Coupled effect of viscosity and density gradients on fingering instabilities of a miscible slice in porous media

Abstract

Miscible displacements in porous media exhibit interesting spatio-temporal patterns.A deeper understanding of the physical mechanisms of these emergent patterns isrelevant in a number of physicochemical processes. Here, we have numerically investigatedthe instabilities in a miscible slice in vertical porous media. Depending on theviscosity and density gradients at the two interfaces, four distinct flow configurationsare obtained, which are partitioned into two different groups, each containing a pairof equivalent flows until the interaction between the two interfaces. An analysis of thepressure drop around the respective unstable interface(s) supports numerical results.We classify the stabilizing and destabilizing scenarios in a parameter space spannedby the log-mobility ratio (R) and the displacement velocity (U). When the viscosityand density gradients are unstably stratified at the opposite interfaces, the stabilitycharacteristics are very complex. The most notable findings of this paper are theexistence of a stable region between two unstable regions in the R-U plane andoccurrence of secondary instabilities. We further show that the stability regions inthe R-U plane depend strongly on the slice width, and beyond a threshold valueof it the stable zone remains almost unaltered. For thin sample, the stable regionexpands and the secondary instabilities disappear.