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A 2D mixed fracture–pore seepage model and hydromechanical coupling for fractured porous media

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Abstract

A novel two-dimensional mixed fracture–pore seepage model for fluid flow in fractured porous media is presented based on the computational framework of finite-discrete element method (FDEM). The model consists of a porous seepage model in triangular elements bonded by unbroken joint elements, as well as a fracture seepage model in broken joint elements. The principle for determining the fluid exchange coefficient of the unbroken joint element is provided to ensure numerical accuracy and efficiency. The mixed fracture–pore seepage model provides a simple but effective tool for solving fluid flow in fractured porous media. In this paper, examples of 1D and 2D seepage flow in porous media and porous media with a single fracture or multiple fractures are studied. The simulation results of the model match well with theoretical solutions or results obtained by commercial software, which verifies the correctness of the mixed fracture–pore seepage model. Furthermore, combining FDEM mechanical calculation and the mixed fracture–pore seepage model, a coupled hydromechanical model is built to simulate fluid-driven dynamic propagation of cracks in the porous media, as well as its influence on pore seepage and fracture seepage.

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References

  1. Areias P, Msekh MA, Rabczuk T (2016) Damage and fracture algorithm using the screened Poisson equation and local remeshing. Eng Fract Mech 158:116–143. https://doi.org/10.1016/j.engfracmech.2015.10.042

    Article  Google Scholar 

  2. Areias P, Reinoso J, Camanho PP, César de Sá J, Rabczuk T (2018) Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Eng Fract Mech 189:339–360. https://doi.org/10.1016/j.engfracmech.2017.11.017

    Article  Google Scholar 

  3. Baca RG, Arnett RC, Langford DW (1984) Modelling fluid flow in fractured-porous rock masses by finite-element techniques. Int J Numer Methods Fluids 4(4):337–348

    Article  Google Scholar 

  4. Barenblatt GI, Zheltov IP, Kochina IN (1960) Basic concept in the theory of homogeneous liquids in fissured rocks. J Appl Math Mech 24(5):1286–1303

    Article  Google Scholar 

  5. Bastian P, Chen Z, Ewing RE, Helmig R, Jakobs H, Reichenberger V (2000) Numerical simulation of multiphase flow in fractured porous media. Numerical treatment of multiphase flows in porous media. Springer, Berlin

    MATH  Google Scholar 

  6. Benedetto MF, Berrone S, Pieraccini S, Scialò S (2014) The virtual element method for discrete fracture network simulations. Comput Methods Appl Mech Eng 280:135–156. https://doi.org/10.1016/j.cma.2014.07.016

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Berrone S, Borio A, Vicini F (2019) Reliable a posteriori mesh adaptivity in Discrete Fracture Network flow simulations. Comput Method Appl Mech Eng 354:904–931. https://doi.org/10.1016/j.cma.2019.06.007

    Article  MathSciNet  MATH  Google Scholar 

  9. Bourbiaux B (2010) Fractured reservoir simulation: a challenging and rewarding issue. Oil Gas Sci Technol 65(2):227–238. https://doi.org/10.2516/ogst/2009063

    Article  Google Scholar 

  10. COMSOL Multiphysics® v. 5.4 (2018). COMSOL AB, Stockholm, Sweden

  11. Cipolla CL, Lolon EP, Erdle JC, Rubin B (2010) Reservoir modeling in shale-gas reservoirs. SPE Reserv Eval Eng 13(4):638–653

    Article  Google Scholar 

  12. de Dreuzy JR, Méheust Y, Pichot G (2012) Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks. J Geophys Res Solid Earth. https://doi.org/10.1029/2012JB009461

    Article  Google Scholar 

  13. Dverstorp B, Andersson J, Nordqvist W (1992) Discrete fracture network interpretation of field tracer migration in sparsely fractured rock. Water Resour Res 28(9):2327–2343

    Article  Google Scholar 

  14. FLAC (2005) User’s guide. Itasca Consulting Group Inc, Minnesota

    Google Scholar 

  15. Farsi A, Bedi A, Latham JP, Bowers K (2019) Simulation of fracture propagation in fibre-reinforced concrete using FDEM: an application to tunnel linings. Comput Part Mech. https://doi.org/10.1007/s40571-019-00305-5

