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Acta Mechanica Solida Sinica

, Volume 22, Issue 5, pp 443–452 | Cite as

Cohesive Zone Finite Element-Based Modeling of Hydraulic Fractures

  • Zuorong Chen
  • A. P. Bunger
  • Xi Zhang
  • Robert G. Jeffrey
Article

Abstract

Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.

Key words

hydraulic fracture cohesive zone model finite element method 

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References

  1. [1]
    Jeffrey, R.G., Settari, A., Mills, K.W., Zhang, X., and Detournay, E., Hydraulic fracturing to induce caving: fracture model development and comparison to field data. Rock Mechanics in the National Interest, 2001, 1–2: 251–259.Google Scholar
  2. [2]
    van As, A. and Jeffrey, R.G., Hydraulic fracturing as a cave inducement technique at Northparkes mines. In: Proceedings of MASSMIN 2000, 2000, 165–172.Google Scholar
  3. [3]
    Sun, R.J., Theoretical size of hydraulically induced horizontal fractures and corresponding surface uplift in an idealized medium. Journal of Geophysical Research, 1969, 74(25): 5995–6011.CrossRefGoogle Scholar
  4. [4]
    Spence, D.A. and Turcotte, D.L., Magma-driven propagation of cracks. Journal of Geophysical Research-Solid Earth and Planets, 1985, 90(NB1): 575–580.CrossRefGoogle Scholar
  5. [5]
    Lister, J.R. and Kerr, R.C., Fluid-mechanical models of crack-propagation and their application to magma transport in dykes. Journal of Geophysical Research-Solid Earth and Planets, 1991, 96(B6): 10049–10077.CrossRefGoogle Scholar
  6. [6]
    Rubin, A.M., Propagation of magma-filled cracks. Annual Review of Earth and Planetary Sciences, 1995, 23: 287–336.CrossRefGoogle Scholar
  7. [7]
    Adachi, A., Siebrits, E., Peirce, A., and Desroches, J., Computer simulation of hydraulic fractures. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(5): 739–757.CrossRefGoogle Scholar
  8. [8]
    Bunger, A.P., Detournay, E., and Garagash, D.I., Toughness-dominated hydraulic fracture with leak-off. International Journal of Fracture, 2005, 134(2): 175–190.CrossRefGoogle Scholar
  9. [9]
    Bunger, A.P. and Detournay, E., Experimental validation of the tip asymptotics for a fluid-driven crack. Journal of the Mechanics and Physics of Solids, 2008, 56(11): 3101–3115.CrossRefGoogle Scholar
  10. [10]
    Clifton, R.J., Three-Dimensional Fracture-Propagation Model. In: Recent Advances in Hydraulic Fracturing — SPE Monograph, 1989, 95–108.Google Scholar
  11. [11]
    Detournay, E., Propagation regimes of fluid-driven fractures in impermeable rocks. International Journal of Geomechanics, 2004, 4(1): 35–45.CrossRefGoogle Scholar
  12. [12]
    Khristianovic, S.A. and Zheltov, Y.P., Formation of vertical fractures by means of highly viscous liquid. In: Proceedings of the Fourth World Petroleum Congress. Rome, 1955, 579–586.Google Scholar
  13. [13]
    Perkins, T.K. and Kern, L.R., Widths of hydraulic fractures. Transactions of the Society of Petroleum Engineers of AIME, 1961, 222(9): 937–949.Google Scholar
  14. [14]
    Geertsma, J. and Klerk, F.D., A rapid method of predicting width and extent of hydraulically induced fractures. Journal of Petroleum Technology, 1969, 21: 1571–1581.CrossRefGoogle Scholar
  15. [15]
    Abe, H., Mura, T., and Keer, L.M., Growth-rate of a penny-shaped crack in hydraulic fracturing of rocks. Journal of Geophysical Research, 1976, 81(29): 5335–5340.CrossRefGoogle Scholar
  16. [16]
    Lecamplon, B. and Detournay, E., An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag. Computer Methods in Applied Mechanics and Engineering, 2007, 196: 4863–4880.MathSciNetCrossRefGoogle Scholar
  17. [17]
    Zhang, X., Detournay, E. and Jeffrey, R., Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space. International Journal of Fracture, 2002, 115(2): 125–158.CrossRefGoogle Scholar
  18. [18]
    Zhang, X., Jeffrey, R.G. and Thiercelin, M., Deflection and propagation of fluid-driven fractures at frictional bedding interfaces: A numerical investigation. Journal of Structural Geology, 2007, 29(3): 396–410.CrossRefGoogle Scholar
  19. [19]
    Zhang, X. and Jeffrey, R.G., The role of friction and secondary flaws on deflection and re-initiation of hydraulic fractures at orthogonal pre-existing fractures. Geophysical Journal International, 2006, 166(3): 1454–1465.CrossRefGoogle Scholar
  20. [20]
    Lecampion, B., An extended finite element method for hydraulic fracture problems. Communications in Numerical Methods in Engineering, 2009, 25(2): 121–133.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Zhao, C.B., Hobbs, B.E., Ord, A. and Peng, S.L., Particle simulation of spontaneous crack generation associated with the laccolithic type of magma intrusion processes. International Journal for Numerical Methods in Engineering, 2008, 75(10): 1172–1193.CrossRefGoogle Scholar
  22. [22]
    Peirce, A. and Detournay, E., An implicit level set method for modeling hydraulically driven fractures. Computer Methods in Applied Mechanics and Engineering, 2008, 197(33–40): 2858–2885.CrossRefGoogle Scholar
  23. [23]
    Barenblatt, G.I., The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics, 1962(7): 55–129.Google Scholar
  24. [24]
    Dugdale, D.S., Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 1960, 8(2): 100–104.CrossRefGoogle Scholar
  25. [25]
    Shet, C. and Chandra, N., Analysis of energy balance when using cohesive zone models to simulate fracture processes. Journal of Engineering Materials and Technology-Transactions of the ASME, 2002, 124(4): 440–450.CrossRefGoogle Scholar
  26. [26]
    Tomar, V., Zhai, J., and Zhou, M., Bounds for element size in a variable stiffness cohesive finite element model. International Journal for Numerical Methods in Engineering, 2004, 61(11): 1894–1920.CrossRefGoogle Scholar
  27. [27]
    Batchelor, G.K., An Introduction to Fluid Dynamics. London: Cambridge University Press, 1967.zbMATHGoogle Scholar
  28. [28]
    ABAQUS Documentation, Version 6.7–1, 2007.Google Scholar
  29. [29]
    Rice, J.R., The mechanics of earthquake rupture. In: Physics of the Earth’s Interior. Amsterdam: North-Holland Publishing Company, 1980.Google Scholar
  30. [30]
    Savitski, A.A. and Detournay, E., Propagation of a penny-shaped fluid-driven fracture in an impermeable rock: asymptotic solutions. International Journal of Solids and Structures, 2002, 39(26): 6311–6337.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2009

Authors and Affiliations

  • Zuorong Chen
    • 1
  • A. P. Bunger
    • 1
  • Xi Zhang
    • 1
  • Robert G. Jeffrey
    • 1
  1. 1.CSIRO Petroleum ResourcesClaytonAustralia

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