Fundamental Bioengineering E-Book
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- Herausgeber: Wiley-VCH
- Kategorie: Fachliteratur
- Serie: Advanced Biotechnology
- Sprache: Englisch
A thorough introduction to the basics of bioengineering, with a focus on applications in the emerging "white" biotechnology industry.
As such, this latest volume in the "Advanced Biotechnology" series covers the principles for the design and analysis of industrial bioprocesses as well as the design of bioremediation systems, and several biomedical applications. No fewer than seven chapters introduce stoichiometry, kinetics, thermodynamics and the design of ideal and real bioreactors, illustrated by more than 50 practical examples. Further chapters deal with the tools that enable an understanding of the behavior of cell cultures and enzymatically catalyzed reactions, while others discuss the analysis of cultures at the level of the cell, as well as structural frameworks for the successful scale-up of bioreactions. In addition, a short survey of downstream processing options and the control of bioreactions is given.
With contributions from leading experts in industry and academia, this is a comprehensive source of information peer-reviewed by experts in the field.
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Veröffentlichungsjahr: 2015
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CONTENTS
Cover
Related Titles
Title Page
Copyright
List of Contributors
About the Series Editors
Chapter 1: Introduction and Overview
Part One: Fundamentals of Bioengineering
Chapter 2: Experimentally Determined Rates of Bio-Reactions
Summary
2.0 Introduction
2.1 Mass Balances for a CSTR Operating at Steady State
2.2 Operation of the Steady-State CSTR
References
Chapter 3: Redox Balances and Consistency Check of Experiments
Summary
3.1 Black-Box Stoichiometry Obtained in a CSTR Operated at Steady State
3.2 Calculation of Stoichiometric Coefficients by Means of a Redox Balance
3.3 Applications of the Redox Balance
3.4 Composition of the Biomass X
3.5 Combination of Black-Box Models
3.6 Application of Carbon and Redox Balances in Bio-Remediation Processes
References
Chapter 4: Primary Metabolic Pathways and Metabolic Flux Analysis
Summary
4.0 Introduction
4.1 Glycolysis
4.2 Fermentative Metabolism: Regenerating the NAD+ Lost in Glycolysis
4.3 The TCA Cycle: Conversion of Pyruvate to NADH + FADH2, to Precursors or Metabolic Products
4.4 NADPH and Biomass Precursors Produced in the PP Pathway
4.5 Oxidative Phosphorylation: Production of ATP from NADH (FADH2) in Aerobic Fermentation
4.6 Summary of the Biochemistry of Primary Metabolic Pathways
4.7 Metabolic Flux Analysis Discussed in Terms of Substrate to Product Pathways
4.8 Metabolic Flux Analysis Discussed in Terms of Individual Pathway Rates in the Network
4.9 Propagation of Experimental Errors in MFA
4.10 Conclusions
References
Chapter 5: A Primer to
13
C Metabolic Flux Analysis
Summary
5.1 Introduction
5.2 Input and Output Data of 13C MFA
5.3 A Brief History of 13C MFA
5.4 An Illustrative Toy Example
5.5 The Atom Transition Network
5.6 Isotopomers and Isotopomer Fractions
5.7 The Isotopomer Transition Network
5.8 Isotopomer Labeling Balances
5.9 Simulating an Isotope Labeling Experiment
5.10 Isotopic Steady State
5.11 Flux Identifiability
5.12 Measurement Models
5.13 Statistical Considerations
5.14 Experimental Design
5.15 Exchange Fluxes
5.16 Multidimensional Flux Identifiability
5.17 Multidimensional Flux Estimation
5.18 The General Parameter Fitting Procedure
5.19 Multidimensional Statistics
5.20 Multidimensional Experimental Design
5.21 The Isotopically Nonstationary Case
5.22 Some Final Remarks on Network Specification
5.23 Algorithms and Software Frameworks for 13C MFA
Glossary
References
Chapter 6: Genome-Scale Models
Summary
6.1 Introduction
6.2 Reconstruction Process of Genome-Scale Models
6.3 Genome-Scale Model Prediction
6.4 Genome-Scale Models of Prokaryotes
6.5 Genome-Scale Models of Eukaryotes
6.6 Integration of Polyomic Data into Genome-Scale Models
Acknowledgment
References
Chapter 7: Kinetics of Bio-Reactions
Summary
7.1 Simple Models for Enzymatic Reactions and for Cell Reactions with Unstructured Biomass
7.2 Variants of Michaelis–Menten and Monod kinetics
7.3 Summary of Enzyme Kinetics and the Kinetics for Cell Reactions
7.4 Cell Reactions with Unsteady State Kinetics
7.5 Cybernetic Modeling of Cellular Kinetics
7.6 Bioreactions with Diffusion Resistance
7.7 Sequences of Enzymatic Reactions: Optimal Allocation of Enzyme Levels
References
Chapter 8: Application of Dynamic Models for Optimal Redesign of Cell Factories
Summary
8.1 Introduction
8.2 Kinetics of Pathway Reactions: the Need to Measure in a Very Narrow Time Window
8.3 Tools for In Vivo Diagnosis of Pathway Reactions
8.4 Examples: The Pentose-Phosphate Shunt and Kinetics of Phosphofructokinase
8.5 Additional Approaches for Dynamic Modeling Large Metabolic Networks
8.6 Dynamic Models Used for Redesigning Cell Factories. Examples: Optimal Ethanol Production in Yeast and Optimal Production of Tryptophan in E. Coli
8.7 Target Identification for Drug Development
References
Chapter 9: Chemical Thermodynamics Applied in Bioengineering
Summary
9.0 Introduction
9.1 Chemical Equilibrium and Thermodynamic State Functions
