Advertisement

Dielectric and acoustic response of rocks

  • P. N. Sen
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 154)

Abstract

A self-similar model is developed to explain the conductivity, dielectric, and acoustic response of rocks. The model explicitly takes into account the correlations that lead to a zero percolation threshold, and gives the d.c. conductivity of rock (r(0) - σw(0)θm, with σw(0) the d.c. conductivity of the brine, θ the porosity. The exponent m depends on the grain shape. Using well-known results, it is shown that a small concentration, η, of plate-like grains of aspect ratio 8,8 < < 1, can give rise to a large (≈104) low-frequency dielectric constant εs, and explain its salinity and frequency dependences. The case 8<-q, η-0, corresponds to the well-known Maxwell-Wagner effect where a divergent e8 is accompanied with a conductivity threshold σ(0)-0. The case δ-0,,η-0,δ>,η gives rise to a new result, previously overlooked, with divergent es and non-zero σ(0). The velocity v of Biot second wave at high frequency and the fourth sound wave in 4He saturated plug are given by v - vF/n, VF being the velocity in the free fluid, n2=θσw,(0)/σ(0) (exact) =θ1-m (self-similar model).

Keywords

Dielectric Constant Effective Medium Theory Effective Dielectric Constant Acoustic Response Depolarization Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. N. Sen, C. Scala and M. H. Cohen, Geophysics 46, 781 (1981).Google Scholar
  2. 2.
    P. N. Sen, Soc. Petrol. Eng., Talk No. 9379 (Fall Meeting, 1980).Google Scholar
  3. 3.
    P. N. Sen, Geophysics (to appear in Dec. 1981 issue).Google Scholar
  4. 4.
    D. L. Johnson and P. N. Sen (to appear in Phys. Rev. B).Google Scholar
  5. 5.
    J. H. Scott, R. D. Carroll and D. R. Cunningham, J. Geo. Res. 72, 5101, (1967).Google Scholar
  6. 6.
    J. Ph. Poley., J. J. Nooteboom and P. J. DeWaal, Log Analyst, 8 (May, 1978).Google Scholar
  7. 7.
    D. L. Johnson, Appl. Phys. Lett., 37, 1065 (1980).Google Scholar
  8. 8.
    G. Schwarz, J. Phys. Chem., 66, 2636 (1962).Google Scholar
  9. 9.
    P. N. Sen, unpublished.Google Scholar
  10. 10.
    H. P. Schwan, N.Y. Acad. of Sci., 303 (1977).Google Scholar
  11. 11.
    J. Ziman, Models of Disorder, Cambridge U. Press (N.Y.), 1979.Google Scholar
  12. 12.
    J. A. Stratton, Electromagnetic Theory: McGraw Hill (N.Y.) 1941.Google Scholar
  13. 13.
    E. Schlomann, J. Appl. Phys. 33, 2825 (1962).Google Scholar
  14. 14.
    M. Hod, J. Math. Phys. 18, 487 (1977) and references therein.Google Scholar
  15. 15.
    P. P. Ewald, Ann. der Physik, 49, 1 (1916); C. W. Oseen, Ibid 48, 1 (1915).Google Scholar
  16. 16.
    J. C. Maxwell, A Treatise on Electricity and Magnetism (1873), Dover Edition (1954) N.Y.Google Scholar
  17. 17.
    H. C. Van de Hulst, Light Scattering by Small Particles, Wiley, N.Y. (1957).Google Scholar
  18. 18.
    A. K. Veinberg, Soviet Phys. Doklady 11, 593 (1967).Google Scholar
  19. 19.
    K. Mendelson and M. H. Cohen (unpublished).Google Scholar
  20. 20.
    D. A. G. Bruggeman, Ann. Phy. Lpz. 24, 636 (1935).Google Scholar
  21. 21.
    C. Kittel, Introduction to Solid State Physics, 5th Ed., John Wiley, N.Y. (1976), p. 430.Google Scholar
  22. 22.
    E. M. Purcell, Electricity and Magnetism, McGraw Hill, N.Y. (1963).Google Scholar
  23. 23.
    P. N. Sen and D. B. Tanner: Unpublished.Google Scholar
  24. 24.
    D. B. Tanner: Private communication; N. E. Russel, J. C. Garland and D. B. Tanner, Phys. Rev. B 23, 632 (1981).Google Scholar
  25. 25.
    Lord J. W. S. Rayleigh, Phil. Mag. 34, 481 (1892).Google Scholar
  26. 26.
    G. K. Batchelor, Ann. Rev. Fluid Mech. 6, 227 (1974).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • P. N. Sen
    • 1
  1. 1.Schlumberger-Doll ResearchRidgefield

Personalised recommendations