Abstract Fractal parameters of porous media have been a focus of study in petroleum engineering and hydrogeology for several decades because they provide an effective way to describe the complexity of pore structure across a wide range of scales. This paper combines 3D process-driven digital rock modeling with fractal analysis in order to understand the effect of varying sorting, compaction, cementation, and the fine grain fraction of binary models on the fractal parameters and specific surface area of porous media. Digital rock models (DRMs) were constructed to simulate sandstone using a process-driven modeling technique which simulates sedimentation. The fractal parameters of the resulting pore geometry were calculated using the box-counting method on 2D and 3D representations of the DRMs. Our simulations indicate that increasing compaction or cementation lead to significant decreases in fractal dimension, specific surface area (SSp) and porosity, showing that these two diagenetic processes can affect the pore microstructure of the rock significantly. While interface fractal dimension (Di) and SSp both increase slightly with decreases in sorting (grain size variety), and porosity decreases slightly. Examining the behavior of binary models, the porosity of our digital models shows a V-shaped curve as fine grain fraction increases from 0 to 1, consistent with, but higher than the theoretical values, which we attribute to incomplete packing of the grains arising from the simplified packing algorithm and finite boundary of models. The value of both SSp and Di increase as the fine grain fraction increases. However, we must notice that the porosity may be underestimated, and the fractal dimension may be overestimated when we use models consisting of very fine spherical grains due to the effect of image resolution.

中文翻译：

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孔隙结构分形特性的 3D 数字岩石建模

摘要 多孔介质的分形参数几十年来一直是石油工程和水文地质学研究的热点，因为它们提供了一种有效的方法来描述大范围内孔隙结构的复杂性。本文将 3D 过程驱动的数字岩石建模与分形分析相结合，以了解不同分选、压实、胶结和二元模型的细粒分数对多孔介质分形参数和比表面积的影响。构建数字岩石模型 (DRM) 以使用模拟沉积的过程驱动建模技术来模拟砂岩。使用盒计数方法对 DRM 的 2D 和 3D 表示法计算所得孔隙几何形状的分形参数。我们的模拟表明，压实或胶结作用的增加导致分形维数、比表面积 (SSp) 和孔隙度的显着降低，表明这两种成岩过程可以显着影响岩石的孔隙微观结构。而界面分形维数 (Di) 和 SSp 都随着分选（晶粒尺寸变化）的减少而略有增加，孔隙率略有下降。检查二元模型的行为，我们的数字模型的孔隙率显示出 V 形曲线，因为细颗粒分数从 0 增加到 1，与理论值一致，但高于理论值，我们将其归因于由简化的打包算法和模型的有限边界。随着细晶粒分数的增加，SSp 和 Di 的值都增加。然而，