mechanical vapor recompression (MVR) 360 f, 366 mechanistic models 198ff mediation regulatory relation 255 melting point 649, 734, 779 membrane - compartments 143 - distillation 297, 314ff - separation systems 3, 137, 142 ff - surface effects 144 -

merit function 17 ff MESH column model 276ff mesh refinement 68 ff messenger RNA (mRNA) 228ff, 236 f, 240 ff metabolic cell reactions 94 metaheuristc approaches 469 ff, 484, 487 ff methods of characteristics (MOC) 88 ff, 96 methods of lines (MOL) 37, 40ff, 67f methods of moments 154f, 157ff methyl acetate process 297f, 544-551 methylisobutyl ketone 649 Metropolis sampling 117 microbial culture processes 35, 75 ff microbial systems 247 ff microcanonical NVE 114 microcapsule encapsulation 653 microelectronic industries 413 microorganisms 3, 223-264 microreaction technology 300 microscale multiscale process modeling 206 middle-out strategies 195 middleware standards 760 minimum energy requirement (MER) 328-382 minimum exergy losses 395 minimum temperature difference 331 mining operation 672 Minsky model 672 mixed-integer linear programming (MILP) - educational modules 778 - hybrid processes 594 - life cycle modeling 673 - real-time optimization 586 - refrigeration cycles 360, 364ff - resource planning 449 ff, 469 ff - supply-chain management 624, 636 ff mixed-integer nonlinear programming (MINLP) - resource planning 448 ff,469 ff - distillation 274f, 290ff - educational modules 778 - electrode heating 403 - intensification 305ff, 310ff, 315f, 320ff - life cycle modeling 673 - product scheduling 483, 489,497 f, 500 ff - separation systems 141 - supply chain management 698 f - utility systems 333ff mixed-integer programming (MIP) 271 mixed-integer quadratic program (MIQP) 586 mixed-logical dynamics (MLD) optimization 584 mixer superstructures 321 MIXPROPS thermophysical databases 736 mixture design 648 ff model integration - batch chromatography 554ff

Subject Index I 8 7 1

chemical product-process design 657 ff equipment design 390 f - life cycle modeling 678 - multiscale process modeling 189, 193, 197 model tuning/discrimination 171-188 Mode1.L.a package 680 model-based control 541 -576 model-based predictive control (MPC) 577 ff, 631 model-based statistical methods 517 ff ModelEnterprise package 499 Modelica package 680, 691 modeling 171-188 - computer-aided 11-264 - equipment design 390 f - lac operon 232ff - life cycle modeling 675 - molecular 2, 1 3 ,, 107-136 - multiscale process modeling 195 ff - partial models 202 - supply chains 712 modeling functions of microbial systems (MFM) 254ff ModKit package 680 modules - educational 775-800 - environmental 707 - financial 711, 725 - supply chain management 703 f, 707 modulons. regulatory networks 241, 244 ff mole balances 792 molecular dynamics 115, 204 molecular electrostatic potential (MEP) analysis 131 molecular interactions 246 molecular mechanics 110, 122 f molecular modeling 2, 13,. 107-136 molecular properties 734 molecule structure design 648 ff, 661 molten aluminum 399 moments methods 154ff, 163ff momentum transfer 191 monetary units (ME) 349 monitoring 517-540 monitoring/forecasting techniques 830 monodimensional approach 25 monolithic reactors 297 Monte Carlo methods - crystallization processes 154, 163 - life cycle modeling 679 - molecular modeling 108 - product scheduling 505 morphological analysis 428 MoT/ICAS modules 790ff mother-cell division death term 93 moving finite difference (MFD) 71 -

