Membrane reactors are inherently two-dimensional systems that require complex models for an accurate description of the different transport phenomena involved. However, when their performance is limited by mass transport within the reactor rather than by the selective product permeation across the membrane, the 2D model may be significantly simplified. Here we extend results previously found for methane steam reforming membrane reactors to show that such simplified two-dimensional model admits either a straightforward analytical solution for the cross-section averaged concentration profile, or can be reduced to a 1D model with an enhanced Sherwood number, depending on the stoichiometry of the reaction considered. Interestingly, the stoichiometry does not affect the expression of the enhanced Sherwood number, indicating that a versatile tool has been developed for the determination of membrane reactor performance at an extremely low computational cost and good degree of accuracy.
Keywords: Sherwood number; hydrogen; mass transport; membrane reactor; propane dehydrogenation.