Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Abstract

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.

Experimental Investigation of the Effects of Porosity, Hydraulic Conductivity, Strength, and Flow Rate on Fluid Flow in Weakly Cemented Bio-Treated Sands

“…While competent and dense rock has been extensively studied [36][37][38][39], the behaviour of weaker, transitional materials is still not well understood since such weakly cemented materials (found in shallow to intermediate depths underground) have been rarely characterised under certain fluid injection regimes (e.g., radial-uniform flow, viscosity dominated, viscous drag-dominated, grain displacement or fracturing, non-invasive fracturing capillary dominated and viscous dominated regimes) [40][41][42].…”

Experimental study on seepage characteristics of microfracture with different aperture

“…Cubic law is the most popularity single joint seepage model. It simplifies the rough joint as two ideal smooth parallel plates and reveals the seepage characteristics of single joint 6 . In the cubic law, the permeability is only related to the fracture aperture.…”