An efficient numerical algorithm for solving viscosity contrast Cahn–Hilliard–Navier–Stokes system in porous media

•Direct numerical simulations of two-phase flow in 3D rock images.•Nonlinear relationship between viscosity ratios and wettability at the pore scale.•Work highlights the impact of local dynamic patterns of phase propagation in rocks. Two-phase flow with viscosity contrast at the pore scale is modeled by a time-dependent Cahn–Hilliard–Navier–Stokes model and belongs to the class of diffuse interface method. The model allows for moving contact line and varying wettability. The numerical scheme utilizes an efficient pressure-correction projection algorithm, in conjunction with interior penalty discontinuous Galerkin schemes for space discretization developed within the framework of a distributed parallel pore-scale flow simulation system. The effect of viscosity contrast on the phase distribution is studied in relation with capillary forces and wettability. The algorithm is numerically robust and lends itself naturally to large-scale 3D numerical simulations.