Multicomponent Gas Transport Modeling in Nanopo Rous Media with Adsorption

Multicomponent gas transport in nanoporous adsorption media, such as organic-rich shales, is influenced by various mechanisms of mass transport and storage, posing challenges to understanding fluid transport in these porous media. We present a predictive diffusion-based model for the transport of multicomponent gas through nanoporous media using modified Maxwell-Stefan formulations for the free and sorbed phases. The developed model considers the transport of free and sorbed phases through nanopores and incorporates the extended Langmuir isotherm for multicomponent adsorption. The diffusive mass fluxes for both phases are coupled to obtain the governing equations with multicomponent effective diffusion coefficients and capacity factors that account for adsorption. The governing equations are functions of the free-phase composition and pressure and are solved numerically. The model is utilized to conduct a sensitivity analysis of the effective diffusion coefficients, capacity factors, and sorbed-phase porosity with respect to the pressure and fluid composition. Furthermore, co- and counter-diffusion processes are simulated to investigate CO₂/CH₄ flux from and CO₂ injection into organic-rich shale and coal samples, representing moderate and high adsorption capacity systems. The pore-volume fraction of each phase is calculated to determine the overall contribution of the phases to total gas transport. The results show that the sorbed phase occupies nearly half of the pore volume in the chosen coal sample. The results also show that the diffusion coefficients for CH₄ and CO₂ in shale and coal are inversely proportional to the adsorption capacity. Thus, low or moderate adsorption systems have higher effective and apparent diffusion coefficients. During the co-diffusion process on the shale sample, the sorbed phase stops contributing to production after 12 months but continues to produce in the coal sample even after 12 years of production. For the counter-diffusion process in coal and shale samples, CO₂ takes up the sorbed phase faster than it does the free phase, leading to a faster decrease in the sorbed phase concentration of CH₄. For both co- and counter-diffusion processes, the sorbed phase concentrations are higher in the coal sample than in shale, while the free phase concentrations are higher in shale samples than in coal. The contribution of the sorbed phase to the total mass is dependent on both pore size and adsorption affinity for low-pressure systems while it depends only on adsorption affinity for high-pressure systems.