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

We present a continuum-scale diffusion-based model informed by pore-scale data for gas transport in organic nanoporous media. A mass transfer and an adsorption model are developed by considering multiple transport and storage mechanisms, including bulk diffusion and Knudsen diffusion for free phase, surface diffusion and multilayer adsorption for sorbed phase. A diffusion-based governing equation is derived based on free phase concentration for the overall mass conservation of free and sorbed phases, carrying a newly-defined effective diffusion coefficient and a capacity factor to account for multilayer adsorption. Diffusion of free and sorbed phases is coupled through a pore-scale simplified local density method based on the modified Peng-Robinson equation of state for confinement effect. The model is first utilized to analyze pore-scale adsorption data from a krypton (Kr) gas adsorption experiment on graphite. Then we implement the model to conduct sensitivity analysis of the effects of pore size on gas transport for Kr-graphite and methane-coal systems. The model is finally used to study Kr diffusion profiles through a coal matrix obtained through X-ray micro-CT 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. The comparison between BET-based and Langmuir-based models shows that Langmuir-based models can only match the adsorption isotherm at low pressure and yield lower effective surface diffusion coefficients. Therefore, implementing a Langmuir-based model may be erroneous for an organic-rich reservoir with strong adsorption capacity during the early depletion period when the reservoir pressure is high.