Mixed ionic-electronic conducting (MIEC) membrane reactors are attractive for partial oxidation and oxidative coupling of methane (OCM) because of their ability to separate oxygen from air with a low energetic penalty, and introduce the oxygen into a reaction zone with spatial and temporal control. To facilitate design and optimization of such reactors, two numerical models for MIEC membrane reactors for methane reforming are introduced: a computationally inexpensive, coupled, two-chamber CSTR model, and a CFD model for reacting flow. The CFD model considers diffusive transport with a mixture averaged model, and was shown to agree well with previous experimental and modelling works. Both models utilize a detailed gas-phase chemical kinetic mechanism and a membrane oxygen permeation model that considers the local oxygen concentration. It is demonstrated that the CSTR model can be used to evaluate a large number of reactor parameters efficiently to identify optimal conditions for OCM. The most promising reactor operating points identified using the CSTR for a particular reactor size are further considered with spatial detail using the CFD model. It is shown that the coupling between oxygen permeation, gas phase chemical kinetics, and flow field can have a significant impact on the reactor performance. Here the flow direction in a typical button reactor was reversed, which resulted in a 40% increase in predicted C-2 yield. The increase is attributed to the shorter post-reaction residence time of the C-2 products in the reactor, thereby inhibiting deeper oxidation. This significant impact on the reactor performance can be utilized to improve the yield of partially oxidized products from membrane reactors. (C) 2018 Elsevier Ltd. All rights reserved.