An Empirical Model for Estimating the Rock Lithology and the Cation Exchange Capacity from Dielectric Permittivity Data

Linear regression analysis has been used in this study to develop a predictive model for the CEC using a data base of dielectric and petrographic parameters for both carbonate and sandstone rocks. Among several predictors of CEC, regression analysis indicates that only five variables are statistically significant for estimating the CEC. These are the static relative dielectric permittivity (ζ_s), the fractal dimension $(d′MC)$⁠, the rock specific surface area (SA), the rock lithology, and the porosity (ϕ). The linear regression model has been tested independently with a random sample that has not been used in the correlation development, yielding an average error of 25% for the tested samples with a standard deviation on the error of approximately 18%. This model appears to be robust in predicting the CEC value, and offers a novel approach for estimating the rock cation exchange capacity using petrographic properties and dielectric parameters.

The CEC increases with increasing (ϕ· SA) values, and increases with increasing ζ_s values. As anticipated, for a constant porosity value, the CEC increases with increasing specific surface area. For sedimentary rocks, the cation exchange capacity is a surface phenomenon value that depends on the cation substitution sites, and on the localization on the negative charges on the substitution sites residing on the surface of the particles. This dependence, physically ties the CEC to the specific surface area. This dependence was not obvious when correlating the CEC to the specific area alone, but was clear when the CEC was correlated to the product (ϕ·SA). In general, greater values of the fractal dimension implicate a greater degree of fractionation of the rock material, and are, therefore, associated with finer textures. Whereas smaller values of the fractal dimension implicate coarser textures. A greater degree of fractionation implicates a larger reactive surface which may lead to a higher CEC value when the rock texture is clay-dominated. However, for the relatively, clean sandstone and carbonate rock samples used, an increase in the fractal dimension causes a decrease in the CEC value.

Discriminant analysis is performed on the same data base of petrographic and dielectric permittivity parameters, for the purpose of developing a lithology classification model. Results of the discriminant analysis indicate that only four variables (ζ_s, ζ_∞, ϕ, CEC) are sufficient to identify rock lithology, with ζ_∞ being a real number representing the high-frequency relative dielectric permittivity of the water-saturated rock. The analysis reveals the existence of a significant discriminant function to distinguish among the groups defined by the rock lithology type. A lithology classification model based on dielectric permittivity and petrographic data is, therefore, introduced. The model has been validated by an independent set of testing samples. Out of 23 cases tested, the introduced model has successfully identified the rock lithology of 21 samples, giving a success rate of 91%.