This work reports the development of a nonisothermal and nonadiabatic pseudo-homogeneous model to study a completely back-mixed membrane reactor with a polymeric catalytic membrane, for conducting the consecutive hydrogenation of propyne to propene and then to propane. The performance of the reactor is analyzed in terms of the propyne concentration in the permeate stream (the only outlet stream from the reactor), the conversion of propyne and hydrogen, and the selectivity and overall yield to the intermediate product propene. The operating and system parameters considered are the Thiele modulus, the dimensionless contact time, the Stanton number, and the effective hydrogen sorption and diffusion coefficients. To define the regions where the catalytic membrane reactor may perform better than a conventional reactor, a comparison between both reactors is made. For the range of parameter values considered, the reactor model in this study demonstrates that the catalytic membrane reactor performs better than the conventional catalytic reactor in some regions of the Thiele modulus parametric space, for medium to high Stanton number values and for the total flow-through configuration (total permeation condition). Concerning the effective sorption and diffusion coefficients of hydrogen, they shall be higher than the ones of the hydrocarbons.