Математичне моделювання процесу нанофільтрації: аналітичний огляд

[1] Gumnitsky, J.; Sabadash, V.; Matsuska, O.; Lyuta, O.; Hyvlud, A.; Venger, L. Dynamics of Adsorption of Copper Ions in Fixed- Bed Column and Mathematical Interpretation of the First Stage of the Process. Chem. Chem. Technol. 2022, 16, 267–273. https://doi.org/10.23939/chcht16.02.267

[2] Semenyshyn, Y.; Atamanyuk, V.; Rymar, T.; Ivashchuk, O.; Hlukhaniuk, A. Mass Transfer in the Solid-Liquid System: Mecha- nism and Kinetics of the Extraction Process. Chem. Chem. Technol. 2020, 14, 121–128. https://doi.org/10.23939/chcht14.01.121

[3] Havryshko, M.; Popovych, O.; Yaremko, H.; Tymchuk, I.; Malovanyy, M. Analysis of Prospective Technologies of Food Production Wastewater Treatment. Ecol. Eng. Environ. Technol. 2022, 2, 33–40. https://doi.org/10.12912/27197050/145201

[4] Ramana, K. V.; Mohan, K. C.; Ravindhranath, K.; Babu, B. H. Bio-Sorbent Derived from Annona Squamosa for the Removal of Methyl Red Dye in Polluted Waters: A Study on Adsorption Poten- tial. Chem. Chem. Technol. 2022, 16, 274–283. https://doi.org/10.23939/chcht16.02.274

[5] Shon, H. K.; Phuntsho, S.; Chaudhary, D. S.; Vigneswaran, S., Cho, J. Nanofiltration for Water and Wastewater Treatment – A Mini Review. Drink Water Eng Sci. 2013, 6, 47–53. https://doi.org/10.5194/dwes-6-47-2013

[6] Huliienko, S. V.; Korniienko, Y. M.; Gatilov, K. O. Modern Trends in the Mathematical Simulation of Pressure-Driven Mem- brane Processes. J. Eng. Sci. 2020, 71, F1–F21. https://doi.org/10.21272/jes.2020.7(1).f1

[7] Huliienko, S. V.; Korniyenko, Y. M.; Muzyka, S. M.; Holubka K. Simulation of Reverse Osmosis Process: Novel Approaches and Development Trends. J. Eng. Sci. 2022, 92, F6–F36. https://doi.org/10.21272/jes.2022.9(2).f2

[8] Yaroshchuk, A.; Bruening, M. L.; Zholkovskiy, E. Modelling Nanofiltration of Electrolyte Solutions. Adv. Colloid Interface Sci. 2019, 268, 39–63. https://doi.org/10.1016/j.cis.2019.03.004

[9] Agboola, O.; Maree J.; Kolesnikov, A.; Mbaya, R.; Sadiku, R. Theoretical Performance of Nanofiltration Membranes for Waste- water Treatment. Environ. Chem. Lett. 2015, 13, 37–47. https://doi.org/10.1007/s10311-014-0486-y

[10] Marchetti, P.; Livingston, A. G. Predictive Membrane Trans- port Models for Organic Solvent Nanofiltration: How Complex Do We Need to Be? J. Membr. Sci. 2015, 476, 530–553. https://doi.org/10.1016/j.memsci.2014.10.030

[11] Schmidt, P.; Lutze, Ph. Characterisation of Organic Solvent Nanofiltration Membranes in Multi-Component Mixtures: Phenom- ena-based Modelling and Membrane Modelling Maps. J. Membr. Sci. 2013, 445, 183–199.

https://doi.org/10.1016/j.memsci.2013.05.062

[12] Zhang, Sh.; Zhou, J.; Fan, L.; Qiu, Y.; Jiang, L.; Zhao, L. Investigating the Mechanism of Nanofiltration Separation of Gluco- samine Hydrochloride and N-acetyl Glucosamine. Bioresour. Bio- process. 2016, 3, 34. https://doi.org/10.1186/s40643-016-0112-x

[13] Anand, A.; Unnikrishnan, B.; Mao, J.-Y.; Lin, H.-J.; Huang, Ch.-Ch. Graphene-based Nanofiltration Membranes for Improving Salt Rejection, Water Flux and Antifouling–A review. Desalination 2018, 429, 119–133. https://doi.org/10.1016/j.desal.2017.12.012 [14] Mohammad, A.W.; Teow, Y.H.; Ang, W.L.; Chung, Y.T.; Oatley-Radcliffe, D.L.; Hilal, N. Nanofiltration Membranes Re- view: Recent Advances and Future Prospects. Desalination 2015, 356, 226–254. https://doi.org/10.1016/j.desal.2014.10.043

[15] Ahmed, F. E.; Hashaikeh, R.; Diabat, A.; Hilal, N. Mathemati- cal and Optimization Modelling in Desalination: State-of-the-art and Future Direction. Desalination 2019, 469, 114092. https://doi.org/10.1016/j.desal.2019.114092

