1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 62, Issue 6
  5. Article
Volume 62, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

In this work, we assess the use of explicit methods for estimating the effective conductivity of anisotropic fractured media. Explicit methods are faster and simpler to use than implicit methods but may have a more limited range of validity. Five explicit methods are considered: the Maxwell approximation, the T‐matrix method, the symmetric and asymmetric weakly self‐consistent methods, and the weakly differential method, where the two latter methods are novelly constructed in this paper. For each method, we develop simplified expressions applicable to flat spheroidal “penny‐shaped” inclusions. The simplified expressions are accurate to the first order in the ratio of fracture thickness to fracture diameter. Our analysis shows that the conductivity predictions of the methods fall within known upper and lower bounds, except for the T‐matrix method at high fracture densities and the symmetric weakly self‐consistent method when applied to very thin fractures. Comparisons with numerical results show that all the methods give reliable estimates for small fracture densities. For high fracture densities, the weakly differential method is the most accurate if the fracture geometry is non‐percolating or the fracture/matrix conductivity contrast is small. For percolating conductive fracture networks, we have developed a scaling relation that can be applied to the weakly self‐consistent methods to give conductivity estimates that are close to the results from numerical simulations.

Copyright © 2014 European Association of Geoscientists & Engineers © 2014 European Association of Geoscientists & Engineers
Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12173
2014-09-16
2024-04-20

  • From This Site

    /content/journals/10.1111/1365-2478.12173
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. BarthélémyJ.‐F.2008. Effective permeability of media with a dense network of long and micro fractures. Transport in Porous Media76, 153–178.
     [Google Scholar]
  2. BerrymanJ.G. and BergeP.A.1996. Critique of two explicit schemes for estimating elastic properties of multiphase composites. Mechanics of Materials22, 149–164.
     [Google Scholar]
  3. BerrymanJ.G. and HoverstenG.M.2013. Modelling electrical conductivity for earth media with macroscopic fluid‐filled fractures. Geophysical Prospecting61, 471–493.
     [Google Scholar]
  4. BogdanovI., MourzenkoV., ThovertJ.‐F. and AdlerP.2007. Effective permeability of fractured porous media with power‐law distribution of fracture sizes. Physical Review E76, 036309.
     [Google Scholar]
  5. CacasM.C., DanielJ.M. and LetouzeyJ.2001. Nested geological modelling of naturally fractured reservoirs. Petroleum Geoscience7, S43–S52.
     [Google Scholar]
  6. CorlessR.M., GonnetG.H., HareD.E.G., JeffreyD.J. and KnuthD.E.1996. On the Lambert W function. Advances in Computational Mathematics5, 329–359.
     [Google Scholar]
  7. DuanH., KarihalooB., WangJ. and YiX.2006. Effective conductivities of heterogeneous media containing multiple inclusions with various spatial distributions. Physical Review B73, 113.
     [Google Scholar]
  8. FokkerP.2001. General anisotropic effective medium theory for the effective permeability of heterogeneous reservoirs. Transport in Porous Media44, 205–218.
     [Google Scholar]
  9. HuG. and WengG.2000. The connections between the double‐inclusion model and the Ponte Castañeda‐Willis, Mori‐Tanaka, and Kuster‐Toksoz models. Mechanics of Materials32, 495–503.
     [Google Scholar]
  10. JakobsenM.2007. Effective hydraulic properties of fractured reservoirs and composite porous media. Journal of Seismic Exploration16, 199–224.
     [Google Scholar]
  11. JakobsenM., SkjervheimJ.A. and AanonsenS.I.2007. Characterization of fractured reservoirs by effective medium modelling and joint inversion of seismic and production data. Journal of Seismic Exploration16, 175–197.
     [Google Scholar]
  12. LandauL.D. and LifshitzE.M.1960. Electrodynamics of Continuous Media. Pergamon Press.
     [Google Scholar]
  13. MiltonG.W.2002. The Theory of Composites. Cambridge University Press.
     [Google Scholar]
  14. MoriT. and TanakaK.1973. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica21, 571–574.
     [Google Scholar]
  15. MourzenkoV., ThovertJ.‐F. and AdlerP.2005. Percolation of three‐dimensional fracture networks with power‐law size distribution. Physical Review E72, 036103.
     [Google Scholar]
  16. MourzenkoV.V., ThovertJ.‐F. and AdlerP.M.2011. Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities. Physical Review E84, 036307.
     [Google Scholar]
  17. Ponte Casta nedaP. and WillisJ.R.1995. The effect of spatial distribution on the effective behavior of composite materials and cracked media. Journal of the Mechanics and Physics of Solids43, 1919–1951.
     [Google Scholar]
  18. PozdniakovS. and TsangC.‐F.2004. A self‐consistent approach for calculating the effective hydraulic conductivity of a binary, heterogeneous medium. Water Resources Research40, W05105.
     [Google Scholar]
  19. SævikP.N., BerreI., JakobsenM. and LienM.2012. Electrical conductivity of fractured media: A computational study of the self‐consistent method. SEG Technical Program Expanded Abstracts 2012, 1–5. Society of Exploration Geophysicists.
     [Google Scholar]
  20. SævikP.N., BerreI., JakobsenM. and LienM.2013. A 3D computational study of effective medium methods applied to fractured media. Transport in Porous Media100(1), 115–142.
     [Google Scholar]
  21. TorquatoS.2002. Random heterogeneous materials. Interdisciplinary Applied Mathematics16.
     [Google Scholar]
  22. WillisJ.1977. Bounds and self‐consistent estimates for the overall properties of anisotropic composites. Journal of the Mechanics and Physics of Solids25, 185–202.
     [Google Scholar]
  23. WuT.T.1966. The effect of inclusion shape on the elastic moduli of a two‐phase material. International Journal of Solids and Structures2, 1–8.
     [Google Scholar]
  24. YiY. and TawerghiE.2009. Geometric percolation thresholds of interpenetrating plates in three‐dimensional space. Physical Review E79, 1–6.
     [Google Scholar]
  25. YiY.B. and EsmailK.2012. Computational measurement of void percolation thresholds of oblate particles and thin plate composites. Journal of Applied Physics111, 124903.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12173
Loading
Anisotropic effective conductivity in fractured rocks by explicit effective medium methods
Geophysical Prospecting 62, 1297 (2014); https://doi.org/10.1111/1365-2478.12173
/content/journals/10.1111/1365-2478.12173
/content/journals/10.1111/1365-2478.12173
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Anisotropy; Mathematical formulation; Numerical study; Resistivity; Rock physics

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