Bioprocess Technology

t1ETHODOl06ICAl ASPECTS

ethics

ecology

modeling

design &. development

economy

quantification

UP STREAM

BIOREACTOR PERFORMANCE

ENZYME ENGINEERING FERMENTATION ENGINEERING

multj-S I multi X -processing PLANT &. ANIMAL CELL

DOWN STREAM MEASURE &. CONTROL

ENGINEERING

FIElD or APPlICA TlON

BIOPROCESS TECHNOLOGV

Engineering Disciplines in Biotechnologies Health care (Pharma) Agro &. Food Environmental Industrial

Anton Moser

Bioprocess Technology Kinetics and Reactors

Revised and Expanded Translation

Translated by Philip Manor

With 279 Illustrations

Springer-Verlag New York Wien

Professor Dr. ANTON MOSER Institut fUr Biotechnologie, Mikrobiologie und Abfalltechnologie, Technische Universitat Graz, A-SOlO Graz, Austria

Translator Dr. PHILIP MANOR

Library of Congress Cataloging-in-Publication Data Moser, Anton, Dipl.-Ing. Dr. techno

Bioprocess technology. Rev. and translated from the German ed.:

Bioprozesstechnik: Berechnungsgrundlagen der Reaktionstechnik biokatalytischer Prozesse. Bibliography: p. Includes index. 1. Biochemical engineering. I. Title.

TP248.3.M6713 1988 660'.63 87-26590

Printed on acid-free paper.

Revised and expanded translation from the German edition Bioprozesstechnik: Berechnungsgrundlagen der Reaktionstechnik biokatalytischer Prozesse. © 1981 by Springer-Verlag Wien. ISBN -13 :978-1-4613-8750-3 © 1988 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1988

All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc. in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

Typeset by Asco Trade Typesetting Ltd., Hong Kong.

9 8 7 6 543 2 1

ISBN -13:978-1-4613-8750-3 e-ISBN -13 :978-1-4613-8748-0 DOl: 10.1007/978-1-4613-8748-0

Preface

This book is based on a 1981 German language edition published by Springer­Verlag, Vienna, under the title Bioprozesstechnik. Philip Manor has done the translation, for which I am deeply grateful.

This book differs from the German edition in many ways besides language. It is substantially enlargened and updated, and examples of computer simula­tions have been added together with other appendices to make the work both more comprehensive and more practical.

This book is the result of over 15 years of experience in teaching and research. It stems from lectures that I began in 1970 at the Technical University of Graz, Austria, and continued at the University of Western Ontario in London, Canada, 1980; at the Free University of Brussels, 1981; at Chalmers Technical University in G6teborg, Sweden; at the Academy of Sciences in lena, East Germany; at the "Haus der Technik" in Essen, West Germany, 1982; at the Academy of Science in Sofia, Bulgaria; and at the Technical University of Delft, Netherlands, 1986.

The main goals of this book are, first, to bridge the gap that always exists between basic principles and applied engineering practice, second, to enhance the integration between biological and physical phenomena, and, third, to contribute to the internal development of the field of biotechnology by describing the process-oriented field of bioprocess technology.

To achieve these goals, I have attempted to unify the many interdisciplinary fields that continue to become ever more specialized. For better comprehen­siveness, quantitative facts are often followed by a qualitative discussion but without complete derivation of the final equations-these can be found in the original references. Since a major goal is to contribute to the development of a biotechnical methodology by integrating several fields of science into one, details are often omitted in that they are thought to be not significant for the overall concept of integrating strategy. This approach aims to foster new orientation, a unified, process-oriented strategy of "bioprocess technology" that follows a systematic method of thinking and working. This strategy, as an expression of research philosophy, includes four working principles: (a) working with simplifica.tions, that is-making distinctions between the

vi Preface

important and the unimportant, (b) quantifying, (c) process (regime) analysis, that is, separating biological from physical phenomena, and (d) thinking and working in terms of mathematical models.

In conjunction with the irreplaceable element of intuition, which always serves as the starting point, mathematical models should be considered as working hypotheses that can assist process development. Within the frame­work of adaptive model building, these models can be compared with, and fitted to, the experimental realit-y of biological processes.

The book is organized into chapters that seem sensible from a pedagogical viewpoint. After the defitrltion of bioprocess technology and its delineation with respect to the whole area of biotechnology in Chapter 1, and description of principles of thinking and working to be used in the integration in Chapter 2, Chapters 3 through 5 discuss bioprocess analysis. Chapter 3 characterizes bioreactors quantitatively, as does Chapter 4, which also covers the general utilization of bioreactors for obtaining kinetic data in the analysis of specific processes. In Chapter 5 the use of mathematical models for simulating the kinetics of biological processes is described. Chapter 6 discusses the synthesis of biological data (kinetics) and physical data (transport phenomena) in order to estimate bioreactor performance, that is, the conversion and productivity of the most important types and operations of reactors.

