Scale-Dependent Mixing for Adverse Mobility Ratio Flows in Heterogeneous Porous Media

Mixing is a scale-dependent phenomenon that has been shown to increase with increasing heterogeneity, mobility ratio, longitudinal correlation length, aspect ratio and distance traveled. The interface between miscible fluids may be dilated by velocity variations, which are promoted by certain characteristics of a porous medium, or by a high mobility ratio. Here we use a high-resolution numerical scheme to compute local dispersivities by fitting grid-block concentration histories to the 1D convection–diffusion equation. We provide new insights on the scale dependence of local dispersivity in heterogeneous porous media. We explain that irreversible mixing only increases monotonically with increasing longitudinal correlation length (layering) for unit mobility ratio displacements. The combination of an adverse mobility ratio and reservoir layering causes mixing to increase, peak and then decline with distance traveled by the injectant. We show that mixing evolves non-monotonically in layered porous media due to the effect of channeling (and not viscous fingering) at adverse mobility ratios. We also examine the effect of diffusion on local dispersivity as modeled in Eulerian simulation. The level of dispersivity is increased when diffusion is explicitly modeled, although molecular diffusion is much smaller than numerical diffusion, even in our high-resolution simulations. Diffusion is more important to consider when sharp concentration gradients exist, as is the case when mobility ratio is large and permeabilities are highly correlated in the longitudinal direction (i.e., layered). This combination gives rise to pronounced channelized flow in which a sharp concentration gradient drives diffusion over a large area of contact between fluids.