Coupled flow network and discrete element modeling of injection-induced crack propagation and coalescence in brittle rock

Abstract

We present a numerical analysis on injection-induced crack propagation and coalescence in brittle rock. The DEM network coupling model in PFC is modified to capture the evolution of fracture geometry. An improved fluid flow model for fractured porous media is proposed and coupled with a bond-based DEM model to simulate the interactions among cracks induced by injecting fluid in two nearby flaws at identical injection rates. The material parameters are calibrated based on the macro-properties of Lac du Bonnet granite and KGD solution. A grain-based model, which generates larger grains from assembles of particles bonded together, is calibrated to identify the microscopic mechanical and hydraulic parameters of Lac du Bonnet granite such that the DEM model yields a ratio between the compressive and tensile strength consistent with experiments. The simulations of fluid injection reveal that the initial flaw direction plays a crucial role in crack interaction and coalescence pattern. When two initial flaws are aligned, cracks generally propagate faster. Some geometrical measures from graph theory are used to analyze the geometry and connectivity of the crack network. The results reveal that initial flaws in the same direction may lead to a well-connected crack network with higher global efficiency.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

References

  1. 1.

    Adachi JI, Detournay E (2008) Plane strain propagation of a hydraulic fracture in a permeable rock. Eng Fract Mech 75(16):4666–4694

    Article  Google Scholar 

  2. 2.

    Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44(5):739–757

    Article  Google Scholar 

  3. 3.

    Al-Busaidi A (2005) Distinct element modeling of hydraulically fractured Lac du Bonnet granite. J Geophys Res 110:B06302. https://doi.org/10.1029/2004jb003297

    Article  Google Scholar 

  4. 4.

    Al-Raoush R, Alshibli KA (2006) Distribution of local void ratio in porous media systems from 3D X-ray microtomography images. Physica A 361(2):441–456

    Article  Google Scholar 

  5. 5.

    Al-Raoush R, Willson C (2005) Extraction of physically realistic pore network properties from three-dimensional synchrotron X-ray microtomography images of unconsolidated porous media systems. J Hydrol 300(1):44–64

    Article  Google Scholar 

  6. 6.

    Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res Solid Earth (1978–2012) 89(B6):4077–4114

    MathSciNet  Article  Google Scholar 

  7. 7.

    Bahrani N, Kaiser PK, Valley B (2014) Distinct element method simulation of an analogue for a highly interlocked, non-persistently jointed rockmass. Int J Rock Mech Min Sci 71:117–130

    Article  Google Scholar 

  8. 8.

    Bewick RP, Kaiser PK, Bawden WF, Bahrani N (2013) DEM, simulation of direct shear: 1. Rupture under constant normal stress boundary conditions. Rock Mech Rock Eng 47(5):1647–1671

    Article  Google Scholar 

  9. 9.

    Bewick RP, Kaiser PK, Bawden WF (2013) DEM, simulation of direct shear: 2. Grain boundary and mineral grain strength component influence on shear rupture. Rock Mech Rock Eng 47(5):1673–1692

    Article  Google Scholar 

  10. 10.

    Boone TJ, Ingraffea AR, Roegiers J-C (1991) Simulation of hydraulic fracture propagation in poroelastic rock with application to stress measurement techniques. Int J Rock Mech Min Sci Geomech Abstr 28:1–14

    Article  Google Scholar 

  11. 11.

    Bunger AP, Detournay E, Garagash DI (2005) Toughness-dominated Hydraulic Fracture with Leak-off. Int J Fract 134(2):175–190

    MATH  Article  Google Scholar 

  12. 12.

    Carrier B, Granet S (2012) Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng Fract Mech 79:312–328

    Article  Google Scholar 

  13. 13.

    Cho N, Martin CD, Sego DC (2007) A clumped particle model for rock. Int J Rock Mech Min Sci 44(7):997–1010

    Article  Google Scholar 

  14. 14.

