1887
Volume 64, Issue 5
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

We derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10−3 Hz to 103 Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity.

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2016-02-01
2020-09-21
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References

  1. BiotM.A.1956a. Theory of propagation of elastic waves in a fluid‐saturated porous rock: I. Low‐frequency range. The Journal of the Acoustical Society of America28, 168–178.
    [Google Scholar]
  2. BiotM.A.1956b. Theory of propagation of elastic waves in a fluid‐saturated porous rock: II. Higher frequency range. The Journal of the Acoustical Society of America28, 179–191.
    [Google Scholar]
  3. BiotM.A.1962. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics33(4), 1482–1498.
    [Google Scholar]
  4. ChouetB.1981. Ground motion in the near field of a fluid‐driven crack and its interpretation in the study of shallow volcanic tremor. Journal of Geophysical Research86(B7), 5985–6016.
    [Google Scholar]
  5. ChouetB.1986. Dynamics of a fluid‐driven crack in three dimensions by the finite‐different method. Journal of Geophysical Research91(B14), 13967–13992.
    [Google Scholar]
  6. ChouetB.1988. Resonance of a fluid‐driven crack: Radiation properties and implications for the source of long‐period events and harmonic tremor. Journal of Geophysical Research93(B5), 4375–4400.
    [Google Scholar]
  7. DvorkinJ., MavkoG. and NurA.1992. The dynamics of viscous compressible fluid in a fracture. Geophysics57(5), 720–726.
    [Google Scholar]
  8. FerrazziniV. and AkiK.1987. Slow waves trapped in a fluid‐filled infinite crack: Implications for volcanic tremor. Journal of Geophysical Research92, 9215–9223.
    [Google Scholar]
  9. JohnsonD.L.1989. Scaling function for dynamic permeability in porous media. Physical Review Letter63, 580.
    [Google Scholar]
  10. JohnsonD.L., KoplikJ. and DashenR.1987. Theory of dynamic permeability and tortuosity in fluid‐saturated porous media. Journal of Fluid Mechanics176, 379–402.
    [Google Scholar]
  11. HenryF.2005. Characterization of borehole fractures by the interface and body waves. PhD thesis, Delft University of Technology, The Netherlands.
  12. HornbyB.E., JohnsonD.L., WinklerK.W. and PlumbR.A.1989. Fracture evaluation using reflected Stoneley wave arrivals. Geophysics54(10), 1274–1288.
    [Google Scholar]
  13. KorneevV.2008. Slow waves in fractures filled with viscous fluid. Geophysics73(1), N1–N7.
    [Google Scholar]
  14. KorneevV.2010. Low‐frequency fluid waves in fractures and pipes. Geophysics75(6), N97–N107.
    [Google Scholar]
  15. KorneevV., BakulinA. and ZiatdinovS.2006. Tube‐wave monitoring of oil fields. 76th SEG meeting, New Orleans, USA, Expanded Abstracts, 374–378.
  16. KorneevV., ParraJ. and BakulinA.2005. Tube‐wave effects in cross‐well seismic data at Stratton Field. 75th SEG meeting, Houston, USA, Expanded Abstracts, 336–339.
  17. KostekS., JohnsonD.L., WinklerK.W. and HornbyB.E.1989. The interaction of tube waves with borehole fractures, Part II: Analytical models. Geophysics63(3), 809–815.
    [Google Scholar]
  18. KrauklisP.V.1962. About some low frequency oscillation of a liquid layer in elastic medium. Prikladnaya Matematika i Mekhanika26, 1111–1115 (in Russian).
    [Google Scholar]
  19. NaganoK. and NiitsumaH.1996. Crack stiffness from crack wave velocities. Geophysical Research Letters23(6), 689–692.
    [Google Scholar]
  20. PaigeR.W., RobertsJ.D.M., MurrayL.R. and MellorD.W.1992. In: Fracture Measurement Using Hydraulic Impedance Testing. SPE 24824, 68th Annual Technical Conference and Exhibition, Washington, DC, 4–7 October 1992.
  21. PailletF.L. and WhiteJ.E., 1982. Acoustic models of propagation in the borehole and their relationship to rock properties. Geophysics47, 1215–1228.
    [Google Scholar]
  22. PlyushchenkovB.D. and NikitinA.A. 2010. Borehole acoustic and electric Stoneley waves and permeability. Journal of Computational Acoustics (JCA)18(2), 1–29.
    [Google Scholar]
  23. PlyushchenkovB.D. and TurchaninovV.I.2006. Solution of Prides equations through potentials. International Journal of Modern Physics C17(6), 877–908.
    [Google Scholar]
  24. StoneleyR.1924. Elastic waves at the surface of separation of two solids. Proceedings of the Royal Society of London A106(October 1), 416–428.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Acoustics , Attenuation , Modelling , Seismics and Wave
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