A generalized Maxwell‐Wagner theory for membrane polarization in shaly sands

Abstract

The effects of charged clay platelets on the frequency dependent electrical properties of shaly materials are analyzed using simplified models for the membrane polarization around charged spheres immersed in electrolytic solutions, under a thin double layer approximation. The polarization is defined through two possible mechanisms: (1) a surface conductivity related with a modified Stern double layer model (S‐model) according to Schurr‐Schwarz theory; (2) a coupled electro‐diffusional mechanism occurring in a Guoy‐Chapman double layer using Fixman’s approach (D‐model). By comparing the electric potential in such microscopic models with the external potentials derived for the equivalent homogeneous sphere using a Maxwell‐Wagner approach, we obtain the total current conductivity functions for these two models. The theory, therefore, provides explicit expressions relating the total conductivity functions to the model parameters. The behavior of the S‐model is described by a complex conductivity exhibiting a simple Debye characteristic. In the D‐model, both the conductivity and the dielectric permittivity are given as complex properties, showing similar but much wider dispersion than that of a Debye substance. Our representation of the grains and their associated ionic double layers by an equivalent sphere with effective properties allows us to extend our results to simulate rocks containing clays. This is accomplished using generalized mixture equations written in terms of the total conductivity functions. The frequency behavior of both models are compared and their fit to experimental data on clay‐water systems and shaly materials suggest that the D‐model is more appropriate for representing the dielectric behavior of clay bearing rocks. The theory can be adapted to estimate the clay parameters of a shaly sandstone using electromagnetic borehole measurements.