This paper aims at investigating the performance of a cylindrical ion transport reactor designed for oxy-fuel combustion. The cylindrical reactor walls are made of dense, nonporous, mixed-conducting ceramic membranes that only allow oxygen permeation from the outside air into the combustion chamber. The sweep gas (CO2 and CH4) enters the reactor from one side and mixes with the oxygen permeate, and the products are discharged from the other side. The process of oxygen permeation through the reactor walls is influenced by the flow condition and composition of air at the feed side (inlet air side) and the gas mixture at the permeate side (sweep gas side). The modeling of the flow process is based on the numerical solution of the conservation equations of mass, momentum, energy, and species in the axisymmetric flow domain. The membrane is modeled as a selective layer in which the oxygen permeation depends on the prevailing temperatures as well as the oxygen partial pressure at both sides of the membrane. The CFD calculations were carried out using fluent 12.1 (ANSYS, Inc., Canonsburg, PA, USA), whereas the mass transfer of oxygen through the membrane is modeled by a set of user defined functions. The model results were validated against previous experimental data, and the comparison showed a good agreement. The study focused on the effect of oxygen partial pressure and temperature on the resulting combustion zones inside the reactor for the two cases of co-current and counter-current flow regimes. The results indicated that the oxygen to fuel mass ratio increases as the percentage of CO2 increases in the inflow sweep gas for both co-current and counter-current flows. The obtained sweep mixture ratio (CO2/CH4) of 24 is found within the stoichiometric limit over most of the reactor length in the co-current configuration, whereas the sweep mixture ratio of 15.67 is found in the counter-current configuration owing to the high O-2 permeation. Copyright (c) 2012 John Wiley & Sons, Ltd.