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Influence of fracture roughness and void space morphology on nonlinear fluid flow through rock fractures

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Abstract

The effects of fracture roughness and geometric morphology of void space between two fracture walls on nonlinear fluid flow through rock fractures were investigated by performing fluid dynamic computation on mated and non-mated rock fractures. The fractal dimension D was used to characterize to the morphology of fracture void space, and it shows a positive correlation with either the root mean square of the height of the fracture void space morphology or the standard deviation of roughness angle. Forchheimer equation describes the nonlinear flow behavior through rock fractures well. Compared to mated rock fractures, the unmatched morphology of fracture void space of non-mated rock fractures increased the flow heterogeneities, producing prominent preferential flow and obvious eddy flow in non-mated rock fractures. This renders the nonlinear coefficient in the Forchheimer equation of non-mated rock fractures is generally greater than that of mated rock fractures of identical fracture aperture and roughness. For mated rock fractures, a power-law relationship was proposed to quantify the nonlinear coefficient b in terms of fracture peak asperity Rz, the first derivative of the profile Z2 and fracture aperture eh, and then, the critical Reynolds number for the onset of nonlinear fluid flow was derived. To further describe the influence of fracture void space morphology on the nonlinear fluid flow through non-mated rock fractures, an extended power-law model was proposed by quantifying b in terms of fracture surface roughness parameters Rz, Z2, aperture eh and fractal dimension D, and the critical Reynolds number to demark the onset of nonlinear flow was subsequently derived. The predicted critical Reynolds number agrees well with that of fluid dynamic computation for both mated and non-mated rock fractures, validating the proposed power-law and extended power-law relationships. Our research also shows that the critical Reynolds number generally decreased with the increase in fractal dimension.

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Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request. This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the correspondind author.]

Abbreviations

ρ :

Fluid density

U :

Flow velocity vector

μ :

Fluid viscosity

F :

Body force vector

P :

Fluid pressure

∇P :

Pressure gradient

a :

Linear term coefficient

b :

Nonlinear term coefficient

Q :

Volumetric flow rate

w :

Fracture width normal to the flow direction

e h :

Hydraulic aperture

A :

Cross section area of fracture, A = ehw

k 0 :

Intrinsic permeability

β :

Non-Darcy coefficient

Re:

Reynolds number

v :

Flow velocity

E :

Non-Darcy effect factor

Rec :

Critical Reynolds number

u x :

X-Direction flow velocity

u y :

Y-Direction flow velocity

u z :

Z-Direction flow velocity

R q :

Root mean square of the height of the profile

R z :

Peak asperity height

Z 2 :

Root mean square of the first derivative of the profile

σ i :

Standard deviation of the roughness angle

θ :

Average roughness angle of the profile

L :

Projected length of fracture profile

z i :

Asperity height at point i

N :

The number of sampling points

z a :

Distance of profile from the mean elevation line

z max :

Maximum asperity height

z min :

Minimum asperity height

dz :

Increment of z of the profile

dx :

Increment of x of the profile

JRC:

Joint roughness coefficient

S(δ):

Total area of the fracture surface element

S 1, S 2, S 3 and S 4 :

Areas of four triangles in the schematic diagram of the triangular prism surface area method

δ :

Size of a square grid

h 0 :

Elevation at the center of the grid cell

a 1, b 1, c 1 :

Side length of the triangle

l 1 :

Perimeter of the triangle

N(δ):

Number of total grid cells with scale δ × δ

D :

Fractal dimension

χ :

Fitting coefficient in the relationship between S(δ) and δ2

P inlet :

Inlet pressure

c :

Coefficient dependent on the surface roughness index

m, n, m 1, n 1, p :

Dimensionless regression coefficients in the relationship between b and roughness parameters Rz, Z2 and D

k :

Uplift distance of fracture surface

d :

Dislocation distance

i, j :

Sequence number

References

  1. S.R. Brown, Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. Solid Earth. 92(B2), 1337–1347 (1987). https://doi.org/10.1029/JB092iB02p01337

