UPSCALING OF DUAL-POROSITY MODELS FOR GAS TRANSPORT IN ORGANIC-RICH SHALES

We consider the gas transport in organic-rich shales, consisting of a nanoporous organic material, microporous inorganic matrix, and a system of secondary fractions. The proposed model incorporates free gas diffusion and filtration, as well as the effect of adsorption and diffusion of desorbed gas. We treat an organic-rich shale matrix as a dual porosity system consisting of organic (kerogen) nanopores and inorganic micropores. An organic phase appears as small inclusions scattered in the inorganic phase. The contrast of the properties and spatial scales between the matrix and inclusions brings in a multiscale feature which is important for fluid storage and transport. The double porosity model is derived as a system of coupled parabolic equations; the interchange of the fluid between the matrix and the inclusions is taken into account. We apply a multiscale analysis to mass balance and constitutive equations. We derive a homogenized macroscopic problem for the distribution of an amount of free gas in an effective medium for the given initial and boundary conditions. The problem contains a source term that represents the flow of desorbed gas from kerogen into the inorganic material. The properties of the effective medium depend on the size and spatial distribution of the inclusions, as well as on properties of both inclusions and matrix.