Calculation of optimal design and ideal productivities of volumetrically lightened photobioreactors using the constructal approach

This article examines the optimal design and ideal kinetic performances of volumetrically lightened photobioreactors (PBR). From knowledge models developed for several years by the author, simple theoretical rules are established at first to define the optimal functioning of solar and artificially lightened PBR. The constructal approach is then used accordingly, which allows the emergence of the optimal design, or the best lighting structures assembly, in Cartesian and curvilinear geometries, with a privileged treatment for the practical case of the 2D-cylindrical geometry. The obtained results confirm the considerable potential of this approach which is applied here for the first time to the case of the radiant light transfer in participating and reactive media. This enables to define clearly, from a theoretical point of view, the concept of ideal PBR (both for solar or artificial illuminations), which is demonstrated to correspond exactly in most cases to volumetrically lightened PBR, mainly for the solar DiCoFluV (Dilution Contrôlée du Flux en Volume) concept developed in this article. For this last case, the results of the calculations allow to announce maximal biomass productivities as thermodynamic limits, what can contribute to clarify a today confused debate on this point. The work proposed in this article finally establishes guidelines to conceive more efficient large-scale PBR of any desired geometry and criteria like volume (for artificial illumination) or surface (for solar illumination) maximum productivities and internal or external irradiation.