Transport in Porous Media

, Volume 79, Issue 3, pp 359–375 | Cite as

Attenuated Wave Field in Fluid-Saturated Porous Medium with Excitations of Multiple Sources

  • Guoqing Wang
  • Liming DaiEmail author
  • Mingzhe Dong


This research addresses the investigation of an elastic wave field in a homogeneous and isotropic porous medium which is fully saturated by a Newtonian viscous fluid. A new methodology is developed for describing the wave field in the medium excited by multiple energy sources. To quantify the relative displacements between the fluid and solid of the medium, the governing equations of the elastic wave propagation are derived in the form of displacements specially. The velocities and attenuation of the waves are considered as functions of viscosity and frequency. Making use of the Hankel function and the moving-coordinate method, a model of the wave motion with multiple cylindrical wave sources is built. Making use of the model established in this research, the relative displacement between the fluid and the solid can be quantified, and the wave field in the porous media can then be determined with the given energy sources. Numerical simulations of cylindrical waves from multiple energy sources propagating in the porous medium saturated by viscous fluid are performed for demonstrating the practicability of the model developed.


Porous medium Wave propagation Multi-source wave model Viscous fluid Moving-coordinate method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andrews G.E., Askey R., Roy R.: Special Functions. Cambridge University Press, Cambridge (2001)Google Scholar
  2. Bardet J.P., Sayed H.: Velocity and attenuation of compression waves in nearly saturated soils. Soil. Dyn. Earthq. Eng. 12(7), 391–402 (1993). doi: 10.1016/0267-7261(93)90002-9 CrossRefGoogle Scholar
  3. Beresnev I.A., Johnson P.A.: Elastic-wave stimulation of oil production: a review of methods and results. Geophysics 59(6), 1000–1017 (1994). doi: 10.1190/1.1443645 CrossRefGoogle Scholar
  4. Berryman J.G.: Scattering by a spherical inhomogeneity in a fluid-saturated porous medium. J. Math. Phys. 26, 1408–1419 (1985). doi: 10.1063/1.526955 CrossRefGoogle Scholar
  5. Biot M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid, part I: low frequency range. J. Acoust. Soc. Am. 28, 168–178 (1956a). doi: 10.1121/1.1908239 CrossRefGoogle Scholar
  6. Biot M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid, part II: higher frequency range. J. Acoust. Soc. Am. 28, 179–191 (1956b). doi: 10.1121/1.1908241 CrossRefGoogle Scholar
  7. Biot M.A., Willis D.G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech 24, 594–601 (1957)Google Scholar
  8. Carcione J.M.: Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic and Porous Media. Pergamon, NY (2001)Google Scholar
  9. Gurevich B., Kelder O., Smeulders D.M.J.: Validation of the slow compressional wave in porous media: comparison of experiments and numerical simulations. Transp. Porous Media 36, 149–160 (1999). doi: 10.1023/A:1006676801197 CrossRefGoogle Scholar
  10. Hamidzadeh, H.R., Luo, A.C.J.: A semi-analytical for response of the surface of an elastic half-space subjected to vertical, harmonic, concentrated forces. The Symposium on Continuous Vibration and Control in ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, 5–10 Nov 2000. Vibration and Control of Continuous Systems, DE-vol. 107, pp. 39–44, (2000)Google Scholar
  11. Iassonov, P.P., Beresnev, I.A.: A model for enhanced fluid percolation in porous media by application of low-frequency elastic waves. J. Geophys. Res. 108(No. B3), (2003). doi: 10.1029/2001JB000683
  12. Lin, C.H., Lee, V.W., Trifunac, M.D.: On the reflection of waves in a poroelastic half-space saturated with non-viscous fluid. Report No. CE 01-04, Los Angeles, California (2001)Google Scholar
  13. Pao Y.H., Mow C.C.: Diffraction of Elastic Waves and Dynamic Stress Concentration. Crane-Russak Inc., New York (1973)Google Scholar
  14. Pham N.H., Carcione J.M., Helle H.B., Ursin B.: Wave velocities and attenuation of shaley sandstones as a function of pore pressure and partial saturation. Geophys. Prospect. 50, 615–627 (2002). doi: 10.1046/j.1365-2478.2002.00343.x CrossRefGoogle Scholar
  15. Plona T.J., Johnson D.L.: Acoustic properties of porous systems: I. Phenomenologicaldescription. In: Johnson, D.L., Sen, P.N. (eds) Physics and Chemistry of Porous Media, pp. 89–104. American Institute of Physics, New York (1984)Google Scholar
  16. Smeulders D.M.J., Eggels R.L.G., van Dongen M.E.H.: Dynamic permeability: reformulation of theory and new experimental and numerical data. J. Fluid Mech. 245, 211–227 (1992). doi: 10.1017/S0022112092000429 CrossRefGoogle Scholar
  17. Tsiklaur D., Beresnev I.: Properties of elastic waves in a non-Newtonian (Maxwell) fluid-saturated porous medium. Transp. Porous Media 53, 39–50 (2003). doi: 10.1023/A:1023559008269 CrossRefGoogle Scholar
  18. Vardoulakis I., Beskos D.: Dynamic behavior of nearly saturated porous media. Mech. Compos. Mater 5, 87–108 (1986)Google Scholar
  19. Wang G., Liu D.: Scattering of SH-wave by multiple circular cavities in half space. J. Earthq. Eng. Eng. Vib 1(1), 36–44 (2002). doi: 10.1007/s11803-002-0005-1 CrossRefGoogle Scholar
  20. White J.E.: Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40, 224–232 (1975). doi: 10.1190/1.1440520 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Mathematics and PhysicsNorth China Electric Power UniversityBeijingP. R. China
  2. 2.Industrial Systems EngineeringUniversity of ReginaReginaCanada
  3. 3.Department of Chemical and Petroleum EngineeringUniversity of CalgaryCalgaryCanada

Personalised recommendations