Advertisement

Transport in Porous Media

, Volume 124, Issue 1, pp 1–30 | Cite as

Computational Modeling of Hydraulic Properties of a Sheared Single Rock Fracture

  • Amir A. Mofakham
  • Matthew Stadelman
  • Goodarz Ahmadi
  • Kevin T. Shanley
  • Dustin CrandallEmail author
Article
  • 291 Downloads

Abstract

Flow through a single mechanically sheared Marcellus shale fracture was investigated computationally and experimentally. To provide a better understanding of the variation of hydraulic and geometrical characteristics of a fracture subjected to shearing, coupled shear flow tests on the fracture for four shearing displacement steps under constant normal stress were performed. At the end of each shearing step, computed tomography (CT) scans with resolution 26.8 μm were obtained and the corresponding fracture geometries were evaluated. The CT images were used to generate full aperture maps of the fracture configuration. In addition, average aperture maps were also created by averaging the full-resolution data over 10 × 10 pixels, smoothing out fine structural details. Computational modeling of water flow through the fractures at different shearing steps was performed using a modified local cubic law approach and the 3D full Navier–Stokes equations with the use of the ANSYS-Fluent software. Both the average aperture maps and full maps were used in these simulations. The experimental pressure drops of the fracture at shearing step 1, which has very small apertures, poorly matched the numerical results, quite likely because the fracture structure was inadequately captured by the scanning resolution. Shearing typically increased the aperture height of the fracture, whose features were then better captured by the CT scan. Good agreement between the experimental data and the numerical results of the full map for shearing step 2 was observed. The simulations were performed for both full and average aperture maps, and the effects of scan resolution and surface roughness on the accuracy of the results were studied. The modified local cubic law and full Navier–Stokes simulations of the averaged map fracture were found to be in good agreement. It was conjectured that this was because the nonlinear losses were insignificant for the smoothed out averaged map fracture. Similar comparisons with those of the full map showed agreement in trends, but there were some quantitative differences. The averaged fracture map simulations also predicted lower pressure drops compared to the full map, particularly for high flow rates. These differences were due to the fine-scale geometrical complexity (surface roughness) of fracture geometry that affects the fluid flow in the fracture. An improved cubic law model was also proposed, and its accuracy was verified by comparing its predictions with those of the Navier–Stokes simulations.

Keywords

Coupled shear flow Computed tomography Local cubic law Improved cubic law Navier–Stokes 

Notes

Acknowledgements

The authors would like to thank Karl Jarvis and Bryan Tennant for their superior laboratory assistance in the described experimental tests. Thanks are also given to Sara Brown, Magdalena Gill, and Johnathon Moore of NETL for review of the manuscript and helpful comments. This research was supported in part by an appointment from the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education. The author’s affiliation with The MITRE Corporation is provided for identification purposes only and is not intended to convey or imply MITRE’s concurrence with, or support for, the positions, opinions, or viewpoints expressed by the author.