This book does not primarily provide an exhaustive survey of the literature, but concentrates on the most significant facts. Rather, its principal feature is its description of a generally valid approach to calculations for bioprocess technology. The problems of achieving a quantitative understanding are primary, especially the problems of understanding kinetics as a cycle of engineering considerations and calculations. The biological synthesis of the products of intermediary metabolism and all biochemicaljbiological aspects are excluded; they are well described in other books, for example, volumes 1 through 8 of Biotechnology-A Comprehensive Treatise (Rehm, H.J., and Reed, G., eds., 1982ff) and Comprehensive Biotechology (Moo-Young, 1985). Discussion of the technical aspects of quantifying reactors and process develop­ment is limited in favor of description of working procedures for the analysis and synthesis of production-scale biological processes. As a consequence of the novel strategy being developed here, I hope to close a gap I perceive in the literature, especially for students and for people involved in industry.

The title "Bioprocess Technology" for this edition has been chosen in accordance with the semantic definition of "technology" as the "science of industrial arts" This title was preferred to the "working title" "Bioprocess Engineering." (Another possibility was "Bioprocess Engineering Sciences.") I believe that the conception of engineering basically means the area of applied sciences, that is, execution of the science of industrial arts, including mechan­ical aspects, auxiliary equipment, and measurement and control techniques, perhaps even being dominated by them (cf. title of the journal Bioprocess Engineering).

Preface Vll

This book attempts to present the formal kinetic macro-approach following Einstein's dictum that "Everything should be made as simple as possible, but not simpler." And I firmly believe that "Nothing is more practical than theory, and-at the same time-nothing is more theoretical than practice." as a typical example if the "Yin & Yang" principle, which is at present stressed by Fritjof Capra in order to achieve a holistic, ecological paradigm.

Graz, Austria ANTON MOSER

Contents

Preface .................................................. . Nomenclature (List of Symbols) ............................. .

Subscripts ............................................. . Abbreviations .......................................... . Greek Symbols ......................................... .

Chapter 1 Introduction ................................... .

1.1 Biotechnology: A Definition and Overview .................. . 1.2 Bioprocess Technology ................................. .

Bibliography ......................................... .

Chapter 2 The Principles of Bioprocess Technology ........... .

2.1 Empirical Pragmatic Process Development .................. . 2.1.1 Production Strains .................................... . 2.1.2 Starting Points ....................................... . 2.1.3 Different Modes (or Strategies) in Process Development ........ . 2.1.4 Process Development Without Mathematical Models .......... .

2.2 Basics of Quantification Methods for Bioprocesses ............ . 2.2.1 Concepts of a Uniform Nomenclature for Bioprocess Kinetics .... . 2.2.2 The Rates of a Bioprocess ............................... . 2.2.3 Stoichiometry and Thermodynamics ....................... . 2.2.4 Productivity, Conversion, and Economics (Profit) ............. .

2.3 Systematic, Empirical Process Development with Mathematical

2.3.1

2.3.2

2.4 2.4.1 2.4.2 2.4.3

Models ............................................ " An Integrating Strategy-A Basis for Biotechnological Methodology ........................................ . Working Principles of Bioprocess Technology ................ .

Mathematical Modeling in Bioprocessing ................... . General Remarks ..................................... . Model Building ....................................... . Different Levels and Types of Kinetic Models ................ . Bibliography ......................................... .

v xv

xxv XXVll

xxviii

1 5

12

13

13 13 13 15 15 18 19 20 25 38

41

41 46 49 49 51 54 62

x Contents

Chapter 3 Bioreactors....................................... 66

3.1 Overview: Industrial Reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.1.1 Microbiological Reactors (Fermenters, Cell Tissue Culture Vessels,

and Waste Water Treatment Plants) ......................... 66 3.1.2 Enzyme Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.1.3 Sterilizers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.2 3.2.1 3.2.2 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.3.6 3.3.7 3.3.8 3.3.9 3.3.10 3.3.11 3.4 3.5 3.5.1

3.5.2

3.5.3

3.5.4

3.5.5 3.5.6 3.5.7 3.5.8

3.6

Systematics of Bioreactors ................................ . Homogeneous Versus Heterogeneous Systems ................. . Mixing Behavior ....................................... . Quantification Methods .................................. . Residence Time Distribution (RTD)-Macromixing ............ . Micromixing .......................................... . Oxygen Transfer Rate (OTR) .............................. . Degree of O2 Utilization, '102 •••••••••••••••••••••••••••••••

Degree of Hinterland, HI ................................. . Power Consumption, P .................................. . O2 Efficiency (Economy) E02 •••••••••••••••••••••••••••••••

