Fractal Dimension of Digital 3D Rock Models with Different Pore Structures

Abstract

The macroscopic physical properties of rocks are profoundly determined by their microstructure, and the research of accurately characterizing rock pore structure has been extensively carried out in the fields of petroleum engineering and geoscience. Fractal geometry is an effective means of quantitatively estimating the pore structure properties of porous media. In this study, the evolution law of the fractal dimension and the quantitative relationship between the fractal dimension and porosity were investigated based on the digital 3D rock models. First, three kinds of models with gradually changing pore structures, namely sedimentation, compaction, and cementation, were systematically reconstructed by the process-based approach. Then, the fractal dimensions of the skeleton, pore, and surface of the models were computed and analyzed. Finally, the relationships among the fractal dimension, porosity, and complexity were explored qualitatively. These works reveal the changing laws of three types of fractal dimensions for different pore structure models. The pore structure differences in sedimentation model can only be distinguished by the surface fractal dimension, while both pore and surface fractal dimensions are available parameters for characterizing different pore structures in compaction and cementation models. The quantitative relations between box-counting fractal dimension and porosity were established, which can be expressed by combining linear and logarithmic formulas. The comparison of fractal dimensions of compaction and cementation models proves that fractal dimensions can distinguish the subtle pore structure differences in digital 3D rock models. Understanding the evolution law between the fractal dimension and pore structure parameters provides more references for classifying and evaluating rock pore structure features using fractal dimensions.