[16] Zhou, D.; Zhu, L.; Fu, Y.; Zhu, M.; Xue, L. Development of Lower Cost Seawater Desalination Processes Using Nanofiltration Technologies — A Review. Desalination 2015, 376, 109–116. https://doi.org/10.1016/j.desal.2015.08.020

[17] Souza, V. C.; Quadri, M. G. N. Organic-inorganic hybrid membranes in separation processes: a 10-year review. Braz. J. Chem. Eng. 2013, 30, 683–700. https://doi.org/10.1590/S0104-66322013000400001

[18] Wang, J.; Dlamini, D. S.; Mishra, A. K.; Pendergast, M. Th. M.; Wong, M. C. Y.; Mamba, B. B.; Freger, V.; Verliefd, A. R. D.; Hoek, E. M. V. A Critical Review of Transport through Osmotic Membranes. J. Membr. Sci. 2014, 454, 516–537. https://doi.org/10.1016/j.memsci.2013.12.034

[19] Keir, G.; Jegatheesan, V. A Review of Computational Fluid Dynamics Applications in Pressure-Driven Membrane Filtration. Rev. Environ. Sci. Biotechnol. 2013, 13, 183–201. https://doi.org/10.1007/s11157-013-9327-x

[20] Ebro, H.; Kim, Y. M.; Kim, J. H. Molecular Dynamics Simula- tions in Membrane-Based Water Treatment Processes: A Systematic Overview. J. Membr. Sci. 2013, 438, 112–125. https://doi.org/10.1016/j.memsci.2013.03.027

[21] Zhang, Y.; Zhu, Y.; Wang, A.; Gao, Q.; Qin, Y.; Chen, Y.; Lu, X. Progress in Molecular-Simulation-Based Research on the Effects of Interface-induced Fluid Microstructures on Flow Resistance. Chin. J. Chem. Eng. 2019, 27, 1403–1415. https://doi.org/10.1016/j.cjche.2019.02.002

[22] Peshev, D.; Livingston, A. G. OSN Designer, a Tool for Pre- dicting Organic Solvent Nanofiltration Technology Performance Using ASPEN ONE, MATLAB and CAPE OPEN. Chem. Eng. Sci. 2013, 104, 975–987. https://doi.org/10.1016/j.ces.2013.10.033

[23] Abejon, R.; Garea, A.; Irabien, A. Organic Solvent Recovery and Reuse in Pharmaceutical Purification Processes by Nanofiltra- tion Membrane Cascades. Chem. Eng. Trans. 2015, 43, 1057–1062. https://doi.org/10.3303/CET1543177

[24] Hidalgo, A. M.; León, G.; Gómez, M.; Murcia, M. D.; Gómez, E.; Macario, J. A. Removal of Different Dye Solutions: A Compari- son Study Using a Polyamide NF Membrane. Membranes 2020, 10,408. https://doi.org/10.3390/membranes10120408

[25] Yan, Z-Q.; Zeng, L-M.; Li, Q.; Liu, T-Y.; Matsuyama, H.; Wang, X-L. Selective Separation of Chloride and Sulfate by Nano- filtration for High Saline Wastewater Recycling. Sep. Purif. Tech-nol. 2016, 166, 135–141.https://doi.org/10.1016/j.seppur.2016.04.009

[26] Shahmansouri, A.; Bellona, C. Application of Quantitative Structure–Property Relationships (QSPRs) to Predict the Rejection of Organic Solutes by Nanofiltration. Sep. Purif. Technol. 2013, 118, 627–638. https://doi.org/10.1016/j.seppur.2013.07.050

[27] Schlackl, K.; Herchl, R.; Samhaber, W. Nanofiltration of Suc- cinic Acid in Strong Alkaline Conditions. Membranes 2019, 9, 147. https://doi.org/10.3390/membranes9110147

[28] Kim, J. H.; Na, J.-G.; Shim, H. J.; Chang, Y. K. Modeling of Ammonium Lactate Recovery and Impurity Removal from Simu- lated Fermentation Broth by Nanofiltration. J. Membr. Sci. 2012, 396, 110–118. https://doi.org/10.1016/j.memsci.2012.01.003

[29] Nair, R. R.; Protasova, E.; Strand, S.; Bilstad, T. Implementa- tion of Spiegler–Kedem and Steric Hindrance Pore Models for Analyzing Nanofiltration Membrane Performance for Smart Water Production. Membranes 2018, 8, 78. https://doi.org/10.3390/membranes8030078

[30] Peddie, W. L.; van Rensburg, J. N.; Vosloo, H. C. M.; van der Gryp, P. Technological Evaluation of Organic Solvent Nanofiltra- tion for the Recovery of Homogeneous Hydroformylation Catalysts. Chem. Eng. Res. Des. 2017, 121, 219–232.https://doi.org/10.1016/j.cherd.2017.03.015

