Enhanced mixing of a miscible circular blob in rectilinear displacement in porous media

In this study, we investigate the rectilinear displacement and deformation of a highly viscous, miscible circular blob influenced by a less viscous fluid within a homogeneous porous medium featuring physically realistic no-flux boundaries. We utilize a fourth-order accurate compact finite difference scheme for the spatial discretization of the nonlinear partial differential equations that govern this phenomenon. The resulting semi-discrete equations are then integrated using the second-order Crank–Nicolson method. We conduct numerical simulations for wide ranges of Péclet number (500 ≤ Pe≤3000) and log –mobility ratio (0≤R≤7), which reveal three distinct pattern formations: comet shape, lump shape, and viscous fingering (VF) instability. It is observed that when Pe is doubled (from 1500 to 3000), the critical window for VF increases almost by 40%. Our results demonstrate that the deformation, spreading, and mixing of the blob vary non-ideally with both Pe and R, a behavior attributed to the blob's initial curvature. Consequently, enhanced mixing can be achieved at intermediate values of Pe and R, suggesting the existence of an optimal mixing condition. These findings have significant implications for fields such as oil recovery, CO2 sequestration, pollution remediation, and chromatography separation.