Experimental Study on Nonlinear Flow in Granite Tensile and Shear Fractures
Publication: International Journal of Geomechanics
Volume 22, Issue 12
Abstract
Water flow experiments in single tensile and shear granite fractures were conducted to investigate the nonlinear flow behavior. Fracture geometry parameters based on single fracture wall (Rp, Z2, Z3, Z4, JRC) and two fracture walls (aperture distribution, cluster coefficient) were calculated and compared. The effect of these fracture geometry characteristics on nonlinear flow behavior was explored. Fracture transmissivity, critical Reynolds number, pressure gradient, and normalized transmissivity were analyzed in detail. The result shows that shear fracture geometry has the characteristics of higher mean aperture with higher standard deviation, more clustering contact, and rougher fracture surface. The shear to tensile fracture transmissivity ratio increases from 2.3 to around 370 with the increase of confining pressure from 2 to 60 MPa and the stress-dependence coefficient of shear fractures is close to 1/22 of tensile fractures. The critical pressure gradient increases as confining pressure, indicating that it requires a higher pressure gradient to drive the linear flow to nonlinear flow, namely, when the injection pressure gradient keeps unchanged, high confining pressure causes the nonlinear flow to turn to linear flow. The critical gradient of the shear fracture is 0.004–0.527 MPa/m on average, which is much lower than that of tensile fractures (0.011–26.862 MPa/m), meaning that a lower pressure gradient can drive the linear flow to nonlinear flow in a shear fracture. The average Forchheimer coefficient β for tensile fractures is 0.133, which is about half of the shear fracture (0.253). Regression analysis indicates that a linear relationship exists between β and the fracture geometry parameters (mean aperture η and cluster coefficient ς) and the correlation coefficient is about 0.925 and 0.920, respectively. Further investigation confirms the “weak inertial effect” with the (T0/T − 1)/Re data points falling in a straight line before the “strong inertial effect,” where the data points fall in an approximately horizontal line.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is jointly supported by the Natural Science Foundation Project of Chongqing (Grant No. cstc2021jcyj-msxmX0929), the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN202100726), the Fundamental Research Funds for the Central Universities (Grant No. 2022CDJJJ-001), the National Natural Science Foundation of China (Grant No. 51904042), the Science Foundation of Chongqing Jiaotong University (Grant No. 20JDKJC-B029), and China Postdoctoral Science Foundation (Grant No. 2020M683257). The authors wish to thank Junhui Mu for her help in conducting the flow experiments.
References
Barton, N. 1973. “Review of a new shear-strength criterion for rock joints.” Eng. Geol. 7 (4): 287–332. https://doi.org/10.1016/0013-7952(73)90013-6.
Barton, N., and V. Choubey. 1977. “The shear strength of rock joints in theory and practice.” Rock Mech. Rock Eng. 10 (1): 1–54.
Brown, S. R., R. L. Kranz, and B. P. Bonner. 1986. “Correlation between the surfaces of natural rock joints.” Geophys. Res. Lett. 13 (13): 1430–1433. https://doi.org/10.1029/GL013i013p01430.
Chen, Y. D., H. J. Lian, W. G. Liang, J. F. Yang, V. P. Nguyen, and S. P. A. Bordas. 2019. “The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses.” Int. J. Rock Mech. Min. Sci. 113: 59–71. https://doi.org/10.1016/j.ijrmms.2018.11.017.
Chen, Y. D., W. G. Liang, H. J. Lian, J. F. Yang, and V. P. Nguyen. 2017. “Experimental study on the effect of fracture geometric characteristics on the permeability in deformable rough-walled fractures.” Int. J. Rock Mech. Min. Sci. 98: 121–140. https://doi.org/10.1016/j.ijrmms.2017.07.003.
