A simplified model for the steady-state biofilm-activated sludge reactor

A simplified mathematical model is proposed to describe the steady-state completely mixed biofilm-activated sludge reactor (hybrid reactor). The model is derived based on Monod kinetic expressions and the Fickian diffusion law in biofilm. In addition, it considers all the essential concepts that describe the two types of growth (suspended and attached) and the competition between them for limiting substrate. Also the present study has been extended to investigate simple and accurate mathematical expressions for describing the substrate diffusion in biofilm (J). The expression for substrate flux has an explicit solution, which may be useful in the proposed model and many other applications. The application of the model for the hybrid system has been explained for a given set of data and verified by comparison with another solution. Also the model was applied to experimental results for a trace level of suspended biomass concentration (X). It was found that the biofilm flux (J) is the key factor in the model prediction, hence the accuracy of the model output is influenced by the accuracy of J. Compared with other solutions for such systems the model is simple, easy to use, and provides an accurate tool for describing such systems based on fundamental principles.