Structural Engineering and Mechanics

  • 제49권4호
  • /
  • Pages.427-448
  • /
  • 2014
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Theoretical modelling of post - buckling contact interaction of a drill string with inclined bore-hole surface

  • Gulyayev, V.I. (Department of Mathematics, National Transport University) ;
  • Andrusenko, E.N. (Department of Mathematics, National Transport University) ;
  • Shlyun, N.V. (Department of Mathematics, National Transport University)
  • 투고 : 2013.04.12
  • 심사 : 2013.12.24
  • 발행 : 2014.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

At present, the time of easy oil and gas is over. Now, the largest part of fossil fuels is concentrated in the deepest levels of tectonic structures and in the sea shelves. One of the most cumbersome operations of their extraction is the bore-hole drilling. In connection with austere tectonic and climate conditions, their drivage every so often is associated with great and diversified technological difficulties causing emergencies on frequent occasions. As a rule, they are linked with drill string accidents. A key role in prediction of these situations should play methods of theoretical modelling. For this reason, there is a growing need for development and implementation of new numerical methods for computer simulation of critical and post-critical behavior of drill strings (DSs). In this paper, the processes of non-linear deforming of a DS in cylindrical cavity of a deep bore-hole are considered. On the basis of the theory of curvilinear flexible rods, non-linear constitutive differential equations are deduced. The effects of the longitudinal non-uniform preloading, action of torque and interaction between the DS and the bore-hole surface are taken into account. Owing to the use of curvilinear coordinates in the constraining cylindrical surface and a specially chosen concomitant reference frame, it became possible to separate the desired variables and to reduce the total order of the equation system. To solve it, the method of continuation the solution by parameter and the transfer matrix technique are applied. As a result of the completed numerical analysis, the critical states of the DS loading in the cylindrical channels of inclined bore-holes are found. It is shown that the modes of the post-critical deforming of the DS are associated with its irregular spiral curving prevailing in the zone of bottom-hole-assembly. The possibility of invariant state generation during post-critical deforming is established, condition of its bifurcation is formulated. It is shown that infinite variety of loads can correspond to one geometrical configuration of the DS. They differ each from other by contact force functions.

