1887
Volume 67, Issue 8
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Propagation of harmonic plane waves is studied in a patchy‐saturated porous medium. Patchy distribution of the two immiscible fluids is considered in a porous frame with uniform skeletal properties. A composition of two types of patches, connected through continuous paths, constitutes a double‐porosity medium. Different compressibilities of pore‐fluids in two porous phases facilitate the wave‐induced fluid‐flow in this composite material. Constitutive relations are considered with frequency‐dependent complex elastic coefficients, which define the dissipative behaviour of porous aggregate due to the flow of viscous fluid in connected patches. Relevant equations of motion are solved to explain the propagation of three compressional waves and one shear wave in patchy‐saturated porous solids. A numerical example is solved to illustrate dispersion in phase velocity and quality factor of attenuated waves in patchy‐saturated porous materials. Role of fluid–solid inertial coupling in Darcy's law is emphasized to keep a check on the dispersion of wave velocities in the porous composite. Effects of patchy saturation on phase velocities and quality factors of attenuation are analysed using the double‐porosity formulation as well as the reduced single‐porosity equivalents.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12806
2019-09-10
2024-04-18
Loading full text...

Full text loading...

References

  1. AgersborgR., JohansenT.A. and JakobsenM.2009. Velocity variations in carbonate rocks due to dual porosity and wave‐induced fluid flow. Geophysical Prospecting57, 81–98.
    [Google Scholar]
  2. BiotM.A.1956. Theory of propagation of elastic waves in a fluid‐saturated porous solid. I. Low frequency range, II. Higher frequency range. Journal of the Acoustical Society of America28, 168–191.
    [Google Scholar]
  3. BiotM.A.1962. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics33, 1482–1498.
    [Google Scholar]
  4. BiotM.A. and WillisD.G.1957. The elastic coefficients of the theory of consolidation. Journal of Applied Mechanics24, 594–601.
    [Google Scholar]
  5. CadoretT., MavkoG. and ZinsznerB.1998. Fluid distribution effect on sonic attenuation in partially saturated limestones. Geophysics63, 154–160.
    [Google Scholar]
  6. DuttaN.C. and OdéH.1979a. Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model) – part I: Biot theory. Geophysics44, 1777–1788.
    [Google Scholar]
  7. DuttaN.C. and OdéH.1979b. Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model) – part II: results. Geophysics44, 1789–1805.
    [Google Scholar]
  8. DuttaN.C. and SeriffA.J.1979. On White's model of attenuation in rocks with partial gas saturation. Geophysics44, 1806–1812.
    [Google Scholar]
  9. GelinskyS. and ShapiroS.A.1997. Dynamic‐equivalent medium approach for thinly layered saturated sediments. Geophysical Journal International128, F1–F4.
    [Google Scholar]
  10. GurevichB. and LopatnikovS.L.1995. Velocity and attenuation of elastic waves in finely layered porous rocks. Geophysical Journal International121, 933–947.
    [Google Scholar]
  11. JohnsonD.L.2001. Theory of frequency dependent acoustics in patchy‐saturated porous media. Journal of the Acoustical Society of America110, 682–694.
    [Google Scholar]
  12. KnightR., DvorkinJ. and NurA.1998. Acoustic signatures of partial saturation. Geophysics63, 132–138.
    [Google Scholar]
  13. LebedevM., TomsJ., ClennellB., PervukhinaM., ShulakovaV., PatersonL., MüllerT.M., GurevichB. and WenzlauF.2009. Direct laboratory observation of patchy saturation and its effects on ultrasonic velocities. The Leading Edge28, 24–27.
    [Google Scholar]
  14. MurphyW.F. III.1982. Effects of partial water saturation on attenuation in Massilon sandstone and Vycor porous‐glass. Journal of the Acoustical Society of America71, 1458–1468.
    [Google Scholar]
  15. MurphyW.F. III.1984. Acoustic measures of partial gas saturation in tight sandstones. Journal of Geophysical Research89, 1549–1559.
    [Google Scholar]
  16. NorrisA.N.1993. Low‐frequency dispersion and attenuation in partially saturated rocks. Journal of the Acoustical Society of America94, 359–370.
    [Google Scholar]
  17. PrideS.R. and BerrymanJ.G.2003a. Linear dynamics of double‐porosity dual‐permeability materials. I. Governing equations and acoustic attenuation. Physical Review E68, 036603.
    [Google Scholar]
  18. PrideS.R. and BerrymanJ.G.2003b. Linear dynamics of double‐porosity dual‐permeability materials. II. Fluid transport equations. Physical Review E68, 036604.
    [Google Scholar]
  19. PrideS.R., BerrymanJ.G. and HarrisJ.M.2004. Seismic attenuation due to wave‐induced flow. Journal of Geophysical Research109, B01201.
    [Google Scholar]
  20. RubinoJ.G. and HolligerK.2012. Seismic attenuation and velocity dispersion in heterogeneous partially saturated porous rocks. Geophysical Journal International188, 1088–1102.
    [Google Scholar]
  21. SharmaM.D.2017. Wave propagation in double‐porosity dual‐permeability materials: velocity and attenuation. Advances in Water Resources106, 132–143.
    [Google Scholar]
  22. SkemptonA.W.1954. The pore‐pressure coefficients A and B. Geotechnique4, 143–147.
    [Google Scholar]
  23. TomsJ., MüllerT.M. and GurevichB.2006. Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks. Soil Dynamics and Earthquake Engineering.26, 548–565.
    [Google Scholar]
  24. TomsJ., MüllerT.M. and GurevichB.2007. Seismic attenuation in porous rocks with random patchy saturation. Geophysical Prospecting55, 671–678.
    [Google Scholar]
  25. WhiteJ.E.1975. Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics40, 224–232.
    [Google Scholar]
  26. WhiteJ.E., MikhaylovaN.G. and LyakhovitskyF.M.1975. Low‐frequency seismic waves in fluid‐saturated layered rocks. Physics of the Solid Earth11, 654–659.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12806
Loading
/content/journals/10.1111/1365-2478.12806
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Attenuation; Multicomponent; Reservoir geophysics; Velocity; Wave

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