We are developping a new reactor model able to perform catalytic activation and separation simultaneously : the catalytic membrane reactor. This paper analyses the influence of gas diffusion through the membrane on mass transfer in the catalytic reactor with an inert membrane wall. A mathematical description of these reactors often leads to partial differential equations (PDE) with complex boundary conditions. Two efficient techniques are used to solve these equations. The method implies an orthogonal collocation on finite elements in the spacial dimension followed by a global orthogonal collocation. Theoretical comparisons are made between the concentration profiles in the radial direction obtained for both reactors. The effect of radial dispersion on the performance of the inert membrane reactor is examined. The applicability of approximate methods for membrane transport model is also discussed.