Hydrogen Gas Driven Permeation through Asymmetric Membranes in Diffusion Limited and Surface Limited Regimes: Interplay between Analytical and Numerical Calculations

Validity of analytical solutions for the gas driven permeation of H in the Diffusion Limited Regime (DLR) and Surface Limited Regime (SLR) is analyzed by comparison with numerical calculations. Margins for analytical formulas have been established in terms of the permeation factors W = KLSp 1/2 / D on the inlet ( W 1 ) and outlet ( W 2 ) sides of the membrane. The DLR analytical formula gives perfect result (error less than 0.5%) if both W 2 ≥ 10 4 and W 1 ≥ 10 2 conditions are satisfied simultaneously. Decrease of both margins by two orders of magnitude leads to 10% error. The SLR analytical formula gives a very good result (error less than 0.5%) if both W 1 ≤ 10 -2 and W 2 W 1 ≤ 10 -3 conditions are satisfied simultaneously. Increase of both margins by two orders of magnitude leads to 10% error. It has been shown that the inlet side and the outlet side conditions are different in their importance for validity of the analytical formulas. In DLR the condition is softer on the inlet side and more rigid on the outlet side, while in SLR the condition is softer on the outlet side and more rigid on the inlet side.