Nonlinear Flow Properties of Newtonian Fluids through Rough Crossed Fractures

Abstract

The nonlinear flow properties of Newtonian fluids through crossed fractures are estimated by considering the influences of length, aperture, and surface roughness of fractures. A total of 252 computational runs are performed by creating 36 computational domains, in which the Navier-Stokes equations are solved. The results show that the nonlinear relationship between flow rate and hydraulic gradient follows Forchheimer’s law–based equation. When the hydraulic gradient is small (i.e., 10−6), the streamlines are parallel to the fracture walls, indicating a linear streamline distribution. When the hydraulic gradient is large (i.e., 100), the streamlines are disturbed by a certain number of eddies, indicating a nonlinear streamline distribution. The patterns of eddy distributions depend on the length, aperture, and surface roughness of fractures. With the increment of hydraulic gradient from 10−6 to 100, the ratio of flow rate to hydraulic gradient holds constants and then decreases slightly and finally decreases robustly. The fluid flow experiences a linear flow regime, a weakly nonlinear regime, and a strongly nonlinear regime, respectively. The critical hydraulic gradient ranges from 3.27 × 10−5 to 5.82 × 10−2 when fracture length = 20–100 mm and mechanical aperture = 1–5 mm. The joint roughness coefficient plays a negligible role in the variations in critical hydraulic gradient compared with fracture length and/or mechanical aperture. The critical hydraulic gradient decreases with increasing mechanical aperture, following power-law relationships. The parameters in the functions are associated with fracture length.