9.2 Thermodynamic Properties Obtained from Galvanic Cells
9.3 Conversion of Free Energy Harbored in NADH and FADH2 to ATP in Oxidative Phosphorylation
9.4 Calculation of Heat of Reaction Q=(−ΔHc) and of (−ΔGc) Based on Redox Balances
References
Part Two: Bioreactors
Chapter 10: Design of Ideal Bioreactors
Summary
10.0 Introduction
10.1 The Design Basis for a Once-Through Steady-State CSTR
10.2 Combination of Several Steady-State CSTRs in Parallel or in Series
10.3 Recirculation of Biomass in a Single Steady-State CSTR
10.4 A Steady-State CSTR with Uptake of Substrates from a Gas Phase
10.5 Fed-Batch Operation of a Stirred Tank Reactor in the Bio-Industry
10.6 Loop Reactors: a Modern Version of Airlift Reactors
References
Chapter 11: Mixing and Mass Transfer in Industrial Bioreactors
Summary
11.0 Introduction
11.1 Definitions of Mixing Processes
11.2 The Power Input P Delivered by Mechanical Stirring
11.3 Mixing and Mass Transfer in Industrial Reactors
11.4 Conclusions
References
Part Three: Downstream Processing
Chapter 12: Product Recovery from the Cultures
Summary
12.0 Introduction
12.1 Steps in Downstream Processing and Product Recovery
12.2 Baker's Yeast
12.3 Xanthan Gum
12.4 Penicillin
12.5 α-A Interferon
12.6 Insulin
12.7 Conclusions
References
Chapter 13: Purification of Bio-Products
Summary
13.1 Methods and Types of Separations in Chromatography
13.2 Materials Used in Chromatographic Separations
13.3 Chromatographic Theory
13.4 Practical Considerations in Column Chromatographic Applications
13.5 Scale-Up
13.6 Industrial Applications
13.7 Some Alternatives to Column Chromatographic Techniques
13.8 Electrodialysis
13.9 Electrophoresis
13.10 Conclusions
References
Part Four: Process Development, Management and Control
Chapter 14: Real-Time Measurement and Monitoring of Bioprocesses
Summary
14.1 Introduction
14.2 Variables that should be Known
14.3 Variables Easily Accessible and Standard
14.4 Variables Requiring More Monitoring Effort and Not Yet Standard
14.5 Data Evaluation
References
Chapter 15: Control of Bioprocesses
Summary
15.1 Introduction
15.2 Bioprocess Control
15.3 Principles and Basic Algorithms in Process Control
References
Chapter 16: Scale-Up and Scale-Down
Summary
16.1 Introduction
16.2 Description of the Large Scale
16.3 Scale-Down
16.4 Investigations at Lab Scale
16.5 Scale-Up
16.6 Outlook
References
Chapter 17: Commercial Development of Fermentation Processes
Summary
17.1 Introduction
17.2 Basic Principles of Developing New Fermentation Processes
17.3 Techno-economic Analysis: the Link Between Science, Engineering, and Economy
17.4 From Fermentation Process Development to the Market
17.5 The Industrial Angle and Opportunities in the Chemical Industry
17.6 Evaluation of Business Opportunities
17.7 Concluding Remarks and Outlook
Acknowledgment
References
Index
EULA
List of Tables
Table 3.1
Table 4.1
Table 4.2
Table 5.1
Table 6.1
Table 6.2
Table 6.3
Table 7.1
Table 7.2
Table 7.3
Table 7.4
Table 9.1
Table 9.2
Table 9.3
Table 9.4
Table 10.1
Table 11.1
Table 12.1
Table 12.2
Table 13.1
Table 13.2
Table 15.1
Table 16.1
Table 16.2
Table 16.3
Table 16.4
Table 16.5
Table 16.6
Table 16.7
Table 16.8
Table 17.1
Table 17.2
Table 17.3
Table 17.4
Table 17.5
Table 17.6
Table 17.7
Table 17.8
List of Illustrations
Figure 2.1
Figure 2.2
Figure 2.3
Figure 4.1
Figure 4.2
Figure 4.3
Figure 4.4
Figure 4.5
Figure 4.6
Figure 4.7
Figure 4.8
Figure 4.9
Figure 4.10
Figure 4.11
Figure 4.12
Figure 4.13
Figure 4.14
Figure 4.15
Figure 4.16
Figure 5.1
Figure 5.2
Figure 5.3
Figure 5.4
Figure 5.5
Figure 5.6
Figure 5.7
Figure 5.8
Figure 5.9
Figure 5.10
Figure 5.11
Figure 5.12
Figure 5.13
Figure 5.14
Figure 5.15
Figure 5.16
Figure 5.17
Figure 5.18
Figure 5.19
Figure 6.1
Figure 6.2
Figure 6.3
Figure 6.4
Figure 6.5
Figure 6.6
Figure 6.7
Figure 6.8
Figure 6.9
Figure 7.1
Figure 7.2
Figure 7.3
Figure 7.4
Figure 7.5
Figure 7.6
Figure 7.7
Figure 7.8
Figure 7.9
Figure 7.10
Figure 7.11
Figure 7.12
Figure 7.13
Figure 7.14
Figure 7.15
Figure 7.16
Figure 7.17
Figure 7.18
Figure 8.1
Figure 8.2
Figure 8.3
Figure 8.4
Figure 8.5
Figure 8.6
Figure 8.7
Figure 8.8
Figure 8.9
Figure 8.10
Figure 8.11
Figure 8.12
Figure 8.13
Figure 8.14
Figure 8.15
Figure 8.16
Figure 8.17
Figure 8.18
Figure 8.19
Figure 8.20
Figure 8.21
Figure 8.22
Figure 8.23
Figure 8.24
Figure 8.25
Figure 8.26
Figure 8.27
Figure 8.28
Figure 8.29
Figure 8.30
Figure 8.31
Figure 8.32
Figure 8.33
Figure 8.34
Figure 8.35
Figure 9.1
Figure 9.2
Figure 10.1
Figure 10.2
Figure 10.3
Figure 10.4
Figure 10.5
Figure 10.6
Figure 10.7
Figure 10.8
Figure 10.9
Figure 10.10
Figure 11.1
Figure 11.2
Figure 11.3
Figure 11.4
Figure 12.1
Figure 12.2
Figure 12.3
Figure 12.4
Figure 12.5
Figure 12.6
Figure 13.1
Figure 13.2
Figure 15.1
Figure 15.2
Figure 15.3
Figure 15.4
Figure 15.5
Figure 15.6
Figure 15.7
Figure 15.8
Figure 16.1
Figure 16.2
Figure 16.3
Figure 16.4
Figure 17.1
Figure 17.2
Figure 17.3
Figure 17.4
Figure 17.5
Figure 17.6
Figure 17.7
Figure 17.8
Figure 17.9
Figure 17.10
Figure 17.11
Figure 17.12
Figure 17.13
Guide
Cover
Table of Contents
Part 1
Chapter 1
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Edited by John Villadsen
Fundamental Bioengineering
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
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The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.
© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
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ISSN: 2365-3035
Print ISBN: 978-3-527-33674-6
ePDF ISBN: 978-3-527-69746-5
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List of Contributors
Basti Bergdahl
Danmarks Tekniske Universitet
Novo Nordisk Foundation Center for Biosustainability
Kogle Allé 6
2970 Hørsholm
Denmark
Jochen Förster
Danmarks Tekniske Universitet
Novo Nordisk Foundation Center for Biosustainability
Kogle Allé 6
2970 Hørsholm
Denmark
Thomas Grotkjær
Novozymes A/S
Biomass Conversion Business Development
Novo Allé
2880 Bagsvaerd
Copenhagen
Denmark
Markus Herrgård
Danmarks Tekniske Universitet
Novo Nordisk Foundation Center for Biosustainability
Kogle Allé 6
2970 Hørsholm
Denmark
Jakob Kjøbsted Huusom
Technical University of Denmark
Department of Chemical and Biochemical Engineering
Anker Engelunds Vej 1
Bygning 101A
2800 Kgs Lyngby
Denmark
Daniel Machado
Universidade do Minho
Centro de Engenharia Biológica
4710-057 Braga
Portugal
Sunil Nath
Indian Institute of Technology, Delhi
Department of Biochemical Engineering and Biotechnology
Hauz Khas
New Delhi 110016
India
Sebastian Niedenführ
Forschungszentrum Jülich GmbH
Institute of Bio- and Geosciences
IBG-1: Biotechnology
52425 Jülich
Germany
Katharina Nöh
Forschungszentrum Jülich GmbH
Institute of Bio- and Geosciences
IBG-1: Biotechnology
52425 Jülich
Germany
Henk Noorman
DSM Biotechnology Center
A. Fleminglaan 1
2613 CA Delft
The Netherlands
Matthias Reuss
University of Stuttgart
Stuttgart Research Center Systems Biology
Nobelstr. 15
70569 Stuttgart
Germany
Nikolaus Sonnenschein
Danmarks Tekniske Universitet
Novo Nordisk Foundation Center for Biosustainability
Kogle Allé 6
2970 Hørsholm
Denmark
Bernhard Sonnleitner
Zurich University of Applied Sciences (ZHAW)
Institute for Chemistry and Biological Chemistry (ICBC)
Biochemical Engineering
Einsiedlerstrasse 29
8820 Waedenswil
Switzerland
John Villadsen
Technical University of Denmark (DTU)
Department of Chemical and Biochemical Engineering
Building 229
2800 Kgs Lyngby
Denmark
Wolfgang Wiechert
Forschungszentrum Jülich GmbH
Institute of Bio- and Geosciences
IBG-1: Biotechnology
52425 Jülich
Germany
About the Series Editors
Sang Yup Lee is Distinguished Professor at the Department of Chemical and Biomolecular Engineering at the Korea Advanced Institute of Science and Technology. At present, Prof. Lee is the Director of the Center for Systems and Synthetic Biotechnology, Director of the BioProcess Engineering Research Center, and Director of the Bioinformatics Research Center. He has published more than 500 journal papers, 64 books, and book chapters, and has more than 580 patents (either registered or applied) to his credit. He has received numerous awards, including the National Order of Merit, the Merck Metabolic Engineering Award, the ACS Marvin Johnson Award, Charles Thom Award, Amgen Biochemical Engineering Award, Elmer Gaden Award, POSCO TJ Park Prize, and HoAm Prize. He is Fellow of American Association for the Advancement of Science, the American Academy of Microbiology, American Institute of Chemical Engineers, Society for Industrial Microbiology and Biotechnology, American Institute of Medical and Biological Engineering, the World Academy of Science, the Korean Academy of Science and Technology, and the National Academy of Engineering of Korea. He is also Foreign Member of National Academy of Engineering, USA. In addition, he is honorary professor of the University of Queensland (Australia), honorary professor of the Chinese Academy of Sciences, honorary professor of Wuhan University (China), honorary professor of Hubei University of Technology (China), honorary professor of Beijing University of Chemical Technology (China), and advisory professor of the Shanghai Jiaotong University (China). Apart from his academic associations, Prof. Lee is the editor-in-chief of the Biotechnology Journal and is also contributing to numerous other journals as associate editor and board member. Prof. Lee is serving as a member of Presidential Advisory Committee on Science and Technology (South Korea).
Jens Nielsen is Professor and Director to Chalmers University of Technology (Sweden) since 2008. He obtained an MSc degree in chemical engineering and a PhD degree (1989) in biochemical engineering from the Technical University of Denmark (DTU) and after that established his independent research group and was appointed full professor there in 1998. He was Fulbright visiting professor at MIT in 1995–1996. At DTU, he founded and directed the Center for Microbial Biotechnology. Prof. Nielsen has published more than 350 research papers and coauthored more than 40 books, and he is inventor of more than 50 patents. He has founded several companies that have raised more than 20 million in venture capital. He has received numerous Danish and international awards and is member of the Academy of Technical Sciences (Denmark), the National Academy of Engineering (USA), the Royal Danish Academy of Science and Letters, the American Institute for Medical and Biological Engineering and the Royal Swedish Academy of Engineering Sciences.
Gregory Stephanopoulos is the W.H. Dow Professor of Chemical Engineering at the Massachusetts Institute of Technology (MIT, USA) and Director of the MIT Metabolic Engineering Laboratory. He is also Instructor of Bioengineering at Harvard Medical School (since 1997). He received his BS degree from the National Technical University of Athens and his PhD from the University of Minnesota (USA). He has coauthored about 400 research papers and 50 patents, along with the first textbook on metabolic engineering. He has been recognized by numerous awards from the American Institute of Chemical Engineers (AIChE) (Wilhelm, Walker and Founders awards), American Chemical Society (ACS), Society of Industrial Microbiology (SIM), BIO (Washington Carver Award), the John Fritz Medal of the American Association of Engineering Societies, and others. In 2003, he was elected member of the National Academy of Engineering (USA) and in 2014 President of AIChE.
1Introduction and Overview
John Villadsen
Bioengineering is a relatively new addition to a long list of terms starting with “bio.” It is broadly defined as “the application of engineering principles to biological systems.” Bioengineering can include elements of chemical, electrical and mechanical engineering, computer science, materials, chemistry and biology. The systems that are analyzed range from cell cultures and enzymes applied in the bio-industry and in bioremediation to prosthetics, construction of models for organs such as liver, drug-delivery systems and numerous other subjects in biomedical engineering, all requiring an understanding of transport phenomena (mass, heat, and momentum transfer) and kinetics, combined in often large mathematical models. Besides a working knowledge of these core chemical engineering disciplines, a successful study of a problem in bioengineering requires an insight into the core disciplines of biology and biochemistry, specifically in human physiology when the goal is, for example, to construct a new cancer drug delivery system.
