Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 810493, 9 pages
http://dx.doi.org/10.1155/2014/810493
Research Article

Extended Finite Element Method for Predicting Productivity of Multifractured Horizontal Wells

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China

Received 24 March 2014; Accepted 25 June 2014; Published 23 July 2014

Academic Editor: Indra Vir Singh

Copyright © 2014 Youshi Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. M. Hegre and L. Larsen, “Productivity of multifractured horizontal wells,” in Proceedings of the European Petroleum Conference, pp. 393–404, London, UK, October 1994. View at Scopus
  2. B. Guo, X. Yu, and M. Khoshgahdam, “A simple analytical model for predicting productivity of multifractured horizontal wells,” SPE Reservoir Evaluation & Engineering, vol. 12, no. 6, pp. 879–885, 2009. View at Google Scholar
  3. M. Al-Kobaisi, E. Ozkan, and H. Kazemi, “A hybrid numerical-analytical model of finite-conductivity vertical fractures intercepted by a horizontal well,” in Proceedings of the SPE International Petroleum Conference, SPE 92040, Puebla Pue., Mexico, November 2004.
  4. J. Wan and K. Aziz, “Semi-analytical well model of horizontal wells with multiple hydraulic fractures,” SPE Journal, vol. 7, no. 4, pp. 437–445, 2002, SPE 81190-PA. View at Google Scholar
  5. S. Kocberber, “Finite-element black oil simulation system for heterogeneous reservoirs with horizontal wells having vertical hydraulic fractures,” in Proceedings of the 12th SPE Symposium on Reservoir Simulation, pp. 423–433, New Orleans, La, USA, February-March 1993, Paper SPE 25269. View at Scopus
  6. A. Zerzar and Y. Bettam, “Interpretation of multiple hydraulically fractured horizontal wells in closed systems,” in Proceedings of the SPE International Improved Oil Recovery Conference in Asia Pacific (IIORC '03), pp. 295–307, Alberta, Canada, October 2003. View at Scopus
  7. C. Daux, N. Moës, J. Dolbow, N. Sukumar, and T. Belytschko, “Arbitrary branched and intersecting cracks with the extended finite element method,” International Journal for Numerical Methods in Engineering, vol. 48, no. 12, pp. 1741–1760, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. J. Oswald, R. Gracie, R. Khare, and T. Belytschko, “An extended finite element method for dislocations in complex geometries: thin films and nanotubes,” Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 21–26, pp. 1872–1886, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. N. Moës, M. Cloirec, P. Cartraud, and J.-F. Remacle, “A computational approach to handle complex microstructure geometries,” Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 28–30, pp. 3163–3177, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. J. M. Melenk and I. Babu{\vS}ka, “The partition of unity finite element method: basic theory and applications,” Computer Methods in Applied Mechanics and Engineering, vol. 139, no. 1–4, pp. 289–314, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. T. Belytschko and T. Black, “Elastic crack growth in finite elements with minimal remeshing,” International Journal for Numerical Methods in Engineering, vol. 45, no. 5, pp. 601–620, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. N. Moës, J. Dolbow, and T. Belytschko, “A finite element method for crack growth without remeshing,” International Journal for Numerical Methods in Engineering, vol. 46, no. 1, pp. 131–150, 1999. View at Google Scholar
  13. N. Sukumar, N. Moës, B. Moran, and T. Belytschko, “Extended finite element method for three-dimensional crack modeling,” International Journal for Numerical Methods in Engineering, vol. 48, no. 11, pp. 1549–1570, 2000. View at Google Scholar
  14. T. Belytschko, N. Moës, S. Usui, and C. Parimi, “Arbitrary discontinuities in finite elements,” International Journal for Numerical Methods in Engineering, vol. 50, no. 4, pp. 993–1013, 2001. View at Publisher · View at Google Scholar
  15. M. Stolarska, D. L. Chopp, N. Moës, and T. Belytschko, “Modelling crack growth by level sets in the extended finite element method,” International Journal for Numerical Methods in Engineering, vol. 51, no. 8, pp. 943–960, 2001. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Fries, “A corrected XFEM approximation without problems in blending elements,” International Journal for Numerical Methods in Engineering, vol. 75, no. 5, pp. 503–532, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. N. Sukumar, D. L. Chopp, N. Moës, and T. Belytschko, “Modeling holes and inclusions by level sets in the extended finite-element method,” Computer Methods in Applied Mechanics and Engineering, vol. 190, no. 46-47, pp. 6183–6200, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. A. R. Lamb, G. J. Gorman, O. R. Gosselin, and A. Onaisi, “Finite element voupled deformation and fluid flow in fractured porous media,” in Proceedings of the SPE EUROPEC/EAGE Annual Conference and Exhibition, SPE 131725, Barcelona, Spain, June 2010.
  19. H. Huang, T. A. Long, J. Wan, and W. P. Brown, “On the use of enriched finite element method to model subsurface features in porous media flow problems,” Computational Geosciences, vol. 15, no. 4, pp. 721–736, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. T. Mohammadnejad and A. R. Khoei, “An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model,” Finite Elements in Analysis and Design, vol. 73, pp. 77–95, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  21. M. Sheng, G. Li, S. N. Shah, and X. Jin, “Extended finite element modeling of multi-scale flow in fractured shale gas reservoirs,” in Proceedings of the SPE Annual Technical Conference and Exhibition (ATCE '12), pp. 3812–3831, San Antonio, Tex, USA, October 2012. View at Scopus
  22. K. X. Yan, Advanced Fluid Mechanics, China Science and Technology Press, 2nd edition, 2010.
  23. T. Belytschko, H. Chen, J. Xu, and G. Zi, “Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment,” International Journal for Numerical Methods in Engineering, vol. 58, no. 12, pp. 1873–1905, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  24. W. X. Cheng, Finite Element Method, Tsinghua University Press, Beijing, China, 1999.
  25. H. Li, Z. Jia, and Z. Wei, “A new method to predict performance of fractured horizontal well behavior,” in Proceedings of the SPE International Conference on Horizontal Well Technology, SPE-37051-MS, Calgary, Canada, November 1996. View at Publisher · View at Google Scholar