Finite-element simulations of miscible fingering problems

Abstract

We present finite-element approaches to investigate the dynamical evolution of two-dimensional miscible porous media flows in the quarter five-spot arrangement. This takes into account the appearance of viscous fingers and its influence on the breakthrough time of the injected fluid and on the reservoir sweep. Then, two viscosity-concentration relationships for larger values of mobility ratios (the rate between the viscosities of resident and solvent fluids) and Péclet numbers are considered. The numerical discretization is carried out by two stabilized finite-element formulations, with the concentration calculated via a fully Galerkin/least-squares space-time (GLS/ST) method and a streamline upwind Petrov–Galerkin semi-discrete approach. Darcy's equation (velocity approximation) is treated via a precise post-processing technique. Some numerical test cases are exhibited demonstrating good physical behaviours in the presence of finger instabilities. Besides, the influence of the two parameters: mobility ratio and Péclet number on the reservoir recovery are also addressed showing that the GLS/ST approach is a good alternative to deal with miscible fingering problems.