In this volume, coauthored by nine scientists, mostly working in academic institutions or in the bio-industry, the focus is on application of bioengineering in the emerging “white biotechnology” industry. The design of bioremediation systems closely follows the principles of analysis and design of industrial bioprocesses. This text will also prove valuable for environmental engineers. The biomedical applications of the text are, however, also quite obvious. Thus, the important but complex application of mesenchymal stem cells to treat osteoporosis is based on an optimal growth strategy of the cell culture on a scaffold at the right liquid flow with the right oxygen and nutrient availability. Here, kinetics and transport phenomena are coupled to basic biology and biochemistry, and design of the system is based on a complex model for the interaction between scaffold, cells, and nutrients.
In Chapters 5, 6, and 8, the reader will find self-contained accounts of the tools that together make it possible to understand the behavior of cell cultures and enzymatically catalyzed reactions: The interaction of metabolic network reactions in steady state and during transients, analyzed by mathematical models and solved by state-of-the-art computer software.
In Chapter 16, a structural framework for successful scale-up of bioreactions from laboratory scale to large industrial scale is presented. In Chapter 17, the sequence of management decisions that may lead to new business ventures in the bio-industry is discussed.
The analyses of cultures on the level of the cell are authored by three leading European scientists. Each author gives - as far as possible - a complete account of his subject, illustrated with examples and with sufficient detail to give readers, both in industry and in graduate classes at universities, a fair chance to understand and utilize the very powerful analytical tools presented in the three chapters.
The two Chapters 16 and 17 on large-scale bioreactors and on the business opportunities in the bio-industry are written by leading experts from two major bio-industrial companies, DSM in the Netherlands and Novozymes in Denmark. These chapters could serve as guidelines for prospective business ventures in the industry.
Although the focus of this book is on the bioreactor, Chapters 12 and 13 cover further processing of the effluent from the bioreactor. The author, a distinguished Indian bioscientist, gives a short introduction to the subject of downstream processing. Also, a survey of measuring, monitoring, and control of bioreactions is included. In Chapter 14, a leading expert on chemical analysis to capture key fermentation variables and on using the experimental data in analysis of fermentation broths gives an easy-to-read but largely complete survey of the subject. In Chapter 15, a young expert in control of chemical processes, discusses control problems in bioreactors, specifically addressing the challenges of bio-system control.
Finally, the content of the book is tied together by seven chapters (2, 3, 4, 7, 9, 10, and 11) written by the editor of this work. These chapters introduce a common nomenclature for the whole book, with introductory material on stoichiometry, kinetics, thermodynamics, and design of ideal and real bioreactors. It is hoped that the introductory chapters, illustrated with many simple examples, will make it easier to read the advanced chapters, especially since there are frequent cross references between introductory and advanced chapters.
Part OneFundamentals of Bioengineering
2Experimentally Determined Rates of Bio-Reactions
John Villadsen
Summary
Rates of bioreactions are introduced as measured terms in steady-state mass balances for a continuous stirred tank reactor (CSTR). Both mass balances and the reaction rates have the same form for enzymatically catalyzed reactions and for reactions with living cells. In cell reactions, the rate of biomass formation is included through a separate mass balance. Reactants absorbed in the liquid phase from a gas phase are treated separately, and it is shown how experimental errors can lead to errors in the calculated rates. The black-box model for a cell-reaction stoichiometry is introduced and the yield coefficients are defined. Finally, different methods of controlling the CSTR at steady state are discussed.
2.0 Introduction
The rate of an enzymatically catalyzed bioreaction, or of a reaction that involves living cells (microbial, animal, or plant cells), can be determined experimentally in a bioreactor. The bioreactors used in academic research or in an industrial R&D department to obtain reaction rates are normally glass vessels of 0.5–5 l working volume V. A typical laboratory reactor is shown in Figure 2.1. It is well stirred either by an internal mechanical stirrer (a hydrofoil or a turbine) or by a magnetic stirrer, operated from the outside of the reactor. In all cases, the mixing of liquid feed into the medium volume V is supposed to be good enough to ensure that there is no spatial variation of substrates or products in the reactor. Batch operation or continuous operation of the reactor is typically used, and the assumption of perfect mixing in the medium volume V will ensure that the concentrations Si of substrates and Pi of products are the same at any point in the reactor. If the continuous stirred tank reactor (CSTR) is operated in steady state, there is no accumulation of either products or substrates. The liquid flow vf and the feed concentrations of substrates sf,i are kept constant in time. Now the medium volume V and the concentrations of substrates and products both in the reactor [si, pj] and in the effluent concentrations [se,i, pe,i] are constant in time. In the batch reactor, one starts with a high concentration of substrates si0 (+ a small amount of biomass for a fermentation), and Si are converted to Pj over time. The volume of medium V in the reactor is constant in time.
Figure 2.1 CSTR with substrate feed of liquid medium and of gas through a sparger. A separate feed of acid/alkali for pH control is used. In pH auxostats (see below) the feed of alkali is used as control variable.
A gas-phase substrate is introduced to the liquid through a sparger. It is absorbed in the liquid and is consumed by the reaction. Gaseous products are transferred to the gas phase by desorption from the liquid.
Then, mass balances for substrates and products are set up. These mass balances define the reaction rates, and solution of the mass balances allows the rates to be calculated based on measured concentrations [si, pi]. To illustrate the procedure we shall use mass balances derived for a steady state CSTR, and the equipment is shown in Figures 2.1 and 2.2.
Figure 2.2 A commercial laboratory reactor (Biostat® A plus from Sartorious) for medium volume between 0.4 and 5 l. The reactor is supported by packages for either microbial cell or animal/plant cell cultures. The microbial package includes two 6-blade Rushton turbines (see Chapter 11), two gas-inlets, ports for inoculation, automatic and manual samplers, and temperature control via a heating blanket and cooling finger. Control of pH, T, dissolved oxygen (DO), stirrer speed, air flow rate, and foam control.
2.1 Mass Balances for a CSTR Operating at Steady State
The steady-state mass balances for a continuous reactor with a working volume V, for example, in m3 liquid medium, in which an enzymatically catalyzed reaction occurs, is given by Eq. (2.1).
