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Fed-Batch Cultures

Book Description

Many, if not most, industrially important fermentation and bioreactor operations are carried out in fed-batch mode, producing a wide variety of products. In spite of this, there is no single book that deals with fed-batch operations. This is the first book that presents all the necessary background material regarding the 'what, why and how' of optimal and sub-optimal fed-batch operations. Numerous examples are provided to illustrate the application of optimal fed-batch cultures. This unique book, by world experts with decades of research and industrial experience, is a must for researchers and industrial practitioners of fed-batch processes (modeling, control and optimization) in biotechnology, fermentation, food, pharmaceuticals and waste treatment industries.

Table of Contents

  1. Coverpage
  2. Fed-Batch Cultures
  3. Cambridge Series in Chemical Engineering
  4. Title page
  5. Copyright page
  6. Dedication
  7. Contents
  8. Preface
  9. Acknowledgments
  10. 1 Introduction to Fed-Batch Cultures
    1. 1.1 Batch Cultures
    2. 1.2 Continuous Cultures
    3. 1.3 Fed-Batch Cultures
      1. 1.3.1 Reasons for Fed-Batch Cultures
      2. 1.3.2 Applications of Fed-Batch Cultures
      3. 1.3.3 A Simple Example of a Fed-Batch Culture
    4. 1.4 Alternatives to Fed-Batch Cultures
  11. 2 Idealized Reactors and Fed-Batch Reactors
    1. 2.1 Material Balances
    2. 2.2 Various Types of Ideal Reactors
      1. 2.2.1 Batch Reactor Operation
      2. 2.2.2 Continuous-Flow Reactor Operation
      3. 2.2.3 Semi-Batch Reactor Operation
      4. 2.2.4 Fed-Batch Cultures
  12. 3 Maximization of Reaction Rates and Fed-Batch Operation
    1. 3.1 Intuitive Maximization of a Single Reaction Rate
      1. 3.1.1 Optimum One-Reactor Operations
      2. 3.1.2 Optimum Two-Reactor Operations
      3. 3.1.3 One-Reactor Operation Mimicking a Two-Reactor Operation
      4. 3.1.4 Rationale for Mimicking Optimal Two-Reactor Operations
    2. 3.2 Optimization of Multiple Reactions
      1. 3.2.1 Case of Constant Yields
      2. 3.2.2 Case of Variable Yields
    3. 3.3 Maximization of Cell Mass of a Simple Microbial Fed-Batch Culture
      1. 3.3.1 Feed Rate to Maintain the Substrate Concentration That Maximizes the Specific Growth Rate, S = Sm
      2. 3.3.2 Optimal Feed Rate Sequence for a Fed-Batch Culture
  13. 4 Phenomena That Favor Fed-Batch Operations
    1. 4.1 Chemical Phenomena
      1. 4.1.1 Substrate Inhibition
      2. 4.1.2 Glucose (Crabtree) Effect
      3. 4.1.3 Catabolite Repression
      4. 4.1.4 Utilization of Auxotrophic Mutants
    2. 4.2 Physical Phenomena
      1. 4.2.1 High Cell Density
      2. 4.2.2 Extension of Operational Period
      3. 4.2.3 Alleviation of High Broth Viscosity
      4. 4.2.4 Makeup for Lost Water by Evaporation
      5. 4.2.5 Better Plasmid Stability of Recombinant Cells
    3. 4.3 Other Phenomena
      1. 4.3.1 Experimental Kinetic Studies
      2. 4.3.2 Various Other Situations
  14. 5 Classification and Characteristics of Fed-Batch Cultures
    1. 5.1 Classification Based on Feeding Patterns
      1. 5.1.1 Mass Balance Equations
      2. 5.1.2 Cell Mass Balance
      3. 5.1.3 Substrate Balance
      4. 5.1.4 Product Balance
      5. 5.1.5 Overall Mass Balance
      6. 5.1.6 Fed-Batch Cultures with Constant Feed Rates
      7. 5.1.7 Fed-Batch Cultures with Linearly Varying Feed Rates
      8. 5.1.8 Fed-Batch Cultures with Exponential Feed Rates
      9. 5.1.9 Extended Fed-Batch Cultures
      10. 5.1.10 Fed-Batch Cultures with Intermittent Feed Rates
      11. 5.1.11 Fed-Batch Cultures with Empirical Feed Rates
      12. 5.1.12 Fed-Batch Cultures with Optimal Feed Rates
    2. 5.2 Classification Based on Number of Operational Cycles
      1. 5.2.1 Single-Cycle Operations
      2. 5.2.2 Multiple-Cycle Operations, Repeated Fed-Batch Operations
  15. 6 Models Based on Mass Balance Equations
