Electrical-impedance spectroscopy of sedimentary rocks

Abstract

The electrical-impedance response of brine-saturated rocks is similar to the electrical-impedance responses of other ionically conducting solids in that they all exhibit small but constant phase angles at low frequencies. The origin of this constant phase response is still not well understood; in fact, some investigators claim that it is an experimental artifact. The focus of this research has been first, to experimentally verify the existence of the low-frequency constant phase angle response for brine-saturated rocks, and second, to theoretically model the electric polarization mechanisms which give rise to the characteristic electrical impedance response of rocks. Two-electrode and four-electrode impedance measurement system s have been developed to measure the complex dielectric response of brine saturated rocks over the frequency range of 0.01 Hz to 40 MHz. Detailed calibrations and error analyses, made with these measurement systems, show that the constant phase angle responses of brine-saturated rocks are indeed real, and not experimental artifacts. Furthermore, these measurement system scan be used to accurately characterize the broadband complex dielectric response of brine-saturated rocks as a function of their solution chemistries and their microgeometries. These types of measurements, on samples with well characterized physical and chemical properties, are necessary to properly constrain theoretical models. Electrical impedance measurements of Berea sandstone are used to test a new model for the complex dielectric response of brine-saturated rocks. The model accounts for both electrochemical and interfacial polarizations of a concentrated mixture of spherical grains with varying grain sizes. In simulating the measured complex dielectric response of Berea sandstone, the model parameters are constrained by independent measures of the microgeometry and the surface chemistry of the sample. The good fit of the model to the data, over the frequency range of 0.1 Hz to 40 MHz, indicates the validity of the model. Using this model, the real part of the complex dielectric response of brine-saturated rocks can be inverted for a grain volume distribution. Tests on synthetic data show that this linear inverse problem is inherently very unstable; however, by transforming the problem into log-space, the inversion can iterate with variable damping towards the true solution. The grain volume distribution of Berea sandstone obtained using this dielectric inversion method is in fairly good agreement with the grain volume distribution obtained from optical images of the sample in thin section.