-

moving finite element (MFE) 71 moving grid methods 35 ff, 68-75 Mozilla standards 752 MS Excel 674 Mulliken population analysis 131 multiagent systems (MAS) standards 702 f, 712, 718f 765 multicomponent distillation 272 mukicomponent molecular systems 124 muhicriteria piecewise linearization 842 multidimensional optimization 23 multidisciplinary tools, process -product design 777 multidomain framework 211 multiechelon supply-chain 700 multienterprise supply-chain management 635 multifunctional heat exchangers 300 multilevel flow modeling (MFM) 251 ff, 257f multimedia collection standards 764 multiobjective generic algorithms (MOGA) 471 multiparametric quadratic programming (mpQP) 582, 586ff multiperiod problems - location-allocation 624 - product scheduling 504 - resource planning 459 - utility systems 367 f multiphase reactor equipment 393 ff multiphase systems 130 multiple crew strategies 468 multiple sensors 532 multiple-input multiple-output (MIMO) block architecture 242, 820 multiprocess plants 329 f multiproduct batch plant 831 multiproduct plants - cost-effective manufacturing 829 - product scheduling 485 ff - supply-chain management 621 multipurpose batch processes 609 multipurpose equipment 448 multipurpose plants 485 ff, 493 ff multipurpose supply-chain management 621 multiresource generalized assignment problem (MRGP) 471 multiscale capacity planning 462 multiscale modeling 3, 189-222 multiscale modeling - chemical product-process design 655 f - life cycle modeling 675 - life cycles 675 - molecular modeling 107 f, 111ff multisite planning - integer optimization 627 - product scheduling 481 ff - supply-chain management 621, 628ff, 696

872

I

Subject Index multiskill strategies 468 multistage production 448 multistage stochastic programming 505 multizonal computational fluid dynamics 100f MySQL standards 752

n Nash-type objective functions 637 natural frameworks, regulatory networks 249 natural gas 355, 812 Navier - Stokes equation 100, 389 negated regulatory conditions 255 negotiation module 703-716, 726ff Nelder-Mead algorithm 831, 843 ff net present values (NPV) 450, 461 network regulatory motifs 241 ff,246 f network representations 392 network superstructures see: superstructures Neumann’s boundary condition 36 neural networks - life cycle modeling 674, 680 - model-based control 567 - product development 423,436ff new product development (NPD) 421 ff,427 ff, 460 new-born cell birth term 93 Newton homotopy 32 Newton methods 20-30 - distributed dynamic models 39, 64 - separation systems 142 Newtonian fluids 209 Newton-Raphson method 523 NIST chemistry WebBook 736 ff nitrile groups 131f, 824 no intermediate storage (NIS) 485, 593 noise 542, 560, 673 nominal optimization 405 nonazeotropic mixture distillation 286 nonconvex optimization model 637 nonisothermal systems 308 noniterative CE/SE method 65 nonlinear cost functions, utility systems 361 nonlinear equation systems (NLS) 15-34 nonlinear isotherms 562 f nonlinear model predictive control (NMPC) 6, 542 E 567ff nonlinear multiscale process modeling 199 nonlinear Nash-type objective functions 637 nonlinear ODE-based models 246 nonlinear optimization strategies 365 f nonlinear programming (NLP) - data reconciliation 523 ff - distillation 287 - intensification 305, 315 f - resource planning 456 nonlinear-based control 545

Nose-Hoover method 117 nuclear power plants 825 nucleation - crystallization processes 149ff - distributed dynamic models 75, 87 ff - granulation 196 numerical methods - crystallization processes 154ff - data reconciliation 523 - life cycle modeling 672 - molecular modeling 108, 115 ff - multiscale process modeling 203, 214 - partial differential equations 37 ff numerical standard deviation 108 numerical thermophysical databases 735 Nusselt number 387 Nylon-6 process 765 0

OASIS standards 751 f, 759 object management group (OMG) standards 751 objective functions - cost-effective manufacturing 831-849 - exergymodel 362 - model-based control 557ff - real-time optimization 583 f - supply-chain management 637 observable variables 185, 524f, 531 ff, 676 octanol-water partition coefficient, fentanyl 779 offline initialization 610 offline optimization 541,585 oil processing - data validation 826 - eStandards 756f - life cycle modeling 682 ff oilfields 456 f oleic acid methyl ester removal 649 one-way coupling 207 online monitoring 823 online parameter adaptation 542, 556, 568 ff online production accounting 827 online scheduling 482 ontology web language (OWL) 767 ontological representation (OntoCAPE) 691, 765 OPC process /control system standards 750ff open standards 750 ff operation conditions - chemical product-processes 654 - data validation 802, 822 - flexible recipe model 601 ff, 613 - hybrid processes 594 - life cycle modeling 669 ff - multiscale processes 195