    Choo J, Sun W (2018) Cracking and damage from crystallization in pores: Coupled chemo-hydro-mechanics and phase-field modeling. Comput Methods Appl Mech Eng 335:347–379

    MathSciNet  Article  Google Scholar 

  15. 15.

    Choo J, Sun W (2018) Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow. Comput Methods Appl Mech Eng 330:1–32

    MathSciNet  Article  Google Scholar 

  16. 16.

    Clark JB (1949) A hydraulic process for increasing the productivity of wells. J Petrol Technol 1(01):1–8

    Article  Google Scholar 

  17. 17.

    Cook NGW (1992) Natural joints in rock: mechanical, hydraulic and seismic behaviour and properties under normal stress. Int J Rock Mech Min Sci Geomech Abstr 29:198–223

    Article  Google Scholar 

  18. 18.

    Cook BK, Lee MY, DiGiovanni AA, Bronowski DR, Perkins ED, Williams JR (2004) Discrete element modeling applied to laboratory simulation of near-wellbore mechanics. Int J Geomech 4(1):19–27

    Article  Google Scholar 

  19. 19.

    Cui ZD, Liu DA, Zeng RS, Niu JR, Wang HJ, Shi XS (2013) Resistance of caprock to hydraulic fracturing due to CO2 injection into sand lens reservoirs. Eng Geol 164:146–154

    Article  Google Scholar 

  20. 20.

    Dahi Taleghani A (2009) Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures. The University of Texas at Austin, Austin

    Google Scholar 

  21. 21.

    Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4(1):35–45

    Article  Google Scholar 

  22. 22.

    Detournay E (2016) Mechanics of hydraulic fractures. Annu Rev Fluid Mech 48:311–339

    MathSciNet  MATH  Article  Google Scholar 

  23. 23.

    Dijkstra EW (1959) A note on two problems in connexion with graphs. Numer Math 1(1):269–271

    MathSciNet  MATH  Article  Google Scholar 

  24. 24.

    Downie R, Kronenberger E, Maxwell SC (2010) Using microseismic source parameters to evaluate the influence of faults on fracture treatments: a geophysical approach to interpretation. In: SPE annual technical conference and exhibition: society of petroleum engineers

  25. 25.

    Eberhardt E, Stimpson B, Stead D (1999) Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures. Rock Mech Rock Eng 32(2):81–99

    Article  Google Scholar 

  26. 26.

    Eberhardt E, Stead D, Stimpson B (1999) Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression. Int J Rock Mech Min Sci 32(2):361–380

    Article  Google Scholar 

  27. 27.

    Falls SD, Young RP, Carlson SR, Chow T (1992) Ultrasonic tomography and acoustic emission in hydraulically fractured Lac du Bonnet grey granite. J Geophys Res Solid Earth (1978–2012) 97(B5):6867–6884

    Article  Google Scholar 

  28. 28.

    Fu P, Johnson SM, Carrigan CR (2013) An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks. Int J Numer Anal Meth Geomech 37(14):2278–2300

    Article  Google Scholar 

  29. 29.

    Gale JFW, Reed RM, Holder J (2007) Natural fractures in the Barnett Shale and their importance for hydraulic fracture treatments. AAPG Bull 91(4):603–622

    Article  Google Scholar 

  30. 30.

    Geertsma J, De Klerk F (1969) A rapid method of predicting width and extent of hydraulically induced fractures. J Petrol Technol 21(12):571–581

    Article  Google Scholar 

  31. 31.

    Helmons RLJ, Miedema SA, Alvarez Grima M, van Rhee C (2016) Modeling fluid pressure effects when cutting saturated rock. Eng Geol 211(Supplement C):50–60

    Article  Google Scholar 

  32. 32.

    Hunsweck MJ, Shen Y (2013) Lew Aa, n J. A finite element approach to the simulation of hydraulic fractures with lag. Int J Numer Anal Meth Geomech 37(9):993–1015

    Article  Google Scholar 

  33. 33.

    Ishida T, Chen Q, Mizuta Y, Roegiers JC (2004) Influence of fluid viscosity on the hydraulic fracturing mechanism. J Energy Res Technol 126(3):190–200

    Article  Google Scholar 

  34. 34.