    1. 6.1 Mass Balance Equations
      1. 6.1.1 Total Mass Balance Equation
      2. 6.1.2 Component Mass Balances
    2. 6.2 Unstructured Models
      1. 6.2.1 Specific Growth Rate of Cells, μ
      2. 6.2.2 Specific Product Formation Rate, π
      3. 6.2.3 Specific Substrate Consumption Rate, σ
      4. 6.2.4 Net Specific Rates
      5. 6.2.5 Temperature and pH Effects on Specific Rates
      6. 6.2.6 Maintenance Term
    3. 6.3 Structured Models
    4. 6.4 Parameter Estimation
      1. 6.4.1 All State Variables Are Measurable
      2. 6.4.2 Some State Variables Are Not Measurable but Are Observable
    5. Appendix : Some Models Proposed in Literature
  16. 7 Non–Equation-Based Models
    1. 7.1 Neural Networks
      1. 7.1.1 Basic Architecture of Neural Networks
      2. 7.1.2 Back-Propagation Training Algorithm
    2. 7.2 Neural Networks in Fed-Batch Fermentation
      1. 7.2.1 Yeast Fed-Batch Fermentation
      2. 7.2.2 Hybrid Neural Networks
  17. 8 Specific Rate Determination
    1. 8.1 Determination of Specific Rates by Classical Methods
      1. 8.1.1 Specific Rates by Shake Flask Cultures
      2. 8.1.2 Specific Rates by Batch Cultures
      3. 8.1.3 Specific Rates by Continuous Cultures
      4. 8.1.4 Specific Rates by Fed-Batch Cultures
    2. 8.2 A New Method of Determining Specific Rates Using Fed-Batch Cultures
      1. 8.2.1 Constant-Feed Fed-Batch Cultures
      2. 8.2.2 Utilization of Quasi Steady State
    3. Appendix : Equal-Area Graphical Differentiation of Discrete Experimental Data
  18. 9 Optimization by Pontryagin's Maximum Principle
    1. 9.1 Impulse and Parameter Optimizations
    2. 9.2 Optimization Criteria
      1. 9.2.1 Performance Indices
      2. 9.2.2 Free and Fixed Final Times
      3. 9.2.3 Free and Fixed Initial and Final States
      4. 9.2.4 Various Constraints
    3. 9.3 Choice of Manipulated Variables
    4. 9.4 Feed Rate Problem Formulation and Solution
      1. 9.4.1 Pontryagin's Maximum Principle
      2. 9.4.2 Boundary Conditions on Adjoint Variables
      3. 9.4.3 Hamiltonian
    5. 9.5 Handling of Problems in Nonstandard Forms
      1. 9.5.1 Nonautonomous Processes
      2. 9.5.2 Performance Indices Depend Explicitly on the Final Time
      3. 9.5.3 Other Forms of Performance Index
      4. 9.5.4 Constraints on State Variables
      5. 9.5.5 Constraints on Control Variables
    6. 9.6 Optimization of Initial Conditions
    7. 9.7 Generalized Legendre–Clebsch Condition
    8. 9.8 Transformation to Nonsingular Problem
      1. 9.8.1 Transformation of Singular Problems into Nonsingular Problems
      2. 9.8.2 Substrate Concentration as Single Manipulated Variable
      3. 9.8.3 Singular Problems with Multiple Manipulated Variables
  19. 10 Computational Techniques
    1. 10.1 Computational Techniques for Processes with Known Mathematical Models
      1. 10.1.1 Boundary Condition Iterations (Simple Shooting Method)
      2. 10.1.2 Multiple Shooting Method
      3. 10.1.3 Control Vector Iterations
      4. 10.1.4 Nonlinear Programming
      5. 10.1.5 A Special Transformation to Convert Singular to Nonsingular Problems
    2. 10.2 Numerical Techniques for Processes without Mathematical Models
      1. 10.2.1 Neural Network
      2. 10.2.2 Genetic Algorithm
  20. 11 Optimization of Single and Multiple Reactions
    1. 11.1 Single Reactions with a Single Feed Rate
      1. 11.1.1 Optimal Feed Rate Profile
    2. 11.2 Single Reactions with Both Feed and Withdrawal Rates
      1. 11.2.1 Solution via Pontryagin's Maximum Principle
      2. 11.2.2 Switching Space Analyses
      3. 11.2.3 Modal Analyses
      4. 11.2.4 Feasible Modes
      5. 11.2.5 Optimal Policies
    3. 11.3 Optimization of Multiple Reactions with a Feed Rate
      1. 11.3.1 Constant Yields
      2. 11.3.2 Variable Yields
  21. 12 Optimization for Cell Mass Production
    1. 12.1 Optimization by Pontryagin's Maximum Principle
    2. 12.2 Maximization of Cell Mass at Fixed and Free Final Times
