Dispersive mixing dynamics of dense miscible plumes: natural perturbation initiation by local-scale heterogeneities

Abstract

Two-dimensional, coupled variable-density flow and transport simulations with heterogeneous media advance understanding of how local-scale non-idealities create and control instabilities. Dense plumes (5000 mg l −1 NaCl) are introduced into a domain (1.50×0.56 m) with synthetically generated permeability fields. Simulations with the first set of realizations [mean permeability ( k)=5.7×10 −11 m 2, ln( k) variance=0.25, longitudinal correlation length ( τ x )=0.10 m, transverse correlation length ( τ z )=0.02 m] illustrate how the lower plume boundary is naturally perturbed by local-scale heterogeneities. Some of these perturbations are stable, some are highly bounded or pseudostable in certain portions of the field, while others rapidly destabilize the lower plume boundary. Even with similar macroscopic field statistics, widely varying degrees of density-induced mixing occur among different realizations. Unstable perturbations result in complex mixing features, such as coalescing of instability lobes as different portions of the plume sample various regions of the permeability field. Such mixing greatly enhances and controls the dispersion process. Based on the control that local field characteristics exhibit on instability growth and decay, the applicability of stability criteria to plume-type displacements in natural heterogeneous media is likely inappropriate. Additional simulations employing fields of lower variance and lower densities illustrate the delicate balance between these variables and the ability of the field to propagate unstable perturbations.