The interpretation of diverging hydrogen and carbon dioxide permeations with temperature across silica-based membranes

Hydrogen (H2) permeance across silica-based membranes increases with temperature, but carbon dioxide (CO2) permeance decreases. Because of the opposite signs of activation energies for H2 and CO2 permeation, silica-based membranes are widely used in separating H2 and CO2 at high temperatures due to the elevated difference between H2 and CO2 permeabilities. However, there has not been an explanation of the diverging permeance between H2 and CO2 with temperature. This study developed a gas permeation model encompassing gas penetration through silica matrix, Knudsen diffusion, and viscous flow. An Oscillator model with an effective medium approach was used to screen all possible pore size distributions and calculate the gas penetration through the silica matrix. However, no pore size distribution could allow positive activation energy for hydrogen and negative activation energy for carbon dioxide at the same time. After including Knudsen diffusion and viscous flow, the diverging permeance between H2 and CO2 with temperature was successfully interpreted. The pore size distribution and the fractional contribution from Knudsen diffusion and viscous flow, which could best fit experimental activation energies for H2 and CO2 permeation, were identified. In the silica matrix that formed the membranes, 5-membered rings were the dominant structures in pores, which was responsible for the positive apparent activation energy for H2. The negative CO2 apparent activation energy indicated that it was inevitable to have some Knudsen diffusion and viscous flow through some imperfections of the membrane. Our model demonstrated the importance of high-temperature gas separation, as high temperature could minimize the undesirable gas flow through imperfections. This study also implied that further improvement of H2/CO2 separation by silica-based membranes could be achieved by reducing imperfections.