Numerical investigation of viscous flow instabilities in multiphase heterogeneous porous media

Abstract

A critical aspect of multiphase flow in porous media is the displacement efficiency, which measures the amount of fluid that can be pushed by another fluid driven by pressure gradient. Migration of contaminants and reservoir waterflooding are typical applications where understanding the dynamics of immiscible fluid displacement helps mitigating water resources contamination and improving hydrocarbons production, respectively. Due to large viscosity ratios, flow instabilities at fluids’ interface may arise leading to the formation of fingers, i.e., uneven fronts with elongation at the outside edge of fluids interface with strong impact on the displacement efficiency. Initial studies of viscous instabilities indicated that the development of fingers mostly depends on mobility and capillary forces, however heterogeneity of the porous domain may also affect the onset of instabilities. Therefore, the main aim of this work is to numerically investigate formation and growth of viscous fingers in heterogeneous porous media. The model used here is based on a novel control volume finite element method (CVFEM) formulation with families of FE-pairs, PnDG-Pm and PnDG-PmDG, specially tailored for Darcean flows. Dynamic mesh adaptivity enables capturing fingers development whilst saving computational overheads. Numerical experiments were performed to investigate the impact of viscosity ratio and heterogeneity on Saffmann–Taylor instabilities. Numerical simulations demonstrated that the heterogeneity of the domain triggers the early-onset formation of fingers under prescribed viscosity ratio conditions. Also, effective numerical capture of growth (in particular tip-splitting) and coalescence of dendritic finger branching induced by large viscosity ratio largely depends on mesh resolution at the fluids interface.