Image-based micro-continuum model for gas flow in organic-rich shale rock

The physical mechanisms that control the flow dynamics in organic-rich shale are not well understood. The challenges include nanometer-scale pores and multiscale heterogeneity in the spatial distribution of the constituents. Recently, digital rock physics (DRP), which uses high-resolution images of rock samples as input for flow simulations, has been used for shale. One important issue with images of shale rock is sub-resolution porosity (nanometer pores below the instrument resolution), which poses serious challenges for instruments and computational models. Here, we present a micro-continuum model based on the Darcy-Brinkman-Stokes framework. The method couples resolved pores and unresolved nano-porous regions using physics-based parameters that can be measured independently. The Stokes equation is used for resolved pores. The unresolved nano-porous regions are treated as a continuum, and a permeability model that accounts for slip-flow and Knudsen diffusion is employed. Adsorption/desorption and surface diffusion in organic matter are also accounted for. We apply our model to simulate gas flow in a high-resolution 3D segmented image of shale. The results indicate that the overall permeability of the sample (at fixed pressure) depends on the time scale. Early-time permeability is controlled by Stokes flow, while the late-time permeability is controlled by non-Darcy effects and surface-diffusion.