Macroscale model and viscousinertia effects for NavierStokes flow in a radial fracture with corrugated walls

Abstract

The radial Navier–Stokes flow in a fracture bounded by impermeable corrugated rock surfaces is significantly different from the commonly used creeping flow model between two parallel surfaces, described by Darcy's law on the macroscale. Continuous variations in the Reynolds number along the radial coordinate determine the important role of the nonlinear inertial effects, which are reinforced by local oscillations of the velocity field caused by wall corrugation. The system behaviour is studied both analytically and numerically. A solution for the full system of Navier–Stokes equations in a thin cylindrical domain with oscillating walls is developed as a biparametric and two-scale asymptotic expansion with respect to fracture aperture and corrugation period. The numerical solution is derived based on the finite volume method. A new macroscale flow equation is obtained, which explicitly displays the relative roles of viscous dissipation caused by corrugation, local and global inertia, and cross inertia–viscous effects. The effective flow parameters are defined using analytical relationships.

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

“…For instance, Fourar and Lenormand (2001) generated an artificial SF by gluing a layer of glass beads to two glass plates to study two‐phase flow at high velocities through such an SF. Bues et al (2004, Figure 1) studied flow in an SF with rectangular corrugation or roughness. One goal of this study is to examine a generic relationship between the flow rate and the hydraulic gradient for flow in an SF based on various controlled surface roughnesses.…”

Non-Darcian flow in a single confined vertical fracture toward a well

“…Qian et al (2005) have provided experimental evidence for the fully developed turbulent flow in a single fracture. Bues et al (2004) have shown that radial Navier-Stokes flow in a fracture with corrugated rock surface is significantly different from Darcian flow. Kohl et al (1997) have provided clear experimental evidence of non-Darcian flow at the hot dry rock (HDR) test site Soultz of France.…”

Flow of yield stress and Carreau fluids through rough‐walled rock fractures: Prediction and experiments

“…Using the asymptotic expansions method in a thin cylindrical channel with oscillating walls and averaging over the channel diameter, Buès et al . [] and Panfilov and Fourar [] presented a macroscopic flow equation which proved to be in good agreement with numerical simulations in rectangular and cylindrical fractures at high flow rates. This flow equation was expressed in the form of a full cubic law: where β and d are the inertial coefficients which may be positive or negative, depending on the channel geometry.…”