In this contribution, the operation of a membrane reactor network (MRN) for the oxidative coupling of methane is optimized. Therefore, three reactors, a fixed bed reactor (FBR) and two packed bed-membrane reactors, are modeled. For the (CPBMR), a two-dimensional (2-D) model is presented. This model incorporates radial diffusion and thermal conduction. In addition, two 10 cm long cooling segments for the CPBMR are implemented based on the idea of a fixed cooling temperature positioned outside the reactor shell. The model is discretized using a newly developed 2-D orthogonal collocation on finite elements with a combination of Hermite for the radial and Lagrangian polynomials for the axial coordinate. Membrane thickness, feed compositions, temperatures at the inlet and for the cooling, diameters, and the amount of inert packing in the reactors are considered as decision variables. The optimization results in C-2 yields of up to 40% with a selectivity in C-2 products of more than 60%. The MRN consisting of an additional packed-bed membrane reactor with an alternative feeding policy and a FBR shows a lower yield than the individual CPBMR. (c) 2013 American Institute of Chemical Engineers AIChE J, 60: 170-180, 2014