LAPSE:2026.0308
Published Article
LAPSE:2026.0308
Optimal Simulation of an Electrodialysis Reactor for the Desalination and Regeneration of Multi-Ionic Wastewater
June 12, 2026
Abstract
The objective of the present work is to optimize the simulation of an electrodialysis reactor for the desalination and regeneration of multi-ionic wastewater with high salt contents and conductivities, within the framework in the Sustainable Development Goal 6 (clean water and sanitation) and remarking the Electrodialysis (ED) as a highly energy-efficient and sustainable technology. The mathematical modelling has been carried out by using a semiempirical model that involves an algebraic system of differential equations, including mass and charge balances (taking into account the ions present in the wastewater: Na?, Ca²?, Mg²?, Cl?, SO4²?, and HCO3?), and the total electrodialysis stack voltage considering ohmic drops (in the dilute and concentrate compartments), the potential of membrane in each cell pair, and the electrode potentials. In the simulation process, different theoretical and experimental parameters are necessary such as number of cells, membrane working areas, efficiency, diffusion coefficients, molar conductivity at infinite dilution, etc.The experimental parameters have been obtained initially with a specially designed batch reactor printed with 3D technology, to imitate the hydrodynamics and the behavior of the industrial final reactor used. Additionally, to increase the accuracy of the simulation results, same parameters such as the resistance of the membranes (rm), the transport numbers and the mass transfer coefficient (km) can be optimized by using a metaheuristic derivative-free optimizer, specifically a proprietary version of Particle Swarm Optimization (PSO) implemented in MatLab®.The results obtained yield a satisfactory reproduction of the observed experimental behavior, analyzing the evolution over time of the intensity, conductivity, and concentration of the concentrated and diluted currents, respectively. In addition, the evolution of the different contributions of the stack voltage and the membrane resistances are shown, in order to confirm the coherence of the results obtained.
The objective of the present work is to optimize the simulation of an electrodialysis reactor for the desalination and regeneration of multi-ionic wastewater with high salt contents and conductivities, within the framework in the Sustainable Development Goal 6 (clean water and sanitation) and remarking the Electrodialysis (ED) as a highly energy-efficient and sustainable technology. The mathematical modelling has been carried out by using a semiempirical model that involves an algebraic system of differential equations, including mass and charge balances (taking into account the ions present in the wastewater: Na?, Ca²?, Mg²?, Cl?, SO4²?, and HCO3?), and the total electrodialysis stack voltage considering ohmic drops (in the dilute and concentrate compartments), the potential of membrane in each cell pair, and the electrode potentials. In the simulation process, different theoretical and experimental parameters are necessary such as number of cells, membrane working areas, efficiency, diffusion coefficients, molar conductivity at infinite dilution, etc.The experimental parameters have been obtained initially with a specially designed batch reactor printed with 3D technology, to imitate the hydrodynamics and the behavior of the industrial final reactor used. Additionally, to increase the accuracy of the simulation results, same parameters such as the resistance of the membranes (rm), the transport numbers and the mass transfer coefficient (km) can be optimized by using a metaheuristic derivative-free optimizer, specifically a proprietary version of Particle Swarm Optimization (PSO) implemented in MatLab®.The results obtained yield a satisfactory reproduction of the observed experimental behavior, analyzing the evolution over time of the intensity, conductivity, and concentration of the concentrated and diluted currents, respectively. In addition, the evolution of the different contributions of the stack voltage and the membrane resistances are shown, in order to confirm the coherence of the results obtained.
