Quantitative characterization of single-phase flow through rough-walled fractures with variable apertures

An FH, Cheng YP (2014) An explanation of large-scale coal and gas outbursts in underground coal mines: the effect of low-permeability zones on abnormally abundant gas. Nat Hazards Earth Syst Sci 14:2125–2132. https://doi.org/10.5194/nhess-14-2125-2014 Bennour Z, Watanabe S, Chen Y et al (2018) Evaluation of stimulated reservoir volume in laboratory hydraulic fracturing with oil, water and liquid carbon dioxide under microscopy using the fluorescence method. Geomech Geophys Geo-Energy Geo-Resour 4:39–50. https://doi.org/10.1007/s40948-017-0073-3 Berry MV, Lewis ZV, Nye JF (1980) On the Weierstrass-Mandelbrot fractal function. Proc R Soc A Math Phys Eng Sci 370:459–484. https://doi.org/10.1098/rspa.1980.0044 Brown SR (1987) Fluid flow through rock joints: the effect of surface roughness. J Geophys Res 92:1337–1347. https://doi.org/10.1029/JB092iB02p01337 Brush DJ, Thomson NR (2003) Fluid flow in synthetic rough-walled fractures: Navier–Stokes, Stokes, and local cubic law simulations. Water Resour Res. https://doi.org/10.1029/2002WR001346 Cheung NJ, Ding X, Shen H (2017) A nonhomogeneous cuckoo search algorithm based on quantum mechanism for real parameter optimization. IEEE Trans Cybern 47:391–402. https://doi.org/10.1109/TCYB.2016.2517140 D’Humières DD, Lallemand P, Frisch U (1986) Lattice gas models for 3D hydrodynamics. EPL 2:291–297. https://doi.org/10.1209/0295-5075/2/4/006 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. https://doi.org/10.1016/j.ijrmms.2014.11.002 Drazer G, Auradou H, Koplik J, Hulin JP (2004) Self-affine fronts in self-affine fractures: large and small-scale structure. Phys Rev Lett 92:014501. https://doi.org/10.1103/PhysRevLett.92.014501 Ge S (1997) A governing equation for fluid flow in rough fractures. Water Resour Res 33:53–61. https://doi.org/10.1029/96WR02588 Gutfraind R, Hansen A (1995) Study of fracture permeability using lattice gas automata. Transp Porous Media 18:131–149. https://doi.org/10.1007/BF01064675 Hajjar A, Scholtès L, Oltéan C, Buès MA (2018) Effects of the geometry of two-dimensional fractures on their hydraulic aperture and on the validity of the local cubic law. Hydrol Process 32:2510–2525. https://doi.org/10.1002/hyp.13181 Hariri-Ardebili MA, Seyed-Kolbadi SM, Mirzabozorg H (2013) A smeared crack model for seismic failure analysis of concrete gravity dams considering fracture energy effects. Struct Eng Mech 48:17–39. https://doi.org/10.12989/sem.2013.48.1.017 Hyman JD, Jiménez-Martínez J (2018) Dispersion and mixing in three-dimensional discrete fracture networks: nonlinear interplay between structural and hydraulic heterogeneity. Water Resour Res 54:3243–3258. https://doi.org/10.1029/2018WR022585 Ishibashi T, Elsworth D, Fang Y et al (2018) Friction-stability-permeability evolution of a fracture in granite. Water Resour Res 54:9901–9918. https://doi.org/10.1029/2018WR022598 Jin Y, Dong JB, Zhang XY et al (2017) Scale and size effects on fluid flow through self-affine rough fractures. Int J Heat Mass Transf 105:443–451. