Approximate multiscale flow solver for unstructured pore networks

Pore-scale simulations of multiphase flow in porous media are useful in understanding the relations between macroscopic variables relevant in many applications. It is critical that simulation domains are large enough to be considered representative elementary volumes for the relevant macroscopic quantities such as relative permeability, macroscopic capillary pressure and average saturation. However, multiphase pore-scale solvers, such as dynamic flow solvers for pore network models, are typically computationally expensive due to the required solution of a global pressure problem at every time-step. In this paper, an approximate multiscale flow solver is presented, which overcomes this limitation. The solver is applicable to arbitrary unstructured pore networks and consists of three main steps. First, the global pressure problem is solved using the multiscale finite volume (MSFV) method in combination with the multiscale restricted-smoothed basis (MsRSB) prolongation operator. The computed pressure field leads to conservative fluxes across pre-defined subnetwork boundaries. Second, these conservative fluxes are used as boundary conditions to solve local problems on the subnetworks. Third, once these local problems are solved, the subnetworks are synchronized. Validation studies are presented and results obtained using the multiscale solver are compared to results obtained using an existing dynamic network flow solver.