Advertisement

Investigation of the notch angle in hydraulic fracturing using XFEM

  • Edel R. MartínezEmail author
  • Márcio Muniz de Farias
  • Francisco Evangelista Junior
Technical Paper
  • 92 Downloads

Abstract

This paper analyzes the initiation and propagation of hydraulic fracturing by nonlinear numerical modeling. A notch located at the wellbore stimulates hydraulic fracturing. The notch has a pivotal role in hydraulic fracturing. There is evidence that the notch can affect the required fluid pressure and the fracture propagation and velocity. Therefore, it has been associated with the effectiveness of hydraulic fracturing in tight gas reservoirs. The objective of this study is to explore the effect of the notch angle on hydraulic fracturing. Models in two- and three dimensions are presented and analyzed. These models are used to find the breakdown pressure and stress intensity factors, respectively. The numerical approximation of hydraulically driven fracture propagation is based on the extended finite element method (XFEM). XFEM enriches finite elements and nodes at elements intersected by the crack during the crack propagation. XFEM reproduces the discontinuity in the displacement domain without the discretization of this property directly in the mesh. Therefore, the generated mesh is independent of the crack propagation. The accuracy of the numerical approach is validated by reproducing laboratory-scale hydraulic fracturing tests and comparing results.

Keywords

Hydraulic fracturing Notch angle Extended finite element method Breakdown pressure High-performance computing 

Notes

Acknowledgements

The authors are grateful to the Brazilian National Research Council (CNPq) for the supporting funds for this research. The authors also thank the Graduate Program in Geotechnical Engineering at the University of Brasilia.