    Article  Google Scholar 

  16. Fukuda D, Mohammadnejad M, Liu H, Dehkhoda S, Chan A, Cho SH, Min GJ, Han H, Ji K, Fujii Y (2019) Development of a GPGPU-parallelized hybrid finite-discrete element method for modeling rock fracture. Int J Numer Anal Methods Geomech. https://doi.org/10.1002/nag.2934

    Article  Google Scholar 

  17. Gan Q, Elsworth D (2016) A continuum model for coupled stress and fluid flow in discrete fracture networks. Geomech Geophys Geo-energy Geo-Resour 2(1):43–61. https://doi.org/10.1007/s40948-015-0020-0

    Article  Google Scholar 

  18. Gläser D, Helmig R, Flemisch B, Class H (2017) A discrete fracture model for two-phase flow in fractured porous media. Adv Water Resour 110:335–348. https://doi.org/10.1016/j.advwatres.2017.10.031

    Article  MATH  Google Scholar 

  19. Guo L, Latham J-P, Xiang J (2017) A numerical study of fracture spacing and through-going fracture formation in layered rocks. Int J Solids Struct 110–111(N):44–57. https://doi.org/10.1016/j.ijsolstr.2017.02.004

    Article  Google Scholar 

  20. Hoteit H, Firoozabadi A (2008) An efficient numerical model for incompressible two-phase flow in fractured media. Adv Water Resour 31(6):891–905. https://doi.org/10.1016/j.advwatres.2008.02.004

    Article  Google Scholar 

  21. Huang Z, Yan X, Yao J (2015) A two-phase flow simulation of discrete-fractured media using mimetic finite difference method. Commun Comput Phys 16(3):799–816. https://doi.org/10.4208/cicp.050413.170314a

    Article  MathSciNet  MATH  Google Scholar 

  22. Juanes R, Samper J, Molinero J (2002) A general and efficient formulation of fractures and boundary conditions in the finite element method. Int J Numer Methods Eng 54(12):1751–1774. https://doi.org/10.1002/nme.491

    Article  MATH  Google Scholar 

  23. Karimi-Fard M, Durlofsky LJ, Aziz K (2003) An efficient discrete fracture model applicable for general purpose reservoir simulators. SPE J 9(2):227–236

    Article  Google Scholar 

  24. Kim JG, Deo MD (2000) Finite element, discrete-fracture model for multiphase flow in porous media. AIChE J 46(6):1120–1130

    Article  Google Scholar 

  25. Lei Z, Rougier E, Munjiza A, Viswanathan H, Knight EE (2019) Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite-discrete element method. Int J Numer Anal Methods Geomech. https://doi.org/10.1002/nag.2929

    Article  Google Scholar 

  26. Li S, Zeng X, Ren B, Qian J, Zhang J, Jha AK (2012) An atomistic-based interphase zone model for crystalline solids. Comput Method Appl Methods 229–232:87–109. https://doi.org/10.1016/j.cma.2012.03.023

    Article  MathSciNet  MATH  Google Scholar 

  27. Lisjak A, Grasselli G, Vietor T (2014) Continuum–discontinuum analysis of failure mechanisms around unsupported circular excavations in anisotropic clay shales. Int J Rock Mech Min Sci 65:96–115. https://doi.org/10.1016/j.ijrmms.2013.10.006

    Article  Google Scholar 

  28. Lisjak A, Tatone BSA, Mahabadi OK, Grasselli G, Marschall P, Lanyon GW, Rdl V, Shao H, Leung H, Nussbaum C (2016) Hybrid finite-discrete element simulation of the EDZ formation and mechanical sealing process around a microtunnel in Opalinus Clay. Rock Mech Rock Eng 49(5):1849–1873. https://doi.org/10.1007/s00603-015-0847-2

    Article  Google Scholar 

  29. Long JCS, Remer JS, Wilson CR (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18(3):645–658

    Article  Google Scholar 

  30. Long JCS (1983) Investigation of equivalent porous medium permeability in networks of discontinuous fractures. Ph.D. Thesis, University of California, Berkeley

