Fractal analysis of sandstone pore space geometry

Abstract

Fractal analysis is currently one of the fastest evolving branches of science. Numerous objects in nature exhibit a fractal structure. Additionally, the vast majority of rocks - especially reservoir rocks - take the form of a fractal. Computer image analysis based on thin-section images has been used for examining the fractal structure of pore spaces, directly applying the definition of the fractal box-counting dimension. For the examined sandstone sample, thin sections were made and photographed, and the corresponding values of the fractal dimension and lacunarity were calculated. Each of the photos was encompassed by porosity that was calculated based on the number of pixels. Furthermore, the volatility of the fractal dimension and lacunarity were studied as well as their relationships with the porosity. A correlation analysis between the fractal parameters and the porosity was carried out. The results were compared with the data obtained from a mercury porosimetry of the same sample of sandstone.