Vorticity interaction mechanisms in variable-viscosity heterogeneous miscible displacements with and without density contrast

The vorticity interaction mechanisms governing miscible displacements in three-dimensional heterogeneous porous media are investigated by means of detailed simulations in the regimes of viscous fingering, dispersion, and resonant amplification. The computational results for spatially periodic and random permeability distributions are analysed in detail with respect to the characteristic wavenumbers and norms associated with the individual vorticity components. This allows the identification of the mechanisms dominating specific parameter regimes. Nominally axisymmetric displacements such as the present quarter five-spot configuration are particularly interesting in this respect, since some of the characteristic length scales grow in time as the front expands radially. This leads to displacement flows that can undergo resonant amplification during certain phases, while being dominated by fingering or dispersion at other times. The computational results also provide insight into the effects of density-driven gravity override on the interactions among these length scales. While this effect is known to play a dominant role in homogeneous flows, it is suppressed to some extent in heterogeneous displacements, even for relatively small values of the heterogeneity variance. This is a result of the coupling between the viscous and permeability vorticity fields in the viscous fingering and resonant amplification regimes. In the dispersive regime, gravity override is somewhat more effective because the coupling between the viscous and permeability vorticity fields is less pronounced, so that the large-scale structures become more responsive to buoyancy effects.