Two-phase water flooding simulations on dynamic adaptive octree grids with two-point nonlinear fluxes

摘要

We present a method for numerical simulation of the two-phase water flooding problem on general polyhedral grids not aligned with permeability tensor K (K-non-orthogonal grids) and dynamic octree grids adapted to the front between the phases. The discretization is based on the cell-centered monotone finite volume (FV) method with the nonlinear two-point flux approximation (TPFA) applicable to general K-non-orthogonal polyhedral grids. We use fully implicit discretization in time to avoid the restriction on the time step caused by the minimal mesh size. In our numerical experiments we demonstrate the superiority of the nonlinear TPFA on a K-non-orthogonal grid over linear TPFA and considerable speed-up of the simulation on a dynamically adapted octree grid with minimal loss in accuracy compared to the simulation on a fine regular grid.