In Eq. (2.1), v is the liquid flow through the reactor in, for example, m3 liquid h−1. v/V is defined as the dilution rate D (h−1). si is the concentration of the ith substrate in the reactor, se,i the concentration in the liquid effluent, and sf,i the concentration in the feed. For the steady-state continuous reactor (see also Section 10.1), si = se,i. The same nomenclature is used for the product concentrations.
For each substrate, the volumetric rate of production qs,i of Si, for example, in units of g Si or C-mol Si l−1 h−1, is multiplied by the reactor volume V to give the production rate of Si (e.g., in g Si h−1). To the production term is added vsf,I, the amount of Si introduced through the feed and subtracted vse,i, the substrate that leaves the reactor. The sum of the three terms of the steady-state mass balance is zero. The mass balance for product Pj contains the same terms.
qs,i (i = 1, 2,…, N) and qp,j (j = 1, 2,…, M) are always defined as (volumetric) rates of production. Hence qs,i are always negative and – qs,i is, therefore, the volumetric rate of consumption of Si.
As is the case for any catalyzed reaction, the rate can be defined either per volume reactor (q) or per unit of catalyst (r), for example, per unit mass of catalyst added to each l of reactor. This second definition defines the specific reaction rates rs,i and rp,j, which are obtained from qs,i and qp,j by division with e, the concentration of enzyme E, for example, in units of g E l−1. The specific rates define the activity of the enzyme E to convert Si to Pj. These definitions are further discussed in Section 7.1.
In reactions with living cells, the cell mass catalyzes the conversion of Si to Pj, but the substrate is also used to form more biomass X – the reaction is autocatalytic. Hence biomass is also a product, and similar to Eq. (2.1) one obtains:
The unit of ri could be g Si produced/g biomass/h (i.e., rsi is negative), g Pi (g X h)−1, g X (g X h)−1.
rx is defined as the specific growth rate of the culture, and in most biotechnology literature rx is called µ. We shall only use this latter symbol when its meaning is obvious. It is seen that µ is the ability (or activity) of the biomass in the reactor to make more biomass. An active culture can make much biomass per g biomass present per hour – a resting culture has a low value of rx = µ.
Since some substrates (e.g., O2) are captured from the gas phase and some products (e.g., CO2) are released to the gas phase, one needs to add an extra term in Eqs. (2.1) and (2.2) for these reaction species. This term is qskT or qpmT (e.g., in moles of O2 or CO2 transferred (l h)−1).
In Eq. (2.4), the term qskT is positive (there is an influx of O2 to the liquid), while qpmT is negative.
The amount of reaction species k and m transferred between the gas and the liquid phase can be determined from a mass balance on the gas phase.
Here, (vg,f, vg) are the volumetric gas flows (l h−1) in and out of the reactor, and (πk,f, πk) and (πm,f, πm) are the partial pressures of the substrate k and of the product m in the inlet and in the outlet from the reactor. πk,f = ykP, where yk is the volume fraction of Sk in the gas (e.g., 0.21 mol O2 (mol vgf)−1 for O2 in the inlet when the reactor is sparged with air) and P is the total pressure. vg,fπk,f/RT = mol O2 fed to the reactor per hour, and (1/RT)(vg,fπk,f − vgπk) is the moles of O2 transported to the liquid phase. With π in atm and T in K, the value of the gas constant R is 0.08205 l atm (mol K)−1.
The mass transfer can also be calculated by Eq. (2.6). This is an empirical relation between a driving force (sk*−sk) and qskT, the volumetric mass transfer. sk is the liquid phase concentration of substrate Sk and sk* is the saturation concentration of Sk in equilibrium with a gas phase with (approximately) the partial pressure (πk,f + πk)/2 – or a more complicated expression for the average gas-phase partial pressure as explained in Chapter 11. kla is the volumetric mass transfer coefficient, a first-order rate constant (unit e.g., h−1) for the mass transfer process. The mass transfer coefficient depends on the power consumption (unit, for example, W) to mix the liquid phase.
Combination of Eqs. (2.5) and (2.6) is one way of experimentally determining kla by simultaneous measurement of [sk, πkf, πk] and [vgf,vg] at different stirring intensities of the liquid. Once an empirical relation has been set up between the power input and the rate constant kla, the relation can be used under similar conditions to predict the mass transfer qskT for any power input.
When the rate of formation of one of the reaction species has been determined, then, for a single enzymatic reaction or fermentation process, the rates of formation for all other reaction species can be calculated via the yield coefficients Yij. Yij is defined as the rate of formation of component j relative to the formation of another component i. Yij=rj/ri=qj/qi. The symbol || is used to ensure that Yij is positive also when the numerator and denominator have different signs.
Based on the yield coefficient, any rate qjdifferent from the key rate qi can be found as follows:
It must be emphasized that Eq. (2.7) is only true if the yield coefficients are constant in the range of investigation of the reaction. This is the case if the reaction is described by a single stoichiometric equation for all investigated values of the dilution rate D.
Example 2.1 Calculation of Rates and Stoichiometry Based on the Key Reactant
Catalase breaks down hydrogen peroxide by the stoichiometric equation H2O2 → H2O + ½O2. This is the only overall stoichiometric equation by which O2 is formed from H2O2. The kinetic mechanism of the reaction is, however, not at all revealed from the overall stoichiometry. Similarly, lactobionic acid (lba) is produced from lactose in the reaction: lactose + O2 + H2O → lba + H2O2 catalyzed by a carbohydrate oxidase, a reaction discussed further in Example 7.4. In the first reaction, YH2O2,O2=½mol/mol, and in the second Ylactose,O2=Ylactose,H2O2=Ylactose,lab=1mol/mol. The production of lactobionic acid is qlba = Ylac,lba (−qlactose) or D (clba − clba,f) = Ylac, lba (clactose,f − clactose). The last relation shows that the effluent concentration of lactobionic acid (and of H2O2) can be calculated from [clactose,f, clactose].