    Itasca Consulting Group I (2008) Manual PFC2D (Particle Flow Code), Version 4.0 Users’ Guide. Minneapolis, Minnesota, USA: Itasca, Minneapolis

  35. 35.

    Khristianovic S, Zheltov Y (1955) Formation of vertical fractures by means of highly viscous fluids. In: Proceedings of 4th world petroleum congress, Rome, p 579–586

  36. 36.

    Koyama T, Jing L (2007) Effects of model scale and particle size on micro-mechanical properties and failure processes of rocks—A particle mechanics approach. Eng Anal Boundary Elem 31(5):458–472

    MATH  Article  Google Scholar 

  37. 37.

    Kuhn MR, Sun W, Wang Q (2015) Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability. Acta Geotech 10(4):399–419

    Article  Google Scholar 

  38. 38.

    Latora V, Marchiori M (2003) Economic small-world behavior in weighted networks. Eur Phys J B—Condens Matter 32(2):249–263

    Google Scholar 

  39. 39.

    Li Y, Chen YF, Zhang GJ, Liu Y, Zhou CB (2017) A numerical procedure for modeling the seepage field of water-sealed underground oil and gas storage caverns. Tunn Undergr Space Technol 66:56–63

    Article  Google Scholar 

  40. 40.

    Liu G, Rong G, Peng J, Zhou CB (2015) Numerical simulation on undrained triaxial behavior of saturated soil by a fluid coupled-DEM model. Eng Geol 193:256–266

    Article  Google Scholar 

  41. 41.

    Liu G, Cai M, Huang M (2018) Mechanical properties of brittle rock governed by micro-geometric heterogeneity. Comput Geotech. https://doi.org/10.1016/j.compgeo.2017.11.013

    Article  Google Scholar 

  42. 42.

    Marcus D (2008) Graph theory: a problem oriented approach. Mathematical Association of America, Washington, DC

    Google Scholar 

  43. 43.

    Martin CD (1993) The strength of massive Lac du Bonnet granite around underground openings. Ph.D. thesis, University of Manitoba, Winnipeg, Canada

  44. 44.

    Na S, Sun W (2018) Computational thermomechanics of crystalline rock, part I: a combined multi-phase-field/crystal plasticity approach for single crystal simulations. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2017.12.022

    MathSciNet  Article  Google Scholar 

  45. 45.

    Nguyen VP, Lian H, Rabczuk T, Bordas S (2017) Modelling hydraulic fractures in porous media using flow cohesive interface elements. Eng Geol 225:68–82

    Article  Google Scholar 

  46. 46.

    Nordgren RP (1972) Propagation of a vertical hydraulic fracture. Soc Petrol Eng J 12(04):306–314

    Article  Google Scholar 

  47. 47.

    Ouchi H, Katiyar A, York J, Foster JT, Sharma MM (2015) A fully coupled porous flow and geomechanics model for fluid driven cracks: a peridynamics approach. Comput Mech 55(3):561–576

    MathSciNet  MATH  Article  Google Scholar 

  48. 48.

    Park CH, Bobet A (2009) Crack coalescence in specimens with open and closed flaws: A comparison. Int J Rock Mech Min Sci 46(5):819–829

    Article  Google Scholar 

  49. 49.

    Park CH, Bobet A (2010) Crack initiation, propagation and coalescence from frictional flaws in uniaxial compression. Eng Fract Mech 77(14):2727–2748

    Article  Google Scholar 

  50. 50.

    Peng J, Wong LNY, Teh CI (2017) Influence of grain size heterogeneity on strength and microcracking behavior of crystalline rocks. J Geophysical Res Solid Earth 122(2):1054–1073

    Article  Google Scholar 

  51. 51.

    Perkins TK, Kern LR (1961) Widths of hydraulic fractures. J Petrol Technol 13(09):937–949

    Article  Google Scholar 

  52. 52.

