A novel box-counting method for quantitative fractal analysis of three-dimensional pore characteristics in sandstone

Abstract

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks, crucial for understanding the storage and migration characteristics of media within these rocks. Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity, this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective. By employing a composite denoising approach that integrates Fourier transform (FT) and wavelet transform (WT), coupled with multimodal pore extraction techniques such as threshold segmentation, top-hat transformation, and membrane enhancement, we successfully crafted accurate digital rock models. The improved box-counting method was then applied to analyze the voxel data of these digital rocks, accurately calculating the fractal dimensions of the rock pore distribution. Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions, porosity, and absolute permeability. The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider, more uneven pore distribution, suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties. The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.