A mathematical model for a catalytic membrane reactor for oxidative coupling of methane (OCM), in which the membrane acts as an oxygen distributor to a bed of catalyst, is presented. From experimental data obtained using several silica membranes impregnated with Li and/or Na, which were prepared by the sol-gel method using alumina supports, the catalytic activity of the membrane was included in the so-called real membrane reactor (RMR) model. Then, the RMR performance was compared with that of the ideal membrane reactor (IMR), whose membrane was supposed to have no activity for the OCM and with experimental data obtained in membrane reactors. Since the membrane activity was implemented in the RMR model, for the first time in the literature, maxima in the hydrocarbon selectivity-methane conversion curves were predicted in agreement with previous experimental trends. Besides, the IMR performance was compared with that of the fixed-bed reactor (FBR), giving the maximum improvement of a membrane reactor over the FBR. Key factors for the future improvement of the performance in this kind of membrane reactor are deduced from these simulations.