Numerical investigation of viscous fingering in a three-dimensional cubical domain

Abstract

We perform three-dimensional numerical simulations to understand the role of viscous fingering in sweeping a high-viscous fluid (HVF). These fingers form due to the injection of a low-viscous fluid (LVF) into a porous media containing the high-viscous fluid. We find that the sweeping of HVF depends on different parameters such as the injection velocity (U0) of the LVF, ease of diffusion of the fluid (D), and the logarithmic viscosity ratio of HVF and LVF ℜ. The two-phase Darcy's law module of COMSOL Multiphysics is used to simulate different cases with varying parameters. At high values of U0 and ℜ and lower values of D, the fingers grow non-linearly, resulting in earlier tip splitting of the fingers and breakthrough, further leading to poor sweeping of the HVF. In contrast, the fingers evolve uniformly at low values of U0 and ℜ, resulting in an efficient sweeping of the HVF, while a higher diffusion coefficient leads to a smooth flow with fewer fingers. We also estimate the sweep efficiency and conclude that the parameters U0, D, and ℜ be chosen optimally to minimize the non-linear growth of the fingers to achieve an efficient sweeping of the HVF.