A simplified monodimensional approach for modeling coupling between radiant light transfer and growth kinetics in photobioreactors

Local information is essential to photobioreactor modeling because of medium anisotropy in radiant light energy. Local available energy can be calculated using complex equations, applying the physical laws of radiative transfer and independently accounting for light absorption and scattering in the reactor. In this paper, these equations are simplified postulating monodimensional approximation for the radiation field. This simplification is established for rectangular, cylindrical and spherical coordinates, leading to simple analytical solutions for available radiant energy profiles inside the reactor. This approach provides a method of determining working illuminated volume defined as the photobioreactor volume with sufficient radiant light energy for microorganism growth. This enables the coupling between radiant light transfer and growth kinetics to be easily studied. Physical light transfer models are used to simulate volumetric biomass growth rates in a cylindrical photobioreactor with kinetic parameters obtained from batch cultures of the cyanobacterium Spirulina platensis in rectangular photoreactors. These calculations are compared with experimental data obtained on continuous cultures in a wide range of incident radiant energy fluxes. The model is found to have a good predictability and robustness.