Pore‐scale modelling of complex conductivity of saturated granular materials

References

1. AndräH., CombaretN., DvorkinJ., GlattE., HanJ., KabelM. et al. 2013a. Digital rock physics benchmarks—Part I: Imaging and segmentation.Computers & Geosciences50, 25–32.
   [Google Scholar]
2. AndräH., CombaretN., DvorkinJ., GlattE., HanJ., KabelM. et al. 2013b. Digital rock physics benchmarks—Part II: Computing effective properties.Computers & Geosciences50, 33–43.
   [Google Scholar]
3. ArchieG.E.1942. The electrical resistivity log as an aid in determining some reservoir characteristics.Petroleum Transactions of AIME146, 54–62.
   [Google Scholar]
4. BairleinK., BückerM., HördtA. and HinzeB.2016. Temperature dependence of spectral induced polarization data: experimental results and membrane polarization theory.Geophysical Journal International205, 440–453.
   [Google Scholar]
5. BluntM.J., BijeljicB., DongH., GharbiO., IglauerS., MostaghimiP. et al. 2013. Pore‐scale imaging and modelling.Advances in Water Resources51, 197–216.
   [Google Scholar]
6. BörnerF.D. and SchönJ.H.1991. A relation between the quadrature component of electrical conductivity and the specific surface area of sedimentary rocks.The Log Analyst32.
   [Google Scholar]
7. BückerM. and HördtA.2013. Analytical modelling of membrane polarization with explicit parametrization of pore radii and the electrical double layer.Geophysical Journal International194, 804–813.
   [Google Scholar]
8. BussianA.1983. Electrical conductance in a porous medium.Geophysics48, 1258–1268.
   [Google Scholar]
9. ChenY. and OrD.2006. Effects of Maxwell‐Wagner polarization on soil complex dielectric permittivity under variable temperature and electrical conductivity.Water Resources Research42.
   [Google Scholar]
10. ChengH. and TorquatoS.1997. Effective conductivity of periodic arrays of spheres with interfacial resistance.Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences453, 145–161.
    [Google Scholar]
11. FredrichJ.T.1999. 3D imaging of porous media using laser scanning confo‐cal microscopy with application to microscale transport processes.Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy24, 551–561.
    [Google Scholar]
12. GarbocziE.J.1998. Finite Element and Finite Difference Programs for Computing the Linear Electric and Elastic Properties of Digital Images of Random Materials.
13. GloverP.W., HoleM.J. and PousJ.2000. A modified Archie’s law for two conducting phases.Earth and Planetary Science Letters180, 369–383.
    [Google Scholar]
14. GloverP.W.J., MeredithP.G., SammondsP.R. and MurrellS.A.F.1994. Ionic surface electrical conductivity in sandstone.Journal of Geophysical Research: Solid Earth99, 21635–21650.
    [Google Scholar]
15. GuibertR., HorgueP., DebenestG. and QuintardM.2016. A comparison of various methods for the numerical evaluation of porous media permeability tensors from pore‐scale geometry.Mathematical Geosciences48(3), 329–347.
    [Google Scholar]
16. HanaiT.1960. Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions.Kolloid‐Zeitschrift171, 23–31.
    [Google Scholar]
17. HördtA., BairleinK., BielefeldA., BückerM., KuhnE., NordsiekS. et al. 2016. The dependence of induced polarization on fluid salinity and pH, studied with an extended model of membrane polarization.Journal of Applied Geophysics135, 408–417.
    [Google Scholar]
18. JohnsonD.L., KoplikJ. and SchwartzL.M.1986. New pore‐size parameter characterizing transport in porous media.Physical Review Letters57, 2564–2567.
    [Google Scholar]
19. KemnaA., BinleyA., CassianiG., NiederleithingerE., RevilA., SlaterL. et al. 2012. An overview of the spectral induced polarization method for near‐surface applications.Near Surface Geophysics10, 453–468.
    [Google Scholar]
20. KidnerN., IngramB., HomrighausZ., MasonT. and GarbocziE.2002. Impedance/dielectric spectroscopy of electroceramics in the nanograin regime.MRS Proceedings756.
    [Google Scholar]
21. LeroyP., RevilA., KemnaA., CosenzaP. and GhorbaniA.2008. Complex conductivity of water‐saturated packs of glass beads.Journal of Colloid and Interface Science321, 103–117.
