Batch Fermentation: Modeling, Monitoring, and Control

BATCH FERMENTATION Modeling, Monitoring, and Control fill Cinar Satish J. Parcilekar Ccnk Undey Illinois Institute of Technology Chicago, Illinois, U.S.A.

Gtilnur Birol Northwestern University Evans ton, Illinois, U.S.A.

MARCEL

MARCEL DEKKER, INC.

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Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-4034-3 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-260-6300; fax: 41-61-260-6333 World Wide Web http: //www. dekker. com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above.

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To Mine and Bedirhan, my heroes and best friends — AC

To my family, for their encouragement, love, and support

— SJP

To my parents, Gultekin and Giilderen, who gave me life, and mind, and to my sweet Ceylan, my love and inspiration — CU

To Inane, Ulug and Defne — GB

Copyright © 2003 by Taylor & Francis Group, LLC

Preface This book deals with batch process modeling, monitoring, fault diagnosis, and control, focusing on batch fermentation processes. Fermentation is one of the main bioprocesses used in pharmaceutical, food, and chemical industries. Most fermentation processes are carried out as batch or fed-batch operations. Batch processes have been around for many millennia, and received increasing attention in the second half of the twentieth century. Although batch processes are simple to set up and operate, modeling, monitoring, and control of these processes is quite challenging. Even in simple fermentation processes, diverse organisms and the large numbers of cells that are produced in various phases of the batch by complex metabolic reactions provide significant challenges to successful process operation. Slight changes in operating conditions during critical phases may have a significant influence on the growth and differentiation of organisms, and impact the quality and yield of the final product. Accurate process models are necessary to monitor and control the progress of the batch, determine transition times to new phases of activity, and diagnose the causes of unacceptable process behavior and product quality. Significant advances have been made in recent years in the development of powerful modeling, monitoring, diagnosis, and control techniques. Various new modeling paradigms have been proposed to develop models of desired accuracy for a specific task. Real-time multivariate process monitoring techniques have been developed to complement quality control based on laboratory analysis of the final product and to permit timely corrective actions to save a batch run destined to produce low quality products during the progress of the run. Control methods that consider desired future trajectories of critical variables, process constraints, and sensor faults have been developed for tighter control of multivariate processes. This book offers a unified presentation of these new methods and illustrates their implementation with a case study of penicillin fermentation. The book integrates fundamental concepts from biochemical engineering, multivariate statistical theory, model identification, systems theory, and process control, and presents powerful methods for multivariable non-

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vi

Preface

linear processes with nonstationary and correlated data. Methods are introduced for finding optimal reference trajectories and operating conditions, and for manufacturing the product profitably in spite of variations in the characteristics of raw materials and ambient conditions, malfunctions in equipment, and variations in operator judgment and experience. The book presents both fundamental and data-based empirical modeling methods, several monitoring techniques ranging from simple univariate statistical process control to advanced multivariate process monitoring techniques, many fault diagnosis paradigms and a variety of simple to advanced process control approaches. The integration of techniques in model development, signal processing, data reconciliation, process monitoring, fault detection and diagnosis, quality control, and process control for a comprehensive approach in managing batch process operations by a supervisory knowledgebased system is illustrated. Most of these methods have been presented in various conferences and have been discussed in research journals, but they have not appeared in books for the general technical audience. The focus of the book is on batch fermentation in pharmaceutical processes. However, the methods presented can be used for batch processes in other areas by paying attention to the special characteristics of a specific process. The book will be a useful resource for engineers and scientists working with fermentation processes, as well as students in biotechnology, modeling, reaction engineering, quality control, and process control courses. One objective of the book is to provide detailed information for understanding, comparing, and implementing new techniques reported in the research literature. Various paradigms are introduced in each subject to provide a balanced view. Some of them are based on the research of the authors, while others have been proposed by other researchers. A welldocumented industrial process, penicillin fermentation, is used throughout the book to illustrate the methods, their strengths and limitations. Another objective is to provide a detailed case study to the reader to practice these methods and become comfortable in using them. Data sets, models, and software are provided to encourage the reader to gain hands-on experience. A dynamic simulator for batch penicillin fermentation is available as a web-based application and downloadable material. The fermentation simulator, batch process monitoring software, and software tools for supervision of batch process operations are provided at the website www. chee. lit. edu/~cinar/batchbook.html. Convincing the reader about the strengths and limitations of the techniques discussed in this book would be impossible without reference to proper theory. Theoretical derivations are kept at an appropriate level to enhance the readability of the text, and references are provided for readers seeking more rigorous theoretical treatment. The level of the treatment of Copyright © 2003 by Taylor & Francis Group, LLC

