Permeability prediction of porous media with non-circular pores using a modified Kozeny–Carman equation enhanced by fractal theory

The Kozeny–Carman (K–C) equation and its variants have been widely used for permeability prediction in geotechnical engineering, but their prediction accuracy is often compromised by the assumption of circular pore shape. To enhance the accuracy of the K–C equation and clarify the influences of structural parameters on the porous media permeability, we derive a novel fractal analytical model for permeability and K–C constant, which incorporates irregular pore shape and contains no empirical constants. The fractal analytical model for permeability and K–C constant is related to parameters including the average pore shape factor, the pore size distribution fractal dimension, the tortuosity fractal dimension, the maximum pore diameter, and porosity. Based on the publicly available digital core data, the predictions of the new model were compared with those of other permeability equations, validating the effectiveness and applicability of the proposed model. We analysed the influence of the average pore shape factor on dimensionless permeability and K–C constant. An increase in the average pore shape factor leads to a nonlinear decrease in K–C constant and a nonlinear increase in dimensionless permeability. The influence of pore shape irregularity on permeability aligns with physical principles. Sensitivity analysis using the Sobol method was conducted on the parameters affecting permeability and K–C constant. The results indicate that accurately determining K–C constant by obtaining precise values for the pore size distribution fractal dimension, the average pore shape factor, and the tortuosity fractal dimension is key to reducing permeability prediction errors. In summary, the novel fractal analytical model established in this study can enhance the prediction accuracy of permeability for porous media with non-circular pores, further reveal the fluid transport mechanisms in such media, and provide a more solid theoretical foundation for geotechnical engineering and related fields.