1887
Volume 63, Issue 2
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Wave‐induced oscillatory fluid flow in the vicinity of inclusions embedded in porous rocks is one of the main causes for ‐wave dispersion and attenuation at seismic frequencies. Hence, the ‐wave velocity depends on wave frequency, porosity, saturation, and other rock parameters. Several analytical models quantify this wave‐induced flow attenuation and result in characteristic velocity–saturation relations. Here, we compare some of these models by analyzing their low‐ and high‐frequency asymptotic behaviours and by applying them to measured velocity–saturation relations. Specifically, the Biot–Rayleigh model considering spherical inclusions embedded in an isotropic rock matrix is compared with White's and Johnson's models of patchy saturation. The modeling of laboratory data for tight sandstone and limestone indicates that, by selecting appropriate inclusion size, the Biot‐Rayleigh predictions are close to the measured values, particularly for intermediate and high water saturations.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12196
2014-11-14
2024-04-25
Loading full text...

Full text loading...

References

  1. AchenbachJ.1987. Wave Propagation in Elastic Solids. North Holland Publishing, Amsterdam.
    [Google Scholar]
  2. BaJ., CaoH., CarcioneJ.M., TangG., YanX.F., SunW.T.et al. 2013. Multiscale rock‐physics templates for gas detection in carbonate reservoirs. Journal of Applied Geophysics93, 77–82.
    [Google Scholar]
  3. BaJ., CarcioneJ.M., CaoH., DuQ.Z., YuanZ.Y. and LuM.H.2012. Velocity dispersion and attenuation of P waves in partially‐saturated rocks: wave propagation equations in double‐porosity medium. Chinese Journal of Geophysics55, 219–231.
    [Google Scholar]
  4. BaJ., CarcioneJ.M. and NieJ.X.2011. Biot‐Rayleigh theory of wave propagation in double‐porosity media. Journal of Geophysical Research116, B06202.
    [Google Scholar]
  5. BaJ., NieJ.X., CaoH. and YangH.Z.2008. Mesoscopic fluid flow simulation in double‐porosity rocks. Geophysical Research Letter35, L04303.
    [Google Scholar]
  6. BacriJ.‐C. and SalinD.1986. Sound velocity of a sandstone with oil and brine at different concentrations. Geophysical Research Letters13, 326–328.
    [Google Scholar]
  7. BerrymanJ.G.1979. Theory of elastic properties of composite materials. Applied Physics Letters35, 856–858.
    [Google Scholar]
  8. BerrymanJ.G.1980. Confirmation of Biot's theory. Applied Physics Letters37, 382–384.
    [Google Scholar]
  9. BiotM.A.1962. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics33, 1482–1498.
    [Google Scholar]
  10. CadoretT., MarionD. and ZinsznerB.1995. Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones. Journal of Geophysical Research100, 9789–9803.
    [Google Scholar]
  11. CadoretT., MavkoG. and ZinsznerB.1998. Fluid distribution effect on sonic attenuation in partially saturated limestones. Geophysics63, 154–160.
    [Google Scholar]
  12. CarcioneJ.M.2007. Wave Fields in Real Media: Theory and Numerical Simulation of Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media. Elsevier.
    [Google Scholar]
  13. CarcioneJ.M. and HelleH.B.2002. Rock physics of geopressure and prediction of abnormal pore fluid pressures using seismic data. CSEG Recorder27, 8–32.
    [Google Scholar]
  14. CarcioneJ.M. and PicottiS.2006. P‐wave seismic attenuation by slow‐wave diffusion: effects of inhomogeneous rock properties. Geophysics71, O1–O8.
    [Google Scholar]
  15. CaspariE., MüllerT.M. and GurevichB.2011. Time‐lapse sonic logs reveal patchy CO2 saturation in‐situ. Geophysical Research Letters38, L13301.
    [Google Scholar]