Preface

vii

methodology in the book requires little background information in various areas such as biotechnology, statistics, system theory, and process control. An outline of the book and various roadmaps to read it are presented in Section 1.4. Introductory books to review the fundamentals are also suggested in Section 1.4, and advanced books are referenced in appropriate chapters in the book. Details of the algorithms are summarized in the text to permit the reader to develop software in his/her favorite environment. Executable software modules are also provided in the aforementioned website for readers who may prefer using our programs. The book also discusses recent advances that may have an impact on the next generation of modeling, monitoring, and control methods. Metabolic pathway engineering, real-time knowledge-based systems, and nonlinear dynamics are introduced as some of the powerful paradigms that would be of interest. This book could not have been written without the strong cooperation of the authors and the sacrifices of many family members and friends. The labor and agony of writing a multidisciplinary book tested the strength of several relationships. All four authors are grateful for the encouragement and support they have received from their loved ones. One of the authors, Cenk Undey, has done a magnificent job in coordinating the work of all authors, integrating the manuscript and providing technical support in the use of LaTeX to the others. All four authors are also grateful to Dr. Inane Birol for contributing an important chapter on System Science Methods for Nonlinear Model Development (Chapter 5). It is certain that the impact of the methods and tools discussed in that chapter will increase in future years in analyzing the dynamics of many nonlinear batch fermentation processes and developing new monitoring and control methods. His insight and knowledge have enhanced the value of the book. It seems that no book can be published free of errors. As time progresses, errors, omissions, and better ways to express the material discussed in the book will be discovered. Each author apologizes for the remaining errors and agrees that they are the fault of the other three. Batch fermentation operations are abundant in industries that touch many human lives. Pharmaceutical, food, and chemical industries have made significant contributions in improving health and the quality of life. They have also been cited at times for causing challenges to nature and humans. Health, food, comfort, and safety also remind us of disease, limited resources, hunger, and pollution. Advances in technology may play an important role in resolving many conflicts. The authors hope that the methods presented in this book will contribute to the safety and productivity

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viii

Preface

of batch process operations, and ultimately to improving the quality of life and harmony with nature. Ali Cinar Satish J. Parulekar Cenk Undey Giilnur Birol

Copyright © 2003 by Taylor & Francis Group, LLC

Contents Prefac e Nomenclatur

e

1 Introduction 1.1 Characteristics of Batch Processes 1.2 Focus Areas of the Book6 1.2.1 Batch Process Modeling 1.2.2 Process Monitoring 1.2.3 Process Control12 1.2.4 Fault Diagnosis 1.3 Penicillin Fermentation 1.4 Outline of the Book

13 13 15

2 Kinetics and Process Models 2.1 Introduction and Background 2.2 Mathematical Representation of Bioreactor Operation . . . 2.3 Bioreactor Operation Modes 2.3.1 Batch Operation 2.3.2 Fed-Batch Operation 2.3.3 Continuous Operation 2.4 Conservation Equations for a Single Bioreactor 2.4.1 Conservation Equations for the Gas Phase 2.4.2 Conservation Equations for Cell Culture 2.5 Unstructured Kinetic Models 2.5.1 Rate Expressions for Cell Growth 2.5.2 Rate Expressions for Nutrient Uptake 2.5.3 Rate Expressions for Metabolite Production 2.5.4 Miscellaneous Remarks 2.6 Structured Kinetic Models

21 21 23 24 25 26 26 27 28 30 33 34 37 37 39 39

IX

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7 11

x

CONTENTS 2.6.1 2.6.2 2.6.3 2.6.4 2.7 Case 2.7.1 2.7.2

Morphologically Structured Models Chemically Structured Models Chemically and Morphologically Structured Models Genetically Structured Models Studies An Unstructured Model for Penicillin Production . . A Structured Model for Penicillin Production . . . .

40 43 44 47 49 49 58

3 Experimental Data Collection and Pretreatment 67 3.1 Sensors 68 3.2 Computer-Based Data Acquisition 71 3.3 Statistical Design of Experiments 73 3.3.1 Factorial Design 75 3.3.2 Fractional Factorial Design 83 3.3.3 Analysis of Data from Screening Experiments . . . . 86 3.4 Data Pretreatment: Outliers and Data Reconciliation . . . 89 3.4.1 Data Reconciliation 90 3.4.2 Outlier Detection 92 3.5 Data Pretreatment: Signal Noise Reduction 99 3.5.1 Signal Noise Reduction Using Statistical Techniques 100 3.5.2 Wavelets and Signal Noise Reduction 103 3.6 Theoretical Confirmation/Stoichiometry and Energetics of Growth 110 3.6.1 Stoichiometric Balances 110 3.6.2 Thermodynamics of Cellular Growth 112 4 Methods for Linear Data-Based Model Development 119 4.1 Principal Components Analysis 121 4.2 Multivariable Regression Techniques 125 4.2.1 Stepwise Regression 127 4.2.2 Ridge Regression 127 4.2.3 Principal Components Regression 128 4.2.4 Partial Least Squares 129 4.3 Input-Output Modeling of Dynamic Processes 131 4.3.1 Time Series Models 131 4.3.2 State-Space Models 135 4.3.3 State Estimators 142 4.3.4 Batch Modeling with Local Model Systems 152 4.4 Functional Data Analysis 158 4.5 Multivariate Statistical Paradigms for Batch Process Modelingl64 Copyright © 2003 by Taylor & Francis Group, LLC

