NUMERICAL STUDY OF SUBSTANCE TRANSFER PROBLEMS IN POROUS MEDIA ON THE BASE OF MULTI-STEP KINETICS

Abstract

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