  16. DuttaN.C. and OdéH.1979a. Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model).1. Biot theory. Geophysics44, 1777–1788.
    [Google Scholar]
  17. DuttaN.C. and OdéH.1979b. Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model).2. Results. Geophysics44, 1789–1805.
    [Google Scholar]
  18. DuttaN.C. and SeriffA.J.1979. On White's model of attenuation in rocks with partial gas saturation. Geophysics44, 1806–1812.
    [Google Scholar]
  19. DvorkinJ., MavkoG. and NurA.1995. Squirt Flow in fully saturated rocks. Geophysics60, 97–107.
    [Google Scholar]
  20. DvorkinJ. and NurA.1993. Dynamic poroelasticity ‐ a unified model with the squirt and the Biot mechanisms. Geophysics58, 524–533.
    [Google Scholar]
  21. HillR.1963. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids11, 357–372.
    [Google Scholar]
  22. HillR.1964. Theory of mechanical properties of fibre‐strengthened materials: I. elastic behaviour. Journal of the Mechanics and Physics of Solids12, 199–212.
    [Google Scholar]
  23. JohnsonD.L.1986. Recent developments in the acoustic properties of porous media. In: Frontiers in Physical Acoustics XCIII (ed D.Sette ), pp. 255–290. Elsevier, New York.
    [Google Scholar]
  24. JohnsonD.L.2001. Theory of frequency dependent acoustics in patchy‐saturated porous media. Journal of the Acoustical Society of America110, 682–694.
    [Google Scholar]
  25. LebedevM., Toms‐StewartJ., ClennellB., PervukhinaM., ShulakovaV., PatersonL.et al. 2009. Direct laboratory observation of patchy saturation and its effects on ultrasonic velocities. The Leading Edge28, 24–27.
    [Google Scholar]
  26. MavkoG., MukerjiT. and DvorkinJ.2009. The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media . Cambridge University Press.
  27. MüllerT.M. and GurevichB.2004. One‐dimensional random patchy saturation model for velocity and attenuation in porous rocks. Geophysics69, 1166–1172.
    [Google Scholar]
  28. MüllerT.M., GurevichB. and LebedevM.2010. Seismic wave attenuation and dispersion resulting from wave‐induced flow in porous rocks – a review. Geophysics75, A147–A164.
    [Google Scholar]
  29. RayleighL.1917. On the pressure developed in a liquid during the collapse of a spherical cavity. Philosophical Magazine34, 94–98.
    [Google Scholar]
  30. RuizF. and Ilgar AzizovR.2011. Fluid substitution in tight shale using the soft‐porosity model. 81st SEG annual meeting, San Antonio, USA, 2272–2276.
  31. SunW., BaJ., MüllerT.M., CarcioneJ.M., CaoH., DuQ.et al. 2012. P‐Wave dispersion and attenuation in patchy‐saturated rocks: White, Dutta, Johnson and Biot‐Rayleigh theories . 74th EAGE in Copenhagen, Copenhagen, Denmark.
    [Google Scholar]
  32. TomsJ., MüllerT.M., CizR. and GurevichB.2006. Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks. Soil Dynamics and Earthquake Engineering26, 548–565.
    [Google Scholar]
  33. TomsJ., MüllerT.M. and GurevichB.2007. Seismic attenuation in porous rocks with random patchy saturation. Geophysical Prospecting55, 671–678.
    [Google Scholar]
  34. WhiteJ.E.1975. Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics40, 224–232.
    [Google Scholar]
  35. WhiteJ.E., MikhaylovaN.G. and LyakhovitskiyF.M.1975. Low‐frequency seismic waves in fluid‐saturated layered rocks. The Journal of the Acoustical Society of America57, S30.
    [Google Scholar]
  36. WoodA.B.1955. A Textbook of Sound; Being an Account of the Physics of Vibrations with Special Reference to Recent Theoretical and Technical Developments. Macmillan, New York.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12196
Loading
/content/journals/10.1111/1365-2478.12196
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error