1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 53, Issue 5
  5. Article
Volume 53, Issue 5
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

An approach to determining the effective elastic moduli of rocks with double porosity is presented. The double‐porosity medium is considered to be a heterogeneous material composed of a homogeneous matrix with primary pores and inclusions that represent secondary pores. Fluid flows in the primary‐pore system and between primary and secondary pores are neglected because of the low permeability of the primary porosity. The prediction of the effective elastic moduli consists of two steps. Firstly, we calculate the effective elastic properties of the matrix with the primary small‐scale pores (matrix homogenization). The porous matrix is then treated as a homogeneous isotropic host in which the large‐scale secondary pores are embedded. To calculate the effective elastic moduli at each step, we use the differential effective medium (DEM) approach. The constituents of this composite medium – primary pores and secondary pores – are approximated by ellipsoidal or spheroidal inclusions with corresponding aspect ratios.

We have applied this technique in order to compute the effective elastic properties for a model with randomly orientated inclusions (an isotropic medium) and aligned inclusions (a transversely isotropic medium). Using the special tensor basis, the solution of the one‐particle problem with transversely isotropic host was obtained in explicit form.

The direct application of the DEM method for fluid‐saturated pores does not account for fluid displacement in pore systems, and corresponds to a model with isolated pores or the high‐frequency range of acoustic waves. For the interconnected secondary pores, we have calculated the elastic moduli for the dry inclusions and then applied Gassmann's tensor relationships. The simulation of the effective elastic characteristic demonstrated that the fluid flow between the connected secondary pores has a significant influence only in porous rocks containing cracks (flattened ellipsoids). For pore shapes that are close to spherical, the relative difference between the elastic velocities determined by the DEM method and by the DEM method with Gassmann's corrections does not exceed 2%. Examples of the calculation of elastic moduli for water‐saturated dolomite with both isolated and interconnected secondary pores are presented. The simulations were verified by comparison with published experimental data.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.2005.00498.x
2005-08-15
2024-04-20

