154
J.-F. Cornet et al.
3.5.4 Continuous Cultures in Cylindrical Photobioreactors ...............
195
3.6 Dark Cycle: Respiration ...................................
196
4 Growth Kinetics Under Mineral Limitations .........................
196
4.1 Physiological Effects of Nitrogen, Sulphur and Phosphorus Mineral Limitations on
Spirulina Growth ........................................
196
4.1.1 Nitrate Limitation ...................................
196
4.1.2 Sulfate Limitation ....................................
197
4.1.3 Phosphate Limitation .................................
198
4.2 General Laws for Limiting Mineral Substrates ......................
198
4.3 Compartment Model for Spirulina Growth Under Mineral Limitation by N, S and P
200
4.3.1 Compartment Models .................................
200
4.3.2 Definition of Overall Absorption and Scattering Mass Coefficients .......
202
4.3.3 Kinetic Model ......................................
202
5 Limitation by the Carbon Source ................................
206
5.1 Different Cases in COz Transfer and HCO;- Consumption Rates ...........
206
5.2 Physical and Chemical Equilibria for the CO2 HCO3--CO 2- System ........
207
5.2.1 Gas-Liquid Equilibrium ................................
207
5.2.2 Chemical Equilibria ...................................
207
5.3 Conservation Law for the COz HCO3- CO32- System .................
208
5.4 Effects on Spirulina Growth .................................
209
6 Biochemically Structured Model of Growth ..........................
210
6.1 Coupling Photophosphorylations and Photosynthesis: ATP/2e Determination
and Biomass Composition Prediction ...........................
211
6.1.1 Basic Formalism for a Structured Model of S. platensis Growth ........
211
6.1.2 Bioenergetic Analysis of Coupling Photophosphorylations and Photosynthesis
212
6.1.3 Comparison of Experimental and Theoretical Values of P/2e- . ........
217
6.2 Thermodynamic Efficiency for Batch and Continuous Cultures ............
219
7 Conclusion ..............................................
221
8 References ..............................................
222
This paper provides the basis for the description and quantitative analysis of cultures of photosynthetic micro-organisms in batch and in continuous photobioreactors. The methodology generally
accepted for modeling submerged aerobic or anaerobic cultures is used and applied to the growth of
the blue-green algae Spirulina platensis.
From analysis of the metabolic pathways inside the cell, stoichiometric equations are derived for
the main metabolic events which must be considered for Spirulina growth, including exopolysaccharide formation. Together with the description of the reaction kinetics, it forms the basis for
modeling.
As the rate of growth is closely related to the light energy available inside the culture medium,
special attention is paid to the description of light energy transfer inside a dense liquid medium
which absorbs and scatters the light, and the useful concept of working illuminated volume is
introduced. The reaction kinetics accounts too for the mineral limitations (nitrogen, sulphur and
phosphorus) as well as physical and physiological limitations by the carbon source.
Finally, a so-called biochemically structured model gives a unified vision of yields and rates of
growth observed for various light energy inputs and different nutrients limitations. The proposed
methodology enables one to define and calculate the thermodynamic efficiency for the light energy
conversion process in photobioreactors.
J.-F. Cornet et al.
3.5.4 Continuous Cultures in Cylindrical Photobioreactors ...............
195
3.6 Dark Cycle: Respiration ...................................
196
4 Growth Kinetics Under Mineral Limitations .........................
196
4.1 Physiological Effects of Nitrogen, Sulphur and Phosphorus Mineral Limitations on
Spirulina Growth ........................................
196
4.1.1 Nitrate Limitation ...................................
196
4.1.2 Sulfate Limitation ....................................
197
4.1.3 Phosphate Limitation .................................
198
4.2 General Laws for Limiting Mineral Substrates ......................
198
4.3 Compartment Model for Spirulina Growth Under Mineral Limitation by N, S and P
200
4.3.1 Compartment Models .................................
200
4.3.2 Definition of Overall Absorption and Scattering Mass Coefficients .......
202
4.3.3 Kinetic Model ......................................
202
5 Limitation by the Carbon Source ................................
206
5.1 Different Cases in COz Transfer and HCO;- Consumption Rates ...........
206
5.2 Physical and Chemical Equilibria for the CO2 HCO3--CO 2- System ........
207
5.2.1 Gas-Liquid Equilibrium ................................
207
5.2.2 Chemical Equilibria ...................................
207
5.3 Conservation Law for the COz HCO3- CO32- System .................
208
5.4 Effects on Spirulina Growth .................................
209
6 Biochemically Structured Model of Growth ..........................
210
6.1 Coupling Photophosphorylations and Photosynthesis: ATP/2e Determination
and Biomass Composition Prediction ...........................
211
6.1.1 Basic Formalism for a Structured Model of S. platensis Growth ........
211
6.1.2 Bioenergetic Analysis of Coupling Photophosphorylations and Photosynthesis
212
6.1.3 Comparison of Experimental and Theoretical Values of P/2e- . ........
217
6.2 Thermodynamic Efficiency for Batch and Continuous Cultures ............
219
7 Conclusion ..............................................
221
8 References ..............................................
222
This paper provides the basis for the description and quantitative analysis of cultures of photosynthetic micro-organisms in batch and in continuous photobioreactors. The methodology generally
accepted for modeling submerged aerobic or anaerobic cultures is used and applied to the growth of
the blue-green algae Spirulina platensis.
From analysis of the metabolic pathways inside the cell, stoichiometric equations are derived for
the main metabolic events which must be considered for Spirulina growth, including exopolysaccharide formation. Together with the description of the reaction kinetics, it forms the basis for
modeling.
As the rate of growth is closely related to the light energy available inside the culture medium,
special attention is paid to the description of light energy transfer inside a dense liquid medium
which absorbs and scatters the light, and the useful concept of working illuminated volume is
introduced. The reaction kinetics accounts too for the mineral limitations (nitrogen, sulphur and
phosphorus) as well as physical and physiological limitations by the carbon source.
Finally, a so-called biochemically structured model gives a unified vision of yields and rates of
growth observed for various light energy inputs and different nutrients limitations. The proposed
methodology enables one to define and calculate the thermodynamic efficiency for the light energy
conversion process in photobioreactors.