Abstract
The presence of fracture roughness and the occurrence of nonlinear flow complicate the fracture flow process. In the present study, water flow tests were conducted to comparatively study the flow behavior in smooth (Joint Roughness Coefficient (JRC) = 0–2) and rough (JRC = 18–19) fractures. The confining stress is in the range of 2–60 MPa and the injection pressure is in the range of 0.1–12 MPa to ensure obtaining a wide range of experimental data points. Surface roughness parameters (Rp, Z2, JRC) based on a single fracture surface and aperture distribution based on both surfaces were calculated and their effect on the flow behavior was explored. Transmissivity, flow regimes and the Forchheimer coefficient β were analysed in detail. The results show that the mean aperture size of tensile fracture is lightly smaller than that of cut fracture, with a much smaller standard deviation. Tensile fracture also has a higher peak frequency, indicating that the two fracture surfaces match more perfectly. The intrinsic transmissivity ratio of cut to tensile fracture increases from 1.6 under 2 MPa to 9740.7 under 60 MPa, which may be attributed to the fact that cut fracture has an about \(1/30\) stress-dependence coefficient λ of the tensile fracture. Flow data for cut fracture scatter in transition and turbulent flow regions while scatter in laminar and transition flow regions in tensile fracture, and it is supposed to be quite difficult for flow in tensile facture to enter into turbulent flow. For tensile fracture, a linear relationship exists between Forchheimer coefficient β and mean aperture size η (\(\beta = a_{1} \eta + b_{1}\)) and the correlation coefficients is up to 0.988, while for cut fracture, an exponential model relating β with both confining stress and mean aperture size η was proposed (\(\beta = a_{2} e^{{\left( {b_{2} - c_{2} \eta } \right)^{\sigma } }}\)) and the correlation coefficients is up to 0.978.
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All data that support the fifindings of this study are available from the corresponding author upon reasonable request.
References
Amadei B, Illangasekare T (1994) A mathematical model for flow and solute transport in non-homogeneous rock fractures. Int J Rock Mech Min Sci Geomech Abstr 31(6):719–731
Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech Rock Eng 10(1):1–54
Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25(8):861–884
Brown SR, Kranz RL, Bonner BP (1986) Correlation between the surfaces of natural rock joints. Geophys Res Lett 13(13):1430–1433
Brown S (1987) Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 92:1337–1347
Chen YF, Zhou JQ, Hu SH, Hu R, Zhou CB (2015) Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. J Hydrol 529:993–1006
Chen YD, Lian HJ, Liang WG, Yang JF, Nguyen VP, Bordas SPA (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
Develi K, Babadagli T (2015) Experimental and visual analysis of single-phase flow through rough fracture replicas. Int J Rock Mech Min Sci 73:139–155
Fakherdavood MJN, Ramezanzadeh A, Jenabi H (2019) Laboratory investigation of nonlinear flow characteristics through natural rock fractures. Q J Eng Geol Hydroge 52(4):519–528
Gao C, Xie LZ, Xie HP, He B, Li CB, Wang J, Luo Y (2016) Coupling between the statistical damage model and permeability variation in reservoir sandstone: theoretical analysis and verification. J Nat Gas Sci Eng 37:375–385
Guo P, Wang M, He M, Wang Y, Gao K, Gong W (2020) Experimental investigation on macroscopic behavior and microfluidic field of nonlinear flow in rough-walled artificial fracture models. Adv Water Resour 142:103637
Jang HS, Kang SS, Jang BA (2014) Determination of joint roughness coefficients using roughness parameters. Rock Mech Rock Eng 47(6):2061–2073
Kulatilake PHSW, Park JY, Balasingam P, Morgan R (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
Li HL, Lu YY, Zhou L, Tang JR, Han SB, Ao X (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
Liu RC, Huang N, Jiang YJ, Han GS, Jing HW (2020) Effect of Shear Direction Change on Shear-Flow-Transport Processes in Single Rough-Walled Rock Fractures. Transp Porous Med 133:373–395