References

  1. ANSYS® FLUENT Academic Research: Release 16.1 (2015)Google Scholar
  2. Barton, N., Bandis, S., Bakhtar, K.: Strength, deformation and conductivity coupling of rock joints. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 3, 121–140 (1985)CrossRefGoogle Scholar
  3. Barton, N., Choubey, V.: The shear strength of rock joints in theory and practice. Rock Mech. Rock Eng. 10(1), 1–54 (1977)Google Scholar
  4. Barton, N., de Quadros, E.F.: Joint aperture and roughness in the prediction of flow and groutability of rock masses. Int. J. Rock Mech. Min. Sci. 34(3–4), e251–e252 (1997)Google Scholar
  5. Bear, J., Braester, C.: On the flow of two immscible fluids in fractured porous media. Dev. Soil Sci. 2, 177–202 (1972)Google Scholar
  6. Bertels, S.P., DiCarlo, D.A., Blunt, M.J.: Measurement of aperture distribution, capillary pressure, relative permeability, and in situ saturation in a rock fracture using computed tomography scanning. Water Resour. Res. 37(3), 649–662 (2001)CrossRefGoogle Scholar
  7. Brown, S.R.: Fluid flow through rock joints: the effect of surface roughness. J. Geophys. Res. Solid Earth 92(B2), 1337–1347 (1987)CrossRefGoogle Scholar
  8. Brown, S.R.: Simple mathematical model of a rough fracture. J. Geophys. Res. Solid Earth 100(B4), 5941–5952 (1995)CrossRefGoogle Scholar
  9. Brown, S.R., Kranz, R.L., Bonner, B.P.: Correlation between the surfaces of natural rock joints. Geophys. Res. Lett. 13(13), 1430–1433 (1986)CrossRefGoogle Scholar
  10. Brown, S.R., Stockman, H.W., Reeves, S.J.: Applicability of the Reynolds equation for modeling fluid flow between rough surfaces. Geophys. Res. Lett. 22(18), 2537–2540 (1995)CrossRefGoogle Scholar
  11. Brush, D.J., Thomson, N.R.: Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resour. Res. 39(4), 1085 (2003)CrossRefGoogle Scholar
  12. Cnudde, V., Boone, M.N.: High-resolution X-ray computed tomography in geosciences: a review of the current technology and applications. Earth Sci. Rev. 123, 1–17 (2013)CrossRefGoogle Scholar
  13. Crandall, D., Ahmadi, G., Smith, D.H.: Computational modeling of fluid flow through a fracture in permeable rock. Transp. Porous Media 84(2), 493–510 (2010a)CrossRefGoogle Scholar
  14. Crandall, D., Bromhal, G., Karpyn, Z.T.: Numerical simulations examining the relationship between wall-roughness and fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci. 47(5), 784–796 (2010b)CrossRefGoogle Scholar
  15. Crandall, D., Bromhal, G., McIntyre, D.: Evaluating the influence of wall-roughness on fracture transmissivity with CT scanning and flow simulations. Adv. Comput. Tomogr. Geomaterials GeoX 2010, 270–278 (2010c)Google Scholar
  16. Crandall, D., Moore, J., Gill, M., Stadelman, M.: CT scanning and flow measurements of shale fractures after multiple shearing events. Int. J. Rock Mech. Min. Sci. 100, 177–187 (2017)Google Scholar
  17. Esaki, T., Du, S., Mitani, Y., Ikusada, K., Jing, L.: Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint. Int. J. Rock Mech. Min. Sci. 36(5), 641–650 (1999)CrossRefGoogle Scholar
  18. Gangi, A.F.: Variation of whole and fractured porous rock permeability with confining pressure. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15(5), 249–257 (1978)CrossRefGoogle Scholar
  19. Ge, S.: A governing equation for fluid flow in rough fractures. Water Resour. Res. 33(1), 53–61 (1997)CrossRefGoogle Scholar
  20. Ge, Y., Tang, H., Ez Eldin, M., Wang, L., Wu, Q., Xiong, C.: Evolution process of natural rock joint roughness during direct shear tests. Int. J. Geomech. 17, E4016013 (2016)CrossRefGoogle Scholar
  21. Hakami, E.: Aperture Distribution of Rock Fractures. Royal Institute of Technology Stockholm, Sweden (1995)Google Scholar
