Bioreaction Engineering Principles

Second Edition

Bioreaction Engineering Principles Second Edition

Jens Nielsen and John Villadsen Technical University (!f Denmark Lyngby, Denmark

and

Gunnar Liden Lund University Lund, Sweden

Springer Science+Business Media, LLC

Bioreaction Engineering Principles Second Edition

Jens Nielsen and John Villadsen Technical University (!f Denmark Lyngby, Denmark

and

Gunnar Liden Lund University Lund, Sweden

Springer Science+Business Media, LLC

Library of Congress Cataloging-in-Publieation Data

Nielsen, Jens Hpiriis. Bioreaetion engineering prineiples.-2nd ed./Jens Nielsen and John Villadsen and

Gunnar Liden. p. em.

Includes bibliographieal referenees and index. ISBN 978-1-4613-5230-3 ISBN 978-1-4615-0767-3 (eBook) DOI 10.1007/978-1-4615-0767-3

1. Bioreactors. 1. Villadsen, John. II. Liden, Gunnar. III. Title.

TP248.25.B55 N53 2002 660.6-dc21

2002034178

The First Edition of Bioreaclion Engineering Principles by Jens Nielsen and John Villadsen was published in 1994 by Plenum Press, New York

ISBN 978-1-4613-5230-3

©2003 Springer Science+Business Media New York Originally published by Kluwer Academic / Plenum Publishers in 2003

Softcover reprint ofthe hardcover2nd edition 2003 http://www.wkap.nll

10 9 8 7 6 5 4 3 2

A c.I.P. record for this book is available from the Library of Congress

AII rights reserved

No part of this book may be reproduced. stored in a rctrieval systcm, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work

Library of Congress Cataloging-in-Publieation Data

Nielsen, Jens Hpiriis. Bioreaetion engineering prineiples.-2nd ed./Jens Nielsen and John Villadsen and

Gunnar Liden. p. em.

Includes bibliographieal referenees and index. ISBN 978-1-4613-5230-3 ISBN 978-1-4615-0767-3 (eBook) DOI 10.1007/978-1-4615-0767-3

1. Bioreactors. 1. Villadsen, John. II. Liden, Gunnar. III. Title.

TP248.25.B55 N53 2002 660.6-dc21

2002034178

The First Edition of Bioreaclion Engineering Principles by Jens Nielsen and John Villadsen was published in 1994 by Plenum Press, New York

ISBN 978-1-4613-5230-3

©2003 Springer Science+Business Media New York Originally published by Kluwer Academic / Plenum Publishers in 2003

Softcover reprint ofthe hardcover2nd edition 2003 http://www.wkap.nll

10 9 8 7 6 5 4 3 2

A c.I.P. record for this book is available from the Library of Congress

AII rights reserved

No part of this book may be reproduced. stored in a rctrieval systcm, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work

Preface

This is the second edition of the text "Bioreaction Engineering Principles" by Jens Nielsen and John Villadsen, originally published in 1994 by Plenum Press (now part of Kluwer).

Time runs fast in Biotechnology, and when Kluwer Plenum stopped reprinting the first edition and asked us to make a second, revised edition we happily accepted. A text on bioreactions written in the early 1990's will not reflect the enormous development of experimental as well as theoretical aspects of cellular reactions during the past decade.

In the preface to the first edition we admitted to be newcomers in the field. One of us (JV) has had 10 more years of job training in biotechnology, and the younger author (IN) has now received international recognition for his work with the hottest topics of "modem" biotechnology. Furthermore we are happy to have induced Gunnar Liden, professor of chemical reaction engineering at our sister university in Lund, Sweden to join us as co-author of the second edition. His contribution, especially on the chemical engineering aspects of "real" bioreactors has been of the greatest value.

Chapter 8 of the present edition is largely unchanged from the first edition. We wish to thank professor Martin Hjortso from LSU for his substantial help with this chapter.

As was the case for the first edition numerous people helped us by carefully reviewing individual chapters. Professor Lars K Nielsen of University of Queensland was a constant sparring partner, both in Australia and lately as a visiting professor at DTU. The help of Dr. Mats Akesson and of our PhD students, in particular Mikkel Nordkvist, Thomas Grotkjrer, Jochen Forster and Morten Skov Hansen is also gratefully acknowledged. MSc student Rebecca Munk Vejborg was of great help in her careful editing of the final version of the manuscript.

