<p>This paper presents a mathematical model based on the balance <br /> equation of substance transport, its deposition, and re-mobilization, considering <br /> multi-stage kinetics. The model accounts for anomalous transport kinetics, as well <br /> as local accumulation and diffusion in the balance equation. Specific problems <br /> are formulated based on the model, and their numerical solutions are obtained. <br /> Computational experiments examine the influence of anomalous parameters on <br /> substance transport, leading to relevant conclusions. The relevance of this study is <br /> driven by the need to develop high-precision models for drinking and wastewater <br /> treatment, improve the efficiency of oil and gas fields, and optimize hydrodynamic <br /> processes. The study's goal is to improve mathematical models that show strange <br /> substance transport in porous media by taking into account multi-stage deposition <br /> kinetics and to come up with numerical solution methods. This study focuses on <br /> applying fractional-order balance and kinetic equations to model complex processes <br /> in porous media. The research methodology includes mathematical modeling, <br /> computational mathematics, and numerical experiments. When fractional-order <br /> equations are used, they let you look at the physicochemical properties of porous <br /> media and how uncertainties change over time in the transport of substances. <br /> The study has led to the development of new mathematical models for substance <br /> transport in porous media, which incorporate multi-stage deposition kinetics. <br /> Additionally, efficient algorithms and software tools for numerical analysis of these <br /> processes have been created. The sindings have scientific and practical signisicance <br /> in hydrogeology, fluid and gas mechanics, environmental protection, and industrial <br /> technologies</p>