Top

Hydrogeology Journal

Published in:

25-02-2022 | Paper

A model for nonlinear flow behavior in two-dimensional fracture intersections and the estimation of flow model coefficients

Authors: Zhechao Wang, Jie Liu, Liping Qiao, Jinjin Yang, Jiafan Guo, Kanglin Li

Published in: Hydrogeology Journal | Issue 3/2022

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

There are multiple flow paths with different flow directions in fracture intersections. A general flow model synthetically describing the nonlinear flow behavior of multiple flow paths in different directions in two-dimensional fracture intersections was proposed for the analysis of fluid flow in rock fracture networks. The flow behavior of seven typical fracture intersection models, according to a geological investigation, was simulated. Through numerical simulations and experimental observations, it was validated that the flow model was capable of describing the nonlinear flow behavior in each flow direction in the fracture intersections at the same time. In this flow model, the coefficient matrices include linear coefficients for each fracture branch and nonlinear coefficients for each flow path. The relations between the hydraulic pressure drops and the flow rates reflect the influence of intersection configurations and flow directions on flow behavior in the fracture intersections. Based on the flow model and corresponding non-Darcy effect factor for fracture intersections, the critical Reynolds numbers to describe the transition of the flow regime in fracture intersections were determined and found to range from 51 to 105. Furthermore, the transition of the flow regime in the fracture intersections calculated with the proposed model was found to be closely related to the evolution of microscopic flow structures in the numerical simulations.

previous article Laboratory experimental study on pumping-induced earth fissures

next article Groundwater contamination source estimation based on a refined particle filter associated with a deep residual neural network surrogate

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10:1–54. https://doi.org/10.1007/BF01261801CrossRef

Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25(8):861–884. https://doi.org/10.1016/S0309-1708(02)00042-8CrossRef

Brown SR, Stockman HW, Reeves SJ (1995) Applicability of the Reynolds equation for modeling fluid flow between rough surfaces. Geophys Res Lett 22(18):2537–2540. https://doi.org/10.1016/0148-9062(96)84991-6CrossRef

Brush DJ, Thomson NR (2003) Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resour Res 39(4):1085. https://doi.org/10.1029/2002WR001346CrossRef

Chen YF, Hu SH, Hu R, Zhou CB (2015a) Estimating hydraulic conductivity of fractured rocks from high-pressure packer tests with an Izbash’s law-based empirical model. Water Resour Res 51(4):2096–2118. https://doi.org/10.1002/2014WR016458CrossRef

Chen YF, Zhou JQ, Hu SH, Hu R, Zhou CB (2015b) 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.2015.09.021CrossRef

Cherubini C, Giasi CI, Pastore N (2012) Bench scale laboratory tests to analyze non-linear flow in fractured media. Hydrol Earth Syst Sci 9(4):5575–5609. https://doi.org/10.5194/hess-16-2511-2012CrossRef

Forchheimer PH (1901) Water movement through soil (in German). J Assoc Ger Eng 45:1782–1788

Ghane E, Fausey NR, Brown LC (2014) Non-Darcy flow of water through woodchip media. J Hydrol 519:3400–3409CrossRef

Hu YJ, Mao GH, Cheng WP, Zhang JJ (2005) Theoretical and experimental study on flow distribution at fracture intersections. J Hydraulic Res 43(3):321–327CrossRef

Iwai K (1976) Fundamental studies of fluid flow through a single fracture. PhD Thesis, California University, Berkeley. https://doi.org/10.1016/0148-9062(79)90543-6

Javadi M, Sharifzadeh M, Shahriar K, Mitani Y (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/10.1002/2013WR014610CrossRef

Jing L, Stephansson O (2007) Fundamentals of discrete element methods for rock engineering: theory and applications. Elsevier, Amsterdam, pp 111–138CrossRef

Johnson J, Brown S, Stockman H (2006) Fluid flow and mixing in rough-walled fracture intersections. J Geophys Res-Solid Earth 111(B12). https://doi.org/10.1029/2005JB004087