All three authors are chemical engineers by education, and we followed in the footsteps of other chemical engineers who "converted" to biotechnology, but retained their passion for a quantitative treatment of problems from the physical world. One of the greatest innovators of biochemical engineering, professor James E. Bailey was also a chemical engineer by education. We wish to dedicate this book to the memory of this eminent scientist, who was a close colleague and a friend (of the senior author for more than 35 years), and whose work is admired by all three of us. If the pages of this book could inspire some students in the way Jay Bailey inspired hundreds of chemical engineering and biochemical engineering students we could hope for no better reward.

John Villadsen and Jens Nielsen BioCentrum-DTU

v

Gunnar Liden. Kemicentrum, Lund University

Contents

List of Symbols XI

Chapter 1. Bioreaction Engineering: From Bioprocess Design to Systems Biology I 1.1 The Structure of the Book 3 1.2 Some Comments on Nomenclature used in the Book 7 1.3 A Final Note 8 References 8

Chapter 2. From Cellular Function to Industrial Products 9 2.1 Cellular Growth 10

2.1.1 From Genotype to Phenotype 13 2.1.2 Transport Processes 15

2.1.2.1 Free Diffusion 16 2.1.2.2 Facilitated Diffusion 20 2.1.2.3 Active Transport 22

2.1.3 Catabolism 24 2.1.3.1 Glycolysis 25

2.1.3.2 TCA Cycle and Oxidative Phosphorylation 27 2.1.3.3 Fermentative Pathways 29

2.1.4 Anabolism 30 2.1.5 Secondary Metabolism 35 2.1.6 Secreted Proteins 37

2.2 Biotech Processes - An Overview 37 2.2.1 Strain Design and Selection 38 2.2.2 Fermentation Media 40 2.2.3 Criteria for Design and Optimization 41 2.2.4 Strain Improvement 42

References 45

Chapter 3. Biochemical Reactions - A First Look 47 3.1 The Continuous Stirred Tank Reactor 47 3.2 Yield Coefficients 53 3.3 Black Box Stoichiometries 57 3.4 Degree of Reduction Balances 60 3.5 Systematic Analysis of Black Box Stoichiometries 73 3.6 Identification of Gross Measurement Errors 77 Problems 88 References 92

Chapter 4. Thermodynamics of Biochemical Reactions 95 4.1 Chemical Equilibrium and Thermodynamic State Functions 95

4.1.1 Changes in Free Energy and Enthalpy 97 4.1.2 Combustion - A Change in Reference State 102

4.2 Heat of Reaction 103 4.3 Non-equilibrium Thermodynamics 109 Prob lems 115 References 118

vii

viii

Chapter 5. Biochemical Reaction Networks 5.1 Basic Concepts 5.2 Growth Energetics

5.2.1 Consumption of A TP for Cellular Maintenance 5.2.2 Energetics of Anaerobic Processes 5.2.3 Energetics of Aerobic Processes

5.3 Simple Metabolic Networks 5.4 Flux Analysis in Large Metabolic Networks

5.4.1 Use of Measurable Rates 5.4.2 Use of Labeled Substrates 5.4.3 Use of Linear Programming

Problems References

Chapter 6. Enzyme Kinetics and Metabolic Control Analysis 6.1 Michaelis-Menten and Analogous Enzyme Kinetics 6.2 More Complicated Enzyme Kinetics

6.2.1 Variants of Michaelis-Menten Kinetics 6.2.2 Cooperativity and Allosteric Enzymes

6.3 Metabolic Control Analysis Problems References

Chapter 7. Modeling of Growth Kinetics 7.1 Model Structure and Complexity 7.2 A General Structure for Kinetic Models

7.2.1 Specification of Reaction Stoichiometries 7.2.2 Reaction Rates 7.2.3 Dynamic Mass Balances

7.3 Unstructured Growth Kinetics 7.3.1 The Black Box Model 7.3.2 Multiple Reaction Models 7.3.3 The Influence of Temperature and pH

7.4 Simple Structured Models 7.4.1 Compartment Models 7.4.2 Cybernetic Models

7.5 Mechanistic Models 7.5.1 Genetically Structured Models 7.5.2 Single Cell Models

7.6 Morphologically Structured Models 7.6.1 Oscillating Yeast Cultures 7.6.2 Growth of Filamentous Microorganisms

Problems References

Chapter 8. Population Balance Equations Problems References

Chapter 9. Design of Fermentation Processes 9.1 The Stirred Tank Bioreactor

9.1.1 Batch Operation 9.1.2 The Continuous Stirred Tank Reactor 9.1.3 Biomass Recirculation 9.1.4 The Stirred Tank with Substrate Extracted from a Gas Phase

