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

The complex dielectric permittivity epsilon* 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 cont ent. At high frequencies, f>10 MHz, both the real part of the complex diele ctric permittivity epsilon' and the conductivity a of water-bearing rocks a re correctly predicted by the Maxwell-Wagner-Bruggeman-Hanai (MWBH) theory of composite dielectrics. This theory takes into account only the bulk prop erties of components, their partial volumes and the configuration of partic les. The theory ignores two important factors: the surface contribution to polarization and the effect of clustering of components. At frequencies f<1 0 MHz there are certain frequency domains which exhibit relaxation processe s not predicted by MWBH theory. The characteristic times of these processes range from 10(-6) to 10 s. These relaxation effects are related to differe nt surface polarization processes which are, in order of increasing water c ontent, (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) polarizati on of the 'open' double layer, implying free exchange of excess ions with t he bulk electrolyte and generation of transient diffusional potentials, whi ch lag behind the applied field. Some theoretical models predict large effe ctive values of relative dielectric constants in the range 10(5)-10(6) at l ow frequencies. Knowledge of the characteristic signatures of these physica l mechanisms is important for the correct interpretation of experimental da ta. Analysis of existing theories of polarization of heterogeneous media shows that electrical spectroscopy can be useful for the interpretation of freque ncy spectra of complex dielectric permittivity or conductivity of water-bea ring rocks and porous materials in general, and for the determination of wa ter content, its thermodynamic state, the connectivity of water-bearing cha nnels and their correlation lengths and the surface to volume ratio and sur face charge in particular, in addition to the traditional formation factor, which is obtained from ohmic conductivity measurements.