Mathematical Model for the Biofilm–Activated Sludge Reactor

Abstract

A steady state mathematical model is developed for describing the completely mixed biofilm–activated sludge reactor (hybrid reactor). The model is derived by simultaneously considering Monod kinetics expressions and Fickian’s diffusion theory for substrate in biofilm. In addition, it includes the basic concepts, which describe both culture (suspended and attached) and the competition between them for limiting substrate. By using this model the suspended biomass concentration can be obtained for this system. Subsequently, the other remaining parameters of the system can be computed. Therefore it helps to design and operate the hybrid reactor under different conditions for any given set of kinetic parameters. The utility of the model has been explained for a given set of data and verified by comparing with another solution. It is found that for the same set of data, the model is accurate in the results. The model has been presented in more than one form, each form having an explicit solution of the system. Compared with other solutions of such a system, the model provides a good tool for describing such a system based on fundamental principles.