    Article  Google Scholar 

  2. B. Berkowitz, Characterizing flow and transport in fractured geological media: a review. Adv. Water Resour. 25(8–12), 861–884 (2002). https://doi.org/10.1016/s0309-1708(02)00042-8

    Article  Google Scholar 

  3. D. Cunningham, H. Auradou, S. Shojaei-Zadeh, G. Drazer, The effect of fracture roughness on the onset of nonlinear flow. Water Resour. Res. 56(11), e2020WR028049 (2020). https://doi.org/10.1029/2020wr028049

    Article  Google Scholar 

  4. J.Z. Qian, H.B. Zhan, Z. Chen, H. Ye, Experimental study of solute transport under non-Darcian flow in a single fracture. J. Hydrol. 399(3–4), 246–254 (2011). https://doi.org/10.1016/j.jhydrol.2011.01.003

    Article  Google Scholar 

  5. R. Ghasemizadeh, F. Hellweger, C. Butscher, I. Padilla, D. Vesper, M. Field, A. Alshawabkeh, Review: groundwater flow and transport modeling of karst aquifers, with particular reference to the North Coast Limestone aquifer system of Puerto Rico. Hydrogeol. J. 20(8), 1441–1461 (2012). https://doi.org/10.1007/s10040-012-0897-4

    Article  Google Scholar 

  6. C.M. Oldenburg, K. Pruess, S.M. Benson, Process modeling of CO2 injection into natural gas reservoirs for carbon sequestration and enhanced gas recovery. Energy Fuels. 15(2), 293–298 (2001). https://doi.org/10.1021/ef000247h

    Article  Google Scholar 

  7. M.L. Godec, V.A. Kuuskraa, P. Dipietro, Opportunities for using anthropogenic CO2 for enhanced oil recovery and CO2 storage. Energy Fuels 27(8), 4183–4189 (2013). https://doi.org/10.1021/ef302040u

    Article  Google Scholar 

  8. A. Kamali-Asl, E. Ghazanfari, N. Perdrial, N. Bredice, Experimental study of fracture response in granite specimens subjected to hydrothermal conditions relevant for enhanced geothermal systems. Geothermics 72, 205–224 (2018). https://doi.org/10.1016/j.geothermics.2017.11.014

    Article  Google Scholar 

  9. K. Pruess, Leakage of CO2 from geologic storage: Role of secondary accumulation at shallow depth. Int. J. Greenh. Gas Control 2(1), 37–46 (2008). https://doi.org/10.1016/s1750-5836(07)00095-3

    Article  Google Scholar 

  10. A.S. Ranathunga, M.S.A. Perera, P.G. Ranjith, G.P.D. De Silva, A macro-scale view of the influence of effective stress on carbon dioxide flow behaviour in coal: an experimental study. Geomech. Geophys. Geo-Energy Geo-Resour. 3(1), 13–28 (2017). https://doi.org/10.1007/s40948-016-0042-2

    Article  Google Scholar 

  11. T. Phillips, N. Kampman, K. Bisdom, N.D.F. Inskip, S.A.M. den Hartog, V. Cnudde, A. Busch, Controls on the intrinsic flow properties of mudrock fractures: a review of their importance in subsurface storage. Earth-Sci. Rev. 211, 103390 (2020). https://doi.org/10.1016/j.earscirev.2020.103390

    Article  Google Scholar 

  12. Y.W. Tsang, P.A. Witherspoon, Hydromechanical behavior of a deformable rock fracture subject to normal stress. J. Geophys. Res. 86(NB10), 9287–9298 (1981). https://doi.org/10.1029/JB086iB10p09287

    Article  Google Scholar 

  13. T. Phillips, T. Bultreys, K. Bisdom, N. Kampman, S. Van Offenwert, A. Mascini, V. Cnudde, A. Busch, A systematic investigation into the control of roughness on the flow properties of 3D-printed fractures. Water Resour. Res. 57(4), e2020WR028671 (2021). https://doi.org/10.1029/2020wr028671

