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, H2 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 H2 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%. ► A two-dimensional numerical method is developed to simulate concentration polarization. ► Hydrogen permeation in a Pd-based membrane tube is studied. ► Increasing pressure difference or membrane permeance tends to trigger concentration polarization. ► When Reynolds number or H2 molar fraction decreases, the deviation of PFR from CSTR grows. ► H2 permeation rate can be predicted by Sieverts’ law if the H2 permeation ratio is no larger than 30%.