NUMERICAL-SIMULATION OF MISCIBLE DISPLACEMENT PROCESSES IN POROUS-MEDIA FLOWS UNDER GRAVITY

The nonlinear evolution of the interface between two miscible fluids of different densities and viscosities is simulated numerically for flow in a two-dimensional porous medium in which gravity is directed at various angles to the interface. Global velocities tangential to the interface are included in the analysis in addition to a normal displacing velocity. In unstable configurations, the viscous fingers that result translate as they amplify when nonzero tangential velocities are present. The increased stabilization by tangential shearing velocities reported in [A. Rogerson and E. Meiburg, Phys. Fluids A 5, 1344 (1993)] affects the growth and wavelength selection of the emerging fingers. Tangential shearing also breaks the symmetry in the shape and concentration distribution of emerging fingers. In addition to the fingering mechanisms reported in previous studies, new mechanisms of diagonal fingering, trailing-lobe detachment, and secondary side-finger instability, resulting from the presence of gravity and tangential velocities, have been identified. These phenomena are reflected in one-dimensional averaged profiles of the concentration field. Also, how different density-concentration relations influence the interfacial evolution is investigated. When the dependence of viscosity and density on the concentration has different functional forms, the region of instability may be localized. The nature of the interfacial development is altered by varying the density relation and thereby changing the region of instability, suggesting that careful modeling of the density and viscosity relations is warranted.