Nonlinear dynamics of spherical hydroacoustic devices used in oil and gas industry

Svetlana A. Mitskevich, Irina V. Papkova, Alena A. Zakharova, Anton V. Krysko

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The relevance of research. Oil production is one of the most important industries in the Russian economy at present time. It depends to a large extent on the level of applied geophysical information and measurement systems on the basis of physical methods of obtaining information. The acoustic method is one of the leading ones in borehole geophysics. The amounts of using this method are about 10 % of all volume of well logging. The relevance of the study is caused by the need to improve the accuracy of the data obtained using acoustic logging. The effectiveness of the acoustic logging depends on the quality of the package of elastic waves. It is detected by the acoustic logging devices. The development of a mathematical model of the element motion in flexible spherical converter and study of the frequency characteristics of elastic vibrations are very important scientific and practical problems. The aim of the research is to study the forced vibrations of a spherical transducer, which is a part of the acoustic logging. Results. The authors have constructed the initial differential equations of motion of an axisymmetric spherical shell element using the variational principles and taking into account the geometric nonlinearity in the form of the Kirchhoff-Love and developed the algorithm for solving the systems of nonlinear differential equations using the finite difference method, the matrix and Runge-Kutta methods. Nonlinear vibrations of a spherical shell were analyzed based on non-linear dynamics and the qualitative theory of differential equations. It is shown that the dents in the vicinity of certain surface lines are possible in problems of nonlinear dynamics of axisymmetric spherical shells. It was found that the transition from harmonic vibrations to chaotic ones occurs according to the scenario of Ruelle-Takens-Newhouse for rigidly clamped spherical shell (excitation frequency is close to the natural frequency of the shell).

Original languageEnglish
Pages (from-to)17-23
Number of pages7
JournalBulletin of the Tomsk Polytechnic University, Geo Assets Engineering
Volume327
Issue number11
Publication statusPublished - 1 Jan 2016

Fingerprint

Acoustic logging
Underwater acoustics
acoustic logging
Gas industry
gas industry
oil industry
Oils
shell
vibration
Differential equations
Well logging
Geophysics
borehole geophysics
Runge Kutta methods
Elastic waves
acoustic method
physical method
Boreholes
Finite difference method
well logging

Keywords

  • Axially symmetric spherical shell
  • Dents
  • Ruelle-Takens-Newhouse scenario
  • Scripts of chaos appearance
  • Transition from harmonic to random fluctuations
  • Wavelet analysis

ASJC Scopus subject areas

  • Economic Geology
  • Geotechnical Engineering and Engineering Geology
  • Fuel Technology
  • Management, Monitoring, Policy and Law
  • Waste Management and Disposal
  • Materials Science (miscellaneous)

Cite this

Nonlinear dynamics of spherical hydroacoustic devices used in oil and gas industry. / Mitskevich, Svetlana A.; Papkova, Irina V.; Zakharova, Alena A.; Krysko, Anton V.

In: Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering, Vol. 327, No. 11, 01.01.2016, p. 17-23.

Research output: Contribution to journalArticle

@article{e1b981ce127b435794b42272a38313a7,
title = "Nonlinear dynamics of spherical hydroacoustic devices used in oil and gas industry",
abstract = "The relevance of research. Oil production is one of the most important industries in the Russian economy at present time. It depends to a large extent on the level of applied geophysical information and measurement systems on the basis of physical methods of obtaining information. The acoustic method is one of the leading ones in borehole geophysics. The amounts of using this method are about 10 {\%} of all volume of well logging. The relevance of the study is caused by the need to improve the accuracy of the data obtained using acoustic logging. The effectiveness of the acoustic logging depends on the quality of the package of elastic waves. It is detected by the acoustic logging devices. The development of a mathematical model of the element motion in flexible spherical converter and study of the frequency characteristics of elastic vibrations are very important scientific and practical problems. The aim of the research is to study the forced vibrations of a spherical transducer, which is a part of the acoustic logging. Results. The authors have constructed the initial differential equations of motion of an axisymmetric spherical shell element using the variational principles and taking into account the geometric nonlinearity in the form of the Kirchhoff-Love and developed the algorithm for solving the systems of nonlinear differential equations using the finite difference method, the matrix and Runge-Kutta methods. Nonlinear vibrations of a spherical shell were analyzed based on non-linear dynamics and the qualitative theory of differential equations. It is shown that the dents in the vicinity of certain surface lines are possible in problems of nonlinear dynamics of axisymmetric spherical shells. It was found that the transition from harmonic vibrations to chaotic ones occurs according to the scenario of Ruelle-Takens-Newhouse for rigidly clamped spherical shell (excitation frequency is close to the natural frequency of the shell).",
keywords = "Axially symmetric spherical shell, Dents, Ruelle-Takens-Newhouse scenario, Scripts of chaos appearance, Transition from harmonic to random fluctuations, Wavelet analysis",
author = "Mitskevich, {Svetlana A.} and Papkova, {Irina V.} and Zakharova, {Alena A.} and Krysko, {Anton V.}",
year = "2016",
month = "1",
day = "1",
language = "English",
volume = "327",
pages = "17--23",
journal = "Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering",
issn = "2500-1019",
publisher = "Tomsk Polytechnic University",
number = "11",

