The Effect of Fracture Roughness on the Onset of Nonlinear Flow

Abstract

Abstract In fractures where surface fluctuations are large compared to their aperture ( narrow fractures ), the flow is forced to move in tortuous paths that produce additional viscous friction and are subject to inertia effects. We consider the relation between the magnitude of surface roughness and the onset of inertial effects in the pressure driving the flow through a single open fracture. We performed experiments systematically varying the average aperture of the open fracture and covering a wide range of Reynolds numbers. For each aperture, we analyze the data in terms of the Forchheimer equation and show that the critical Reynolds number, defined as the Reynolds number at which inertial effects contribute 10% of the total pressure losses, is highly correlated with the roughness of the surface. In particular, we show that significant inertial effects appear earlier as the relative importance of surface roughness increases. Finally, we present results showing that the magnitude of the deviations in the pressure field compared to a linear profile, taken at different points in the fracture along the flow direction, is directly related to the relative surface roughness of the fracture.