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This paper deals with the control of a catalytic reverse flow reactor. The aim of this process is to reduce, by catalytic reaction, the amount of volatile organic compounds (VOCs) released into the atmosphere. The peculiarity of this process is that the gas flow inside the reactor is periodically reversed in order to trap the heat released during the reaction. This allows use of the reactor in a heat saving mode. The goal of this work is to provide a model predictive control (MPC) framework to significantly enhance the poor overall performance currently obtained through the actual control strategy. It is directly addressed for the nonlinear parabolic partial differential equations (PDEs) that describe the catalytic reverse flow reactor. In the context of the application of MPC to this particular distributed parameter system, we propose a method that aims to reduce the online computation time needed by the control algorithm. The nonlinear model is linearized around a given operating trajectory to obtain the model to be solved on-line in the approach. MPC strategy combined with internal model control (IMC) structure allows using less accurate and less time-consuming control algorithm. Method efficiency is illustrated in simulation for this single-input-single-output system.