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Dependence of the Electrical Conductivity on Saturation in Real Porous Media

^a Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
^b Dep. of Physics and Dep. of Geology, Wright State Univ., Dayton, OH 45435

View larger version (14K): [in a new window]   Fig. 1. Comparison of the data and equation of Rhoades et al. (1976) and a percolation-based formulation. The two equations produce similar curves when plotted with (a) linear axes; differences are clearer in (b) logarithmic space. (, volumetric water content; c, critical water content; , electrical conductivity; b, bulk solution electrical conductivity; µ, universal scaling exponent for conductivity.)

View larger version (17K): [in a new window]   Fig. 2. Plot of the –D (porosity–fractal dimension) plane showing regions of validity for percolation scaling, using the criterion cross-over water content x 0.9. Below the electrical conductivity, (), lines, scaling is valid for electrical conductivity; below the hydraulic conductivity, K(), line, scaling is valid for hydraulic conductivity. Blue lines represent the criteria in Eq. [18] and [19]; red represent the Balberg (1987) formulation.

View larger version (14K): [in a new window]   Fig. 3. Values of the conductivity exponent µ* calculated across a moving range of water contents = 0.01 for the given porosity and several values of the pore space fractal dimension D. Data following one of these curves could be interpreted as having a nonuniversal value of µ*.

View larger version (16K): [in a new window]   Fig. 4. Values of the conductivity exponent µ* calculated across a moving range of water contents = 0.01 for the given porosity and two values of the pore space fractal dimension D, for cases where the critical water content (c) is underestimated, correct, and overestimated.

View larger version (19K): [in a new window]   Fig. 5. Comparison of data on electric conductivity as a function of water content, (), from Binley et al. (2001, 2002) with Eq. [20] and model results of Cassiani et al. (2005).

View larger version (14K): [in a new window]   Fig. 6. Direct comparison of measured and predicted electrical conductivity () values for the data in Fig. 5.

View larger version (12K): [in a new window]   Fig. 7. Electrical conductivity () of unsaturated silica sand at different solution contents () and conductivities.

View larger version (16K): [in a new window]   Fig. 8. Comparison of data with zero-parameter predictions of electrical conductivity () of silica sand at various water contents (), after subtracting the solid-phase electrical conductivity (s).

View larger version (14K): [in a new window]   Fig. 9. Predicted and measured electrical conductivity () as a function of water content () in tuff, using both deionized water (DW) and a standard solution (J-13).

View larger version (15K): [in a new window]   Fig. 10. Comparison of predicted with measured electrical conductivity () in loessial soils.

View larger version (18K): [in a new window]   Fig. 11. Comparison of predicted with measured electrical conductivity () in four soils.

View larger version (19K): [in a new window]   Fig. 12. Comparison of predicted with measured electrical conductivity () in soils presented by Mori et al. (2003, labeled MHMK2003) and Tuli and Hopmans (2004, labeled TH2004) at different bulk solution (b) values.

View larger version (16K): [in a new window]   Fig. 13. Triplicate electrical conductivity () as a function of water content () with predicted values based on the assumption of non-zero contact resistance (Eq. [22]).

View larger version (25K): [in a new window]   Fig. 14. Summary plot of all the data sets presented in Table 1, showing consistent adherence to the predicted behavior. For all data sets, water content () was normalized by subtracting its critical value (c), and electrical conductivity () was normalized by subtracting the solid-phase contribution (s), then dividing by 0 (the prefactor from Eq. [5]) to account for brine activity. Data follow the line given by the universal conductivity exponent µ.