Spherical coordinates:The modeling of microalgal photosynthetic biomass production draws some support from the abundant literature on bioprocess modeling, in particular when mineral or CO 2 mass-transfer limitations on growth rates are considered in the same way as substrate and O 2 -transfer limitations in engineered bacterial cultivation. However, photosynthetic biomass growth exhibits highly specific features owing to its need for light energy: unlike dissolved nutrients, assumed to be homogeneous in well-mixed conditions, light energy is heterogeneously distributed in the culture due to absorption and scattering by cells, independently of the mixing conditions. As light is the principal energy source for photosynthesis, this heterogeneity alone sets microalgal cultivation systems apart from other classical bioprocesses, as they are generally limited by light transfer inside the culture media. Hence the design, optimization and control of photobioreactors (PBRs) require specific approaches.This chapter deals with developing useful knowledge models for engineering microalgal cultivation systems. Prerequisites and main concepts will be presented. Concrete illustrations will be given that use modeling to gain a deeper understanding of the complex influence of light transfer on the process, and to predict biomass productivities as a function of cultivation system engineering variables (especially depth of culture) and operating settings (residence time and incident light flux) in both artificial constant light and natural sunlight conditions. Theoretical background for radiation measurement and handling Main physical variablesGiven the crucial importance of radiative transfer description in photobioreactor modeling, it is essential to have a broad overview of the main physical quantities and definitions involved in radiation measurement and theory, together with a thorough knowledge of the conversion factors linking the two main practical systems of units (joules and micromoles of photons). There is often much confusion on these points in the microalgal growth modeling literature, conducive to misin-

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A microorganism culture process is a complex system in which physical operating parameters and biological responses strongly interact. Mathematical formulation and modelling of the different phenomena involved in the process...