Many industrial processes produce wastewater containing pollutants, the concentration of which must be reduced before the wastewater can be discharged. One way to do this is through the use of a biological species (`biomass') that consumes the pollutant (`substrate'). In a membrane bioreactor the biomass is constrained to remain within the reactor whereas the feed stream flows through it.
We investigate the behaviour of a reaction governed by Contois growth kinetics in both single and double membrane reactor configurations. The optimal performance of both configurations is determined and compared. It is found that in many cases the cascade reactor may outperform the single reactor by two orders of magnitude.