A MsCV framework using a non-orthodox MPFA-D for the simulation of two-phase flows on truly unstructured grids

Abstract

Modern geocellular models may contain up to hundreds million cells, while practical petroleum reservoir models handle at most a fraction of this quantity turning the direct numerical simulation of multiphase flow in heterogeneous and anisotropic medium infeasible. To overcome these problems Multiscale Finite Volume Methods (MsFVM) uses restriction algorithm to transfer information onto a lower-resolution grid, solve the resulting coarse system and by using a set of basis function, project back the solution onto the higher-resolution grid. Nonetheless, the MsFVM basis function fail to deal with high-resolution geological properties on general grids as they often rely on TPFA, which is only consistent for k-orthogonal grids. Furthermore, MsFVM possess no framework capable of generating the geometric entities needed for simulation on unstructured coarse-scale meshes. The Multiscale Restricted Smoothed Basis (MsRSB) method creates this framework and expands the multiscale approach to unstructured coarse meshes. However, it fails to produce consistent solutions on fine-scale unstructured meshes and for arbitrary permeability tensors as it also uses TPFA. In this thesis, we couple a Multi- Point Flux Approximation (MPFAD) with a Diamond stencil to the MsRSB to extend its use to general unstructured grids. The resulting framework showed prominent results producing accurate solutions for two-phase flow simulation in heterogeneous and mildly anisotropic medium with unstructured grids on a coarse and a fine scale.