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.