Kinetics and Energetics of Photosynthetic Micro-Organisms in Photobioreactors
205
A one-dimensional approximation of Schuster has been assumed for the determination of the available radiant energy profiles in the medium to minimize the
calculation time, allowing the identification of parameters ~th and Kj, which
have been discussed above. The results of the identification procedure are as
follows (the parameters for light limitation are recalled here) [73]:
!
~tM = 0.49 h- 1
Kj = 20 W.m-2
KN = 5.3" 10 -3 kgNO~-.m -3
Ks = 2.5" 10 -4 kgSO42-.m -3
Kp = 2.7.10 -4 kgHPO42-.m -3
Kac = 0.06 kg.m- 3
; = 0.55
Solid lines in Figs. 10, 11 and 12 show the numerical simulations obtained
for nitrate, sulfate and phosphate limitations respectively. For each culture, the
percentage of N, S or P recovery (defined as the total mass of N, S or P recovered
in the synthesized biomass divided by the mass of N, S or P contained in the
respective mineral substrates, nitrate, sulfate, phosphate) was respectively 96%,
91%, and 97%. This confirms that the main species involved initially in the
process were correctly identified.
For nitrate and sulfate limitations, the model is in close agreement with the
experimental results, thereby confirming the ability of the model to provide
satisfactory predictions of biological kinetics in the photobioreactor until
phycocyanins have totally disappeared. These kinetic parameters, identified
here with a simple one dimensional model, may be extended to more complex
geometries, such as cylindrical photobioreactors, and to more complex physical
models related to light limitation. This has been done for cultures performed in
cylindrical reactor with high incident radiant energy flux and with nitrate
limitation [7]. In this case, the light transfer model used the numerical gridding
in specific intensity presented in Sect. 3 (Eq. 95) and the kinetic model used the
value of KN previously given. The results obtained by simulation and the
experimental data agree closely (results not shown) confirming the validity of the
previous kinetic parameters over a wide range of operating conditions.
For phosphate limitations the simulation results are less accurate in the
limiting phosphate concentration range. This shows that the Monod law is not
satisfactory for modeling phosphate limitation. This is probably due to the large
intracellular reserve of polyphosphates that are mobilized in a complicated way,
and to the key role played by phosphates in the energy metabolism of cells.
Some authors have proposed kinetic models for phosphate limitation in which
the extra- and intracellular phosphate concentrations are considered [39, 89].
The prime hypothesis advanced in this section concerning the additive effects of
limitations should perhaps be reconsidered in this case.
205
A one-dimensional approximation of Schuster has been assumed for the determination of the available radiant energy profiles in the medium to minimize the
calculation time, allowing the identification of parameters ~th and Kj, which
have been discussed above. The results of the identification procedure are as
follows (the parameters for light limitation are recalled here) [73]:
!
~tM = 0.49 h- 1
Kj = 20 W.m-2
KN = 5.3" 10 -3 kgNO~-.m -3
Ks = 2.5" 10 -4 kgSO42-.m -3
Kp = 2.7.10 -4 kgHPO42-.m -3
Kac = 0.06 kg.m- 3
; = 0.55
Solid lines in Figs. 10, 11 and 12 show the numerical simulations obtained
for nitrate, sulfate and phosphate limitations respectively. For each culture, the
percentage of N, S or P recovery (defined as the total mass of N, S or P recovered
in the synthesized biomass divided by the mass of N, S or P contained in the
respective mineral substrates, nitrate, sulfate, phosphate) was respectively 96%,
91%, and 97%. This confirms that the main species involved initially in the
process were correctly identified.
For nitrate and sulfate limitations, the model is in close agreement with the
experimental results, thereby confirming the ability of the model to provide
satisfactory predictions of biological kinetics in the photobioreactor until
phycocyanins have totally disappeared. These kinetic parameters, identified
here with a simple one dimensional model, may be extended to more complex
geometries, such as cylindrical photobioreactors, and to more complex physical
models related to light limitation. This has been done for cultures performed in
cylindrical reactor with high incident radiant energy flux and with nitrate
limitation [7]. In this case, the light transfer model used the numerical gridding
in specific intensity presented in Sect. 3 (Eq. 95) and the kinetic model used the
value of KN previously given. The results obtained by simulation and the
experimental data agree closely (results not shown) confirming the validity of the
previous kinetic parameters over a wide range of operating conditions.
For phosphate limitations the simulation results are less accurate in the
limiting phosphate concentration range. This shows that the Monod law is not
satisfactory for modeling phosphate limitation. This is probably due to the large
intracellular reserve of polyphosphates that are mobilized in a complicated way,
and to the key role played by phosphates in the energy metabolism of cells.
Some authors have proposed kinetic models for phosphate limitation in which
the extra- and intracellular phosphate concentrations are considered [39, 89].
The prime hypothesis advanced in this section concerning the additive effects of
limitations should perhaps be reconsidered in this case.