Effect of adsorption coefficient and sorption intensity on the spatiotemporal variation of contaminant concentration in saturated porous media using the fractional advection–dispersion equation

This study presents a numerical solution of time and space fractional advection–dispersion equation (FADE) using the explicit Euler method, combined with the standard Grünwald formula and the Caputo fractional time derivative. The research aims to contribute to a better understanding and optimization of pollutant retention in subsurface environments, accounting for Freundlich parameters. The FADE model demonstrated a greater capacity for solute mass retention. Additionally, in a saturated porous medium, solute movement is more effectively influenced by the absorption parameter associated with the retardation factor. In other words, this parameter has a notable impact on pollutant dispersion in porous media. This work emphasizes the importance of accurately characterizing these parameters to optimize pollutant retention and better understand transport mechanisms in complex porous media.