Complex conductivity of soils

Abstract

The complex conductivity of soils remains poorly known despite the growing importance of this method in hydrogeophysics. In order to fill this gap of knowledge, we investigate the complex conductivity of 71 soils samples (including four peat samples) and one clean sand in the frequency range 0.1 Hz to 45 kHz. The soil samples are saturated with six different NaCl brines with conductivities (0.031, 0.53, 1.15, 5.7, 14.7, and 22 S m−1, NaCl, 25°C) in order to determine their intrinsic formation factor and surface conductivity. This data set is used to test the predictions of the dynamic Stern polarization model of porous media in terms of relationship between the quadrature conductivity and the surface conductivity. We also investigate the relationship between the normalized chargeability (the difference of in‐phase conductivity between two frequencies) and the quadrature conductivity at the geometric mean frequency. This data set confirms the relationships between the surface conductivity, the quadrature conductivity, and the normalized chargeability. The normalized chargeability depends linearly on the cation exchange capacity and specific surface area while the chargeability shows no dependence on these parameters. These new data and the dynamic Stern layer polarization model are observed to be mutually consistent. Traditionally, in hydrogeophysics, surface conductivity is neglected in the analysis of resistivity data. The relationships we have developed can be used in field conditions to avoid neglecting surface conductivity in the interpretation of DC resistivity tomograms. We also investigate the effects of temperature and saturation and, here again, the dynamic Stern layer predictions and the experimental observations are mutually consistent.

Three‐Dimensional Electrical Conductivity and Induced Polarization Tomography of a Rock Glacier

“…In Figure , we plot, for all cells, the normalized chargeability versus the conductivity of the material (the ratio of both being the chargeability). With the exception of the data located close to the graphite‐rich rocks, we see clearly that the data form a linear trend that is consistent with the soil data of Revil et al (; see Figure ). The slope is equal to R = 8 × 10 −2 , which is here again clearly independent of the temperature and saturation in agreement with equation .…”

“…In order to go further, we need a model for the polarization of the nonmetallic grains shown in Figure . According to the dynamic Stern layer model developed by Revil (, ), the normalized chargeability and instantaneous conductivity of the background material can be written as (Revil et al, ) where θ (dimensionless) denotes the water content (product of the porosity by the saturation) of the liquid water phase, σ w (in S/m) denotes the pore water conductivity, ρ g is the grain density (in kg/m 3 , typically ρ g = 2,650 kg/m 3 for minerals in sedimentary rocks), and CEC denotes the cation exchange capacity (in C/kg) of the background. The CEC denotes the quantity of exchangeable cation on the surface of minerals.…”

“…The impedance meter is used to determine the complex conductivity written as The in‐phase conductivity σ ′ (in S/m) denotes the ability of the porous material to conduct electrical currents, while the quadrature (imaginary) conductivity σ ″ (in S/m) characterizes the ability of the porous material to polarize (i.e., to store reversibly electrical charged under the influence of a primary electrical field). In absence of metallic particles, the quadrature conductivity and the normalized chargeability are linearly related to each other as discussed further below (see Revil et al, , for further details).…”

Complex Conductivity of Graphitic Schists and Sandstones

“…The CEC is mainly sensitive to the clay type (e.g., kaolinite, illite, smectite) and the weight fraction of these clay minerals in the rock. In equations and , the quantity B (expressed in m 2 ·s −1 ·V −1 ) denotes the apparent mobility of the counterions for surface conduction and the quantity λ (expressed in m 2 ·s −1 ·V −1 ) denotes the apparent mobility of the counterions for the polarization associated with the quadrature conductivity (see Revil et al, , and references therein). A dimensionless number R is also introduced with (see Revil et al, for further explanations).…”

“…We discuss now the temperature dependence of the complex conductivity above the freezing temperature (typically but not necessarily around 0 °C). Following Vinegar and Waxman (), the pore water conductivity and mobilities B and λ have all the following linear temperature dependence: where T 0 and T are the reference temperature ( T 0 = 25 °C) and the temperature (in °C), respectively; Θ( T ) corresponds to σ w ( T ), B ( T ), or λ ( T ); and Θ( T 0 ) corresponds to the same property at T 0 , and the sensitivity α T is in the range 0.019–0.022/°C (e.g., Revil et al, ). According to equation , the conductivity goes to zero at a temperature of −25 °C, remarkably close to the so‐called eutectic temperature T E close to −21 °C for NaCl.…”