Heat Transfer Rate, Hv TR ................................ . Characteristic Diameter of Biocatalytic Mass J;, ............... . Comparison of Process Technology Data for Bioreactors ........ . Biological Test Systems .................................. . Operational Modes and Bioreactor Concepts ................. . Bioreactor Models ...................................... . Modell: The Ideal Discontinuous Stirred Tank Reactor (DCSTR) ............................................. . Model 2: The Ideal Continuous Stirred Tank Reactor (CSTR) with V = Constant ..................................... . Model 3: The Ideal Semicontinuous Stirred Tank Reactor (SCSTR) with V = Variable ...................................... . Model 4: The Ideal Continuous Plug Flow Reactor (CPFR) or Tubular Reactor ....................................... . Model 5: The Real Plug Flow Reactor CPFR with Dispersion ..... . Model 6: The Discontinuous Recycle Reactor (DCRR) .......... . Model 7: The Continuous Recycle Reactor (CRR) .............. . Multiple Phase Bioreactor Models .......................... . "Perfect Bioreactors" in Bench and Pilot Scale for Process Kinetic Analysis .............................................. . Bibliography .......................................... .

69 70 70 73 74 81 90 99 99

100 101 101 105 105 110 112 118

119

119

119

121 122 123 123 124

126 130

Chapter 4 Process Kinetic Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

4.1 Kinetic Analysis in Different Types of Reactors . . . . . . . . . . . . . . . . . 138 4.2 Regime Analysis-General Concept and Guidelines ............. 141 4.3 Test of Pseudo homogeneity . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 146 4.4 Parameter Estimation of Kinetic Models with Bioreactors. . . . . . . . . 151 4.4.1 Integral and Differential Reactors ........................... 151 4.4.2 Integral and Differential Reactor Data Evaluation Methods ....... 154

4.4.3

4.5 4.5.1 4.5.2 4.5.3 4.5.4 4.5.5

Contents xi

Results of Differential and Integral Analysis: Linearization Diagrams ............................................. . Modeling Heterogeneous Processes .......................... . External Transport Limitations ............................. . Internal Transport Limitations ............................. . Combined Internal and External Transport Limitations .......... . Transport Enhancement .................................. . Concluding Remarks ..................................... . Bibliography ........................................... .

157 168 171 175 183 188 192 193

Chapter 5 Bioprocess Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

5.1 Temperature Dependence, k(T), Water Activity, aw, and Enthalpy/

5.2

5.2.1 5.2.2 5.2.3

5.3

5.3.1

5.3.2

5.3.3

5.3.4

5.3.5 5.3.6 5.3.7 5.3.8

5.3.9 5.4 5.4.1 5.4.2 5.5 5.5.1 5.5.2 5.5.3 5.6 5.6.1 5.6.2 5.7

Entrophy Compensation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 Microkinetic Equations Derived from the Kinetics of Chemical and Enzymatic Reactions ..................................... . The Dynamic Flow Equilibrium Approach to Life Processes ....... . Contribution of Enzyme Mechanism to Bioprocess Kinetic Models .. . Contribution of Chemical Kinetic Laws to Bioprocess Kinetic Modeling ............................................. . Basic Unstructured Kinetic Models of Growth and Substrate Utilization (Homogeneous Rate Equations) .................... . It = It(s): Simple Model Functions ofInhibition-Free Substrate Limitation (Saturation-Type Kinetics) ........................ . It = It(x): Influence of Biomass Concentration on Specific Growth Rate ................................................. . It = It(t): Extensions of Monod-Type Kinetics to Stationary and Lag Phase ............................................. . Negative Biokinetic Rates-The Case of Microbial Death and Endogenous Metabolism .................................. . Kinetic Model Equations for Inhibition by Substrates and Products .. Kinetic Model Equations for Repression ...................... . It = It(pH) ............................................. . Kinetic Pseudo homogeneous Modeling of Mycelial Filamentous Growth Including Photosynthesis ........................... . Kinetic Modeling of Biosorption ............................ . Kinetic Models for Microbial Product Formation ............... . Metabolites and End Products ............................. . Heat Production in Fermentation Processes ................... . Multisubstrate Kinetics ................................... . Sequential Substrate-Utilization Kinetics ..................... . Simultaneous Substrate-Utilization Kinetics ................... . Generalizations in Multisubstrate Kinetics .................... . Mixed Population Kinetics ................................ . Classification of the Types of Microbial Interactions ............. . Kinetic Analysis of Microbial Interactions ..................... . Dynamic Models for Transient Operation Techniques (Nonstationary Kinetics) .............................................. .