    Potyondy DO (2010) A grain-based model for rock: approaching the true microstructure. In: Proceedings of rock mechanics in the Nordic Countries

  53. 53.

    Potyondy D (2012) A flat-jointed bonded-particle material for hard rock. In: 46th US Rock mechanics/geomechanics symposium: American Rock Mechanics Association

  54. 54.

    Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  55. 55.

    Reyes O, Einstein HH (1991) Failure mechanisms of fractured rock—a fracture coalescence model. In: 7th ISRM Congress: International Society for Rock Mechanics

  56. 56.

    Rong G, Liu G, Hou D, Zhou CB (2013) Effect of particle shape on mechanical behaviors of rocks: a numerical study using clumped particle model. Sci World J. https://doi.org/10.1155/2013/589215

    Article  Google Scholar 

  57. 57.

    Rong G, Peng J, Wang X, Liu G, Hou D (2013) Formation mechanism of deep cracks in the left bank slope of Jinping-i hydropower station. Disaster Adv 6(3):4–11

    Google Scholar 

  58. 58.

    Rummel F (1987) Fracture mechanics approach to hydraulic fracturing stress measurements. Academic Press London, Fracture mechanics of rock, pp 217–239

    Google Scholar 

  59. 59.

    Salimzadeh S, Khalili N (2011) Coupling reservoir simulation in naturally fractured reservoir: Implicit versus explicit formulation. In: International Association for Computer Methods and Advances in Geomechanics (IACMAG 13th), Melbourne, Australia, pp 25–30

  60. 60.

    Salimzadeh S, Khalili N (2015) A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation. Comput Geotech 69:82–92

    Article  Google Scholar 

  61. 61.

    Satake M (1992) A discrete-mechanical approach to granular materials. Int J Eng Sci 30(10):1525–1533

    Article  Google Scholar 

  62. 62.

    Shimizu H, Murata S, Ishida T (2011) The distinct element analysis for hydraulic fracturing in hard rock considering fluid viscosity and particle size distribution. Int J Rock Mech Min Sci 48(5):712–727

    Article  Google Scholar 

  63. 63.

    Souley M, Homand F, Pepa S, Hoxha D (2001) Damage-induced permeability changes in granite: a case example at the URL in Canada. Int J Rock Mech Min Sci 38(2):297–310

    Article  Google Scholar 

  64. 64.

    Spence DA, Sharp P (1985) Self-similar solutions for elastohydrodynamic cavity flow. Proc R Soc Lond A Math Phys Eng Sci 400:289–313

    MathSciNet  MATH  Article  Google Scholar 

  65. 65.

    Sun W (2015) A stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain. Int J Numer Meth Eng 103(11):798–839

    MathSciNet  MATH  Article  Google Scholar 

  66. 66.

    Sun W, Andrade JE, Rudnicki JW, Eichhubl P (2011) Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations. Geophys Res Lett 38(10):L10302. https://doi.org/10.1029/2011GL047683

    Article  Google Scholar 

  67. 67.

    Sun W, Andrade JE, Rudnicki JW (2011) Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability. Int J Numer Meth Eng 88(12):1260–1279

    MathSciNet  MATH  Article  Google Scholar 

  68. 68.

    Sun W, Chen Q, Ostien JT (2014) Modeling the hydro-mechanical responses of strip and circular punch loadings on water-saturated collapsible geomaterials. Acta Geotech 9(5):903–934

    Article  Google Scholar 

  69. 69.

    Thallak S, Rothenburg L, Dusseault M et al (1991) Simulation of multiple hydraulic fractures in a discrete element system. In: The 32nd US symposium on rock mechanics (USRMS): American Rock Mechanics Association

  70. 70.

    Valentini L, Perugini D, Poli G (2007) The, “small-world” topology of rock fracture networks. Physica A 377(1):323–328

    Article  Google Scholar 

  71. 71.

    Valentini L, Perugini D, Poli G (2007) The ‘small-world’ nature of fracture/conduit networks: possible implications for disequilibrium transport of magmas beneath mid-ocean ridges. J Volcanol Geoth Res 159(4):355–365

    Article  Google Scholar 

  72. 72.