Contents

119 119 124 125 128 132 142 lSI 153 163 171 179 186

189 190 195 195 201 207 233 234

235 237 240 240 242 244 245 245 253 261 265 265 274 278 279 289 290 295 300 306 311

315 335 338

339 340 342 352 359 364

Contents ix

9.1.5 Fed-batch Operation 367 9.2 The Plug Flow Reactor 372 9.3 Dynamic Analysis of Continuous Stirred Tank Bioreactors 380

9.3.1 Dynamic Response of the Reactor for Simple, Unstructured Kinetic Models 380 9.3.2 Stability Analysis of a Steady State Solution 388 9.3.3 Dynamics of the Continuous Stirred Tank for a Mixed Microbial Population 397

Problems 409 References 420

Chapter 10. Mass Transfer 423 10.1 Gas-Liquid Mass Transfer 425

10.l.lModelsfork, 428 10.1.2 Interfacial Area and Bubble Behavior 430 10.1.3 Empirical Correlations for k,a 438 10.1.4 Mass Transfer Correlations Based on Dimensionless Groups 442 10.1.5 Gas-Liquid Oxygen Transfer 448 10.1.6 Gas-Liquid Mass Transfer of Components Other than Oxygen 453

10.2 Mass Transfer to and into Solid Particles 456 10.2.1 External Mass Transfer 456 10.2.2 Intraparticle Diffusion 460

Problems 469 References 474

Chapter 11. Scale-Up of Bioprocesses 477 11.1 Scale-up Phenomena 477 11.2 Bioreactors 478

11.2.1 Basic Requirements and Reactor Types 478 11.2.2 The Stirred Tank Bioreactor 480

11.3 Physical Processes of Importance for Scale-Up 482 11.3.1 Mixing 482 11.3.2 Power Consumption 486 11.3.3 Heat Transfer 491 11.3.4 Scale-Up Related Effects on Mass Transfer 495 11.3.5 Rheology of Fermentation Broths 496 11.3.6 Flow in Stirred Tank Reactors 501

11.4 Metabolic Processes Affected by Scale-up 508 1l.5 Scale-up in Practice 510 Problems 514 References 517

Index 519

List of Symbols

Symbols that are defined and used only within a particular Example, Note, or Problem are not listed. It should be noted that a few symbols are used for different purposes in different chapters. For this reason more than one definition may apply for a given symbol.

a a

ad acell

A b(y) Bi B

c Cij

C; c· db

~ dmean

dmem

ds

dSauter

D Dmax Dmem

DeJf

D; Da eo Eg E Ec Em f(y,t) F g G GO L1Gd

Cell age (h) Specific interfacial area (m2 per m3 of medium) Specific interfacial area (m2 per m3 of gas-liquid dispersion) Specific cell surface area (m2 per gram dry weight) Matrix of stoichiometric coefficients for substrates, introduced in Eq. 7.2 Breakage frequency (h- l) Biot number, given by Eq. (l0.59) Matrix of stoichiometric coefficients for metabolic products, introduced in Eq. 7.2 Concentration of the ith chemical compound (kg m-3)

Saturation concentration of the ith chemical compound (kg m-3)

Vector of concentrations (kg m-3)

Concentration control coefficient of the jth intermediate with respect to the activity of the ith enzyme

Flux control coefficient with respect to the activity of the ith enzyme

Matrix containing the control coefficients [defined in Eq. (6.44)] Bubble diameter (m) Thickness ofliquid film (m) Mean bubble diameter (m) Lipid membrane thickness (m) Stirrer diameter (m) Mean Sauter bubble diameter (m), given by Eq. (10.18) Dilution rate (h-\ given by Eq. (3.1) Maximum dilution rate (h-') Diffusion coefficient in a lipid membrane (m2 sol) Effective diffusion coefficient (m2 sol) Diffusion coefficient of the ith chemical compound (m2 sol) Damk6hler number, given by Eq. (10.37) Enzyme concentration (g enzyme L-') Activation energy of the growth process in Eq. (7.27) Elemental matrix for all compounds Elemental matrix for calculated compounds Elemental matrix for measured compounds Distribution function for cells with property y in the population, Eq. (8.1) Variance-covariance matrix Gravity (m S-2)