204 204 206

214

216

217

224

225

227 231 237 237

237 238 240 240 247 250 251 253 254 259 260 261

272

xu Contents

5.7.1 Definitions of Balanced Growth and Steady-State Growth ........ 272 5.7.2 Mathematical Modeling of Dynamic Process Kinetics. . . . . . . . . . .. 274

5.8 Kinetic Models of Heterogeneous Bioprocesses . . . . . . . . . . . . . . . .. 283 5.8.1 Biofilm Kinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 283 5.8.2 Unstructured Models of Pellet Growth ............. . . . . . . . . .. 288 5.8.3 Linear Growth ......................................... 290 5.9 Pseudo kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 290 5.10 Kinetics of Sterilization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 292 5.10.1 Basic Kinetic Approaches in Sterilization Kinetics. . . . . . . . . . . . . .. 292 5.10.2 Multicomponent Systems in Food Technology ................. 294

Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 295

Chapter 6 Bioreactor Performance: Process Design Methods ... . .. 307

6.1 The Ideal Single-Stage, Constant-Volume Continuous Stirred Tank Reactor, CSTR (Pseudo homogeneous L-Phase Reactor Model) . . . .. 308

6.1.1 Performance of the CSTR with Simple Kinetics. . . . . . . . . . . . . . . .. 308 6.1.2 Performance of the CSTR with Complex Kinetics. . . . . . . . . . . . . .. 311 6.1.3 Stability Analysis and Transient Behavior of the CSTR . . . . . . . . . .. 318 6.2 Variable Volume CSTR Operation (Fed-Batch and Transient

Reactor Operation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 325 6.3 Multistage Single and Multistream Continuous Reactor Operation.. 329 6.3.1 Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 329 6.3.2 Potentialities of Multistage Systems. . . . . . . . . . . . . . . . . . . . . . . . .. 330 6.3.3 Single-Stream Multistage Operation. . . . . . . . . . . . . . . . . . . . . . . . . 331 6.3.4 Multistream Multistage Operation .......................... 334

6.4 Continuous Plug Flow Reactors (CPFR) . . . . . . . . . . . . . . . . . . . . .. 337 6.4.1 Performance Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 6.4.2 Potential Advantages of CPFR Operation. . . . . . . . . . . . . . . . . . . .. 339 6.4.3 Principal Properties and Design of CPFRs Compared with CSTRs .. 340 6.4.4 Applications ofCPFR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 347 6.4.5 One-Phase (Liquid) Reactors with Arbitrary Residence Time

Distribution and Micromixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 347

6.5 Recycle Reactor Operation ................................ 351 6.5.1 Performance Equations of Recycle Reactors. . . . . . . . . . . . . . .. . .. 351 6.5.2 Application of CRR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 356 6.6 Gas/Liquid (Two-Phase) Reactor Models in Bioprocessing ........ 357 6.7 Biofilm Reactor Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 358 6.7.1 Potentialities of Biofilm Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . .. 359 6.7.2 Performance Equations of Biofilm Reactors. . . . . . . . . . . . . . . . . . .. 360 6.7.3 Application of Biofilm Reactors. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 370 6.8 Dialysis and Synchronous Culture Operation .................. 371 6.8.1 Dialysis (Membrane) Reactor Operation. . . . . . . . . . . . . . . . . . . . .. 371 6.8.2 Synchronous Culture Operation ............................ 378 6.9 Integrating Strategy as General Scale-Up Concept in Bioprocessing. 381 6.9.1 Stoichiometry (Balancing Methods) Applied in Bioprocess Design. .. 382 6.9.2 Interactions Between Biology and Physics via Viscosity of

Fermentation Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 385

Contents xiii

6.9.3 Influence of Mycelium-The Morphology Factors {"Apparent Morphology") . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 389

6.9.4 Structured Modeling of Bioreactors (OTR) . . . . . . . . . . . . . . . . . . . .. 392 6.10 Final Note ............................................. 395

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 396

Appendix I

Appendix II Appendix III

Fundamentals of Stoichiometry of Complex Reaction Systems .............................. . Computer Simulations .......................... . Microkinetics: Derivation of Kinetic Rate

406 412

Equations from Mechanisms. . . . . . . . . . . . . . . . . . . . .. 436

Index..... .... .............. .... .. . . . ...... ...... ........ .. 441

Nomenclature (List of Symbols)

ARABIC

A [m2 ] surface area [A] Ampere

A,B,C,D compounds (general) {A} activated state of

compound A a [m-I] specific area a, b, c, d, e, f coefficients (esp. in

element-species matrix, cf. Equ. 11.6)

a, d, c, d [kg·m-3 ] concentration of compounds

aLl [m2 ·m-3 ]

aw water activity (Equ. 5.1)

BOD [kg·m-3 ·CI] biological oxygen demand

Bv [kg·m-3 ·h-l ] volumetric mass loading rate (Equ. 6.129)

Bx [h-I] mass loading rate per unit sludge biomass (Equ. 5.212)

Bi Biot number (Bi = DL2 • bLZ/D .. bs )

Bo Bodenstein number (Bo = v·L/Dd

C [kg] amount of CO2

C [$] costs C integration constant

xvi Nomenclature (List of Symbols)

