A petrophysical basis for ground penetrating radar and very early time electromagnetics : electrical properties of sand-clay mixtures

A series of laboratory experiments was conducted to investigate relationships between electrical properties and hydrogeologic properties of unlithified geologic materials. Mixtures of sand, clay, air and water were used to systematically vary porosity (0.24 to 0.80), clay content (0.00 to 1.00), permeability (5.4x10⁻¹² to 4.4x10⁻⁶ cm²) and water saturation (0.00 to 1.00). Different lithologies were simulated by varying the relative proportion of sand and clay in the mixtures. Compaction was simulated by packing different amounts of the same material into the sample holder. Water saturation was varied by imbibition and evaporative drying. For each mixture, measurements were made of effective electrical conductivity δ[sub ef] and dielectric constant K over the frequency range 100 kHz to 10 MHz. Conductivity values range from 1.8x10⁻⁷ S/m (dry quartz sand, 100 kHz) to 1.0x10⁻² S/m (water-saturated kaolinite, 10 MHz), and dielectric constant values range from 1.9 (dry kaolinite, 10 MHz) to 200 (dry montmorillonite, 100 kHz). Crossplots and petrophysical modeling are used to investigate the relationships between the various electrical and hydrogeologic parameters. Results show that electrical properties depend upon volumetric, geometric and electrochemical factors, and that the relative importance of these factors changes with frequency. For instance, in suites of sand-clay mixtures at low confining pressure, conductivity increases dramatically as clay volume fraction increases from 0.00 to about 0.20; this is due to clay packets forming critical conductive paths through the sand framework. At higher clay contents, clay is the load-bearing material and conductivity shows little sensitivity to clay content. This behavior is characteristic of percolation and illustrates the importance of component microgeometry. When the samples are saturated with water, ionic conduction through the fluid replaces surface conduction along the clay as the dominant conduction mechanism. Saturation eliminates much of the frequency dependence observed in the conductivity response of dry sand-clay mixtures. For a given mixture, conductivity values increase and dielectric constant values decrease with increasing frequency. This is due to the way in which in-phase and out-of-phase components of conduction and polarization currents combine to form the measured electrical parameters. High values of the out-of-phase conduction component are the primary reason why high dielectric constant values (i.e., K > 80) are observed at low frequencies; this component is also the one that is most sensitive to geometric and electrochemical factors. Volumetric factors (e.g., porosity and water saturation) dominate electrical properties at high frequencies, while geometric and electrochemical factors dominate electrical properties at low frequencies. The experimental data are compared to the predictions of three interrelated petrophysical models: (1) a microgeometrical model which describes the relationship between porosity and clay content in sand-clay mixtures, (2) a permeability model based on the Kozeny-Carmen equation, and (3) a dielectric model which incorporates geometric and electrochemical information through the use of wetted matrix parameters. Results show excellent agreement between predicted and measured data, even though relationships such as porosity-clay content, porosity-permeability and dielectric constant-permeability are nonlinear and multivalued. This suggests that, at least for these mixtures, accurate porosity, permeability and water saturation estimates may indeed be derived from dielectric measurements given appropriate constraints. The insights developed in this study provide a petrophysical basis for improved modeling, stratigraphic interpretation and inversion of very early time electromagnetic (VETEM) and ground penetrating radar (GPR) field data. Given appropriate constraints, these data may be inverted for hydrogeologic parameters such as porosity, permeability and water saturation.Science, Faculty ofEarth, Ocean and Atmospheric Sciences, Department ofGraduat