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separates stoichiometric analysis of the metabolic conversions and the establishment of reaction kinetic laws; the specific problem of radiative transfer is
examined independently.
In the second section, the various classes of models are presented for the
stoichiometric characterization of the main metabolic events that have to be
considered for growth. The third section presents light energy diffusion models
of varying mathematical complexities from the simple Lambert-Beer model to
sophisticated gridding techniques. The effect of mineral limitations (nitrogen,
sulphur and phosphorus) on Spirulina growth, including their influence on
synthesis rates and resulting biomass composition, is examined in the fourth
section. Various classes of physical or physiological limitations by the carbon
source are presented in the fifth section. The sixth section describes a more
refined technique of modeling growth that uses a biochemically structured
model that affords a comprehensive representation of yields and rates of growth
vs various light energy inputs and nutrient limitations. Finally, the thermodynamic efficiency for the light energy conversion process in photobioreactors is
defined and calculated.
2 Modeling Photobioreactors: Application to Growth
of Spirulina platensis
2.1 General Approach of Modeling Photobioreactors
Mathematical modeling of the growth kinetics of a photosynthetic microorganism can be performed using the general approach for characterizing
submerged cultures of micro-organisms. Formally, the macroscopic description
of the culture, i.e. the mathematical representation of the state variables involves
simultaneous handling of two types of mechanisms.
- physiological behavior including characterization of metabolic activity,
determination of bioreaction stoichiometries, and the establishment of kinetic
laws for the conversion of substrates into biomass or products;
- physical controlling steps including gas liquid transfer rates, mixing characteristics of the bioreactors, thermodynamic equilibria and the light energy
transfer characterization.
The physical characterization of the light energy transfer throughout the
liquid volume of a photobioreactor is clearly vital for proper understanding of
the rate controlling processes and must be carefully described. However, the
final mathematical model of the photobioreactor is formed by the association of
the transport phenomena models with the micro-kinetics of biological conversions.
Thus kinetic modeling of the metabolic activity must be performed in such
a way that it can be coupled to the physical rate-controlling process of light
J.-F. Cornet et al.
separates stoichiometric analysis of the metabolic conversions and the establishment of reaction kinetic laws; the specific problem of radiative transfer is
examined independently.
In the second section, the various classes of models are presented for the
stoichiometric characterization of the main metabolic events that have to be
considered for growth. The third section presents light energy diffusion models
of varying mathematical complexities from the simple Lambert-Beer model to
sophisticated gridding techniques. The effect of mineral limitations (nitrogen,
sulphur and phosphorus) on Spirulina growth, including their influence on
synthesis rates and resulting biomass composition, is examined in the fourth
section. Various classes of physical or physiological limitations by the carbon
source are presented in the fifth section. The sixth section describes a more
refined technique of modeling growth that uses a biochemically structured
model that affords a comprehensive representation of yields and rates of growth
vs various light energy inputs and nutrient limitations. Finally, the thermodynamic efficiency for the light energy conversion process in photobioreactors is
defined and calculated.
2 Modeling Photobioreactors: Application to Growth
of Spirulina platensis
2.1 General Approach of Modeling Photobioreactors
Mathematical modeling of the growth kinetics of a photosynthetic microorganism can be performed using the general approach for characterizing
submerged cultures of micro-organisms. Formally, the macroscopic description
of the culture, i.e. the mathematical representation of the state variables involves
simultaneous handling of two types of mechanisms.
- physiological behavior including characterization of metabolic activity,
determination of bioreaction stoichiometries, and the establishment of kinetic
laws for the conversion of substrates into biomass or products;
- physical controlling steps including gas liquid transfer rates, mixing characteristics of the bioreactors, thermodynamic equilibria and the light energy
transfer characterization.
The physical characterization of the light energy transfer throughout the
liquid volume of a photobioreactor is clearly vital for proper understanding of
the rate controlling processes and must be carefully described. However, the
final mathematical model of the photobioreactor is formed by the association of
the transport phenomena models with the micro-kinetics of biological conversions.
Thus kinetic modeling of the metabolic activity must be performed in such
a way that it can be coupled to the physical rate-controlling process of light