# MATHEMATICAL MODELING SINGULARLY PERTURBED PROCESSES OF WATER SOFTENING ON SODIUM-CATIONITE FILTERS

### Abstract

Mathematical model of the process of water softening using ion exchange pre-treatment of waters to desalination, with a view to removal of scale forming components, such as calcium and magnesium, are formed in the paper. In this process, no additional chemicals, except for brines formed during desalination, are required for regeneration of ion-exchanger in operation cycles. An asymptotic approximation of a solution of a corresponding model problem is constructed. Theoretical description and modelling assumptions included the set of differential equations of mass balance, initial, boundary and operational conditions. The paper deals with the development of a computer model for description and prediction of the performance of ion exchange columns.

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Published : 2019-03-03

Safonyk, A., Prysiazhniuk, I., Prysiazhniuk, O., & Naumchuk, O. (2019). MATHEMATICAL MODELING SINGULARLY PERTURBED PROCESSES OF WATER SOFTENING ON SODIUM-CATIONITE FILTERS. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 9(1), 37-40. https://doi.org/10.5604/01.3001.0013.0901

Andrii Safonyk  safonik@ukr.net
National University of Water and Environmental Engineering, Department of Automation, Electrical Engineering and Computer-Integrated Technologies  Ukraine
http://orcid.org/0000-0002-5020-9051
Ihor Prysiazhniuk
Rivne State University of Humanities, Department of Mathematics  Ukraine
http://orcid.org/0000-0003-4531-1788
Olena Prysiazhniuk
National University of Water and Environmental Engineering, Department of Automation, Electrical Engineering and Computer-Integrated Technologies  Ukraine
http://orcid.org/0000-0003-0003-3518
Oleksandr Naumchuk
National University of Water and Environmental Engineering, Department of Automation, Electrical Engineering and Computer-Integrated Technologies  Ukraine
http://orcid.org/0000-0003-2483-4141