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.

Quantitative prediction of natural and induced phenomena in fractured rock is one of the great challenges in the Earth and Energy Sciences with far-reaching economic and environmental impacts. Fractures occupy a very small volume of a subsurface formation but often dominate flow, transport and mechanical deformation behavior. They play a central role in CO2 sequestration, nuclear waste disposal, hydrogen storage, geothermal energy production, nuclear nonproliferation, and hydrocarbon extraction. These applications require prediction of fracture-dependent quantities of interest such as CO2 leakage rate, hydrocarbon production, radionuclide plume migration, and seismicity; to be useful, these predictions must account for uncertainty inherent in subsurface systems. Here, we review recent advances in fractured rock research that cover field- and laboratory-scale experimentation, numerical simulations, and uncertainty quantification. We discuss how these have greatly improved the fundamental understanding of fractures and one’s ability to predict flow and transport in fractured systems. Dedicated field sites provide quantitative measures of fracture flow that can be used to identify dominant coupled processes and to validate models. Laboratory-scale experiments fill critical knowledge gaps by providing direct observations and measurements of fracture geometry and flow under controlled conditions that cannot be obtained in the field. Physics-based simulation of flow and transport provide a bridge in understanding between controlled simple laboratory experiments and the massively complex field-scale fracture systems. Finally, we review the use of machine learning-based emulators to rapidly investigate different fracture property scenarios and to accelerate physics-based models by orders of magnitude to enable uncertainty quantification and near real-time analysis.