On numerical homogenization of shale gas transport

In this paper, we study the numerical homogenization for the gas transport in organic rich shale with heterogeneous kerogen distribution. We consider organic rich shale as the domain with two subdomains: inorganic matrix and kerogen. The processes in both regions are described by nonlinear parabolic equations, which take into account the filtration, diffusion, and adsorption. We follow the work of Yucel Akkutlu et al. (2015), where the authors develop homogenization techniques for the gas transport in organic rich shale. We use the framework of Yucel Akkutlu et al. (2015) and develop numerical homogenization for two dimensional examples. We discuss local subgrid calculations and the approaches to compute the effective properties numerically. In our methods, the local problems use Dirichlet boundary conditions. We compare the properties of the fine-grid reference solution against those of the coarse grid model. Our approaches show a good agreement between macroscopic quantities.