A PDE-ODE Coupled Model for Biofilm Growth in Porous Media That Accounts for Longitudinal Diffusion and Its Effect on Substrate Degradation

We derive a one-dimensional macroscopic model for biofilm formation in a porous medium reactor to investigate the role of longitudinal diffusion of substrate and suspended bacteria on reactor performance. By comparing an existing base model—one without longitudinal diffusion, which was the point of departure for our work, to the new model—we noticed significant changes in system dynamics. Our results suggest that neglecting it can lead to underestimation of quenching length and biofilm accumulation downstream, even in the advection-dominated regime. The effects of attachment and detachment of suspended bacteria on biofilm formation and substrate degradation were also examined. In the one-dimensional model, it was found that attachment has a stronger influence on substrate depletion, which becomes more pronounced as diffusion in the pore space increases.