Kolditz O (2001) Non-linear flow in fractured rock. Int J Numer Method H 11(6):547–575. https://doi.org/10.1108/EUM0000000005668CrossRef

Konzuk JS, Kueper BH (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/10.1029/2003WR002356CrossRef

Kosakowski G, Berkowitz B (1999) Flow pattern variability in natural fracture intersections. Geophy Res Lett 26(12):1765–1768. https://doi.org/10.1029/1999GL900344CrossRef

Kumar R, Kumar A, Goel V (2017) Computational fluid dynamics based study for analyzing heat transfer and friction factor in semi-circular rib roughened equilateral triangular duct. Int J Numer Method H 27(4):941–957. https://doi.org/10.1108/hff-10-2015-0438CrossRef

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

Li GM (2002) Tracer mixing at fracture intersections. Environ Geol 42(2–3):137–144. https://doi.org/10.1007/s00254-001-0483-xCrossRef

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. https://doi.org/10.1007/s10040-020-02297-6

Liu RC, Li B, Jiang YJ (2016a) Critical hydraulic gradient for nonlinear flow through rock fracture networks: the roles of aperture, surface roughness, and number of interactions. Adv Water Resour 88:53–65. https://doi.org/10.1016/j.advwatres.2015.12.002CrossRef

Liu RC, Li B, Jiang YJ (2016b) A fractal model based on a new governing equation of fluid flow in fractures for characterizing hydraulic properties of rock fracture networks. Comput Geotech 75:57–68. https://doi.org/10.1016/j.compgeo.2016.01.025CrossRef

Long JCS, Remer JS, Wilson CR, Witherspoon PA (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18(3):645–658. https://doi.org/10.1029/WR018i003p00645CrossRef

Moutsopoulos KN, Papaspyros INE, Tsihrintzis VA (2009) Experimental investigation of inertial flow processes in porous media. J Hydrol 374(3):242–254. https://doi.org/10.1016/j.jhydrol.2009.06.015CrossRef

Mourzenko VV, Thovert JF, Adler PM (1995) Permeability of a single fracture: validity of the Reynolds equation. J Phys II 5(3):465–482. https://doi.org/10.1051/jp2:1995133CrossRef

Munson BR, Young DF, Okiishi TH (1994) Fundamentals of fluid mechanics. Wiley, New York

National Research Council (1996) Rock fractures and fluid flow: contemporary understanding and applications. National Academy Press, Washington, DC, 65 pp

Park Y, Dreuzy JD, Lee K, Berkowitz B (2001) Transport and intersection mixing in random fracture networks with power law length distributions. Water Resour Res 37(10):2493–2502. https://doi.org/10.1029/2000WR000131CrossRef

Park Y, Lee KK, Kosakowski G, Berkowitz B (2003) Transport behavior in three-dimensional fracture intersections. Water Resour Res 39(8):472–477. https://doi.org/10.1029/2002WR001801CrossRef

Peacock DCP, Sanderson DJ, Rotevatn A (2018) Relationships between fractures. Water Resour Res 106:41–53. https://doi.org/10.1016/j.jsg.2017.11.010CrossRef

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

Su BY, Zhan ML, Guo XE (1997) Experimental study on fluid flow in crossed fractures (in Chinese). J Hydraul Eng 5:1–6

Tian KM (1986) The hydraulic properties of crossing-flow in an intersected fracture. Acta Geol Sin 2:202–214. https://doi.org/10.1111/j.1365-3091.1986.tb00751.xCrossRef

Tzelepis V, Moutsopoulos KN, Papaspyros JNE, Tsihrintzis VA (2015) Experimental investigation of flow behavior in smooth and rough artificial fractures. J Hydrol 521(2):108–118. https://doi.org/10.1016/j.jhydrol.2014.11.054CrossRef