    Article  Google Scholar 

  14. C.F. Tsang, I. Neretnieks, Flow channeling in heterogeneous fractured rocks. Rev. Geophys. 36(2), 275–298 (1998). https://doi.org/10.1029/97rg03319

    Article  Google Scholar 

  15. L.C. Zou, L.R. Jing, V. Cvetkovic, Shear-enhanced nonlinear flow in rough-walled rock fractures. Int. J. Rock Mech. Min. Sci. 97, 33–45 (2017). https://doi.org/10.1016/j.ijrmms.2017.06.001

    Article  Google Scholar 

  16. Y.D. Chen, H.J. Lian, W.G. Liang, J.F. Yang, V.P. Nguyen, S.P.A. Bordas, The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses. Int. J. Rock Mech. Min. Sci. 113, 59–71 (2019). https://doi.org/10.1016/j.ijrmms.2018.11.017

    Article  Google Scholar 

  17. G. Rong, J. Tan, H.B. Zhan, R.H. He, Z.Y. Zhang, Quantitative evaluation of fracture geometry influence on nonlinear flow in a single rock fracture. J. Hydrol. 589, 125162 (2020). https://doi.org/10.1016/j.jhydrol.2020.125162

    Article  Google Scholar 

  18. Z.H. Wang, C.T. Zhou, F. Wang, C.B. Li, H.P. Xie, Channeling flow and anomalous transport due to the complex void structure of rock fractures. J. Hydrol. 601, 126624 (2021). https://doi.org/10.1016/j.jhydrol.2021.126624

    Article  Google Scholar 

  19. Z.Y. Zhang, J. Nemcik, Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J. Hydrol. 477, 139–151 (2013). https://doi.org/10.1016/j.jhydrol.2012.11.024

    Article  Google Scholar 

  20. Y.F. Chen, J.Q. Zhou, S.H. Hu, R. Hu, C.B. Zhou, Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. J. Hydrol. 529, 993–1006 (2015). https://doi.org/10.1016/j.jhydrol.2015.09.021

    Article  Google Scholar 

  21. P.A. Witherspoon, J.S.Y. Wang, K. Iwai, J.E. Gale, Validity of Cubic Law for fluid flow in a deformable rock fracture. Water Resour. Res. 16(6), 1016–1024 (1980). https://doi.org/10.1029/WR016i006p01016

    Article  Google Scholar 

  22. R.W. Zimmerman, G.S. Bodvarsson, Hydraulic conductivity of rock fractures. Transp. Porous Media 23(1), 1–30 (1996). https://doi.org/10.1007/BF00145263

    Article  Google Scholar 

  23. Y.W. Tsang, The effect of tortuosity on fluid flow through a single fracture. Water Resour. Res. 20(9), 1209–1215 (1984). https://doi.org/10.1029/WR020i009p01209

    Article  Google Scholar 

  24. L.C. Wang, M.B. Cardenas, D.T. Slottke, R.A. Ketcham, J.M. Sharp, Modification of the Local Cubic Law of fracture flow for weak inertia, tortuosity, and roughness. Water Resour. Res. 51(4), 2064–2080 (2015). https://doi.org/10.1002/2014wr015815

    Article  Google Scholar 

  25. Z.H. Wang, C.S. Xu, P. Dowd, A Modified Cubic Law for single-phase saturated laminar flow in rough rock fractures. Int. J. Rock Mech. Min. Sci. 103, 107–115 (2018). https://doi.org/10.1016/j.ijrmms.2017.12.002

    Article  Google Scholar 

  26. J.B. Dong, Y. Ju, Quantitative characterization of single-phase flow through rough-walled fractures with variable apertures. Geomech. Geophys. Geo-Energy Geo-Resour. 6(3), 42 (2020). https://doi.org/10.1007/s40948-020-00166-w

