Electrical spectroscopy of porous rocks: a review-I.Theoretical models

Abstract

The complex dielectric permittivity ε* of porous water‐bearing rocks in the frequency range from a few to hundreds of megahertz reveals several intensive relaxation effects and a non‐trivial dependence on the water content. At high frequencies, f > 10 MHz, both the real part of the complex dielectric permittivity ε′ and the conductivity σ of water‐bearing rocks are correctly predicted by the Maxwell–Wagner–Bruggeman–Hanai (MWBH) theory of composite dielectrics. This theory takes into account only the bulk properties of components, their partial volumes and the configuration of particles. The theory ignores two important factors: the surface contribution to polarization and the effect of clustering of components. At frequencies f < 10 MHz there are certain frequency domains which exhibit relaxation processes not predicted by MWBH theory. The characteristic times of these processes range from 10−6 to 10 s. These relaxation effects are related to different surface polarization processes which are, in order of increasing water content, (i) orientational polarization of bound water, (ii) polarization of liquid films or pockets, producing a polarization catastrophe effect, (iii) polarization of rough fractal surfaces, (iv) polarization of the ‘closed’ electrical double layer (EDL), when the displacement of the excess surface charges is limited by the external boundary of the EDL, and (v) polarization of the ‘open’ double layer, implying free exchange of excess ions with the bulk electrolyte and generation of transient diffusional potentials, which lag behind the applied field. Some theoretical models predict large effective values of relative dielectric constants in the range 105–106 at low frequencies. Knowledge of the characteristic signatures of these physical mechanisms is important for the correct interpretation of experimental data. Analysis of existing theories of polarization of heterogeneous media shows that electrical spectroscopy can be useful for the interpretation of frequency spectra of complex dielectric permittivity or conductivity of water‐bearing rocks and porous materials in general, and for the determination of water content, its thermodynamic state, the connectivity of water‐bearing channels and their correlation lengths and the surface to volume ratio and surface charge in particular, in addition to the traditional formation factor, which is obtained from ohmic conductivity 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.…”

“…the reversible storage of electrical charges) of porous materials (Kemna et al 2012). Polarization of oxides and carbonates minerals such as calcite is related to the polarization of the electrical double layer (EDL) surrounding the particles under an external alternating current or electrical field (Chelidze & Gueguen 1999;Jougnot et al 2010;Revil & Florsch 2010). When a sinusoidal current at a range of frequencies is applied to the charged porous medium and the resulting difference of electrical potential is measured, complex conductivity is referred to as spectral induced 124 P. Leroy et al polarization (SIP) (Collet 1990;Weller & Borner 1996;Luo & Zhang 1998;Huisman et al 2015).…”

Dependence of spectral‐induced polarization response of sandstone on temperature and its relevance to permeability estimation

“…In granular media the MW polarization can be modeled by effective medium approximations [e.g., Chelidze and Gueguen, 1999;Cosenza et al, 2009]. MW polarization contributes significantly to the effective polarization at relatively high frequencies (f > 100 Hz).…”

Frequency-Dependent Electrical Characterization of Rock Types from Ewekoro, Eastern Dahomey Basin, Nigeria

“…The Debye response has been frequently used to describe dielectric dispersion in a system with a single relaxation time 39,40 . For a Debye-type relaxation process in which a single relaxation time  is assumed, this should produce a semi-circle with centre on the horizontal axis 25 . However, many materials, including rocks, deviate from Debye behaviour, suggesting the presence of a distribution of relaxation times.…”

“…As a result of their sensitivity to ionic content and surface texture, dielectric measurements of saturated rocks exhibit frequency dispersions of dielectric properties 23,24 . In addition, surface contributions due to solid-liquid interface and clustering effects have to be taken into consideration for the determination of electrical properties [25][26][27] . Frequency-dependent properties of materials result from different mechanisms of charge transport and charge storage.…”