Surface roughness and boundary load effect on nonlinear flow behavior of fluid in real rock fractures
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ORIGINAL PAPER
Surface roughness and boundary load effect on nonlinear flow behavior of fluid in real rock fractures Jiangyu Wu 1,2 & Qian Yin 1,2 & Hongwen Jing 1 Received: 24 October 2019 / Accepted: 20 May 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper experimentally evaluated the influences of the surface roughness and boundary load on the nonlinear flow behavior of real three-dimensional rock fractures. The rough fractures with various joint roughness coefficient (JRC) values in the range of 2.59 to 19.31 were generated with a fractal governing function, and the corresponding fractured granite specimens of a square plate shape in the size of 495 × 495 × 16 mm were manufactured. The fluid flow tests on these fractures were conducted with respect to various hydraulic pressures ranged from 0 to 0.6 MPa and various boundary loads ranged from 7 to 35 kN. The results show that Forchheimer’s law provides an excellent presentation of the relation between the hydraulic gradient and the flow rate, and both the linear and nonlinear fitting coefficients in the Forchheimer’s law show an increasing trend with both increases in the surface roughness and boundary load. The critical hydraulic gradient and critical Reynolds number decrease with the surface roughness. The critical hydraulic gradient increases more significantly under a small boundary load in the range of 7 to 14 kN than that under a high boundary load in the range of 21 to 35 kN. A cubic polynomial function is applied to analyze the transmissivity as a function of the hydraulic gradient, and the transmissivity shows a decreasing trend when the surface roughness and boundary load increase. The flow behavior is assessed by depicting the normalized transmissivity of the fractures based on the hydraulic gradient, and an increase in the surface roughness shifts the fitting curves downwards. The hydraulic aperture shows a hyperbolic decrease as the boundary load increased, and a power-law equation can be used to evaluate the variations in the nonlinear coefficient in terms of the hydraulic aperture. Keywords Nonlinear flow . Rough-walled fracture . Boundary load . Normalized transmissivity . Critical Reynolds number
List of symbols JRC Joint roughness coefficient u Flow velocity tensor P Hydraulic pressure ρ Fluid density Q Volume flow rate w Fracture width eh Hydraulic aperture J Hydraulic gradient
* Qian Yin [email protected] 1
State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
2
School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
a, b E Jc Re Rec T T0 T/T0 β D xi, yi M F, Fx, Fy, Fz μ L g λ, m
Linear and nonlinear coefficients in Forchheimer’s law Judge parameter of fluid flow regime Critical hydraulic gradient Reynolds number Critical Reynolds number Transmissivity Intrinsic transmissivity Normalized transmissivity Dimensionless coefficient Fractal dimension Co
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