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Dynamic interaction of an eccentric multipole cylindrical radiator suspended in a fluid-filled borehole within a poroelastic formation

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Abstract

Acoustic radiation and the dynamic field induced by a cylindrical source of infinite extent, undergoing angularly periodic and axially-dependent harmonic surface vibrations, while eccentrically suspended in a fluid-filled cylindrical cavity embedded within a fluid-saturated porous elastic formation, are analyzed in an exact manner. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation, is of practical importance with a multitude of possible applications in seismo-acoustics. The formulation utilizes the novel features of Biot dynamic theory of poroelasticity along with the translational addition theorem for cylindrical wave functions to obtain a closed-form series solution. The basic dynamic field quantities such as the resistive and the reactive components of the modal acoustic radiation impedance load on the source in addition to the radial and transverse stresses induced in the surrounding formation by an eccentric pulsating/oscillating cylinder in a water-filled borehole within a water-saturated Ridgefield sandstone medium are evaluated and discussed. Special attention is paid to the effects of source eccentricity, excitation frequency, and mode of surface oscillations on the modal impedance values and the dynamic stresses. Limiting cases are considered and good agreements with available solutions are obtained.

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References

  1. Hasheminejad S.M. and Badsar S.A. (2005). Elastic wave scattering by two spherical inclusions in a poroelastic medium. J. Eng. Mech. (ASCE) 131: 953–965

    Article  Google Scholar 

  2. Gurevich B., Kelder O. and Smeulders D.M.J. (1999). Validation of the slow compressional wave in porous media: comparsion of experiments and numerical simulations. Transp. Porous Media 36: 149–160

    Article  Google Scholar 

  3. Biot M.A. (1962). Mechanics of deformation and acoustic propagation in porous medium. J. Appl. Phys. 33: 1482–1498

    Article  MATH  MathSciNet  Google Scholar 

  4. Haldorsen J.B.U., Johnson D.L., Plona T., Sinha B., Valero H-P. and Winkler K. (2006). Borehole acoustic waves. Oilfield Rev. 18: 34–43

    Google Scholar 

  5. Biot M.A. (1952). Propagation of elastic waves in a cylindrical bore containing a fluid. J. Appl. Phys. 23: 997–1005

    Article  MATH  MathSciNet  Google Scholar 

  6. Kubenko V.D. and Dzyuba V.V. (2000). The acoustic field in a rigid cylindrical vessel excited by a sphere oscillating by a definite law. Int. J. Appl. Mech. 36: 779–788

    MathSciNet  Google Scholar 

  7. Kubenko V.D. and Dzyuba V.V. (2001). Interaction between an oscillating sphere and a thin elastic shell filled with a compressible liquid, (Internal axisymmetric problem). J. Appl. Mech. 37: 222–230

    Article  Google Scholar 

  8. Dzyuba V.V. and Kubenko V.D. (2002). Axisymmetric interaction problem for a sphere pulsating inside an elastic cylindrical shell filled with and immersed into a liquid. J. Appl. Mech. 38: 1210–1219

    Article  Google Scholar 

  9. Kubenko V.D. and Savin V.A. (2002). Dynamics of a semi-infinite cylindrical shell with a liquid containing a vibrating spherical segment. Int. Appl. Mech. 28: 974–982

    Article  Google Scholar 

  10. Kubenko V.D. and Dzyuba V.V. (2004). Dynamic interaction of an oscillating sphere and an elastic cylindrical shell filled with a fluid and immersed in an elastic medium. Int. Appl. Mech. 40: 1002–1011

    Article  Google Scholar 

  11. White J.E. (1984). Radiation from a borehole. Colo. Sch. Mines Q. 2: 46–50

    Google Scholar 

  12. Poterasu V.F. (1993). Coupled vibrations of a cavity filled with a pulsating fluid in elastic infinite media by the boundary element method. Comput. Methods Appl. Mech. Eng. 106: 285–296

