Hydrodynamics influence on light conversion in photobioreactors: An energetically consistent analysis

Hydrodynamics conditions are supposed to affect light conversion in photobioreactors (PBRs), by modifying light availability of suspended photosynthetic cells. The present study aims at rigorously analyzing mixing conditions influence on PBR efficiency. Investigation is based on a Lagrangian formulation, which is well adapted to characterize individual cell history. Its association with a radiative-transfer model to characterize light availability is emphasized.Such approach has already been applied in PBR modeling, but with an over-simplified formulation where both cell trajectories and radiative transfer were solved independently. As energetic balances on the material and photonic phases will show, it is however necessary to introduce influence of the heterogeneous light access implied by non-ideal mixing conditions in the non-linear radiation field resolution.The proposed energetically consistent Lagrangian method will be finally associated to a standard photosynthetic growth model to simulate batch cultivation in a torus PBR, retained here as a practical example. Although hydrodynamics will be introduced in the calculation, simulations will show that, without a dynamic interaction between photosynthetic conversion and fluctuating light regimes implied by cell movement along light gradient (the so-called light/dark cycles effects), PBR efficiency for a given species is only dependent on the light input and reactor geometry, according to the first principle of thermodynamics.