Kinetics and Energetics of Photosynthetic Micro-Organisms in Photobioreactors
221
obtained for the mean radiant energy available in the reactor J'o 4rcJa d~. are less
than 10 W.m-2, which corresponds to the maximum quantum yield for photosynthesis.
It should be emphasized that the general behaviour of the thermodynamic
efficiency can be represented solely as a function of the volumetric rate of radiant
energy absorbed whether batch or continuous cultures are concerned. This
quantity appears to be a key variable for correlating the conversion yield of light
energy into chemical affinity.
7 Conclusion
Given the obvious difficulties in representing photosynthetic micro-organisms
growth kinetics, it is useful to consider the overall strategy that can be applied.
Clearly, the modeling of growth can be systematically forced using
a stoichiometric approach which insures the elemental conservation balances
are satisfied. At the simplest level, i.e. a single stoichiometric equation, the
determination of a fixed elemental composition for biomass enables one to
calculate the stoichiometric coefficients corresponding to biomass growth and
thereby to predict, without requiring any experimental data, all the conversion
yields that are assumed to remain constant during the growth process.
This stoichiometric model can be used to improve the physical light transfer
models responsible for light energy distribution through an absorbing and
scattering dense medium. The models presented are of varying mathematical
complexity. The simplest Lambert-Beer model fails to represent correctly the
culture behaviour with a fixed physical coefficient (light attenuation coefficient)
and constant physiological coefficients. Schuster's model, which has been
explored for different bioreactor geometries, has an acceptable mathematical
complexity without excessive loss of accuracy in representing the physics of the
problem. The concept of working illuminated volume affords a tractable system
of equations that enables computer simulations and the identification of the
physiological coefficients from experimental data. The most elaborate model for
the description of the light energy transfer involves numerical gridding techniques for solving the radiative transfer equations. The main point is certainly
that it is possible to represent the behaviour of Spirutina platensis cultures over
a wide range of experimental conditions (rectangular and cylindrical photobioreactors, batch and continuous cultures, incident light flux ranging between
5 and 300 W.m-2) with constant physiological coefficients provided the light
transfer problem is correctly handled.
The influence of mineral limitations (nitrogen, sulphur, phosphorus) has
been studied via a compartment model allowing a variable biomass composition
to be represented as a function of the depletion of the different nutrients. The
mathematical model involves independent kinetic rates for proteins,
221
obtained for the mean radiant energy available in the reactor J'o 4rcJa d~. are less
than 10 W.m-2, which corresponds to the maximum quantum yield for photosynthesis.
It should be emphasized that the general behaviour of the thermodynamic
efficiency can be represented solely as a function of the volumetric rate of radiant
energy absorbed whether batch or continuous cultures are concerned. This
quantity appears to be a key variable for correlating the conversion yield of light
energy into chemical affinity.
7 Conclusion
Given the obvious difficulties in representing photosynthetic micro-organisms
growth kinetics, it is useful to consider the overall strategy that can be applied.
Clearly, the modeling of growth can be systematically forced using
a stoichiometric approach which insures the elemental conservation balances
are satisfied. At the simplest level, i.e. a single stoichiometric equation, the
determination of a fixed elemental composition for biomass enables one to
calculate the stoichiometric coefficients corresponding to biomass growth and
thereby to predict, without requiring any experimental data, all the conversion
yields that are assumed to remain constant during the growth process.
This stoichiometric model can be used to improve the physical light transfer
models responsible for light energy distribution through an absorbing and
scattering dense medium. The models presented are of varying mathematical
complexity. The simplest Lambert-Beer model fails to represent correctly the
culture behaviour with a fixed physical coefficient (light attenuation coefficient)
and constant physiological coefficients. Schuster's model, which has been
explored for different bioreactor geometries, has an acceptable mathematical
complexity without excessive loss of accuracy in representing the physics of the
problem. The concept of working illuminated volume affords a tractable system
of equations that enables computer simulations and the identification of the
physiological coefficients from experimental data. The most elaborate model for
the description of the light energy transfer involves numerical gridding techniques for solving the radiative transfer equations. The main point is certainly
that it is possible to represent the behaviour of Spirutina platensis cultures over
a wide range of experimental conditions (rectangular and cylindrical photobioreactors, batch and continuous cultures, incident light flux ranging between
5 and 300 W.m-2) with constant physiological coefficients provided the light
transfer problem is correctly handled.
The influence of mineral limitations (nitrogen, sulphur, phosphorus) has
been studied via a compartment model allowing a variable biomass composition
to be represented as a function of the depletion of the different nutrients. The
mathematical model involves independent kinetic rates for proteins,