The effective permittivity of dense packings of glass beads, quartz sand and their mixtures immersed in different dielectric backgrounds

Dielectric methods, which measure the effective dielectric permittivity of granular materials, e.g., rocks, sediments and soils are often applied to estimate water or oil content. To test physically based models requires that the permittivity values of all phases are known. Measurements of the solid permittivity of glass spheres, quartz sand grains and their mixtures are made using an immersion method. The results obtained are tested against several classical models including the Maxwell Garnett, the symmetric effective medium approximation (SEMA) and the non-SEMA. The results demonstrate inadequate predictions between these models and the measured data. However, the Maxwell Garnett model comes close to predicting the effective permittivity of the media. Divergence between this model and the measurements is known to be due to interaction effects between grains that is not accounted for by a model based simply on the mixing of volumetric fractions of the components. With water as the background (contrast of 10 for glass) the Maxwell Garnett model overestimates the effective permittivity ∼5% as the contrast reduces this error decreases. For contrasts <4 the error for the permittivity estimate using the Maxwell Garnett formula was <3%. The modeling is simply used to demonstrate that the permittivity of the inclusions, for practical purposes, can be considered a linear function of the volumetric fraction times its respective permittivity.