Development of an Empirical Model for Predicting the Cation Exchange Capacity of Shaly Sandstones Using Complex Dielectric Permittivity Measurements

Dimensional analysis is applied on measured complex dielectric permittivity data of shaly sandstone rock samples, for the purpose of modeling the cation exchange capacity (CEC). These measured variables consist of rock porosity, specific surface area, and five other parameters of the Cole-Cole function, which describe the frequency dependence of the complex permittivity of rock samples in the range of 10–1300 MHz. The Cole-Cole function parameters are the characteristic relaxation time, the spread parameter, the real dc conductivity of water saturated rocks, the static dielectric permittivity, and the high-frequency dielectric permittivity of the water-saturated shaly-sandstone rocks. The dimensional analysis revealed the existence of two dimensionless groups, denoted as the cationic dispersion number (π₁), and the conductivity number (π₂). The former group π₁ stands for the ratio of the cation exchange capacity to the electrical double layer dispersion. The latter group π₂ represents the ratio of the low-frequency ionic conductivity to the high-frequency electronic polarization. The dimensionless groups have been validated using measured complex permittivity data of 92 shaly sandstone rocks. The dimensional analysis resulted in the derivation of a model for the CEC as a function of fast and non-invasive dielectric properties measurements. In return, accurate and fast estimates of CEC are useful in many petroleum engineering applications. They can be used to identify clay types, and to quantify the volume of hydrocarbon in shaly sands using well log resistivity data. The results of this study represent a major advantage for formation evaluation and wellbore stability analysis, as well as for designing stimulation jobs.