Scale-independent relationship between permeability and resistivity in mated fractures with natural rough surfaces

•Numerical flow simulations reproduce experimental transport properties in fractures.•Fracture permeability and formation factor are scale-independent versus aperture.•Formulates a scale-independent relation between permeability and formation factor.•Empirical parameters of this relation correspond to microstructures of the fracture.•Connectivity of flow paths subdivides the permeability–formation factor relation. Geothermal systems consisting of fractures in impermeable rocks are difficult to characterize by in situ methods. In an effort to link characteristics of small-scale and large-scale fractures, this study investigated possible relations between their geophysical parameters. We upscaled the relationship between fracture permeability and formation factor in a laboratory specimen to larger fracture dimensions. Microscopic flow characteristics indicate that this relationship is related to the tortuosity of flow paths. We derived an empirical formula that directly predicts changes in fracture permeability from changes in formation factor. This relation may make it possible to monitor subsurface hydraulic activities through resistivity observations.