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Transport in Porous Media

, Volume 118, Issue 2, pp 301–326 | Cite as

Fluid Flow Through Single Fractures With Directional Shear Dislocations

  • Long Cheng
  • Guan RongEmail author
  • Jie Yang
  • Chuangbing Zhou
Article

Abstract

This paper numerically investigates the fluid flow behavior through single fractures with directional shear dislocations. Synthetic fractures are generated with directional shear dislocations, and the lattice Boltzmann method is used to simulate the fracture flow. With an ignorance of tortuosity effect, a notable overestimation of hydraulic conductivity is observed when the simplified local cubic law is used. During the closure process, the decreasing rate of conductivity is found to be highly related to the roughness of fractures. The conductivity of smoother fractures decreases faster than that of rougher fractures. By conducting simulations on fractures with a constant shear displacement, the effective conductivity is found to vary with the shear directions. The results show that the conductivity of rougher fractures is less sensitive to the shear directions than that of smoother fractures. As fracture surfaces come into contact, a sharp decrease in effective conductivity is observed and the decreasing trend flattens as the contact ratio continues to increase. A new model is proposed based on the bottleneck model to predict the conductivity of sheared fractures. By integrating the tortuosity and channeling effects into the original model, the proposed new model shows a better performance in predicting the conductivity, especially for fractures with rougher surfaces.

Keywords

Fracture Flow Roughness Lattice Boltzmann method (LBM) Tortuosity 

List of symbols

\(D_\mathrm{f}\)

Fractal dimension

\(K_x\)

Conductivity in x-axis direction

p

Pressure

\(\nabla p\)

Pressure gradient

q

Volumetric flow rate

Re

Reynolds number

\(\mathbf u \)

Velocity vector

\({\mu }\)

Dynamic viscosity

\(d_{0}\)

Constant separation between parallel plates

\({\rho }\)

Density of fluid

\({{\beta }}\)

Inclination angle between the macroscopic flow direction and shear direction

W

Width of the fracture

Pin, Pout

Constant pressure set on the inlet and outlet of the fracture, respectively

\(\Delta {P}\)

Driving pressure

h(xy)

Local aperture at point (xy)

\(\langle \,\,\,\rangle \)

Arithmetic mean

\(\left\langle {h(x,y)} \right\rangle _0\)

Initial aperture with only a single contact point between the opposing surfaces

\(\left\langle {h(x,y)^{3}} \right\rangle \)

Arithmetic mean local conductivity

\(\left\langle {h(x)^{-3}} \right\rangle ^{-1}\)

Nominal conductivity in x-axis direction

\({R}_{0}\), \({{\delta }}\) and \({{\lambda }}\)

Geometrical parameters of sinusoidal constricted pipes

\({{n}}_{{c}},{{N}}_{{c}}\)

\({{n}}_{{c}}\) is the number of contact points, and \({{N}}_{{c}}\) is the total number of data points

\({\eta }\)

Contact ratio

\({{D}}_{{x}}\)

Real conductivity of fracture

\(\left\langle {\tau _x^2} \right\rangle \)

Hydraulic tortuosity parameter in x-axis

\(\chi _{\ell _1 }^2 \)

In-plane tortuosity parameter of the most constrictive path \(\ell _1 \)

\(\left\langle {\tau _{\ell _2 }^2 } \right\rangle \)

Averaged mean geometrical tortuosity for preferential channels

\(\Delta \)

Width of the bottleneck region

\(\mathrm{d}\vec {l}, \vec {e}_y \)

Direction vector of the most constrictive path and unit vector in y-axis direction, respectively

\(\delta x\), \(\delta y\)

Lattice unit length in x-axis and y-axis directions

COB

The contribution fraction of bottleneck structure to the pressure drop.

Notes

Acknowledgements

The authors are grateful for the National Natural Science Foundation of China (Grant No. 51579189), the National Basic Research Program of China (“973” Program, Grant No. 2011CB013501), and the Fundamental Research Funds for the Central Universities (2042016kf0171) for providing financial support.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Long Cheng
    • 1
    • 2
  • Guan Rong
    • 1
    • 2
    Email author
  • Jie Yang
    • 1
    • 2
  • Chuangbing Zhou
    • 1
    • 2
  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of EducationWuhan UniversityWuhanChina

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