Mathematical modeling of submerged membrane adsorption hybrid system and parameter estimation for adsorption of cesium from radioactive wastewater implementing eco-friendly adsorbent
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Talib M. Albayati
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Wasan A. Muslim
Abstract
This study presents a comprehensive mathematical modeling and experimental investigation of a submerged membrane adsorption hybrid system (SMAHS) for the removal of cesium (Cs(I)) from radioactive wastewater. An eco-friendly adsorbent was synthesized and characterized for its adsorption performance. The homogeneous surface diffusion model (HSDM) model integrates surface diffusion as the dominant mass transfer mechanism and estimates key parameters, including the external mass transfer coefficient (K), surface diffusion coefficient (Ds), and membrane correlation coefficient (MCC). The pore and surface diffusion model (PSDM) is a comprehensive diffusion-based model that accounts for all diffusion processes in the solid phase. Experiments identified optimal operational conditions: pH 6.5, adsorbent dose 1.5 g/L, and contact time of 90 min, achieving over 95 % cesium removal. Ion selectivity tests demonstrated preferential adsorption of cesium in the presence of competing metal ions such as Na+, K+, and Ca2+. Regeneration studies showed that the adsorbent maintained over 85 % removal efficiency after five adsorption-desorption cycles, indicating cost-effectiveness. Model validation against experimental data exhibited strong agreement (R2 = 0.98), confirming the model’s suitability for design and scale-up of hybrid treatment systems. This work provides new insights into adsorption kinetics, hybrid system optimization, and eco-friendly adsorbent applications for radionuclide wastewater remediation.
Acknowledgments
We gratefully acknowledge the scientific support of the Department of Chemical Engineering, University of Technology-Iraq; Iraqi Atomic Energy Commission (IAEC)/Radiation and Nuclear Safety Directorate, Baghdad, Iraq, and to the Iraqi Geological Survey/Ministry of Industry and Minerals.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: W.A.M. and T.M.A.; methodology, S.K.A.; validation, W.A.M. and A.S.A.; investigation; resources, A.S.A. and I.K.S.; writ-ing—original draft preparation, S.K.A. and T.M.A.; writing review and editing, T.M.N., W.A.M. and I.K.S..; visualization, T.M.A., and S.K.A; supervision, K.T.R..; project administration. All authors have read and agreed to the published version of the manuscript.
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Use of Large Language Models, AI and Machine Learning Tools: Not applicable.
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Declaration of AI Technology usage: We declare that no Artificial Intelligence (AI) technologies or AI-assisted tools were utilized in any capacity during the writing and preparation of this article.
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Conflict of interest: The authors have no conflict interests to declare that are relevant to the content of this article.
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Research funding: None declared.
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Data availability: All relevant data and material are presented in the main paper.
Sample of calculation for K, MCC, Dₛ for mathematical model.
The values of K are estimated by the inclination of the curve C/C 0 versus t.
The data of batch adsorption kinetic study of bentonite can be used by the plotting of C/C₀ vs t as shown in the figure below:
The slope of the curve of C/C₀ vs t from the figure = −6 × 10⁻⁶ s⁻¹
From eq 2.27:
m (adsorbent amount) in g = 0.25 g
S (surface area of adsorbent) = 77.7 m²/g
V (volume of solution) = 200 ml = 0.0002 m³
The values of MCC are estimated from eq 2.29:
The values of Dₛ are estimated from eq 2.30:
Where
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