Fluid flow in synthetic rough‐walled fractures: Navier‐Stokes, Stokes, and local cubic law simulations

The results of three‐dimensional Navier‐Stokes (NS) and Stokes simulations and two‐dimensional local cubic law (LCL) simulations of fluid flow through single rough‐walled fractures are presented. Synthetic rough‐walled fractures were created by combining random fields of aperture and the mean wall topography or midsurface, which quantifies undulation about the fracture plane. A finite volume formulation of the LCL that incorporates geometric corrections for fracture undulation is presented. Simulations of fluid flow through planar fractures with sinusoidal variation in aperture were compared to published results. The rough‐walled fracture simulations demonstrated that the total flow rates predicted by the corrected LCL were within 10% of those predicted by the Stokes equations for all the fractures examined in this work. Differences between the NS and Stokes simulations clearly demonstrated that inertial forces can significantly influence the internal flow field within a fracture and the total flow rate across a fracture. By limiting the total flow rate differences between the NS and Stokes simulations, constraints for three kinematic parameters were determined. For all the fractures presented in this work, the corrected LCL was determined to be an acceptable approximation to the NS equations, provided that the kinematic and geometric constraints were met.