  22. Hammack, R., Harbert, W., Sharma, S., Stewart, B., Capo, R., Wall, A.: An evaluation of fracture growth and gas/fluid migration as horizontal Marcellus Shale gas wells are hydraulically fractured in Greene County, Pennsylvania. National Energy Technology Laboratory: NETL-TRS-3-2014. https://www.netl.doe.gov/File%20Library/Research/onsite%20research/publications/NETL-TRS-3-2014_Greene-County-Site_20140915_1_1.pdf (2014). Accessed 25 Jan 2017
  23. Hans, J., Boulon, M.: A new device for investigating the hydro-mechanical properties of rock joints. Int. J. Numer. Anal. Meth. Geomech. 27(6), 513–548 (2003)CrossRefGoogle Scholar
  24. Javadi, M., Sharifzadeh, M., Shahriar, K., Mitani, Y.: Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resour. Res. 50(2), 1789–1804 (2014)CrossRefGoogle Scholar
  25. Kang, P.K., Brown, S., Juanes, R.: Emergence of anomalous transport in stressed rough fractures. Earth Planet. Sci. Lett. 454, 46–54 (2016)CrossRefGoogle Scholar
  26. Karpyn, Z., Grader, A., Halleck, P.: Visualization of fluid occupancy in a rough fracture using micro-tomography. J. Colloid Interface Sci. 307(1), 181–187 (2007)CrossRefGoogle Scholar
  27. Konzuk, J.S., Kueper, B.H.: Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resour. Res. 40, W02402 (2004)Google Scholar
  28. Koyama, T., Li, B., Jiang, Y., Jing, L.: Numerical modelling of fluid flow tests in a rock fracture with a special algorithm for contact areas. Comput. Geotech. 36(1), 291–303 (2009)CrossRefGoogle Scholar
  29. Koyama, T., Neretnieks, I., Jing, L.: A numerical study on differences in using Navier–Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear. Int. J. Rock Mech. Min. Sci. 45(7), 1082–1101 (2008)CrossRefGoogle Scholar
  30. Kutchko, B., Crandall, D., Gill, M., McIntyre, D., Spaulding, R., Strazisar, B., Rosenbaum, E., Haljasmaa, I., Benge, G., Cunningham, E.: Computed Tomography and Statistical Analysis of Bubble Size Distributions in Atmospheric-Generated Foamed Cement. DOE-NETL Internal Publication, Pittsburgh (2013)Google Scholar
  31. Lee, H., Cho, T.: Hydraulic characteristics of rough fractures in linear flow under normal and shear load. Rock Mech. Rock Eng. 35(4), 299–318 (2002)CrossRefGoogle Scholar
  32. Li, B., Jiang, Y., Koyama, T., Jing, L., Tanabashi, Y.: 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)CrossRefGoogle Scholar
  33. Li, B., Liu, R., Jiang, Y.: 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)CrossRefGoogle Scholar
  34. Makedonska, N., Painter, S.L., Bui, Q.M., Gable, C.W., Karra, S.: Particle tracking approach for transport in three-dimensional discrete fracture networks. Comput. Geosci. 19(5), 1123–1137 (2015)CrossRefGoogle Scholar
  35. Matsuki, K., Chida, Y., Sakaguchi, K., Glover, P.: Size effect on aperture and permeability of a fracture as estimated in large synthetic fractures. Int. J. Rock Mech. Min. Sci. 43(5), 726–755 (2006)CrossRefGoogle Scholar
  36. Matsuki, K., Kimura, Y., Sakaguchi, K., Kizaki, A., Giwelli, A.: Effect of shear displacement on the hydraulic conductivity of a fracture. Int. J. Rock Mech. Min. Sci. 47(3), 436–449 (2010)CrossRefGoogle Scholar
  37. Matsuki, K., Lee, J.-J., Sakaguchi, K.: Size effect in flow conductance of a closed small-scale hydraulic fracture in granite. Geotherm. Sci. Technol. 6(1–4), 113–138 (1999)Google Scholar
  38. McKoy, M.L., Sams, W.N.: Tight gas reservoir simulation: modeling discrete irregular strata-bound fracture networks and network flow, including dynamic recharge from the matrix. In: Proceedings of the Natural Gas Conference Emerging Technologies for the Natural Gas Industry. US Department of Energy’s Federal Energy Technology Center Publication, Washington, DC (1997)Google Scholar
  39. Méheust, Y., Schmittbuhl, J.: Flow enhancement of a rough fracture. Geophys. Res. Lett. 27(18), 2989–2992 (2000)CrossRefGoogle Scholar
