Transport-permeation regimes in an annular membrane separator for hydrogen purification

A transport model is proposed, accounting for full coupling between mass and momentum transport, for a H2/CO2 mixture entering a packed-bed annular volume in the presence of a hydrogen permeable membrane whose permeation process is governed by Sieverts' law. As a consequence of mass/momentum coupling, radial convective fluxes typically arise, which, in turn, impact upon the fine structure of radial concentration profiles of the species. As overall indicators of equipment performance, we target the total hydrogen permeate flowrate and recovery, and investigate their dependence on the operating pressure while keeping inlet gas velocity constant. We show that the permeate dependence on pressure displays a sharp cross-over between a transport-limited linear regime and a square-root membrane-limited regime, ultimately ensuing from Sieverts' law. Based on the closed-form solutions of simplified equations describing the two limiting regimes, a complete analytical prediction of the permeate on the operating pressure is developed. An important fallout of this approach is the identification of a critical pressure which yields optimal operating conditions, allowing the largest hydrogen production compatible with sustained values of the recovery at fixed gas velocity. The closed-form prediction of the permeate flowrate is tested in a range of parameters that mimic a wide variety of operating conditions, from millimeter-scale laboratory prototypes up to parameter values pertaining to full scale industrial equipment. Comparison of model predictions vs. experimentally determined values of the recovery available in the literature proves the fitness of the analytical prediction to industrially relevant process conditions. The same approach developed here can be used with minor modifications in all of the cases where the permeation flux through the membrane can be modeled by a power-law expression characterized by an exponent strictly lower than unity.