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

Artur Castiel Reis de Souza¹; Lorena Monteiro Cavalcanti Barbosa¹; Darlan Karlo Elisiário de Carvalho)¹; Paulo Roberto Maciel Lyra¹

¹ UFPE

doi:10.20906/CPS/CILAMCE2017-0074

Resumo

Modern geocellular models may contain up to hundreds million cells, while petroleum reservoir models handle at most a fraction of this quantity turning the direct numerical simulation of multiphase flow in heterogeneous and anisotropic media infeasible. To overcome this problems Multiscale Finite Volume Methods (MsFVM) uses operators to project the fine-scale system of equations onto a coarse-scale space originated from a lower-resolution grid. The resulting coarse system is solved and by using the multiscale operator projected back onto the higher-resolution grid. Nonetheless, the MsFVM operators fail to capture high-resolution geological properties on unstructured 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 to the simulation on unstructured coarse-scale meshes. The Multiscale Restricted Smoothed Basis (MsRSB) method creates this framework and expands the multiscale approach to unstructured coarse grids. However, it fails to produce consistent solutions on fine-scale unstructured grids and for arbitrary permeability tensors as it uses TPFA method. In this article, we couple a Multi-Point Flux Approximation with a Diamond stencil to the MsRSB to extend its use to general unstructured grids. We call our framework the "Multiscale Control Volume" (MsCV) method.

Palavras-chave: Multiscale Reservoir Simulation; MsRSB; MsCV; MPFA-D; Unstructured Meshes; MsFV