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Mathematical Problems in Engineering
Volume 2014, Article ID 485028, 14 pages
http://dx.doi.org/10.1155/2014/485028
Research Article

A New Mathematical Model for Pressure Transient Analysis in Stress-Sensitive Reservoirs

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Xindu Avenue No. 8, Xindu District, Chengdu City, Sichuan 610500, China

Received 16 December 2013; Accepted 10 April 2014; Published 29 April 2014

Academic Editor: Oluwole Daniel Makinde

Copyright © 2014 Junjie Ren and Ping Guo. 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. H.-X. Wang, G. Wang, Z.-X. J. Chen, and R. C. K. Wong, “Deformational characteristics of rock in low permeable reservoir and their effect on permeability,” Journal of Petroleum Science and Engineering, vol. 75, no. 1-2, pp. 240–243, 2010. View at Publisher · View at Google Scholar · View at Scopus
  2. N. H. Kilmer, N. R. Morrow, and J. K. Pitman, “Pressure sensitivity of low permeability sandstones,” Journal of Petroleum Science and Engineering, vol. 1, no. 1, pp. 65–81, 1987. View at Google Scholar · View at Scopus
  3. P. M. T. M. Schutjens, T. H. Hanssen, M. H. H. Hettema et al., “Compaction-induced porosity/permeability reduction in sandstone reservoirs: data and model for elasticity-dominated deformation,” SPE Reservoir Evaluation & Engineering, vol. 7, no. 3, pp. 202–216, 2004. View at Google Scholar · View at Scopus
  4. S. A. Sonnenberg and A. Pramudito, “Petroleum geology of the giant Elm Coulee field, Williston Basin,” AAPG Bulletin, vol. 93, no. 9, pp. 1127–1153, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Ma, S. Zhang, T. Guo, G. Zhu, X. Cai, and M. Li, “Petroleum geology of the Puguang sour gas field in the Sichuan Basin, SW China,” Marine and Petroleum Geology, vol. 25, no. 4-5, pp. 357–370, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. F. Cappa, Y. Guglielmi, P. Fénart, V. Merrien-Soukatchoff, and A. Thoraval, “Hydromechanical interactions in a fractured carbonate reservoir inferred from hydraulic and mechanical measurements,” International Journal of Rock Mechanics and Mining Sciences, vol. 42, no. 2, pp. 287–306, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Vairogs, C. L. Hearn, D. Dareing, and V. W. Rhoades, “Effect of rock stress on gas production from low- permeability reservoirs,” Journal of Petroleum Technology, vol. 23, pp. 1161–1167, 1971. View at Google Scholar · View at Scopus
  8. X. J. Xiao, H. Sun, Y. Han, and J. Yang, “Dynamic characteristic evaluation methods of stress sensitive abnormal high pressure gas reservoir,” in Proceedings of the SPE Annual Technical Conference and Exhibition (ATCE '09), pp. 2045–2057, New Orleans, La, USA, October 2009. View at Scopus
  9. I. Fatt and D. H. Davis, “Reduction in permeability with overburden pressure,” Transactions of AIME, vol. 195, p. 329, 1952. View at Google Scholar
  10. R. A. Farquhar, B. G. D. Smart, A. C. Todd, D. E. Tompkins, and A. J. Tweedie, “Stress sensitivity of low petroleum sandstones from the rotliegendes sandstone,” in Proceedings of the 68th SPE Annual Technical Conference and Exhibition, pp. 851–861, Houston, Tex, USA, October 1993. View at Scopus
  11. Z. Zeng, R. Grigg, and D. B. Gupta, “Laboratory investigation of stress- sensitivity of non-Darcy gas flow parameters,” in Proceedings of the SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Okla, USA, April 2004. View at Scopus
  12. S. L. Yang, X. Q. Wang, J. L. Feng, and Y. X. Su, “Test and study of the rock pressure sensitivity for KeLa-2 gas reservoir in the Tarim basin,” Petroleum Science, vol. 1, no. 4, pp. 11–16, 2004. View at Google Scholar
  13. H. H. Abass, A. M. Tahini, Y. N. Abousleiman, and M. Khan, “New technique to determine Biot coefficient for stress sensitive dual porosity reservoirs,” in SPE Annual Technical Conference and Exhibition (ATCE '09), pp. 2292–2301, New Orleans, La, USA, October 2009. View at Scopus
