The complex and heterogeneous microstructure of underground porous media usually results from geological processes such as deposition, compaction, cementation and fluid-mineral interactions. Variations in these microstructural characteristics largely determine the differences in the transport properties of porous media. The fractal geometry theory has been successfully applied to characterize the microstructure and transport properties of underground reservoirs. In this study, two-dimensional porous media with differently heterogeneous structures are reconstructed by utilizing the quartet structure generation set method. Fractal dimension and lacunarity are implemented to quantify the complex microstructure and analyze the relationships among these parameters. Under specific porosity, the fractal dimension increases with the reduction of lacunarity according to a power law relationship. Meanwhile, permeability has a perfect power law relationship with porosity under the same heterogeneity. The stronger heterogeneity increases the degree of pore aggregation, resulting in increased pore radius for fluid flow. For porous media with the same porosity, permeability has a significant positive power law relationship with lacunarity and a negative relationship with fractal dimension. The results demonstrate that fractal parameters are helpful to fully understand the influence of complex microstructure and chemical reactions on the macroscopic physical properties of porous media.

地下多孔介质复杂且非均质的微观结构通常是由沉积、压实、胶结和流体-矿物相互作用等地质过程造成的。这些微观结构特征的变化在很大程度上决定了多孔介质传输特性的差异。分形几何理论已成功应用于表征地下储层的微观结构和输运特性。本研究利用四重结构生成集方法重构了具有不同异质结构的二维多孔介质。使用分形维数和空隙度来量化复杂的微观结构并分析这些参数之间的关系。在特定孔隙率下，根据幂律关系，分形维数随着空隙度的减少而增加。同时，在相同的非均质性下，渗透率与孔隙度具有完美的幂律关系。更强的非均质性增加了孔隙聚集的程度，导致流体流动的孔隙半径增加。对于孔隙度相同的多孔介质，渗透率与孔隙度呈显着的正幂律关系，与分形维数呈负相关。结果表明，分形参数有助于充分理解复杂微观结构和化学反应对多孔介质宏观物理性质的影响。更强的非均质性增加了孔隙聚集的程度，导致流体流动的孔隙半径增加。对于孔隙度相同的多孔介质，渗透率与孔隙度呈显着的正幂律关系，与分形维数呈负相关。结果表明，分形参数有助于充分理解复杂微观结构和化学反应对多孔介质宏观物理性质的影响。更强的非均质性增加了孔隙聚集的程度，导致流体流动的孔隙半径增加。对于孔隙度相同的多孔介质，渗透率与孔隙度呈显着的正幂律关系，与分形维数呈负相关。结果表明，分形参数有助于充分理解复杂微观结构和化学反应对多孔介质宏观物理性质的影响。