Miscible rectilinear displacements with gravity override. Part 2. Heterogeneous porous media

The effects of permeability heterogeneities on rectilinear displacements with viscosity contrast and density variations are investigated computationally by means of direct numerical simulations. Physical interpretations are given in terms of mutual interactions among the three vorticity components related to viscous, density and permeability effects. In homogeneous environments the combined effect of the unfavourable viscosity gradient and the potential velocity field generated by the horizontal boundaries was seen to produce a focusing mechanism that resulted in the formation of a strong vorticity layer and the related growth of a dominant gravity tongue (Ruith & Meiburg 2000). The more randomly distributed vorticity associated with the heterogeneities tends to ‘defocus’ this interaction, thereby preventing the formation of the vorticity layer and the gravity tongue. When compared to neutrally buoyant flows, the level of heterogeneity affects the breakthrough recovery quite differently. For moderate heterogeneities, a gravity tongue still forms and leads to early breakthrough, whereas the same result is accomplished for large heterogeneities by channelling. At intermediate levels of heterogeneity, these tendencies partially cancel each other, so that the breakthrough recovery reaches a maximum. Similarly, the dependence of the breakthrough recovery on the correlation length is quite different in displacements with density contrasts compared to neutrally buoyant flows. For neutrally buoyant flows the resonant interaction between viscosity and permeability vorticities typically leads to a minimal recovery at intermediate values of the correlation length. In contrast, displacements with density contrast give rise to a gravity tongue for both very small and very large values of this length, so that the recovery reaches a maximum at intermediate values.