Subject fndex I 8 7 3

process monitoring 517, 531 f supply-chain management 630 operation costs - resource planning 450 - supply-chain management 623 - utility systems 334 operation modeling - shale oil processing 687 - supply chain management 714 operational planning, gas fields 458 operons 244f optical databases 734 optimization - biochemical processes 409 ff - complex multiphase reactor 405 - costs 361, 842f - crystallizers 159 - data reconciliation 526, 529ff - distillation 271 - intensification 305, 320 f - life cycles 675 - membrane-based gas separation 143f - model-based control 541 ff - product scheduling 483,490f - real-time 577-590 - supply-chain management 621-642 - utility systems 333 f, 345 ff, 369 f ordinary differential equations (ODE) 15-34 - computational fluid dynamics 101 - crystallization processes 155 f, 158, 165 f - data reconciliation 526 - distributed dynamic models 36 ff - educational modules 778 - life cycle modeling 680 - process models 171, 184 - regulatory networks 238 f organic Rankine cycles 344 orthogonal collocation 51, 315 orthogonal systems 18 oscillatory cell population behavior 75 oscillatory yeast rates 94 outlet temperatures 355 overall modeling - biochemical processes 410 - masses 173 - multiscale processes 195 -

-

P

paper manufacturing 508 parallel multiscale process modeling 204- 216 parameters 182 - continuation method 32 - molecular modeling 110 - multiscale process modeling 217 - partial models 201 - real-time control 578-585

- recommended 735 - shale oil processing 682 Pareto curves 319, 716f partial consistency 183 partial differential algebraic equations (PDAEs) 2, 13-106 partial differential equations (PDEs) 173ff - complex multiphase reactor 402 - computational fluid dynamics 35 - 106 - distributed dynamic models 35 - large-scale algebraic systems 2, 13-34 - regulatory networks 238 partial models 196ff, 200ff partial pressure 142 particle size distribution (PSD) - cvstallization processes 153ff, 161ff, l64f - distributed dynamic models 87 particle surface effects 144 partitioning 15 - educational modules 795 - molecular modeling 114, 117ff partnerships, supply chains 716 pdxi data exchange 681 pdXML standards 753, 757 peak demand period 452 Peclet number 80, 85 penalty composite curves 373 penalty function 532,802 penalty parameters 548 pentanelhexane system 127 performance criterion 602, 606 performance indicators 518, 802-827 permeate compartment 147 permeation modeling 684 permutation schedule 487 perturbations - flexible recipe model 614 - model-based control 560ff pesticides 653 Petlyuk columns 282, 286 Petri-nets 631, 679 petroleum fractions 192, 818 petroleum supply chains 457 Pehov-Galerkin method 155 pharmaceuticals - chemical product-process design 648 - product development 432-437 - supply chain 460, 632 phase boundary 311 phase diagrams 778 ff phase equilibrium 8, 734 - educational modules 779 - methyl acetate process 545 - molecular modeling 109, 119ff phase stability 386 phosphoenopymvate (PEP) 234

a74

I

Subject Index

phosphoric acid fuel cells 338 phosphotransferase (PTS) 234 photochemical oxidant formation 711 photovoltaic industries 413, 466 physical agents 703 ff physical models - distillation 271ff - life cycles 672ff physical phenomena 17 - distributed dynamic models 75 - equipment design 383 - hybrid processes 592 - intensification 301 - product development 422 physical properties 171 - molecular modeling 107-136 - process monitoring 530 PHYSPROPS, thermophysical databases 736 phytochemical manufacturing 650 piecewise afine systems (PWA) 584 piecewise linearization 361, 842 pilot plants 303, 508 pinch point analysis - complex multiphase reactor 396 - intensification 320 ff, 328 ff - utility systems 331, 361 - water use 374 Pinto- Grossmann method 490 ff planning techniques - cost-effective manufacturing 830-852 - experimental product development 432 - resources 452 - supply-chain management 624 plant design 303 plant management 10 - product scheduling 504 - resource planning 452 - supply-chain management 621 plant measurements 801 plant simulation 592 plant structure 815 plug flow grinding process 161 poly(ether urethane urea) membrane 317 polymer composites 438 polymerase enzymes 228 polysulfone membranes 315 population balance equation (PBE) - computational fluid dynamics 100 - crystallization processes 151f, 160 f - distributed dynamic models 75, 87 ff, 92 ff - fluid bed reactor 414 population generation 532 porcine somatropin (pST) 409 POSC standards 753, 757 powder feed rate, granulation 196 Powell method 16,27f, 39