Wang ZC, Li SC, Qiao LP (2015) Design and test aspects of a water curtain system for underground oil storage caverns in China. Tunn Undergr Space Technol 48:20–34. https://doi.org/10.1016/j.tust.2015.01.009CrossRef

Wang ZC, Li W, Bi LP, Qiao, LP, Liu RC, Liu J (2018a) Estimation of the REV size and equivalent permeability coefficient of fractured rock masses with an emphasis on comparing the radial and unidirectional flow configurations. Rock Mech Rock Eng 51(5):1457–1471. https://doi.org/10.1007/s00603-018-1422-4

Wang ZC, Li W, Qiao LP, Liu J, Yang JJ (2018b) Hydraulic properties of fractured rock mass with correlated fracture length and aperture in both radial and unidirectional flow configurations. Comput Geotech 104:167–184. https://doi.org/10.1016/j.compgeo.2018.08.017CrossRef

Wilcox DC (1998) Turbulence modeling for CFD, 2nd edn. DCW Industries. https://doi.org/10.1007/3-540-59280-6_150

Wilson CR, Witherspoon PA (1976) Flow interference effects at fracture intersections. Water Resour Res 12(1):102–104. https://doi.org/10.1029/WR012i001p00102CrossRef

Wu ZJ, Fan LF, Zhao SH (2018) Effects of hydraulic gradient, intersecting angle, aperture, and fracture length on the nonlinearity of fluid flow in smooth intersecting fractures: an experimental investigation. Geofluids 2018:1–14. https://doi.org/10.1155/2018/9352608CrossRef

Xiong F, Wei W, Xu C, Jiang Q (2020) Experimental and numerical investigation on nonlinear flow behaviour through three dimensional fracture intersections and fracture networks. Comput Geotech 121:103446. https://doi.org/10.1016/j.compgeo.2020.103446CrossRef

Zeng Z, Grigg R (2006) A criterion for non-Darcy flow in porous media. Transp Porous Media 63(1):57–59. https://doi.org/10.1007/s11242-005-2720-3CrossRef

Zhang Z, Nemcik J (2013a) Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J Hydrol 477(1):139–151. https://doi.org/10.1016/j.jhydrol.2012.11.024CrossRef

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

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. https://doi.org/10.1007/s00603-016-0960-xCrossRef

Zhu HG, Yi C, Jiang YD, Xie HP, Yang MZ (2015) Effect of fractures cross connection on fluid flow characteristics of mining-induced rock (in Chinese). J China Univ Min Technol 44(1):24–28. https://doi.org/10.13247/j.cnki.jcumt.000283CrossRef

Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transp Porous Media 23(1):1–30. https://doi.org/10.1007/bf00145263CrossRef

Zimmerman RW, Al-Yaarubi A, Pain CC, Grattoni CA (2004) Nonlinear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41(3):163–169. https://doi.org/10.1016/j.ijrmms.2004.03.036CrossRef

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

Title: A model for nonlinear flow behavior in two-dimensional fracture intersections and the estimation of flow model coefficients
Authors: Zhechao Wang
Jie Liu
Liping Qiao
Jinjin Yang
Jiafan Guo
Kanglin Li
Publication date: 25-02-2022
Publisher: Springer Berlin Heidelberg
Published in: Hydrogeology Journal / Issue 3/2022
Print ISSN: 1431-2174
Electronic ISSN: 1435-0157
DOI: https://doi.org/10.1007/s10040-022-02453-0

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 3/2022

Continual long-term monitoring of methane in wells above the Utica Shale using total dissolved gas pressure probes

Assessment of the level of activity of advective transport through fractures and faults in marine deposits by comparison between stable isotope compositions of fracture and pore waters

A novel probe for point injections in groundwater monitoring wells

Laboratory experimental study on pumping-induced earth fissures

Estimation of groundwater recharge rates using soil-water isotope profiles: a case study of two contrasting dune types on Langeoog Island, Germany

Groundwater contamination source estimation based on a refined particle filter associated with a deep residual neural network surrogate