Exponents for the Pressure Dependence of Hydrogen Permeation through Pd and Pd−Ag Alloy Membranes

Abstract

A frequently employed boundary condition for H permeation of membranes is p down ≈ 0 and, for this case, the flux is given by J = (KD H/d)p up n , where K is a constant and d is the membrane thickness. Values of n can then be obtained from slopes of plots of ln J against ln p up. When the H solution is ideal, n = 0.5, and D H is concentration-independent, but when the H solution is nonideal, i.e., when the H atoms interact, n ≠ 0.5 and D H is concentration-dependent. An equation is derived for n, which includes the effects of nonideality of H on both D H and the solubility. The terms in this equation for n can be obtained from the appropriate equilibrium H2 isotherms for Pd or its alloys. Good agreement is found between the derived values of n and the experimental values for the pressure dependence of H2 permeation through Pd, Pd0.77Ag0.23, and Pd0.50Ag0.50 membranes. By comparing experimental n ≠ 0.50 values to those calculated from the equilibrium isotherms, a decision can be made about whether bulk diffusion is the slow step.

Modelling and systematic experimental investigation of mass transfer in supported palladium-based membrane separators

“…Here, N m is the transmembrane flux, defined at the radial coordinate of the palladium layer (r m ), Q(T) is the temperature-dependent permeance, p H 2 ,r and p H 2 ,p are the retentate-side and permeate-side H 2 partial pressures, respectively. Later authors have added that, at higher H 2 partial pressures, corrections for the nonideality of the H-Pd system, surface effects, or thermal effects will lead to increased values of n (Hara et al, 2009;Flanagan and Wang, 2010;Bhargav et al, 2010;Skorpa et al, 2012). For the purpose of the present study, it is sufficient to fit the parameters Q and n in Eq.…”

“…Ward and Dao (1999) have developed detailed rate models for the elementary steps in the permeation of hydrogen through palladium, which have found widespread use. More recently, several authors have added the effects of thermodynamic nonideality (Hara et al, 2009;Flanagan and Wang, 2010;Bhargav et al, 2010). However, with a decrease in palladium thickness and an accompanying increase in flux, other resistances to mass transfer have become increasingly more important, viz.…”

An Innovative Procedure to Evaluate the Hydrogen Diffusion Coefficient in Metals from Absorption Measurements

“…In several cases, the literature reports the evidence of a deviation of the hydrogen permeation flow from Equation (3) especially with regard to the square root dependence [6][7][8]. From a practical point of view, this means that in real systems, both the hydrogen diffusivity and solubility in the metal lattice are influenced by the hydrogen concentration or the hydrogen equilibrium pressure.…”

Evaluation of Step Resistance in Multilayered Ceramic-Supported Pd-Based Membranes for Hydrogen Purification in the Presence of Concentration Polarisation

“…Furthermore, the hydrogen profile through the metal layer is generally more than linear due to the "non-ideality" of the diffusion coefficient in the Pd-based layer, as diffusivity is an increasing function of hydrogen concentration in the conditions of interest of the present paper [44][45][46][47][48]. In light of such functionality, the profile non-linearity is progressively more pronounced as the hydrogen concentration increases.…”

“…However, as also remarked elsewhere [38], it could be convenient sometimes to choose a different driving force, such as, for example, the pressure difference or another difference of pressure functionality taking into account the non-ideality of internal diffusion in the metal lattice in terms of a pressure exponent different from 0.5 [22,[44][45][46].…”