О динамической устойчивости бурильных колонн в сверхзвуковом потоке газа
DOI:
https://doi.org/10.26577/jmmcs-2018-1-488Ключевые слова:
бурильная колонна, устойчивость, нелинейность, поток газаАннотация
В работе изучается устойчивость нелинейной динамики бурильной колонны, осложненной
действием внешней осевой нагрузки, начальной кривизной колонны, геометрической
нелинейностью и влиянием сверхзвукового потока газа как циркулирующей среды.
Бурильная колонна моделируется в виде вращающегося упругого изотропного стержня
постоянного поперечного сечения. Давление потока газа, который применяется для
очистки скважины и переноса бурового шлама с забоя на поверхность, определяется
нелинейными зависимостями поршневой теории в третьем приближении. Использование
метода Галеркина позволяет перейти к обыкновенному дифференциальному уравнению
относительно обобщенной временной функции, содержащему несимметричную нелинейную
характеристику, которую удается исключить введением соответствующей замены.
Задавая системе малое возмущение и применяя метод гармонического баланса,
строятся характеристические определители, дающие уравнения границ зон динамической
неустойчивости основного резонанса, которые позволят определить диапазон опасных
частотных режимов и повысить безопасность процесса бурения скважин.
Библиографические ссылки
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at ENOC 2017, Budapest, Hungary, June 25-30, 2017.
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Journal of Sound and Vibration 265 (2003): 401-415. https://doi.org/10.1016/S0022-460X(02)01456-6.
[3] Bhattiprolu, U., A.K. Bajaj, P. Davies. “Periodic Response Predictions of Beams on Nonlinear and Viscoelastic Unilateral
Foundations Using Incremental Harmonic Balance Method.” International Journal of Solids and Structures 99 (2016): 28-39.
[4] Chen, J., Q.S. Li. “Analysis of Flutter and Nonlinear Dynamics of a Composite Laminated Plate.” International Journal
of Structural Stability and Dynamics 16 (2016): 1550019-1-20.
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[6] Ghasemloonia, A., D.G. Rideout, S.D. Butt. “Coupled Transverse Vibration Modeling of Drillstrings Subjected to Torque
and Spatially Varying Axial Load.” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical
Engineering Science 227(5) (2013): 946-960. https://doi.org/10.1177/0954406212455126.
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Applied Mechanics 42(6) (2006): 692-698.
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Drilling Conference, New Orleans, Louisiana, February 23-25, 2000.
[10] Jansen, J.D. Nonlinear Dynamics of Oilwell Drillstrings. Delft University Press, 1993.
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Flow.” Fluid Dynamics 44(1) (2009): 135-140.
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Drill Strings].” Paper presented at X All-Russian Conference on “Nonlinear Vibrations of Mechanical Systems”, Nizhny
Novgorod, Russia, September 26-29, 2016.
[13] Kudaibergenov, Askat K., Askar K. Kudaibergenov, L.A. Khajiyeva. “On resonance regimes of drill string nonlinear dynamics.”
Paper presented at International Conference on Mathematical Methods & Computational Techniques in Science
& Engineering (MMCTSE 2017), Cambridge, UK, February 24-26, 2017.
[14] Khajiyeva, L., Askar Kudaibergenov, Askat Kudaibergenov. “The effect of gas and fluid flows on nonlinear lateral vibrations
of rotating drill strings.” Communications in Nonlinear Science and Numerical Simulation 59 (2018): 565-579.
https://doi.org/10.1016/j.cnsns.2017.12.008.
[15] Kudaibergenov, Askhat, Askar Kudaibergenov, L. Khajiyeva. “Stability Analysis of Drill Rods as Shells in the Gas Stream.”
Journal of Applied Mechanics and Materials 665 (2014): 593-596.
[16] Lian, Zh., Q. Zhang, T. Lin, F. Wang. “Experimental and Numerical Study of Drill String Dynamics in
Gas Drilling of Horizontal Wells.” Journal of Natural Gas Science and Engineering 27 (2015): 1412-1420.
https://doi.org/10.1016/j.jngse.2015.10.005.
[17] Librescu, L., P. Marzocca. “Supersonic/Hypersonic Flutter and Postflutter of Geometrically Imperfect Circular Cylindrical
Panels.” Journal of Spacecraft and Rockets 39(5) (2002): 802-812.
[18] Liu, X., N. Vlajic, X. Long, G. Meng, B. Balachandran. “State-Dependent Delay Influenced Drill-String Oscillations and
Stability Analysis.” Journal of Vibration and Acoustics – Transactions of the ASME 136 (2014): 051008-1-9.
