1887
Volume 15 Number 6
  • ISSN: 1569-4445
  • E-ISSN: 1873-0604

Abstract

ABSTRACT

Membrane polarization is one process that might describe the causes of induced polarization in sediments at the pore scale. Here, we investigate the practical relevance of one particular model, which consists of two cylindrical pores with different radii r and lengths L, for which the impedance can be calculated analytically. We derive approximate equations that relate polarizabilities and relaxation times directly to r and L. Based on these relations and on a systematic exploration of the parameter space, we investigate under which conditions membrane polarization is relevant in the sense that it produces measurable phase shifts in the frequency range typically observed in the laboratory or at the field scale.

In principle, a wide range of spectra can be obtained. Maximum phase shifts up to hundreds of milliradian can be simulated, and the characteristic time scales cover the entire range typically measured in the laboratory. We discuss some specific constraints in the context of results from mercury injection porosimetry and recently published laboratory data and show that the required geometries are not unrealistic, even if a moderate ratio between pore length and width is included as an additional condition. We conclude that membrane polarization as a possible mechanism is not limited to a particular frequency range. We also provide evidence that the pore length of the wide pore is likely to control the measured relaxation times in practical situations. The results encourage further attempts to combine impedances of two‐pore systems to approach the simulation of real sediments, with the aim to extract pore space parameters from measured data.

Loading

Article metrics loading...

/content/journals/10.3997/1873-0604.2017053
2017-10-01
2019-12-06
Loading full text...

Full text loading...

