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Mathematical Models for Water Treatment Problems
(Український державний університет науки і технологій, Дніпро, 2025) Biliaiev, Mykola M.; Kozachyna, Vitalii A.; Kyrychenko, M. V.; Skuratov, M. O.; Chirkov, A. O.; Filonenko, H. K.
ENG: Purpose. Assessing the efficiency of water treatment in different structures is a problem of big importance. To solve this a problem, it is necessary to have mathematical models that allow to quickly obtain data on the cleaning effect in different structures. The aim of the work is to develop numerical models to determine the efficiency of water treatment in an aeration tanks, settlers and mixers. Methodology. For mathematical modeling of the process of water treatment in a bioreactor, balance equations were used. These equations allow to determine concentrations of substrate, activated sludge and dissolved oxygen in s structure. The Monod model is used to calculate the substrate oxidation process. To study effectiveness of water treatment process in vertical settler Euler’s equation were used with convective-diffusive equation. To simulate reagent mixing in mixer equation of potential and convective-diffusive equation were used. To solve governing equations finite- difference schemes of splitting were used. Findings. A tool for theoretical assessment mass transfer processes in aeration tank, vertical settler, mixer was developed. Originality. Effective numerical models to simulate water treatment in bioreactor, vertical settler, mixer were developed. Fundamental equations of Fluid Dynamics and Mass Transfer were used to build the models. Proposed models can be used in practice at the stage of «sketch designing». The models take into account the main physical parameters which influence the process of Mass Transfer and are quick computing. Practical value. The constructed mathematical model can be useful during the reconstruction and designing structures for water treatment. Computer programs have been developed to carry out numerical experiment. The results of a computer experiment are presented.
Ієрархія математичних моделей для розрахунку аеротенків
(Український державний університет науки і технологій, Дніпро, 2026) Biliaiev, Mykola M.; Chirkov, A. O.
ENG: Purpose. Aeration tanks are widely used in wastewater treatment. Complex processes of mass transfer of impurities, activated sludge, and oxygen occur in an aeration tank. Therefore, it is very important to have specialized mathematical models that allow for a comprehensive consideration of complex multifactorial processes in aeration tanks. The aim of this work is to identify the advantages and disadvantages of mathematical models used to evaluate the efficiency of water treatment in aeration tanks, as well as to develop numerical models for analyzing the operation of aeration tanks. Methodology. System analysis methods used in accordance with hydrodynamics and mass transfer models in wastewater treatment tasks in aeration tanks. The solution of the hydrodynamics problem is based on the use of potential flow model. Mass transfer equations that take into account convective and diffusive transport are used to describe the process of impurity movement in an aeration tank. The development of numerical models is based on the use of the method of splitting modeling equations. Findings. Numerical models for calculating the efficiency of water purification in an aeration tank have been developed and implemented in software. These models are a modern tool for mathematical modeling of complex, multifactorial mass transfer processes in aeration tanks. Originality. Based on a systematic analysis, the advantages and disadvantages of the models used to analyze the efficiency of aeration tanks have been identified. The construction of effective numerical models for calculating hydrodynamics and mass transfer in aeration tanks has been considered. Practical value. The proposed numerical models of hydrodynamics and mass transfer in aeration tanks can be useful for rapid assessment of the efficiency of wastewater treatment in aeration tanks.