Fractal Characterization and Petrophysical Analysis of 3D Dynamic Digital Rocks of Sandstone

Abstract

It is a crucial issue to comprehensively study the relations between microstructure and seepage capacity of porous media. Several physical-based parameters of fractal geometry can analyze the pore structure of rocks, while permeability and electrical conductivity are used to study seepage capacity. In this paper, we first created 3D dynamic digital models of nine different sandstones with varying clay content, cements, and intragranular pores in feldspar. These nine models were divided into three groups. Then, fractal dimension, lacunarity, and succolarity, permeability, and electrical properties of the models were calculated, and their relationships were investigated. We used fractal parameters to interpret the correlation between fluid flow and pore structure as one of the main petrophysical properties of a rock. Results showed that the coefficient of determination for cementation exponent m and fractal dimension is 0.869, while between m and porosity, and succolarity, it is 0.784 and 0.781, respectively. This indicates that the fractal dimension and cementation exponent describe the complexity of pores. The coefficient of determination between permeability and succolarity is 0.975, which is higher than that between permeability and the fractal dimension or porosity. The coefficient of determination between formation factor and succolarity is 0.957, which is higher than that between formation factor and the fractal dimension or porosity. Overall, a stronger relationship between petrophysical parameters, permeability in particular, and succolarity allows this lesser-used fractal parameter to be a good measure for characterizing the connectivity of pore space and pore network.