Evaluation of Mass Transfer Characteristics of Reverse Osmosis Desalination Process Based on the Spiegler-Kedem-Katchalsky Model

Mohammed, Dnya Sharif; Kamal, Ibtisam; Abdulhameed, Abdulsamad

doi:10.22075/jhmtr.2025.33417.1527

Evaluation of Mass Transfer Characteristics of Reverse Osmosis Desalination Process Based on the Spiegler-Kedem-Katchalsky Model

Document Type : Full Length Research Article

Authors

Dnya Sharif Mohammed ¹

Ibtisam Kamal ²

Abdulsamad Abdulhameed ³

¹ Kurdistantechnical Institute, Kurdistan Region, Iraq

² Petroleum Engineering Department, College of Science and Technology, University of Basrah, Basrah, Iraq

³ Siemens Energy, Department of Operation, Khormala Power Plant, Erbil, Iraq

10.22075/jhmtr.2025.33417.1527

Abstract

In previous work, the reverse osmosis (RO) process was evaluated based on the potential synergy of Process Design and response surface methodology (RSM) methodologies, and the effects of membrane age, percentage recovery, concentrations of salts, pH, temperature, and pressure of feed water and the rejected brine concentration were optimized and modeled. The current work includes the determination of phenomenological parameters of mass transfer for RO membrane systems using the Spiegler-Kedem-Katchalsky model. The mass transfer coefficient and membrane permeability for salts were determined as a function of temperature and percentage recovery. The calculations of mass transfer parameters were based on a reference RO membrane (ESPA4-LD-4040), a three stage RO process, a 3-year membrane age with 95% and 85% recovery, a permeate flow 20 m3/h, pH 7, a constant feed TDS of 800 mg/l, constant pump pressure for feed water of 15 bar, and feed-water temperatures of 4, 8.2, 25, 30, and 42oC. The results showed that when the temperature increases from 4°C to 42°C, the mass transfer coefficient increases by 35.44% for 95% recovery, and 83.97% for 85% recovery, respectively. A general mathematical model describing the relationship between the mass transfer coefficient and feed water temperature, water permeability, and salt permeability was developed. The Spiegler-Kedem-Katchalsky model proved its capability for membrane performance evaluation through the determination and correlation of the phenomenological parameters of mass transfer for the membrane system.

Keywords

Mass transfer coefficient

Temperature

Recovery

Water permeability

Salt permeability

Permeate flux

Subjects

Mass Transfer

[1] Hailemariam, R. H., Woo, Y. C., Damtie, M. M., Kim, B. C., Park, K. D. and Choi, J. S., 2020. Reverse osmosis membrane fabrication and modification technologies and future trends: A review. Advances in Colloid and Interface Science, 276, p. 102100. doi: 10.1016/j.cis.2019.102100.
[2] Murthy, Z. V. P. and Gupta, S. K., 1997. Estimation of mass transfer coefficient using a combined nonlinear membrane transport and film theory model. Desalination, 109(1), pp. 39–49. doi: 10.1016/S0011-9164(97)00051-9.
[3] Wang, L., He, J., Heiranian, M., Fan, H., Song, L., Li, Y. and Elimelech, M., 2023. Water transport in reverse osmosis membranes is governed by pore flow, not a solution-diffusion mechanism. Science Advances, 9(15), pp. 1–12. doi: 10.1126/sciadv.adf8488.
[4] Spiegler, K. S. and Kedem, O., 1966. Thermodynamics of hyperfiltration (reverse osmosis): Criteria for efficient membranes. Desalination, 1, pp. 311–326.
[5] Zhao, Y., 2004. Modeling of membrane solute mass transfer in NF/RO membrane systems. Doctoral Dissertation, University of Central Florida, pp. 2004–2019.
[6] Goosen, M. F. A., Sablani, S. S., Al-Maskari, S. S., Al-Belushi, R. H. and Wilf, M., 2002. Effect of feed temperature on permeate flux and mass transfer coefficient in spiral-wound reverse osmosis systems. Desalination, 144(1–3), pp. 367–372. doi: 10.1016/S0011-9164(02)00345-4.
[7] Salinas-Rodríguez, S. G., Schippers, J. C., Amy, G. L., Kim, I. S. and Kennedy, M. D., 2021. Seawater Reverse Osmosis Desalination: Assessment and Pre-treatment of Fouling and Scaling. IWA Publishing, doi: 10.2166/9781780409863.
[8] Hung, L. Y., Lue, S. J. and You, J. H., 2011. Mass-transfer modeling of reverse-osmosis performance on 0.5-2% salty water. Desalination, 265(1–3), pp. 67–73. doi: 10.1016/j.desal.2010.07.033.
[9] Sutzkover, I., Hasson, D. and Semiat, R., 2000. Simple technique for measuring the concentration polarization level in a reverse osmosis system. Desalination, 131(1–3), pp. 117–127. doi: 10.1016/S0011-9164(00)90012-2.
[10] Al-Mutaz, I. S. and Al-Ghunaimi, M. A. Performance of reverse osmosis units at high temperatures. https://ida.memberclicks.net/assets/docs/1099.1.pdf
[11] Farhat, A., Ahmad, F., Hilal, N. and Arafat, H. A., 2013. Boron removal in new generation reverse osmosis (RO) membranes using two-pass RO without pH adjustment. Desalination, 310, pp. 50–59. doi: 10.1016/j.desal.2012.10.003.
[12] Boussouga, Y. A. and Lhassani, A., 2017. Study of mass transfer mechanisms for reverse osmosis and nanofiltration membranes intended for desalination. Journal of Materials and Environmental Science, 8(3), pp. 1128–1138.
[13] Wang, L., Cao, T., Dykstra, J. E., Porada, S., Biesheuvel, P. M. and Elimelech, M., 2021. Salt and water transport in reverse osmosis membranes: Beyond the solution-diffusion model. Environmental Science & Technology, 55(24), pp. 16665–16675. doi: 10.1021/acs.est.1c05649.
[14] Okamoto, Y. and Lienhard, J. H., 2019. How RO membrane permeability and other performance factors affect process cost and energy use: A review. Desalination, 470, pp. 0–30. doi: 10.1016/j.desal.2019.07.004.
[15] Martin-Pascual, J., Rodríguez, F. A., Reboleiro-Rivas, P., González-Lopez, J., Hontoria, E. and Poyatos, J. M., 2012. Influence of the temperature in the permeate flux of the membrane in a membrane bioreactor with moving bed biofilm reactor. Procedia Engineering, 44, pp. 275–277. doi: 10.1016/j.proeng.2012.08.385.
[16] Eriksson, P., 1988. Water and salt transport through two types of polyamide composite membranes. Journal of Membrane Science, 36, pp. 297–313. doi: 10.1016/0376-7388(88)80024-3.