Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation

We consider miscible displacements in two-dimensional homogeneous porous media where the displacing fluid is less viscous and has a different density than the displaced fluid. We find that the dynamics evolve through nine possible regimes depending on the viscosity ratio, strength of density variations and the strength of the background flow, as characterized by the Peclet number. At early times the interface is dominated by longitudinal diffusion before undergoing a transition to a slumping regime where vertical flow is important. At intermediate times, vertical flow and diffusion can be neglected and there are three different limiting solutions: a fingering limit; an injection-driven gravity-current limit; and a density-driven gravity-current limit. Finally at late times, transverse diffusion becomes important and there is a transition from an apparent shutdown regime to a viscously enhanced Taylor-slumping regime. In each of the regimes, the dominant scalings are identified and reduced-order models for the evolution of the concentration field are developed. Lastly, three case studies are considered to illustrate the dominant physical balances in the geophysically relevant setting of geological CO2 storage.

Automated summary

This study investigates miscible displacements in 2D homogeneous porous media, considering the viscosity ratio, density variations, and background flow represented by the Peclet number. The dynamics evolve through nine regimes, involving processes like longitudinal diffusion, vertical flow, and gravity currents. Simplified models are developed to describe the evolution of the concentration field in each regime. Three case studies are also conducted to illustrate the physical balances in CO2 geological storage.