In this report we use a system of two first order non-linear differential equations to model the behaviour of a bioreactor. In this process a micro-organism (X) is used to purify polluted water by consuming a substrate, or nutrient (S), to produce more cells until the substrate has been removed. This report uses methods of steady-state analysis including stability of steady-states and what conditions need to satisfied to attain stability.
This model has many applications including experiments on microbial growth in a flow reactor. Particularly in the food industry, in which slurries or wastewaters in which high concentrations of biodegradable materials are produced. These include effluent from the following process examined by earlier researchers