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

•The effect of non-ideal internal diffusion and external mass transfer is studied.•The functionality of the pressure exponent with operating parameters is provided.•Sieverts law is inadequate to model H2 permeation with strong external resistance.

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 – referred to as “non-ideal” behaviour – 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.

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