A two-dimensional (2D) model of a packed-bed membrane reactor was developed to describe ethylene production by oxidative coupling of methane (OCM). The model covers all relevant energy and mass transport processes in the reactor and allows a more precise prediction of the temperature and conversion patterns. It is demonstrated that the fast OCM reaction leads to oxygen depletion in the vicinity of the membrane, causing strong radial concentration gradients in the bed. Further results indicate that the detailed 2D model can provide more accurate predictions of experimental data than the simplified one.