@Article{cmes.2023.025414,
AUTHOR = {Zhenguo Liu, Shuchen Li, Richeng Liu, Changzhou Zheng},
TITLE = {Nonlinear Flow Properties of Newtonian Fluids through Rough Crossed Fractures},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {136},
YEAR = {2023},
NUMBER = {2},
PAGES = {1427--1440},
URL = {http://www.techscience.com/CMES/v136n2/51568},
ISSN = {1526-1506},
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<sup>−6</sup>), the streamlines are parallel to the fracture walls, indicating a linear streamline distribution. When the hydraulic gradient is large (i.e., 10<sup>0</sup>), 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<sup>−6</sup> to 10<sup>0</sup>, 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<sup>−5</sup> to 5.82 × 10<sup>−2</sup> 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.},
DOI = {10.32604/cmes.2023.025414}
}