Modeling integrated fixed-film activated sludge and moving-bed biofilm reactor systems I: Mathematical treatment and model development

A mathematical model for integrated fixed-film activated sludge (IFAS) and moving-bed biofilm reactor wastewater treatment processes was developed. The model is based on theoretical considerations that include simultaneous diffusion and Monod-type reaction kinetics inside the biofilm, competition between aerobic autotrophic nitrifiers, non-methanol-degrading facultative heterotrophs, methanol-degrading heterotrophs, slowly biodegradable chemical oxygen demand, and inert biomass for substrate (when appropriate) and space inside the biofilm; and biofilm and suspended biomass compartments, which compete for both the electron donor and electron acceptor. The model assumes identical reaction kinetics for bacteria within suspended biomass and biofilm. Analytical solutions to a 1-dimensional biofilm (assuming both zero- and first-order kinetics) applied to describe substrate flux across the biofilm surface are integrated with a revised and expanded matrix similar to that presented as the International Water Association (London, United Kingdom) Activated Sludge Model Number 2d (ASM2d) stoichiometric and kinetic matrix. The steady-state mathematical model describes a continuous-flow stirred-tank reactor.