A finite outlet volume correction to the time lag method: The case of hydrogen permeation through V-alloy and Pd membranes

Abstract

The time-lag method is a technique to derive the permeability of a membrane from the time-variant outflux of a permeate. The original formulation assumes an invariant outlet pressure; however, for practical reasons, the permeate is often contained in a finite outlet volume, and the outflux is evaluated using the increase in the outlet pressure. The outlet pressure change inevitably introduces an error in the diffusivity and in the solubility, i.e., Sieverts' constant. We demonstrate that when a time lag is obtained from the tangent line at the maximum flux, the error in the diffusivity stays within ca. 2% under usual experimental conditions. On the other hand, Sieverts' constant is underestimated to a larger degree if the outlet pressure change is not considered. To solve this problem, we propose a finite outlet volume correction to the time-lag method for the case of hydrogen permeation. The proposed scheme is an approximate solution that is valid when a linear hydrogen concentration profile is developed across the membrane. When the correction method is applied to characterize V-alloy and Pd membranes, the simulated outlet pressure from the corrected Sieverts' constant closely approximates the experimental data. The proposed method does not require any additional measurements and greatly improves the accuracy of the permeability measurement.