Abstract: In order to analyze how the heterogeneity of the pore structure of porous media affects its permeability characteristics, the theory of geological entropy for porous media, along with a heterogeneity index called the entropy scale, are introduced based on the principle of information entropy. Utilizing a model consisting of spherical particles with varying distances between their centers, a comparative analysis is carried out between the entropy scale and traditional geometric parameter indicators, which demonstrates the rationality of using the entropy scale for assessing both the heterogeneity of the pore structure and the permeability characteristics of porous media. Using the improved four-parameter random growth method and lattice-Boltzmann method, heterogeneous porous media with different degrees of heterogeneity were established and fluid seepage was simulated. The relationship between the entropy scale of heterogeneous porous media and their heterogeneity and permeability characteristics was analyzed. The results indicate that when porosity is constant, the entropy scale can consider the spatial arrangement and distribution of pore structures, providing a more accurate description of how pore structure heterogeneity affects permeability. The average equivalent particle diameter shows a positive correlation with the entropy scale: stronger heterogeneity leads to a wider range of changes in the average equivalent particle diameter and entropy scale, resulting in increased permeability of porous media and a more pronounced dominance of preferential flow effects. The differences in the size of the particles, along with the irregular and random arrangement of these particles, contribute to the fundamental factors responsible for the increased heterogeneity observed in the pore structure. Tortuosity, connected porosity, and specific surface area collectively play a crucial role in the influencing mechanism through which the heterogeneity of pore structure affects permeability. Their product values exhibit a higher positive correlation with the entropy scale; larger entropy scales correspond to higher permeability. The nonlinear relationship between entropy scale and permeability approximately follows an exponential function.