Powell's dogleg algorithm 523 power market, resource planning 465 ff Poynting correction factor 782 precedence constraints 714 precipitation 152 precision - data validation 807 - process monitoring 531 prediction - distributed dynamic models 60 - flexible recipes model 610 - real-time control 577, 586 preferential sampling 118 prefractionator 286 preparative chromatography 35, pressure 171 - distillation 283 - equipment design 384 - flexible recipe model GO1 - gas separation 148 - molecular modeling 113 pressure drop - gas separation 147 - methyl acetate process 545 pressure-swing adsorption (PSA) separation 13, 137ff, 789 pricing optimization 636, 639 principal component analysis (PCA) 520, 527, 821 prize collecting salesman problem 490 proactive capabilities 702 probability demand function 833 ff, 852 probability density, molecular modeling 113f probability of stock-outs (PSO) 631 ff, 635 ProCAMD modules 785 f process and materials network (PMN) 594 process control OPC standards 755 process design 383-418 - chemical products 648 - decision chain 527 - integrated 647-668 process flow diagrams (PFD) - chemical product-process design 651 - data validation 804, 812 process history database (PHD) 681 process intensification 4, 297-326 process life cycle modeling 667-694 process models - computational fluid dynamics 98- 106 - flexible recipe model 613 - hybrid processes 592, 597 - resource planning 448 ff - scheduling 482 ff, 501 - separation systems 137 - utility systems 329 process monitoring 5, 517-540

Subject Index I 8 7 5 process simulation - educational modules 775 - hybrid processes 592 - see also: simulation process solvent systems 317 ff process synthesis - intensification 302 ff - separation 269 - 296 process system enterprise (PSE) 474 process-molecule synthesis supermodel 318 f producer-product relation 255 product demand see: demands product development 4, 419-442 product engineering 189f product portfolio 462 product scheduling 481 -516 product selectivity 823 product specifications - chemical process design 647 ff - flexible recipe model 602 ff - multiscale process modeling 190 - needs 657 product testing 431 product yield 405 production accounting 827 production life cycle 669 ff production planning - cost-effective manufacturing 830-852 - flexible recipe model 603 - resource planning 472 production profiles 450 production recipes 483 production scheduling 5 production time 832 production-distribution-inventory systems 696 productivity, biochemical processes 412 product-oriented methods 431,65Off, 661 product-process design, integrated 647-668 profile-based approach 308 profit profiles - cost-effective manufacturing 831-852 - expected 716, 838 - real-time optimization 580 - supply-chain management 624 PRO-I1 simulator 680, 775, 789 f prokaryotic organisms 224, 228ff, 237ff, 244f Propred module 780 property relations 173f property relations - educational modules 779 f - multiscale process modeling 198 propionitrile 131 PROSYN-MINLP synthesizer 276 protein networks 223 - 264 protein-DNA interactions 224, 247

protein-protein interactions 224, 237, 247 proteins 409 proton exchange membranes 338 pseudocomponent concept 818 purge separation 141 purification - batch chromatography 552 ff, 568 - biochemical process design 409 ff - carbothermic aluminum process 400 - chemical product-process design 651 - fluid bed reactor 413 f PVT behavior, thennophysical databases 734 pyrolysis 682

