Numerical Modeling of Liquid Solution Filtration in a Cylindrical Porous Filter
DOI:
https://doi.org/10.71310/pcam.5_69.2025.04Keywords:
hydrodynamics of porous media, mass transport, Brinkman-Darcy equations, numerical approximation, liquid purificationAbstract
A mathematical and numerical model is presented for the process of liquid solution filtration in a cylindrical porous filter. The model is based on the Brinkman-Darcy equations, describing fluid motion in a porous medium with porosity and permeability linked through the Kozeny-Carman relation. The transport of dissolved substances is governed by the advection-diffusion-reaction system, complemented by the LDF kinetics and the Langmuir isotherm for adsorption. The model also incorporates a clogging (colmatation) equation that accounts for particle deposition and temporal reduction of filter porosity. A finite-difference numerical algorithm with iterative pressure correction using the conjugate gradient method is developed, ensuring stability according to the Courant-Friedrichs-Lewy criterion. The proposed approach enables analysis of the coupled hydrodynamic, mass transfer, and adsorption phenomena, allowing for assessment of filtration efficiency and prediction of filter lifespan in liquid purification systems.
References
Ravshanov N., Abdullaev Z., Khafizov O. Modeling the Filtration of Groundwater In Multilayer Porous Media // Construction of Unique Buildings and structures. – 2020. – Vol. 92, No. 9206.
Ravshanov N., Turakulov J., Turkmanova S., Ungalov S. Numerical study of technological process of liquid solution filtration // AIP Conf. Proc.. – 2025. – Vol. 3256. – 040017. – doi: http://dx.doi.org/10.1063/5.0267147.
Kalandarbekov I., Smuleac L., Jurakhonzoda R., Rasulov U. Mathematical model construction of the isotropic filtration process based on Darcy’s law // Research Journal of Agricultural Science. – 2022. – Vol. 54, No. 1. – P. 90-95.
Karimova I.M., Turdiev T.T. Problems And Major Problems Of Mathematical Modeling of The Process Of Fluid Movement In Non-Homismal Pool Floors // The American Journal of Engineering and Technology. – Vol. 3, No. 2-12. – P. 83-89. – doi: http://dx.doi.org/10.37547/tajet.
Safonyk A., Zhukovska N., Khrystyuk A., Koziar M., Ilkiv I. Mathematical modeling of the water purification process taking into account the inverse effect of the process characteristics on the characteristics of the environment // International Journal of Applied Mathematics. – 2022. – Vol. 35, No. 3. – P. 459-472. – doi: http://dx.doi.org/10.12732/ijam.v35i3.8.
Havryliuk V., Bomba A., Pinchuk O., Gerasimov I., Klimov S., Tkachuk M., Turcheniuk V. Mathematical modelling of filtration processes in drainage systems with different depths of drainage // Journal of water and land development. – 2021. – P. 74-78.
Kajumov Sh., Arzikulov G.P., Bekchanov Sh.Je., Husanov Je.A. Matematicheskie modeli fil’tracii fljuidov v trehslojnoj srede // Vestnik oshskogo gosudarstvennogo universiteta matematika. fizika. tehnika. – 2024. – .1(4). – doi: http://dx.doi.org/10.52754/16948645_2024_1(4)_20.
Gizzatullina A. Mathematical modeling of filtration flows in a hydraulic fracturing crack using the technology of paired horizontal wells // Socar proceedings. – 2024. – .4. – P. 72-78.
Kayumov S., Arzikulov G., Bekchanov S., Zuyadullayeva S. A multiparameter mathematical model for the problem of nonlinear filtration of fluids in two-layer media // Journal of Physics: Conference Series. – 2024. – Vol. 2697. – 012042. – doi: http://dx.doi.org/10.1088/1742-6596/2697/1/012042.
Nikolay P., Svetlana N., Petrova, Korzhavina V. Mathematical modeling of the filtration flows movement in contaminated wells // E3S Web of Conferences. – 2024. – Vol. 537. – 06007. – doi: http://dx.doi.org/10.1051/e3sconf/202453706007.
Tokareva M.A., Papin A.A. Filtration of two immiscible liquids in a viscoelastic porous medium // J. Sib. Fed. Univ. Math. Phys.. – 2025. – Vol. 18, No. 2. – P. 253-261.
Kayumov Sh., Mardanov A.P., Tuychieva S.T., Kayumov A.B. Mathematical modeling of structured and Newtonian fluids in associated layer // E3S Web of Conferences. – 2023. – Vol. 401. – 01086. – doi: http://dx.doi.org/10.1051/e3sconf/202340101086.
Seyfi H., Shafiei S., Dehghanzadeh R., Amirabedi P. Mathematical Modeling and Parameters Optimization of the Degradation of Acrylonitrile in Biofilters // Iranian Journal of Chemical Engineering. – 2021. – Vol. 18, No. 3. – P. 3-15.
Khuzhayorov B., Djiyanov T.O., Zokirov M.S. Generalized relaxation fractional differential model of fluid filtration in a porous medium // International Journal of Applied Mathematics. – 2024. – Vol. 37, No. 1. – P. 119-132. – doi: http://dx.doi.org/10.12732/ijam.v37i1.10.
Makhmudov J.M., Usmonov A.I., Kuljanov J.B. Problem of anomalous filtration in nonhomogeneous porous medium // International Journal of Applied Mathematics. – 2023. – Vol. 36, No. 2. – P. 189-203.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 N. Ravshanov
This work is licensed under a Creative Commons Attribution 4.0 International License.
