The combustion of lean methane air mixtures in a catalytic flow reversal reactor (CFRR) is studied using a two dimensional heterogeneous continuum model, based on mole and energy balance equations for the solid (the inert and catalytic sections of the reactor) and the fluid phases. Following a design of experiments (DOE), many simulations were carried out to investigate the reactor performance. The results show the impact on the methane conversion and the maximum temperature in the reactor of key process parameters such as the methane inlet concentration, the superficial gas velocity, the switching time, and the mass extraction rate. A simple empirical model is deduced to predict the maximum temperature and conversion of methane in the reactor at stationary state. This model is combined with a model predictive control (MPC) strategy in the form of a terminal constraint to improve the controller performance. Results show that the control of the reactor is improved.