    Article  Google Scholar 

  27. R.W. Zimmerman, A. Al-Yaarubi, C.C. Pain, C.A. Grattoni, Non-linear regimes of fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci. 41(3), 384–384 (2004). https://doi.org/10.1016/j.ijrmms.2003.12.045

    Article  Google Scholar 

  28. Y. Luo, Z.Y. Zhang, Y.K. Wang, J. Nemcik, J.H. Wang, On fluid flow regime transition in rough rock fractures: insights from experiment and fluid dynamic computation. J. Hydrol. 607, 127558 (2022). https://doi.org/10.1016/j.jhydrol.2022.127558

    Article  Google Scholar 

  29. C.C. Mei, J.L. Auriault, The effect of weak inertia on flow through a porous medium. J. Fluid Mech. 222, 647–663 (1991). https://doi.org/10.1017/s0022112091001258

    Article  MathSciNet  MATH  Google Scholar 

  30. E. Skjetne, J.L. Auriault, High-velocity laminar and turbulent flow in porous media. Transp. Porous Media. 36(2), 131–147 (1999). https://doi.org/10.1023/a:1006582211517

    Article  MathSciNet  MATH  Google Scholar 

  31. P.G. Ranjith, W. Darlington, Nonlinear single-phase flow in real rock joints. Water Resour. Res. 43(9), W09502 (2007). https://doi.org/10.1029/2006wr005457

    Article  Google Scholar 

  32. C.C. Xia, X. Qian, P. Lin, W.M. Xiao, Y. Gui, Experimental investigation of nonlinear flow characteristics of real rock joints under different contact conditions. J. Hydraul. Eng. ASCE 143(3), 04016090 (2017). https://doi.org/10.1061/(asce)hy.1943-7900.0001238

    Article  Google Scholar 

  33. M. Javadi, M. Sharifzadeh, K. Shahriar, A new geometrical model for non-linear fluid flow through rough fractures. J. Hydrol. 389(1–2), 18–30 (2010). https://doi.org/10.1016/j.jhydrol.2010.05.010

    Article  Google Scholar 

  34. R.C. Liu, C.S. Wang, B. Li, Y.J. Jiang, H.W. Jing, Modeling linear and nonlinear fluid flow through sheared rough-walled joints taking into account boundary stiffness. Comput. Geotech. 120, 103452 (2020). https://doi.org/10.1016/j.compgeo.2020.103452

    Article  Google Scholar 

  35. B. Li, R.C. Liu, Y.J. Jiang, Influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect on nonlinear flow behavior at single fracture intersections. J. Hydrol. 538, 440–453 (2016). https://doi.org/10.1016/j.jhydrol.2016.04.053

    Article  Google Scholar 

  36. Y. Zhang, J.R. Chai, C. Cao, T. Shang, Combined influences of shear displacement, roughness, and pressure gradient on nonlinear flow in self-affine fractures. J. Pet. Sci. Eng. 198, 108229 (2021). https://doi.org/10.1016/j.petrol.2020.108229

    Article  Google Scholar 

  37. W.G. Dang, W. Wu, H. Konietzky, J.Y. Qian, Effect of shear-induced aperture evolution on fluid flow in rock fractures. Comput. Geotech. 114, 103152 (2019). https://doi.org/10.1016/j.compgeo.2019.103152

    Article  Google Scholar 

  38. X.B. Xiong, B. Li, Y.J. Jiang, T. Koyama, C.H. Zhang, Experimental and numerical study of the geometrical and hydraulic characteristics of a single rock fracture during shear. Int. J. Rock Mech. Min. Sci. 48(8), 1292–1302 (2011). https://doi.org/10.1016/j.ijrmms.2011.09.009

    Article  Google Scholar 

  39. Q. Yin, G.W. Ma, H.W. Jing, H.D. Wang, H.J. Su, Y.C. Wang, R.C. Liu, Hydraulic properties of 3D rough-walled fractures during shearing: an experimental study. J. Hydrol. 555, 169–184 (2017). https://doi.org/10.1016/j.jhydrol.2017.10.019

