The steady-state treatment of industrial wastewaters in a cascade reactor with recycle is analyzed. A number of cascades with alternative arrangements of the settling units are considered. Specifically, we consider the case when the recycle stream leaving a settling unit which is placed around a reactor goes back into the feed stream for that reactor. The Contois kinetic model is used to study the degradation of biodegradable organic materials.
The steady-states for the model are found and their stability determined as a function of the total residence time in the cascade. Asymptotic solutions in the limit of large total residence time are obtained for the effluent concentration leaving a cascade. This analysis is used to determine the reactor configuration that minimizes the effluent concentration leaving the final reactor.
It is found that, when settling units are deployed, the optimised reactor cascade is obtained by using perfect recycle around the final reactor and imperfect recycle around the preceding reactors. When only one settling unit is used we find the performance of the reactor cascade is optimized at short residence times by placing it around the first reactor whilst at large total residence times the performance is optimized by placing it around the final reactor. However, at sufficiently large total residence times there is a little benefit gained by using any settling units.