Oxidative coupling of methane in a solid oxide fuel cell with 1 wt% Sr/La2O3-Bi2O3-Ag-YSZ (yttria stabilized zirconia) membrane was studied by the two mathematical models based on well mixed flow (CSTM) or plug Bow (PFM). The model predictions were in good agreement with the experimental results. The performance of the solid oxide fuel cell was evaluated by investigating the effect of reaction conditions and the degree of back mixing,