키워드

참고문헌

  1. Argiris, J.H. (1982), "An excursion into large rotations", Comput. Methods Appl. Mech Eng., 32, 85-155. https://doi.org/10.1016/0045-7825(82)90069-X
  2. Arici, M. and Granata, M.F. (2011), "Generalized curved beam on elastic foundation solved by transfer matrix method", Struct. Eng. Mech., 40(2), 279-295. https://doi.org/10.12989/sem.2011.40.2.279
  3. Atluri, S.N. and Cazzani, A. (1995), "Rotations in computational solid mechanics", Arch. Comput. Methods Eng., 2, 49-138. https://doi.org/10.1007/BF02736189
  4. Chang, K.W. and Howes, F.A. (1984), Nonlinear Singular Perturbation Phenomena, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo.
  5. Dubrovin, B.A., Novikov, S.P. and Fomenko, A.T. (1992), Modern Geometry-Methods and Applications, Springer-Verlag, Berlin, Heidelberg, New York.
  6. Fang, J., Li, S.Y. and Chen, J.S. (2013), "On a compressed spatial elastica constrained inside a tube", Acta Mechanica, 224(11), 2635-2647. https://doi.org/10.1007/s00707-013-0889-z
  7. Goldstein, H., Poole, Ch. and Safko, J. (2011), Classical Mechanics, San Francisco, Boston, New York, Tokyo, Capetown, Hong-Kong, London, Madrid, Mexico City, Montreal, Munich, Paris, Singapore, Sydney, Toronto.
  8. Gulyayev, V.I. and Borshch, O.I. (2011), "Free vibrations of drill strings in hyper deep vertical bore-wells", J. Petr. Sci. Eng., 78, 759-764. https://doi.org/10.1016/j.petrol.2011.09.001
  9. Gulyayev, V.I., Gaidaichuk, V.V. and Koshkin, V.L. (1992), Elastic Deforming, Stability and Vibrations of Flexible Curvilinear Rods, Naukova Dumka, Kiev. (in Russian)
  10. Gulyayev, V.I., Gaidaichuk, V.V., Solovjov, I.L. and Gorbunovich, I.V. (2009), "The buckling of elongated rotating drill strings", J. Petr. Sci. Eng., 67, 140-148. https://doi.org/10.1016/j.petrol.2009.05.011
  11. Gulyayev, V.I., Gaidaichuk, V.V., Solov'ev, I.L. and Gorbunovich, I.V. (2010), "Quasistatic bifurcation states of super-deep vertical drill strings", J. Mining Sci., 46(5), 546-553. https://doi.org/10.1007/s10913-010-0068-8
  12. Gulyayev, V.I. and Glushakova, O.V. (2011), "Large-scale and small-scale self-excited torsional vibrations of homogeneous and sectional drill strings", Interact. Multiscale Mech., 4(4), 291-311. https://doi.org/10.12989/imm.2011.4.4.291
  13. Gulyayev, V.I., Hudoly, S.N. and Glovach, L.V. (2011), "The computer simulation of drill column dragging in inclined bore-holes with geometrical imperfections", Int. J. Solids Struct., 48, 110-118. https://doi.org/10.1016/j.ijsolstr.2010.09.009
  14. Gulyayev, V.I. and Tolbatov, E.Y. (2004), "Dynamics of spiral tubes containing internal moving masses of boiling liquid", J. Sound Vib., 274, 233-248. https://doi.org/10.1016/j.jsv.2003.05.013
  15. Huang, N.C. and Pattillo, P.D. (2000), "Helical buckling of a tube in an inclined well bore", Int. J. Nonlin. Mech., 35, 911-923. https://doi.org/10.1016/S0020-7462(99)00067-0
  16. Ibrahimbegovic, A. (1997), "On the choice of finite rotations parameters", Comput. Methods Appl. Mech. Eng., 149, 49-71. https://doi.org/10.1016/S0045-7825(97)00059-5
  17. Krauberger, N., Saje, M., Planinc, I. and Bratina, S. (2007), "Exact buckling load of a restrained RC column", Struct. Eng. Mech., 27(3), 293-310. https://doi.org/10.12989/sem.2007.27.3.293
  18. Kwon, Y.W. (1988), "Analysis of helical buckling", SPE Drill Eng., 3, 211-216. https://doi.org/10.2118/14729-PA
  19. Lubinski, A. (1987), Developments in Petroleum Engineering, Vol. 1. Gulf Publishing Company, Houstan, TX, USA.
  20. Mitchell, R.F. (2007), "The effect of friction on initial buckling of tubing and flowlines", SPE Drill. Compl., 22(2), 112-118. https://doi.org/10.2118/99099-PA
  21. Mitchell, R.F. and Miska, S. (2006), "Helical buckling of pipe with connectors and torque", SPE Drill. Compl., 21(2), 108-115. https://doi.org/10.2118/87205-PA
  22. Mitchell, R.F. (2008), "Tubing buckling-the state of art", SPE Drill. Compl., 23(4), 361-370. https://doi.org/10.2118/104267-PA
  23. Neimark, J.I. and Fufaev, N.A. (1972), Dynamics of Nonholonomic Systems, Translation of mathematical monographs, 33, Amer. Math. Soc., Providence, RI.
  24. Singh, S.B. and Kumar, D. (2008), "Postbuckling response and failure of symmetric laminated plates with rectangular cutouts under uniaxial compression", Struct. Eng. Mech., 29(4), 276-287.
  25. Sun, C. and Lukasiewicz, S. (2006), "A new model on the buckling of a rod in tubing", J. Petr. Sci. Eng., 50, 78-82. https://doi.org/10.1016/j.petrol.2005.10.001
  26. Thompson, J.M.T., Silveira, M., van der Heijden, G.H.M., and Wiercigroch, M. (2012), "Helical postbuckling of a rod in a cylinder: with applications to drill-strings", Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences, 468(2142), 1591-1614. https://doi.org/10.1098/rspa.2011.0558
  27. Van der Heijden, G.H.M., Champneys, A.R. and Thompson, J.M.T. (2002), "Spatially complex localisation in twisted elastic rods constrained to a cylinder", Int. J. Solids Struct., 39(7), 1863-1883. https://doi.org/10.1016/S0020-7683(01)00234-7
  28. Yu, Y.P. and Sun, Y.H. (2012), "Analytical approximate solutions for large post-buckling response of a hydrothermal beam", Struct. Eng. Mech., 43(2), 211-213. https://doi.org/10.12989/sem.2012.43.2.211
  29. Zhao, M.H., He,W. and Li, Q.S. (2010), "Post-bucking analysis of piles by perturbation method", Struct. Eng. Mech., 35(2), 236-251.
  30. Ziegler, H. (1968), Principles of Structural Stability, Blaisdell Publishing Company, Waltham-Massachusetts-Toronto-London.

피인용 문헌

  1. Influence of friction on buckling of a drill string in the circular channel of a bore hole vol.13, pp.4, 2016, https://doi.org/10.1007/s12182-016-0122-5
  2. Effect of wellhead tension on buckling load of tubular strings in vertical wells 2018, https://doi.org/10.1016/j.petrol.2018.01.059
  3. Global analysis of drill string buckling in the channel of a curvilinear bore-hole vol.40, 2017, https://doi.org/10.1016/j.jngse.2017.01.021
  4. Critical buckling of drill strings in curvilinear channels of directed bore-holes vol.129, 2015, https://doi.org/10.1016/j.petrol.2015.03.004
  5. Drill String Bit Whirl Simulation With the Use of Frictional and Nonholonomic Models vol.138, pp.1, 2016, https://doi.org/10.1115/1.4031985