Chen, Y. F., S. H. Hu, K. Wei, C. B. Zhou, and L. R. Jing. 2014. “Experimental characterization and micromechanical modeling of damage-induced permeability variation in Beishan granite.” Int. J. Rock Mech. Min. Sci. 71: 64–76. https://doi.org/10.1016/j.ijrmms.2014.07.002.
Chen, Y. F., J. Q. Zhou, S. H. Hu, R. Hu, and C. B. Zhou. 2015. “Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures.” J. Hydrol. 529: 993–1006. https://doi.org/10.1016/j.jhydrol.2015.09.021.
Chen, Z., S. P. Narayan, Z. Yang, and S. S. Rahman. 2000. “An experimental investigation of hydraulic behaviour of fractures and joints in granitic rock.” Int. J. Rock Mech. Min. Sci. 37 (7): 1061–1071. https://doi.org/10.1016/S1365-1609(00)00039-3.
Develi, K., and T. Babadagli. 2015. “Experimental and visual analysis of single-phase flow through rough fracture replicas.” Int. J. Rock Mech. Min. Sci. 73: 139–155. https://doi.org/10.1016/j.ijrmms.2014.11.002.
Gao, C., L. Z. Xie, H. P. Xie, B. He, C. B. Li, J. Wang, and Y. Luo. 2017. “Coupling between the statistical damage model and permeability variation in reservoir sandstone: Theoretical analysis and verification.” J. Nat. Gas Sci. Eng. 37: 375–385. https://doi.org/10.1016/j.jngse.2016.10.053.
Jang, H. S., S. S. Kang, and B. A. Jang. 2014. “Determination of joint roughness coefficients using roughness parameters.” Rock Mech. Rock Eng. 47 (6): 2061–2073. https://doi.org/10.1007/s00603-013-0535-z.
Javadi, M., M. Sharifzadeh, K. Shahriar, and Y. Mitani. 2014. “Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes.” Water Resour. Res. 50 (2): 1789–1804. https://doi.org/10.1002/2013WR014610.
Konzuk, J. S., and B. H. Kueper. 2004. “Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture.” Water Resour. Res. 40 (2): W02402. https://doi.org/10.1029/2003WR002356.
Kulatilake, P. H. S. W., J. Y. Park, P. Balasingam, and R. Morgan. 2008. “Quantification of aperture and relations between aperture, normal stress and fluid flow for natural single rock fractures.” Geotech. Geol. Eng. 26 (3): 269–281. https://doi.org/10.1007/s10706-007-9163-2.
Kulatilake, P. H. S. W., J. Y. Park, and X. P. Su. 2020. “Fluid flow through natural single-rock fractures: Experimental and numerical investigations.” Int. J. Geomech. 20 (10): 04020168. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001790.
Li, B., F. Ju, M. Xiao, and P. Ning. 2019. “Mechanical stability of granite as thermal energy storage material: An experimental investigation.” Eng. Fract. Mech. 211: 61–69. https://doi.org/10.1016/j.engfracmech.2019.02.008.
Li, H. L., Y. Y. Lu, L. Zhou, J. R. Tang, S. B. Han, and X. Ao. 2018. “Experimental and model studies on loading path-dependent and nonlinear gas flow behavior in shale fractures.” Rock Mech. Rock Eng. 51 (1): 227–242. https://doi.org/10.1007/s00603-017-1296-x.
Lomize, G. M. 1951. Flow in fractured rocks. Moscow: Gosenergoizdat.
Louis, C., and Y. Maini. 1970. “Determination of in-situ hydraulic parameters in jointed rock.” In Proc., 2nd Congress of Rock Mechanics. Belgrade, Serbia: Institut za Vodoprivredu Jaroslav Cerni.
Maerz, N. H., J. A. Franklin, and C. P. Bennett. 1990. “Joint roughness measurement using shadow profilometry.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 27 (5): 329–343. https://doi.org/10.1016/0148-9062(90)92708-M.
Mandelbrot, B. B. 1983. The fractal geometry of nature. 1st ed. New York: Freeman.
