Dielectric spectroscopy of sedimentary rocks

Abstract

A physiochemical model for the complex dielectric response of sedimentary rocks is used to invert broadband dielectric spectra for effective grain size distributions. The complex dielectric response of each grain within the “water‐wet” granular matrix is obtained by superimposing the polarization of the electrochemical double layer, which is assumed to surround each grain, with the complex dielectric response of the dry mineral grain. The effective complex dielectric response of the water‐wet matrix (grains and surface phase) is obtained by volume averaging over the entire distribution of particle sizes. The complex dielectric response of the total mixture (water‐wet matrix and bulk pore solution) is obtained using the Bruggeman‐Hanai‐Sen effective medium theory. Studies of Berea sandstone show that the grain size distribution, obtained by inverting the real part of the complex dielectric spectra, is similar to the grain size distribution obtained from optical images of the sample in thin section. The current model, however, does not account for surface roughness effects or the polarization of counterions over multiple grain lengths; therefore the grain size distribution obtained by dielectric spectroscopy is broader than the image‐derived distribution. The dielectric‐derived grain size distribution can be fit with two separate power laws that crossover at R ≅ 1 μm, which corresponds to a relaxation frequency of 2 kHz. The low‐frequency dielectric response (f < 2 kHz) is primarily controlled by the macroscopic grain fraction (mainly quartz grains), which has a fractal dimension of d = 1.84±0.05. The high‐frequency dielectric response (f > 2 kHz) is primarily controlled by the clay size grains and surface roughness, which has a fractal dimension of d = 2.48±0.07. At very low frequencies (f < 0.1 Hz) the dielectric response appears to be controlled by the electrochemical polarization of counterions over multiple grain lengths. A more general model should account for the effects of surface roughness and grain interactions on the dielectric response. It would also be useful to develop a simplified version of this model, perhaps similar in form to the empirically derived Cole‐Cole response, which could be more easily used to model and interpret electrical geophysical field surveys (e.g., induced‐polarization, ground‐penetrating radar, and time domain reflectometery measurements).