This paper models the performance of a membrane reactor. The membrane, a composite alumina-based one, is packed with a catalyst and allows low molecular weight gases to diffuse through it at a faster rate than gases with a higher molecular weight. This allows a greater conversion to be achieved in one pass through the reactor. The reaction that is specifically considered in this paper is the dehydrogenation of methyl-cyclohexane to toluene with the production of hydrogen. This latter species is preferentially removed by the membrane. Data for the performance of the membrane have been estimated from previous experiments using single gases and the mechanisms considered are Knudsen and bulk flow. Surface flow is not considered in the model as it is possibly not important as the endothermic reaction is carried out at a high temperature. A standard kinetic model is also incorporated in the calculations. The correlations of maximum effective length of membrane reactors and maximum percentage conversion as functions of the feed velocity and the membrane diameter are demonstrated in this paper. This paper also considers the behaviour of a compound reactor in which the first section is a straightforward ‘plug flow’ reactor where the catalyst is confined in an impermeable tube with the same internal diameter as the membrane. This is followed by a section containing the membrane. The reason for considering this configuration is to avoid unnecessary leakage of methyl-cyclohexane feed in the initial stages of the reaction. This innovation leads to predicted increases in the overall conversion of the process.