Computational investigation of viscous fingering in immiscible two-phase displacement flow

This study presents a numerical investigation of immiscible viscous fingering (VF) during two-phase displacement in a two-dimensional Hele–Shaw cell (HSC). The cell is initially saturated with engine oil, which is displaced by a less viscous fluid. As the displacing fluid penetrates the oil phase, interfacial instabilities develop in the form of a finger-shaped pattern, a phenomenon known as VF. The evolution of these instabilities and the resulting displacement efficiency depend on the viscosity of the displacing fluid. Therefore, three fluids — water, silicon oil and glycerine are considered to evaluate their effectiveness in mobilizing engine oil. The governing equations are solved using a pressure-based solver with explicit transient formulation, while the volume of fluid (VOF) method is employed to capture interface dynamics. Interfacial instabilities are characterized, and displacement efficiencies are quantified through image processing. Results indicate that glycerine achieves the highest displacement efficiency (97%) due to its higher viscosity, which suppresses fingering. The simulations highlight an inverse relationship between fingering severity and fluid viscosity, showing that higher-viscosity displacing fluids lead to more stable fronts and enhanced recovery. These findings provide computational insights into controlling interfacial instabilities, with implications for optimizing immiscible displacement in enhanced oil recovery (EOR) and carbon dioxide sequestration.