CONTENTS 4.5.1 4.5.2 4.5.3

Multiway Principal Component Analysis-MPCA . . Multiway Partial Least Squares-MPLS Multiblock PLS and PCA Methods for Modeling Complex Processes 4.5.4 Multivariate Covariates Regression 4.5.5 Other Three-way Techniques 4.6 Artificial Neural Networks 4.6.1 Structures of ANNs 4.6.2 ANN Applications in Fermentation Industry . . . . 4.7 Extensions of Linear Modeling Techniques to Nonlinear Model Development 4.7.1 Nonlinear Input-Output Models in Time Series Modeling Literature 4.7.2 Nonlinear PLS Models

xi 164 165 168 173 174 175 177 183 185 185 192

5 System Science Methods for Nonlinear Model Development by Inang Birol 195 5.1 Deterministic Systems and Chaos 196 5.2 Nonlinear Time Series Analysis 215 5.2.1 State-Space Reconstruction 215 5.2.2 Nonlinear Noise Filtering 222 5.2.3 System Classification 227 5.3 Model Development 228 5.4 Software Resources 239 6 Statistical Process Monitoring 6.1 SPM Based on Univariate Techniques 6.1.1 Shewhart Control Charts 6.1.2 Cumulative Sum (CUSUM) Charts 6.1.3 Moving Average Control Charts for Individual Measurements 6.1.4 Exponentially Weighted Moving-Average Chart . . . 6.2 SPM of Continuous Processes with Multivariate Statistical Techniques 6.2.1 SPM of Continuous Processes with PCA 6.2.2 SPM of Continuous Processes with PLS 6.3 Data Length Equalization and Determination of Phase Landmarks in Batch Fermentation 6.3.1 Indicator Variable Technique 6.3.2 Dynamic Time Warping 6.3.3 Curve Registration 6.4 Multivariable Batch Processes Copyright © 2003 by Taylor & Francis Group, LLC

243 245 246 255 257 260 261 264 264 269 271 277 303 315

xii

CONTENTS 6.4.1 6.4.2 6.4.3

Reference Database of Normal Process Operation . . Multivariate Charts for SPM Multiway PCA-based SPM for Postmortem Analysis 6.4.4 Multiway PLS-based SPM for Postmortem Analysis 6.4.5 Multiway Multiblock Methods 6.4.6 Multiscale SPM Techniques Based on Wavelets . . . 6.5 On-line Monitoring of Batch/Fed-Batch Fermentation Processes 6.5.1 MSPM Using Estimates of Trajectories 6.5.2 Adaptive Hierarchical PCA 6.5.3 Online MSPM and Quality Prediction by Preserving Variable Direction 6.5.4 Kalman Filters for Estimation of Final Product Quality 6.6 Monitoring of Successive Batch Runs

7 Process Control

316 318 326 331 339 346 352 353 360 366 377 378

383

7.1 Introduction 383 7.2 Open-Loop (Optimal) Control 387 7.2.1 Nonlinear Models of Bioreactor Dynamics 387 7.2.2 Background on Optimal Control Theory 388 7.2.3 Singular Control 391 7.2.4 Optimal Control 392 7.2.5 Case Study - Feeding Policy in Single-Cycle and Repeated Fed-Batch Operations 393 7.3 Forced Periodic Operations 406 7.3.1 Preliminaries on the 7r-Criterion 407 7.3.2 Case Study - Forced Periodic Operations 413 7.4 Feedback Control 423 7.4.1 State-Space Representation 423 7.4.2 Multi-Loop Feedback Control 424 7.5 Optimal Linear-Quadratic Feedback Control 434 7.6 Model Predictive Control 436

8 Fault Diagnosis 8.1 Contribution Plots 8.2 Statistical Techniques for Fault Diagnosis 8.2.1 Statistical Discrimination and Classification 8.2.2 FDD with Fisher's Discriminant Analysis 8.2.3 FDD with Neural Networks Copyright © 2003 by Taylor & Francis Group, LLC

