Abstract
We present a mathematical model for one-dimensional gas transport in organic-rich nanoporous media subject to nonequilibrium sorption. The model is developed from two governing equations to simulate Knudsen diffusion and viscous flow in the free phase, and surface diffusion in the sorbed phase. The pore space is shared between the free and sorbed phases by defining concentration-dependent free- and sorbed-phase volume fractions. The governing equations are coupled through a source/sink term described by a kinetic sorption model. The impact of the reduced effective pore space and sorption on free-phase mass transfer is characterized by defining effective diffusion coefficients. The governing equations are numerically solved based on the finite element method. The diffusion model is utilized to analyze the temporal and spatial concentration data obtained using X-ray micro-CT scans from two experiments, including Krypton transport into a coal sample and Xenon uptake into a shale sample. The proposed model can closely reproduce total concentration profiles in both experiments. The model also captures the concentration peak in Xe-shale system due to the significant nonequilibrium sorption and slower process of reaching equilibrium. The results show that surface diffusion dominates the total mass transport in Xe-shale system with higher adsorption affinity. In Kr-coal system with lower adsorption affinity, the sorbed phase contributes significantly to the total mass transport mostly at high pressures. In addition, the sorbed phase can occupy up to 30% of pore space, which reduces the free-phase diffusion coefficient by 40% in Xe-shale and 80% in Kr-coal. Accordingly, neglecting the sorbed-phase volume in nanoporous media may overestimate the effective free-phase diffusion coefficient.