  • From This Site

    /content/journals/10.1111/j.1365-2478.2005.00498.x
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. AuriaultJ.L. and BoutinC.1992. Deformable porous media with double porosity. Quasistatic: 1. Coupling effect. Transport in Porous Media7, 63–82.
    [Google Scholar]
  2. BagrintsevaK.I.1999. Conditions of generation and properties of carbonate reservoirs of oil and gas . RGGU, Moscow (in Russian).
     [Google Scholar]
  3. BarrenblattG.I., ZheltovI.P. and KochinaI.N.1960. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. Prikladnaya Matematica y Mechanica24, 852–864. (English translation in Soviet Applied Mathematics and Mechanics 24 , 1286–1303).
     [Google Scholar]
  4. BergeP.A., BerrymanJ.G. and BonnerB.P.1993. Influence of microstructure on rock elastic properties. Geophysical Research Letters20, 2619–2622.
    [Google Scholar]
  5. BerrymanJ.G.1980. Long wavelength propagation in composite elastic media. Journal of the Acoustical Society of America68, 1809–1831.
    [Google Scholar]
  6. BerrymanJ.G.1992. Single‐scattering approximations for coefficients in Biot's equations of poroelasticity. Journal of the Acoustical Society of America91, 551–571.
    [Google Scholar]
  7. BerrymanJ.G., PrideS.R. and WangH.F.2002. A differential scheme for elastic properties of rocks with dry or saturated cracks. Geophysical Journal International151, 597–611.
    [Google Scholar]
  8. BerrymanJ.G. and WangH.F.2000. Elastic wave propagation and attenuation in a double‐porosity dual‐permeability medium. International Journal of Rock Mechanics and Mining Sciences37, 63–78.
    [Google Scholar]
  9. BiotM.A.1962. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics33, 1482–1498.
    [Google Scholar]
  10. BrownR. and KorringaJ.1975. On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics40, 608–616.
    [Google Scholar]
  11. BruggemanD.A.1935. Berechnung verschidener physikalischer konstanten von heterogenen substanzen. Annalen Physical Leipzig24, 636–679.
    [Google Scholar]
  12. ChinhP.D.2000. Hierarchical unsymmetrical effective medium approximations for the electrical conductivity of water‐saturated porous rocks. Zeitschrift für Angewandte Mathematik und Physik51, 135–142.
    [Google Scholar]
  13. ClearyM.P., ChenI. and LeeS.M.1980. Self‐consistent techniques for heterogeneous media. American Society of Civil Engineers Journal of Engineering Mechanics106, 861–887.
    [Google Scholar]
  14. EshelbyJ.D.1957. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society, London A241, 376–396.
    [Google Scholar]
  15. GassmannF.1951. Über die Elastizität poröser Medien. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich96, 1–23.
    [Google Scholar]
  16. HashinZ.1988. The differential scheme and its application to cracked materials. Journal of Mechanics and Physics of Solids36, 719–734.
    [Google Scholar]
  17. HashinZ. and ShtrikmanS.A.1962. Variational approach to the elastic behavior of multiphase materials. Journal of Mechanics and Physics of Solids11, 127–140.
    [Google Scholar]
  18. HornbyB.E., SchwartzL.M. and HudsonJ.A.1994. Anisotropic effective‐medium modeling of elastic properties of shales. Geophysics59, 1570–1583.
    [Google Scholar]
  19. HudsonJ.A.1980. Overall properties of a cracked solid. Mathematical Proceedings of the Cambridge Philosophical Society88, 371–384.
    [Google Scholar]
  20. HudsonJ.A.1981. Wave speed attenuation of elastic waves in materials containing cracks. Geophysical Journal of the Royal Astronomical Society64, 133–150.
    [Google Scholar]
  21. HudsonJ.A., LiuE. and CrampinS.1996. The mechanical properties of materials with interconnected cracks and pores. Geophysical Journal International124, 105–112.
    [Google Scholar]
  22. HudsonJ.A., PointerY. and LiuE.2001. Effective‐medium theories for fluid‐saturated materials with aligned cracks. Geophysical Prospecting49, 509–522.
    [Google Scholar]
  23. JacobsenM., HudsonJ.A., MinshullT.A. and SinghS.C.2000. Elastic properties of hydrate‐bearing sediments using effective medium theory. Journal of Geophysical Research105, 561–577.
    [Google Scholar]
  24. KanaunS.K. and LevinV.M.1994. Effective field method in mechanics of matrix composite materials. In: Advances in Mathematical Modeling of Composite Materials , pp. 1–58. World Scientific, Singapore .
    [Google Scholar]
  25. KazatchenkoE. and MarkovM.2003. Analysis of models for calculating the elastic characteristics of the cemented sedimentary rocks. Geofizika1, 20–25.
    [Google Scholar]
  26. KazatchenkoE., MarkovM. and MousatovA.2004a. Joint modeling of acoustic velocities and electrical conductivity from unified microstructure of rocks. Journal of Geophysical Research109, 2003JB002443, p. 8.
    [Google Scholar]
  27. KazatchenkoE., MarkovM. and MousatovA.2004b. Joint inversion of acoustic and resistivity data for carbonate microstructure evaluation. Petrophysics45(2), 130–140.
    [Google Scholar]
  28. KrönerE.1953. Das fundamentalintegral der anisotropen elastischen differentialgleichungen. Zeitschrift für Physik136, 402–410.
    [Google Scholar]
  29. KusterG. and ToksözN.1974. Velocity and attenuation of seismic waves in two‐phase media: 1. Theoretical formulations. Geophysics39, 587–606.
    [Google Scholar]
  30. Le RavalecM. and GuéguenY.1996. High and low frequency elastic moduli for a saturated porous/cracked rock. Differential self consistent and poroelastic theories. Geophysics61, 1080–1094.
    [Google Scholar]
  31. LinS. and MuraT.1973. Elastic fields of inclusions in anisotropic media. Physics Status Solidi5, 281–285.
    [Google Scholar]
  32. MavkoG., MukerjiT. and DvorkinJ.1998. The Rock Physics Handbook Tools for Seismic Analysis in Porous Media . Cambridge University Press.
    [Google Scholar]
  33. MendelsonK.S. and CohenM.N.1982. The effect of grain anisotropy on the electrical properties of isotropic sedimentary rocks. Geophysics47, 257–263.
    [Google Scholar]
  34. Nemat‐NasserS. and HoriM.1993. Micromechanics: Overall Properties of Heterogeneous Materials . North Holland Publishing Co.
    [Google Scholar]
  35. NorrisA.1985. A differential scheme for the effective moduli of composites. Mechanics of Materials4, 1–16.
    [Google Scholar]
  36. RathoreJ.S., FjaerE., HoltR.M. and RenlieL.1995. P‐ and S‐wave anisotropy of a synthetic sandstone with controlled crack geometry. Geophysical Prospecting43, 711–728.
    [Google Scholar]
  37. SaegerE.H. and ShapiroS.A.2002. Effective velocities in fractured media: a numerical study using the rotated staggered finite‐difference grid. Geophysical Prospecting50, 183–194.
    [Google Scholar]
  38. SenP., ScalaC. and CohenM.H.1981. A self‐similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. Geophysics46, 781–796.
    [Google Scholar]
  39. SeymourR.H., ZimmermanR.W. and WhiteR.E.2003. Multiple porosity differential effective medium models – improvements and approximations. 65th EAGE conference, Stavanger , Norway , Expanded Abstracts, Paper E‐18.
  40. ShengP.1991. Consistent modeling of the electrical and elastic properties of sedimentary rocks. Geophysics56, 1236–1243.
    [Google Scholar]
  41. ThomsenL.1995. Elastic anisotropy due to aligned cracks in porous rocks. Geophysical Prospecting43, 805–829.
    [Google Scholar]
  42. TodS.R.2003. An anisotropic fractured poroelastic effective medium theory. Geophysical Journal International155, 1006–1020.
    [Google Scholar]
  43. VaculenkoA.A.1998. On the effective properties and strength of ceramic composites. Mechanics of Solids6, 50–71.
    [Google Scholar]
  44. WilsonR.K. and AifantisE.C.1982. On the theory of consolidation with double porosity. International Journal of Engineering Science20, 1009–1035.
    [Google Scholar]
  45. WuT.T.1966. The effect of inclusion shape on the elastic moduli of a two‐phase material. International Journal of Solids Structures2, 1–8.
    [Google Scholar]
  46. XuS. and WhiteR.E.1995. A new velocity model for clay–sand mixtures. Geophysical Prospecting43, 91–118.
    [Google Scholar]
  47. YooM.H.1974. Elastic interaction of small defects and defect clusters. Physics Status Solidi (B)61, 411–418.
    [Google Scholar]
  48. ZimmermanR.D.1985. The effect of microcracks on the elastic moduli of brittle materials. Journal of Material Science Letters4, 1457–1460.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.2005.00498.x
Loading
Elastic properties of double‐porosity rocks using the differential effective medium model
Geophysical Prospecting 53, 733 (2005); https://doi.org/10.1111/j.1365-2478.2005.00498.x
/content/journals/10.1111/j.1365-2478.2005.00498.x
/content/journals/10.1111/j.1365-2478.2005.00498.x
Loading

Data & Media loading...

  • Article Type: Research Article

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