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Nonlinear Flow Properties of Newtonian Fluids through Rough Crossed Fractures

Zhenguo Liu1,2, Shuchen Li1,3, Richeng Liu3,*, Changzhou Zheng2

1 Geotechnical and Structural Engineering Research Center, Shandong University, Jinan, 250061, China
2 Sinohydro Foundation Engineering Co., Ltd., Tianjin, 301700, China
3 State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, China

* Corresponding Author: Richeng Liu. Email: email

Computer Modeling in Engineering & Sciences 2023, 136(2), 1427-1440. https://doi.org/10.32604/cmes.2023.025414

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.

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Cite This Article

Liu, Z., Li, S., Liu, R., Zheng, C. (2023). Nonlinear Flow Properties of Newtonian Fluids through Rough Crossed Fractures. CMES-Computer Modeling in Engineering & Sciences, 136(2), 1427–1440.



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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