  14. R. Raghavan, J. D. T. Scorer, and F. G. Miller, “An investigation by numerical methods of the effect of pressure-dependent rock and fluid properties on well flow tests,” SPE Journal, vol. 12, no. 3, pp. 267–275, 1972. View at Google Scholar
  15. V. F. Samaniego, W. E. Brigham, and F. G. Miller, “An investigation of transient flow of reservoir fluids considering pressure-dependent rock and fluid properties,” SPE Journal, vol. 17, no. 2, pp. 140–150, 1977. View at Google Scholar · View at Scopus
  16. V. F. Samaniego and H. Cinco-Ley, “On the determination of the pressure-dependent characteristics of a reservoir through transient pressure testing,” in Proceedings of the SPE Annual Technical Conference and Exhibition, pp. 20–19774, San Antonio, Tex, USA, October 1989. View at Scopus
  17. O. A. Pedrosa, “Pressure transient response in stress-sensitive formations,” in Proceedings of the SPE California Regional Meeting, Oakland, Calif, USA.
  18. J. Kikani and O. A. Pedrosa Jr., “Perturbation analysis of stress-sensitive reservoirs,” SPE Formation Evaluation, vol. 6, no. 3, pp. 379–386, 1991. View at Google Scholar · View at Scopus
  19. M. Y. Zhang and A. K. Ambastha, “New insights in pressure-transient analysis for stress-sensitive reservoirs,” in Proceedings of the SPE Annual Technical Conference and Exhibition, pp. 617–628, New Orleans, La, USA, September 1994. View at Scopus
  20. A. K. Ambastha and M. Y. Zhang, “Iterative and numerical solutions for pressure-transient analysis of stress-sensitive reservoirs and aquifers,” Computers & Geosciences, vol. 22, no. 6, pp. 601–606, 1996. View at Publisher · View at Google Scholar · View at Scopus
  21. T. A. Jelmert and H. Selseng, “Pressure transient behavior of stress-sensitive reservoirs,” in Proceedings of the Latin American and Caribbean Petroleum Engineering Conference, Rio de Janeiro, Brazil, 1997.
  22. Y.-S. Wu and K. Pruess, “Integral solutions for transient fluid flow through a porous medium with pressure-dependent permeability,” International Journal of Rock Mechanics and Mining Sciences, vol. 37, no. 1-2, pp. 51–61, 2000. View at Google Scholar · View at Scopus
  23. Y. G. Zhang and D. K. Tong, “The pressure transient analysis of deformation of fractal medium,” Journal of Hydrodynamics B, vol. 20, no. 3, pp. 306–313, 2008. View at Publisher · View at Google Scholar
  24. S. L. Marshall, “Nonlinear pressure diffusion in flow of compressible liquids through porous media,” Transport in Porous Media, vol. 77, no. 3, pp. 431–446, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. T. Friedel and H. D. Voigt, “Analytical solutions for the radial flow equation with constant-rate and constant-pressure boundary conditions in reservoirs with pressure-sensitive permeability,” in Proceedings of the SPE Rocky Mountain Petroleum Technology Conference, pp. 95–113, Denver, Colo, USA, 2009.
  26. L. Zhang, J. Guo, and Q. Liu, “A well test model for stress-sensitive and heterogeneous reservoirs with non-uniform thicknesses,” Petroleum Science, vol. 7, no. 4, pp. 524–529, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. L.-H. Zhang, J.-J. Guo, and Q.-G. Liu, “A new well test model for stress-sensitive and radially heterogeneous dual-porosity reservoirs with non-uniform thicknesses,” Journal of Hydrodynamics B, vol. 23, no. 6, pp. 759–766, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. F. Qanbari and C. R. Clarkson, “Rate transient analysis of stress-sensitive formations during transient linear flow period,” in Proceedings of the SPE Canadian Unconventional Resources Conference, Calgary, Canada, 2012.
  29. S. Ai and Y. D. Yao, “Flow model for well test analysis of low-permeability and stress-sensitive reservoirs,” Special Topics and Reviews in Porous Media, vol. 3, no. 2, pp. 125–138, 2012. View at Publisher · View at Google Scholar · View at Scopus
  30. X. Y. Yi, Z. Zhang, C. Y. Li, D. C. Li, and S. B. Wang, “Well test interpretation method of horizontal well in stress-sensitive gas reservoir,” Applied Mechanics and Materials, vol. 295, pp. 3183–3191, 2013. View at Google Scholar
