The light attenuation in a photobioreactor is determined using a fully predictive model. The optical properties were first calculated, using a data bank of the literature, from only the knowledge of pigments content, shape, and size distributions of cultivated cells which are a function of the physiology of the current species. The radiative properties of the biological turbid medium were then deduced using the exact Lorenz-Mie theory. This method is experimentally validated using a large-size integrating sphere photometer. The radiative properties are then used in a rectangular, one-dimensional two-flux model to predict radiant light attenuation in a photobioreactor, considering a quasi-collimated field of irradiance. Combination of this radiative model with the predictive determination of optical properties is finally validated by in situ measurement of attenuation profiles in a torus photobioreactor cultivating the microalgae Chlamydomonas reinhardtii, after a complete and proper characterization of the incident light flux provided by the experimental set-up.

This article establishes and discusses the consistency and the range of applicability of a simple but general and predictive analytical formula, enabling to easily assess the maximum volumetric biomass growth rates (the productivities) in several kinds of photobioreactors with more or less 15% of deviation. Experimental validations are performed on photobioreactors of very different conceptions and designs, cultivating the cyanobacterium Arthrospira platensis, on a wide range of volumes and hemispherical incident light fluxes. The practical usefulness of the proposed formula is demonstrated by the fact that it appears completely independent of the characteristics of the material phase (as the type of reactor, the kind of mixing, the biomass concentration...), according to the first principle of thermodynamics and to the Gauss-Ostrogradsky theorem. Its ability to give the maximum (only) kinetic performance of photobioreactors cultivating many different photoautotrophic strains (cyanobacteria, green algae, eukaryotic microalgae) is theoretically discussed but experimental results are reported to a future work of the authors or to any other contribution arising from the scientific community working in the field of photobioreactor engineering and potentially interested by this approach.

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