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

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 (U-0) 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 U-0 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 U-0 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 U-0, D, and R be chosen optimally to minimize the non-linear growth of the fingers to achieve an efficient sweeping of the HVF.