Experimental study of the effect of roughness and Reynolds number on fluid flow in rough‐walled single fractures: a check of local cubic law

Abstract

Abstract:Local cubic law (LCL) is one of the most commonly applied physical laws for flow in single fractures (SF) and fractured media. The foundation of LCL is Darcian flow. This experimental study examines if LCL is valid for flow in a single rough fracture and how the fracture roughness and Reynolds number (Re) affect flow. Similar to the Moody diagram for flow in pipes, a diagram for flow in a single rough fracture has been generated to relate the friction coefficient with Re and the roughness. Under the experimental condition of this study, flow appears to be substantially different from Darcian flow. The flow law of q / e n J m appears to be valid for describing the flow scheme where q, e, and J are the unit width flux, the average aperture, and the hydraulic gradient. The value of the power index m is found to be around 0Ð83 ¾ 0Ð98, less than what has been used in Darcian flow (m D 1). The power index n is around 11Ð2 and 13Ð0, much greater than the n value used in the LCL (n D 3), and it increases with the average velocity. The Moody type of diagram shows that the friction factor for flow in SFs is influenced by Re and the roughness. It decreases with Re when Re is small, and becomes less sensitive to Re when Re is large enough. It also increases with the roughness.

On the cubic law and variably saturated flow through discrete open rough-walled discontinuities

“…The cubic law was devised under a situation in which the fracture walls were represented as smooth, and thus any roughness present in a fracture hinders the applicability of the cubic law [50] [55]. In order to address this, the use of the cubic law locally at each void space in a fracture (hence sometimes called LCL) is often assumed to be applicable [43].…”

“… Numerous authors have highlighted the possible from the cubic nature of the law through, for instance, recommended e 6-Dt where Dt is a number between one and two related to flow tortuosity [44], e 5 for the quantic law, or as high as e 13 [50].…”

Hydrogeologic Characterization of Fractured Rock Masses Intended for Disposal of Radioactive Waste

“…However, other studies suggest power law distributions (Gustafson & Fransson, 2005;Kozubowski et al, 2008) and that these lognormal distributions, similar to length, could be caused by censoring flow data possibly due to instrument limitations. Additionally, flow through rough-walled fractures can be non-Darcian (Cardenas et al, 2007;Qian et al, 2011;Quinn et al, 2011). This may further complicate the estimation of hydraulic conductivity in field hydraulic tests as flow is no longer linearly proportional to a pressure gradient as described by (6).…”

Laboratory Investigation of Flow Paths in 3D Self-Affine Fractures with Lattice Boltzmann Simulations

“…Among different experimental approaches, X-ray computed tomography and 3D laser scanning techniques have been proved as effective experimental approaches to characterize fracture surfaces with variable apertures [8][9][10]. Experimental studies show that fracture roughness determines fracture aperture density distribution and affects fluid flow through fractures [11][12][13][14][15].…”