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

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

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.


Keywords:

mathematical modelling, ion exchange, adsorption

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Published
2019-03-03

Cited by

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

Authors

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

Authors

Ihor Prysiazhniuk 

Rivne State University of Humanities, Department of Mathematics Ukraine
http://orcid.org/0000-0003-4531-1788

Authors

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

Authors

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

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