  31. Mohajerani S, Baghbanan A, Wang G, Forouhandeh SF (2017) An efficient algorithm for simulating grout propagation in 2D discrete fracture networks. Int J Rock Mech Min Sci 98:67–77. https://doi.org/10.1016/j.ijrmms.2017.07.015

    Article  Google Scholar 

  32. Mohajerani S, Wang G, Huang D, Jalali SME, Torabi SR, Jin F (2019) An efficient computational model for simulating stress-dependent flow in three-dimensional discrete fracture networks. KSCE J Civ Eng 23(3):1384–1394. https://doi.org/10.1007/s12205-019-0470-y

    Article  Google Scholar 

  33. Moinfar A, Varavei A, Sepehrnoori K, Johns RT, (2013) Development of a coupled dual continuum and discrete fracture model for the simulation of unconventional reservoirs. SPE Reservoir Simulation Symposium. Society of Petroleum Engineers

  34. Monteagudo JEP, Firoozabadi A (2004) Control-volume method for numerical simulation of two-phase immiscible flow in two- and three-dimensional discrete-fractured media. Water Resour Res 40(7):7405. https://doi.org/10.1029/2003wr002996

    Article  Google Scholar 

  35. Munjiza A (2004) The combined finite-discrete element method. Wiley, London

    Book  Google Scholar 

  36. Munjiza A (2011) Computational mechanics of discontinua. Wiley, London

    Book  Google Scholar 

  37. Munjiza A, Andrews K, White J (1999) Combined single and smeared crack model in combined finite-discrete element analysis. Int J Numer Methods Eng 44(1):41–57

    Article  Google Scholar 

  38. Munjiza A, Knight EE, Rougier E (2015) Large strain finite element method: a practical course. John Wiley & Sons

  39. Noorishad J, Mehran M (1982) An upstream finite element method for solution of transient transport equation in fractured porous media. Water Resour Res 18(3):588–596

    Article  Google Scholar 

  40. Paul B, Faivre M, Massin P, Giot R, Colombo D, Golfier F, Martin A (2018) 3D coupled HM–XFEM modeling with cohesive zone model and applications to non planar hydraulic fracture propagation and multiple hydraulic fractures interference. Comput Method Appl Methods 342:321–353. https://doi.org/10.1016/j.cma.2018.08.009

    Article  MathSciNet  MATH  Google Scholar 

  41. Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13):2316–2343. https://doi.org/10.1002/nme.1151

    Article  MATH  Google Scholar 

  42. Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Comput Method Appl Mech Eng 199(37–40):2437–2455. https://doi.org/10.1016/j.cma.2010.03.031

    Article  MATH  Google Scholar 

  43. Rayudu NM, Tang X, Singh G (2019) Simulating three dimensional hydraulic fracture propagation using displacement correlation method. Tunn Undergr Space Technol 85:84–91. https://doi.org/10.1016/j.tust.2018.11.010

    Article  Google Scholar 

  44. Ren H, Zhuang X, Cai Y, Rabczuk T (2016) Dual-horizon peridynamics. Int J Numer Methods Eng 108(12):1451–1476. https://doi.org/10.1002/nme.5257

    Article  MathSciNet  Google Scholar 

  45. Ren H, Zhuang X, Rabczuk T (2017) Dual-horizon peridynamics: a stable solution to varying horizons. Comput Methods Appl Mech Eng 318:762–782. https://doi.org/10.1016/j.cma.2016.12.031

    Article  MathSciNet  MATH  Google Scholar 

  46. Rougier E, Knight EE, Broome ST, Sussman AJ, Munjiza A (2014) Validation of a three-dimensional Finite-Discrete Element Method using experimental results of the Split Hopkinson Pressure Bar test. Int J Rock Mech Min Sci 70(N):101–108. https://doi.org/10.1016/j.ijrmms.2014.03.011

    Article  Google Scholar 

  47. Sun Y, Liu Z, Tang X (2020) A hybrid FEMM-Phase field method for fluid-driven fracture propagation in three dimension. Eng Anal Bound Elem 113:40–54. https://doi.org/10.1016/j.enganabound.2019.12.018

    Article  MathSciNet  MATH  Google Scholar 

  48. Tang X, Rutqvist J, Hu M, Rayudu NM (2019) Modeling three-dimensional fluid-driven propagation of multiple fractures using TOUGH-FEMM. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-018-1715-7

