Stabilization of a finite slice in miscible displacement in homogeneous porous media

We numerically studied the miscible displacement of a finite slice of variable viscosity and density. The stability of the finite slice depends on different flow parameters, such as displacement velocity $U$, mobility ratio $R,$ and the density contrast. Series of numerical simulations corresponding to different ordered pair ($R$, $U)$ in the parameter space, and a given density contrast reveal six different instability regions. We have shown that independent of the width of the slice, there always exists a region of stable displacement, and below a critical value of the slice width, this stable region increases with decreasing slice width. Further we observe that the viscous fingering (buoyancy-induced instability) at the upper interface induces buoyancy-induced instability (viscous fingering) at the lower interface. Besides the fundamental fluid dynamics understanding, our results can be helpful to model CO2 sequestration and chromatographic separation.