CTD circulation time distribution

c, Ci , cj [kg· m- 3 ] concentration (general) of component i or j

C [kg· m- 3 ] concentration of CO2

CIL constant in Equ. 5.218 Cp [kJ' kg-1 . °C-I] specific heat at

p = constant CR [kg· m- 3 ] concentration of

ribosomes Cst [n j 'm- 3 ] sterilization level

D [m2 's- l ] diffusion or dispersion coefficient

D [h-1 ] dilution rate Dc [h-I] critical dilution rate

where washout occurs DM [h-I] dilution rate with

maximum productivity DIO [h] decimal reduction time

(Equ.5.8) Da (Dao, DaLls, Daold Damkoehler number

(Equs. 4.3,4.5,4.7) Da( Damkoehler number of

first degree (Equ. 6.89) Dan Damkoehler number of

second degree (Equ. 4.74) d em] diameter (general term) d constant d em] mean diameter dB em] bubble diameter dj em] impeller diameter dp em] particle diameter dp em] active particle diameter

(Equ. 5.258) dT em] tank diameter

E [m 2 's-1 ] convection coefficient (Equ. 3.30d)

E (EOTR ) enhancement factor (Equ. 4.115) of OTR

Ea , Eon Ed [J. mole-I] activation energy, general (growth or death)

E, ES, EP, EI

{ES}

e, es, ep, ei

Fr

F(t)

f(t)

f2

fo'

G

Ga

Nomenclature (List of Symbols) xvii

[kg O2 . kWh-1]

[kg]

[m3 ·h-1 ]

[m3 ·h-1 ]

[m3 ·h-1 ]

[m3 ·h-1 ]

[kg·m-3 . h-1]

oxygen economy (Equ. 3.66) (oxygen efficiency) amount of enzyme, enzyme-substrate, enzyme-product, enzyme-inhibitor complex activated state of ES-complex concentration of components

volumetric flow rate bleed rate feed rate pumping capacity substrate feed rate (Equ.11.30) Froude number (Fr = v2/g. L) mathematical RTD function acc. to step method mathematical RTD function acc. to pulse method singular f(t) (Equ. 3.14) kinetic term for overlapping multi­substrate degradation kinetic term for repression of substrate degradation by other substrates correction factor for oxygen saturation calculation (Equ. 3.40)

Material in "G compartment" proteins and DNA) Galilei number

XVlll Nomenclature (List of Symbols)

AG g

H H

He

Ha

HI

h

I

J

K

[J. mole- 1 ]

[cm· S-2]

Em] [m3 atm· mol-1 ]

[J. kg-l]

[J. s]

[J·m- 2 ·h-1 ·K-1 ]

[kg·m-3 ]

free reaction enthalpy acceleration of gravity (980) universal gravitational constant (6.671 . 10-8 )

height Henry distribution coefficient dimensionless Henry distribution coefficient Hatta number (Equ.4.112) degree of hinterland (Equ.3.59) reaction enthalpy (molar) reaction enthalpy per unit mass of X or S heat of combustion of components amount of volumetric heat of fermentation Planck constant (6.6. 10-34)

heat transfer coefficient concentration of H+ ions crowding factor (Equ.6.188) "concentration" of volumetric heat

amount of inhibitor concentration of inhibitor increments in Equ. 3.34

degree of segregation (Equ.3.1)

material in "K compartment" (RNA mainly)

Nomenclature (List of Symbols) xix

K [kg·m-3 ] constant of equilibrium or saturation (general term)

Kadapt constant of metabolic adaptation in Equ. 5.227

Kc [(Nsm- Z )1/2] constant in Casson law (Equ. 6.166), "Casson-viscosity"

Ko constant diffusional resistance in Equ. 5.43

Ke constant for endogenous metabolism in Equ. 5.87

Keq constant of thermo-dynamic equilibrium (Equ. 5.22) "Haldane relationship"

Kd constant for microbial death (Equ. 5.86)

KIS ' KIP (KISX' KIPX) [kg·m-3 ] inhibition constant of growth by substrate or product

K m , Ks, K L , K F , KH [kg·m-3 ] saturatien constant for substrate in kinetic equation acc. to Michaelis-Menten, Monod, Langmuir, Freundlich, and Hill

Ko,Kp [kg·m-3 ] saturation constant in Monod-type kinetics for oxygen or product

Ko constant in Equ. 3.34 KR (KISP) [kg·m-3 ] constant for repression K 1,Kz constants for pH

function (Equ. 5.107) k [(m3 • mol-1 )n-1 . S-l] rate constant (general

term) k number of elements for

elemental balancing method (Sect. 2.4.2.2)

kB [J. K-1 ] Boltzmann constant (1.38' IO- Z3 )

kcat [mole P' mole E-1 • S-l] catalytic constant or turnover number

kd [h-1 ] specific dead rate

xx Nomenclature (List of Symbols)