9

quadratic programming problems 582 qualitative differential equations (QDEs) 238 quality - chemical product-process design 647 ff - equipment design 384 - hybrid processes 597, 601 ff - thermophysical databases 733 quality function deployment (QFD) 424ff quantitative performance measurements 623 quantum models 110, 121ff,673 quasi-Newton family 2, 13, 23, 27ff quaternary separation 272 queuing models 673 quick-to-market 671

r radiation risk 688 rafinates 139ff rain water percolation 684 Randolph- Larson model 151 f random noise 527 random number generation 115 ff Rankine cycles 344 raw materials 327, 597 Rayleigh number 387 reactant conversion 607, 649 reaction rates 173 - educational modules 792 - model-based control 569 reaction system models 673 reaction transfer models 304 reactive distillation process 543 ff reactive scheduling 482, 503 ff reactive separations 301, 309 ff reactive simulated moving bed (SBM) 565 reactor/mass exchanger (RMX) 311, 315 reactors - educational modules 791 - intensification 311 reactor- separator-recycle process network synthesis 310

876

I

Subject Index

real models 562 real physical distributed systems control 702 real-time adjustments 697 real-time control 518 real-time environment 697 real-time expert system 674 real-time optimization (RTO) 577-590 real-time scheduling 503 reboilers 270ff, 283-291, 394 receding horizon 586 recipe-based representations 501, 591-615 recommended parameters 735 reconciliation tools 330 reconfiguration, supply chains 697 recovery - batch chromatography 562 - carbothermic aluminum process 401 - chemical product-processes 651 rectifier 282, 311 recycling 79, 305, 668 redundancy analysis - data validation 803 ff, 815 ff - process monitoring 517, 519ff - real-time optimization 582 refineries - blending 579 - datavalidation 826 - resource planning 448 ff, 456 ff refinery and petrochemical modeling system (RPMS) 456 refluxratio 548 refrigeration - computer-aided integration 369 - product development 437 - utility systems 359, 370 regression analysis - complex multiphase reactor 407 - distillation 285 - life cycle modeling 679 - molecular modeling 126 regulatory control 525, 568 regulatory microorganism networks 223-264 regulons 244f rehabilitation phase 672 relative concentration dynamics 233 remediation 669 ff repartitioning 452 report generation 533 repository of modeling environment (ROME) 690 repressilators 239 ff repressor gene, lac operon 231 f, 258 ff requirement - parameter translation 424 ff rescheduling strategy 610f research modeling 682 residuals 19

- crystallization processes 163 distributed dynamic models 55 real-time optimization 580 residues curves 787 resource planning 447-480 - constraint frameworks 467, 483 f, 489 f - cost-effective manufacturing 830 - decomposition methods 498 - hybrid processes 592 - life cycle modeling 673 - product development 429 - supply chain management 696 resource-task network (RTN) 454, 496 f, 592 responsiveness 398, 696 restricted matches 364, 373 retentate compartment 147 retiming strategy 611 retrofit 674 reuse models 690 reverse engineering 117ff, 226 ff Reynolds number 387 ribosome-binding site 241 risk-based management (RBM) - life cycle modeling 671 - shale oil processing 687 - supply-chain 626 RNA polymerase enzymes 228 ff rolling horizon algorithm 454,457 rubber mixtures 436 rule-based methods - chemical product-process design 661 - product development 423,438 ff - product scheduling 488 Runge-Kutta method 37ff, 96 run-time deviations 610 -

s

Sacharomyces cerevisiae 93, 224, 237 f safety - chemical product-process design 649 - data validation 807 - thermophysical databases 734 safety-health-environment (SHE) concept 667 sales maximization 624, 831 salts-water systems 323 sampling 111, 115ff SAP packages 474, 638 satisfaction level 716 saturation composition 781 scale identification 193, 697 scale invariance homotopy 32 scaling laws 387 scenario-based approaches 451 scheduling techniques 481 -516 - flexible recipe model 603 f, 609 f, 614

