1887
Volume 65, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Analytical models are provided that describe how the elastic compliance, electrical conductivity, and fluid‐flow permeability of rocks depend on stress and fluid pressure. In order to explain published laboratory data on how seismic velocities and electrical conductivity vary in sandstones and granites, the models require a population of cracks to be present in a possibly porous host phase. The central objective is to obtain a consistent mean‐field analytical model that shows how each modeled rock property depends on the nature of the crack population. The crack populations are described by a crack density, a probability distribution for the crack apertures and radii, and the averaged orientation of the cracks. The possibly anisotropic nature of the elasticity, conductivity, and permeability tensors is allowed for; however, only the isotropic limit is used when comparing to laboratory data. For the transport properties of conductivity and permeability, the percolation effect of the crack population linking up to form a connected path across a sample is modeled. However, this effect is important only in crystalline rock where the host phase has very small conductivity and permeability. In general, the importance of the crack population to the transport properties increases as the host phase becomes less conductive and less permeable.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12435
2016-08-30
2024-03-28
Loading full text...

Full text loading...

References

  1. ArchieG. E.1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Transactions of the AIME146, 54–62.
    [Google Scholar]
  2. BatzleM. and WangZ.1992. Seismic properties of pore fluids. Geophysics57, 1396–1408.
    [Google Scholar]
  3. BenvenisteY.1987. A new approach to the application of Mori—Tanaka theory in compositematerials. Mechanics of Materials6, 147–157.
    [Google Scholar]
  4. BerrymanJ.G.2016. Role of fluid injection in the evolution of fractured reservoirs. International Journal of Engineering Science103, 45–58.
    [Google Scholar]
  5. 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]
  6. BiotM.A.1956. Theory of propagation of elastic waves in a fluid‐saturated porous solid. I. Low‐frequency range. The Journal of the Acoustical Society of America28, 168–178.
    [Google Scholar]
  7. BiotM.A. and WillisD.G.1957. The elastic coefficients of the theory of consolidation. Journal of Applied Mechanics24, 594–601.
    [Google Scholar]
  8. BraceW., OrangeA. and MaddenT.1965. The effect of pressure on the electrical resistivity of water‐saturated crystalline rocks. Journal of Geophysical Research70, 5669–5678.
    [Google Scholar]
  9. CastagnaJ.P., BatzleM.L. and EastwoodR.L.1985. Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks. Geophysics50, 571–581.
    [Google Scholar]
  10. ChengC.H. and ToksözM.N.1979. Inversion of seismic velocities for the pore aspect ratio spectrum of a rock. Journal of Geophysical Research84, 7533–7543.
    [Google Scholar]
  11. DaleyT.M., SchoenbergM.A., RutqvistJ., and NiheiK.T.2006. Fractured reservoirs: an analysis of coupled elastodynamic and permeability changes from pore‐pressure variation. Geophysics71, O33–O41.
    [Google Scholar]
  12. FortinJ., SanchitsS., DresenG. and GuegenY.2009. Acoustic emissions monitoring during inelastic deformation of porous sandstone: comparison of three modes of deformation. Pure and Applied Geophysics.
    [Google Scholar]
  13. GangiA. F.1978. Variation of whole and fractured porous rock permeability with confining pressure. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts15, 249–257.
    [Google Scholar]
  14. GarbocziE., SnyderK., DouglasJ. and ThorpeM.1995. Geometrical percolation threshold of overlapping ellipsoids. Physical Review E52, 819–828.
    [Google Scholar]
  15. GarbocziE., ThorpeM., DevriesM. and DayA.1991. Universal conductivity curve for a plane containing random holes. Physical Review A43, 6473–6482.
    [Google Scholar]
  16. GassmannF.1951. Über die Elastizität poröser medien. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich96, 1–23.
    [Google Scholar]
  17. GrechkaV. and KachanovM.2006a. Effective elasticity of rocks with closely spaced and intersecting cracks. Geophysics71, D85–D91.
    [Google Scholar]
  18. GrechkaV. and KachanovM.2006b. Influence of crack shape on effective elasticity of fractured rocks. Geophysics71, D93–D105.
    [Google Scholar]
  19. HanD., NurA. and MorganD.1986. Effects of porosity and clay content on wave velocities in sandstones. Geophysics51, 2093–2107.
