Natural fractures are ubiquitous in the subsurface and can be the fundamental controls on fluid flow in geological reservoirs; however, their multi-scale properties are notoriously difficult to characterize, quantify, and model (e.g., Berkowitz, 2002;Kazemi & Gilman, 1993;Neuman, 2005). Hydraulically well-connected fractures form high-permeability networks that provide the essential pathways for fluid flow in a geological formation while isolated or poorly connected fractures tend to enhance the permeability of the formation. Both scenarios usually lead to enhanced spreading of groundwater contaminants, early breakthrough of injected fluids (e.g., cold water in a geothermal reservoir or gas/water in a hydrocarbon reservoir), or rapid migration and potential leakage of CO 2 during subsurface CO 2 storage.When two fluid phases coexist in a fractured geological formation, for example, during CO 2 injection into a saline aquifer or during oil production from a hydrocarbon reservoir, the wettability of the rock matrix is also a key factor that impacts the migration of the fluids because the balance between capillary, viscous, and gravitational forces controls how readily fluids are exchanged between fractures and rock matrix (e.g.,