Transport in Porous Media

, Volume 118, Issue 1, pp 1–16 | Cite as

Electrical Conductivity of Partially Saturated Packings of Particles

  • Behzad GhanbarianEmail author
  • Muhammad Sahimi


We address the problem of predicting saturation-dependent electrical conductivity \(\sigma \) in packings of particles during drainage and imbibition. The effective-medium approximation (EMA) and the universal power law of percolation for \(\sigma \) are used, respectively, at higher and low water saturations to predict the conductivity, with the crossover between the two occurring at some intermediate saturation \(S_{\mathrm{wx}}\). The main input to the theory is a single parameter that we estimate using the capillary pressure data. The predictions are compared with experimental, as well as numerical data for three distinct types of packings. The results for drainage in all the packings indicate that the universal power law of percolation is valid over the entire range of \(S_{\mathrm{w}}\). For imbibition, however, the universal power law may cross over to the EMA at \(S_{\mathrm{wx}} = 0.5\). We also find that the effect of the pore-size distribution on the \(\sigma {-}S_{\mathrm{w}}\) relation is minimal during both drainage and imbibition.


Drainage Imbibition Packings of particles Electrical conductivity Partially saturated 



B. G. is grateful to Chloe Mawer, Silicon Valley Data Science, for providing the results of numerical simulation of drainage and imbibition used in this study, and to Hugh Daigle, the University of Texas at Austin, for his comments on the very first draft of this paper. Publication was authorized by the Director, Bureau of Economic Geology.


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Bureau of Economic Geology, Jackson School of GeosciencesUniversity of Texas at AustinAustinUSA
  2. 2.Mork Family Department of Chemical Engineering and Materials ScienceUniversity of Southern CaliforniaLos AngelesUSA

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