Continuum-Scale Gas Transport Modeling in Organic Nanoporous Media Based on Pore-Scale Density Distributions

We present a continuum-scale mass transport model informed by pore-scale density distribution for gas diffusion through organic nanoporous media. A diffusion model and a sorption model are developed by considering multiple transport and storage mechanisms, including bulk diffusion and Knudsen diffusion for free phase, and surface diffusion and multilayer adsorption for sorbed phase. The continuum-scale diffusion equation is derived based on the free-phase concentration for the overall mass conservation of free and sorbed phases, carrying a newly defined effective diffusion coefficient and capacity factor to account for multilayer adsorption. Diffusion in free and sorbed phases is coupled with the sorption model, which provides pore-scale multilayer adsorption properties by utilizing a pore-scale simplified local density (SLD) method combined with the modified Peng-Robinson equation of state (PR-EOS) for confinement effect. The model was first implemented to analyze adsorption data from a krypton (Kr) adsorption experiment on graphite. Then, we applied the developed diffusion model to conduct the sensitivity analysis of the effects of pore size on gas transport for Kr-graphite and methane-coal systems. The model was finally used to study Kr diffusion profiles through a coal matrix obtained by using X-ray micro-computed tomography (microCT) imaging. The results show that the sorbed phase occupies most of the pore space in organic nanopores with less than 10 nm due to multilayer adsorption, and surface diffusion contributes significantly to the total mass flux. Therefore, neglecting the volume of sorbed phase and surface diffusion in organic nanoporous rocks may result in considerable errors in the prediction of hydrocarbon production. We also compared Brunauer-Emmett-Teller (BET) and Langmuir models by analyzing adsorption data for the wide pressure range up to the saturation pressure. The comparison between BET and Langmuir models shows that the Langmuir model can only match the adsorption isotherm at low pressure and yield lower effective surface diffusion coefficients. Therefore, implementing a Langmuir model may be erroneous for organic nanoporous media with strong adsorption capacity, particularly when pore pressure is high.