Sieverts law pressure exponent for hydrogen permeation through Pd-based membranes: coupled influence of non-ideal diffusion and multi-component external mass transfer

This paper focuses on the suitability of using a Sieverts-type empirical law to describe hydrogen permeation through Pd-based membranes in the presence of both concentration-dependent hydrogen transport through the selective layer e referred to as "non-ideal" behaviour e and external mass transfer resistance. In particular, the functionality of the pressure exponent with temperature, pressure and membrane thickness is provided, showing that the Sieverts-type empirical law can be used to incorporate the external mass transfer influence just up to a moderate external resistance. The explanation for this fact is recognised in the inadequacy of the Sieverts-type empirical law to describe the behaviour of the flux limited by external resistance for a sufficiently large permeation driving force. The methodology described in this paper is effective also when the permeation-determining steps cannot be established, helping researchers to a correct interpretation of permeation tests in the presence of severe mass transfer resistance.