Record ID
Subject
Suggested Citation
Ayala-Andreu V, Montiel MA, Montiel V, Labarta JA. Optimal Simulation of an Electrodialysis Reactor for the Desalination and Regeneration of Multi-Ionic Wastewater. Systems and Control Transactions 5:846-854 (2026) https://doi.org/10.69997/sct.132131
Author Affiliations
Ayala-Andreu V: Applied Electrochemistry and Electrocatalysis (LEQA) Research Group, University Institute of Electrochemistry, University of Alicante. PO 99, E-03080, Alicante, Spain [ORCID]
Montiel MA: Applied Electrochemistry and Electrocatalysis (LEQA) Research Group, University Institute of Electrochemistry, University of Alicante. PO 99, E-03080, Alicante, Spain [ORCID]
Montiel V: Applied Electrochemistry and Electrocatalysis (LEQA) Research Group, University Institute of Electrochemistry, University of Alicante. PO 99, E-03080, Alicante, Spain [ORCID]
Labarta JA: Computer Optimization of Chemical Engineering Processes and Technologies (COnCEPT) Research Group, University Institute of Chemical Process Engineering, University of Alicante, Po99, Alicante, E-03080, Spain. Department of Chemical Engineering, University [ORCID]
[Login] to see author email addresses.
Montiel MA: Applied Electrochemistry and Electrocatalysis (LEQA) Research Group, University Institute of Electrochemistry, University of Alicante. PO 99, E-03080, Alicante, Spain [ORCID]
Montiel V: Applied Electrochemistry and Electrocatalysis (LEQA) Research Group, University Institute of Electrochemistry, University of Alicante. PO 99, E-03080, Alicante, Spain [ORCID]
Labarta JA: Computer Optimization of Chemical Engineering Processes and Technologies (COnCEPT) Research Group, University Institute of Chemical Process Engineering, University of Alicante, Po99, Alicante, E-03080, Spain. Department of Chemical Engineering, University [ORCID]
[Login] to see author email addresses.
Journal Name
Systems and Control Transactions
Volume
5
First Page
846
Last Page
854
Year
2026
Publication Date
2026-06-12
Version Comments
Original Submission
Other Meta
PII: 0846-0854-21-SCT-5-2026, Publication Type: Journal Article
Record Map
Published Article
LAPSE:2026.0308
This Record
External Link
https://doi.org/10.69997/sct.132131
Publisher Version
Download
Meta
Record Statistics
Record Views
14
Version History
[v1] (Original Submission)
Jun 12, 2026
Verified by curator on
Jun 12, 2026
This Version Number
v1
Citations
Most Recent
This Version
URL Here
http://psecommunity.org/LAPSE:2026.0308
Record Owner
PSE Press
Links to Related Works
References Cited
- Intrasungkha N, Keller J, Blackall LL. Biological nutrient removal efficiency in treatment of saline wastewater. Water Sci Technol 39 (6): 183-190 (1999) https://doi.org/10.1016/S0273-1223(99)00138-9
- Corral AM, Val del Río Á, Campos Gómez JL. Treatment and valorisation of saline wastewater: principles and practice. IWA Publishing (2021) https://doi.org/10.2166/9781789060645
- Singh N, Poonia T, Siwal SS, Srivastav AL; Sharma HK, Mittal SK. Challenges of water contamination in urban areas. Current Directions in Water Scarcity Research 9: 173- 202 (2022) https://doi.org/10.1016/b978-0-323-91838-1.00008-7
- Lefebvre O, Moletta R. Treatment of organic pollution in industrial saline wastewater: a literature review. Water Research 40:3671-3682 (2006) https://doi.org/10.1016/j.watres.2006.08.027
- Berger E, Frör O, Schäfer RB. Salinity impacts on river ecosystem processes: a critical mini-review. Phil. Trans. R. Soc. B 374:20180010 (2018) https://doi.org/10.1098/rstb.2018.0010
- Ayers RS, Westcot DW. Water quality for agriculture. FAO Irrigation and Drainage Paper Vol. 29 (1) (1985) https://www.fao.org/4/T0234e/T0234e00.htm
