Fractal analysis of rock pore structure: A comparative study of the Matlab-based image method and the mercury intrusion method

Abstract

As a naturally porous medium, rocks have a very strong heterogeneity in their internal pore structure, which has an important impact on the mechanical and chemical properties of rocks, etc. Therefore, it is very important to quantitatively characterise the heterogeneity of the pore structure of rocks. Fractal dimension has long been recognised as an effective means of characterising the heterogeneity of the pore structure of porous media and is widely used in oil and gas exploitation, construction materials, mining, and water engineering. There are different methods to calculate the fractal dimension. To verify the consistency between different methods, this paper compares the results of fractal analysis using the mercury intrusion method and MATLAB image fractal analysis using three rock samples with large differences in porosity and calculates the fractal dimension in three different ways on the basis of the mercury intrusion method. The results demonstrate that the fractal dimension of the mercury intrusion method and the box counting dimension of the image analysis obtained by the three methods, although slightly different in numerical value, are consistent in their numerical relationship, i.e., they all conform to the rule that the stronger the non-homogeneity of the pore throat, the larger the fractal dimension. The results of this paper show that fractal dimension is indeed an effective means of characterising rock homogeneity.