A Mechanistic Derivation of The Monod Equation For Biofilm in Porous Media

Abstract

A mechanistic derivation of the Monod bioreaction equation is presented. The numerical model developed for this derivation involves four processes. 1)On the pore scale, substrate diffuses from the bulk aqueous phase crossing a diffusion boundary layer to the stationary biofilm. 2) On the biofilm scale, the substrate concentration is uniform in the Extracellular Polymeric Substance (EPS) matrix, which equals to that at the biofilm surface. 3) On the microscale, substrates diffuse from the EPS matrix through the EPS layer towards each spherical bacterial cell. 4) Then substrates transport across the cell membrane and react within the microbe for biological reactions. In this numerical model, the derivation incorporates growth kinetics for the bacterial cells and production kinetics for the EPS. The evolution of biofilms and mass transfer processes are simulated under nutrient-limiting and laminar flow conditions. Model parameter sensitivity is examined using data from Reardon et al. (2000), indicating that the diffusive transport of substrate from the aqueous phase to the biofilm is not the most limiting process.