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.