In enzymatically catalyzed reactions, the yield coefficients Yij are true stoichiometric coefficients, exact numbers just as in conversion of N2 and H2 to NH3 by the stoichiometry N2 + 3 H2 → 2 NH3. This is also the case for reactions involving living cells if the same stoichiometry holds for all operational conditions, for example, for all permissible D values between 0 and Dmax. At Dmax > vmax/V, the flow through the reactor is larger than the maximum production rate of cells. The culture washes out and steady-state operation cannot be maintained. In the stoichiometry of fermentation reactions, the coefficients are empirical numbers that can be interpreted when, as in Chapter 4, a good metabolic model is constructed for the reaction. Thus, in anaerobic fermentation with the yeast Saccharomyces cerevisiae, the substrate, glucose, is converted to ethanol, glycerol, CO2, and more biomass. When the elementary composition of S. cerevisiae is given by X = CH1.74O0.6N0.12, one obtains the following equation [1]:
In (Eq. 1) all carbon-containing compounds are normalized to contain 1 C-mol carbon. This leads to somewhat unusual formulas for ethanol (CH3O0.5), glycerol (CH8/3O), and glucose (CH2O), but the nomenclature is useful in quantitative work since the basis is always 12 g carbon, whereas molecules such as C6H12O6 break down to smaller molecules (such as trioses in the glycolysis pathway (see Figure 4.2) or combine to larger molecules (such as Butyryl-CoA by condensation of two molecules of Acetyl-CoA in the solvent producing pathways of Clostridium acetobutylicum (see Figure 4.14). The advantage of writing the fermentation stoichiometry on a C-mol basis becomes apparent in later chapters. Here, we are content to notice that the closing of the carbon balance is immediately obvious when the yield coefficients on both sides of (Eq. 1) are compared: 1 = ΣYsj (j = 1–4). Ysn = 0.01658 can be obtained from Ysx since for each carbon in the biomass 0.12 mol N is consumed and there are no other sinks for N in the stoichiometry, that is, Yxn = 0.12, Ysn = 0.12 · 0.1381 = 0.01658. Ysw = 0.037 can be obtained from either an H or an O balance on the stoichiometry.
The rate of production of, for example, ethanol is related to the rate of consumption of glucose by qe = 0.5160 (−qs) or ce − cef = 0.5160 (23/30) (sf − s) g l−1. Thus, if the feed contains 25 and the effluent 1.378 g glucose l−1, then ce − cef = 9.34 g/l. Unless the reactor considered receives its feed from a preceding reactor in a sequence of CSTRs, the feed is sterile and contains no products, [xf, pjf] = [0,0]. In that case, [x, ce = e, cglycerol = g] = [0.1370 · 25.02 · 23.622/30 = 2.70, 9.34, 1.67] g/l. In this calculation, the formula weights of [S, X, E, G] = [30, 25.02, 23, 30.33] g (C-mol)−1 have been used to find Ys,pj in g g−1 from the stoichiometry given in (Eq. 1).
Since the stoichiometry (1) is supposed to hold for all acceptable D values, one can finally calculate the reactor volume needed for a given production rate. Let the desired production rate of ethanol be 900 kg h−1 in an industrial reactor design based on the stoichiometry (1). Then v = 900/9.34 = 96.4 m3 h−1. If the process is carried out at D = 0.32 h−1, one needs a reactor of working volume V = 96.4/0.32 = 301 m3.
This last example illustrates how the so-called “black box” stoichiometric (Eq. 1) can be set up based on steady-state experiments in a CSTR. To find the yield coefficients, one just needs the effluent concentrations [s, x, e, g] = [23.622, 2.70, 9.34, 1.67] calculated above. The yield coefficient for CO2 can be found using the carbon balance, even when the CO2 production is not measured. In fact, it will be demonstrated in Example 4.5 that with a reliable metabolic model in hand only one production rate, for example, qx (or rx), needs to be measured to find all the yield coefficients on the right-hand side of (Eq. 1) when the substrate consumption rate is normalized to 1. Nevertheless, it is highly advisable to include all available measured data in the vector of experimental results since, as shown in Chapter 4, experimental errors can significantly distort the calculated yield coefficients if only the minimum amount of data (in the example above the effluent glucose and biomass concentrations) are used. Although the experimental work of [1] on which (Eq. 1) is based is done with the highest possible precision obtainable in a state-of-the-art laboratory bioreactor, the C balance (the author had also measured qCO2) fits to “only” 0.995. Today, one must demand that experimental data obtained in a good laboratory reactor are accurate enough to make the carbon balance close to 0.985–0.99; otherwise, the data are suspicious. The use of the carbon and a redox balance to be introduced in Chapter 3 is either to calculate missing yield coefficients or to check for inconsistencies in the experimental data. Another use of these two fundamental balances is illustrated in Chapter 4. There the goal is to find parameters in metabolic models, especially empirical yield coefficients in the metabolic reaction that describes biomass formation.
Example 2.2 Calculation of Rates for Reaction Species that are Both in the Gas Phase and in the Liquid Phase
It appears to be fairly simple to apply Eqs. (2.4) and (2.5) to determine the transfer rate qiT and thereafter the rate of production qi of reaction species that are present both in the liquid phase and in the gas phase. Still the rates can be erroneously calculated, and in this example it will be shown how the measured data must be treated to obtain the correct rate values.
First the rates of transfer of oxygen and carbon dioxide [qoT,qcT] as determined from continuous readings of the headspace molar fractions will be considered. All modern bioreactors are equipped with sufficiently good monitoring equipment for these variables, and readings are considered to be accurate to within a few percent relative. Hence, they are considered as keys to an efficient control of the reactor. For example, in aerobic cultivations with glucose as C substrate, the respiratory quotient RQ qc/(−qo) is in the range 1.04–1.06 when no metabolic products are formed, except biomass and CO2.
Consider the production of biomass by aerobic cultivation of the bacterium Methylococcus capsulatus on methanol. M. capsulatus can grow on both methane and methanol, and the product is sold as “single-cell protein (SCP)” as feed to a range of animals both in husbandry and in aquacultures. In this process, a valuable product (∼US$ 1600 per ton) is obtained from raw materials that are available in huge quantities and with a price in the range of US$ 200 per ton based on shale gas.
A 10 l well-stirred continuous bioreactor is sparged with air (21% O2, 79% N2 + Ar, and 0.04% CO2) at a feed rate of vg,f = 10 l min−1 (1 volume gas per volume medium per minute = 1 vvm). The total pressure is 1 atm, and the temperature of the air is equal to the cultivation temperature, T = 45 °C. Both the inlet and the effluent gas are free of water. In the effluent, one measures the mole fractions [yo, yc] = [0.180, 0.0174].
