Fractal Geometry, porosity and complex resistivity: from rough pore interfaces to hand specimens

• Published in: Development in Petrophysics Vol. 122; no. 1; pp. 277 - 286
• Main Authors: Da Rocha, Brígida Ramati P., Habashy, Tarek M.
• Format: Book Chapter Journal Article
• Language: English
• Published: The Geological Society of London 1997; The Geological Society, London; Geological Society of London
• Series: Geological Society, London, Special Publications
• Subjects: Geology, Exploration & Drilling; Oil & Gas Engineering
• ISBN: 1897799810; 9781897799819
• ISSN: 0305-8719; 2041-4927
• DOI: 10.1144/GSL.SP.1997.122.01.16

We propose a new model to interpret the electrical behavior of rocks containing metallic or clay particles. This new model encompasses some of the other commonly used models as special cases. This model is a generalization of two models, one developed by Dias (Journal of Geophysical Research 77, 4945–4956, 1972) and another by Pelton et al. (Geophysics Geophysics, 589–609, 1978). Its circuit analog includes an impedance K(iω)−η which simulates the effects of the fractal rough pore interfaces between the conductive grains (metallic or clay minerals which are blocking the pore paths) and the electrolyte. This generalized Warburg impedance is in series with the resistance of the blocking grains and both are shunted by the double layer capacitance. This combination is in series with the resistance of the electrolyte in the blocked pore passages. The unblocked pore paths are represented by a resistance which corresponds to the normal DC resistivity of the rock. The parallel combination of this resistance with the ‘bulk’ sample capacitance is finally connected in parallel to the rest of the above-mentioned circuit. The model was tested over a wide range of frequencies against experimental data obtained for amplitude and phase of resistivity or conductivity as well as for the complex dielectric constant. The samples studied are those of sedimentary, metamorphic and igneous rocks.