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.