基于分形理论的饱和多孔介质电导率模型建立

多孔介质具有复杂的内部孔隙结构，其固体基质的组成成分、内部孔隙的几何形状及其赋存于内部孔隙的液体成分都对多孔介质的电导率有较大影响，因此很难对其导电特性进行准确表征。多孔介质内部孔隙的不规则性表现出极强的分形特性，其分形维数在一定程度上能反映多孔介质的内部微观结构特征，且分形几何理论已经被用于多孔介质输运特性的研究中。为进一步丰富多孔介质电导率模型，促进对微观物理结构如何影响其宏观电导性的理解，本文基于分形理论，以多孔介质微结构参数（孔隙度、孔隙分形维数和曲率分形维数）为基础，建立了多孔介质的电导率模型。以现有试验数据为基础，对推导电导率模型的正确性进行验证，结果表明，两者具有较高的一致性，说明该电导率模型的正确性和有效性。

Research on Electrical Conductivity Model of Saturated Porous Media Based on Fractal Theory

Porous media has a complex internal pore structure. The composition of the solid matrix, the geometry of the internal pores and the liquid composition of the internal pores all have a great impact on the electrical conductivity of the porous media. As a consequence, it is difficult to accurately characterize its electrical conductivity. The irregularity of internal pores in porous media shows strong fractal characteristics. To a certain extent, the fractal dimension can reflect the internal microstructure of porous media and the fractal geometry theory has been used in the study of transport properties of porous media. To further enrich the electrical conductivity model of porous media and promote the understanding of how the microscopic physical structure affects its macroscopic electrical conductivity, based on the fractal theory and the microstructure parameters (porosity, pore fractal dimension and tortuosity fractal dimension) of porous media, an electrical conductivity model is established. Based on the existing test data, the correctness of the deduced conductivity model is verified. The data analysis shows that the results calculated by the fractal electrical conductivity model are in good agreement with the existing data, indicating the accuracy and effectiveness of the proposed electrical conductivity model.