McCraw, C., K. Edlmann, J. Miocic, S. Gilfllan, R. S. Haszeldine, and C. I. McDermott. 2016. “Experimental investigation and hybrid numerical analytical hydraulic mechanical simulation of supercritical CO2 flowing through a natural fracture in caprock.” Int. J. Greenhouse Gas Control 48 (1): 120–133. https://doi.org/10.1016/j.ijggc.2016.01.002.
Myers, N. O. 1962. “Characterization of surface roughness.” Wear 5 (3): 182–189. https://doi.org/10.1016/0043-1648(62)90002-9.
Nasvi, M. C. M., P. G. Ranjith, J. Sanjayan, and A. Haque. 2013. “Sub- and super-critical carbon dioxide permeability of wellbore materials under geological sequestration conditions: An experimental study.” Energy 54 (2): 231–239. https://doi.org/10.1016/j.energy.2013.01.049.
Nazridoust, K., G. Ahmadi, and D. H. Smith. 2006. “A new friction factor correlation for laminar, single-phase flows through rock fractures.” J. Hydrol. 329 (1-2): 315–328. https://doi.org/10.1016/j.jhydrol.2006.02.032.
Nemoto, K., N. Watanabe, N. Hirano, and N. Tsuchiya. 2009. “Direct measurement of contact area and stress dependence of anisotropic flow through rock fracture with heterogeneous aperture distribution.” Earth Planet. Sci. Lett. 281 (1–2): 81–87. https://doi.org/10.1016/j.epsl.2009.02.005.
Qian, J. Z., Z. Chen, H. B. Zhan, and H. C. Guan. 2011. “Experimental study of the effect of roughness and Reynolds number on fluid flow in rough-walled single fractures: A check of local cubic law.” Hydrol. Processes 25 (4): 614–622. https://doi.org/10.1002/hyp.7849.
Qian, J. Z., H. B. Zhan, S. H. Luo, and W. D. Zhao. 2007. “Experimental evidence of scale-dependent hydraulic conductivity for fully developed turbulent flow in a single fracture.” J. Hydrol. 339 (3–4): 206–215. https://doi.org/10.1016/j.jhydrol.2007.03.015.
Ren, X. Y., L. Zhou, J. P. Zhou, Z. H. Lu, and X. P. Su. 2020. “Numerical analysis of heat extraction efficiency in a multilateral-well enhanced geothermal system considering hydraulic fracture propagation and configuration.” Geothermics 87: 101834. https://doi.org/10.1016/j.geothermics.2020.101834.
Roy, A., and E. Perfect. 2014. “Lacunarity analyses of multifractal and natural grayscale patterns.” Fractals 22 (3): 1440003. https://doi.org/10.1142/S0218348X14400039.
Rutqvist, J., and O. Stephansson. 2003. “The role of hydromechanical coupling in fractured rock engineering.” Hydrogeol. J. 11: 7–40. https://doi.org/10.1007/s10040-002-0241-5.
Schmittbuhl, J., A. Steyer, L. Jouniaux, and R. Toussaint. 2008. “Fracture morphology and viscous transport.” Int. J. Rock Mech. Min. Sci. 45 (3): 422–430. https://doi.org/10.1016/j.ijrmms.2007.07.007.
Schrauf, T. W., and D. D. Evans. 1986. “Laboratory studies of gas flow through a single natural fracture.” Water Resour. Res. 22 (7): 1038–1050. https://doi.org/10.1029/WR022i007p01038.
Shen, Z. H., L. Zhou, H. L. Li, Z. H. Lu, and J. C. Cai. 2020. “Experimental and numerical study on the anisotropic and nonlinear gas flow behavior of a single coal fracture under loading.” Energy Fuels 34 (4): 4230–4242. https://doi.org/10.1021/acs.energyfuels.0c00012.
