In this study we measured high-velocity pressure loss over Bentheimer sandstone fractures with varying fracture widths. Direct measurements of the roughness showed that the fractures were self-affine. The new results suport the rough fracture high-velocity pressure loss model. The high-velocity pressure loss was described by a Forchheimer equation with a dominating square term. The square term is a power law in fracture width, and the power is given by a roughness exponent. For low velocities the pressure loss was not described by the Forchheimer equation. In agreement with theory, there exists a weak inertia flow regime, which separates the Darcy flow regime from the Forchheimer flow regime. An expression for the incremental high-velocity skin of a pinched-out hydraulic fracture was derived. The skin is a power law in fracture width.
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