A mathematical and empirical model of the performance of a membrane-coupled anaerobic fermentor.

A mathematical model was developed to describe the performance of a membrane-coupled anaerobic fermentor (MCAF)-based process. In our experimental results, higher volatile fatty acid (VFA) recovery ratios were obtained at greater filtration ratios. The VFA recovery ratio peaked at an HRT of 12 h and a membrane filtration ratio of 0.95 at a constant SRT. Based on our simulation, the HRT and filtration ratio should be maintained at less than 1 day and above 0.9, respectively, to exceed an organic materials recovery ratio of 35% at a constant SRT of 10 days. Our empirical model, which predicts the effluent VFA concentration (C(o)), described the performance of the MCAF adequately. The model demonstrated that the outlet VFA concentration was a function of three independent parameters -HLR, input organic concentration (C(i)) and membrane filtration ratio (Φ). Multiple regression analyses were conducted using 50 measurements of the MCAF, yielding the following relationship: C(o) = 0.278Φ(1.13) C(i) (1.93) HLR(0.11). The correlation coefficient (R(2)) was 0.90. The simulation results were consistent with the observed data; therefore, due to its simplicity, this model predicts the effluent VFA concentration of an MCAF adequately.