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: upstreamhydrogen molar fraction ([0, . . ., 1]), totalpressure of upstream([200, . . ., 1000] kPa), total pressure of down-stream ([100, . . ., 800] kPa), temperature ([300, . . ., 500] °C), membrane thickness ([1, . . ., 150]m), permeance ([0.1, . . ., 20]mmolm-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 (1-5m ca.), but also when thicker ones (100m 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.