Gibbs free energy (kJ mokl) Gibbs free energy at standard conditions (kJ mole-i) Gibbs free energy of combustion of the ith reaction component (kJ mole-i)

xi

xii

L1G{~

Gr h h(y) h+(y) h-(y) HA LlHei

mf I J ko ki

kg k{ k,a ks Ka K, K Keq

Km m m mATP

ms Ma(t) n N NA Nf Np P PA PrY, y*,t) Pi P P P Pg p Pe

q~ qA,Obs

qx q qt

List of Symbols

Gibbs free energy of denaturation (kJ mok\ Eq. (7.28) Gibbs free energy of combustion of the ith reaction component at standard conditions (kJ mole· l )

Gibbs free energy of formation at standard conditions (kJ mok l )

Grashofnumber, defined in Table 10.6 Test function, given by Eq. (3.52) Net rate offormation of cells with property y upon cell division (cells h· l )

Rate of formation of cells with property y upon cell division (cells h· l )

Rate of disappearance of cells with property y uponcell division (cells h· l )

Henry's constant for compound A (atm L mole-I) Enthalpy of combustion of the ith reaction component (kJ mole-I) Enthalpy of formation (kJ mole-I) Identity matrix (diagonal matrix with I in the diagonal) Jacobian matrix, Eq. (9.102) Enzyme activity (g substrate [g enzymer l h· l )

Rate constant (e.g. kg kg· 1 h· l )

Mass transfer coefficient for gas film (e.g. mole atm- I S-I m-2)

Mass transfer coefficient for a liquid film surrounding a gas bubble ( m S-I) Volumetric mass transfer coefficient (S-I) Mass transfer coefficient for a liquid film surrounding a solid particle (m S-I) Acid dissociation constant (moles L- I) Overall mass transfer coefficient for gas-liquid mass transfer (m S-I) Partition coefficient Equilibrium constant Michaelis constant (g L- I), Eq. (6.1) Amount of biomass (kg) Degree of mixing, defined in Eq. (11.1) Maintenance-associated ATP consumption (moles ATP [kg DWr l h· l )

Maintenance-associated specific substrate consumption (kg [kg DW]·I h-I) The nth moment of a one-dimensional distribution function, given by Eq. (8.9) Number of cells per unit volume (cells m-3), Eq. (8.1) Stirring speed (S·I) Aeration number, defined in Eq. (11.9) Flow number Power number, defined in Eq. (11.5) Extracellular metabolic product concentration (kg m-3)

Partial pressure of compound A (e.g. atm) Partitioning function, Eq. (8.5) Productivity of species i in a chemostat (e.g. kg m-3 h· l)

Dimensionless metabolic product concentration Permeability coefficient (m S-I) Power input to a bioreactor (W) Power input to a bioreactor at gassed conditions (W) Variance-covariance matrix for the residuals, given by Eq. (3.46) Peclet number, defined in Table 10.6

Volumetric rate of transfer of A from gas to liquid (moles L·I h· l )

Observed volumetric formation rate of A (kg m-3 h-\ Eq. (10.45) Volumetric rate off ormation of biomass (kg DW m-3 h-I) Volumetric rate vector (kg m-3 h-I) Vector of volumetric mass transfer rates (kg m·3 h· l)

List of Symbols

rs rp rx r(y,t) R R R Rr Re s s sf S bS Sc Sh

Ve

vf Vg

Vi

Vpump

V

V Vd Vg VI Vy Wi

X

X

Number of morphological fonns Heat of reaction (kJ mole-I) Fraction of repressor-free operators, given by Eq. (7.52) Fraction of promo tors being activated, given by Eq. (7.58)

xiii

Fraction of promoters, which fonn complexes with RNA polymerase, in Eq. (7.60) Specific reaction rate (kg [kg DW]-I h· l )

Enzymatic reaction rate (Chapter 6) (g substrate L- I h· l )

Specific ATP synthesis rate (moles of ATP [kg DW]·I h- I) Specific reaction rate vector (kg [kg DWr l h- I) Specific substrate fonnation rate vector (kg [kg DW]·I h- I) Specific product fonnation rate vector (kg [kg DW]·I h- I) Specific fonnation rate vector of biomass constituents (kg [kg DW]-I h- I) Vector containing the rates of change of properties, in Eq. (8.2) Gas constant (=8.314 J K"I mole-I) Recirculation factor Redundancy matrix, given by Eq. (3.39) Reduced redundancy matrix Reynolds number, defined in Table 10.6 Extracellular substrate concentration (kg m-3)

Extracellular substrate concentration vector (kg m-3)

Substrate concentration in the feed to the bioreactor (kg m-3)

