Miscible, porous media displacements with density stratification.

High accuracy, three-dimensional numerical simulations of miscible displacements with gravity override, in both homogeneous and heterogeneous porous media, are discussed for the quarter five-spot configuration. The influence of viscous and gravitational effects on the overall displacement dynamics is described in terms of the vorticity variable. Density differences influence the flow primarily by establishing a narrow gravity layer, in which the effective Peclet number is enhanced due to the higher flow rate. Although this effect plays a dominant role in homogeneous flows, it is suppressed to some extent in heterogeneous displacements. This is a result of coupling between the viscous and permeability vorticity fields. When the viscous wavelength is much larger than the permeability wavelength, gravity override becomes more effective because coupling between the viscous and permeability vorticity fields is less pronounced. Buoyancy forces of a certain magnitude can lead to a pinch-off of the gravity layer, thereby slowing it down.