A model for incomplete mixing in a bioreactor
In many models for biological processes it is assumed that the reactor contents are well mixed. This assumption may be good if the reactor is small but for a large reactor this assumption is not so good. Here we analyse a model for a bioreactor with imperfect mixing. We use a two parameter mixing model in which the reactor is split into two compartments: a large compartment and a small compartment, with mixing between the two compartments. In each compartment there are two equations: one for the concentration of substrate and one for the concentration of microorganism. The interaction between the substrate and biomass is governed by Monod growth kinetics. We investigate how the effluent concentration leaving the reactor depends upon the degree of mixing in the reactor (δ) and the size of the small compartment (ε). The model has two limits. When delta is equal to zero there is no mixing between the compartments and when delta is equal to infinity we have perfect mixing. When delta is equal to zero the effluent concentration is higher than when delta is equal to infinity. It might be expected that as the value of delta increases from zero the effluent concentration decreases. However, for small values of delta the effluent concentration actually increases. Therefore, an important conclusion from this work is that a very small amount of mixing is actually worse than no mixing.