    Article  MATH  MathSciNet  Google Scholar 

  13. Hasheminejad S.M. and Hosseini H. (2002). Radiation loading of a cylindrical source in a fluid-filled cylindrical cavity embedded within a fluid saturated poroelastic medium. ASME J. Appl. Mech. 69: 675–683

    Article  MATH  Google Scholar 

  14. Hasheminejad S.M. and Hosseini H. (2002). Dynamic stress concentration near on a fluid-filled permeable borehole induced by general modal vibrations of an internal cylindrical radiator. Soil Dyn. Earthq. Eng. 22: 441–458

    Article  Google Scholar 

  15. Byun J. and Nafi Toksoz M. (2006). Effects of an off-centered tool on dipole and quadrupole logging. Geophysics 71: F91–F100

    Article  Google Scholar 

  16. Shen J., Chen Y. and Zhang H. (2002). Numerical study on acoustic field on borehole generated by eccentric sonic source near the borehole. Cejing Jishu/Well Logging Technol. 26: 184–188

    Google Scholar 

  17. Schmitt D.P. (1993). Dipole logging in cased boreholes. J. Acoust. Soc. Am. 93: 640–657

    Article  Google Scholar 

  18. Pierce A.D. (1991). Acoustics: An Introduction to Its Physical Principles and Applications. American Institute of Physics, New York

    Google Scholar 

  19. Skudrzyk E. (1971). The Foundations of Acoustics. Springer, New York

    MATH  Google Scholar 

  20. Junger M.C. and Feit D. (1986). Sound, Structures and Their Interaction, 2nd edn. MIT Press, Massachusetts

    Google Scholar 

  21. Abramowitz M. and Stegun I.A. (1965). Handbook of Mathematical Functions. National Bureau of Standards, Washington, D.C

    Google Scholar 

  22. Bourbie T., Coussy O. and Zinszner B.E. (1987). Acoustics of Porous Media. Gulf Publishing, Houston

    Google Scholar 

  23. Allard J.F. (1993). Propagation of Sound in Porous Media, Modeling Sound Absorbing Materials. Elsevier, London

    Google Scholar 

  24. Johnson D.L., Koplik J. and Dashen R. (1987). Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mech. 76: 379–402

    Article  Google Scholar 

  25. Ivanov Y.A. (1970). Diffraction of Electromagnetic Waves on Two Bodies. National Aeronautics and Space Administration, Washington, D.C

    Google Scholar 

  26. Hasheminejad S.M. and Azarpeyvand M. (2003). Energy distribution and radiation loading of a cylindrical source suspended within a nonconcentric cylindrical fluid cylinder. Acta Mech. 164: 15–30

    Article  MATH  Google Scholar 

  27. Hasheminejad S.M. and Geers T.L. (1993). Modal impedances for two spheres in a thermoviscous fluid. J. Acoust. Soc. Am. 94: 2205–2214

    Article  Google Scholar 

  28. White J.E. (1983). Underground Sound: Application of Seismic Waves. Elsevier, Amsterdam

    Google Scholar 

  29. Johnson D.L., Plona T.J. and Kojima H. (1994). Probing porous media with first and second sound, II: Acoustic properties of water-saturated porous media. J. Appl. Phys. 76: 115–125

    Article  Google Scholar 

  30. Winbow G.A. (1993). Borehole stresses created by downhole seismic sources. Geophysics 56: 1055–1057

    Article  Google Scholar 

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Authors and Affiliations

  1. Acoustics Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844, Iran

    Seyyed M. Hasheminejad & Amir K. Miri

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  1. Seyyed M. Hasheminejad
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  2. Amir K. Miri
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Correspondence to Seyyed M. Hasheminejad.

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Hasheminejad, S.M., Miri, A.K. Dynamic interaction of an eccentric multipole cylindrical radiator suspended in a fluid-filled borehole within a poroelastic formation. Acta Mech Sin 23, 399–408 (2007). https://doi.org/10.1007/s10409-007-0094-1

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  • DOI: https://doi.org/10.1007/s10409-007-0094-1

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