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.
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 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.
 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.
 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
 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.
 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:
 B. Ksenofontov, Models of complex process of water purification, AIP Conference
Proceedings, 2195, No 1 (2019); DOI: 10.1063/1.5140154.
 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:
 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.
 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:
 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.
 A. Safonyk, O. Prysiazhniuk, Matematychne modeliuvannia protsesu otrymannia
koahuliantu metodom elektrokoahuliatsii, Tekhnichna Elektrodynamika,
4 (2019), 77-84; DOI: 10.1016/j.ultsonch.2020.105163
 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
 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.
 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:
 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