We consider a model to describe the performance of a membrane-coupled anaerobic fermentor which was developed and calibrated using experimental data by Kim and Chung (2010). The model consists of six differential equations, modelling the concentration of five biochemical species and the rate of gasification. In the original work it was assumed that reactor is well-mixed. We use a two parameter mixing model to investigate the effect of incomplete mixing upon the performance of this process. The parameters in the mixing mode are the size of the stagnant region and a parameter controlling the degree of mixing between the regions. Perfect mixing corresponds to the limit in which delta approaches infinity. There are six differential equations in each region. We investigate how the concentration of volatile fatty acids in the agitated region depends upon the degree of mixing in the reactor and the size of the stagnant region.