Applied Chemical Engineering

Theoretical principles of modeling for the regeneration process of cation exchanger

Zurab Megrelishvili

Department of Technology and Engineering Management, Technologies Faculty, Batumi Shota Rustaveli State University,Batumi, 6010, Georgia

Ibraim Didmanidze

Center of languages and information technologies by the faculty of Exact Science and Education, Batumi Shota Rustaveli State University, Batumi, 6010, Georgia

Remzi Didmanidze

Department of Machine and Tractor Fleet Operation, Federal State Budgetary Educational Institution of Higher Education "State Agrarian University - Timiryazev Agricultural Academy"

Nino Dondoladze

Department of Engineering and Construction, Technologies Faculty, Batumi Shota Rustaveli State University, Batumi, 6010, Georgia

Teimuraz Jojua

Department of Engineering and Construction, Technologies Faculty, Batumi Shota Rustaveli State University, Batumi, 6010, Georgia

Aleksandre Bakuridze

Department of Engineering and Construction, Technologies Faculty, Batumi Shota Rustaveli State University, Batumi, 6010, Georgia

Mzevinar Bakuridze

Department of Engineering and Construction, Technologies Faculty, Batumi Shota Rustaveli State University, Batumi, 6010, Georgia

DOI: https://doi.org/10.59429/ace.v9i2.5993

Keywords: cation exchanger, regeneration solution, dilution, modeling

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Abstract

Optimization of a cation-exchange softening plant requires linking reagent demand with the working capacity of the ion exchange layer. This, in turn, requires solving two preliminary problems: establishing the distribution of hardness ions across the depth of the layer after completion of the loosening stage and determining the change in concentration at the entrance to the layer when regenerating and washing water is supplied. A new combined mixing scheme is proposed, in which the solution entering the filter is mixed with a water cushion located above the filter bed. At the same time, the volume involved in the mixing changes over time. An analytical expression is obtained for the change in concentration of the solution entering the upper layer of the filter bed during both the regeneration and backwash stages. Obtained is an equation that allows us to determine the transit time with maximum concentration through exchanger load.

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References

[1]. Zamfir, F.-S., Carbureanu, M., Mihalache, S.F. Application of Machine Learning Models in Optimizing Wastewater Treatment Processes: A Review. Appl. Sci. 2025; 15: 8360. https://doi.org/10.3390/app15158360

[2]. Savun-Hekimoğlu B., İşler Z., Hekimoğlu M. et al. Optimization of wastewater treatment systems for growing industrial parks, Science of The Total Environment 2023; Volume 905: 167223, https://doi.org/10.1016/j.scitotenv.2023.167223

[3]. Sorlini S., Collivignarelli MC., Castagnola F. et al. Methodological approach for the optimization of drinking water treatment plants' operation: a case study. Water Sci Technol. 2015;71(4):597-604. doi: 10.2166/wst.2014.503. PMID: 25746653.

[4]. Douglas B., Twum S. A Review of Water Quality Optimisation Models and Techniques. Journal of Applied Mathematics and Physics. 2020: 08: 424-433. DOI: 10.4236/jamp.2020.83032.

[5]. Abdulbaki D, Al-Hindi M, Yassine A, Abou Najm M, An optimization model for the allocation of water resources, Journal of Cleaner Production 2017: Volume 164: 994-1006, https://doi.org/10.1016/j.jclepro.2017.07.024.

[6]. Da Costa MFP, Araújo RdS, Silva AR, Pereira L, Silva GMM. Predictive Artificial Neural Networks as Applied Tools in the Remediation of Dyes by Adsorption—A Review. Applied Sciences. 2025; 15(5):2310. https://doi.org/10.3390/app15052310

[7]. Li H, Liu C, Guo X, Sun H, Li X, Jiang H, Miao S. Applying Machine Learning Approach to Design Operational Control Strategies for a Wastewater Treatment Plant in Typical Scenarios. Water. 2025; 17(3):310. https://doi.org/10.3390/w17030310

[8]. Korotaj B., Novak H., Hure N. et al. Optimization of a drinking water treatment plant operation via sequential linear programming. Journal of Water Process Engineering 2025: Volume 79: 108868, Published by Elsevier Ltd https://doi.org/10.1016/j.jwpe.2025.108868

[9]. Lee S., Jaeyoung Choi J., Hyeonsoo Choi H. et al. Assessment and optimization of wastewater treatment plant in terms of effluent quality, energy footprint, and greenhouse gas emissions: An integrated modeling approach. Ecotoxicology and Environmental Safety 2024: Volume 283: 15 116820, https://doi.org/10.1016/j.ecoenv.2024.116820

[10]. Savun-Hekimoğlu B., İşler Z, Mustafa Hekimoğlu M. et al. Optimization of wastewater treatment systems for growing industrial parks, Science of The Total Environment 2023: Volume 905: 167223, https://doi.org/10.1016/j.scitotenv.2023.167223