References

  1. BairleinK., BückerM., HrdtA., HinzeB. and NordsiekS.2016. Temperature dependence of spectral induced polarization data: experimental data and membrane polarization theory.Geophysical Journal International205, 440–453.
    [Google Scholar]
  2. BinleyA., SlaterL.D., FukesM. and CassianiG.2005. Relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone.Water Resources Research41, w12417.
    [Google Scholar]
  3. BlaschekR. and HördtA.2009. Numerical modelling of the IP‐effect at the pore scale.Near Surface Geophysics7, 579–588.
    [Google Scholar]
  4. BuchheimW. and IrmerG.1979. Zur Theorie der induzierten galvanis‐chen Polarisation in Festkorpern mit elektrolytischer Porenfullung.Gerlands Beitrdge zur Geophysik88, 53–72.
    [Google Scholar]
  5. BückerM. and HördtA.2013a. Long and short narrow pore models for membrane polarization.Geophysics78, E299–E314.
    [Google Scholar]
  6. BückerM. and HördtA.2013b. Analytical modelling of membrane polarization with explicit parameterization of pore radii and the electrical double layer.Geophysical Journal International
    [Google Scholar]
  7. ChuprinkoD. and TitovK.2017. Influence of mineral composition on spectral induced polarization in sediments.Geophysical Journal International209, 186–191.
    [Google Scholar]
  8. FridrikhsbergD.A. and SidorovaM.P.1961. Issledovanie sviazi yavlenia vyzvannoi polarizatsii s electrokineticheskimi svoistvami kapillarnyh sistem (A study of the relationship between the induced polarization phenomenon and the electrokinetic properties of capillary systems). Vestnik Leningradskogo Universiteta, seria chimia 4, 222–226 (in Russian).
    [Google Scholar]
  9. HördtA., BairleinK., BielefeldA., BtickerM., KuhnE., Nordsieket 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]
  10. KosmulskiM.2011. The pH‐dependent surface charging and points of zero charge V. Update.Journal of Colloid and Interface Science353(1), 1–15.
    [Google Scholar]
  11. KruschwitzS., BinleyA., LesmesD. and ElshenawyA.2010. Textural controls on low‐frequency electrical spectra of porous media.Geophysics75, WA113–WA123.
    [Google Scholar]
  12. KruschwitzS., PrinzC. and ZimathiesA.2016. Study into the correlation of dominant pore throat size and SIP relaxation frequency.Journal of Applied Geophysics135, 375–386.
    [Google Scholar]
  13. LeroyP., LassinA., AzaroualM. and AndreL.2010. Predicting the surface tension of aqueous 1:1 electrolyte solutions at high salinity.Geochimica Et Cosmochimica Acta74(19), 5427–5442.
    [Google Scholar]
  14. LeroyP. and RevilA.2009. A mechanistic model for the spectral induced polarization of clay materials.Journal of Geophysical Research114, B10202.
    [Google Scholar]
  15. LeroyP., RevilA., KemnaA., CosenzaA. and GhorbaniA.2008. Complex conductivity of water‐saturated packs of glas beads.Journal of Colloid and Interface Science321, 103–117.
    [Google Scholar]
  16. MarshallD.J. and MaddenT.R.1959. Induced polarization: a study of its causes.Geophysics24, 780–816.
    [Google Scholar]
  17. PapeH., ClauserC. and IfflandJ.1999. Permeability prediction based on fractal pore‐space geometry.Geophysics64, 1447–1460.
    [Google Scholar]
  18. RevilA.2012. Spectral induced polarization of shaly sands: influence of the electrical double layer.Water Resources Research48, W02517.
    [Google Scholar]
  19. 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]
  20. RevilA. and FlorschN.2010. Determination of permeability from spectral induced polarization in granular media.Geophysical Journal International181, 1480–1498.
    [Google Scholar]
  21. SchmittM., HalischM., MüllerC. and FernandesC.P.2016. Classification and quantification of pore shapes in sandstone reservoir rocks with 3D X‐ray micro‐computed tomography.Solid Earth7, 285–300.
    [Google Scholar]
  22. SchwarzG.1962. A theory of the low‐frequency dielectric dispersion of colloidal particles in electrolyte solution.The Journal of Physical Chemistry66, 2636–2642.
    [Google Scholar]
  23. ScottJ.B.T. and BarkerR.D.2003. Determining pore‐throat size in Permo‐Triassic sandstones from low‐frequency electrical spectrosco‐py.Geophysical Research Letters30, 1450.
    [Google Scholar]
  24. StebnerH. and HördtA.2017. Simulation of membrane polarization of porous media with 2D and 3D impedance networks.Near‐Surface Geophysics (submitted, this issue).
    [Google Scholar]
  25. TitovK., KomarovV.TarasovV. and LevitskiA.2002. Theoretical and experimental study of time domain‐induced polarization in water‐saturated sands.Journal of Applied Geophysics50, 417–433.
    [Google Scholar]
  26. TitovK., TarasovA., IlyinY., SeleznevN. and BoydA.2010. Relationships between induced polarization relaxation time and hydraulic properties of sandstone.Geophysical Journal International180, 1095–1106.
    [Google Scholar]
  27. VolkmannJ. and KlitzschN.2010. Frequency‐dependent electric properties of microscale rock models for frequencies from one millihertz to ten kilohertz.Vadoze Zone Journal9, 858–870.
    [Google Scholar]
  28. WellerA., BreedeK., SlaterL. and NordsiekS.2011. Effect of changing water salinity on complex conductivity spectra of sandstones.Geophysics76, F315–F327.
    [Google Scholar]
  29. WellerA., SlaterL., HuismannJ.A., EsserO. and HaegelF.‐H.2015. On the specific polarizability of sands and sand‐clay mixtures.Geophysics76, F315–F327.
    [Google Scholar]
  30. 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]
  31. WellerA., SlaterL. and NordsiekS.2014. Reply to the discussion.Geophysics79, X6–X10.
    [Google Scholar]
  32. WellerA., ZhangZ., SlaterL., KruschwitzS. and HalischM.2016. Induced polarization and pore radius—A discussion.Geophysics81, D519–D526.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.3997/1873-0604.2017053
Loading
/content/journals/10.3997/1873-0604.2017053
Loading

Data & Media loading...

  • Article Type: Research Article
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