Stability of boreholes in a geologic medium including the effects of anisotropy

  • Dinesh Gupta
  • Musharraf Zaman
Article

Abstract

An analytical formulation is developed to investigate the stability of a deep, inclined borehole drilled in a geologic medium and subjected to an internal pressure and a non-hydrostatic stress field. The formulation consists of a three-dimensional (3-D) analysis of stresses around a borehole, combined with internal pressurization of the borehole to obtain an approximate solution of the overall stress distribution. The orientation of the borehole, the in-situ stresses and bedding plane can all be arbitrarily related to each other to represent the actual field situations. Both tensile failure and shear failure potentials of a borehole are investigated. The failure criteria applied assume that when the least principal stress exceeds the strength of the formation in tension, a tensile failure occurs. Shear failure is represented using the modified Drucker-Prager failure criterion for anisotropic materials. A parametric study is carried out to assess the effect of material anisotropy, bedding plane inclination and in-situ stress conditions on borehole stability. Results of the parametric study indicate that wellbore stability is significantly influenced by a high borehole inclination, high degree of material anisotropy, in-situ stress conditions and high formation bedding plane inclination.

The stability of a borehole in an elasto-plastic medium is also investigated. In order to evaluate the extent of the plastic zone around a borehole and the effect of anisotropy of the material on this plastic zone, a mathematical formulation is developed using theories of elasticity and plasticity. The borehole is assumed to be vertical, subjected to hydrostatic stresses, and drilled in a transversely isotropic geologic medium. A parametric study is carried out to investigate the effect of material anisotropy on the plastic behavior of the geologic medium. Results indicate that the stress distribution around a borehole, the extent of the plastic zone, and the failure pressure are influenced by the degree of material anisotropy and value of in-situ overburden stresses. It was observed that the borehole becomes less stable as the degree of anisotropy of the geologic medium increases.

Key words

stability of borehole tensile failure shear failure failure criteria stress distribution 

CLC number

TB122 TE21 

References

  1. [1]
    Aadnoy B S. Continuum mechanics analysis of the stability of boreholes in anisotropic rock formations[D]. Ph D Thesis. Norway: Norwegian Institute of Technology, University of Trondheim, 1987.Google Scholar
  2. [2]
    Ong S H. Borehole stability [D]. Ph D Dissertation. Norman OK: University of Oklahoma, 1994.Google Scholar
  3. [3]
    Lekhnitskii S G.Theory of Elasticity of an Anisotropic Body [M]. Moscow: Mir Publishers, 1981.Google Scholar
  4. [4]
    Amader B. Rock anisotropy and theory of stress measurements[A]. In: Brebbia, Orszag Eds.Lecture Notes in Engineering[C]. Springer Verlag, 1983.Google Scholar
  5. [5]
    Aadnoy B S. A complete elastic model for fluid-induced and in-situ generated stresses with the presence of a borehole[J].Energy Sources, 1987,9:239–259.CrossRefGoogle Scholar
  6. [6]
    Bradley W B. Failure of inclined boreholes[J].Journal of Energy Resources Technology Trans, ASME, 1979,101:232–239.Google Scholar
  7. [7]
    Hsiao C. Growth of plastic zone in porous medium around a wellbore[J].Offshore Technology Conference, 1988,26:439–448.Google Scholar
  8. [8]
    Westergaard H M. Plastic state of stresses around a deep well[J].Journal of the Boston Society of Civil Engineers, 1940,27(1):1–5.Google Scholar
  9. [9]
    Gnirk P F. The mechanical behavior of uncased wellbores situated in elastic/plastic media under hydrostatic stress[J].Society of Petroleum Engineers Journal, 1972,12:49–59.Google Scholar
  10. [10]
    Risnes R, Bratli R K, Horsud P. Sand stresses around a wellbore[J].Society of Petroleum Engineers Journal, 1982,22:883–898.Google Scholar
  11. [11]
    Biot M A. Theory of elasticity and consolidation for a porous anisotropic solid[J].Journal of Applied Physics, 1941,26(2):182–185.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Yew C H, Li Y. Fracture of a deviated well[J].SPE Production Engineering, 1988,3: 429–437.Google Scholar
  13. [13]
    Chen Dar-Hao. Three dimensional testing and constitutive modeling of coal for analysis of ground subsidence due to mining [D]. M S Thesis. Norman OK: University of Oklahoma, 1992.Google Scholar
  14. [14]
    Drucker D C, Prager W. Soil mechanics and plastic analysis or limit design[J].Quart Appl Math, 1992,10:157–165.MathSciNetGoogle Scholar
  15. [15]
    Faruque M O, Chang C. New cap model for failure and yielding of pressure sensitive materials[J].Journal of Engineer Mechanics Division, ASCE, 1986,112:1041–1053.Google Scholar
  16. [16]
    Najjar Y M. Constitutive modelling and finite element analysis of ground subsidence due to mining[D]. Ph D Thesis. Norman OK: University of Oklahoma, 1990.Google Scholar
  17. [17]
    Lama R D, Vutukuri V S.Handbook on Mechanical Properties of Rocks[M]. Series on Rock and Soil Mechanics Vol. II. Ohio: Trans Tech Publications, 1978.Google Scholar
  18. [18]
    Infante E F, Chenevert M E. Stability of boreholes drilled through salt formations displaying plastic behavior[J].Society of Petroleum Engineers Drilling Engineering (SPEDE), 1989,4:57–65.Google Scholar
  19. [19]
    Gupta D J. Stability of boreholes in a transversely isotropic geologic medium[D]. M S Thesis. Norman OK: University of Oklahoma, 1994.Google Scholar
  20. [20]
    Aadnoy B S. Stability of highly inclined boreholes[J].SPEDE, 1987,2:364–374.Google Scholar
  21. [21]
    Aadnoy B S. Modeling of the stability of highly inclined boreholes in anisotropic rock formations[J].SPEDE, 1988,2:259–267.Google Scholar
  22. [22]
    Aadnoy B S. Method for fracture-gradient prediction for vertical and inclined boreholes [J].SPEDE, 1989,4:99–103.CrossRefGoogle Scholar
  23. [23]
    Aadnoy B S. Stresses around horizontal boreholes drilled in sedimentary rocks[J].Journal of Petroleum Science and Engineering, 1989,2:349–360.CrossRefGoogle Scholar
  24. [24]
    Aadnoy B S. Effects of reservoir depletion on borehole stability[J].Journal of Petroleum Science and Engineering, 1991,5:57–61.CrossRefGoogle Scholar
  25. [25]
    Bratli R K, Risnes R. Stability and failure of sand arches[J].Society of Petroleum Engineers Journal, 1981,21:236–248.CrossRefGoogle Scholar
  26. [26]
    Tsai S W, Wu E M. A general theory of strength for anisotripic materials[J].J Composite Material, 1971,5:58–80.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Dinesh Gupta
    • 1
  • Musharraf Zaman
    • 1
  1. 1.School of Civil Engineering and Environmental ScienceUniversity of OklahomaNormanU S A

Personalised recommendations