Influence of initial plume shape on miscible porous media flows under density and viscosity contrasts

Abstract

The effect of the initial condition upon the transport dynamics of miscible flowing fluids in a porous medium is investigated under viscosity and density contrasts. Such flows have attracted significant attention due to their importance in many fields of science and engineering, such as $\mathrm {CO}_2$ sequestration and aquifer remediation. Using high-resolution two-dimensional numerical simulations, we illustrate the impact of viscosity and density contrasts on the temporal evolution of the spreading and mixing quantities. We show that such impact depends on the initial shape of the source distribution where the solute is injected and on the intensity of the horizontal background flux. We find that rates of mixing are dependent on whether the solute is more or less viscous than the ambient fluid, a result usually not taken into consideration in studies on gravity fingering. At higher background flux, the effects due to horizontal viscous fingering dominate over gravitational fingering. Our computational analysis also suggests a non-trivial relationship between mixing and the length of the plume's interface under fingering instabilities. Finally, we show how a stratified permeability field can interact with these sources of instabilities and affect the transport behaviour of the plume.