[19] Novozhilov, V.V. Foundations of the Nonlinear Theory of Elasticity. New York: Dover Publications, 1999.
[20] Meng, Y., H. Li, G. Li, L. Zhu, N. Wei, N. Lin. “Investigation on Propagation Characteristics of the Pressure Wave in
Gas Flow through Pipes and its Application in Gas Drilling.” Journal of Natural Gas Science and Engineering 22 (2015):
163-171. https://doi.org/10.1016/j.jngse.2014.11.026.
[21] Nandakumar, K., M. Wiercigroch. “Stability Analysis of a State Dependent Delayed, Coupled Two DOF Model of Drillstring
Vibration.” Journal of Sound and Vibration 332 (2013): 2575-2592. https://doi.org/10.1016/j.jsv.2012.12.020.
[22] Sahebkar, S.M., M.R. Ghazavi, S.E. Khadem, M.H. Ghayesh. “Nonlinear Vibration Analysis of an Axially Moving Drillstring
System with Time Dependent Axial Load and Axial Velocity in Inclined Well.” Mechanism and Machine Theory
46 (2011): 743-760. https://doi.org/10.1016/j.mechmachtheory.2010.12.003.
[23] Szemplinska-Stupnicka, W. “Higher Harmonic Oscillations in Heteronomous Non-linear Systems with One Degree Of
Freedom.” International Journal of Non-Linear Mechanics 3 (1968): 17 30.
[24] Szemplinska-Stupnicka, W. “Non-Linear Normal Modes” and the Generalized Ritz Method in the Problems of Vibrations
of Non-Linear Elastic Continuous Systems.” International Journal of Non-Linear Mechanics 18(2) (1983): 149-165.
https://doi.org/10.1016/0020-7462(83)90042-2.
[25] Vaz, M.A., M.H. Patel. “Analysis of Drill Strings in Vertical and Deviated Holes Using the Galerkin techniques.” Engineering
Structures 17(6) (1995): 437-442.
[26] Volmir A.S. Ustojchivost’ deformiruemyh sistem [Stability of Deformable Systems]. Moscow: Nauka, 1967.
at ENOC 2017, Budapest, Hungary, June 25-30, 2017.
[2] Al-Hiddabi, S.A., B. Samanta, A. Seibi. “Non-linear Control of Torsional and Bending Vibrations of Oilwell Drillstrings.”
Journal of Sound and Vibration 265 (2003): 401-415. https://doi.org/10.1016/S0022-460X(02)01456-6.
[3] Bhattiprolu, U., A.K. Bajaj, P. Davies. “Periodic Response Predictions of Beams on Nonlinear and Viscoelastic Unilateral
Foundations Using Incremental Harmonic Balance Method.” International Journal of Solids and Structures 99 (2016): 28-39.
[4] Chen, J., Q.S. Li. “Analysis of Flutter and Nonlinear Dynamics of a Composite Laminated Plate.” International Journal
of Structural Stability and Dynamics 16 (2016): 1550019-1-20.
[5] Christoforou, A.P., A.S. Yigit. “Dynamic Modeling of Rotating Drillstrings with Borehole Interactions.” Journal of Sound
and Vibration 206(2) (1997): 243-260. https://doi.org/10.1006/jsvi.1997.1091.
[6] Ghasemloonia, A., D.G. Rideout, S.D. Butt. “Coupled Transverse Vibration Modeling of Drillstrings Subjected to Torque
and Spatially Varying Axial Load.” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical
Engineering Science 227(5) (2013): 946-960. https://doi.org/10.1177/0954406212455126.
[7] Gulyaev, V.I., P.Z. Lugovoi, M.A. Belova, I.L. Solov’ev. “Stability of the Equilibrium of Rotating Drillstrings.” International
Applied Mechanics 42(6) (2006): 692-698.
[8] Hayashi, Ch. Nonlinear Oscillations in Physical Systems. New Jersey: Princeton University Press, 1986.
[9] Heisig, G, M. Neubert. “Lateral Drillstring Vibrations in Extended-Reach Wells.” Paper presented at the 2000 IADC/SPE
Drilling Conference, New Orleans, Louisiana, February 23-25, 2000.
[10] Jansen, J.D. Nonlinear Dynamics of Oilwell Drillstrings. Delft University Press, 1993.
[11] Kiiko, I.A., V.V. Pokazeev. “On the Formulation of the Problem of Strip Oscillations and Stability in Supersonic Gas
Flow.” Fluid Dynamics 44(1) (2009): 135-140.