    [Google Scholar]
22. LeroyP., DevauN., RevilA. and BiziM.2013. Influence of surface conductivity on the apparent zeta potential of amorphous silica nanoparticles.Journal of Colloid and Interface Science410, 81–93.
    [Google Scholar]
23. LeroyP., LiS., JougnotD., RevilA. and WuY.2017. Modeling the evolution of complex conductivity during calcite precipitation on glass beads.Geophysical Journal International209(1), 123–140.
    [Google Scholar]
24. LesmesD.P. and FryeK.M.2001. Influence of pore fluid chemistry on the complex conductivity and induced polarization responses of Berea sandstone.Journal of Geophysical Research: Solid Earth106(B3), 4079–4090.
    [Google Scholar]
25. LyklemaJ., DukhinS.S. and ShilovV.N.1983. The relaxation of the double layer around colloidal particles and the low‐frequency dielectric dispersion: Part I. Theoretical considerations.Journal of Electroanalytical Chemistry and Interfacial Electrochemistry143(1–2), 1–21.
    [Google Scholar]
26. MadonnaC., AlmqvistB.S.G. and SaengerE.H.2012. Digital rock physics: numerical prediction of pressure‐dependent ultrasonic velocities using micro‐CT imaging.Geophysical Journal International189, 1475–1482.
    [Google Scholar]
27. MarshallD.J. and MaddenT.R.1959. Induced polarization, a study of its causes.Geophysics24, 790–816.
    [Google Scholar]
28. MendelsonK.S.1975. A theorem on the effective conductivity of a two‐dimensional heterogeneous medium.Journal of Applied Physics46(11), 4740–4741.
    [Google Scholar]
29. McBrideM.1989. Surface chemistry of soil minerals.Minerals in Soil Environments35–88.
    [Google Scholar]
30. NiuQ. and RevilA.2016. Connecting complex conductivity spectra to mercury porosimetry of sedimentary rocks.Geophysics81(1), E17–E32.
    [Google Scholar]
31. NiuQ., PrasadM., RevilA. and SaidianM.2016a. Textural control on the quadrature conductivity of porous media.Geophysics81(5), E297–E309.
    [Google Scholar]
32. NiuQ., RevilA. and SaidianM.2016b. Salinity dependence of the complex surface conductivity of the Portland sandstone.Geophysics81(2), D125–D140.
    [Google Scholar]
33. NiuQ. and ZhangC.2017. Joint inversion of NMR and SIP data to estimate pore size distribution of geomaterials.Geophysical Journal International (under review).
    [Google Scholar]
34. O’KonskiC.T.1960. Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes.The Journal of Physical Chemistry64, 605–619.
    [Google Scholar]
35. PrideS.1994. Governing equations for the coupled electromagnetics and acoustics of porous media.Physical Review B50, 15678–15696.
    [Google Scholar]
36. RevilA.2012. Spectral induced polarization of shaly sands: influence of the electrical double layer.Water Resources Research48, W02517.
    [Google Scholar]
37. RevilA.2013. Effective conductivity and permittivity of unsaturated porous materials in the frequency range 1 mHz‐1 GHz.Water Resources Research49, 306–327.
    [Google Scholar]
38. A.Weller
    RevilA.2014. Comment on “On the relationship between induced polarization and surface conductivity: Implications for petrophysical interpretation of electrical measurements” ( A.Weller , L.Slater and S.Nordsiek , Geophysics78(5), D315–D325). Geophysics 79, X1–X5.
    [Google Scholar]
39. RevilA. and GloverP.W.J.1998. Nature of surface electrical conductivity in natural sands, sandstones, and clays.Geophysical Research Letters25, 691–694.
    [Google Scholar]
40. RevilA. and SkoldM.2011. Salinity dependence of spectral induced polarization in sands and sandstones.Geophysical Journal International187, 813–824.
    [Google Scholar]
41. RevilA., KaraoulisM., JohnsonT. and KemnaA.2012. Review: some low‐frequency electrical methods for subsurface characterization and monitoring in hydrogeology.Hydrogeology Journal20, 617–658.
    [Google Scholar]
42. RevilA., FlorschN. and CamerlynckC.2014a. Spectral induced polarization porosimetry.Geophysical Journal International198, 1016–1033.
    [Google Scholar]
43. RevilA., KessouriP. and Torres‐VerdínC.2014b. Electrical conductivity, induced polarization, and permeability of the Fontainebleau sandstone.Geophysics79, D301–D318.
