Application of rod mechanics fundamentals for analysis of stress-strain state of the tubing

Authors

  • Руслан Владимирович Рачкевич Ivano Frankivsk National Technical University of Oil and Gas, str. Karpatska 15, Ivano-Frankivsk, 76019, Ukraine https://orcid.org/0000-0003-4113-1907

DOI:

https://doi.org/10.15587/2312-8372.2016.79609

Keywords:

stress-strain state, tubing, local bend of the well axis

Abstract

A method for analysis of stress-strain state of the tubing column in the spatially curved well section with an arbitrary intensity of changes as the zenith and azimuth angle is developed in the article.

Stresses and strains are calculated using the rod mechanics fundamentals. The system of vector differential equilibrium equations in the projections on the axes of the moving coordinate system is used for the analysis of elastic equilibrium of the tubing axis.

The analysis is carried out by solving the direct problem of the rod bending by means of iterative numerical method implemented in software-oriented mathematical environment.

A method to account for the limiting effect of the well walls to move of the elastic tubing axis is provided based on the processing of its geometrical parameters, as well as data and directional survey and profilometric research of the well bore.

Using the designed calculation schemes, it is found that local bend of the well axis substantially increases the bending stress, which can reach the yield strength of the tubing material. For example that discussed in the article, the bending stress is approximately 300 MPa, while the minimum yield strength of steel, which are made tubing, is equal to 379 MPa.

Moreover, the axial force change caused by the reciprocating motion of a rod suspension may initiate the occurrence of cyclic bending moments and stresses in the tubing. So, for the considered operating conditions, we received the following: the minimum stress of the cycle σmin = 303 MPa; the maximum stress of the cycle σmax = 346 MPa; stress amplitude of the cycle σa = 43 MPa; loading cycle asymmetry factor Rσ = 0,88. This load pattern allows to speak about the cyclic fatigue of the tubing.

Author Biography

Руслан Владимирович Рачкевич, Ivano Frankivsk National Technical University of Oil and Gas, str. Karpatska 15, Ivano-Frankivsk, 76019

Candidate of Technical Sciences, Associate Professor

Department of mechanics of machines

References

  1. Kryzhanivs'kyj, Je., Ivasiv, V., Rachkevych, R., Vasylyshyn, V. (2015). Vtomna dovhovichnist rizbovykh ziednan nasosno-kompresornykh trub v kryvoliniinykh diliankakh sverdlovyn. Naukovyi visnyk NHU, 5, 14–21.
  2. Gulyaev, V. I., Solov’ev, I. L., Gorbunovich, I. V. (2009, July). Stability of drillstrings in ultradeep wells: an integrated design model. International Applied Mechanics, Vol. 45, № 7, 772–779. doi:10.1007/s10778-009-0219-2
  3. Miller, J. T., Su, T., Dussan V., E. B., Pabon, J., Wicks, N., Bertoldi, K., Reis, P. M. (2015, October). Buckling-induced lock-up of a slender rod injected into a horizontal cylinder. International Journal of Solids and Structures, Vol. 72, 153–164. doi:10.1016/j.ijsolstr.2015.07.025
  4. Miller, J. T., Su, T., Pabon, J., Wicks, N., Bertoldi, K., Reis, P. M. (2015, June). Buckling of a thin elastic rod inside a horizontal cylindrical constraint. Extreme Mechanics Letters, Vol. 3, 36–44. doi:10.1016/j.eml.2015.03.002
  5. Mitchell, R. F. (2007, June 1). The Effect of Friction on Initial Buckling of Tubing and Flowlines. SPE Drilling & Completion, Vol. 22, № 2, 112–118. doi:10.2118/99099-pa
  6. Mitchell, R. F. (2008, December 1). Tubing Buckling –The State of the Art. SPE Drilling & Completion, Vol. 23, № 4, 361–370. doi:10.2118/104267-pa
  7. Thompson, J. M. T., Silveira, M., van der Heijden, G. H. M., Wiercigroch, M. (2012, February 22). Helical post-buckling of a rod in a cylinder: with applications to drill-strings. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, № 2142, 1591–1614. doi:10.1098/rspa.2011.0558
  8. Gao, G., Di, Q., Miska, S., Wang, W. (2012, September 1). Stability Analysis of Pipe With Connectors in Horizontal Wells. SPE Journal, Vol. 17, № 3, 931–941. doi:10.2118/146959-pa
  9. Gulyaev, V. I., Lugovoi, P. Z., Khudolii, S. N., Glovach, L. V. (2007, November). Theoretical identification of forces resisting longitudinal movement of drillstrings in curved wells. International Applied Mechanics, Vol. 43, № 11, 1248–1255. doi:10.1007/s10778-007-0128-1
  10. Svetlitskii, V. A. (1987). Mehanika sterzhnei. Part 1. Statika. Moscow: Vysshaia shkola, 320.
  11. Korn, G. A., Korn, T. M. (1973). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (Dover Civil and Mechanical Engineering). Translation from English. Moscow: Nauka, 832.
  12. Shneider, V. E., Slutskii, A. I., Shumov, A. S. (1972). Kratkii kurs vysshei matematiki. Moscow: Vysshaia shkola, 640.

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Published

2016-09-29

How to Cite

Рачкевич, Р. В. (2016). Application of rod mechanics fundamentals for analysis of stress-strain state of the tubing. Technology Audit and Production Reserves, 5(1(31), 35–44. https://doi.org/10.15587/2312-8372.2016.79609

Issue

Vol. 5 No. 1(31) (2016): Mathematical modeling. Mechanical engineering and machine building. Electrical engineering and industrial electronics

Section

Mechanical engineering and machine building

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Copyright (c) 2016 Руслан Владимирович Рачкевич

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