[12] Kudaibergenov, Askat K. “Ob ustojchivosti nelinejnyh kolebanij buril’nyh kolonn [On Stability of Nonlinear Vibrations of
Drill Strings].” Paper presented at X All-Russian Conference on “Nonlinear Vibrations of Mechanical Systems”, Nizhny
Novgorod, Russia, September 26-29, 2016.
[13] Kudaibergenov, Askat K., Askar K. Kudaibergenov, L.A. Khajiyeva. “On resonance regimes of drill string nonlinear dynamics.”
Paper presented at International Conference on Mathematical Methods & Computational Techniques in Science
& Engineering (MMCTSE 2017), Cambridge, UK, February 24-26, 2017.
[14] Khajiyeva, L., Askar Kudaibergenov, Askat Kudaibergenov. “The effect of gas and fluid flows on nonlinear lateral vibrations
of rotating drill strings.” Communications in Nonlinear Science and Numerical Simulation 59 (2018): 565-579.
https://doi.org/10.1016/j.cnsns.2017.12.008.
[15] Kudaibergenov, Askhat, Askar Kudaibergenov, L. Khajiyeva. “Stability Analysis of Drill Rods as Shells in the Gas Stream.”
Journal of Applied Mechanics and Materials 665 (2014): 593-596.
[16] Lian, Zh., Q. Zhang, T. Lin, F. Wang. “Experimental and Numerical Study of Drill String Dynamics in
Gas Drilling of Horizontal Wells.” Journal of Natural Gas Science and Engineering 27 (2015): 1412-1420.
https://doi.org/10.1016/j.jngse.2015.10.005.
[17] Librescu, L., P. Marzocca. “Supersonic/Hypersonic Flutter and Postflutter of Geometrically Imperfect Circular Cylindrical
Panels.” Journal of Spacecraft and Rockets 39(5) (2002): 802-812.
[18] Liu, X., N. Vlajic, X. Long, G. Meng, B. Balachandran. “State-Dependent Delay Influenced Drill-String Oscillations and
Stability Analysis.” Journal of Vibration and Acoustics – Transactions of the ASME 136 (2014): 051008-1-9.
[19] Novozhilov, V.V. Foundations of the Nonlinear Theory of Elasticity. New York: Dover Publications, 1999.
[20] Meng, Y., H. Li, G. Li, L. Zhu, N. Wei, N. Lin. “Investigation on Propagation Characteristics of the Pressure Wave in
Gas Flow through Pipes and its Application in Gas Drilling.” Journal of Natural Gas Science and Engineering 22 (2015):
163-171. https://doi.org/10.1016/j.jngse.2014.11.026.
[21] Nandakumar, K., M. Wiercigroch. “Stability Analysis of a State Dependent Delayed, Coupled Two DOF Model of Drillstring
Vibration.” Journal of Sound and Vibration 332 (2013): 2575-2592. https://doi.org/10.1016/j.jsv.2012.12.020.
[22] Sahebkar, S.M., M.R. Ghazavi, S.E. Khadem, M.H. Ghayesh. “Nonlinear Vibration Analysis of an Axially Moving Drillstring
System with Time Dependent Axial Load and Axial Velocity in Inclined Well.” Mechanism and Machine Theory
46 (2011): 743-760. https://doi.org/10.1016/j.mechmachtheory.2010.12.003.
[23] Szemplinska-Stupnicka, W. “Higher Harmonic Oscillations in Heteronomous Non-linear Systems with One Degree Of
Freedom.” International Journal of Non-Linear Mechanics 3 (1968): 17 30.
[24] Szemplinska-Stupnicka, W. “Non-Linear Normal Modes” and the Generalized Ritz Method in the Problems of Vibrations
of Non-Linear Elastic Continuous Systems.” International Journal of Non-Linear Mechanics 18(2) (1983): 149-165.
https://doi.org/10.1016/0020-7462(83)90042-2.
[25] Vaz, M.A., M.H. Patel. “Analysis of Drill Strings in Vertical and Deviated Holes Using the Galerkin techniques.” Engineering
Structures 17(6) (1995): 437-442.
[26] Volmir A.S. Ustojchivost’ deformiruemyh sistem [Stability of Deformable Systems]. Moscow: Nauka, 1967.
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Как цитировать
Kudaibergenov, A. K., & Khajiyeva, L. A. (2018). О динамической устойчивости бурильных колонн в сверхзвуковом потоке газа. Вестник КазНУ. Серия математика, механика, информатика, 97(1), 101–110. https://doi.org/10.26577/jmmcs-2018-1-488
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