  31. R. L. Luo, A study of deformation and percolation mechanisms of deep gas reservoir and its application [Ph.D. thesis], China University of Petroleum, Beijing, China, 2006.
  32. R.-L. Luo, L.-S. Cheng, J.-C. Peng, and H.-Y. Zhu, “New method of determining relationship between permeability and effective overburden pressure for low-permeability reservoirs,” Journal of China University of Petroleum, vol. 31, no. 2, pp. 87–90, 2007. View at Google Scholar · View at Scopus
  33. R. L. Luo and J. D. Feng, “Deformation characteristics of low permeability rocks under confining pressure,” in Proceedings of the International Forum on Porous Flow and Applications, Wuhan, China, 2009.
  34. N. Zisser and G. Nover, “Anisotropy of permeability and complex resistivity of tight sandstones subjected to hydrostatic pressure,” Journal of Applied Geophysics, vol. 68, no. 3, pp. 356–370, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. X. W. Wang, Study on micro pore structure and seepage flow in ultra-low permeability of Daqing oilfield [Ph.D. thesis], Chinese Academy of Sciences, Beijing, China, 2010.
  36. G. Xiao, M. Jingjing, C. Yiwei, and L. Weixin, “An integration approach for evaluating well deliverability in ultra deep sands,” in Proceedings of the SPE Production and Operations Conference and Exhibition, pp. 177–198, Tunis, Tunisia, June 2010. View at Scopus
  37. J. F. Evers and E. Soeiinah, “Transient tests and long-range performance predictions in stress-sensitive gas reservoirs,” Journal of Petroleum Technology, vol. 29, no. 8, pp. 1025–1030, 1977. View at Google Scholar · View at Scopus
  38. A. F. van Everdingen and W. Hurst, “The application of the Laplace transformation to flow problems in reservoirs,” Journal of Petroleum Technology, vol. 1, no. 12, pp. 305–324, 1949. View at Google Scholar
  39. A. K. Ambastha and H. J. Ramey Jr., “Well-test analysis for a well in a finite, circular reservoir,” Journal of Canadian Petroleum Technology, vol. 32, no. 6, pp. 34–38, 1993. View at Google Scholar
  40. C. Chakrabarty, S. M. F. Ali, and W. S. Tortike, “Analytical solutions for radial pressure distribution including the effects of the quadratic-gradient term,” Water Resources Research, vol. 29, no. 4, pp. 1171–1177, 1993. View at Publisher · View at Google Scholar · View at Scopus
  41. S. Braeuning, T. A. Jelmert, and S. A. Vik, “The effect of the quadratic gradient term on variable-rate well-tests,” Journal of Petroleum Science and Engineering, vol. 21, no. 3-4, pp. 203–222, 1998. View at Publisher · View at Google Scholar · View at Scopus
  42. X. L. Cao, D. K. Tong, and R. H. Wang, “Exact solutions for nonlinear transient flow model including a quadratic gradient term,” Applied Mathematics and Mechanics, vol. 25, no. 1, pp. 102–109, 2004. View at Publisher · View at Google Scholar
  43. H. Eslami, F. Mozaffari, J. Moghadasi, and F. Müller-Plathe, “Molecular dynamics simulation of confined fluids in isosurface-isothermal- isobaric ensemble,” The Journal of Chemical Physics, vol. 129, no. 19, Article ID 194702, 2008. View at Publisher · View at Google Scholar · View at Scopus
  44. H. Eslami and F. Müller-Plathe, “Molecular dynamics simulation of water influence on local structure of nanoconfined polyamide-6,6,” The Journal of Physical Chemistry B, vol. 115, no. 32, pp. 9720–9731, 2011. View at Publisher · View at Google Scholar · View at Scopus
  45. N. Mehdipour, N. Mousavian, and H. Eslami, “Molecular dynamics simulation of the diffusion of nanoconfined fluids,” Journal of the Iranian Chemical Society, vol. 11, no. 1, pp. 47–52, 2014. View at Publisher · View at Google Scholar
  46. H. Stehfest, “Numerical inversion of Laplace transforms,” Communications of the ACM, vol. 13, no. 1, pp. 47–49, 1970. View at Publisher · View at Google Scholar
  47. J. H. Mathews and K. D. Fink, Numerical Methods Using MATLAB, Prentice Hall, Upper Saddle River, NJ, USA, 1999.