    Article  Google Scholar 

  49. Tatomir A (2007) Numerical investigations of flow through fractured porous media. Master’s Universität Stuttgart, Stuttgart

    Google Scholar 

  50. UDEC (2005) User’s guide. Itasca Consulting Group Inc, Minnesota

    Google Scholar 

  51. Wang Y, Li T, Chen Y, Ma G (2019) A three-dimensional thermo-hydro-mechanical coupled model for enhanced geothermal systems (EGS) embedded with discrete fracture networks. Comput Methods Appl Mech Eng 356:465–489. https://doi.org/10.1016/j.cma.2019.06.037

    Article  MathSciNet  MATH  Google Scholar 

  52. Wu YS, Haukwa C, Bodvarsson GS (1999) A site-scale model for fluid and heat flow in the unsaturated zone of Yucca Mountain, Nevada. J Contam Hydrol 38(1–3):185–215

    Article  Google Scholar 

  53. Wu YS, Qin G (2009) A generalized numerical approach for modeling multiphase flow and transport in fractured porous media. Commun Comput Phys 6(1):85–108

    Article  MathSciNet  Google Scholar 

  54. Yan C, Fan H, Zheng Y, Zhao Y, Ning F (2020) Simulation of the thermal shock of brittle materials using the finite-discrete element method. Eng Anal Bound Elem 115:142–155. https://doi.org/10.1016/j.enganabound.2020.03.013

    Article  MathSciNet  MATH  Google Scholar 

  55. Yan C, Jiao Y-Y (2018) A 2D fully coupled hydro-mechanical finite-discrete element model with real pore seepage for simulating the deformation and fracture of porous medium driven by fluid. Comput Struct 196:311–326. https://doi.org/10.1016/j.compstruc.2017.10.005

    Article  Google Scholar 

  56. Yan C, Jiao Y-Y (2019) A 2D discrete heat transfer model considering the thermal resistance effect of fractures for simulating the thermal cracking of brittle materials. Acta Geotech. https://doi.org/10.1007/s11440-019-00821-x

    Article  Google Scholar 

  57. Yan C, Jiao YY (2019) FDEM-TH3D: a three-dimensional coupled hydrothermal model for fractured rock. Int J Numer Anal Methods Geomech 43:415–444. https://doi.org/10.1002/nag.2869

    Article  Google Scholar 

  58. Yan C, Jiao Y-Y, Yang S (2019) A 2D coupled hydro-thermal model for the combined finite-discrete element method. Acta Geotech 14(2):403–416. https://doi.org/10.1007/s11440-018-0653-6

    Article  Google Scholar 

  59. Yan C, Jiao Y-Y, Zheng H (2018) A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating 3D hydraulic fracturing. Comput Geotech 96:73–89. https://doi.org/10.1016/j.compgeo.2017.10.008

    Article  Google Scholar 

  60. Yan C, Jiao YY, Zheng H (2019) A three-dimensional heat transfer and thermal cracking model considering the effect of cracks on heat transfer. Int J Numer Anal Methods Geomech. https://doi.org/10.1002/nag.2937

    Article  Google Scholar 

  61. Yan C, Ren Y, Yang Y (2019) A 3D thermal cracking model for rockbased on the combined finite–discrete element method. Comput Part Mech. https://doi.org/10.1007/s40571-019-00281-w

    Article  Google Scholar 

  62. Yan C, Zheng H (2016) A two-dimensional coupled hydro-mechanical finite-discrete model considering porous media flow for simulating hydraulic fracturing. Int J Rock Mech Min Sci 88:115–128. https://doi.org/10.1016/j.ijrmms.2016.07.019

    Article  Google Scholar 

  63. Yan C, Zheng H (2016) A two-dimensional coupled hydro-mechanical finite-discrete model considering porous media flow for simulating hydraulic fracturing. Int J Rock Mech Min Sci 88(2016):115–128. https://doi.org/10.1016/j.ijrmms.2016.07.019

    Article  Google Scholar 

  64. Yan C, Zheng H (2017) A coupled thermo-mechanical model based on the combined finite-discrete element method for simulating thermal cracking of rock. Int J Rock Mech Min Sci 91:170–178. https://doi.org/10.1016/j.ijrmms.2016.11.023

