This paper considers and solves the issues of taking into account the inverse effect of process characteristics (liquid concentration and sediment contamination) on the environment characteristics (porosity, filtration, diffusion, mass transfer, etc.) on the example of liquid purification in magnetic and sorption filters. An algorithm for numerical- asymptotic approximation of the corresponding model problem solution is obtained, which is described by a system of non-linear singularly perturbed differential equations of the type “convection-diffusion-mass transfer". Appropriate ratios (formulas) are effective for optimizing the water treatment process and increasing the treatment system productivity as a whole (allow to determine the filter protective time, the filter size, etc.) in cases of convective predominance and sorption components of the corresponding process over diffusion and desorption which occurs in the vast majority of filter systems. On this basis, a corresponding computer experiment was conducted, the results of which show the proposed model advantages in comparison with classical.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 35
Issue: 3
Year: 2022

DOI: 10.12732/ijam.v35i3.8

Download Section

Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.


  1. [1] V. Petrenko, M. Netesa, O. Tiutkin, O. Gromova, V. Kozachyna, Mathematical modeling of water purification with filter, Science and Transport Progress Bulletin of Dnipropetrovsk National University of Railway Transport, 85, No 1 (2020), 17-24; DOI: 10.15802/stp2020/199710.
  2. [2] Yu. Skolubovich, A. Skolubovich, D. Volkov, T. Krasnova, E. Gogina, The mathematical model of environmental waters purification, Journal of Physics: Conference Series, 1425, 1-6 (2019); DOI: 10.1088/17426596/1425/1/012136.
  3. [3] A. Safonyk, I. Ilkiv, Analysis of spatial nonlinear systems of diffusion type with delay, International Journal of Applied Mathematics, 34, No 5 (2021), 1013-1029 (2021); DOI: 10.12732/ijam.v34i5.9. 470 A. Safonyk, N. Zhukovska, A. Khrystyuk, M. Koziar, I. Ilkiv
  4. [4] D. Starks, C. Smith, Mathematical model of an ultrafiltration system for water purification use, Separation Science and Technology, 6, 1179-1191 (2020); DOI: 10.1080/01496390600641587.
  5. [5] V. Istomin, E. Solodova, V. Khlebnikova, Mathematical model of oilcontaining water purification process in the volume of granulated media, Proc. of the Institution of Mechanical Engineers Part M, Journal of Engineering for the Maritime Environment, 253, No 5 (2018); DOI: 10.1177/1475090218794597.
  6. [6] B. Ksenofontov, Models of complex process of water purification, AIP Conference Proceedings, 2195, No 1 (2019); DOI: 10.1063/1.5140154.
  7. [7] L. Ghaffour, M. Noack, J. Reger, T. Laleg-Kirati, Non-asymptotic state estimation of linear reaction diffusion equation using modulating functions, IFAC-Papers OnLine, 53, No 2 (2020), 4196-4201; DOI: 10.1016/j.ifacol.2020.12.2570.
  8. [8] A. Safonyk, V. Garashchenko, O. Garashchenko, Mathematical modeling of the process of liquid medias magnetic purification from multicomponent ferromagnetic impurities, International Journal of Applied Mathematics, 33, No 1 (2020), 49-58; DOI: 10.12732/ijam.v33i1.5.
  9. [9] F. Ranzingera, M. Materna, M. Layerb, G. Guthausenac, M. Wagnerad, N. Derlonb, H. Horn, Transport and retention of artificial and real wastewater particles inside a bed of settled aerobic granular sludge assessed applying magnetic resonance imaging, Water Research, 7 (2020); DOI: 10.1016/j.wroa.2020.100050.
  10. [10] A. Sahu, R. Sheikh, J.n C. Poler, Green sonochemical synthesis, kinetics and functionalization of nanoscaleanion exchange resins and their performance as water purificationmembranes, Ultrasonics Sonochemistry, 67 (2020), Art. 105163.
  11. [11] A. Safonyk, O. Prysiazhniuk, Matematychne modeliuvannia protsesu otrymannia koahuliantu metodom elektrokoahuliatsii, Tekhnichna Elektrodynamika, 4 (2019), 77-84; DOI: 10.1016/j.ultsonch.2020.105163
  12. [12] Safonyk, S. Martynov, S. Kunytskyi, Modeling of the contact removal of iron from groundwater, International Journal of Applied Mathematics, 32, No 1 (2019), 71-82; DOI: 10.12732/ijam.v32i1.7 MATHEMATICAL MODELING OF THE WATER... 471
  13. [13] A. Bomba, A. Safonyk, V. Voloshchuk, Spatial modeling of multicomponent pollution removal for liquid treatment under identification of mass transfer coefficient, Mathematical Modeling and Computing, 5, No 2 (2018), 108-118; DOI: 10.23939/mmc2018.02.108.
  14. [14] S. Battilotti, F. Cacace, M. d’Angelo, A. Germani, Asymptotically optimal distributed filtering of continuous-time linear systems, IFAC-PapersOnLine, 53, No 2 (2020), 3242-3247; DOI: 10.1016/j.ifacol.2020.12.1124.
  15. [15] A. Safonyk, A. Bomba, I. Tarhonii, Modeling and automation of the electrocoagulation process in water treatment, Advances in Intelligent Systems and Computing, 871 (2019), 451-463; DOI: 10.1007/978-3-030-01069-032. 472 A. Safonyk, N. Zhukovska, A. Khrystyuk, M. Koziar, I. Ilkiv