Concentration polarization analysis in self-supported Pd-based membranes

In this work, the concentration polarization phenomenon in hydrogen permeation through self-supported Pd-alloy membranes is evaluated by an opportune coefficient expressed as a function of the ratio of the flux calculated by means of a validated complex model considering all the elementary steps involved in the permeation [A. Caravella, G. Barbieri, E. Drioli, Modelling and Simulation of Hydrogen Permeation through Supported Pd-based membranes with a multicomponent approach, Chemical Engineering Science 63 (8) (2008) 2149–2160] and the one obtained by the Sieverts’ law utilizing the bulk driving force and hydrogen permeance. The polarization coefficient was evaluated as a function of several operating conditions: upstream hydrogen molar fraction ([0, …, 1]), total pressure of upstream ([200, …, 1000] kPa), total pressure of down-stream ([100, …, 800] kPa), temperature ([300, …, 500] °C), membrane thickness ([1, …, 150] μm), permeance ([0.1, …, 20] mmol m −2 s −1 Pa −0.5) and upstream fluid-dynamic conditions (Reynolds’ number). The analysis shows that the polarization effect can be relevant not only when using very thin membranes (1–5 μm ca.), but also when thicker ones (100 μm ca.) are operated in specific conditions. A validation of the analysis is provided by means of some experimental data from literature, finding a good agreement with them. The overall result of the paper is the development of so-called “polarization maps”, on which the influence of concentration polarization can be evaluated quantitatively in different conditions, providing a useful tool to reduce the uncertainties in the hydrogen purification equipment design.