Improved mathematical model of apparent permeability: A focused study on free and multilayer adsorptive phase flow

Abstract

Apparent permeability is the quantification of gas transport in confined pore, which includes the pressure gradient-driven continuous flow (slip flow), the concentration gradient-driven molecular diffusion (Fick's diffusion, Knudsen diffusion) and the chemical gradient-driven surface diffusion. Molecular diffusion of free/adsorbed gas plays an important role in gas transfer, especially in nanopores. Most existing apparent permeability models simply define free gas diffusion as Knudsen diffusion, and surface diffusion as the diffusion of monolayer adsorbed molecules. However, the pore scale-dependent Knudsen diffusion, the molecular diffusion of free gas also includes the pore scale-independent Fick's diffusion. In addition, the empirical formula of surface diffusion coefficient derived from plug core diffusion experiment should be used cautiously, because there are other diffusion regimes involved in the diffusion process in multi-scale pores. In this work, the diffusion mechanisms of adsorbed/free gas were classified. A supercritical multilayer adsorption (SC-DA) model was obtained by fitting the adsorption data of homogeneous nano activated carbon, and the adsorption effect was applied to pore aperture change and surface diffusion, which is suitable for single/multilayer adsorption. Applying the improved surface diffusion flow and free gas diffusion flow into gas transport, a unified mathematical transport model was presented, from which the apparent permeability model was derived. Later, the improved model was verified using the experimental data from the micro-flow permeability of the nanofilms with regular size. Furthermore, the influence of each flow mechanism in nanopores was calculated and compared. The results showed that the gas transport in nanopores is dominated by molecular diffusion, but the contribution of surface diffusion in gas transfer is exaggerated if its diffusion coefficient is not chosen properly.