Numerical characterization on concentration polarization of hydrogen permeation in a Pd-based membrane tube

Sieverts' law has been extensively employed to evaluate hydrogen permeation rate across a hydrogen-permeable membrane based on the concept of continuous stirred tank reactor (CSTR). However, when the hydrogen permeation rate is high to a certain extent, concentration polarization will appear in a membrane tube which results in the deviation of hydrogen permeation rate from Sieverts' law. Under such a situation, the nature of mass transfer in a membrane tube is characterized by plug flow reactor (PFR) rather than CSTR. To figure out the feasibility of Sieverts' law, a two-dimensional numerical method is developed to simulate the phenomena of concentration polarization for hydrogen permeation in a Pd-based membrane tube. Four important parameters affecting hydrogen permeation are taken into account; they include the pressure difference, H ₂ molar fraction in the influence, Reynolds number and membrane permeance. The predictions indicate that increasing pressure difference or membrane permeance facilitates H₂ permeation rate; concentration polarization is thus triggered. Alternatively, when Reynolds number or H ₂ molar fraction decreases along with a higher permeance, the deviation of PFR from CSTR grows, even though H₂ permeation rate declines. From the obtained results, it is concluded that the H₂ permeation rate can be predicted by Sieverts' law if the H₂ permeation ratio is no larger than 30%.