    Article  Google Scholar 

  40. J.Q. Zhou, Y.F. Chen, L.C. Wang, M.B. Cardenas, Universal relationship between viscous and inertial permeability of geologic porous media. Geophys. Res. Lett. 46(3), 1441–1448 (2019). https://doi.org/10.1029/2018gl081413

    Article  Google Scholar 

  41. D. Crandall, G. Bromhal, Z.T. Karpyn, Numerical simulations examining the relationship between wall-roughness and fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci. 47(5), 784–796 (2010). https://doi.org/10.1016/j.ijrmms.2010.03.015

    Article  Google Scholar 

  42. N. Huang, R.C. Liu, Y.Y. Jiang, B. Li, L.Y. Yu, Effects of fracture surface roughness and shear displacement on geometrical and hydraulic properties of three-dimensional crossed rock fracture models. Adv. Water Resour. 113, 30–41 (2018). https://doi.org/10.1016/j.advwatres.2018.01.005

    Article  Google Scholar 

  43. Y.D. Chen, A.P.S. Selvadurai, Z.H. Zhao, Modeling of flow characteristics in 3D rough rock fracture with geometry changes under confining stresses. Comput. Geotech. 130, 103910 (2021). https://doi.org/10.1016/j.compgeo.2020.103910

    Article  Google Scholar 

  44. L.C. Zou, L.R. Jing, V. Cvetkovic, Roughness decomposition and nonlinear fluid flow in a single rock fracture. Int. J. Rock Mech. Min. Sci. 75, 102–118 (2015). https://doi.org/10.1016/j.ijrmms.2015.01.016

    Article  Google Scholar 

  45. M. Wang, Y.F. Chen, G.W. Ma, J.Q. Zhou, C.B. Zhou, Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: Lattice Boltzmann simulations. Adv. Water Resour. 96, 373–388 (2016). https://doi.org/10.1016/j.advwatres.2016.08.006

    Article  Google Scholar 

  46. Z. Dou, B. Sleep, H.B. Zhan, Z.F. Zhou, J.G. Wang, Multiscale roughness influence on conservative solute transport in self-affine fractures. Int. J. Heat Mass Transf. 133, 606–618 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2018.12.141

    Article  Google Scholar 

  47. Z. Zhang, J. Nemcik, Friction factor of water flow through rough rock fractures. Rock Mech. Rock Eng. 46(5), 1125–1134 (2013). https://doi.org/10.1007/s00603-012-0328-9

    Article  Google Scholar 

  48. Y. Zhang, J.R. Chai, Effect of surface morphology on fluid flow in rough fractures: a review. J. Nat. Gas Sci. Eng. 79, 103343 (2020). https://doi.org/10.1016/j.jngse.2020.103343

    Article  Google Scholar 

  49. C. Fallico, M.C. Vita, S. De Bartolo, S. Straface, Scaling effect of the hydraulic conductivity in a confined aquifer. Soil Sci. 177(6), 385–391 (2012). https://doi.org/10.1097/SS.0b013e31824f179c

    Article  Google Scholar 

  50. C. Fallico, S. De Bartolo, M. Veltri, G. Severino, On the dependence of the saturated hydraulic conductivity upon the effective porosity through a power law model at different scales. Hydrol. Process. 30(13), 2366–2372 (2016). https://doi.org/10.1002/hyp.10798

    Article  Google Scholar 

  51. C. Fallico, S. De Bartolo, G.F.A. Brunetti, G. Severino, Use of fractal models to define the scaling behavior of the aquifers’ parameters at the mesoscale. Stoch. Environ. Res. Risk Assess. 35(5), 971–984 (2021). https://doi.org/10.1007/s00477-020-01881-2

    Article  Google Scholar 

  52. G. Rong, J. Yang, L. Cheng, C.B. Zhou, Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process. J. Hydrol. 541, 1385–1394 (2016). https://doi.org/10.1016/j.jhydrol.2016.08.043

