Acta Geotechnica

, Volume 14, Issue 2, pp 377–402 | Cite as

XFEM-based cohesive zone approach for modeling near-wellbore hydraulic fracture complexity

  • Yongcun FengEmail author
  • K. E. Gray
Research Paper


Near-wellbore fracture tortuosity has important impacts on the productivity of fractured oil and gas wells and the injectivity of CO2 or solids disposal injectors. Previous models for simulating near-wellbore fracture tortuosity usually assume fracture growth in linear-elastic media, without considering the effects of porous features of the rock. In this paper, a 2D fully coupled model is developed to simulate near-wellbore fracturing using the XFEM-based cohesive segment method. The model takes into account a variety of crucial physical aspects, including fracture extension and turning, fluid flow in the fracture, fluid leak-off through wellbore wall and fracture surfaces, pore fluid flow, and rock deformation. The proposed model was verified against two sets of published experimental results. Numerical examples were carried out to investigate the effects of various parameters on near-wellbore fracture trajectory, injection pressure, and fracture width. Results show that near-wellbore fracture behaviors are not only dependent on rock elastic properties and field stresses, but also greatly influenced by porous properties of the rock, such as permeability and leak-off coefficient. Some field implications were provided based on the simulation results. By overcoming some limitations of the previous models, the proposed model predicts more realistic fracture evolution in the near-wellbore region and provides an attractive tool for design and evaluation of many field operations, for which near-wellbore fracture behaviors play an important role on their successes.


Cohesive zone model Fracture complexity Near-wellbore fracture Poroelastic effect XFEM 



The authors wish to thank the Wider Windows Industrial Affiliate Program, the University of Texas at Austin, for financial and logistical support of this work. Program support from BHP Billiton, British Petroleum, Chevron, ConocoPhillips, Halliburton, Marathon, National Oilwell Varco, Occidental Oil and Gas, and Shell is gratefully acknowledged. Thanks are due also to Dr. Evgeny Podnos for his manuscript review and suggestions.