Su, X. P., J. L. Liu, H. J. Liu, L. Zhou, H. L. Li, and J. C. Chen. 2021. “Comparison of shear and tensile fracture permeability in granite under loading-unloading stress conditions.” J. Porous Media 24 (12): 93–114. https://doi.org/10.1615/JPorMedia.2021038053.
Su, X. P., L. Zhou, H. L. Li, Y. Y. Lu, Z. H. Shen, and X. Song. 2020. “Effect of mesoscopic structure on hydro-mechanical properties of fractures.” Environ. Earth Sci. 79 (6): 146. https://doi.org/10.1007/s12665-020-8871-2.
Su, X. P., L. Zhou, H. L. Li, B. W. Xia, Z. H. Shen, and Y. Y. Lu. 2019. “Experimental and numerical modelling of nonlinear flow behavior in single fractured granite.” Geofluids 2019: 8623035.
Tan, Y. L., Z. J. Pan, J. S. Liu, Y. T. Wu, A. Haque, and L. D. Connell. 2017. “Experimental study of permeability and its anisotropy for shale fracture supported with proppant.” J. Nat. Gas Sci. Eng. 44: 250–264. https://doi.org/10.1016/j.jngse.2017.04.020.
Terzaghi, K., R. B. Peck, and G. Mesri. 1996. Soil mechanics in engineering practice. 3rd ed. New York: Wiley.
Tse, R., and D. M. Cruden. 1979. “Estimating joint roughness coefficients.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 16 (5): 303–307. https://doi.org/10.1016/0148-9062(79)90241-9.
Wang, C. S., Y. J. Jiang, R. C. Liu, C. Wang, Z. Y. Zhang, and S. Sugimoto. 2020. “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. https://doi.org/10.1007/s00603-020-02068-5.
Witherspoon, P. A., J. S. Y. Wang, K. Iwai, and J. E. Gale. 1980. “Validity of cubic law for fluid flow in a deformable rock fracture.” Water Resour. Res. 16 (6): 1016–1024. https://doi.org/10.1029/WR016i006p01016.
Xia, C. C., X. Qian, P. Lin, W. M. Xiao, and Y. Gui. 2017. “Experimental investigation of nonlinear flow characteristics of real rock joints under different contact conditions.” J. Hydraul. Eng. 143 (3): 04016090. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001238.
Xie, H. P., M. Z. Gao, R. Zhang, H. W. Zhou, F. Gao, and Z. T. Zhang. 2015. “Theoretical and experimental validation of mining-enhanced permeability for simultaneous exploitation of coal and gas.” Environ. Earth Sci. 73 (10): 5951–5962. https://doi.org/10.1007/s12665-015-4113-4.
Xie, J., M. Z. Gao, R. Zhang, G. Y. Peng, T. Lu, and F. Wang. 2020. “Experimental investigation on the anisotropic fractal characteristics of the rock fracture surface and its application on the fluid flow description.” J. Petrol. Sci. Eng. 191: 107190. https://doi.org/10.1016/j.petrol.2020.107190.
Xiong, F., Q. H. Jiang, Z. Y. Ye, and X. B. Zhang. 2018. “Nonlinear flow behavior through rough-walled rock fractures: The effect of contact area.” Comput. Geotech. 102: 179–195. https://doi.org/10.1016/j.compgeo.2018.06.006.
Ye, Z. Y., H. H. Liu, Q. H. Jiang, Y. Z. Liu, and A. P. Cheng. 2017. “Two-phase flow properties in aperture-based fractures under normal deformation conditions: Analytical approach and numerical simulation.” J. Hydrol. 545: 72–87. https://doi.org/10.1016/j.jhydrol.2016.12.017.
Yeo, I. W., M. H. De Freitas, and R. W. Zimmerman. 1998. “Effect of shear displacement on the aperture and permeability of a rock fracture.” Int. J. Rock Mech. Min. Sci. 35 (8): 1051–1070. https://doi.org/10.1016/S0148-9062(98)00165-X.