kE [S-l J rate constant of electrode response

ke [S-lJ rate constant of environmental change

kH (h) [J·m-2·h-1·K-1J true rate coefficient of volumetric heat transfer

kHTR [J·h-1·K-1J rate coefficient of volumetric heat transfer (phenomenological)

km [S-l J first-order rate constant for mixing (Equ. 3.23)

kLla (kLa) [h-1 J volumetric OTR coeffi-cient (GIL interface)

kL2 [m·s-1J transfer coefficients at LIS interface

kp [h-1J rate constant of product formation

kp,d [h-1 J specific rate constant of product degradation

kp1 , kp2 [h-1 J rate constant acc. to Kono equation (Equ. 5.126)

kr (k j , kn) [e 1 (mole/vol)-n+1 J reaction rate constant (ith reaction or for reaction order n)

ks [m' S-l J transport rate coefficient in solid phase

kTR [S-l J transport rate constant (phenomenological)

kv,G [h-1 J transport rate constant of gas phase (Equ. 3.38)

kx [h-1J constant for biomass in Equ. 5.63 or 6.170

ko, k 1, k1/2 [!J rate constants for reactor order n = 0, 1, 1/2

k 1, k2, k3 [!J rate constants in BRE (Equ. 5.239), esp. Equ. 4.25 with 5.240

k+ 1, k-1 [!J rate constants for forward or backward reaction

kt [h-1 J decay coefficient kco [m3. mole-I. S-l J preexponential factor in

Arrhenius equation (Equ.5.3)

Nomenclature (List of Symbols) XXI

L em] length (general term) L e , L t , L u , L H , em] morphology factors

(e.g., Equ. 6.182, 5.109)

M [kg] mass MF morphology factor

(Equ. 6.183) Ins, Ina, InH, [h-1 ] specific maintenance

rate coefficient for S, °2 ,

and Hv In [%] degree of mixing

(Equ.3.17) In power factor in

Equ. 6.164, "flow index" (see also Equ. 6.171)

N number of significant components in balancing method (Sect. 2.4.2.2); number of vessels in senes

NA aeration number (Equ.3.75)

Ni number of molecules of component i

NM mixing number (Equ. 3.73)

NOTR OTR number (Equ. 3.76) Np power number

(Equ. 3.74) NRe (Re) Reynolds number

(Re = V" Llv) Nsc (Sc) Schmidt number

(Sc = vlD) NSh (Sh) Sherwood number

(ShL = kL · LID) n [rps] rotational speed, stirrer

speed n (n., no) reaction order (with

respect to S or 02) n power index n number of microbial

cells ni number (of moles of

component i)

xxii Nomenclature (List of Symbols)

nB

nH

nj

n~ I

0 OTR o (resp. 0*)

obs OUR

P P Pmb

p

p

Q

q

qj (q., qo' qc' qHv' qp)

[kg·m-3 ·s-1 ]

[kg·m-2. S-1]

kg [kg·m-3 ·h-1]

[kg·m- 3 ]

[kg·m-3 ·h-1]

[kg] [WorJ·s-1 ]

[m3 . h-1 • kN-1 ]

[kg·m-3 ]

[bar]

[J ·m-3 . S-1]

[h-1 ] resp. J. kg-1 • h-1 (for qH)

[J ·mol-1 • K-1]

Em]

bed expansion index (Equ.6.139) Hill coefficient (Equ.5.29) volumetric flux of mass (transport rate) (mass) flux through area

amount of O2 O2 transfer rate O2 concentration (resp. saturation value) observed value 02-uptake rate

amount of product power membrane permeability (Equ.6.146a) concentration of product pressure

product formation activity function (Equ. 5.220) rate of heat transfer specific rate of formation or consumption of component i (substrate, O2, CO2, heat, and product) rate of internal production in biomass compartment

gas constant (8.314.107 )

radius rank of matrix (general, of stoichiometrical coefficients and element­species), see App. I Reynold number (NRe )

terminal settling velocity, Re-number of bioparticles (Equ. 6.139)

RTD

r r r

S Sc Sh IlS s

s

s

Nomenclature (List of Symbols) xxiii

[l·m-3 ·h-1 ]

[kg·m-2 ·s-1 ]

[S-l ]

[kg]

[J. mole-1 . K-1 ]

Re-number based on energy dissipation (Equ.4.1b) residence time distribution excretion rate correlation coefficient recycle ratio rate of production or consumption (volumetric) rate of CO2-production rate of production rate of S-consumption rate of growth rate of 02-consumption rate of heat production rate per unit area related reaction rate (general term)

amount of substrate Schmidt number (Nsc)

Sherwood number (NSh)

reaction entropy crowding factor (Equ. 6.183b) for space filling concentration of substrate surface renewal rate (Equ.3.30) standard deviation "sludge loading" =

adsorbed S concentra­tion (biosorption) (Equ. 5.114) critical threshold concentration (Equ. 5.95) concentration of essential and enhancing substrates (Equ. 5.168) "washout state" S concentration (cf. Fig. 6.1a, 6.4, and 6.5)

xxiv Nomenclature (List of Symbols)

