An effective-medium model for complex conductivity of shaly sands in the salinity, frequency, and saturation domains

Abstract

The effective-medium theory for complex conductivity is known to be a useful model for describing the conductive and dielectric properties of heterogeneous media. The validity of the theory for shaly sandstones is explored and analyzed by performing several numerical simulations. The accuracy of the theory is tested by comparing the results given by the proposed model to those obtained by electrical measurements on shaly sandstones published by other authors. In the salinity domain, the proposed model is inverted with respect to an induced polarization dataset, and the results produce realistic values for clay conductivity, clay dielectric constant, and fractional volume of clay. It turns out that the predictions of the proposed model are quite good for normal ranges of clay content, porosity, water conductivity, and water saturation. In the frequency domain, forward modeling examples show theoretically what the effects of these variables should be on measured electrical properties. Also, a new technique for inverse modeling of shaly sands in the frequency domain is presented. This technique solves for the conductivity and relative permittivity of a ubiquitous surface layer by the multiple-embedding procedure. Theoretical predictions of rock dielectric constant and resistivity index are compared to measurement over a wide range of water saturation. No other published model is able to fit dielectric data over the complete range of water saturation. It is concluded that the multiple-embedding procedure uniquely and accurately models shaly sandstone behavior in the salinity and frequency domains and at all partial water saturations.