[11]. MegrelishviliI Z., Ibraim Didmanidze I., Zaslavskyi V, David Chkhubiani D., Didmanidze D. Mathematical and Software Provision for Optimization of Water Treatment Processes. 13th International Conference on Dependable Systems, Services and Technologies (DESSERT). 13-15 October 2023. Athens, Greece. p. 1-5, https://api.semanticscholar.org/CorpusID:267524182

[12]. Burakov, I.A., Burakov, A.Y., Nikitina, I.S., Verkhovsky, A.E., Ilyushin, A.S., Aladushkin, S.V.: Comparison contemporary methods of regeneration sodiumcationic filters. In: IOP Conf. Series: Journal of Physics: Conf. Series, 2017; vol. 891: 012266.

[13]. https://iopscience.iop.org/article/10.1088/1742-6596/891/1/012266/pdf

[14]. Meshcherova E. A., Novoselova J. N., Moreva J. A. Development of Water Softening Method of Intake in Magnitogorsk. In: IOP Conf. Series: Materials Science and Engineering 2017: vol. 262: 012089. https://iopscience.iop.org/article/10.1088/1757-899X/262/1/012089/pdf

[15]. Patel H. Fixed-bed column adsorption study: a comprehensive review. Appl Water Sci 2019; 9: 45. https://doi.org/10.1007/s13201-019-0927-7

[16]. Fernandez, R.M.D.; Estrada, R.J.R.; Tomon, T.R.B.; Dingcong, R.G., Jr.; Amparado, R.F., Jr.; Capangpangan, R.Y.; Malaluan, R.M.; Dumancas, G.G.; Lubguban, A.A.; Alguno, A.C.; et al. Experimental Design and Breakthrough Curve Modeling of Fixed-Bed Columns Utilizing a Novel 3D Coconut-Based Polyurethane-Activated Carbon Composite Adsorbent for Lead Sequestration. Sustainability 2023; 15: 14344. https://doi.org/10.3390/su151914344

[17]. Phuoc Hieu, Le Quang, Pham Tung, Le Tu Thanh. Synthesis of Glue-Free NaA Zeolite Granules from Natural Kaolin for the Adsorption of Pb(II) Ions in Aqueous Solution Using a Fixed-Bed Column Study. ACS Omega 2021; 6(32): 21024-21032, DOI: 10.1021/acsomega.1c02658,

[18]. Bakalis E., Zerbetto F. Adsorption Kinetics: Classical, Fractal, or Fractional? Langmuir 2025; 41(30): 19834-19844 DOI: 10.1021/acs.langmuir.5c01726.

[19]. Futalan CM, Wan M-W. Fixed-Bed Adsorption of Lead from Aqueous Solution Using Chitosan-Coated Bentonite. International Journal of Environmental Research and Public Health. 2022; 19(5):2597. https://doi.org/10.3390/ijerph19052597

[20]. Komarova I.V., Galkina N.K., Prudkovskii A.G., Khamizov R.Kh. Mathematical simulation and calculation of the process of water demineralization in industrial filter Part 1. Hydrodynamics of regeneration and washing of industrial filter. Sorbtsionnye i Khromatograficheskie Protsessy 2017; 17(1): 10-19. (In Russ.)

[21]. Megrelishvili Z. Chkhaidze V. The device for loose materials sampling. Georgian Patent GE P 2010 4952 B. Int. Cl. C 0,1 N 1/20. Pab. 2010 04 12, in Inv. Bul. #7, 2010. (Georgian);

[22]. Water treatment at thermal power plants using Na-cationite filters: monograph / T. S. Airapetyan, I. N. Chub; Kharkov. national university of urban economy named after A. N. Beketova. – Kharkov: A. N. Beketova KhNUGH, 2020. – 146 p. (In Russ.)

[23]. Tiuftiakov N. Yu., Zdrachek E, Bakker E, Ion-exchange and lipophilicity limitations of ionic liquid reference electrodes, Sensors and Actuators B: Chemical 2024; Volume 407: 135474. https://doi.org/10.1016/j.snb.2024.135474.

[24]. Elena Zdrachek E., Eric Bakker E. Time-Dependent Determination of Unbiased Selectivity Coefficients of Ion-Selective Electrodes for Multivalent Ions, Analytical Chemistry 2017; 89 (24): 13441-13448, DOI: 10.1021/acs.analchem.7b03726

[25]. Handbook of Chemistry and Physics. 97th Edition. Editor–in-Chief W.M. Haynes, Associate Editors David R. Lide, Thomas J. Bruno. CRC Press, 2016, 2643 p.

[26]. Kafarov V. V. Methods of cybernetics in chemistry and chemical technology. – 3rd ed. revised and enlarged. Moscow: “Chemistry”, 1976, - 464 p. (In Russ.)