      1. 12.2.1 Problem Formulation
      2. 12.2.2 Solution by Pontryagin's Maximum Principle
      3. 12.2.3 Constant-Yield Coefficients
      4. 12.2.4 Effects of Operating Parameters
      5. 12.2.5 Variable-Yield Coefficients
      6. 12.2.6 Assessment of Singular Regions
      7. 12.2.7 Singular Regions Characterized by Kinetic Parameters, μ(S) and YX/S(S)
    3. 12.3 Maximization of Cellular Productivity, X(tf)V(tf)/tf
      1. 12.3.1 Constant Cell Mass Yield Coefficient
      2. 12.3.2 Variable Cell Mass Yield Coefficient
    4. 12.4 Cell Mass Productivity Maximization through Time Optimal Formulation
      1. 12.4.1 Constant Cell Mass Yield Coefficient and Fixed Final Conditions
      2. 12.4.2 Variable Cell Mass Yield Coefficient and Fixed Final Conditions
    5. 12.5 Specific Rates as Functions of Substrate and Cell Concentrations
      1. 12.5.1 Optimal Feed Rate
      2. 12.5.2 Constant Cell Mass Yield Coefficient, YX/S
      3. 12.5.3 Free Final Time, tf
  22. 13 Optimization for Metabolite Production
    1. 13.1 Product Formation Models
    2. 13.2 General Optimization Problem for Metabolites
      1. 13.2.1 Choice of Manipulated Variables
      2. 13.2.2 Substrate Feed Rate as Manipulated Variable
      3. 13.2.3 Optimization Problem Formulation
    3. 13.3 Necessary Conditions for Optimality for Metabolite Production
      1. 13.3.1 Hamiltonian and Adjoint Vector
      2. 13.3.2 Optimal Feed Rate for Boundary Arc, x3(t) = Vmax
      3. 13.3.3 Optimal Feed Rate for Interior Singular Arc, x3(t) < Vmax
    4. 13.4 Substrate Concentration–Dependent Specific Rates
      1. 13.4.1 Constant-Yield Coefficients and No Maintenance Requirement
      2. 13.4.2 Variable-Yield Coefficients and Maintenance Requirement
    5. 13.5 Substrate and Product Concentration–Dependent Specific Rates, μ(S, P), π(S, P), and σ(S, P)
    6. 13.6 Recombinant Cell Products
      1. 13.6.1 Recombinant Cells with Plasmid Instability
      2. 13.6.2 Recombinant Cells with Plasmid Instability and Subject to Cell Death
    7. 13.7 Higher-Order Models
      1. 13.7.1 Animal Cell Cultures
      2. 13.7.2 Transformation of Singular Problems to Nonsingular Problems
      3. 13.7.3 Transformation of Singular Problems with Multiple Feed Rates
  23. 14 Simple Adaptive Optimization
    1. 14.1 Off-Line Cycle-to-Cycle (Sequential) Optimization
      1. 14.1.1 Off-Line Cycle-to-Cycle Optimization of Penicillin Production
      2. 14.1.2 Experimental Off-Line Cycle-to-Cycle Optimization of Invertase Production
    2. 14.2 On-Line Adaptive Optimization
      1. 14.2.1 Simulation Studies of On-Line Adaptive Optimization of Penicillin Production
      2. 14.2.2 Experimental On-Line Adaptive Optimization of Invertase Production
  24. 15 Measurements, Estimation, and Control
    1. 15.1 Measurements of Process Variables and Parameters
      1. 15.1.1 Physical Properties
      2. 15.1.2 Chemical Properties
      3. 15.1.3 Culture Conditions
    2. 15.2 Estimation Techniques
      1. 15.2.1 Macroscopic Balances
      2. 15.2.2 Mathematical Estimation Techniques
    3. 15.3 Feedback Control Systems
      1. 15.3.1 Single-Loop Control
      2. 15.3.2 Controller Selection and Tuning Methods
      3. 15.3.3 Multiple-Loop Control
    4. 15.4 Indirect Feedback Control
      1. 15.4.1 Carbon Dioxide Evolution Rate
      2. 15.4.2 Specific Growth Rates
    5. 15.5 Optimal Control
      1. 15.5.1 Optimal Open-Loop Control
      2. 15.5.2 Optimal Closed-Loop (Feedback) Control
  25. 16 Feasibility Assessment and Implementable Feed Rates
    1. 16.1 Estimation of Specific Rates
      1. 16.1.1 Shake-Flask and Batch Experiments
      2. 16.1.2 Fed-Batch Operations
    2. 16.2 Sequential Approach to Feasibility Assessment
    3. 16.3 Implementable Optimal–Suboptimal Feed Rates
      1. 16.3.1 Cell Mass as Product
      2. 16.3.2 Metabolites as Product
      3. 16.3.3 Recombinant Cell Products
  26. Index