Combined influences of shear displacement, roughness, and pressure gradient on nonlinear flow in self-affine fractures

Abstract

This study numerically investigated the nonlinear flow behaviors under the combined influences of shear displacement, roughness, and pressure gradient. Two-dimensional (2D) self-affine fractures with five fractal dimensions (1.1–1.5) were generated by the Weierstrass−Mandelbrot (W−M) function. Different conditions with six shear displacements (0.5–3.0 mm) and five pressure gradients (1–100 kPa/m) were applied to each model and the nonlinear flow behaviors were investigated based on microscopic descriptions and macroscopic characterizations. The results show that shear displacement coupled with the effect of high roughness can easily lead to heterogeneous void spaces and emergence of eddies. The flow rate of unmated rough fractures is always larger than that of mated rough fractures due to the effects of geometries and eddies, while this situation may be reversed in relatively smooth fractures. Rougher fractures correspond to lower flow rates under the same conditions and many eddies still exist although the fractures are mated. Increasing the pressure gradient can accelerate the development of eddies in rough fractures, while when the pressure gradient exceeds a certain value, its effect is restrained by apertures. In general, increasing the shear displacement and roughness can enhance the proportion of the quadratic term in Forchheimer's law. However, not all fractures were satisfied with these points. Increasing the shear displacement from 2.5 mm to 3.0 mm in the fracture with fractal dimension of 1.1 and increasing the fractal dimension from 1.4 to 1.5 at the shear displacement of 1.0 mm both decreased the proportion of the quadratic term. The ratio of the mechanical aperture to the hydraulic aperture (E/e) varies between 1.0 and 2.8, and its relationship with the Reynolds number (Re) can be described by a power function for the fractures with the fractal dimension of 1.1–1.4 (or JRC = 0.3–18). The relationship of E/e versus Re is strongly dependent on the fracture roughness, and for a given roughness the relationship is almost the same under different shear displacements and pressure gradients. However, this phenomenon is no longer valid as the fracture becomes rougher. The results of this study can deeply advance the understanding of nonlinear flow in rough fractures and its dependence on shear displacement, roughness, pressure gradient, and especially their combined influences under high Re.