The oxidative coupling of methane (OCM) reaction system was investigated in a packed-bed membrane reactor (PBMR) numerically via a comprehensive computational fluid dynamics (CFD) study. In this context, the complete set of momentum, mass, and energy balances were solved through finite-volume method in cylindrical coordinate system. The fractional-step method was utilized to decouple the reaction source terms from the convection-diffusion terms. The general observed trends for variation of the components' concentrations along the bed were successfully explained by analyzing the rate of reactions. In this study, the effect of membrane thermal conductivity, and oxygen permeation were also examined which can affect the OCM reactor and process performance significantly. Finally, the dynamics behavior of the system was studied and by following the reaction rates and the shift of reactions along the catalytic-bed and with time, the reaction mechanisms were discerned. The results of the performed CFD simulation can be used as a baseline for a possible optimization approach for OCM reactor performance improvement.