Beyond Sieverts' law: A comprehensive microkinetic model of hydrogen permeation in dense metal membranes

Abstract

There is much ongoing research on developing dense metal membranes based on palladium and its alloys for producing high purity hydrogen, e.g., for fuel cells. Such membranes are almost exclusively permeable to hydrogen in a feed gas mixture via the following steps: (s1) dissociative adsorption on the surface; (s2) sub-surface dissolution; (s3) diffusion of interstitial hydrogen atoms within the bulk metal matrix; (s4) evolution from the bulk metal to its permeate side surface; and finally, (s5) associative desorption of hydrogen. The flux is commonly described by the so-called “Sieverts' law,” which expresses the flux as a membrane permeance times the difference in square root of hydrogen pressure on the feed side and that on the permeate side. It is derived by assuming that diffusion (step s3) is controlling, and hydrogen concentration in metal is low, which strictly limits its applicability to relatively high temperatures, thick membranes, and low hydrogen pressures. We describe a comprehensive microkinetic model that includes all five steps, and is shown to be suitable for Pd over a broad range of conditions. It also describes non-ideal hydrogen solution due to phase-transition in Pd, which explains the sharp peak at intermediate temperatures in hydrogen flux observed experimentally, but not so far explained theoretically. The model includes effect of metal surface roughness, not commonly considered so far. Use of an electrical analogy and comparison of step resistances allows a reduction to a three-step (adsorption, diffusion, and desorption control) model that also adequately describes hydrogen permeation over a broad range of conditions.