Fractal Model of Rocks—A Useful Model for the Calculation of Petrophysical Parameters
- 1 Council for Geoscience, Pretoria, South Africa
Abstract
A fractal model containing n -series of spheres and ellipses with corresponding radii, and surrounded by a thin film of adsorbed water has been developed. This model is more suitable to real sedimentary rocks because it not only allows for varying grain sizes and number of fractions, but also takes into consideration the influence of double electrical layers on the physical properties of sediments. Ellipsoid fractal models provide mathematical proof of the phenomenon of supercapillary conductivity observed in laboratory measurements. Using the parameters of the fractal models several petrophysical parameters can be calculated, namely resistivity porosity, and permeability. In a case study, layers with different resistivity were identified on a section taken from a TDEM survey, and porosity and salinity of water bearing layers were estimated using the fractal model. Estimated permeability using the fractal model showed good agreement with other methods.
- G. E. Archie, “The Electrical Resistivity Log as an Aid in Core Analysis Interpretation,” Transactions of AIME, Vol. 146, 1942, pp. 54-62.
- V. N. Kobranova, “Petrophysics, Manual Book,” Nedra, Moscow, 1986.
- O. N. Grigorov, Z. P. Kozmina, A. B. Markovich and D. A. Fridrikhsberg, “Electrokinetic Properties of Capillary Systems,” AN SSSR, Moscow, 1956.
- A. S. Semenov, “Influence of Structure on the Specificresistivity of Aggregates,” Geophysika, Gosgeoltehizdat, Leningrad, Vol. 12, pp. 46-62.
- H. Pape, G. Clauser and J. Iffland, “Variation of Permeability with Porosity in Sandstone Diagnesis Interpreted with Fractal Pore Space Model,” Pure and Applied Geophysics, Vol. 157, No. 4, 2000, pp. 603-619. doi:10.1007/PL00001110
- V. N. Dakhnov, “Interpretation of Results of Geophysical Investigation in Wells,” Gostoptehizdatm, Moscow, 1962.
- D. A. Fridrikhsberg, “Course of Colloid Chemistry,” Khimia, Leningrad, 1974.
- V. V. Kormiltsev, “Electrokinetical Phenomena in Porous Rock,” AN SSSR, Ural Branch, Sverdlovsk, 1995, 47 p.
- D. A. Fridrikhsberg and V. A. Barkovsky, “Study of Surface Conductance, Zeta Potential and Adsorption on Diaphragm of Barium Sulphate,” Kolliodny Journal, Vol. 26, No. 6, 1964, pp. 7-22.
- M. I. Epov, Yu. ADashevsky and I. N. Eltsov, “Automatic Interpretation of Electromagnetic Soundings,” Institute of Geology and Geophysics, Novosibirsk, 1990.
- S. S. Itenberg, “Interpretation of Results of Loggings,” Nedra, Moscow, 1978.
- V. Yu. Zadorozhnaya, “Electroprospecting by TDEM for a Search for Groundwater in Permafrost,” Izv. VUZ, Series, Geologiya i Razvedka, Vol. 3, 1998, pp. 103-106.
- H. A. Baker, “Prediction of Capillary Pressure Curves Using Dielectric Spectra,” Unpublished MSc Thesis, Boston College, Chestnut Hill, 2001.
- R. R. Berg, “Method of Determining Permeability from Reservoir Rock Properties,” Transactions of Gulf Coast Association of Geological Societies, Vol. 20, 1970, pp. 303-317.
- V. Zadorozhnaya and L. P. Maré, “New Model of Polarization of Rocks: Theory and Application,” Acta-Geophysica, Vol. 59, No. 2, 2011, pp. 262-295. doi:10.2478/s11600-010-0041-6