Pore-scale study of miscible density instability with viscosity contrast in porous media

The transport of miscible fluids in porous media is a prevalent phenomenon that occurs in various natural and industrial contexts. However, this fundamental phenomenon is usually coupled with interface instabilities (e.g., viscous/density fingering), which has yet to be thoroughly investigated. In this paper, a multiple-relaxation-time lattice Boltzmann method is applied to study the displacement between two miscible fluids in porous media at the pore scale, with the coexistence of density difference (Rayleigh number Ra), viscosity contrast ( R), and injection velocity ( U top). A parametric study is conducted to evaluate the impact of Ra, R, and U top on the flow stability. For a fixed Ra that can trigger density fingering, the increase in R or U top is found to suppress density fingering. Consequently, under a large U top and a moderate R, the density fingering is fully stabilized and the flow follows a stabile pattern. Furthermore, as both R and U top grow to a sufficiently high level, they can jointly trigger viscous fingering. In addition, the increasing Ra shows an enhancing effect on both density fingering and viscous fingering. Finally, by quantitatively analyzing the fingering length ( l m) and the fingering propagation time ( t e), five different flow patterns are classified as viscosity-suppressed (I), viscosity-enhanced (II), viscosity-unstable (III), displacement-suppressed (IV), and stable (V) regimes. In a three-dimensional parameter space spanned by Ra, R, and U top, the parameter ranges of the five regimes are determined according to l m and t e. These findings hold a significant value in providing guidance for controlling the flow stability by selecting appropriate operating conditions.