Liu J, Wang ZC, Qiao LP, Li W, Yang JJ (2021) Transition from linear to nonlinear flow in single rough fractures: effect of fracture roughness. Hydrogeol J 29:1343–1353
Lomize GM (1951) Flow in fractured rocks. Gosenergoizdat, Moscow
Louis C (1969) A study of groundwater flow in jointed rock and its influence on the stability of rock masses. Rock Mechanics Research Report 10:1–90
Luo Y, Zhang ZY, Wang YK, Nemcik J, Wang JH (2022) On fluid flow regime transition in rough rock fractures: Insights from experiment and fluid dynamic computation. J Hydrol 607:127558
Maerz NH, Franklin JA, Bennett CP (1990) Joint roughness measurement using shadow profilometry. Int J Rock Mech Min Sci Geomech Abstr 27(5):329–343
Masciopinto C (1999) Particles’ transport in a single fracture under variable flow regimes. Adv Eng Softw 30(5):327–337
McCraw C, Edlmann K, Miocic J, Gilfllan S, Haszeldine RS, McDermott CI (2016) Experimental investigation and hybrid numerical analytical hydraulic mechanical simulation of supercritical CO2 flowing through a natural fracture in caprock. Int J Greenh Gas Con 48(1):120–133
Medici G, West LJ, Banwart SA (2019) Groundwater flow velocities in a fractured carbonate aquifer-type: Implications for contaminant transport. J Contam Hydrol 222:1–16
Motiur Rahman M, Khalilur Rahman M (2012) Optimizing hydraulic fracture to manage sand production by predicting critical drawdown pressure in gas well. J Energy Resour-ASME 134(1):013101
Myers NO (1962) Characterization of surface roughness. Wear 5(3):182–189
Nasvi MCM, Ranjith PG, Sanjayan J, Haque A (2013) Sub- and super-critical carbon dioxide permeability of wellbore materials under geological sequestration conditions: an experimental study. Energy 54(2):231–239
Nemoto K, Watanabe N, Hirano N, Tsuchiya N (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
Noiriel C, Gouze P, Made B (2013) 3D analysis of geometry and flow changes in a limestone fracture during dissolution. J Hydrol 486:211–223
Qian JZ, Chen Z, Zhan HB, Guan HC (2011a) 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 Process 25(4):614–622
Qian JZ, Zhan HB, Chen Z, Ye H (2011b) Experimental study of solute transport under non-Darcian flow in a single fracture. J Hydrol 399(3):246–254
Ren XY, Zhou L, Zhou JP, Lu ZH, Su XP (2020) Numerical analysis of heat extraction efficiency in a multilateral-well enhanced geothermal system considering hydraulic fracture propagation and configuration. Geothermics 87:101834
Rong G, Yang J, Cheng L, Zhou CB (2016) Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process. J Hydrol 541:1385–1394
Rutqvist J, Stephansson O (2003) The role of hydromechanical coupling in fractured rock engineering. Hydrogeol J 11:7–40
Schmittbuhl J, Steyer A, Jouniaux L, Toussaint R (2008) Fracture morphology and viscous transport. Int J Rock Mech Min Sci 45:422–430
Sharifzadeh M, Mitani Y, Esaki T (2008) Rock joint surfaces measurement and analysis of aperture distribution under different normal and shear loading using GIS. Rock Mech Rock Eng 41:299–323
Shen ZH, Zhou L, Li HL, Lu ZH, Cai JC (2020) Experimental and numerical study on the anisotropic and nonlinear gas flow behavior of a single coal fracture under loading. Energ Fuel 34(4):4230–4242
Su XP, Zhou L, Li HL, Lu YY, Shen ZH, Song X (2020) Effect of mesoscopic structure on hydro-mechanical properties of fractures. Environ Earth Sci 79:146
Su XP, Liu JL, Liu HJ, Zhou L, Li HL, Chen JC (2021) Comparison of shear and tensile fracture permeability in granite under loading-unloading stress condition. J Porous Media 24(12):93–114
Su XP, Li HL, Liu JL, Shen ZH, Ren XY, Zhou L (2022) Experimental study on nonlinear flow in granite tensile and shear fractures. Int J Geomech 22(12):04022241
Tan YL, Pan ZJ, Liu JS, Wu YT, Haque A, Connell LD (2017) Experimental study of permeability and its anisotropy for shale fracture supported with proppant. J Nat Gas Sci Eng 44:250–264
Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice, 3rd edn. Wiley, New York