}

TY - JOUR

T1 - Nonlinear dynamics of spherical hydroacoustic devices used in oil and gas industry

AU - Mitskevich, Svetlana A.

AU - Papkova, Irina V.

AU - Zakharova, Alena A.

AU - Krysko, Anton V.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - The relevance of research. Oil production is one of the most important industries in the Russian economy at present time. It depends to a large extent on the level of applied geophysical information and measurement systems on the basis of physical methods of obtaining information. The acoustic method is one of the leading ones in borehole geophysics. The amounts of using this method are about 10 % of all volume of well logging. The relevance of the study is caused by the need to improve the accuracy of the data obtained using acoustic logging. The effectiveness of the acoustic logging depends on the quality of the package of elastic waves. It is detected by the acoustic logging devices. The development of a mathematical model of the element motion in flexible spherical converter and study of the frequency characteristics of elastic vibrations are very important scientific and practical problems. The aim of the research is to study the forced vibrations of a spherical transducer, which is a part of the acoustic logging. Results. The authors have constructed the initial differential equations of motion of an axisymmetric spherical shell element using the variational principles and taking into account the geometric nonlinearity in the form of the Kirchhoff-Love and developed the algorithm for solving the systems of nonlinear differential equations using the finite difference method, the matrix and Runge-Kutta methods. Nonlinear vibrations of a spherical shell were analyzed based on non-linear dynamics and the qualitative theory of differential equations. It is shown that the dents in the vicinity of certain surface lines are possible in problems of nonlinear dynamics of axisymmetric spherical shells. It was found that the transition from harmonic vibrations to chaotic ones occurs according to the scenario of Ruelle-Takens-Newhouse for rigidly clamped spherical shell (excitation frequency is close to the natural frequency of the shell).

AB - The relevance of research. Oil production is one of the most important industries in the Russian economy at present time. It depends to a large extent on the level of applied geophysical information and measurement systems on the basis of physical methods of obtaining information. The acoustic method is one of the leading ones in borehole geophysics. The amounts of using this method are about 10 % of all volume of well logging. The relevance of the study is caused by the need to improve the accuracy of the data obtained using acoustic logging. The effectiveness of the acoustic logging depends on the quality of the package of elastic waves. It is detected by the acoustic logging devices. The development of a mathematical model of the element motion in flexible spherical converter and study of the frequency characteristics of elastic vibrations are very important scientific and practical problems. The aim of the research is to study the forced vibrations of a spherical transducer, which is a part of the acoustic logging. Results. The authors have constructed the initial differential equations of motion of an axisymmetric spherical shell element using the variational principles and taking into account the geometric nonlinearity in the form of the Kirchhoff-Love and developed the algorithm for solving the systems of nonlinear differential equations using the finite difference method, the matrix and Runge-Kutta methods. Nonlinear vibrations of a spherical shell were analyzed based on non-linear dynamics and the qualitative theory of differential equations. It is shown that the dents in the vicinity of certain surface lines are possible in problems of nonlinear dynamics of axisymmetric spherical shells. It was found that the transition from harmonic vibrations to chaotic ones occurs according to the scenario of Ruelle-Takens-Newhouse for rigidly clamped spherical shell (excitation frequency is close to the natural frequency of the shell).

KW - Axially symmetric spherical shell

KW - Dents

KW - Ruelle-Takens-Newhouse scenario

KW - Scripts of chaos appearance

KW - Transition from harmonic to random fluctuations

KW - Wavelet analysis

UR - http://www.scopus.com/inward/record.url?scp=85019184539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019184539&partnerID=8YFLogxK

M3 - Article

VL - 327

SP - 17

EP - 23

JO - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

JF - Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering

SN - 2500-1019

IS - 11

ER -