Dimensionless substrate concentration Entropy change (kJ mole-I K· I) Schmidt number, defined in Table 10.6 Sherwood number, defined in Table 10.6 Time (h) Circulation time (s) Mixing time (s) Temperature (K) Total stoichiometric matrix Stoichiometric matrix corresponding to non-measured rates in rows ofTT

Stoichiometric matrix corresponding to known rates ofTT Bubble rise velocity (m S-I) Cybernetic variable, given by Eq. (7.41) Superficial gas velocity (m S·I) Vector containing the specific rates of the metamorphosis reaction (kg kg-I h- I) Liquid flow (m3 h- I) Liquid effluent flow from the reactor (m3 h- I) Liquid feed to the reactor (m3 h- I) Gas flow (m3 h· l)

Flux of reaction i (kg [kg DW]-I h- I) Impeller induced flow (m3 S-I ) Flux vector, i.e. vector of specific intracellular reaction rates (kg [kg DW]·I h- I) Volume (m3)

Total volume of gas-liquid dispersion (m3)

Dispersed gas volume (m3)

Liquid volume (m3)

Total property space, Eq. (8.2) Cybernetic variable, given by Eq. (7.42) Biomass concentration (kg m·3)

Dimensionless biomass concentration

xiv

X; X Y Yij YxATP

Zj

Greek Letters

&

&

Gji E

E 1]

1]ef!

Tej

8 K;

J.lmax J.lq Pcelf

PI (J'

d r

!l>gen

'I'(X)

Abbreviations

ADP AMP ATP CoA DNA Ec

List of Symbols

Concentration of the ith intracellular component (kg [kg DWrl) Vector of concentrations of intracellular biomass components (kg [kg D Wr I) Property state vector Yield coefficient of} from i (kg) per kg of i or C-mole of} per kg of i) ATP consumption for biomass formation (moles of ATP [kg DW]-I) Concentration of the ith morphological form (kg [kg DWrl)

Stoichiometric coefficients for substrate i in intracellular reaction j Stoichiometric coefficient for metabolic product i in intracellular reaction i Shear rate (S-I)

Stoichiometric coefficient for intracellular component i in intracellular reaction} Matrices containing the stoichiometric coefficients for intracellular biomass components Vector of measurement errors in Eq. (3.41) Matrix for stoichiometric coefficients for morphological forms Gas holdup (m] of gas per m] of gas-liquid dispersion) Porosity of a pellet Elasticity coefficients, defined in Eq. (6.37) Vector of residuals in Eq. (3.44) Matrix containing the elasticity coefficients Dynamic viscosity (kg m- I S-I) Internal effectiveness factor, defined in Eq. (10.46) Partial pressure of compound i (atm) Dimensionless time Degree of reduction of the ith compound The specific growth rate of biomass (h- I) The maximum specific growth rate (h- I) The specific growth rate for the qth morphological form (kg DW [kg DWrl h- I ) Cell density (kg wet biomass [m-3 cell]) Liquid density (kg m-3)

Surface tension (N m- I) Variance Space time in reactor (h) Shear stress (N m-2)

Tortuosity factor, used in Eq. (l0.43) Thiele modulus, given by Eq. (10.49) Generalized Thiele modulus, given by Eq. (10.55) Distribution function of cells, Eq (8.8)

Adenosine diphosphate Adenosine monophosphate Adenosine triphosphate Coenzyme A Deoxyribonucleic acid Energy charge

List of Symbols

EMP FAD FADH, FDA F6P GTP G6P MCA NAD+ NADH NADP+ NADPH PEP PP PSS PTS PYR P/O ratio

RNA mRNA rRNA tRNA RQ R5P TCA UQ

Embden-Meyerhof-Pamas Flavin adenine dinucleotide (oxidized form) Flavin adenine dinucleotide (reduced form) Food and Drug Administration F ructose-6-phosphate Guanosine triphosphate Glucose-6-phosphate Metabolic control analysis Nicotinamide adenine dinucleotide (oxidized form) Nicotinamide adenine dinucleotide (reduced form) Nicotinamide adenine dinucleotide phosphate (oxidized form) Nicotinamide adenine dinucleotide phosphate (reduced form) Phosphoenol pyruvate Pentose phosphate Protein synthesizing system Phosphotransferase system Pyruvate Number of molecules of ATP formed per atom of oxygen used in the oxidative phosphorylation Ribonucleic acid Messenger RNA Ribosomal RNA Transfer RNA Respiratory quotient Ribose-5-phosphate Tricarboxylic acid Ubiquinone

xv