Subject lndex 1877 -

life cycle modeling

673

- resource planning 452

Schrodinger equation lloff, 121ff Schubert formula 29 search techniques - intensification 310 - product scheduling 484 segmentation methods 154ff, 162ff, 431 self consistent field molecular orbital concept 122 self-diffusion 116 self-organization 697, 703 semantic networks 439 Semantic Web standards 9, 750& 763-769 semibatch reactive distillation process 543 ff semibatch reactor 791 semiconductor fabrication 203, 508 semidiscretized methods 35, semiempirical methods 121 sensitivity analysis - cost-effective manufacturing 847 ff - process monitoring 517, 524ff, 535 - real-time optimization 580 - supply-chain management 627 sensor network optimization 518, 528, 531 f, 801 sensors 110 separation 137-170 separation - chemical product-process design 660 - chromatographic 552 - costs 566 - product scheduling 484 - synthesis 269-296 separator-centrifuge settling area 411 sequential approach 448, 715 sequential quadratic programming (SQP) 523 ff, 531 ff,802, 810f serial integration framework 208 serial multiscale process modeling 204 f series reactions 791 ff service-oriented architecture (SOA) standards 761 set-point perturbation finite difference method (FDPN) 563 set-point tracking - flexible recipe model 602 - methyl acetate process 549 - model-based control 559, 564 set-up times 448 seven-step procedure 172, 182 f, 193 shadow compartment concept 311 shale oil processing 682 ff shared intermediate storage (SIS) 485 sharp split assumptions 272 ff shock transition 45

shortcut models 271, 274, 283 f short-term scheduling 493 short-term scheduling - flexible recipe model 602 - uncertainties 451, 502 shut-down resource planning 450 side rectifier 282, 286 side stripper column 282 signal converters 518 signaling molecules 223 ff signal-oriented modeling 244 ff signed directed graph (SDG) 185 silane feed 414 silicon 413f simple distillation columns sequences 272-286 simple object access protocol (SOAP), Web services 750, 758 ff,763 ff simplex method 843 simplified solutions 177 - distillation 271ff - model-based control 545 f - multiscale process modeling 207 ff simulated annealing - intensification 310, 315 - product scheduling 487 ff, 506 f - resource planning 469 ff simulated moving bed (SBM) process 565 simulation - computer-aided 11-264, 329 - hybrid processes 592 - life cycle modeling 673, 680 - model-based control 568 - supply-chain management 631, 701 ff simultaneous approaches 195, 207, 661 single-input multiple-output (SIMO) block architecture 242 single-level mathematical formulation 459 single-multiphase reactors 307 single-phase flow model 402 single-site scheduling 483, 492 single-stage refrigeration cycle 359 singular Jacobi matrix 24 site recipes 598 size factor 595 size reduction 287 size-shape relation 387 slack real-time optimization 582 slack resource iterative auction approach 636 slurry bubble column reactor (SBCR) 35, 75, 83 ff smart agents 697 smelting zone 400 SMILES strings 780 smoothness 195 SO2 levels 684

878

I

Subject Index

social frameworks 249 socioeconomic impact analysis 687 sociotechnical risk assessment 667, 673 soft sensors 808 software packages 9 - data reconciliation 527 - multiscale process modeling 214ff - process intensification 299 ff - product scheduling 483,499 ff - resource planning 472 ff - standards 765 - supply-chain management 637 f solar cell production 414 solid conversion 401 solid oxide fuel cells 338 solid phase 84 solubilities 649 SoluCalc toolbox 781 solution methods - crystallization processes 154ff, 162ff - distributed dynamic models 70 - multiscale process modeling 193, 203ff, 215 solvents - design 649 ff, 653 ff - utility systems 328 solver modules 778, 782, 786 source terms - computational fluid dynamics 99 - multiscale process modeling 197 space segmentation 431 sparse systems 28 spatial discretization 37, 41, 48 spatial finite volume method 58 spatial step size 38 specifications - chemical products 647 ff, 651 ff - equipment design 383 - see also: product specifications spinning disk reactor (SDR) 297ff splitter superstructures 272 ff, 321 spring model 122 SQP package 406 stability - distributed dynamic models 50 - dynamical properties 185 standard deviation - data validation 802, 806 - molecular modeling 108, 112 - process monitoring 531 f, 535 standard for exchange of product model data (STEP) 691 standards 749-770 - partial model ingredients 201 Stanton number 85 STAR-CD software 214 state operator network (SON) 276, 289

