Abstract

A modeling technique is proposed that assumes a typical shaly sand to be a three-phase porous mixture: water, quartz, and clay. The complex conductivity of such a mixture can be modeled with an equation containing only the complex conductivity of each constituent and the geometry of the pore structure. The effective medium theory provides the basis for such a model. The model typically handles two phases at a time, but one of the phases can be considered as a submixture and then the model is simply applied again after the first inversion to determine the properties of the submixture. In the first inversion, the two phases are water and matrix. For the second inversion, the matrix conductivities are modeled by a mixture of quartz and clay.The present work relies on a published data set of 19 samples, with measurements as a function of salinity taken at constant frequency (Vinegar and Waxman, 1984). The proposed technique fit this data better than the Vinegar-Waxman model which requires more variables. Moreover, this 'double embedding' procedure yields realistic values for clay conductivity, clay dielectric constant, and fractional volume of clay.

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