2S [kg·m-3 J "non washout state" S concentration (steady state)

3S [kg·m-3 J unstable S concentration (Fig. 6.11)

T [Oe,KJ temperature Tp [KJ isokinetic temperature

(Equ.5.11) TOe total organic carbon

[sJ time (general term) t [hJ mean residence time tc [sJ circulation time tG [sJ mean residence time of

gas phase tH•TR [sJ characteristic time of

heat transfer (Table 4.3a) tL [sJ lag time tM [sJ maturation time

(Equ.5.136) tm (tm,9S) [sJ mixing time

(at m = 95%) tmax [sJ time of maximum

production rate (Equ.5.124)

tOTR [sJ characteristic time of OTR (Table 4.1)

tp [sJ period of oscillation (Equ.5.208)

tq; [sJ characteristic time of consumption or formation rates (cf. Table 4.1)

tr [sJ characteristic reaction time (cf. Table 4.1)

tSt [sJ sterilization time

V [m3 J volume [VJ Volt

v [m' S-l J velocity (general term) v (see r) [kg'm-3 's-1 J reaction rate, esp. of

enzyme kinetics VSL> VSG [m's-1 J superficial velocity of

liquid or gas phase Vt [m' s-l J terminal settling velocity

vrnf

Vms

w

w

x x

y, 1';u

z

SUBSCRIPTS

ads, a agit app ass asym adap av ave

[kg] [W]

adsorption agitation apparent assimilation asymptotic adaptation available average

Nomenclature (List of Symbols) xxv

B

BC bio

C c c

peripheric velocity of stirrer (stirrer top velocity) velocity of minimum fluidization velocity of minimum spouting

weight Watt mass fraction of component

amount of biomass biomass concentration measurement points or significant process variables or arbitrary quantity "washout" and "non­washout state" of biomass concentration (Fig.6.1a) unstable steady state (Fig. 6.11) biomass concentration

yield coefficient (general term) (see Table 2.14)

Z value (Equ. 5.9) electric charge (Equ.3.33) coordinate

bulk or bubble or bleed

bubble column biological

CO2

circulation cold

xxvi Nomenclature (List of Symbols)

calc calculated L liquid phase cat catalytic L longitudinal charact characteristic L1 liquid film at GIL crit, c critical interface

L2 liquid film at LI S d death or decay interface dc (DC) discontinuous degr, M maturation

degrad, d degradation m mixing degree, dist distributor medium, membrane

mm maximum mixedness E electrode or enzyme max maximum

or single mb membrane e endogenous or mIll minimum

environmental or mf minimum fluidization electrons ms minimum spouting

eff effective elim, el, e elimination N number of stages end end N resp. Ni nucleotide resp. est estimated internal nucleotide eq equivalent evap evaporation (heat loss) 0 oxygen ex exit 0 initial value exp experimental obs observed ext external opt optimal

OTR oxygen transfer rate F feed f film, biofilm II product sum ferm fermenter p product

p power G gas phase, gas pr production G G compartment gl glucose R reactor or ribosomes gr growth r reaction or resistant

or recycle H heat, general rad radiation Hv volumetric heat rds rate-determining step

reI relative 1, J number, components repr repression III inlet res reservoir ingest ingestion int internal L sum intersect intersection S solid phase or sub-

strate K K compartment ST stirred tank

Nomenclature (List of Symbols) xxvii

s sensitive COD chemical oxygen salt salt demand Slm simulated CPFR continuous plug flow st stirrer or sterilisation reactor

CRR continuous recycle T tank reactor TR transfer CSTR continuous stirred tank

terminal reactor tot total, global CTCR cycle tube cyclone ts total segregation reactor

CTD circulation time V volumetric distribution v viable

DCRR discontinuous recycle W wall reactor w warm DCSTR discontinuous stirred

tank reactor X biomass DNA desoxyribonucleic acid

z coordinate ES enzyme substrate =I- value of activated complex

complex EFB European Federation /\ normalized value of Biotechnology

mean value (steady E, dE260 extinction esp. at state) 260/lm

ABBREVIATIONS FBBR fluidized bed biofilm

reactor ADH, adh alcohol dehydrogenase FDP fructose diphosphate ADP adenosine diphosphate AMP adenosine mono- G G-compartment in

phosphate structured modeling ATP adenosine triphosphate of cells ATPase adenosine tripho- gapdh glyceraldehyde-3-

sphatease (enzyme) phosphate dehydro-genase

BFF biological film HvTR volumetric heat transfer fermenter rate

BOD biological oxygen demand HK hexokinase

BRE biological rate equation idCPFR ideal continuous plug

CMMFF completely mixed flow reactor microbial film idCSTR ideal continuous stirred fermenter tank reactor

