Mixing and fingering lifecycle in heterogeneous porous media

Miscible displacement processes, where a viscous fluid is injected into a porous medium or Hele-Shaw cell initially saturated with another miscible fluid, are relevant in a number of physical situations. These include enhanced oil recovery, carbon sequestration and subsurface contaminant transport. In many cases the goal is to control the displacement front and the amount of mixing that occurs between the two fluids. In this work, we explore the combined effects of permeability heterogeneities and viscosity variations on the mixing of the ambient and injected fluids, using high-resolution numerical simulations and reduced theoretical modelling.

Specifically, we consider an idealized porous medium consisting of alternating layers of high and low permeability into which a fluid that is equally-viscous, less-viscous or more-viscous than the ambient fluid, is injected. We find that at intermediate times the dynamics depend on the viscosity variations, but eventually the flow enters a shear-enhanced dispersion regime, such that ultimately the mixing depends only on the permeability variations. We investigate the different regimes that arise and develop simplified models that describe the evolution of the concentration field in each case.