Anaerobic fermentation is routinely used for the treatment of both industrial and municipal wastewater. Although the overall process contains multiple steps in series and parallel, involving diverse groups of microorganisms, three stages are recognized as being important. In the first stage organic particulates are hydrolysed. In the second stage, the products of the first stage are converted into volatile fatty acids. In the final stage volatile fatty acids are converted methane.

Many authors have modeled this process under the assumption that the reactor is well mixed. We investigate the effect of incomplete mixing upon the performance of a membrane-coupled anaerobic fermentor. To do this we combine a literature model for this process, consisting of six differential equations, modeling the concentration of five biochemical species and the gasification rate, with a two parameter incomplete mixing model.

In the incomplete mixing model the membrane bioreactor is split into two compartments: a larger and a smaller compartment. The latter representing a stagnant region. The incomplete mixing parameters are the size of the stagnant region (epsilon) and a parameter controlling the degree of mixing between the regions (delta). In the limit that delta approaches zero epsilon becomes a dead volume in the reactor.
Perfect mixing corresponds to the limit in which delta approaches infinity. There are six differential equations in each reactor.
We investigate how the recovery ratio of volatile fatty acids depends upon the degree of mixing in the reactor and the size of the stagnant compartment.