The flow of air from the reactor vg (45 °C, 1 atm) is calculated in the following way: 100 l of vg,f contains 79 l N2 + Ar, while 100 l of vg contains 100 – 18 – 1.74 l = 80.3 l of the inert gases N2 + Ar. Since the content of inert gases has not changed, vg must be smaller than vg,f, and vg = 79/80.3 vg,f = 0.9838 vg,f. The 10 l reactor has received 600 · (0.21 – 0.18 · 0.9838) = 19.75 l O2 h−1 or (19.75 · 1 (atm)/0.08206/318.2 (K))/10 (l) = 0.0756 mol O2 (l h)−1 = qoT. (−qcT) = 600 · (0.0174 · 0.9838 – 0.0004) · 0.00383 = 0.0385 mol CO2 (l reactor h)−1.
The liquid-phase concentration of oxygen is very small, both in the feed and in the effluent. From Eq. (9.2) at 45 °C and with pure O2 in the gas phase (πO2=1atm), one obtains so*=0.98·10−3mol (l reactor)−1. When the gas phase is air with πO2=0.21atm, the saturation concentration is so*=0.21·0.98·10−3=0.206·10−3mol l (reactor)−1. The effluent concentration of O2 is even smaller, perhaps 10% of so*. Hence, in Eq. (2.4), the term D(so,f − so) is several orders of magnitude smaller than qoT, and the rate of oxygen consumption (−qo) is very close to the experimentally determined qoT=0.0756mol O2 (l reactor h)−1. Similarly, for steady-state cultivation, the total concentration of CO2 (as dissolved CO2, HCO3−, and CO3−2) is virtually the same in the inlet and outlet, and qc∼(−qcT)=0.385 mol CO2 (l reactor h)−1.
The accuracy of, especially, the calculation of qoT increases when the difference between the mole fraction in the feed gas and the exhaust gas increases. Thus, with vg,f = 300 l h−1 (0.5 vvm), one obtains the same qoT=0.0756 mol O2 (l reactor h)−1 at an exhaust O2 mole fraction yo = 0.1465. This clearly gives a higher accuracy in the determination of qoT, but one must not decrease vg,f too much, since the mass transfer coefficient kla decreases with vg,f, and it will eventually become difficult to transfer the required qoT. Also, at a low vg,f value, the oxygen in the gas bubbles can become severely diluted with a gaseous product such as CO2, and especially if the inert content of vg,f is small as is the case when enriched air is used, the partial pressure of O2 in the bubbles decreases when the bubbles pass through the liquid phase.
Serious errors in the determination of qiT can result if the content of water in vg,f differs from that of vg. Thus, when vg,f is bone-dry and vg is not adequately dried, qoT is severely overestimated if the water evaporated into the gas is not taken into account. At 45 °C and 1 bar, the vapor pressure of H2O over liquid water is 71.9 mm Hg, that is, the equilibrium mole fraction of H2O in the exhaust gas is 71.9/760 = 0.0946 bar. In the example given above with vg,f = 600 l h−1 bone-dry air and qoT=0.0756mol O2 (l reactor h)−1, the exhaust (wet) air would be vg = 600 − 19.75 + 10.03 + 0.0946 vg → vg = 652 l h−1. The mole fraction of O2 would be yo = (0.21 · 600 − 19.75)/652 = 0.1630. Thus, if one measures vg to be 652 l h−1, the measured value of yo = 0.1630 in the exhaust gas correctly predicts qoT=0.0756mol O2 (l reactor h)−1. If, however, one erroneously assumes that vg = 0.9838 vg,f = 590 l h−1 as is the case when the exhaust air is bone-dry, then the transferred volume of O2 would be calculated to 600 · (0.21 − 0.9838 · 0.1630) = 29.8 l h−1, and qoT would be overestimated by a factor 29.8/19.75 = 1.5.
Another kind of error in the calculation of rates occurs if one of the products formed in the liquid phase is partly stripped to the gas phase. This happens in aerobic cultivations where O2 is supplied by sparging the medium with air (or air enriched with O2). But it also happens in anaerobic cultivations when fully anaerobic conditions are ensured by sparging the medium with an inert, for example, N2.
Let the mole fraction of the product P in the liquid phase be xp=(p/55.5) where p is the concentration of P in the medium (mol l−1) and 55.5 = 1000/18 = moles H2O/l H2O. The equilibrium mole fraction in the gas above the medium yp = γpxpπp, where γp is the activity coefficient of P in the liquid phase and πp is the partial pressure of P in the gas phase = vapor pressure at medium temperature T/total pressure. The amount of P removed to the gas phase is vg,fyp when vg = vg,f, a reasonable assumption since yp is usually very small. For xp → 0, the situation in most bioreactions, γ → γinf dilution, which can be found in many tables or calculated by group contribution methods such as UNIFAC. Thus, for the three fermentation products, ethanol, acetaldehyde, and 1-butanol, γinf dilution = [6.61, 7.5, 49.4] at 30 °C. Even a small xp is magnified to an appreciable yp. Thus, in a 2 wt% 1-butanol aqueous solution xp = 2/(74.12 · 55.5) = 4.86 · 10−4. The vapor pressure of 1-butanol is 10 mm Hg at 30°, and yp = 49.4 · 4.86 10−4 · 10/760 = 3.16 10−4. With an inert gas flow of 600 l h−1 to a 10 l reactor, the loss of 1-butanol to the gas phase is 7.62 10−4 mol (l h)−1. At D = 0.2 h−1, the measured butanol rate of production is = 0.2 · 2/74.12 = 5.4 10−3 mol (l h)−1, while the true production rate is qp = 6.16 10−3 mol (l h)−1.
Acetaldehyde with a vapor pressure of 1076 mm Hg at 30 °C will almost quantitatively be stripped to the gas phase, and the total acetaldehyde production is a factor 7–8 higher than that calculated on the basis of the liquid effluent acetaldehyde concentration.
2.2 Operation of the Steady-State CSTR
Examples 2.1 and 2.2 have shown how production rates qi are calculated for a steady-state continuous stirred tank reactor. In the following the typical laboratory CSTR is described and various ways of obtaining steady-state cultivation conditions are discussed. Figures 2.1 and 2.2 are, respectively, a sketch of a CSTR and a photograph of a state-of-the-art laboratory bioreactor Biostat® A plus from Sartorious.
