# MATHEMATICAL MODELING OF WATER PURIFICATION WITH FILTER

## Authors

• V. D. Petrenko Dnipro National University of Railway Transport named after Academician V. Lazaryan, Ukraine
• M. I. Netesa Dnipro National University of Railway Transport named after Academician V. Lazaryan, Ukraine
• O. L. Tiutkin Dnipro National University of Railway Transport named after Academician V. Lazaryan, Ukraine
• O. V. Gromova Dnipro National University of Railway Transport named after Academician V. Lazaryan, Ukraine
• V. А. Kozachyna Dnipro National University of Railway Transport named after Academician V. Lazaryan, Ukraine

## Keywords:

water purification, mathematical modeling, filter, numerical model

## Abstract

Purpose. To analyze the effectiveness of water purification in water treatment systems, an important task is the development of mathematical models that allow determining the degree of water purification at the design stage. The main purpose of the work is to construct numerical models for calculating the filtration process and mass transfer in the filter. Methodology. The calculation of the filtering process of contaminated water in the filter is carried out in two stages. At the first stage, the flow rate field in the filter is calculated. To solve this problem, the classical filtration equations are used. At the second stage of the calculation, the flow of contaminated water in the filter is simulated. To solve this problem, the mass transfer equation is used, which expresses the law of mass conservation. This equation takes into account the transfer of impurities by the filtration flow, the transfer of impurities due to dispersion and the sorption of impurities in the filter material. The solution of the filtration equation is carried out using the alternating triangular method of A. A. Samarskyi. The unknown pressure value based on this method is determined by the explicit formula of point-to-point computation. For numerical integration of the mass transfer equation in the filter, a difference splitting scheme is used. Findings. The current trend in the field of water supply and sanitation is the creation of multidimensional and multifactor mathematical models. Such models make it possible to replace a physical experiment with a computational one. The complex of water treatment facilities necessarily includes water purification filters. The filter efficiency affects the efficiency of other treatment facilities of the technological treatment scheme. A mathematical model has been developed that allows analyzing the water purification process in the filter. Based on the developed numerical model, a package of application programs has been developed for computer simulation of the filter water purification process. The results of a computational experiment on modeling the filtering process of contaminated water in a filter are presented. Originality. The paper proposes a numerical two-dimensional filter model based on the filtration equation and the mass transfer equation. A feature of the developed mathematical models is the possibility of modeling the velocity field and the process of impurity transfer taking into account the geometric shape of the filter. Practical value. The calculation time for one variant of the task based on the developed numerical model is several seconds, which is important for conducting serial calculations in practice. Models can be used as an alternative to laboratory experiments.

## Author Biographies

### V. D. Petrenko, Dnipro National University of Railway Transport named after Academician V. Lazaryan

Dep. «Bridges and Tunnels», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 15 53, e-mail petrenko.diit@gmail.com

### M. I. Netesa, Dnipro National University of Railway Transport named after Academician V. Lazaryan

Dep. «Build Production and Geodesy», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (067) 195 50 27, e-mail andreynetesa@meta.ua

### O. L. Tiutkin, Dnipro National University of Railway Transport named after Academician V. Lazaryan

Dep. «Bridges and Tunnels», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 15 53, e-mail alexeytutkin@gmail.com

### O. V. Gromova, Dnipro National University of Railway Transport named after Academician V. Lazaryan

Dep. «Аrchitectural Design, Land Management and Building Materials», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (095) 304 73 33, e-mail Gromova_Elen_upbbm_diit@i.ua

### V. А. Kozachyna, Dnipro National University of Railway Transport named after Academician V. Lazaryan

Dep. «Hydraulics and Water Supply», Dnipro National University of Railway Transport named after Academician V. Lazaryan, Lazaryana St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 273 15 09, e-mail v.kozachyna@gmail.com

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2020-03-30

## How to Cite

Petrenko, V. D., Netesa, M. I., Tiutkin, O. L., Gromova, O. V., & Kozachyna V. А. (2020). MATHEMATICAL MODELING OF WATER PURIFICATION WITH FILTER. Science and Transport Progress, (1(85), 17–23. https://doi.org/10.15802/stp2020/199710

## Section

ECOLOGY AND INDUSTRIAL SAFETY