state transitions 216 state-of-the-artcontrol 585 state-sequence network (SSN) 499 state-space representation 581 state-task network (STN) - hybrid processes 592 - product scheduling 493 ff - resource planning 464 statistical error - molecular modeling 115 - see also: error statistical laws 803 statistical thermodynamics lOSf, 112 ff steady-state distillation 17 steady-state properties 194 steady-state systems 521 f, 678 steam networks 356-372 steep moving fronts 64, 75 steepest descent method 20 ff - see also: gradient method steering relation 255 stencil methods 42 stiffness problem 15, 41, 60, 73 stochastic methods - crystallization processes 159, 163f - intensification 307, 310f - life cycle modeling 674, 679 - multiscale process modeling 199 - supply chain management 699 f stochastic programming - product scheduling 487, 505 - resource planning 451 stochastic uncertainty model 406 stock imperatives 483 stock-outs 631 f stoichiometric equations 18 stop criteria 30 storage - product scheduling 485 - resource planning 448 - shale oil processing 683 strategic planning - intensification 305 - life cycle modeling 669 - multiscale process modeling 216 stratospheric none depletion 710 stream flows - chemical product-processes 654 - utility systems 329ff stretching 122 stripping 287, 311 structural analysis - computational properties 183 - distillation 276 structural decomposition 184 structural plant-model 542

Subject lndex

structures 171ff structures - catalyst intensification 300 - dynamical properties 185 - process design 383 - regulatory networks 226 f styrene separation 811 substitution method 20 sulfuric acid 791 Sum-Sandler method 128 superposition principle 199 supersaturation profile 159 superscheduling problem 454 superstructure methods - complex columns 287 - distillation 273 -296 - intensification 305, 312, 321f - steam network 358 supplier’s reliability 830 supply-chain management (SCM) 8, 621-642 supply-chain management (SCM) - capacities 473 - integration 695-732 - life cycle modeling 673 - product scheduling 481 ff support technologies 680 supporting hyperplanes 386 surface potentials 131 surface segmentation 431 surface tension 734 surfactants 653 sustainability 6G7 f synchronization 518 synetics 427 syntactical verification methods 183 synthetic regulatory networks 226ff, 239 ff system for chemical engineering model assembly (SCHEMA) 680, 690 systems biology markup language (SBML) 245

t tablet formulation 435 Tabu search 311,469ff tactical resource planning 462 ff target modeling - chemical product-process design 657 ff - shale oil processing 684 tasks - hybrid processes 592 - product scheduling 484, 493 ff tax regimes 623 Taylor series 21, 27 - distributed dynamic models 59, 65 - molecular modeling 116 TCP/IP standards 750 tearing 15

temperature profiles 171 temperature profiles - carbothermic aluminum process 400 - complex multiphase reactor 396 - equipment design 384 - flexible recipe model 601, 607 - intensification 308 - molecular modeling 108 - process monitoring 519 - utility systems 332, 340-366 temperature-swing adsorption (TSA) separation 139 temporal stepsize 38 termination criterion 561 ternary column sequencing 273, 280f testing - product development 431 - resource planning 461 - supply chain management 710 - see also: applications thermal coupling 270, 285, 290 f THERMAL databases 736 thermal radiation 688 thermal/PV batteries 467 THERMODATA databases 736 thermodynamics - data validation 810 f - distillation 284 - distributed dynamic models 35 - equipment design 384 ff - heat pumps 337 - methyl acetate process 545 - molecular modeling 111 ff - multiscale processes 189 - process monitoring 530 - utility systems 330ff, 350 thermoeconomic models 333 thermophysical databases 733 -748 thermophysical properties 8 Thiele modulus 209 thiol groups 130 Thompson - King model 275 three-point backward (TPB) method 44 time discretization - product scheduling 490 ff - distributed dynamic models 58 - resource pIanning 450, 458 time horizon - data reconciliation 526 - model-based control 543 ff - multiscale process modeling 190ff - product scheduling 484 - supply-chain management 628 time integrators 38 time-based decomposition approaches 470 time-colored Petri-nets 631

