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.
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Abbreviations
- JRC:
-
Joint roughness coefficient
- u :
-
Flow velocity tensor
- P :
-
Hydraulic pressure
- ρ :
-
Fluid density
- Q :
-
Volume flow rate
- w :
-
Fracture width
- e h :
-
Hydraulic aperture
- J :
-
Hydraulic gradient
- a, b :
-
Linear and nonlinear coefficients in Forchheimer’s law
- E :
-
Judge parameter of fluid flow regime
- J c :
-
Critical hydraulic gradient
- Re :
-
Reynolds number
- Re c :
-
Critical Reynolds number
- T :
-
Transmissivity
- T 0 :
-
Intrinsic transmissivity
- T/T0 :
-
Normalized transmissivity
- β :
-
Dimensionless coefficient
- D :
-
Fractal dimension
- xi, yi :
-
Coordinates of fracture profile
- M :
-
Number of sampling points
- F, Fx, Fy, Fz :
-
Boundary load
- μ :
-
Dynamic viscosity
- L :
-
Length of flow path
- g :
-
Gravitational acceleration
- λ, m :
-
Regression coefficient
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Funding
This work was supported by the National Natural Science Foundation of China (51904290), Natural Science Foundation of Jiangsu Province, China (BK20180663) and China Postdoctoral Science Foundation (2019 M661987).
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J.Y. Wu and Q. Yin conceived and designed the experiments. J.Y. Wu and Q. Yin performed the experiments. J.Y. Wu, Q. Yin, and H.W. Jing analyzed the data. J.Y. Wu, Q. Yin, and H.W. Jing wrote the paper.
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Wu, J., Yin, Q. & Jing, H. Surface roughness and boundary load effect on nonlinear flow behavior of fluid in real rock fractures. Bull Eng Geol Environ 79, 4917–4932 (2020). https://doi.org/10.1007/s10064-020-01860-5
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DOI: https://doi.org/10.1007/s10064-020-01860-5