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

The nonlinear evolution of the interface between two miscible fluids o f different densities and viscosities is simulated numerically for flo w in a two-dimensional porous medium in which gravity is directed at v arious angles to the interface. Global velocities tangential to the in terface are included in the analysis in addition to a normal displacin g velocity. In unstable configurations, the viscous fingers that resul t translate as they amplify when nonzero tangential velocities are pre sent. The increased stabilization by tangential shearing velocities re ported in [A. Rogerson and E. Meiburg, Phys. Fluids A 5, 1344 (1993)] affects the growth and wavelength selection of the emerging fingers. T angential shearing also breaks the symmetry in the shape and concentra tion distribution of emerging fingers. In addition to the fingering me chanisms reported in previous studies, new mechanisms of diagonal fing ering, trailing-lobe detachment, and secondary side-finger instability , resulting from the presence of gravity and tangential velocities, ha ve been identified. These phenomena are reflected in one-dimensional a veraged profiles of the concentration field. Also, how different densi ty-concentration relations influence the interfacial evolution is inve stigated. When the dependence of viscosity and density on the concentr ation has different functional forms, the region of instability may be localized. The nature of the interfacial development is altered by va rying the density relation and thereby changing the region of instabil ity, suggesting that careful modeling of the density and viscosity rel ations is warranted.