  40. Montemagno, C.D., Pyrak-Nolte, L.J.: Porosity of natural fracture networks. Geophys. Res. Lett. 22(11), 1397–1400 (1995)CrossRefGoogle Scholar
  41. Moore, J., Crandall, D., Gill, M.: Physical and hydraulic aperture evaluation of shale fractures using computed tomography. In: Paper Presented at the Shales of All Scales: Exploring Coupled Processes, Santa Fe NM, 9–11 June 2015Google Scholar
  42. Myshakin, E., Siriwardane, H., Hulcher, C., Lindner, E., Sams, N., King, S., McKoy, M.: Numerical simulations of vertical growth of hydraulic fractures and brine migration in geological formations above the Marcellus shale. J. Nat. Gas Sci. Eng. 27, 531–544 (2015)CrossRefGoogle Scholar
  43. National Research Council: Rock Fractures and Fluid Flow: Contemporary Understanding and Applications. National Academies Press, Washington DC (1996)Google Scholar
  44. Nazridoust, K., Ahmadi, G., Smith, D.H.: A new friction factor correlation for laminar, single-phase flows through rock fractures. J. Hydrol. 329(1), 315–328 (2006)CrossRefGoogle Scholar
  45. Nemoto, K., Watanabe, N., Hirano, N., Tsuchiya, N.: Direct measurement of contact area and stress dependence of anisotropic flow through rock fracture with heterogeneous aperture distribution. Earth Planet. Sci. Lett. 281(1), 81–87 (2009)CrossRefGoogle Scholar
  46. Nicholl, M., Rajaram, H., Glass, R., Detwiler, R.: Saturated flow in a single fracture: evaluation of the Reynolds equation in measured aperture fields. Water Resour. Res. 35(11), 3361–3373 (1999)CrossRefGoogle Scholar
  47. Nishiyama, S., Ohnishi, Y., Ito, H., Yano, T.: Mechanical and hydraulic behavior of a rock fracture under shear deformation. Earth Planets Space 66(1), 108 (2014)CrossRefGoogle Scholar
  48. Olsson, R., Barton, N.: An improved model for hydromechanical coupling during shearing of rock joints. Int. J. Rock Mech. Min. Sci. 38(3), 317–329 (2001)CrossRefGoogle Scholar
  49. Olsson, W., Brown, S.: Hydromechanical response of a fracture undergoing compression and shear. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 7, 845–851 (1993)CrossRefGoogle Scholar
  50. Oron, A.P., Berkowitz, B.: Flow in rock fractures: the local cubic law assumption reexamined. Water Resour. Res. 34(11), 2811–2825 (1998)CrossRefGoogle Scholar
  51. Patir, N., Cheng, H.: An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. J. Lubr. Technol. 100(1), 12–17 (1978)CrossRefGoogle Scholar
  52. Pruess, K., Oldenburg, C., Moridis, G.: TOUGH2 User’s Guide Version 2. Lawrence Berkeley National Laboratory, Berkeley (1999)CrossRefGoogle Scholar
  53. Pyrak-Nolte, L.J., Myer, L.R., Cook, N.G., Witherspoon, P.A.: Hydraulic and mechanical properties of natural fractures in low permeability rock. In: Paper Presented at the 6th ISRM Congress, Montreal, Canada, 30 Aug–3 Sept 1987Google Scholar
  54. Raimbay, A., Babadagli, T., Kuru, E., Develi, K.: Fractal analysis of single-phase water and polymer solution flow at high rates in open and horizontally displaced rough fractures. Int. J. Rock Mech. Min. Sci. 92, 54–71 (2017)Google Scholar
  55. Rasband, W.S.: ImageJ. U. S. National Institutes of Health, Bethesda, Maryland, USA. http://imagej.nih.gov/ij/(1997–2016). Accessed 16 Nov 2023
  56. Rong, G., Yang, J., Cheng, L., Zhou, C.: Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process. J. Hydrol. 541, 1385–1394 (2016)CrossRefGoogle Scholar
  57. Roman, A., Ahmadi, G.: Computational modeling of fluid flow through a fractured media under overburden pressures. Pet. Eng. Technol. 5(1), 25–43 (2015)Google Scholar
  58. Schlichting, H.: Boundary-Layer Theory. McGraw-hill, New York (1968)Google Scholar
  59. SubTER AGU Townhall TH25I: Paper Presented at the American Geophysical Union Annual Fall Meeting, San Francisco, 15–19 Dec 2015Google Scholar