Yin, Q., G. W. Ma, H. W. Jing, H. D. Wang, H. J. Su, Y. C. Wang, and R. C. Liu. 2017. “Hydraulic properties of 3D rough-walled fractures during shearing: An experimental study.” J. Hydrol. 555: 169–184. https://doi.org/10.1016/j.jhydrol.2017.10.019.
Zeng, Z., and R. Grigg. 2006. “A criterion for non-Darcy flow in porous media.” Transp. Porous Media 63 (1): 57–69. https://doi.org/10.1007/s11242-005-2720-3.
Zhang, X. M., W. Z. Shi, Q. H. Hu, G. Y. Zhai, R. Wang, X. F. Xu, Z. Xu, F. L. Meng, and Y. Z. Liu. 2019. “Pressure-dependent fracture permeability of marine shales in the northeast Yunnan area, Southern China.” Int. J. Coal Geol. 214: 103237. https://doi.org/10.1016/j.coal.2019.103237.
Zhang, Z. Y., and J. Nemcik. 2013a. “Friction factor of water flow through rough rock fractures.” Rock Mech. Rock Eng. 46 (5): 1125–1134. https://doi.org/10.1007/s00603-012-0328-9.
Zhang, Z. Y., and J. Nemcik. 2013b. “Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures.” J. Hydrol. 477: 139–151. https://doi.org/10.1016/j.jhydrol.2012.11.024.
Zhou, J. Q., S. H. Hu, Y. F. Chen, M. Wang, and C. B. Zhou. 2016. “The friction factor in the Forchheimer equation for rock fractures.” Rock Mech. Rock Eng. 49 (8): 3055–3068. https://doi.org/10.1007/s00603-016-0960-x.
Zhou, J. Q., S. H. Hu, S. Fang, Y. F. Chen, and C. B. Zhou. 2015. “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. https://doi.org/10.1016/j.ijrmms.2015.09.027.
Zimmerman, R. W., A. H. Al-Yaarubi, C. C. Pain, and C. A. Grattoni. 2004. “Nonlinear regimes of fluid flow in rock fractures.” Int. J. Rock Mech. Min. Sci. 41: 163–169. https://doi.org/10.1016/j.ijrmms.2004.03.036.
Zimmerman, R. W., and G. S. Bodvarsson. 1996. “Hydraulic conductivity of rock fractures.” Transp. Porous Media 23 (1): 1–30. https://doi.org/10.1007/BF00145263.
Zimmerman, R. W., D. W. Chen, and N. G. W. Cook. 1992. “The effect of contact area on the permeability of fractures.” J. Hydrol. 139 (1–4): 79–96. https://doi.org/10.1016/0022-1694(92)90196-3.
Zimmerman, R. W., S. Kumar, and G. S. Bodvarsson. 1991. “Lubrication theory analysis of the permeability of rough-walled fractures.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 28 (4): 325–331. https://doi.org/10.1016/0148-9062(91)90597-F.
Zou, L., L. Jing, and V. Cvetkovic. 2015. “Roughness decomposition and nonlinear fluid flow in a single rock fracture.” Int. J. Rock Mech. Min. Sci. 75: 102–118. https://doi.org/10.1016/j.ijrmms.2015.01.016.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 12 • December 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 21, 2021
Accepted: Jul 15, 2022
Published online: Oct 13, 2022
Published in print: Dec 1, 2022
Discussion open until: Mar 13, 2023
ASCE Technical Topics:
- Continuum mechanics
- Cracking
- Design (by type)
- Engineering fundamentals
- Engineering mechanics
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Fracture mechanics
- Geometrics
- Highway and road design
- Hydraulic fracturing
- Hydrologic engineering
- Linear flow
- Mathematics
- Nonlinear response
- Parameters (statistics)
- Shear flow
- Shear stress
- Solid mechanics
- Statistics
- Stress (by type)
- Structural analysis
- Structural behavior
- Structural engineering
- Water and water resources
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.