1887
Volume 68, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Biot theory was based on two ideas: the coupling factor to quantify the kinetic energy of fluid and Darcy permeability to quantify the dissipation function. As Biot theory did not well predict attenuation of ultrasonic S wave, we modify the theory to better characterize the S wave attenuation. The range of the coupling factor is at first estimated in view of fluid mechanics. Application of the original theory to water‐saturated Boise sandstone and brine‐saturated Berea sandstone shows that the model prediction significantly underestimates the S wave attenuation ultrasonically measured. For this reason, we replace Darcy permeability with variable permeability to improve the fluid momentum equation. The new model yields predictions of phase velocity and the quality factor both close to the ultrasonic measurements. The reason why the improved model is superior to Biot theory is that variable permeability is based on the Stokes boundary layer at the fluid–solid interface, thus accurately quantifying the viscous stress between the two phases. Finally, the length scale of the viscous stress is calculated in the mesoscopic sense.

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2019-11-14
2024-04-26
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References

  1. AblowitzM.J. and FokasA.S.1997. Complex Variables: Introduction and Applications. Cambridge University Press, New York, NY.
    [Google Scholar]
  2. AuriaultJ.L., BoutinC. and GeindreauC.2009. Homogenization of Coupled Phenomena in Heterogeneous Media. John Wiley & Sons, New York, NY.
    [Google Scholar]
  3. BearJ.1972. Dynamics of Fluids in Porous Medium. Dover, New York.
    [Google Scholar]
  4. BerrymanJ.G. and WangF.W.1995. The elastic coefficients of double‐porosity models for fluid transport in jointed rock. Journal of Geophysical Research100, 24611–24627.
    [Google Scholar]
  5. BiotM.A.1956a. Theory of propagation of elastic waves in a fluid‐saturated porous solid I. Lower frequency range. Journal of Acoustic Society of America28, 168–178.
    [Google Scholar]
  6. BiotM.A.1956b. Theory of propagation of elastic waves in a fluid‐saturated porous solid II. Higher frequency range. Journal of Acoustic Society of America28, 179–191.
    [Google Scholar]
  7. BlairD.P.1990. A direction comparison between vibrational resonance and pulse transmission data for assessment of seismic attenuation in rock. Geophysics55, 55–60.
    [Google Scholar]
  8. BoutinC. and RoyerP.2015. On models of double porosity poroelastic media. Geophysical Journal International203, 1694–1725.
    [Google Scholar]
  9. DvorkinJ., MavkoG. and NurA.1995. Squirt flow in fully saturated rocks. Geophysics60, 97–107.
    [Google Scholar]
  10. GregoryA.R.1976. Fluid saturation effects on dynamic elastic properties of sedimentary rocks. Geophysics41, 895–921.
    [Google Scholar]
  11. JaegerJ.C., CookN.G.W. and ZimmermanR.2007. Fundamentals of Rock Mechanics, 4th edn.Wiley‐Blackwell, New York, NY.
    [Google Scholar]
  12. JohnsonD.L.2001. Theory of frequency dependent acoustics in patchy saturated porous media. Journal of Acoustic Society of America110, 682–694.
    [Google Scholar]
  13. JonesT. and NurA.1983. Velocity and attenuation in sandstone at elevated temperatures and pressures. Geophysical Research Letters10, 140–143.
    [Google Scholar]
  14. KunduP.K.1990. Fluid Mechanics. Academic Press, San Diego, CA.
    [Google Scholar]
  15. LiG., ZhangP. and SunJ.2017. A new model describing the interaction between fluid ressure wave in pores and P wave in rock matrix. Geophysics82, MR105–MR109.
    [Google Scholar]
  16. MavkoG., MukerjiT. and DvorkinJ.2009. The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media, 2nd edn.Cambridge University Press, New York, NY.
    [Google Scholar]
  17. MavkoG. and NurA.1975. Melt squirt in the asthenosphere. Journal of Geophysical Research80, 1444–1448.
    [Google Scholar]
  18. Mochizuki, S. (1982), Attenuation in partially saturated rocks. Journal of Geophysical Research87, 8598–8604.
    [Google Scholar]
  19. MurphyW.M., WinklerK.W. and KleinbergR.L.1984. Frame modulus reduction in sedimentary rocks: the effect of adsorption on grain contacts. Geophysical Research Letters11, 805–808.
    [Google Scholar]
  20. PrideS.R. and BerrymanJ.G.2003a. Linear dynamics of double porosity and dual‐permeability materials I. Governing equations and acoustic attenuation. Physical Review E68, 036603.
    [Google Scholar]
  21. PrideS. R. and BerrymanJ.G.2003b. Linear dynamics of double porosity and dual‐permeability materials II. Fluid transport equations. Physical Review E68, 036604.
    [Google Scholar]
  22. PrideS.R., BerrymanJ.G. and HarrisJ.M.2004. Seismic attenuation due to wave‐induced flow. Journal of Geophysical Research109, B01201.
    [Google Scholar]
  23. RickerN.1977. Transient Waves in Visco‐Elastic Media. Elsevier, Amsterdam.
    [Google Scholar]
  24. SchlichtingH.1968. Boundary Layer Theory. Springer, Berlin.
    [Google Scholar]
  25. Sharma, M.D.2017. Wave propagation in double‐porosity dual‐permeability materials: velocity and attenuation. Advances in Water Resources106, 132–143.
    [Google Scholar]
  26. ToksözM.N., JohnstonD.H. and TimurA.1979. Attenuation of seismic waves in dry and saturated rocks I. Laboratory measurements. Geophysics44, 681–690.
    [Google Scholar]
  27. WalkerE., and GloverP.2018. Measurements of the relationship between microstructure, pH, and the streaming and zeta potentials of sandstones. Transport in Porous Media121, 183–206.
    [Google Scholar]
  28. WangH.2000. Theory of Linear Poroelasticity –with Applications to Geomechanics and Hydrogeology. Princeton University Press, Princeton, NJ.
    [Google Scholar]
  29. Waters, K.H.1981. Reflection Seismology–A Tool for Energy Resource Exploration. Wiley, New York, NY.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Attenuation; Permeability; S waves

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