(362f) Surface and Fluid Phase Transport Effects on Hydrogen Permeability through Palladium-Based Membranes

Palladium and palladium alloy membranes are promising materials for hydrogen separations. These membranes can be reproducibly synthesized either as self supporting foils or thin films on supports, they have relatively high hydrogen fluxes, and are theoretically infinitely selective for hydrogen. Palladium alloy membranes can be applied for hydrogenation and dehydrogenation reactions, hydrogen purification, energy storage, and in fuel cells.

Hydrogen permeation through palladium-based membranes has been modeled using the solution-diffusion approach, in which the hydrogen molecules dissociatively adsorb on the metal surface, absorb into and diffuse through the bulk metal in atomic H form, and recombine and desorb as H₂ at the permeate side. When diffusion of hydrogen atoms through the bulk metal is the rate limiting step, hydrogen permeation flux at steady state, J (mol/m² s), can be described by Sieverts' Law:

where Q is the permeability of hydrogen through membrane (mol/m s Pa^0.5),  is the membrane thickness (m), and P_H2,f and P_H2,p are the feed and permeate side partial pressures of hydrogen, respectively. The derivation of Sieverts' Law also assumes that the surface coverage of H at both the feed and permeate sides of the membrane is in equilibrium with the respective fluid phases, and that the adsorption equilibrium constant is the same on both sides:

where C is the atomic hydrogen concentration on the palladium surface, K is the dissociative adsorption equilibrium constant and P_H2 is the hydrogen partial pressure. The 0.5 exponent comes from dissociative adsorption of a diatomic molecule, and this is where the square root comes from in the flux equation above. Sieverts' Law is widely applied in analyzing hydrogen permeation through Pd and Pd-based alloy membranes, even in some cases where the assumptions made in deriving Sieverts' Law are not valid.  The experimentally varied parameter is the exponent on the hydrogen partial pressure ? the closer this value is to 0.5, the better the membrane is said to behave as Sieverts' Law predicts.  In the literature, values of the exponent from 0.5 to over 1.1 can be found. We will address the sources of these erroneous exponential values through detailed modeling of transport (and reaction) of hydrogen in metal membrane systems.

In cases of hydrogen purification or separation from other gases, concentration polarization can occur in the feed, and hydrogen transport through this fluid film can be rate limiting.  Alternatively, for thin supported metal membranes, transport in the support can provide a significant resistance.  The metal surfaces can be contaminated or metals of the alloy can be segregated, possibly resulting in the assumption of adsorption equilibrium at either side being invalid.  Furthermore, when metal membranes are used in catalytic reactors, surface reactions can potentially be rate limiting.  Even if transport of hydrogen through the bulk is the rate limiting step, sufficiently high pressure can result in Sieverts' Law being invalid.  We have modeled transport of hydrogen in metal membranes considering these and other possible rate limiting steps to systematically assess these effects on hydrogen permeation through metal membranes under non-Sieverts' Law conditions.  Hydrogen permeation at 423-573 K through 25 Pd and Pd-25wt%Ag foils was measured from pure H₂ and H₂/He mixture feeds, with and without He sweep gas.  Transport in the fluid phases was modeled using the Maxwell-Stefan formulation.  The effects of each poor assumption on the value of the exponent determined if Sieverts' Law were to be applied will be summarized and explained.