    [Google Scholar]
44. RevilA., BinleyA., MejusL. and KessouriP.2015. Predicting permeability from the characteristic relaxation time and intrinsic formation factor of complex conductivity spectra.Water Resources Research51, 6672–6700.
    [Google Scholar]
45. RhoadesJ.D., RaatsP.A.C. and PratherR.J.1976. Effects of liquid‐phase electrical‐conductivity, water‐content, and surface conductivity on bulk soil electrical‐conductivity.Soil Science Society of America Journal40, 651–655.
    [Google Scholar]
46. SaengerE.H., EnzmannF., KeehmY. and SteebH.2011. Digital rock physics: effect of fluid viscosity on effective elastic properties.Journal of Applied Geophysics74, 236–241.
    [Google Scholar]
47. SchwarzG.1962. A theory of the low‐frequency dielectric dispersion of colloidal particles in electrolyte solution1, 2.The Journal of Physical Chemistry66, 2636–2642.
    [Google Scholar]
48. ScottJ.B.T. and BarkerR.D.2003. Determining pore‐throat size in Permo‐Triassic sandstones from low‐frequency electrical spectroscopy.Geophysical Research Letters30, 1450.
    [Google Scholar]
49. ShilovV.N., DelgadoA.V., Gonzalez‐CaballeroF. and GrosseC.2001. Thin double layer theory of the wide‐frequency range dielectric dispersion of suspensions of non‐conducting spherical particles including surface conductivity of the stagnant layer.Colloids and Surfaces A: Physicochemical and Engineering Aspects192(1), 253–265.
    [Google Scholar]
50. SihvolaA.H. and KongJ.A.1988. Effective permittivity of dielectric mixtures.IEEE Transactions on Geoscience and Remote Sensing26(4), 420–429.
    [Google Scholar]
51. SkoldM., RevilA. and VaudeletP.2011. The pH dependence of spectral induced polarization of silica sands: experiment and modeling.Geophysical Research Letters38(12).
    [Google Scholar]
52. SlaterL., BarrashW., MontreyJ. and BinleyA.2014. Electrical‐hydraulic relationships observed for unconsolidated sediments in the presence of a cobble framework.Water Resources Research50, 5721–5742.
    [Google Scholar]
53. TorquatoS.1985. Effective electrical conductivity of two‐phase disordered composite media.Journal of Applied Physics58, 3790–3797.
    [Google Scholar]
54. TorrentsJ.M., MasonT.O. and GarbocziE.J.2000. Impedance spectra of fiber‐reinforced cement‐based composites: a modeling approach.Cement and Concrete Research30(4), 585–592.
    [Google Scholar]
55. WellerA. and SlaterL.2012. Salinity dependence of complex conductivity of unconsolidated and consolidated materials: comparisons with electrical double layer models.Geophysics77, D185–D198.
    [Google Scholar]
56. WellerA., SlaterL. and NordsiekS.2013. On the relationship between induced polarization and surface conductivity: implications for petro‐physical interpretation of electrical measurements.Geophysics78, D315–D325.
    [Google Scholar]
57. A.Weller
    WellerA., SlaterL. and NordsiekS.2014. Reply to discussion comment on: “On the relationship between induced polarization and surface conductivity: Implications for petrophysical interpretation of electrical measurements” ( A.Weller , L.Slater and S.Nordsiek , Geophysics78 (5), D315–D325). In: Reply to discussion comment on: “On the relationship between induced polarization and surface conductivity: Implications for petrophysical interpretation of electrical measurements” ( A.Weller , L.Slater and S.Nordsiek, Geophysics 78 (5), D315–D325).
    [Google Scholar]
58. WildenschildD. and SheppardA.P.2013. X‐ray imaging and analysis techniques for quantifying pore‐scale structure and processes in subsurface porous medium systems.Advances in Water Resources51, 217–246.
    [Google Scholar]
59. ZhanX., SchwartzL.M., ToksözM.N., SmithW.C. and MorganF.D.2010. Pore‐scale modeling of electrical and fluid transport in Berea sandstone.Geophysics75, F135–F142.
    [Google Scholar]
60. ZhuravlevL.T.2000. The surface chemistry of amorphous silica. Zhuravlev model.Colloids and Surfaces A: Physicochemical and Engineering Aspects173, 1–38.
    [Google Scholar]