453 456 462 462 470 476

CONTENTS

xiii

8.2.4 Statistical Techniques for Sensor Fault Detection . . 478 8.3 Model-based Fault Diagnosis Techniques 481 8.3.1 Residuals-Based FDD Methods 485 8.3.2 FDD Based on Model Parameter Estimation . . . . 495 8.3.3 FDD with Hidden Markov Models 498 8.4 Model-free Fault Diagnosis Techniques 501 8.4.1 Real-time Knowledge-Based Systems (RTKBS) . . . 503 8.4.2 Real-time Supervisory KBS for Process Monitoring and FDD 510 9 Related Developments 9.1 Role of Metabolic Engineering in Process Improvement . . . 9.2 Contributions of MFA and MCA to Modeling 9.3 Dynamic Optimization of Batch Process Operations . . . . 9.4 Integrated Supervisory KBS for On-line Process Supervision

517 519 524 528 533

Appendix

537

Bibliography

539

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Nomenclature a

Alkaloid in Section 2.6.2

a

Number of equality constraints in Eqs. 7.5 and 7.6

dij

Amount of Ni utilized for production of unit amount of Pj in Eq. 2.19 (g/g)

&ij

State transition probabilities of an HMM from state i to state j

a

Gas-liquid interfacial area per unit culture volume

A, B

Denned in Eqs. 7.79 and 7.105

(l/ m )

A = [a>ij] State transition matrix of an HMM A

Input metabolite in Ch. 2 and 9

A, R

Number of PCs or LVs in Ch. 3, 4, 6 and 8

b

Number of inequality constraints in Eqs. 7.5 and 7.6

B = {bj(k}} Observation symbol probability distribution B

Output metabolite

C, E

Denned in Eqs. 7.105 and 7.106

C — {ci} Initial state distribution (initial state occupancy probability) C?k

Contribution of each element in 2;new,jfc to .D-statistic summed over all r components

Ci k

FCC of kth reaction affected by enzyme i

Cfy

r

Contribution of each element of a new batch run new, jk on the rth score xv

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xvi

Nomenclature

Ci

Concentration of specie i in the bulk liquid

(g/L)

C*

Concentration of specie i in the liquid phase at the gas-liquid interface

(g/L)

k

Cf

Jf 3

Ci

Flux control coefficient for pathway k with respect to enzyme Ei or reaction i, defined in Eqs. 9.4 and 9.5 Concentration control coefficient for the intermediate Xj with respect to enzyme Ei, defined in Eq. 9.7

T( .

Ci °

CCC of intermediate Xj affected by activity of enzyme i

CL

Dissolved O^ concentration in Eqs. 2.47, 2.48, 2.5

(mmole/L)

CL

Dissolved O^ concentration at maximum saturation

(mmole/L)

Cx

Concentration of biomass (cell mass) in culture

CIG

Concentration of specie i in the bulk gas

C*G

Concentration of specie i in the gas phase at the gas-liquid interface

(g/L culture)

(g/L)

CR.

Contribution of new observation vector xnevf,jk to D-statistic

CjK

Contributions to Q-statistic of J variables over the entire batch run

Cjk

Contributions to Q-statistic of variable j at time k

d

p or m^-dimensional vector of disturbance variables

d

Hyphal diameter

di(x.)

Linear discriminant score

(m)

di (x) Quadratic discrimination score for the iih population D

Differential operator in Section 4.4

D

Dilution rate, denned in Eq. 2.11

Die

Molecular diffusivity of specie i in the gas phase

(m 2 /h)

DIL

Molecular diffusivity of specie i in the liquid phase

(m 2 /h)

e, E

Residuals vector and matrix, respectively, in Ch. 4, 6 and 8

e

Predicted error vectors, denned in Eqs. 7.152 and 7.157

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(1/h)

Nomenclature

xvii

e

Output estimation error y — y in Ch. 4, 6 and 8

f

Nonlinear function of d, u, x in Eqs. 2.1 and 7.1

Ei

Enzyme corresponding to the iih reaction step

Ej

Enzyme catalyzing reaction j in a metabolic pathway

F

Volumetric feed rate of nutrient medium

F, /

Bioreactor feed, gas feed or liquid feed as appropriate

Fs

Volumetric feed rate of nutrient medium in singular control (L/h)

(L/h)

/(0,w) Defined in Eqs. 7.88 and 7.89 fh

Fraction of hyphal cells that are capable of synthesizing penicillin

G(q)

Multivariable input-output transfer function matrix

G

Transfer function matrix denned in Eqs. 7.79 and 7.108

GI, G2 Transfer function matrices for multi-loop feedback control denned in Eq. 7.111 Gc(q) Actuator (controlled input) fault TFM G c , G m Transfer function matrices associated with feedback controllers and measuring devices, respectively Ga

Transfer function matrix defined in Eq. 7.108

GI, KI Transfer function matrix and gain matrix, respectively, for the decouplers, Eqs. 7.117-7.120 GM(