    Article  Google Scholar 

  53. R.C. Liu, B. Li, Y.J. Jiang, L.Y. Yu, A numerical approach for assessing effects of shear on equivalent permeability and nonlinear flow characteristics of 2-D fracture networks. Adv. Water Resour. 111, 289–300 (2018). https://doi.org/10.1016/j.advwatres.2017.11.022

    Article  Google Scholar 

  54. C.S. Wang, Y.J. Jiang, R.C. Liu, C. Wang, Z.Y. Zhang, S. Sugimoto, Experimental study of the nonlinear flow characteristics of fluid in 3D rough-walled fractures during shear process. Rock Mech. Rock Eng. 53(6), 2581–2604 (2020). https://doi.org/10.1007/s00603-020-02068-5

    Article  Google Scholar 

  55. S.C. Bandis, A.C. Lumsden, N.R. Barton, Fundamentals of rock joint deformation. Int. J. Rock Mech. Min. Sci. 20(6), 249–268 (1983). https://doi.org/10.1016/0148-9062(83)90595-8

    Article  Google Scholar 

  56. R.W. Zimmerman, D.W. Chen, N.G.W. Cook, The effect of contact area on the permeability of fractures. J. Hydrol. 139(1–4), 79–96 (1992). https://doi.org/10.1016/0022-1694(92)90196-3

    Article  Google Scholar 

  57. F. Xiong, Q.H. Jiang, Z.Y. Ye, X.B. Zhang, Nonlinear flow behavior through rough-walled rock fractures: the effect of contact area. Comput. Geotech. 102, 179–195 (2018). https://doi.org/10.1016/j.compgeo.2018.06.006

    Article  Google Scholar 

  58. J.P. Wang, H.C. Ma, J.Z. Qian, P.C. Feng, X.H. Tan, L. Ma, Experimental and theoretical study on the seepage mechanism characteristics coupling with confining pressure. Eng. Geol. 291, 106224 (2021). https://doi.org/10.1016/j.enggeo.2021.106224

    Article  Google Scholar 

  59. H.C. Ma, P.C. Feng, J.Z. Qian, X.H. Tan, J.P. Wang, L. Ma, Q.K. Luo, Theoretical models of fracture deformation based on aperture distribution. Eur. Phys. J. Plus 137(8), 898 (2022). https://doi.org/10.1140/epjp/s13360-022-03129-0

    Article  Google Scholar 

  60. J.Q. Zhou, S.H. Hu, S. Fang, Y.F. Chen, C.B. Zhou, Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading. Int. J. Rock Mech. Min. Sci. 80, 202–218 (2015). https://doi.org/10.1016/j.ijrmms.2015.09.027

    Article  Google Scholar 

  61. M. Javadi, M. Sharifzadeh, K. Shahriar, Y. Mitani, Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resour. Res. 50(2), 1789–1804 (2014). https://doi.org/10.1002/2013wr014610

    Article  Google Scholar 

  62. N. Huang, R.C. Liu, Y.J. Jiang, Numerical study of the geometrical and hydraulic characteristics of 3D self-affine rough fractures during shear. J. Nat. Gas Sci. Eng. 45, 127–142 (2017). https://doi.org/10.1016/j.jngse.2017.05.018

    Article  Google Scholar 

  63. R.C. Liu, N. Huang, Y.J. Jiang, H.W. Jing, L.Y. Yu, A numerical study of shear-induced evolutions of geometric and hydraulic properties of self-affine rough-walled rock fractures. Int. J. Rock Mech. Min. Sci. 127, 104211 (2020). https://doi.org/10.1016/j.ijrmms.2020.104211

    Article  Google Scholar 

  64. T. Ishibashi, D. Elsworth, Y. Fang, J. Riviere, B. Madara, H. Asanuma, N. Watanabe, C. Marone, Friction-stability-permeability evolution of a fracture in granite. Water Resour. Res. 54(12), 9901–9918 (2018). https://doi.org/10.1029/2018wr022598

