A high-order, fully coupled, upwind, compact discontinuous Galerkin method for modeling of viscous fingering in compressible porous media

We present a new approach for high-fidelity compressible porous media simulations. Our method is based on a fully coupled, upwind, high-order discontinuous Galerkin formulation of the equations of miscible displacement transport. A key feature of the proposed method is the high level of flexibility to compute complex subsurface geometries, maintaining full order of accuracy. The present formulation solves pressure and transport equations in a fully coupled fashion and, as a result, can capture the strong interaction between pressure and concentrations of injected components in highly compressible media. The proposed method also shows very low sensitivity to mesh orientation, in contrast with classical finite volume approximations used in porous media flow simulations. The robustness and accuracy of the method are demonstrated in a number of challenging compressible and incompressible multiphase flow problems. Numerical simulations also reveal interesting phenomena associated with high pore compressibility, such as the reduction of the growth rate of viscous fingers and the alteration of flow patterns near impermeable obstacles. Additional computations performed with an anisotropic permeability tensor reveal that, somewhat against intuition, viscous fingers have a preferential growth along the direction of low permeability.