Fractal Model of Rocks—A Useful Model for the Calculation of Petrophysical Parameters

V. Yu. Hallbauer-Zadorozhnaya

Council for Geoscience, Pretoria, South Africa.

DOI: 10.4236/ijcns.2013.64022                

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.

Keywords

Fractal; Sediments; Resistivity; Porosity; Permeability

Conflicts of Interest

The authors declare no conflicts of interest.

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