Modelling of drill string nonlinear dynamics with a drilling fluid flow
DOI:
https://doi.org/10.26577/mmcs-2018-1-487Keywords:
drill string, mathematical model, geometric nonlinearity, drilling fluid, lateral vibrationsAbstract
In this work the development of mathematical models of drill string dynamics under the influence
of internal drilling fluid flow, which is of great importance for ensuring fast, cost-effective and safe
process of oil and gas well drilling, is conducted. It is a reason for in-depth research of the drilling
fluid influence on the motion of drill strings. The modelling is complicated by consideration of geometric
nonlinearity, rotation of the drill string and the effect of external force factors. Relations
of Novozhilov’s nonlinear theory of elasticity form the model framework. Ostrogradsky-Hamilton’s
variation principle is applied for derivation of the drill string governing equations. It is assumed
that the drilling fluid flow moves at constant speed. The obtained nonlinear mathematical models,
describing lateral vibrations of the drill string as a compressed rod, generalize well-known linear
models taking into account the effect of the drilling fluid. These models will enable to solve a wide
range of problems concerning the drilling equipment nonlinear dynamics on a qualitatively new
and mathematically valid level.
References
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[6] Khajiyeva, Lelya, 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.
[7] Kudaibergenov, Askat K., Askar K. Kudaibergenov. “Modelling of Resonance and Stability of Drill String Nonlinear
Dynamics.” International Journal of Mechanics 11 (2017): 92-100.
[8] Lian, Zhanghua, Qiang Zhang, Tiejun Lin, Fuhui 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.
[9] Liang, Feng, Xiao-Dong Yang, Wei Zhang, Ying-Jing Qian. “Dynamical Modeling and Free Vibration Analysis
of Spinning Pipes Conveying Fluid with Axial Deployment.” Journal of Sound and Vibration 417 (2018): 65-79.
https://doi.org/10.1016/j.jsv.2017.12.005.
[10] Li, Zifeng, Yanshan U., Boyun Guo. “Analysis of Longitudinal Vibration of Drillstring in Air and Gas Drilling.” Paper
presented at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, USA, April 16-18,
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[11] Liu, Yu, Yi Ji, Andrew J. Dick. “Analysis of Longitudinal Vibration of Drillstring in Air and Gas Drilling.” Paper
presented at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, USA, April 16-18,
2007.
[12] Meng, Yingfeng, Hongtao Li, Gao Li, Li Zhu, Na Wei, Nan 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.
[13] Moditis, Kyriakos, Michael Paidoussis, Joe Ratigan. “Dynamics of a Partially Confined, Discharging,
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https://doi.org/10.1016/j.jfluidstructs.2016.03.002.
[14] Novozhilov, V.V. Foundations of the Nonlinear Theory of Elasticity. New York: Dover Publications, 1999.
[15] Rabotnov, Yu.N. Mehanika deformiruemogo tverdogo tela [Mechanics of Deformable Solid Body]. Moscow: Nauka, 1988.
[16] Ritto, T.G., R. Sampaio, Christian Soize. “Drill-String Dynamics Coupled with the Drilling Fluid Dynamics.” Paper
presented at the XIII International Symposium on Dynamic Problems of Mechanics (DINAME 2009), Angra dos Reis,
RJ, Brazil, March 2-6, 2009.
[17] Saldivar B., I. Boussaada, H. Mounier, S. Mondie, S.I. Niculescu. “An Overview on the Modeling of Oilwell Drilling
Vibrations.” Paper presented at the 19th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014.
[18] Wilson, J.K., S.F. Noynaert. “A New Damping Model for Nonlinear Drillstring Dynamics: Understanding the Effects of
Rotation, Eccentricity, and Confined Fluid Flow and Their Impact on Unconventional Drillstring Design.” Paper presented
at the IADC/SPE Drilling Conference and Exhibition, Fort Worth, Texas, USA, March 1-3, 2016.
Acoustic Journal 29 (4) (1983): 428-434.
