The dispersed flow model for a biological reactor as applied to the activated sludge process

A theoretical analysis of a dispersed flow biological reactor is presented in which Monod growth kinetics are used to describe the substrate utilization rate and the bacterial growth rate. Different bacterial and substrate dispersion coefficients are taken into account. Approximate perturbation solutions are established for two limiting situations, when the inverse Peclet number ϵ is very small and when it is very large. In the former case the perturbation analysis is singular. These perturbation solutions are compared with the solutions of the numerically integrated equations over a range of parameters corresponding to actual activated sludge systems. The application to the activated sludge system is discussed.