Model of hydrogen permeation behavior in palladium membranes

A model has been constructed for H₂ permeation through Pd which accounts for external mass transfer, surface adsorption and desorption, transitions to and from the bulk metal, and diffusion within the metal. Reasonable values for all rate parameters have been estimated based on surface science and membrane literature. In the absence of external mass transfer resistance, nearly diffusion-limited permeation is expected for clean Pd for temperatures above approximately 573 K and membrane thicknesses down to 1 μm. Low-temperature permeation is limited by desorption while adsorption is only expected to impact permeation at very low upstream H₂ partial pressures, or under conditions of substantially reduced sticking due to surface contamination. The efficiency of external gas-phase mass transfer is a critical element in permeation flux and apparent Sievert's law behavior for Pd membranes approaching 10 μm and thinner, especially at low H₂ partial pressures or when a porous support is present. Comparison of the calculations with literature results for Pd membranes less than 10 μm thick reveals that permeation rates well below those expected are often observed, indicating the importance of factors related to fabrication methods, such as film microstructure, grain size, and surface or grain boundary contamination.