  1. 1.
    Abass HH, Brumley JL, Venditto JJ (1994) Oriented perforations—a rock mechanics view. In: Presented at the SPE annual technical conference and exhibitionGoogle Scholar
  2. 2.
    Abdollahipour A, Fatehi Marji M, Yarahmadi Bafghi A, Gholamnejad J (2015) Simulating the propagation of hydraulic fractures from a circular wellbore using the Displacement Discontinuity Method. Int J Rock Mech Min Sci 80:281–291CrossRefGoogle Scholar
  3. 3.
    Al-Busaidi A, Hazzard JF, Young RP (2005) Distinct element modeling of hydraulically fractured Lac du Bonnet granite. J Geophys Res Solid Earth 110(B6):B06302CrossRefGoogle Scholar
  4. 4.
    Areias P, Rabczuk T (2017) Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elem Anal Des 132:27–41CrossRefGoogle Scholar
  5. 5.
    Areias P, Rabczuk T, Dias-da-Costa D (2013) Element-wise fracture algorithm based on rotation of edges. Eng Fract Mech 110:113–137CrossRefGoogle Scholar
  6. 6.
    Areias P, Rabczuk T, Camanho PP (2014) Finite strain fracture of 2D problems with injected anisotropic softening elements. Theor Appl Fract Mech 72:50–63CrossRefGoogle Scholar
  7. 7.
    Areias P, Msekh MA, Rabczuk T (2016) Damage and fracture algorithm using the screened Poisson equation and local remeshing. Eng Fract Mech 158:116–143CrossRefGoogle Scholar
  8. 8.
    Behrmann LA, Nolte KG (1999) Perforating requirements for fracture stimulations. SPE Drill Complet 14(04):228–234CrossRefGoogle Scholar
  9. 9.
    Bruno MS, Dorfmann A, Lao K, Honeger C (2001) Coupled particle and fluid flow modeling of fracture and slurry injection in weakly consolidated granular media. In: Presented at the DC Rocks 2001, the 38th U.S. symposium on rock mechanics (USRMS)Google Scholar
  10. 10.
    Camanho PP, Dávila CG (2002) Mixed-mode decohesion finite elements for the simulation of delamination in composite materials. NASA/TM-2002–211737, pp 1–37Google Scholar
  11. 11.
    Chen M, Jiang H, Zhang GQ, Jin Y (2010) The experimental investigation of fracture propagation behavior and fracture geometry in hydraulic fracturing through oriented perforations. Pet Sci Technol 28(13):1297–1306CrossRefGoogle Scholar
  12. 12.
    Cherny S et al (2009) Two-dimensional modeling of the near-wellbore fracture tortuosity effect. Int J Rock Mech Min Sci 46(6):992–1000CrossRefGoogle Scholar
  13. 13.
    Detournay E (2004) Propagation regimes of fluid-driven fractures in impermeable rocks. Int J Geomech 4(1):35–45CrossRefGoogle Scholar
  14. 14.
    Fallahzadeh SH, Rasouli V, Sarmadivaleh M (2015) An investigation of hydraulic fracturing initiation and near-wellbore propagation from perforated boreholes in tight formations. Rock Mech Rock Eng 48(2):573–584CrossRefGoogle Scholar
  15. 15.
    Feng Y, Gray KE (2016) A fracture-mechanics-based model for wellbore strengthening applications. J Nat Gas Sci Eng 29:392–400CrossRefGoogle Scholar
  16. 16.
    Feng Y, Gray KE (2017) Modeling near-wellbore hydraulic fracture complexity using coupled pore pressure extended finite element method. In: Presented at the 51st U.S. rock mechanics/geomechanics symposiumGoogle Scholar
  17. 17.
    Feng Y, Gray KE (2017) Modeling lost circulation through drilling-induced fractures. SPE JGoogle Scholar
  18. 18.
    Feng Y, Arlanoglu C, Podnos E, Becker E, Gray KE (2015) Finite-element studies of hoop-stress enhancement for wellbore strengthening. SPE Drill Complet 30(01):38–51CrossRefGoogle Scholar
  19. 19.
    Garagash DI (2006) Propagation of a plane-strain hydraulic fracture with a fluid lag: early-time solution. Int J Solids Struct 43(18):5811–5835CrossRefzbMATHGoogle Scholar
  20. 20.
    Gordeliy E, Abbas S, Prioul R (2016) Modeling of near-wellbore fracture reorientation using a fluid-coupled 2D XFEM algorithm. In: Presented at the 50th U.S. rock mechanics/geomechanics symposiumGoogle Scholar
  21. 21.
    Haddad M, Sepehrnoori K (2015) Simulation of hydraulic fracturing in quasi-brittle shale formations using characterized cohesive layer: stimulation controlling factors. J Unconv Oil Gas Resour 9:65–83CrossRefGoogle Scholar
  22. 22.
    Jeffrey RG, Zhang X (2010) Mechanics of hydraulic fracture growth from a borehole. In: Presented at the Canadian unconventional resources and international petroleum conferenceGoogle Scholar
  23. 23.
    Li Y, Deng JG, Liu W, Feng Y (2017) Modeling hydraulic fracture propagation using cohesive zone model equipped with frictional contact capability. Comput Geotech 91:58–70CrossRefGoogle Scholar
  24. 24.
    Liu F, Gordon PA, Valiveti DM (2017) Modeling competing hydraulic fracture propagation with the extended finite element method. Acta Geotech. Google Scholar
  25. 25.
    McClure MW, Horne RN (2014) An investigation of stimulation mechanisms in Enhanced Geothermal Systems. Int J Rock Mech Min Sci 72:242–260CrossRefGoogle Scholar
  26. 26.
    Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer. Methods Eng 46(1):131–150CrossRefzbMATHGoogle Scholar
  27. 27.
    Mogilevskaya SG, Rothenburg L, Dusseault MB (2000) Growth of pressure-induced fractures in the vicinity of a wellbore. Int J Fract 104(4):23–30CrossRefGoogle Scholar
  28. 28.
    Nguyen VP, Lian H, Rabczuk T, Bordas S (2017) Modelling hydraulic fractures in porous media using flow cohesive interface elements. Eng Geol 225:68–82CrossRefGoogle Scholar