Tsang CF, Neretnieks I, Tsang Y (2015) Hydrologic issues associated with nuclear waste repositories. Water Resour Res 51(9):6923–6972
Tzelepis V, Moutsopoulos KN, Papaspyros JNE, Tsihrintzis VA (2015) Experimental investigation of flow behavior in smooth and rough artificial fractures. J Hydrol 521:108–118
Wang CS, Jiang YJ, Liu RC, Wang C, Zhang ZY, Sugimoto S (2020) Experimental study of the nonlinear flow characteristics of fluid in 3D rough-walled fractures during shear process. Rock Mech Rock Eng 53:2581–2604
Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) Validity of cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16(6):1016–1024
Wu JY, Yin Q, Jing HW (2020) Surface roughness and boundary load effect on nonlinear flow behavior of fluid in real rock fractures. Bull Eng Geol Environ 79:4917–4932
Xia CC, Qian X, Lin P, Xiao WM, Gui Y (2017) Experimental investigation of nonlinear flow characteristics of real rock joints under different contact conditions. J Hydraul Eng 143(3):04016090
Xie J, Gao MZ, Zhang R, Peng GY, Lu T, Wang F (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
Xiong F, Jiang QH, Ye ZY, Zhang XB (2018) Nonlinear flow behaviour through rough-walled rock fractures: The effect of contact area. Comput Geotech 102:179–195
Ye ZY, Liu HH, Jiang QH, Liu YZ, Cheng AP (2017) Two-phase flow properties in aperture-based fractures under normal deformation conditions: analytical approach and numerical simulation. J Hydrol 545:72–87
Yin Q, Ma GW, Jing HW, Wang HD, Su HJ, Wang YC, Liu RC (2017) Hydraulic properties of 3D rough-walled fractures during shearing: An experimental study. J Hydrol 555:169–184
Yu LY, Liu RC, Jiang YJ (2017) A review of critical conditions for the onset of nonlinear fluid flow in rock fractures. Geofluids 2017:2176932
Zeng Z, Grigg R (2006) A criterion for non-Darcy flow in porous media. Transp Porous Media 63(1):57–69
Zhang ZY, Nemcik J (2013) Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J Hydrol 477:139–151
Zhang XM, Shi WZ, Hu QH, Zhai GY, Wang R, Xu XF, Xu Z, Meng FL, Liu YZ (2019) Pressure-dependent fracture permeability of marine shales in the northeast Yunnan area. Southern China Int J Coal Geol 214:103237
Zhou JQ, Hu SH, Fang S, Chen YF, Zhou CB (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
Zhou JQ, Hu SH, Chen YF, Wang M, Zhou CB (2016) The friction factor in the Forchheimer equation for rock fractures. Rock Mech Rock Eng 49(8):3055–3068
Zhou L, Shen ZH, Wang JD, Li HL, Lu YY (2019) Numerical investigating the effect of nonuniform proppant distribution and unpropped fractures on well performance in a tight reservoir. J Petrol Sci Eng 177:634–649
Zimmerman RW, Al-Yaarubi AH, Pain CC, Grattoni CA (2004) Nonlinear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41:163–169
Acknowledgements
This work is jointly supported by the Natural Science Foundation Project of Chongqing (No. cstc2021jcyj-msxmX0929), the Science and Technology Research Program of Chongqing Municipal Education Commission (No. KJQN202100726), the National Natural Science Foundation of China (No. U21A2030), the Natural Science Foundation of Sichuan Province (No. 2022NSFSC1169), the Natural Science Foundation Project of Chongqing (No. CSTB2022NSCQ-MSX0429), the Science Foundation of Chongqing Jiaotong University (Grant No. 20JDKJC-B029). The authors wish to thank Junhui Mu for her help in conducting the flow experiments.
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Xiaopeng Su: Conceptualization, Methodology Tong Zhang: Formal analysis, Writing - Original Draft Lei Zhou: Supervision and Funding acquisition Junchao Chen: Writing - Review & Editing Xu Wei: Investigation Wentao Yang: Resources
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Su, X., Zhang, T., Zhou, L. et al. Experimental study on nonlinear flow behavior in smooth and rough sandstone fractures subjected to various injection pressure and normal compressive stress. Environ Earth Sci 83, 171 (2024). https://doi.org/10.1007/s12665-023-11415-y
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DOI: https://doi.org/10.1007/s12665-023-11415-y