Сафоник, А. П. та Присяжнюк, О. В. та Ільків, І. В. та Ластовецький, Д. О. (2022) НЕЛІНІЙНА СИНГУЛЯРНО ЗБУРЕНА МАТЕМАТИЧНА МОДЕЛЬ ПРОЦЕСУ ФІЛЬТРУВАННЯ З УРАХУВАННЯМ ТЕМПЕРАТУРНОГО РЕЖИМУ. Вісник Національного університету водного господарства та природокористування (3(99)). с. 82-90.

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Анотація

Розроблено математичну модель процесу очищення води на каркасно-засипних фільтрах шляхом «дифузійного збурення» з урахуванням температурного режиму. Запропоновано метод і побудовано алгоритм розв’язання відповідної нелінійно збуреної задачі. На цій основі проведено комп’ютерний експеримент.

Title in English

NONLINEAR SINGULARLY DISTURBED MATHEMATICAL MODEL OF THE FILTERING PROCESS TAKING THE TEMPERATURE REGIME INTO ACCOUNT

English abstract

The field of applicability of known mathematical models of filtration processes through porous media is limited by numerous assumptions regarding the properties of the filtered liquid. Also, a number of parameters are generalized or frankly neglected. At the same time, the optimization of filtering processes, for which extremely large sums of money are spent in different countries, involves the possibility of reliably predicting the consequences of changing not only the most complex of existing, but also hypothetical filtering conditions. The experience of fundamental science unequivocally indicates the need to introduce a generalized mathematical model of filtration processes through porous media. At present, the question of generalization of known models of water purification processes by means of their diffusion perturbation with the aim of researching non-linear processes of wastewater purification on frame-backfill filters taking into account low diffusion and changes in loading porosity remains relevant. Also, an important factor that is neglected in many cases is the temperature, which, as shown by experimental studies, plays a significant role in the cleaning process. Considering the rather high cost of field experiments, the development of a mathematical model of the process of water purification on frame-backfill filters by means of "diffusion perturbation" taking into account the temperature regime is relevant. Based on this, a mathematical model of wastewater treatment was developed in the work, which describes the processes taking place at treatment facilities taking into account changes in the temperature regime. A method is proposed and an algorithm is built for solving the corresponding nonlinearly perturbed "convection – diffusion – heat – mass transfer" problem. The results of the calculations of the distribution of the pollution concentration with and without taking into account the temperature during the cleaning of the liquid are presented. The obtained results make it possible to predict and automate technological processes of wastewater treatment in more detail and comprehensively.

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