References

  1. 1.
    Lin M, Chen S, Mbia E, Chen Z (2018) Application of reservoir flow simulation integrated with geomechanics in unconventional tight play. Rock Mech Rock Eng 5(1):315–328CrossRefGoogle Scholar
  2. 2.
    Zuo JP, Yao MH, Zhao SK, Jiang YQ (2019) Investigation on fracture toughness and micro-deformation field of SCB sandstone including different inclination angles cracks. Eng Fract Mech 208:27–37CrossRefGoogle Scholar
  3. 3.
    Carter BJ, Desroches J, Ingraffea AR, Wawrzynek PA (2000) Simulating fully 3D hydraulic fracturing. Modell Geomech 200:526–556Google Scholar
  4. 4.
    Zhao X (2010) Imaging the mechanics of hydraulic fracturing in naturally-fractured reservoirs using induced seismicity and numerical modeling. Ph.D. thesis, University of TorontoGoogle Scholar
  5. 5.
    Khristianovic SA, Zheltov YP (1955) Formation of vertical fractures by means of highly viscous liquid. In: Proceeding of the 4th world petroleum congress, vol 5, pp 579–586Google Scholar
  6. 6.
    Berchenko I, Detournay E, Chandler N (1997) Propagation of natural hydraulic fractures. Int J Rock Mech Min Sci 34(3):1–11Google Scholar
  7. 7.
    Economides JM, Nolte GK (2000) Reservoir stimulation. Wiley, ChichesterGoogle Scholar
  8. 8.
    Boone TJ, Detournay E (1990) Response of a vertical hydraulic fracture intersecting a poroelastic formation bounded by semi-infinite impermeable elastic layers. Int J Rock Mech Min Sci 27(3):189–197CrossRefGoogle Scholar
  9. 9.
    Devloo PRB, Fernandes PD, Gomes SM, Bravo CA, Damasa RG (2006) A finite element model for three dimensional hydraulic fracturing. Math Comput Simulat 73:142–155MathSciNetCrossRefGoogle Scholar
  10. 10.
    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 72:310–317CrossRefGoogle Scholar
  11. 11.
    Carrier B, Granet S (2012) Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng Fract Mech 79:312–328CrossRefGoogle Scholar
  12. 12.
    Li LC, Tang CA, Li G, Wang SG, Liang ZZ, Zhang YB (2012) Numerical simulation of 3D hydraulic fracturing based on an improved flow-stress-damage model and a parallel FEM technique. Rock Mech Rock Eng 45:801–818Google Scholar
  13. 13.
    Guangming Z, Chunming X, Jiandong L, Juan J, Luhe S (2011) Finite element analysis method for horizontal well hydraulic fracturing. SREE Conf Eng Model Simul 12:1–8Google Scholar
  14. 14.
    Wangen M (2011) Finite element modeling of hydraulic fracturing on a reservoir scale in 2D. J Pet Sci Eng 77:274–285CrossRefGoogle Scholar
  15. 15.
    Wangen M (2013) Finite element modeling of hydraulic fracturing in 3D. Comput Geosci 17:647–659MathSciNetCrossRefGoogle Scholar
  16. 16.
    Deng JQ, Lin C, Yang Q, Liu YR, Tao ZF, Duan HF (2016) Investigation of directional hydraulic fracturing based on true tri-axial experiment and finite element modeling. Comput Geotech 75:28–47CrossRefGoogle Scholar
  17. 17.
    Dehghan AN, Goshtasbi K, Ahangaru K, Jin Y (2017) 3D numerical modeling of the propagation of hydraulic fracture at its intersection with natural (pre-existing) fracture. Rock Mech Rock Eng 50(2):367–386CrossRefGoogle Scholar
  18. 18.
    Papanastasiou PC (1997) A coupled elastoplastic hydraulic fracturing model. Int J Rock Mech Min Sci 34(3–4):1–15Google Scholar
  19. 19.
    Boone TJ, Ingraffea AR (1990) A numerical procedure for simulation of hydraulically-driven fracture propagation in poroelastic media. Int J Numer Anal Met 14(1):27–47CrossRefGoogle Scholar
  20. 20.
    Desroches J, Detournay E, Lenoach B, Papanastasiou P, Pearson JRA, Thierchlin M, Cheng A (1994) The crack tip region in hydraulic fracturing. Proc R Soc Lond 447:39–48CrossRefGoogle Scholar
  21. 21.
    Al-Busaidi A, Hazzard JF, Young RP (2005) Distinct element modeling of hydraulically fractured Lac du Bonnet granite. J Geophys Res 110:1–14CrossRefGoogle Scholar
  22. 22.
    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):712–727CrossRefGoogle Scholar
  23. 23.
    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. J Coal Geol 121:1–13CrossRefGoogle Scholar
  24. 24.
    Oliveira TAA, Gomes G, Evangelista F Jr (2019) Multiscale aircraft fuselage fatigue analysis by the dual boundary element method. Eng Anal Bound Elem 104:107–119MathSciNetCrossRefGoogle Scholar
  25. 25.
    Lecampion B (2009) An extended finite element method for hydraulic fracture problems. Commun Numer Methods Eng 25:121–133MathSciNetCrossRefGoogle Scholar
  26. 26.
    Gordeliy E, Peirce A (2013) Coupling schemes for modeling hydraulic fracture propagation using the XFEM. Comput Method Appl Mech Eng 253:305–322MathSciNetCrossRefGoogle Scholar
  27. 27.
    Gordeliy E, Peirce A (2013) Implicit level set schemes for modeling hydraulic fractures using the XFEM. Comput Method Appl Mech Eng 266:125–143MathSciNetCrossRefGoogle Scholar
  28. 28.
    Mohammadnejad T, Khoei AR (2013) Hydro-mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method. Int J Numer Anal Met Geomech 37:1247–1279CrossRefGoogle Scholar
  29. 29.
    Mohammadnejad T, Khoei AR (2013) An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model. Finite Elem Anal Des 73:77–95MathSciNetCrossRefGoogle Scholar
  30. 30.
    Chen Z (2013) Implementation of the XFEM for hydraulic fracture problems. In: 13th international conference on fracture, Beijing, CSIRO, pp 1–10Google Scholar
  31. 31.
    Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45:601–620CrossRefGoogle Scholar
  32. 32.
    Moës N, Dolbow J, Belytschko T (1999) A Finite Element Method for crack growth without remeshing. Int J Numer Meth Eng 46:131–150MathSciNetCrossRefGoogle Scholar
  33. 33.
    Evangelista JRF, Roesler JR, Duarte CA (2012) Prediction of potential cracking failure modes in three-dimensional airfield rigid pavements with existing cracks and flaws. Transp Res Record 2266:11–19CrossRefGoogle Scholar
  34. 34.
    Evangelista JRF, Roesler JR, Duarte CA (2013) Two-scale approach to predict multi-site cracking potential in 3-D structures using the generalized finite element method. Int J Solids Struct 50:1991–2002CrossRefGoogle Scholar
  35. 35.
    Gupta P, Duarte CA (2018) Coupled hydromechanical-fracture simulations of nonplanar three-dimensional hydraulic fracture propagation. Int J Numer Anal Methods Geomech 42(1):143–180CrossRefGoogle Scholar
  36. 36.
    Shauer N, Duarte CA (2019) Improved algorithms for Generalized Finite Element simulations of three-dimensional hydraulic fracture propagation. Int J Numer Anal Meth Geomech.  https://doi.org/10.1002/nag.2977 CrossRefGoogle Scholar
  37. 37.
    Sukumar N, Moës N, Moran B, Belytschko T (2000) Extended finite element method for three-dimensional crack modelling. Int J Numer Methods Eng 48:1549–1570CrossRefGoogle Scholar
  38. 38.
    Stolarska M, Chopp DL, Moës N, Beltyschko T (2001) Modelling crack growth by level sets. Int J Numer Methods Eng 51(8):943–960CrossRefGoogle Scholar
  39. 39.
    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 48:573–584CrossRefGoogle Scholar
  40. 40.
    Fjær E, Holt RM, Horsrud P, Raan AM, Risnes R (2008) Petroleum related rock mechanics. Elsevier, AmsterdamGoogle Scholar
  41. 41.
    Systèmes D (2014) ABAQUS 6.14 Online Documentation. Providence, USAGoogle Scholar
  42. 42.
    Chen Y, Meng Q, Zhang J (2018) Effects of the notch angle, notch length and injection rate on hydraulic fracturing under true triaxial stress: an experimental study. Water 10(6):1–11Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of BrasiliaBrasiliaBrazil

Personalised recommendations