Figure 2.1 shows the glass vessel mounted on a balance that continuously records the amount of liquid and biomass in the vessel. An accuracy of a few milligrams in the reading of the weight can be expected. The liquid feed comes from several reservoirs. The main substrate reservoir contains the carbon source, glucose, sucrose, glycerol, methanol, and ethanol-whichever carbon source is to be studied. To keep the pH constant, there will always be reservoirs with acid (H2SO4, HCl, etc.) and with base (NaOH, KOH, NH4OH, etc.). The flow of alkali and acid is controlled individually based on continuous pH measurement in the vessel, while the carbon substrate feed concentration and the concentration of minerals and trace elements is kept constant through each steady-state experiment, hence the size of the reservoir should preferably be large enough to allow each steady state to be studied with only one batch of premixed substrate solution. In order to avoid dilution of the substrate by titration to a fixed pH, it is advantageous to use concentrated acid and base. Here, a common feed line of liquid substrate as shown in Figure 2.1 can be advantageous in order to avoid transient upsets of pH in the mixing of droplets of strong base/acid directly into the vessel. The feed should preferably be in the middle of the reactor, close to the agitator in order to avoid C substrate gradients. In the so-called pH auxostat (see below), the feed of base to keep pH constant when H+ is liberated by uptake and metabolism of substrate must, however, be kept separate from the feed of carbon source. Different gas-sparging systems and mixers are used, often of the so-called Ruston turbine design (Chapter 11), which provide for a considerable power input to give a high mass transfer coefficient kla, but in stress-sensitive cultures (mammalian cells or plant cells) gentler mixers are used. Small reactors can be stirred by a magnetic stirrer. Concentrations of liquid- and gas-phase effluents are measured online (CO2 and O2), at-line, or offline as discussed further in Chapter 14.
All high-quality laboratory reactors (the so-called “ideal bioreactors”) are equipped with a number of monitors for state variables, and some of these are used to control the process. Industrial reactors have much fewer measurements. Typically, temperature T, pressure P, agitator speed, RQ, the ratio between CO2 and O2 concentration in the gas-phase effluent, and the O2 tension in the liquid phase are continuously recorded. A few liquid-phase variables, s and e, are measured at-line. All measurements are stored in the process computer as shown on Figure 2.2.
Steady-state operation of a bioreactor is characterized by time-independent values of all culture variables. The feed concentration so of the C substrate and the concentration of all minerals, including H2PO4−, Cl−, SO4−2, Na+, K+, Cu+, and Mn+2, hormones, growth essential compounds, and so on must be constant in time. The dilution rate D = v/V is a key variable, as well as pH, T, and dissolved oxygen (DO) concentration sO2 that is often measured relative to the saturation concentration sO2*, namely, DO=sO2/sO2*. If in a well-stirred reactor, these essential variables are kept constant by accurate measurements, and with good control algorithms to process the measurements, one can expect all concentrations of substrates and products in the effluents to be virtually time-independent and equal to their concentrations in the reactor medium.
In a few but exhaustively studied cases (see, for example, [2,3]), it is virtually impossible to attain steady-state operation of the continuous stirred tank reactor. This is the case when aerobic yeast fermentation is carried out in well-mixed “ideal” laboratory bioreactors at a dilution rate close to the so-called critical dilution rate, Dcrit. Here, the metabolism suddenly changes from purely respiratory growth with biomass and CO2 as the only products to fermentative (respiro-fermentative) growth in which also ethanol and glycerol are produced. The kinetics of the process around Dcrit is highly nonlinear, and transients between even closely spaced D values are extraordinarily long and follow nearly unpredictable courses. One may even obtain long lasting and apparently stable free oscillations in the outlet concentrations of x, CO2, ethanol, and so on from an uncontrolled continuous reactor where the dilution rate and all input substrate concentrations are meticulously kept constant. It is worth noting that in industrial bioreactors, where the mixing is less perfect and synchronization of the culture does not happen, these oscillations are never observed. This is, indeed, fortunate for the Novo Nordisk company that uses a genetically engineered yeast to produce an expensive, growth-associated product, human insulin, in large (≈75 m3) stirred tanks operated in steady state and close to Dcrit to obtain a high volumetric productivity qp of the desired hormone product. Even slight variations in the effluent concentrations are intolerable for a product that has to pass strict FDA quality tests.
Except in these “pathological” situations, it is easy to study the steady state of a bioreaction in a state-of-the-art bioreactor equipped with a number of control loops and serviced by a computer that automatically steps through a range of D values. At each D value, steady state is reached when the culture is in a “metabolically steady state,” a term to be discussed further in Chapter 7. Basically, metabolic steady state is reached when the catabolic (“energy producing”) pathways and the anabolic (“biomass-building and energy-consuming”) pathways run at the same rate. When a selected D value is close to one at which steady state has been reached, it does not take long for the cell reactions to harmonize, and the new steady state is reached after a time t ≤ D−1. This is the basis for operation of the accelerostat where D is increased (or decreased) in small steps, and a series of steady states is obtained after a reasonably small experimental time. If the new D is far from the preceding D value, D0, especially if D0 is very small, it takes a very long time, perhaps t=5D0−1, to reach a new steady state. Close to D values where the metabolism of the cell changes drastically (as at Dcrit in aerobic yeast cultivation), the transient can last even much longer.
As illustrated below, it is, however, important to choose the right variable to be controlled, since the choice depends on the range of dilution rates to be studied. The example of Figure 2.3 illustrates how different control strategies are chosen.
Figure 2.3 Steady-state aerobic cultivation of Saccharomyces cerevisiae. (a) Biomass concentration x(g l−1) (solid circles), specific CO2 production rate (mol CO2(g X h)−1, solid triangles), specific O2 consumption rate (mol O2(g X h)−1, filled squares). (b) Effluent glucose concentration s (g l−1, solid squares) and ethanol concentration e (gl−1, filled triangles). Feed concentration of glucose 20 gl−1 with no biomass or ethanol in the feed. (Data from Ref. [4,5].)
For low dilution rate (until about D = 0.2–0.22 h−1), the effluent biomass concentration x in Figure 2.3a is almost constant. The specific rates of CO2 production and of O2 consumption increase linearly with D. A good control of steady state is obtained by continuous measurement of the medium weight W(t) and controlling v to give a specific D value = vρmedium/W. The biomass concentration is nearly constant and the measurement of x cannot be used to obtain a desired steady state (D). The ethanol concentration is nearly zero, as is the glucose concentration. With modern, very sensitive measurement methods for glucose, one might use s as control variable, but it is better to use W(t). In this mode of control, the reactor is called a chemostat. At the other end (Figure 2.3b), where washout is reached and s approaches so = 20 g l−1, measurement of W(t) is not sensitive enough to secure a given steady-state value of D, but both x(t) and s(t) can be used. In the auxostat, one is even able to control the reactor at exactly the washout dilution rate, and this can be used to find the maximum specific growth rate rx for a series of different strains [6]. When x(t
