Rock conductivity and fractal nature of porosity

Abstract

While the d.c. electrical properties of a rock, through the volume conductivity, provide information on pore space structure (Formation factor) and pore fluid, the frequency dependence of the electrical parameters allows the characterization of the pore-matrix interfaces. To illustrate these properties, we present here some results of measurements performed on sedimentary rocks (Vosges and Fontainebleau sandstones). These samples have a classical electrical response, i.e. a 'Cole and Cole' frequency behaviour near a certain relaxation frequency and a low-frequency dispersion. We discuss some of the models that have been proposed in the past to explain this behaviour. It appears that most of them are valid near and above the relaxation frequency, but only Dissado and Hill's model seems to be satisfactory over the whole frequency range. The fractal nature of the interfaces, assumed in two of these models but appropriate only for one of them, could also be a convenient explanation for the frequency dependence. Terra Nova, 3,265-275 265 C. RUFFET €T AL.

Electrical spectroscopy of porous rocks: a review-II. Experimental results and interpretation

“…A detailed experimental study and computer modelling of possible ties between dielectric spectra and fractality of surfaces have been carried out by Ruffet (1993), Ruffet et al . (1991a, 1991b) and Glover et al .…”

“…The main volume of ac measurements on rocks is presented in the papers and monographs of Keller & Licastro (1959), Howell & Licastro (1961), Chelidze (1963, 1971, 1984, 1987), Parkhomenko (1967), Chelidze et al . (1977, 1979, 1998), Olhoeft (1981, 1985), Keller (1982), Knight (1983, 1991), Lockner & Byerlee (1985), Sen (1989), Knight & Nolen‐Hoeksema (1990), Ruffet et al . (1991a,b), De Lima & Sharma (1992), Knight & Dvorkin (1992), Ruffet (1993), Roberts & Tyburczy (1994), Garrouch & Sharma (1994), Glover et al .…”

An electrical conductivity model for fractal porous media

“…Katz and Thompson [1985] first presented evidence that the pore spaces of sandstone samples are fractal by analyzing experimental data. Several previous fractal models have been presented for the electrical conductivity of porous systems [Ruffet et al, 1991a[Ruffet et al, , 1991bNigmatullin et al, 1992;Bahr, 1997;Roy and Tarafdar, 1997]. However, we are unaware of any fully analytical expression between electrical conductivity and other physical parameters (e.g., porosity).…”

Electrical and dielectric properties of systems of porous solids and salt-containing nonpolar liquids

“…10,11 If these effects emanate from the bulk material, the complex permittivity does not depend on the sample thickness, whereas the permittivity shows a clear dependence on thickness when electrode effects cause the high permittivities. One way of determining the main cause for these effects-electrode or ''bulk''-is to take one sample that is supposed to be homogeneous on the macroscale ͑the porosity and the grain size distribution do not vary within the sample͒ a͒ Electronic mail: f6bbn@fy.chalmers.se and cut it into pieces of different thicknesses.…”