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Published online 26 May 2006
Published in Vadose Zone J 5:731-741 (2006)
DOI: 10.2136/vzj2005.0107
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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ORIGINAL RESEARCH

Dependence of the Electrical Conductivity on Saturation in Real Porous Media

R. P. Ewinga,* and A. G. Huntb

a Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
b Dep. of Physics and Dep. of Geology, Wright State Univ., Dayton, OH 45435
* Corresponding author (ewing{at}iastate.edu)

Received 29 August 2005.

Archie's Law for the porosity and saturation dependence of electrical conductivity, {sigma}({theta}) = a{sigma}b{phi}m({theta}/{phi})n (where {sigma} is electrical conductivity, the subscript b denotes the brine or bulk solution, {phi} is porosity, {theta} is volume wetness, and a, m, and n are fitting parameters) was recently derived by applying continuum percolation theory to fractal porous media. We have recast Archie's Law in terms of saturation alone to obtain {sigma}({theta}) = {sigma}0 ({theta} – {theta}c)µ, where {theta}c is the critical volume fraction for percolation, and {sigma}0 = a{sigma}b/(1 – {theta}c)µ. The value of the exponent, µ = 2.0 for three-dimensional systems and 1.28 for two, is consistent with theory and simulations. We examined the universality of the exponent's value, and the range of validity of our expression. Drawing on published data, we compared predicted and measured values of {sigma}({theta}) across the full range of saturation, and found that the newly derived expression provides good predictions, is robust with respect to secondary effects such as residual salinity and contact resistance, and yields meaningful physical parameters.

Abbreviations: 2D, two-dimensional • 3D, three-dimensional • CPA, critical path analysis • PT, percolation theory • RS, truncated random fractal model of Rieu and Sposito




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