A fractal-based approach to evaluate the effect of microstructure on the permeability of two-dimensional porous media

Abstract

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.