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.010 Ju Y, Dong J, Gao F, Wang J (2019) Evaluation of water permeability of rough fractures based on a self-affine fractal model and optimized segmentation algorithm. Adv Water Resour 129:99–111. https://doi.org/10.1016/j.advwatres.2019.05.007 Komvopoulos K, Yan W (1997) A fractal analysis of stiction in microelectromechanical systems. J Tribol 119:391–400. https://doi.org/10.1115/1.2833500 Konzuk JS, Kueper BH (2004) Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resour Res 40:W02402. https://doi.org/10.1029/2003WR002356 Krüger T, Kusumaatmaja H, Kuzmin A et al (2016) The lattice boltzmann method: principles and practice. Springer, Berlin Kumar H, Mishra MK, Mishra S (2019) Experimental and numerical evaluation of CBM potential in Jharia coalfield India. Geomech Geophys Geo-Energy Geo-Resour 5:289–314. https://doi.org/10.1007/s40948-019-00114-3 Lang PS, Paluszny A, Nejati M, Zimmerman RW (2018) Relationship between the orientation of maximum permeability and intermediate principal stress in fractured rocks. Water Resour Res 54:8734–8755. https://doi.org/10.1029/2018WR023189 Lee I-H, Ni C-F, Lin F-P et al (2019) Stochastic modeling of flow and conservative transport in three-dimensional discrete fracture networks. Hydrol Earth Syst Sci 23:19–34. https://doi.org/10.5194/hess-23-19-2019 Li K, Ma M, Wang X (2011) Experimental study of water flow behaviour in narrow fractures of cementitious materials. Cem Concr Compos 33:1009–1013. https://doi.org/10.1016/j.cemconcomp.2011.08.005 Li Q, Luo KH, Kang QJ et al (2016) Lattice Boltzmann methods for multiphase flow and phase-change heat transfer. Prog Energy Combust Sci 52:62–105. https://doi.org/10.1016/j.pecs.2015.10.001 Liu R, Li B, Jiang Y (2016) Critical hydraulic gradient for nonlinear flow through rock fracture networks: the roles of aperture, surface roughness, and number of intersections. Adv Water Resour 88:53–65. https://doi.org/10.1016/j.advwatres.2015.12.002 Lomize GM (1951) Flow in fractured rocks. Gosenergoizdat, Moscow (in Russian) Louis C (1969) A study of groundwater flow in jointed rock and its influence on the stability of rock masses. Imperial College of Science and Technology, London Lu Y, Wang L (2015) Numerical simulation of mining-induced fracture evolution and water flow in coal seam floor above a confined aquifer. Comput Geotech 67:157–171. https://doi.org/10.1016/j.compgeo.2015.03.007 Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10:422–437. https://doi.org/10.1137/1010093 McClure JE, Prins JF, Miller CT (2014) A novel heterogeneous algorithm to simulate multiphase flow in porous media on multicore CPU–GPU systems. Comput Phys Commun 185:1865–1874. https://doi.org/10.1016/j.cpc.2014.03.012 Mourzenko VV, Thovert J-F, Adler PM (1995) Permeability of a single fracture; validity of the reynolds equation. J Phys II France 5:465–482. https://doi.org/10.1051/jp2:1995133 Mourzenko VV, Thovert J-F, Adler PM (1996) Geometry of simulated fractures. Phys Rev E 53:5606–5626. https://doi.org/10.1103/PhysRevE.53.5606 Mourzenko VV, Thovert J-F, Adler PM (1999) Percolation and conductivity of self-affine fractures. Phys Rev E 59:4265–4284. https://doi.org/10.1103/PhysRevE.59.4265 Nazridoust K, Ahmadi G, Smith DH (2006) A new friction factor correlation for laminar, single-phase flows through rock fractures. J Hydrol 329:315–328. https://doi.org/10.1016/j.jhydrol.2006.02.032 Oron AP, Berkowitz B (1998) Flow in rock fractures: the local cubic law assumption reexamined. Water Resour Res 34:2811–2825. https://doi.org/10.1029/98WR02285 Paramanathan P, Uthayakumar R (2010) Fractal interpolation on the Koch curve. Comput Math Appl 59:3229–3233. https://doi.org/10.1016/j.camwa.2010.03.008 Qian YH, D’Humieres D, Lallemand P (1992) Lattice BGK models for Navier–Stokes equation. EPL (Europhys Lett) 17:479–484. https://doi.org/10.1006/jcph.2000.6616 Renshaw CE (1995) On the relationship between mechanical and hydraulic apertures in rough-walled fractures. J Geophys Res 100:24629–24636. https://doi.org/10.1029/95JB02159 Renshaw CE, Dadakis JS, Brown SR (2000) Measuring fracture apertures: a comparison of methods. Geophys Res Lett 27:289–292. https://doi.org/10.1029/1999GL008384 Sahimi M, Mukhopadhyay S (1996) Scaling properties of a percolation model with long-range correlations. Phys Rev E 54:3870–3880. https://doi.org/10.1103/PhysRevE.54.3870 Sisavath S, Al-Yaaruby A, Pain CC, Zimmerman RW (2003) A Simple model for deviations from the cubic law for a fracture undergoing dilation or closure. Pure appl Geophys 160:1009–1022. https://doi.org/10.1007/PL00012558 Talon L, Auradou H, Hansen A (2010a) Permeability of self-affine aperture fields. Phys Rev E 82:046108. https://doi.org/10.1103/PhysRevE.82.046108 Talon L, Auradou H, Hansen A (2010b) Permeability estimates of self-affine fracture faults based on generalization of the bottleneck concept. Water Resour Res 46:W07601. https://doi.org/10.1029/2009WR008404 Tang Y, Ma T, Chen P, Ranjith PG (2020) An analytical model for heat extraction through multi-link fractures of the enhanced geothermal system. Geomech Geophys Geo-Energy Geo-Resour. https://doi.org/10.1007/s40948-019-00123-2 Tian ZW, Wang JY (2017) Lattice Boltzmann simulation of CO2 reactive transport in network fractured media. Water Resour Res 53:7366–7381. https://doi.org/10.1002/2017WR021063 Wang S, Komvopoulos K (1994) A fractal theory of the interfacial temperature distribution in the slow sliding regime: Part II—multiple domains, elastoplastic contacts and applications. J Tribol 116:824–832. https://doi.org/10.1115/1.2927341 Wang LC, Cardenas MB, Slottke DT et al (2015) Modification of the Local Cubic Law of fracture flow for weak inertia, tortuosity, and roughness. Water Resour Res 51:2064–2080. https://doi.org/10.1002/2014WR015815 Wang M, Chen YF, Ma GW et al (2016) Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: lattice Boltzmann simulations. Adv Water Resour 96:373–388. https://doi.org/10.1016/j.advwatres.2016.08.006 Wang Z, Xu C, Dowd P (2018) A modified cubic law for single-phase saturated laminar flow in rough rock fractures. Int J Rock Mech Min Sci 103:107–115. https://doi.org/10.1016/j.ijrmms.2017.12.002 Watanabe N, Hirano N, Tsuchiya N (2008) 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. https://doi.org/10.1029/2006WR005411 Witherspoon PA, Wang JSY, Iwai K, Gale JE (1980) Validity of Cubic law for fluid flow in a deformable rock fracture. Water Resour Res 16:1016. https://doi.org/10.1029/WR016i006p01016 Wu J-J (2000) Characterization of fractal surfaces. Wear 239:36–47. https://doi.org/10.1016/S0043-1648(99)00362-2 Yang XS, Deb S (2010) Engineering optimisation by Cuckoo search. Int J Math Model Numer Optim 1:330–343. https://doi.org/10.1504/IJMMNO.2010.035430 Zhang CP, Cheng P, Lu YY et al (2020) Experimental evaluation of gas flow characteristics in fractured siltstone under various reservoir and injection conditions: an application to CO2-based fracturing. Geomech Geophys Geo-Energy Geo-Resour 6:23. https://doi.org/10.1007/s40948-020-00145-1 Zhu HG, Xie HP, Yi C et al (2013) Analysis of properties of fluid flow in rock fractures. Chin J Rock Mech Eng 32:657–663 (in Chinese) Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transp Porous Media 23:1–30. https://doi.org/10.1007/BF00145263 Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids 9:1591–1598. https://doi.org/10.1063/1.869307