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

The complex dielectric permittivity e* 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 e′ 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.