- Patel SK, Biesheuvel PM, Elimelech M. Energy consumption of brackish water desalination: identifying the sweet spots for electrodialysis and reverse osmosis. ACS EST Eng. 1:851-864 (2021) https://doi.org/10.1021/acsestengg.0c00192
- Patel SK, Lee B, Westerhoff P, Elimelech M. The potential of electrodialysis as a cost-effective alternative to reverse osmosis for brackish water desalination. Water Research 250:121009 (2024) https://doi.org/10.1016/j.watres.2023.121009
- Gong Y, Wang XL, Li-xin Y. Process simulation of desalination by electrodialysis of an aqueous solution containing a neutral solute. Desalination 172:157-172 (2005) https://doi.org/10.1016/j.desal.2004.06.200
- Campione A, Gurreri L, Ciofalo M, Micale G, Tamburini A, Cipollina A. Electrodialysis for water desalination: a critical assessment of recent developments on process fundamentals, models and applications. Desalination 434:121-160 (2018) https://doi.org/10.1016/j.desal.2017.12.044
- Li H, Li M, Wang H, Tan M, Zhang G, Huang Z, Yuan X. A review on migration and transformation of nitrogen during sewage sludge thermochemical treatment: focusing on pyrolysis, gasification and combustion. Fuel Processing Technology 240:107562 (2023) https://doi.org/10.1016/j.fuproc.2022.107562
- Van der Bruggen B. Advances in electrodialysis for water treatment. Advances in Membrane Technologies for Water Treatment :185-203 (2015) https://doi.org/10.1016/b978-1-78242-121-4.00006-x
- Yang X, Zhuang Y, Zhu J, Le J, Cheng J. Recent progress on multiscale modeling of electrochemistry. WIREs Comput Mol Sci 12: (2021) https://doi.org/10.1002/wcms.1559
- Ding L, Azimi G. Mathematical modeling of rare earth element separation in electrodialysis with adjacent anion exchange membranes and ethylenediaminetetraacetic acid as chelating agent. Sci Rep 14: (2024) https://doi.org/10.1038/s41598-024-62885-4
- Wright NC, Shah SR, Amrose SE, Winter AG V. A robust model of brackish water electrodialysis desalination with experimental comparison at different size scales. Desalination 443:27-43 (2018) https://doi.org/10.1016/j.desal.2018.04.018
- Ortiz JM, Sotoca JA, Expósito E, Gallud F, García-García V, Montiel V, Aldaz A. Brackish water desalination by electrodialysis: batch recirculation operation modeling. Journal of Membrane Science 252:65-75 (2005) https://doi.org/10.1016/j.memsci.2004.11.021
- ORTIZ J, EXPOSITO E, GALLUD F, GARCIAGARCIA V, MONTIEL V, ALDAZ A. Desalination of underground brackish waters using an electrodialysis system powered directly by photovoltaic energy. Solar Energy Materials and Solar Cells 92:1677-1688 (2008) https://doi.org/10.1016/j.solmat.2008.07.020
- Ayala-Andreu V, García-García V, Labarta JA, Montiel V, Montiel MA. Determination of critical parameters for the mathematical modelling of an electrodialysis process using a 3d-printed reactor. Chemical Engineering Journal 530:173277 (2026) https://doi.org/10.1016/j.cej.2026.173277
- Mekidiche Z, Labarta JA, Javaloyes-Anton J, Caballero JA. From power to heat: strategies for electrifying distillation for sustainable chemical processes. Applied Thermal Engineering 257:124316 (2024) https://doi.org/10.1016/j.applthermaleng.2024.124316
- Haynes WM, Lide DR, Bruno TJ. CRC handbook of chemistry and physics. CRC Press (2016) https://doi.org/10.1201/9781315380476
- Varcoe JR, Atanassov P, Dekel DR, Herring AM, Hickner MA, Kohl PA, Kucernak AR, Mustain WE, Nijmeijer K, Scott K, Xuk T, Zhuangl L. Anion-exchange membranes in electrochemical energy systems. Energy Environ. Sci. 7 (10): 3135-3191 (2014) http://dx.doi.org/10.1039/C4EE01303D
- Atkins P, Paula J. Physical Chemistry. 8th ed. Vol. 1. WH Freeman and Company (2006), pp. 1-1053.
(0.09 seconds)
[0.1 s]