    Article  Google Scholar 

  65. Y.D. Chen, Z.H. Zhao, Correlation between shear induced asperity degradation and acoustic emission energy in single granite fracture. Eng. Fract. Mech. 235, 107184 (2020). https://doi.org/10.1016/j.engfracmech.2020.107184

    Article  Google Scholar 

  66. M.B. Cardenas, Three-dimensional vortices in single pores and their effects on transport. Geophys. Res. Lett. 35(18), L18402 (2008). https://doi.org/10.1029/2008gl035343

    Article  Google Scholar 

  67. K. Chaudhary, M.B. Cardenas, W. Deng, P.C. Bennett, Pore geometry effects on intrapore viscous to inertial flows and on effective hydraulic parameters. Water Resour. Res. 49(2), 1149–1162 (2013). https://doi.org/10.1002/wrcr.20099

    Article  Google Scholar 

  68. B. Li, Y.J. Jiang, T. Koyama, L.R. Jing, Y. Tanabashi, Experimental study of the hydro-mechanical behavior of rock joints using a parallel-plate model containing contact areas and artificial fractures. Int. J. Rock Mech. Min. Sci. 45(3), 362–375 (2008). https://doi.org/10.1016/j.ijrmms.2007.06.004

    Article  Google Scholar 

  69. N. Barton, V. Choubey, The shear strength of rock joints in theory and practice. Rock Mech. 10(1), 1–54 (1977). https://doi.org/10.1007/BF01261801

    Article  Google Scholar 

  70. K.S. Xue, Z.Y. Zhang, C.L. Zhong, Y.J. Jiang, X.Y. Geng, A fast numerical method and optimization of 3D discrete fracture network considering fracture aperture heterogeneity. Adv. Water Resour. 162, 104164 (2022). https://doi.org/10.1016/j.advwatres.2022.104164

    Article  Google Scholar 

  71. K. Xing, J.Z. Qian, W.D. Zhao, H.C. Ma, L. Ma, Experimental and numerical study for the inertial dependence of non-Darcy coefficient in rough single fractures. J. Hydrol. 603, 127148 (2021). https://doi.org/10.1016/j.jhydrol.2021.127148

    Article  Google Scholar 

  72. Z.W. Zeng, R. Grigg, A criterion for non-Darcy flow in porous media. Transp. Porous Media 63(1), 57–69 (2006). https://doi.org/10.1007/s11242-005-2720-3

    Article  Google Scholar 

  73. M.B. Cardenas, D.T. Slottke, R.A. Ketcham, J.M. Sharp, Navier–Stokes flow and transport simulations using real fractures shows heavy tailing due to eddies. Geophys. Res. Lett. 34(14), L14404 (2007). https://doi.org/10.1029/2007GL030545

    Article  Google Scholar 

  74. Y.R. Li, Y.B. Zhang, Quantitative estimation of joint roughness coefficient using statistical parameters. Int. J. Rock Mech. Min. Sci. 77, 27–35 (2015). https://doi.org/10.1016/j.ijrmms.2015.03.016

    Article  Google Scholar 

  75. R. Tse, D.M. Cruden, Estimating joint roughness coefficients. Int. J. Rock Mech. Min. Sci. 16(5), 303–307 (1979). https://doi.org/10.1016/0148-9062(79)90241-9

    Article  Google Scholar 

  76. E. Magsipoc, Q. Zhao, G. Grasselli, 2D and 3D roughness characterization. Rock Mech. Rock Eng. 53(3), 1495–1519 (2020). https://doi.org/10.1007/s00603-019-01977-4

    Article  Google Scholar 

  77. K.C. Clarke, Computation of the fractal dimension of topographic surface using the triangular prism surface-area method. Comput. Geosci. 12(5), 713–722 (1986). https://doi.org/10.1016/0098-3004(86)90047-6