  29. 29.
    Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13):2316–2343CrossRefzbMATHGoogle Scholar
  30. 30.
    Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 196(29):2777–2799MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Rabczuk T, Song J-H, Belytschko T (2009) Simulations of instability in dynamic fracture by the cracking particles method. Eng Fract Mech 76(6):730–741CrossRefGoogle Scholar
  32. 32.
    Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Comput Methods Appl Mech Eng 199(37):2437–2455CrossRefzbMATHGoogle Scholar
  33. 33.
    Remmers JJC, de Borst R, Needleman A (2008) The simulation of dynamic crack propagation using the cohesive segments method. J Mech Phys Solids 56(1):70–92MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Ren H, Zhuang X, Cai Y, Rabczuk T (2016) Dual-horizon peridynamics. Int J Numer Methods Eng 108(12):1451–1476MathSciNetCrossRefGoogle Scholar
  35. 35.
    Renc H, Zhuangd X, Rabczuk T (2017) Dual-horizon peridynamics: a stable solution to varying horizons. Comput Methods Appl Mech Eng 318:762–782MathSciNetCrossRefGoogle Scholar
  36. 36.
    Sepehri J, Soliman MY, Morse SM (2015) Application of extended finite element method to simulate hydraulic fracture propagation from oriented perforations. In: Presented at the SPE hydraulic fracturing technology conferenceGoogle Scholar
  37. 37.
    Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Simulia DS (2016) Abaqus analysis user's manual. Dassault Systemes, ProvidenceGoogle Scholar
  39. 39.
    Snow DT (1969) Anisotropie permeability of fractured media. Water Resour Res 5(6):1273–1289CrossRefGoogle Scholar
  40. 40.
    Song J-H, Areias PMA, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Eng 67(6):868–893CrossRefzbMATHGoogle Scholar
  41. 41.
    Terzaghi K (1943) Theory of consolidation. In: Theoretical soil mechanics. Wiley, New York 1943, pp 265–296Google Scholar
  42. 42.
    Turon A, Camanho PP, Costa J, Dávila CG (2006) A damage model for the simulation of delamination in advanced composites under variable-mode loading. Mech Mater 38(11):1072–1089CrossRefGoogle Scholar
  43. 43.
    Vermeer PA, Verruijt A (1981) An accuracy condition for consolidation by finite elements. Int J Numer Anal Methods Geomech 5(1):1–14MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Wang T, Liu Z, Zeng Q, Gao Y, Zhuang Z (2017) XFEM modeling of hydraulic fracture in porous rocks with natural fractures. Sci China Phys Mech Astron 60(8):084612CrossRefGoogle Scholar
  45. 45.
    Weng X (1993) Fracture initiation and propagation from deviated wellbores. In: Presented at the SPE annual technical conference and exhibitionGoogle Scholar
  46. 46.
    Wu K, Olson JE (2016) Mechanisms of simultaneous hydraulic-fracture propagation from multiple perforation clusters in horizontal wells. SPE J 21(03):1000–1008CrossRefGoogle Scholar
  47. 47.
    Wu K, Olson J, Balhoff MT, Yu W (2017) Numerical analysis for promoting uniform development of simultaneous multiple-fracture propagation in horizontal wells. SPE Prod Oper 32(01):41–50Google Scholar
  48. 48.
    Yao Y (2012) Linear elastic and cohesive fracture analysis to model hydraulic fracture in brittle and ductile rocks. Rock Mech Rock Eng 45(3):375–387CrossRefGoogle Scholar
  49. 49.
    Zhang X, Jeffrey RG, Thiercelin M (2007) Deflection and propagation of fluid-driven fractures at frictional bedding interfaces: a numerical investigation. J Struct Geol 29(3):396–410CrossRefGoogle Scholar
  50. 50.
    Zhang GM, Liu H, Zhang J, Wu HA, Wang XX (2010) Three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture. J Pet Sci Eng 72(3–4):310–317CrossRefGoogle Scholar
  51. 51.
    Zhang X, Jeffrey RG, Bunger AP, Thiercelin M (2011) Initiation and growth of a hydraulic fracture from a circular wellbore. Int J Rock Mech Min Sci 48(6):984–995CrossRefGoogle Scholar
  52. 52.
    Zhang X, Jeffrey RG, Bunger AP (2011) Hydraulic fracture growth from a non-circular wellbore. In: Presented at the 45th U.S. rock mechanics/geomechanics symposiumGoogle Scholar
  53. 53.
    Zhao P, Santana CL, Feng Y, Gray KE (2017) Mitigating lost circulation: a numerical assessment of wellbore strengthening. J Pet Sci Eng 157:657–670CrossRefGoogle Scholar
  54. 54.
    Zhou X, Burbey TJ (2014) Fluid effect on hydraulic fracture propagation behavior: a comparison between water and supercritical CO2-like fluid. Geofluids 14(2):174–188CrossRefGoogle Scholar
  55. 55.
    Zhou J, Zhang L, Pan Z, Han Z (2016) Numerical investigation of fluid-driven near-borehole fracture propagation in laminated reservoir rock using PFC2D. J Nat Gas Sci Eng 36:719–733CrossRefGoogle Scholar
  56. 56.
    Zhou J, Zhang L, Braun A, Han Z (2017) Investigation of processes of interaction between hydraulic and natural fractures by PFC modeling comparing against laboratory experiments and analytical models. Energies 10(7):1001CrossRefGoogle Scholar
  57. 57.
    Zhu H, Guo J, Zhao X, Lu Q, Luo B, Feng Y-C (2014) Hydraulic fracture initiation pressure of anisotropic shale gas reservoirs. Geomech Eng 7(4):403–430CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Petroleum and Geosystems Engineering DepartmentThe University of Texas at AustinAustinUSA

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