Kinetics and Energetics of Photosynthetic
Micro-Organisms in Photobioreactors
Application to Spirulina Growth
J.-F. Cornet, C.G. Dussap, J.-B. Gros
Laboratoire de G6nie Chimique Biologique Universit6 Blaise-Pascal 24,
Avenue des Landais 63177 Aubi6re Cedex, France
List of Abbreviations and Symbols .................................
155
1 Introduction .............................................
159
2 Modeling Photobioreactors: Application to Growth of Spirulina platensis
........
160
2.1 General Approach of Modeling Photobioreactors ....................
160
2.1.1 Characterization of Growth by a Single Stoichiometric Equation ........
161
2.1.2 Balance Equations ...................................
162
2.1.3 Characterization of Growth and Product Formation by Several Stoichiometric
Equations .........................................
164
2.1.4 Biochemically Structured Models ...........................
165
2.2 Main Components of Cell Material .............................
166
2.3 Analysis of Metabolic Pathways ...............................
167
2.3.1 Photosynthesis ......................................
167
2.3.2 Carbon Uptake .....................................
167
2.3.3 Nitrogen Uptake ....................................
169
2.3.4 Respiration ........................................
169
2.4 Stoichiometry of Growth ...................................
169
2.4.1 Synthesis of Cell Material ...............................
169
2.4.2 Respiration ........................................
172
3 Growth Kinetics Under Physical Limitation by Radiant Light Energy Transfer .....
172
3.1 Kinetic Data for Photosynthesis and Respiration .....................
172
3.1.1 Photosynthesis ......................................
172
3.1.2 Respiration ........................................
174
3.1.3 Compensation Point ..................................
174
3.2 Coupling Growth Kinetics and Radiative Transfer ....................
174
3.2.1 What Variables Should be Used to Describe the Available Radiant Light Energy
in a Culture Medium? Radiative Transfer Definitions ...............
174
3.2.2 Kinetic Laws for Photosynthesis and Photoinhibition ..............
176
3.2.3 Coupling Growth Kinetics and Light Transfer Models: The Working
Illuminated Volume ...................................
177
3.3 The Simplified Lambert-Beer Law for Absorption of Light ...............
178
3.4 General Radiative Transfer Theory .............................
180
3.4.1 Light Transfer Parameters and Incident Fluxes Determinations .........
182
3.4.2 Analytical Approximized One-Dimensional Solutions for the Radiative Transfer
Equation: Schuster's Hypotheses ...........................
184
3.4.3 The P-N and Discrete Ordinate Methods for Solving the One-Dimensional
Radiative Transfer Equation .............................
186
3.4.4 Radiative Transfer Theory for Three-Dimensional Applications: General Case
188
3.5 Growth Kinetics of Spirulina platensis in Photobioreactors Under Light Limiting
Conditions ............................................
189
3.5.1 Physical Characteristics of Culture Media with Spirulina platensis .......
189
3.5.2 Comparison Between Lambert, One- and Three-Dimensional Models
for Obtaining the Mean Volumetric Rate of Radiant Energy Absorbed ....
190
3.5.3 Batch Cultures in Rectangular Photobioreactors .................
194
Advances in Biochemical Engineering/
Bioteehnology, Vol. 59
Managing Editor: T. Scheper
9 Springer-Vedag Berlin Heidelberg 1998
Micro-Organisms in Photobioreactors
Application to Spirulina Growth
J.-F. Cornet, C.G. Dussap, J.-B. Gros
Laboratoire de G6nie Chimique Biologique Universit6 Blaise-Pascal 24,
Avenue des Landais 63177 Aubi6re Cedex, France
List of Abbreviations and Symbols .................................
155
1 Introduction .............................................
159
2 Modeling Photobioreactors: Application to Growth of Spirulina platensis
........
160
2.1 General Approach of Modeling Photobioreactors ....................
160
2.1.1 Characterization of Growth by a Single Stoichiometric Equation ........
161
2.1.2 Balance Equations ...................................
162
2.1.3 Characterization of Growth and Product Formation by Several Stoichiometric
Equations .........................................
164
2.1.4 Biochemically Structured Models ...........................
165
2.2 Main Components of Cell Material .............................
166
2.3 Analysis of Metabolic Pathways ...............................
167
2.3.1 Photosynthesis ......................................
167
2.3.2 Carbon Uptake .....................................
167
2.3.3 Nitrogen Uptake ....................................
169
2.3.4 Respiration ........................................
169
2.4 Stoichiometry of Growth ...................................
169
2.4.1 Synthesis of Cell Material ...............................
169
2.4.2 Respiration ........................................
172
3 Growth Kinetics Under Physical Limitation by Radiant Light Energy Transfer .....
172
3.1 Kinetic Data for Photosynthesis and Respiration .....................
172
3.1.1 Photosynthesis ......................................
172
3.1.2 Respiration ........................................
174
3.1.3 Compensation Point ..................................
174
3.2 Coupling Growth Kinetics and Radiative Transfer ....................
174
3.2.1 What Variables Should be Used to Describe the Available Radiant Light Energy
in a Culture Medium? Radiative Transfer Definitions ...............
174
3.2.2 Kinetic Laws for Photosynthesis and Photoinhibition ..............
176
3.2.3 Coupling Growth Kinetics and Light Transfer Models: The Working
Illuminated Volume ...................................
177
3.3 The Simplified Lambert-Beer Law for Absorption of Light ...............
178
3.4 General Radiative Transfer Theory .............................
180
3.4.1 Light Transfer Parameters and Incident Fluxes Determinations .........
182
3.4.2 Analytical Approximized One-Dimensional Solutions for the Radiative Transfer
Equation: Schuster's Hypotheses ...........................
184
3.4.3 The P-N and Discrete Ordinate Methods for Solving the One-Dimensional
Radiative Transfer Equation .............................
186
3.4.4 Radiative Transfer Theory for Three-Dimensional Applications: General Case
188
3.5 Growth Kinetics of Spirulina platensis in Photobioreactors Under Light Limiting
Conditions ............................................
189
3.5.1 Physical Characteristics of Culture Media with Spirulina platensis .......
189
3.5.2 Comparison Between Lambert, One- and Three-Dimensional Models
for Obtaining the Mean Volumetric Rate of Radiant Energy Absorbed ....
190
3.5.3 Batch Cultures in Rectangular Photobioreactors .................
194
Advances in Biochemical Engineering/
Bioteehnology, Vol. 59
Managing Editor: T. Scheper
9 Springer-Vedag Berlin Heidelberg 1998