    Article  Google Scholar 

  78. K. Develi, T. Babadagli, Quantification of natural fracture surfaces using fractal geometry. Math. Geol. 30(8), 971–998 (1998). https://doi.org/10.1023/a:1021781525574

    Article  Google Scholar 

  79. S. Jaggi, D.A. Quattrochi, N.S.N. Lam, Implementation and operation of three fractal measurement algorithms for analysis of remote-sensing data. Comput. Geosci. 19(6), 745–767 (1993). https://doi.org/10.1016/0098-3004(93)90048-a

    Article  Google Scholar 

  80. Y.C. Li, S.Y. Sun, H.W. Yang, Scale dependence of waviness and unevenness of natural rock joints through fractal analysis. Geofluids 2020, 8818815 (2020). https://doi.org/10.1155/2020/8818815

    Article  Google Scholar 

  81. C. Chen, S.X. Wang, C. Lu, Y.X. Liu, J.C. Guo, J. Lai, L. Tao, K.D. Wu, D.L. Wen, Experimental study on the effectiveness of using 3D scanning and 3D engraving technology to accurately assess shale fracture conductivity. J. Pet. Sci. Eng. 208, 109493 (2022). https://doi.org/10.1016/j.petrol.2021.109493

    Article  Google Scholar 

  82. M. Fourar, G. Radilla, R. Lenormand, C. Moyne, On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media. Adv. Water Resour. 27(6), 669–677 (2004). https://doi.org/10.1016/j.advwatres.2004.02.021

    Article  Google Scholar 

  83. N. Barton, E.F. de Quadros, Joint aperture and roughness in the prediction of flow and groutability of rock masses. Int. J. Rock Mech. Min. Sci. 34(3), 252.e214-252.251 (1997). https://doi.org/10.1016/S1365-1609(97)00081-6

    Article  Google Scholar 

  84. C. Louis, A study of groundwater flow in jointed rock and its influence on the stability of rock masses, Rock Mech. Res. Rep. 10 (Imp. Coll., London, 1969).

  85. S. Foroughi, S. Jamshidi, M.R. Pishvaie, New correlative models to improve prediction of fracture permeability and inertial resistance coefficient. Transp. Porous Media. 121(3), 557–584 (2018). https://doi.org/10.1007/s11242-017-0930-0

    Article  MathSciNet  Google Scholar 

  86. Q. Zhang, S.H. Luo, H.C. Ma, X. Wang, J.Z. Qian, Simulation on the water flow affected by the shape and density of roughness elements in a single rough fracture. J. Hydrol. 573, 456–468 (2019). https://doi.org/10.1016/j.jhydrol.2019.03.069

    Article  Google Scholar 

  87. J.Z. Qian, L. Ma, H.B. Zhan, Q.K. Luo, X. Wang, M. Wang, The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion. Hydrol. Process. 30(11), 1718–1726 (2016). https://doi.org/10.1002/hyp.10745

    Article  Google Scholar 

  88. P.M. Quinn, J.A. Cherry, B.L. Parker, Relationship between the critical Reynolds number and aperture for flow through single fractures: evidence from published laboratory studies. J. Hydrol. 581, 124384 (2020). https://doi.org/10.1016/j.jhydrol.2019.124384

    Article  Google Scholar 

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Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (Nos. 51674047 and 51911530152).

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  1. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Yong Luo, Zhenyu Zhang, Kangsheng Xue & Kun Long

  2. Geofluids, Geomechanics and Geoenergy (3G) Research Group, Chongqing University, Chongqing, 400044, China

    Yong Luo, Zhenyu Zhang, Kangsheng Xue & Kun Long

  3. School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

    Lei Zhang

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Luo, Y., Zhang, Z., Zhang, L. et al. Influence of fracture roughness and void space morphology on nonlinear fluid flow through rock fractures. Eur. Phys. J. Plus 137, 1288 (2022). https://doi.org/10.1140/epjp/s13360-022-03499-5

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