Отправлено: 24.05.13 07:25. Заголовок: Fractal Model of Rocks—A Useful Model for the Calculation of Petrophysical Parameters

Int. J. Communications , Network and System Sciences , 2013, 6, 186-196
doi:10.4236/ijcns.2013.64022 Published Online Apr il 2013 (http://www.scirp.org/journal/ijcns)
Fractal Model of Rocks—A Useful Model for the Calculation of Petrophysical Parameters
V. Yu. Hallbauer-Zadorozhnaya
Council for Geoscience, Pretoria, South Africa

Received August 15, 2012; revised September 30, 2012; accepted October 25, 2012

Copyright © 2013 V. Yu. Hallbauer-Zadorozhnaya. This is an open access article distributed under the Creative Commons Attribu-
tion License, which permits unrestricted us e, distribution, and reproduction in any medium, provided the original work is prope rly
cited.

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 super-
capillary conductivity observed in laboratory measurements. Using the parameters of the fractal models several petro-
physical parameters can be calculated, namely resistivity porosity, and permeability. In a case study, layers with differ-
ent 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 permea bility using the fractal model showed good agreement with
other methods.

Keywords: Fractal; Sediments; Resistivity; Porosity; Permeability