Microbial Reactions in Continuous Culture

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General Notions on Chemical and Biochemical Systems

Introduction

This chapter explains about chemical and biochemical systems along with trans-formation and basic terminology related to these systems. It describes briefly about the composition, structure, properties and change of chemical and bio-chemical compounds. Then, it will discuss about how different chemical changes are optimised using different chambers known as reactors and what are the laws governing this change through mathematical equations. Later in the chapter, there is a review on what are the problems faced during the process, different control strategies to avoid such problems and how the energy flows in the process i.e. chemical thermodynamics.

Chemical Kinetics

Everything in our world is built out of atoms, from the smallest piece of pa-per to the biggest, most complicated electronic device. Each atom is unique in terms of mass, size and properties in comparison to other atoms. Electro-static force of attraction between atoms, known as chemical bond, allows the formation of chemical substances that contain two or more atoms. Pure chemi-cal substance consisting of a single type of atom not chemically bonded to each other are known as elements e.g. carbon (C). When atoms form bonds together, they make molecules e.g. molecular hydrogen (H2). A chemical compound is a molecule that involves the chemical bond between at least two different atoms e.g. carbon dioxide (CO2). Atoms or compounds have tendency to transform into new compounds by chemically combining with atoms or compounds of different composition. This process of transformation of one set of chemical compounds called reactants to another set of chemical compounds called products by break-ing and making new chemical bonds between atoms is known as chemical reaction e.g. C +O2 →CO2. | {z } | {z }
Reactan ts Product
Several chemical reactions end up in combined mixture of reactants and products. Such reactions are called reversible reactions i.e. they run in both directions and are represented as:
aA + bB cC + dD,
The speed at which a chemical reaction takes place is known as the rate of a reaction (r). A reversible reaction has two rates of reaction, forward rf and backward rr.
Chemical kinetics deals with the mechanism of rates of chemical reactions. It also includes the investigation of the conditions that can influence the speed of reaction e.g. temperature, concentration as well as developing mathematical models to describe the nature of the reaction. Several theories act as basis for calculating the reaction rates at the molecular level. Some basic theories are as follows:
i) Law of conservation of mass It states that for a closed system the total mass of the system must remain constant i.e. the system mass cannot change quantity if it is not added or removed.
ii) Law of conservation of energy It states that the total energy of an isolated system is constant but it can change from one form to another.
iii) Law of mass action When two reactants, A and B, react together at a given
temperature, the chemical affinity (A) between them is directly proportional to the product of concentration of [A] and [B], each raised to a particular power:
A = α[A]a[B]b. (2.1)
α, a and b are the empirical constants.
iv) Chemical equilibrium It is the state of reversible reactions in which the forward reaction proceeds at the same rate as the reverse reaction and both reactants and products have no further tendancy to change with time i.e. :
rf = rr. (2.2)
v) Stoichiometry It is founded on the law of conservation of mass. It states that the relations among quantities of reactants and products form a ratio of positive integers. These positive integers are known as stoichiometric coefficients and are represented in front of the chemical compounds, for example: CH4 +2O2 → CO2 +2H2O
Here, 1 molecule of CH4 combines with 2 molecules of O2 to form 1 molecule of CO2 and 2 molecules of H2O. 1, 2, 1 and 2 are the stoichiometric coefficients.
Besides these basic laws some other methodologies are there which are pur-posely executed and play an important role in the chemical kinetics.
1. Chemical synthesis It is a deliberate execution of chemical reactions using physical and chemical manipulations to obtain the desired products. It usually increases the number of steps to obtain the desired product and/or change the intermediate product.
2. Catalysis It is the process of increasing the rate of a reaction through participation of an additional compound called catalyst. With catalyst, the reaction mechanism changes and reactions occur faster without the catalyst actually being consumed.

Table of contents :

