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).

Modeling the evolution of complex conductivity during calcite precipitation on glass beads

“…Therefore, a relaxation time or characteristic frequency (inverse of the relaxation time) can be associated with the shape and size of the particle and with the tangential diffusion coefficient of the counterions in the Stern layer. Typically, large micrometric particles or small nanometric particles with a high degree of surface roughness induce high relaxation times and small characteristic frequencies (typically < kHz) (Chelidze & Gueguen 1999;Lesmes & Morgan 2001). These ion movements in the Stern layer were also assumed to control not only the frequency behaviour but also the magnitude of the polarization process, that is high surface density of mobile charges in the Stern layer induces high particle polarization.…”

“…Water dielectric permittivity is written as ε w = ε r ε 0 , where ε r is the relative dielectric permittivity of water (ε r ∼ = 78.3 for bulk water at a pressure of 1 bar and a temperature T of 298 K) and ε 0 is the dielectric permittivity of vacuum (ε 0 ∼ = 8.854 × 10 −12 F m −1 ) (Lide 1990). The complex surface conductivity of the particles of different sizes σ * s is calculated considering the superposition principle (Lesmes & Morgan 2001). It is computed using a volumetric mixing formula assuming that the electrochemical conductions and polarizations of particles of different sizes all add in parallel, that is that the complex conductivity response of particles of same size is weighted by the relative volume of the solid that is occupied by these particles.…”

“…It is computed using a volumetric mixing formula assuming that the electrochemical conductions and polarizations of particles of different sizes all add in parallel, that is that the complex conductivity response of particles of same size is weighted by the relative volume of the solid that is occupied by these particles. The resulting complex surface conductivity of the particles depends on the particle size distribution (PSD) f (d i ), with d i the particle diameter (in m), and is given by (Lesmes & Morgan 2001;Leroy et al 2008):…”

“…At low frequencies (typically <1 kHz), there are two major phenomena controlling electrical charge transport in porous media containing no metallic particles: the complex conductivity of the bulk pore water associated with the electromigration of charge carriers in the interconnected, liquid-filled pore space and the complex interfacial or surface conductivity associated with the conduction and polarization processes in the EDL (Dukhin & Shilov 1974;Vinegar & Waxman 1984;Delima & Sharma 1992;Lesmes & Morgan 2001;Leroy et al 2008;Revil 2012). Conduction in bulk water strongly depends on the water chemical composition, the pore volume occupied by the liquid and the topology of the pore space (i.e.…”

Study of the properties of non-gas dielectric capacitors in porous media

“…and Cl -in view of their conductive property. Therefore, it is crucial to study the conductive and dielectric properties of NaCl solutions (Jonscher 1999;Lesmes and Morgan 2001). The pure water and hydrocarbon molecules cannot conduct current, and the conductive ions are separated from each other by water and hydrocarbon molecules, as shown in Fig.…”