Emergence of Unstable Focused Flow Induced by 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 the 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 (RTI), and flow topology analysis is applied to identify 3D vortices that are caused by the RTI. 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. Groundwater systems are often composed of fractured rocks, and the fractures provide major pathways for groundwater flow and mass transport. Fractured rock aquifers account for about 75% of the Earth's near-surface aquifer systems, and fluids with different densities often coexist in subsurface fractures. Thus, understanding the role of variable-density fluids on fracture flows is essential for managing groundwater resources and predicting, designing, and operating many subsurface applications. The effects of density are strongest in vertical fractures; however, most previous studies on flow and transport through fractures are limited to horizontal fractures, and few have investigated the density effects on flow and mixing through vertical fractures. In this study, we report both experimental and numerical evidence of an intriguing, focused flow path caused by a density contrast between two fluids and elucidate the underlying mechanisms triggering the resulting unstable focused flow in vertical fractures, which we name a "runlet." Further, vortices, which are characterized by rotating flow patterns, are shown to emerge and control the instability of the runlet. Since the runlet dramatically affects fluid distribution, residence time, and mixing, the findings in this study have direct implications for managing groundwater resources and subsurface applications. The density difference between injected and ambient fluids induces unstable focused flow in vertical fracturesFlow topology analysis is used to identify vortices that are caused by Rayleigh-Taylor instabilityFluid inertia controls the instability of the focused flow by affecting the size and movement of vortices, even in laminar flow regimes