    Vogel HJ, Tölke J, Schulz VP, Krafczyk M, Roth K (2005) Comparison of a lattice-Boltzmann model, a full-morphology model, and a pore network model for determining capillary pressure–saturation relationships. Vadose Zone J 4(2):380–388

    Article  Google Scholar 

  73. 73.

    Wang K, Sun W (2017) A unified variational eigen-erosion framework for interacting brittle fractures and compaction bands in fluid-infiltrating porous media. Comput Methods Appl Mech Eng 318(1):1–32

    MathSciNet  Article  Google Scholar 

  74. 74.

    Wang K, Sun W (2018) A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning. Comput Methods Appl Mech Eng 334:337–380

    MathSciNet  Article  Google Scholar 

  75. 75.

    Wang SY, Sun L, Au ASK, Yang TH, Tang CA (2009) 2D-numerical analysis of hydraulic fracturing in heterogeneous geo-materials. Constr Build Mater 23(6):2196–2206

    Article  Google Scholar 

  76. 76.

    Wang T, Zhou W, Chen J, Xiao X, Li Y, Zhao X (2014) Simulation of hydraulic fracturing using particle flow method and application in a coal mine. Int J Coal Geol 121:1–13

    Article  Google Scholar 

  77. 77.

    Wong LNY, Einstein HH (2009) Crack coalescence in molded gypsum and Carrara marble: part 1. Macroscopic observations and interpretation. Rock Mech Rock Eng 42(3):475–511

    Article  Google Scholar 

  78. 78.

    Wong LNY, Einstein HH (2009) Crack coalescence in molded gypsum and Carrara marble: part 2—microscopic observations and interpretation. Rock Mech Rock Eng 42(3):513–545

    Article  Google Scholar 

  79. 79.

    Zhang X, Jeffrey RG (2012) Fluid-driven multiple fracture growth from a permeable bedding plane intersected by an ascending hydraulic fracture. J Geophys Res 117:B12402. https://doi.org/10.1029/2012jb009609

    Article  Google Scholar 

  80. 80.

    Zhang F, Damjanac B, Huang H (2013) Coupled discrete element modeling of fluid injection into dense granular media. J Geophys Res Solid Earth 118(6):2703–2722

    Article  Google Scholar 

  81. 81.

    Zhuang X, Augarde C, Mathisen K (2012) Fracture modeling using meshless methods and level sets in 3D: framework and modeling. Int J Numer Meth Eng 92(11):969–998

    MathSciNet  MATH  Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the Earth Materials and Processes program at the US Army Research Office under grant contracts W911NF-14-1-0658 and W911NF-15-1-0581, Air Force Office of Scientific Research under grant contract FA9550-1186-17-1-0169, US Department of Energy Nuclear Engineering University Program under grant contract DE-NE0008534, National Science Foundation under grant contract EAR-1516300, Anhui Science and technology research projects (No. 1604a0802106), the Open Fund of the Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, the Open fund from state Key Laboratory of Water Resources and Hydropower Engineering Science, China (No. 2016SGG02), the Open Fund of the Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Key Laboratory of Geological Hazards on Three Gorges Reservoir Area (China Three Gorges University), Ministry of Education (No. 2015KDZ03), and Chinese Universities Scientific Fund (No. JZ2016HGBZ1021). These supports are gratefully acknowledged. The first author is also grateful to the China Scholarship Council (CSC) for providing him with a scholarship during his study in the USA. These supports are gratefully acknowledged.

Author information

Affiliations

Authors

Corresponding author

Correspondence to WaiChing Sun.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Liu, G., Sun, W., Lowinger, S.M. et al. Coupled flow network and discrete element modeling of injection-induced crack propagation and coalescence in brittle rock. Acta Geotech. 14, 843–868 (2019). https://doi.org/10.1007/s11440-018-0682-1

Download citation

Keywords

  • Brittle rock
  • Crack coalescence
  • Discrete element method
  • Flow network
  • Fluid-driven fracture