Advection–diffusion constrained metabolic reaction in bioreactor analysis for hydrogen production

The reaction advection–diffusion equation (RADE) is proposed to describe the dynamic processes in a heterogeneous biochemical system involved in hydrogen production in a photobioreactor. The spatial- and temporal-dependent concentration functions of metabolites in the differential equation are assumed as a multiplication of the spatial-dependent function and the temporal-dependent function such that RADE can be uncoupled into spatial-dependent advection–diffusion equation and the kinetics equation. The advection–diffusion equation along with the boundary conditions of the photobioreactor acts as a constraint in solving the kinetics equation. Such a decomposition leads to an approximate analytical solution of the advection–diffusion equation for a batch mode tubular photoreactor under solar radiation. As a constraint, the analytical solution of the advection–diffusion equation is then introduced into the kinetics equation to obtain the dynamics of the concentration of metabolites in an inhomogeneity system. The dynamics of the biochemical processes in a photobioreactor, as an example, was studied and the production of H2 at the mesh grids was calculated for 250 h operation under solar radiation. The results demonstrate the variation of H2 in both the radial and the angular directions with time. The perturbed dynamics of hydrogen production is consistent in trend with the available experimental observations of H2 production in outdoor photobioreactors.