  60. Tsang, Y.: The effect of tortuosity on fluid flow through a single fracture. Water Resour. Res. 20(9), 1209–1215 (1984)CrossRefGoogle Scholar
  61. Tsang, Y.W., Witherspoon, P.: Hydromechanical behavior of a deformable rock fracture subject to normal stress. J. Geophys. Res. Solid Earth 86(B10), 9287–9298 (1981)CrossRefGoogle Scholar
  62. Tse, R., Cruden, D.: Estimating joint roughness coefficients. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 16(5), 303–307 (1979)CrossRefGoogle Scholar
  63. Unsal, E., Matthäi, S.K., Blunt, M.J.: Simulation of multiphase flow in fractured reservoirs using a fracture-only model with transfer functions. Comput. Geosci. 14(4), 527–538 (2010)CrossRefGoogle Scholar
  64. Walsh, J.: Effect of pore pressure and confining pressure on fracture permeability. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 5, 429–435 (1981)CrossRefGoogle Scholar
  65. Watanabe, N., Hirano, N., Tsuchiya, N.: Determination of aperture structure and fluid flow in a rock fracture by high-resolution numerical modeling on the basis of a flow-through experiment under confining pressure. Water Resour. Res. 44, W06412 (2008)Google Scholar
  66. Watanabe, N., Ishibashi, T., Tsuchiya, N., Ohsaki, Y., Tamagawa, T., Tsuchiya, Y., Okabe, H., Ito, H.: Geologic core holder with a CFR PEEK body for the X-ray CT-based numerical analysis of fracture flow under confining pressure. Rock Mech. Rock Eng. 46(2), 413–418 (2013)CrossRefGoogle Scholar
  67. Witherspoon, P.A., Wang, J.S., Iwai, K., Gale, J.E.: Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour. Res. 16(6), 1016–1024 (1980)CrossRefGoogle Scholar
  68. Xie, L., Gao, C., Ren, L., Li, C.: Numerical investigation of geometrical and hydraulic properties in a single rock fracture during shear displacement with the Navier–Stokes equations. Environ. Earth Sci. 73(11), 7061–7074 (2015)CrossRefGoogle Scholar
  69. Xiong, X., Li, B., Jiang, Y., Koyama, T., Zhang, C.: 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)CrossRefGoogle Scholar
  70. Yeo, I., De Freitas, M., Zimmerman, R.: Effect of shear displacement on the aperture and permeability of a rock fracture. Int. J. Rock Mech. Min. Sci. 35(8), 1051–1070 (1998)CrossRefGoogle Scholar
  71. Zimmerman, R.W., Bodvarsson, G.S.: Hydraulic conductivity of rock fractures. Transp. Porous Media 23(1), 1–30 (1996)CrossRefGoogle Scholar
  72. Zimmerman, R.W., Yeo, I.W.: Fluid flow in rock fractures: from the Navier–Stokes equations to the cubic law. Dyn. Fluids Fract. Rock 122, 213–224 (2000)CrossRefGoogle Scholar
  73. Zimmerman, R., Kumar, S., Bodvarsson, G.: Lubrication theory analysis of the permeability of rough-walled fractures. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 4, 325–331 (1991)CrossRefGoogle Scholar
  74. Zimmerman, R.W., Chen, D.-W., Cook, N.G.: The effect of contact area on the permeability of fractures. J. Hydrol. 139(1–4), 79–96 (1992)CrossRefGoogle Scholar
  75. Zimmerman, R.W., Al-Yaarubi, A., Pain, C.C., Grattoni, C.A.: Non-linear regimes of fluid flow in rock fractures. Int. J. Rock Mech. Min. Sci. 41, 163–169 (2004)CrossRefGoogle Scholar

Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply  2018

Authors and Affiliations

  • Amir A. Mofakham
    • 1
  • Matthew Stadelman
    • 2
    • 3
    • 5
  • Goodarz Ahmadi
    • 1
    • 2
    • 3
  • Kevin T. Shanley
    • 2
    • 3
    • 4
  • Dustin Crandall
    • 2
    Email author
  1. 1.Department of Mechanical and Aeronautical EngineeringClarkson UniversityPotsdamUSA
  2. 2.National Energy Technology LaboratoryUS Department of EnergyMorgantownUSA
  3. 3.Oak Ridge Institute for Science EducationOak RidgeUSA
  4. 4.Division of Engineering ProgramsState University of New York at New PaltzNew PaltzUSA
  5. 5.The MITRE CorporationMcLeanUSA

Personalised recommendations