Fractal characteristics of radioactive contaminant transport in porous media: critical porosity threshold analysis

Defining the migration and diffusion behavior of radioactive contaminants in porous media constitutes the theoretical foundation for the effective prevention and control of pollution in deep geological disposal systems. In this study, a fractal capillary seepage model is developed by simplifying the pore structure of porous media using a capillary bundle model, incorporating fractal theory to characterize the heterogeneous and irregular pore geometry, and considering three primary transport mechanisms: molecular diffusion, advection, and mechanical dispersion. Through theoretical derivation and numerical analysis, the influence of porosity on seepage velocity is systematically investigated. The results show that seepage velocity initially increases and then decreases with porosity, reaching a maximum at a porosity of 0.26. When the porosity is below 0.26, the increase in seepage velocity is primarily attributed to the enlargement of the average and maximum pore radii. When porosity exceeds 0.26, although the total flux of radioactive contaminants continues to rise, the total pore surface area increases at a higher rate, leading to a decrease in seepage velocity per unit area. This study provides theoretical insights into the transport mechanisms of radioactive contaminants and supports the optimization of subsurface barrier design.