I

879

880

I

Subject Index

time-scale models 215 - chemical product-process design 655 - life cycle modeling 674 time-to-market 461 timing standards 752 tolerance values 563 toolboxes see: educational / modules / software packages top-down approaches 194 torsion 122 total annualized cost (TAC) - distillation 272 ff, 282 ff - water systems 323 total site integration 363 toxic release models 673 trading structure 629, 716 transcriptional regulation 228, 232 ff transcriptional repressors 239 f transfer coefficients 114, 173, 198 transfer prices 623 transfer times 505 transformations - algebraic 176f - integration framework 208 transient operations 35 transition probability 117 translation models - educational modules 795 - regulatory networks 228 transport mechanisms 175, 282 transport properties 116 - equipment design 387 - thermophysical databases 734 transportation 623 trapezoidal rules 96 tray cascades 270 tray-by-traymodel, distillation 287 TRC thermophysical databases 735 ff triangle distribution 833 triplet assumption variable relation keyword 175 TRIZ method 423,428ff, 439 trouble-shooting 303 true boiling point (TBP) 818 trusted solutions 216 tuning process models 171-188 turbulence model 401 two-phase flow models 401 ff U

UDDI standards 758 uncertainty - clinical trial outcomes 462 - complex multiphase reactor 404 ff - cost-effective manufacturing 829-854 - datavalidation 806

-

process monitoring

535

- resource planning 448, 451 ff supply chain management 396, 399ff, 622, 626, 639, uncertainty product scheduling 483, 502 ff UNIFAC activity coefficients 781 ff unified modeling language (UML),standards 710f,720, 751, 754ff uniform sampling 118 UNIQUAC model 125 ff unique assignment case 493 unit operation (UO) specifications, standards 755 unit-based approach (UBS) 308 united atoms force fields 123f unit-to-task allocation 460, 488, 493 unlimited intermediate storage (UIS) 485, 593 upwind schemes 43 f, 80 USTI method 429 utility systems - computer-aided integration 327-382 - life cycle modeling 689 -

V

vacuum distillation unit (VDU) 323 vacuum-swing adsorption (VSA) separation 139 validation 181 - equipment design 391 - life cycle modeling 676 - multiscale process modeling 216 - process monitoring 517ff - UNIQUAC model 125ff - Valipackage 527 van der Waals repulsion 109, 124f, 130f vapor behavior - distillation 270 - methyl acetate process 545 - molecular modeling 110 - UNIQUACmodel 130 vapor recovery reactor (VRR) 400 vapor-liquid equilibria - crystallization processes 158 - Dortmund database 745 - molecular modeling 108- 108 vapor-liquid-liquid systems 311 variables - process monitoring 521, 524 - partialmodels 201 variance, molecular modeling 114 variational multiscale process modeling 205 vector spaces 384 Verdict package 499 verification - life cycle modeling 676 - multiscale process modeling 194, 216

Subject lndex I881

PDS-ICAS 790 process models 171-188 Verlet algorithm 116 vessel design 673, 686 vibration phenomena 122 Villadsen- Michelsen collocation 52 vinyl chloride monomer (VCM) purification 394 viscosity 80, 99, 114 volatilities 270 f von Wright actions 253 -

W

W3C standards 751 ff, 763ff waiting times 604, 611 warehouse agent 689, 705, 717 waste products - scheduling 508 - intensification 297 - utility systems 328 water management 684 water pinch analysis 320 ff water systems 319f 328E 374ff water/ethanol system 129 w-commerce 697 Web portals standards 764 Web services 9 Web services-SOAPstandards 750, 758 ff, 763 ff Web thermophysical databases 735 ff Web-oriented interfaces 697 weight matrix 18f, 521, 529f weighted residuals 163 weighted stencil methods (WENO)

distributed dynamic models 42, 46 ff, 71 ff, 81, 91 - fxed-bed reactors 81 well-conditioned differential equations 16 wet-etching 508 White-Ydstie model 414 Wilkinson algorithm 455 f Wilson activity coefficient 126ff Wilson equations 545 ff workflow - chemical product-process design 660 - life cycle modeling 675 ff working fluids 372 World-Wide Web standards 750ff -

X

XML (extensible markup language) 680, 750, 757 XPRESS-MP solver 469

Y

Yeomans-Grossmann model 278 yield stress 196 yields 809, 822 Yildirim- Mackey model 230 ff Young's modulus 196

z zeolite membranes 137f, 146ff zero integration error 207, 216 zero-wait (ZW) mode 458ff, 485,491 f zero-wait intermediate storage 593