    [Google Scholar]
  20. JohnsonD.L., KoplikJ. and SchwartzL.M.1986. New pore‐size parameter characterizing transport in porous media. Physical Review Letters57, 2564–2567.
    [Google Scholar]
  21. KaselowA. and ShapiroS.A.2004. Stress sensitivity of elastic moduli and electrical resistivity in porous rocks. Journal of Geophysics and Engineering1, 1–11.
    [Google Scholar]
  22. KestinJ., KhalifaE. and CorreiaR.1981. Tables of the dynamic and kinematic viscosity of aqueous NaCl solutions in the temperature range 20–150°C and the pressure range 0.1–35 MPa. Journal of Physical and Chemical Reference Data10, 71–87.
    [Google Scholar]
  23. KestinJ. and ShanklandR.1984. Viscosity of aqueous NaCl solutions in the temperature range 20–100°C and in the pressure range 0.1–30 MPa. International Journal of Thermophysics5, 241–263.
    [Google Scholar]
  24. KirkpatrickS.1973. Percolation and conduction. Reviews of Modern Physics45, 574–588.
    [Google Scholar]
  25. LiuH.‐H., RutqvistJ. and BerrymanJ.G.2009. On the relationship between stress and elastic strain for porous and fractured rocks. International Journal of Rock Mechanics and Mining Sciences46, 289–296.
    [Google Scholar]
  26. LiuH.‐H., WeiM.‐Y. and RutqvistJ.2013. Normal‐stress dependence of fracture hydraulic properties including two‐phase flow properties. Hydrogeology Journal21, 371–382.
    [Google Scholar]
  27. MassonY.J., PrideS.R. and NiheiK.T.2006. Finite‐difference modeling of Biot's poroelastic equations at seismic frequencies. Journal of Geophysical Research111, B10305.
    [Google Scholar]
  28. MoriT. and TanakaK.1973. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica21, 571–574.
    [Google Scholar]
  29. OdaM.1985. Permeability tensor for discontinuous rock mass. Geotechnique35, 483–495.
    [Google Scholar]
  30. PatersonM.S. and WongT.F.2005. Experimental Rock Deformation –The Brittle Field. Springer.
    [Google Scholar]
  31. Pride, S.1994. Governing equations for the coupled electromagnetics and acoustics of porous media. Physical Review B, 50, 15678–15696.
    [Google Scholar]
  32. PrideS.R.2005. Relationships between seismic and hydrological properties. In: Hydrogeophysics, pp. 253–291. Springer.
    [Google Scholar]
  33. PrideS.R. and BerrymanJ.2009. Goddard rattler‐jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs. Acta Mechanica205, 185–196.
    [Google Scholar]
  34. SayersC. and den BoerL.2012. Characterizing production‐induced anisotropy of fractured reservoirs having multiple fracture sets. Geophysical Prospecting60, 919–939.
    [Google Scholar]
  35. SayersC. and KachanovM.1995. Microcrack‐induced elastic wave anisotropy of brittle rocks. Journal of Geophysical Research100, 4149–4156.
    [Google Scholar]
  36. SchoenbergM.2002. Time‐dependent anisotropy induced by pore pressure variation in fractured rock. Journal of Seismic Exploration11, 83–105.
    [Google Scholar]
  37. StrattonJ.A.1941. Electromagnetic Theory. McGraw‐Hill.
    [Google Scholar]
  38. ThompsonA.H., KatzA.J. and KrohnC.E.1987. The microgeometry and transport properties of sedimentary rock. Advances in Physics36, 625–694.
    [Google Scholar]
  39. TorquatoS.2002. Random Heterogeneous Materials. Springer.
    [Google Scholar]
  40. WaltonK.1987. The effective elastic moduli of a random packing of spheres. Journal of the Mechanics and Physics of Solids35, 213–226.
    [Google Scholar]
  41. WybleD.O.1958. Effect of applied pressure on the conductivity, porosity and permeability of sandstones. Journal of Petroleum Technology10, 57–59.
    [Google Scholar]
  42. YiY. and TawerghiE.2009. Geometric percolation thresholds of interpenetrating plates in threedimensional space. Physical Review E79(4), 041134.
    [Google Scholar]
  43. ZhangY., SayersC. and AdachiJ.2009. The use of effective medium theories for seismic wave propagation and fluid flow in fractured reservoirs under applied stress. Geophysical Journal International177, 205–221.
    [Google Scholar]
  44. ZhuW., MontesiG.J. and WongT.‐F.2002. Effects of stress on the anisotropic development of permeability during mechanical compaction of porous sandstones. Geological Society, London, Special Publications200, 119–136.
    [Google Scholar]
  45. ZimmermanR.W., SomertonW. and KingM.S.1986. Compressibility of porous rocks. Journal of Geophysical Research91, 12765–12777.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12435
Loading
/content/journals/10.1111/1365-2478.12435
Loading

Data & Media loading...

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