We analyse the steady-state treatment of industrial wastewaters in a continuous flow bioreactor and in an idealised continuous flow membrane reactor. The reaction is assumed to be governed by Contois growth kinetics, which is often used to model the growth of biomass in wastewaters containing biodegradable organic materials. We show that a flow reactor with idealised recycle has the same performance as an idealised membrane reactor and that the performance of a non-idealised membrane reactor is identical to an appropriately defined continuous flow bioreactor with non-idealised recycle. The performance of all three reactor types can therefore be obtained by analysing a flow reactor with recycle. The steady-states of the model are found and their stability determined as a function of the residence time. The performance of the reactor at large residence times is obtained. In the limit as the residence time becomes very large, all three reactor configurations have identical performances. Thus the main advantage of using a membrane reactor, or a flow reactor with recycle, for the treatment of industrial wastewaters and slurries is to improve the performance at low residence times.
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