Numerical simulation setup for variable-density flows in vertical fractures

Fluids with different densities often coexist in subsurface fractures and lead to variable-density flows that control subsurface processes such as seawater intrusion, contaminant transport, and geologic carbon sequestration. In nature, fractures have dip angles relative to gravity, and density effects are maximized in vertical fractures. However, most studies on flow and transport through fractures are often limited to horizontal fractures. Here, we study the mixing and transport of variable density fluids in vertical fractures by combining three-dimensional (3D) pore-scale numerical simulations and visual laboratory experiments. Two miscible fluids with different densities are injected through two inlets at the bottom of a fracture and exit from an outlet at the top of the fracture. Laboratory experiments show the emergence of an unstable focused flow path, which we term a “runlet.” We successfully reproduce an unstable runlet using 3D numerical simulations, and elucidate the underlying mechanisms triggering the runlet. Dimensionless number analysis shows that the runlet instability arises due to the Rayleigh-Taylor instability, and flow topology analysis is applied to identify 3D vortices that are caused by the Rayleigh-Taylor instability. Even under laminar flow regimes, fluid inertia is shown to control the runlet instability by affecting the size and movement of vortices. Finally, we confirm the emergence of a runlet in rough-walled fractures. Since a runlet dramatically affects fluid distribution, residence time, and mixing, the findings in this study have direct implications for the management of groundwater resources and subsurface applications.