• Andrij Bomba Department of Computer Science and Applied Mathematics, National University of Water and Environmental Engineering, Rivne, Ukraine
  • Jurij Klimjuk Department of Computer Science and Applied Mathematics, National University of Water and Environmental Engineering, Rivne, Ukraine
Keywords: mathematical model, water purification, adsorption, impurity, rapid multilayer filter


A model of the adsorption purification of water from impurities in rapid multilayer cone-shaped filters with piecewisehomogeneous porous loads with a constant filtration rate taking into account the removal of part of the heat on the surfaces of division of layers is formulated. The proposed model provides an opportunity to conduct computer experiments to study the change in the concentrations of impurities in the filtration flow and adsorbed on the surface of the adsorbent load during physical and chemical adsorption, temperature, characteristics of piecewise-homogeneous porous loads along the filter height and based on their prediction of optimal adsorbent use and increasing the duration of filters.


Dvadnenko M. V., Privalova N. M., Kudayeva I. Yu., Stepura A. G. Adsorption wastewater treatment. Modern science-intensive technologies. 2010. № 10. P. 214–215.

Edzwald J. Water Quality and Treatment. A Handbook on Drinking Water. McGraw-Hill Professional, 2010. 1996 p.

Hendricks D. W. Fundamentals of water treatment unit processes : physical, chemical, and biological. Boca Raton, CRC Press, 2011. 883 p.

Sakalova G. V., Vasilinich T. M. Research of efficiency of sewage treatment from ions of heavy metals with use of natural adsorbents: monograph. Vinnytsia, LLC "Works", 2019. 92 p.

Nevzorova A. B. Fundamentals of automation of water supply and drainage systems: a guide. Gomel, UO "BelGUT", 2005. 115 p.

Makarevich N. A., Bogdanovich N. I. Theoretical foundations of adsorption: a textbook. Arkhangelsk, SAFU, 2015. 362 p.

Zelentsov V. I., Datsko T. Ya., Dvornikova E. E. Influence of temperature on equilibrium and adsorption kinetics of fluoride ions by heat-treated oxy oxyhydrates. Electronic materials processing. 2008, № 3. P. 50–58.

Laptev A. G., Sergeeva E. S. Physical and mathematical modeling of sortion properties of peat for water purification from oil products. Water: chemistry and ecology. 2009, № 3. P. 14–19.

Sperlich A., Schimelpfenning S., Baumgarten B. et al. Predicting anion breakthrough in granular ferric hydroxide (GFH) adsorption filters. Water Res. 2008. 42. P. 2073–2082.

Bomba A. Ya., Safonyk A. P. Modeling of nonlinearly perturbed processes of liquid purification from multicomponent contaminants: monograph. Rivne, NUVGP, 2017. 296 p.

Polyakov V. L. Modeling of water treatment process in adsorber loading. Reports of the National Academy of Sciences of Ukraine. 2012, № 5. P. 63–71.

Kalteh A. M., Hjorth P. and Berndtsson R. Review of the self-organizing map (SOM) approach in water resources: analysis, modelling and application. Environmental Modelling and Software. 2008, vol. 23, № 7. P. 835–845.

Maier H. R., Dandy G. C. Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environmental Modelling and Software. 2000, vol. 15, № 1. P. 101–124.

Heikkinen M., Poutiainen H., Liukkonen M., Heikkinen T. and Hiltunen Y. Self-organizing maps in the analysis of an industrial wastewater treat-ment process. Mathematics and Computers in Simulation. 2011, vol. 82, № 3. P. 450–459.

Safonyk A. P. Modelling the filtration processes of liquids from multicomponent contamination in the conditions of authentication of mass transfer coefficient. International Journal of Mathematical Models and Methods in Applied Sciences. 2015, vol. 9. P. 189–192.

Klymyuk Yu. Ye., Bomba A. Ya. Computer prediction of adsorption purification of water from impurities in rapid multilayer filters of cone-shaped form. Mathematical and computer modelling. Series: Technical sciences: scientific journal. 2019. Issue 20. Kamianets-Podilskyi, Kamianets-Podilskyi National Ivan Ohiienko University, 2019. P. 51–68.

Klimjuk Ju. Je. Modelling of spatial filtration fields for one class of rapid multilayer filters of cone-shaped form with piecewise-homogeneous porous loads. Proceedings of III International scientific conference "Science: new goals". London, SI Universum, 2017. P. 4–10.

Bomba A. Ya., Klymyuk Yu. Ye. Prediction of changes in the characteristics of piecewise homogeneous porous loads of rapid multilayer filters. Bulletin of National Technical University «KhPI» Series: Mathematical modeling in engineering and technologies. Kharkiv, NTU "KhPI". 2018. № 27 (1303). P. 8–15.

Bomba A., Klimjuk Ju. Prediction filter materials optimal use in rapid multilayer filters with piecewise- homogeneous porous loads. Journal of Computational and Applied Mathematics. 2017. No. 1 (124). P. 3–14.