[2] Dobycha nefti i gaza. “Burovye promyvochnye zhidkosti.” [Oil and Gas Mining. “Drilling Fluids.”] Accessed March 23,
2018. http://oilloot.ru/78-tekhnika-i-tekhnologii-stroitelstva-skvazhin/167-burovye-promyvochnye-zhidkosti.
[3] Filippov, A.P. Kolebaniya deformiruemyh system [Oscillations of deformable systems]. 2nd ed. Moscow: Mashinostroenie,
1970.
[4] Gulyayev, V.I., V.V. Gaidaichuk, I.L. Solovjov, I.V. Gorbunovich. “The Buckling of Elongated Rotating Drill Strings.”
Journal of Petroleum Science and Engineering 67 (2009): 140–148. https://doi.org/10.1016/j.petrol.2009.05.011.
[5] Gulyayev, V.I., O.I. Borshch. “Free Vibrations of Drill Strings in Hyper Deep Vertical Bore-Wells.” Journal of Petroleum
Science and Engineering 78 (2011): 759–64. https://doi.org/10.1016/j.petrol.2011.09.001.
[6] Khajiyeva, Lelya, 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.
[7] Kudaibergenov, Askat K., Askar K. Kudaibergenov. “Modelling of Resonance and Stability of Drill String Nonlinear
Dynamics.” International Journal of Mechanics 11 (2017): 92-100.
[8] Lian, Zhanghua, Qiang Zhang, Tiejun Lin, Fuhui 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.
[9] Liang, Feng, Xiao-Dong Yang, Wei Zhang, Ying-Jing Qian. “Dynamical Modeling and Free Vibration Analysis
of Spinning Pipes Conveying Fluid with Axial Deployment.” Journal of Sound and Vibration 417 (2018): 65-79.
https://doi.org/10.1016/j.jsv.2017.12.005.
[10] Li, Zifeng, Yanshan U., Boyun Guo. “Analysis of Longitudinal Vibration of Drillstring in Air and Gas Drilling.” Paper
presented at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, USA, April 16-18,
2007.
[11] Liu, Yu, Yi Ji, Andrew J. Dick. “Analysis of Longitudinal Vibration of Drillstring in Air and Gas Drilling.” Paper
presented at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, USA, April 16-18,
2007.
[12] Meng, Yingfeng, Hongtao Li, Gao Li, Li Zhu, Na Wei, Nan 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.
[13] Moditis, Kyriakos, Michael Paidoussis, Joe Ratigan. “Dynamics of a Partially Confined, Discharging,
Cantilever Pipe with Reverse External Flow.” Journal of Fluids and Structures 63 (2016): 120-139.
https://doi.org/10.1016/j.jfluidstructs.2016.03.002.
[14] Novozhilov, V.V. Foundations of the Nonlinear Theory of Elasticity. New York: Dover Publications, 1999.
[15] Rabotnov, Yu.N. Mehanika deformiruemogo tverdogo tela [Mechanics of Deformable Solid Body]. Moscow: Nauka, 1988.
[16] Ritto, T.G., R. Sampaio, Christian Soize. “Drill-String Dynamics Coupled with the Drilling Fluid Dynamics.” Paper
presented at the XIII International Symposium on Dynamic Problems of Mechanics (DINAME 2009), Angra dos Reis,
RJ, Brazil, March 2-6, 2009.
[17] Saldivar B., I. Boussaada, H. Mounier, S. Mondie, S.I. Niculescu. “An Overview on the Modeling of Oilwell Drilling
Vibrations.” Paper presented at the 19th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014.
[18] Wilson, J.K., S.F. Noynaert. “A New Damping Model for Nonlinear Drillstring Dynamics: Understanding the Effects of
Rotation, Eccentricity, and Confined Fluid Flow and Their Impact on Unconventional Drillstring Design.” Paper presented
at the IADC/SPE Drilling Conference and Exhibition, Fort Worth, Texas, USA, March 1-3, 2016.
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How to Cite
Kudaibergenov, A. K., & Khajiyeva, L. A. (2018). Modelling of drill string nonlinear dynamics with a drilling fluid flow. Journal of Mathematics, Mechanics and Computer Science, 97(1), 91–100. https://doi.org/10.26577/mmcs-2018-1-487
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