1887

Abstract

Summary

Fracture propagation (FP) occurs in various applications including hydraulic fracturing, underground disposal of liquid waste, in-situ stress estimation, and the failure of dams due to underwater cracks. This work develops a numerical model of the hydraulic fracturing process that is widely applied to the extraction of natural gas from shale. Tensile fractures are created due to the injection of the highly pressurized viscous fluid into the brittle and quasi-brittle rock materials.

One issue associated with the modeling of the FP using unstructured fitted meshes is the necessity to remesh each time fractures move forward. The developed XFEM-EDFM scheme allows fractures to propagate without any need for remeshing. The fully coupled and fully implicit schemes ensure the stability of the current method. The J integral is applied to extract the stress intensity factors (SIF) of the mode I and II in the 2D domain. The criterion of the FP is based on the comparison of the SIF to the fracture toughness.

We investigate the fracture propagation algorithm. The hydraulic fracture propagation is also presented to demonstrate the computational capability.

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/content/papers/10.3997/2214-4609.201802263
2018-09-03
2020-07-14
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References

  1. Biot, M. and Willis, D.
    [1957] The elastic coefficients of the theory of consolidation.J. appl. Mech, 24, 594–601.
    [Google Scholar]
  2. Carrier, B. and Granet, S.
    [2012] Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model.Engineering fracture mechanics, 79, 312–328.
    [Google Scholar]
  3. Dean, R.H., Gai, X., Stone, C.M., Minkoff, S.E. et al.
    [2006] A comparison of techniques for coupling porous flow and geomechanics.Spe Journal, 11(01), 132–140.
    [Google Scholar]
  4. Fu, P., Johnson, S.M. and Carrigan, C.R.
    [2013] An explicitly coupled hydro-geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks.International Journal for Numerical and Analytical Methods in Geomechanics, 37(14), 2278–2300.
    [Google Scholar]
  5. Geertsma, J., De Klerk, F. et al.
    [1969] A rapid method of predicting width and extent of hydraulically induced fractures.Journal of Petroleum Technology, 21(12), 1–571.
    [Google Scholar]
  6. Gordeliy, E. and Peirce, A.
    [2013a] Coupling schemes for modeling hydraulic fracture propagation using the XFEM.Computer Methods in Applied Mechanics and Engineering, 253, 305–322.
    [Google Scholar]
  7. [2013b] Implicit level set schemes for modeling hydraulic fractures using the XFEM.Computer Methods in Applied Mechanics and Engineering, 266, 125–143.
    [Google Scholar]
  8. Gupta, P. and Duarte, C.
    [2018] Coupled hydromechanical-fracture simulations of nonplanar three-dimensional hydraulic fracture propagation.International Journal for Numerical and Analytical Methods in Geomechanics, 42(1), 143–180.
    [Google Scholar]
  9. Heister, T., Wheeler, M.F. and Wick, T.
    [2015] A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach.Computer Methods in Applied Mechanics and Engineering, 290, 466–495.
    [Google Scholar]
  10. Howard, G.C., Fast, C. et al.
    [1957] Optimum fluid characteristics for fracture extension. In: Drilling and Production Practice.American Petroleum Institute.
    [Google Scholar]
  11. Hunsweck, M.J., Shen, Y. and Lew, A.J.
    [2013] A finite element approach to the simulation of hydraulic fractures with lag.International Journal for Numerical and Analytical Methods in Geomechanics, 37(9), 9930–1015.
    [Google Scholar]
  12. Jiang, J., Younis, R.M. et al.
    [2016] Hybrid coupled discrete-fracture/matrix and multicontinuum models for unconventional-reservoir simulation.SPE Journal, 21(03), 1–009.
    [Google Scholar]
  13. Khristianovic, S. and Zheltov, Y.
    [1955] Formation of vertical fractures by means of highly viscous fluids. In: Proc. 4th world petroleum congress, Rome, 2. 579–586.
    [Google Scholar]
  14. Lee, S., Wheeler, M.F. and Wick, T.
    [2016] Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model.Computer Methods in Applied Mechanics and Engineering, 305, 111–132.
    [Google Scholar]
  15. Li, L., Lee, S.H. et al.
    [2008] Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media.SPE Reservoir Evaluation & Engineering, 11(04), 750–758.
    [Google Scholar]
  16. Melenk, J.M. and Babuška, I.
    [1996] The partition of unity finite element method: basic theory and applications.Computer methods in applied mechanics and engineering, 139(1–4), 289–314.
    [Google Scholar]
  17. Miehe, C., Welschinger, F. and Hofacker, M.
    [2010] Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations.International Journal for Numerical Methods in Engineering, 83(10), 1273–1311.
    [Google Scholar]
  18. Moës, N., Dolbow, J. and Belytschko, T.
    [1999] A finite element method for crack growth without remeshing.International journal for numerical methods in engineering, 46(1), 131–150.
    [Google Scholar]
  19. Mohammadnejad, T. and Khoei, A.
    [2013] An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model.Finite Elements in Analysis and Design, 73, 77–95.
    [Google Scholar]
  20. Moinfar, A., Varavei, A., Sepehrnoori, K., Johns, R.T. et al.
    [2014] Development of an Efficient Embedded Discrete Fracture Model for 3D Compositional Reservoir Simulation in Fractured Reservoirs.SPE Journal, 19(02), 289–303.
    [Google Scholar]
  21. Nordgren, R. et al.
    [1972] Propagation of a vertical hydraulic fracture.Society of Petroleum Engineers Journal, 12(04), 306–314.
    [Google Scholar]
  22. Peirce, A. and Detournay, E.
    [2008] An implicit level set method for modeling hydraulically driven fractures.Computer Methods in Applied Mechanics and Engineering, 197(33-40), 2858–2885.
    [Google Scholar]
  23. Perkins, T., Kern, L. et al.
    [1961] Widths of hydraulic fractures.Journal of Petroleum Technology, 13(09), 937–949.
    [Google Scholar]
  24. Ren, G., Jiang, J. and Younis, R.M.
    [2018] A Model for Coupled Geomechanics and Multiphase Flow in Fractured Porous Media Using Embedded Meshes.submitted to Advances in Water Resources.
    [Google Scholar]
  25. Salimzadeh, S. and Khalili, N.
    [2015] A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation.Computers and Geotechnics, 69, 82–92.
    [Google Scholar]
  26. Settgast, R.R., Fu, P., Walsh, S.D., White, J.A., Annavarapu, C. and Ryerson, F.J.
    [2017] A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions.International Journal for Numerical and Analytical Methods in Geomechanics, 41(5), 627–653.
    [Google Scholar]
  27. The CGAL Project
    [2018] CGAL User and Reference Manual.CGAL Editorial Board, 4.12 edn.
    [Google Scholar]
  28. Wu, K., Olson, J.E. et al.
    [2016] Mechanisms of simultaneous hydraulic-fracture propagation from multiple perforation clusters in horizontal wells.SPE Journal, 21(03), 1–000.
    [Google Scholar]
  29. Yamamoto, K., Shimamoto, T. and Sukemura, S.
    [2004] Multiple fracture propagation model for a three-dimensional hydraulic fracturing simulator.International Journal of Geomechanics, 4(1), 46–57.
    [Google Scholar]
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