Open Access

ARTICLE

Nonlinear Flow Properties of Newtonian Fluids through Rough Crossed Fractures

by Zhenguo Liu^1,2, Shuchen Li^1,3, Richeng Liu^3,*, 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:

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

Received 11 July 2022; Accepted 27 October 2022; Issue published 06 February 2023

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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Keywords

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