Assessment of Sieverts Law Assumptions and ‘n’ Values in Palladium Membranes: Experimental and Theoretical Analyses

Abstract

Palladium and palladium alloy membranes are superior materials for hydrogen purification, removal, or reaction processes. Sieverts’ Law suggests that the flux of hydrogen through such membranes is proportional to the difference between the feed and permeate side partial pressures, each raised to the 0.5 power (n = 0.5). Sieverts’ Law is widely applied in analyzing the steady state hydrogen permeation through Pd-based membranes, even in some cases where the assumptions made in deriving Sieverts’ Law do not apply. Often permeation data are fit to the model allowing the pressure exponent (n) to vary. This study experimentally assessed the validity of Sieverts’ Law as hydrogen was separated from other gases and theoretically modelled the effects of pressure and temperature on the assumptions and hence the accuracy of the 0.5-power law even with pure hydrogen feed. Hydrogen fluxes through Pd and Pd-Ag alloy foils from feed mixtures (5–83% helium in hydrogen; 473–573 K; with and without a sweep gas) were measured to study the effect of concentration polarization (CP) on hydrogen permeance and the applicability of Sieverts’ Law under such conditions. Concentration polarization was found to dominate hydrogen transport under some experimental conditions, particularly when feed concentrations of hydrogen were low. All mixture feed experiments showed deviation from Sieverts’ Law. For example, the hydrogen flux through Pd foil was found to be proportional to the partial pressure difference (n ≈ 1) rather than being proportional to the difference in the square root of the partial pressures (n = 0.5), as suggested by Sieverts’ Law, indicating the high degree of concentration polarization. A theoretical model accounting for Langmuir adsorption with temperature dependent adsorption equilibrium coefficient was made and used to assess the effect of varying feed pressure from 1–136 atm at fixed temperature, and of varying temperature from 298 to 1273 K at fixed pressure. Adsorption effects, which dominate at high pressure and at low temperature, result in pressure exponents (n) values less than 0.5. With better understanding of the transport steps, a qualitative analysis of literature (n) values of 0.5, 0.5 < n < 1, and n > 1, was conducted suggesting the role of each condition or step on the hydrogen transport based on the empirically fit exponent value.

Study of Static and Dynamic Behavior of a Membrane Reactor for Hydrogen Production

“…Sieverts Law is widely applied in analyzing the steady state hydrogen permeation through Pd-based membranes. Alraeesi and Gardner [24], for instance, have assessed the validity of this law and modelled the effects of pressure and temperature on the accuracy of this power law.…”

On the Potential of Gallium- and Indium-Based Liquid Metal Membranes for Hydrogen Separation

“…This rather simple description of the permeation behavior, as shown in Equation (1), was rationalized by assuming that diffusion through the membrane is the rate-determining step. For palladium-based membranes, this assumption is valid in situations with rather thick membranes, high temperatures and low hydrogen pressures, which is basically the case in all current applications [13,[16][17][18]. For the proposed liquid metal membranes however, it cannot a priori be assumed that this approximation holds.…”

“…The pre-exponential factor for diffusion constitutes parameters related to the diffusive jump distance and unit cell geometry (a and γ D ), these are added to relate the rate of diffusion to the jumping frequency [28]. Alternative descriptions for Equation (18) exist which contain a correction factor for the correlation of subsequent jump directions. The literature only provides values for the case of self-diffusion [15].…”