XXV111 Nomenclature (List of Symbols)

K K-compartment in rCSTR continuous stirred tank structured modeling reactor with cell of cells recycling

RF rotor fermenter mm maximum mixedness rH redox potential

RNA ribonucleic acid NAD nicotinamide adenine RTD residence time

dinucleotide distribution NADH nicotinamide adenine

dinucleotide, reduced S Solid form s substrate or solid

NCSTR cascade of CSTR with SE substrate enzyme N stages complex

Su Sulfur OTR O2 transfer rate SCR semicontinuous reactor OUR O2 uptake rate SCSTR semicontinuous stirred ~O log mean of O2 tank reactor

concentration SOY sum of variances SLTR liquid-phase substrate

PATR pneumatically agitated transfer rate & aerated tubular SsTR solid-phase substrate reactor transfer rate

pfk pyruvate fructokinase PGK phosphoglycerate TLR tubular loop reactor

kinase ThLTBFF thin-layer tubular Ph Phosphorus biofilm fermenter PK pyruvate kinase ThLTR thin-layer tubular PHB polyhydroxy butyric reactor

acid ThLTFF thin-layer tubular film Pr productivity fermenter pyk pyruvate kinase TOC total organic carbon

ts total segregation qss quasi-steady-state ~T log-mean of tempera-q heat (rate) ture

TOC total organic carbon rds rate-determining step TR transport, general

GREEK SYMBOLS

rx(varrx) vanance rx, [3, y, b, coefficients [3 concentration factor of settling device [3 (¢o) modulus (Equ. 4.85) y [!] factor in Equ. 4.123 y [S-1 ] shear rate

Nomenclature (List of Symbols) xxix

Ys,Yx degree of reductance (reduction) () [mJ thickness of film acc. to two-film theory ()* morphology factor (Equ. 6.178) e [m2 • s- 3 J energy dissipation e ratio of Ks values (Equ. 5.137) eG gas hold-up ep volume fraction of particles ex biomass hold-up (Equ. 6.134) (i (relative) conversion of component i (Equ. 2.45) '1 effectiveness factor (general term)

'1 [N·s·m-2 J dynamic viscosity fj overall effectiveness factor (Equ. 4.2) '1app [N·s·m-2 J apparent viscosity

'1D factor in Equ. 3.62 '1E energy efficiency coefficient of growth

(Sect. 2.2.3.4)

'1GIL effectiveness factor of GIL-mass transfer

'1Lls effectiveness factor of LI S-mass transfer

'1M factor in Equ. 3.60 '10 [N·s·m-2 J viscosity of suspending fluid (for l/Js --+ l/J) '102 [%J O 2 utilization (Equ. 3.58)

'1r.A surface-area-related effectiveness factor of reaction (Equ. 4.98)

'1r ('1r. v) effectiveness factor of reaction (volume related)

'1~ effectiveness factor of reaction (Equ. 4.108)

~r effectiveness factor of reaction (Eq u. 4.11 Ob)

'1th thermodynamic efficiency '1TR(E) effectiveness factor of transport (enhancement

factor) e [!J factor in Equ. 3.63 ex [hJ sludge age (Equ. 6.122) /( dimensionless factor for bulk reaction rate in

Fig. 5.75 A [hJ cell age (Equ. 5.134) A [n-1 • cm-1 J conductivity

/1 [h-1 J specific growth rate fJ. [h-2 J first derivation of specific growth rate on time

/1d [h-1 J specific microbial death rate (Equ. 5.86)

/11 first moment (average value) of distribution function (Equ. 6.191)

v [m2 's-1 J kinematic viscosity v [S-l J specific doubling rate of cell number Vi stoichiometric coefficients (Equ. 1.4) ~ [moleJ extent of reaction (Equ. 1.3)

~ads sorption capacity (Equ. 5.115)

xxx Nomenclature (List of Symbols)

II p ~

¢Jlimit

[s] [s] [s] [s]

product sum density sum ionic strength (Equs. 3.33, 5.93) selectivity (Equ. 2.43) deviation (Equ. 4.47) spread of distribution function (Equ. 6.191) variance of distribution function shear stress normalized time (t/f) characteristic time of electrode response characteristic time of environmental change response to signal characteristic time of response acc. to moment method with first-order lags in series (Equ. 351) lag time (transients), Equ. 5.213 yield stress Thiele modulus (Equs. 4.80 and 4.77) (internal limitation) modulus Equ. 5.251 modulus for zero-order reaction (Equ. 4.85) modulus for first-order reaction (Equ. 4.83) generalized Thiele modulus of particles Thiele modulus based on biofilm thickness () (Equ.4.111) Thiele modulus for external S limitation (Equ.4.63) limiting value of ¢lex! (Equ. 4.65) consumption coefficient (Equ. 5.48) Carman factor in Equ. 4.1a volume fraction of suspended solids (Equ. 6.184)