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.

中文翻译：

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砂岩三维孔隙特征定量分形分析的新型计盒法


分形理论为精确描述和量化储层岩石中复杂的孔隙结构提供了强大的工具，这对于了解这些岩石内介质的储存和运移特征至关重要。面对计算岩石孔隙度三维分形维数的挑战，本研究提出了一种创新的计算流程，从几何角度直接计算三维分形维数。通过采用集成傅里叶变换（FT）和小波变换（WT）的复合去噪方法，结合阈值分割、顶帽变换和膜增强等多模态孔隙提取技术，我们成功地制作了精确的数字岩石模型。然后应用改进的盒计数方法来分析这些数字岩石的体素数据，准确计算岩石孔隙分布的分形维数。进一步进行渗透率实验数值模拟，探讨岩石孔隙分形维数、孔隙度和绝对渗透率之间的物理相关性。结果表明，分形维数较高的岩石表现出更复杂的孔隙连通路径以及更宽、更不均匀的孔隙分布，这表明理想的岩石样品应具有更低的分形维数和更高的有效孔隙率，以实现最佳的流体传输性能。本研究的方法和结论为岩石复杂孔隙的定量分析提供了新的工具和见解，有助于探索岩石内介质的分形输运特性。