Nomenclature
1 General Introduction 
1.1 Thesis Framework
1.2 Thesis Contribution
1.3 Thesis Organization
1.4 Publications
2 General Notions on Chemical and Biochemical Systems
2.1 Introduction
2.2 Chemical Kinetics
2.3 Biochemical kinetics
2.3.1 Michaelis-Menten Kinetics
2.3.2 Microbial Kinetics
2.4 Reactors
2.5 Microbial Reactions in Continuous Culture
2.6 Chemical Reaction and Thermodynamics
2.6.1 Energy of a Chemical Reaction
2.6.2 Irreversible Thermodynamics
2.7 State-space Modeling of Reactors
2.7.1 Modeling of Chemical Reactors
2.7.2 Modeling of Bioreactors
2.7.3 Process Modeling Improvisations
2.8 Control of Reactors
2.8.1 Chemical Reactors
2.8.2 Bioreactors
2.8.3 Process Control Algorithms
2.9 Conclusion
3 Port-Hamiltonian Modeling of Continuous Reactors
3.1 Introduction
3.1.1 Role of Energy in Modeling
3.1.2 Passivity
3.2 Energy Based Modeling Tools
3.2.1 Port Based Modeling
3.2.2 Bond Graph Modeling
3.2.3 Port-Hamiltonian Modeling
3.3 Energetic Modeling of Chemical and Biochemical Systems: Literature Review
3.3.1 Bond Graph Review
3.3.2 Port-Hamiltonian Review
3.3.3 Conclusion from Literature review
3.3.3.1 Difficulties and Framework
3.3.3.2 Outcome
3.3.3.3 Choice of Hamiltonian
3.4 Bond Graph and Port-Hamiltonian Model of Open Chemical Systems
3.5 Bond Graph and Port-Hamiltonian Model of Basic Enzyme Reaction With MM Kinetics in a CSTR
3.5.1 Bond Graph Representation
3.5.2 Port Hamiltonian Formulation
3.6 Port-Hamiltonian Model of a Continuous Reactor
3.7 Stoichiometric Port-Hamiltonian Formulation of Open Reaction Networks
3.8 Reaction Port-Hamiltonian Formulation of Open Reaction Networks
3.9 Conclusion
4 Interconnection and Damping Assignment-Passivity Based Control of Continuous Reactors
4.1 Introduction
4.2 Role of Energy in Control
4.3 Energy Based Control Tools
4.3.1 Energy Balancing Control
4.3.2 Energy Shaping Control
4.3.3 Energy Shaping plus Damping Injection Control
4.3.4 Power Shaping Control
4.3.5 Energy Shaping via Control by Interconnection
4.3.6 Casimir Functions and Control by Interconnection
4.3.7 Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC)
4.3.8 Energy Based Control Using Graphical Tools
4.3.8.1 Bond Graph
4.3.8.2 Energetic Macroscopic Representation
4.4 Energetic Control of Continuous Chemical and Biochemical Reactors: A review
4.4.1 Bond Graph Control
4.4.2 Energetic Control of Continuous Chemical Systems
4.4.2.1 Control Using Artificial Energy Functions
4.4.2.2 Control Using True Energy Functions
4.4.3 Biochemical systems
4.4.4 Conclusion From Literature Review
4.5 IDA-PBC of Open Chemical Reactors
4.6 IDA-PBC of SPH Systems
4.7 IDA-PBC of RPH Systems
4.8 PH Formulation and IDA-PBC of Enzymatic Hydrolysis of Cellulose in an Open Reactor
4.8.1 Reaction Mechanism
4.8.2 SPH and RPH formulation of Enzymatic Hydrolysis of Cellulose in a Continuous Bioreactor
4.8.3 Interconnection and Damping Assignment-Passivity Based Control of Enzymatic Hydrolysis of Cellulose in a Continuous Bioreactor
4.8.4 Inlet Substrate Concentration Derivation
4.8.5 Simulations
4.9 Conclusion
5 Passivity Based Modeling and Passivity Based Adaptive Control of Microbial Reactions in Continuous Bioreactors 
5.1 Introduction
5.2 Passivization of Bioreactor System
5.2.1 The General Dynamical Model of a Single Stream Bioreactor
5.2.2 A Useful Coordinate Transformation
5.2.3 Decoupling of Coupled Bioreactions
5.2.4 Passivity Based Model of a Decoupled Bioreactor System
5.2.4.1 Passivity at Zero Equilibrium
5.2.4.2 Passivity at Non-zero Equilibrium
5.3 Passivity Based Control of Bioreactor System
5.4 Passivity Based Adaptive Control of Bioreactor Systems
5.4.1 Passivity Based Adaptive Control Review With a Possible Application to Microbial Reactions in Continuous Bioreactors
5.4.2 The Adaptive Controller Design
5.5 Application to a Single Reaction with Monod kinetics: Aniline Degradation by Pseudomonas putida in CSTR
5.5.1 Coordinate transformation And a Passivity Based Model
5.5.2 Passivity Based Control Design
5.5.3 Passivity Based Adaptive Control Design
5.5.4 Simulations
5.5.5 Alternative Storage Functions
5.5.5.1 IDA-PBC Scheme Using Alternative Storage Functions
5.5.5.2 Adaptive Control Scheme Using Alternative Storage Functions
5.5.6 Simulations Comparing Different Storage Functions
5.6 Application to Multiple Reactions: The Dynamics of Volatile Fatty Acids in Anaerobic Digester
5.7 Conclusion
Concluding Remarks and Future Perspective
Appendix 
Bibliography

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