    Article  Google Scholar 

  65. Yan C, Zheng H (2017) Three-dimensional hydromechanical model of hydraulic fracturing with arbitrarily discrete fracture networks using finite-discrete element method. Int J Geomech 17(6):04016133

    Article  Google Scholar 

  66. Yan C, Zheng H (2017) FDEM-flow3D: a 3D hydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing. Comput Geotech 81:212–228. https://doi.org/10.1016/j.compgeo.2016.08.014

    Article  Google Scholar 

  67. Yan C, Zheng H (2017) FDEM-flow3D: a 3D hydro-mechanical coupled model considering the pore seepage of rock matrix for simulating three-dimensional hydraulic fracturing. Comput Geotech 81(2017):212–228. https://doi.org/10.1016/j.compgeo.2016.08.014

    Article  Google Scholar 

  68. Yan CZ, Zheng H (2017) A new potential function for the calculation of contact forces in the combined finite-discrete element method. Int J Numer Anal Methods Geomech 41(2):265–283. https://doi.org/10.1002/nag.2559

    Article  Google Scholar 

  69. Yan C, Zheng Y, Huang D, Wang G (2021) A coupled contact heat transfer and thermal cracking model for discontinuous and granular media. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2020.113587

    Article  MathSciNet  MATH  Google Scholar 

  70. Yan C, Zheng H, Sun G, Ge X (2016) Combined finite-discrete element method for simulation of hydraulic fracturing. Rock Mech Rock Eng 49(4):1389–1410. https://doi.org/10.1007/s00603-015-0816-9

    Article  Google Scholar 

  71. Yang Y, Tang X, Zheng H, Liu Q, Liu Z (2018) Hydraulic fracturing modeling using the enriched numerical manifold method. Appl Math Model 53:462–486. https://doi.org/10.1016/j.apm.2017.09.024

    Article  MATH  Google Scholar 

  72. Zeng X, Li S (2010) A multiscale cohesive zone model and simulations of fractures. Comput Methods Appl Mech Eng 199(9–12):547–556. https://doi.org/10.1016/j.cma.2009.10.008

    Article  MATH  Google Scholar 

  73. Zeng Q, Yao J, Shao J (2020) An extended finite element solution for hydraulic fracturing with thermo-hydro-elastic-plastic coupling. Comput Method Appl Methods 364:112967. https://doi.org/10.1016/j.cma.2020.112967

    Article  MathSciNet  MATH  Google Scholar 

  74. Zhang K, Woodbury AD (2002) A Krylov finite element approach for multi-species contaminant transport in discretely fractured porous media. Adv Water Resour 25(7):705–721

    Article  Google Scholar 

  75. Zhao Q, Lisjak A, Mahabadi O, Liu Q, Grasselli G (2014) Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method. J Rock Mech Geotech Eng 6(6):574–581. https://doi.org/10.1016/j.jrmge.2014.10.003

    Article  Google Scholar 

  76. Zhou S, Zhuang X, Rabczuk T (2018) A phase-field modeling approach of fracture propagation in poroelastic media. Eng Geol 240:189–203. https://doi.org/10.1016/j.enggeo.2018.04.008

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Numbers 11872340, 11602006; the Hong Kong Scholars Program (XJ2019040, HKSP19EG04) from China National Postdoctoral Council; Hong Kong Research Grants Council grant number N_HKUST621/18; the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUG170657, CUGGC09); and State Key Laboratory of Hydroscience and Engineering Grant 2019-KY-02.

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  1. Faculty of Engineering, China University of Geosciences, Wuhan, 430074, China

    Chengzeng Yan & Hongwei Fan

  2. Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, SAR, China

    Chengzeng Yan & Gang Wang

  3. Department of Hydraulic Engineering, Tsinghua University, Beijing, China

    Duruo Huang

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Yan, C., Fan, H., Huang, D. et al. A 2D mixed fracture–pore seepage model and hydromechanical coupling for fractured porous media. Acta Geotech. 16, 3061–3086 (2021). https://doi.org/10.1007/s11440-021-01183-z

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