[31] ten Kate, A. J. B.; Schutyser, M.A.I.; Kuzmanovic, B.; Wester- ink, J.B.; Manuhutu, F.; Bargeman, G. Thermodynamic Perspective on Negative Retention Effects in Nanofiltration of Concentrated Sodium Chloride Solutions. Sep. Purif. Technol. 2020, 250, 117242. https://doi.org/10.1016/j.seppur.2020.117242

[32] Minelli, M.; Sarti, G. C. Modeling Mass Transport in Dense Polymer Membranes: Cooperative Synergy among Multiple Scale Approaches. Curr. Opin. Chem. Eng. 2020, 28, 43–50. https://doi.org/10.1016/j.coche.2020.01.004

[33] Qian, J.; Yan, R.; Liu, X.; Li, Ch.; Zhang, X. Modification to Solution-Diffusion Model for Performance Prediction of Nanofiltra- tion of Long-alkyl-chain Ionic Liquids Aqueous Solutions Based on Ion Cluster. Green Energy Environ. 2020, 5, 105–113. https://doi.org/10.1016/j.gee.2018.10.001

[34] Li, C.; Ma, Y.; Li, H.; Peng, G. Exploring the Nanofiltration Mass Transfer Characteristic and Concentrate Process of Procyanid- ins from Grape Juice. Food Sci. Nutr. 2019, 7, 1884–1890. https://doi.org/10.1002/fsn3.1045

[35] Abels, C.; Redepenning, C.; Moll, A.; Melin, T.; Wessling, M. Simple Purification of Ionic Liquid Solvents by Nanofiltration in Biorefining of Lignocellulosic Substrates. J. Membr. Sci. 2012, 405–406, 1–10. https://doi.org/10.1016/j.memsci.2011.12.020

[36] Shi, B.; Marchetti, P.; Peshev, D.; Zhang, Sh.; Livingston, A. G. Performance of Spiral-Wound Membrane Modules in Organic Solvent Nanofiltration – Fluid Dynamics and Mass Transfer Charac- teristics. J. Membr. Sci. 2015, 494, 8–24. https://doi.org/10.1016/j.memsci.2015.07.044

[37] Micovic, J.; Werth, K.; Lutze, Ph. Hybrid Separations Combin- ing Distillation and Organic Solvent Nanofiltration for Separation of Wide Boiling Mixtures. Chem. Eng. Res. Des. 2014, 92, 2131–2147. https://doi.org/10.1016/j.cherd.2014.02.012

[38] Werhan, H.; Farshori, A.; von Rohr, Ph. R. Separation of Lig- nin Oxidation Products by Organic Solvent Nanofiltration. J. Membr. Sci. 2012, 423–424, 404–412.https://doi.org/10.1016/j.memsci.2012.08.037

[39] Werth, K.; Kaupenjohann, P.; Knierbein, M.; Skiborowski, M. Solvent Recovery and Deacidification by Organic Solvent Nanofil- tration: Experimental Investigation and Mass Transfer Modelling. J. Membr. Sci. 2017, 528, 369–380.https://doi.org/10.1016/j.memsci.2017.01.021

[40] Keucken, A.; Wang, Y.; Tng, K. H.; Leslie, G.; Spanjer, T.; Köhler, S. J. Optimizing Hollow Fibre Nanofiltration for Organic Matter Rich Lake Water. Water 2016, 8, 430. https://doi.org/10.3390/w8100430

[41] Altaee, A.; Hilal, N. High Recovery Rate NF–FO–RO Hybrid System for Inland Brackish Water Treatment. Desalination 2015, 363, 19–25. https://doi.org/10.1016/j.desal.2014.12.017

[42] Shaaban, A. M. F.; Hafez, A. I.; Abdel-Fatah, M. A.; Abdel- Monem, N. M.; Mahmoud, M. H. Process Engineering Optimization of Nanofiltration Unit for the Treatment of Textile Plant Effluent in View of Solution Diffusion Model. Egypt. J. Pet. 2016, 25, 79–90. https://doi.org/10.1016/j.ejpe.2015.03.018

[43] Marchetti, P.; Butte, A.; Livingston, A. G. An Improved Phe- nomenological Model for Prediction of Solvent Permeation Through Ceramic NF and UF Membranes. J. Membr. Sci. 2012, 415–416, 444–458. https://doi.org/10.1016/j.memsci.2012.05.030

[44] Fierro, D.; Boschetti-de-Fierro, A.; Abetz, V. The Solution- Diffusion with Imperfections Model as a Method to Understand Organic Solvent Nanofiltration of Multicomponent Systems. J. Membr. Sci. 2012, 413–414, 91–101.https://doi.org/10.1016/j.memsci.2012.04.027

[45] Werth, K.; Kaupenjohann, P.; Skiborowski, M. The Potential of Organic Solvent Nanofiltration Processes for Oleochemical Indus- try. Sep. Purif. Technol. 2017, 182, 185–196. https://doi.org/10.1016/j.seppur.2017.03.050

[46] Pérez, L.; Escudero, I.; Arcos-Martínez, M. J.; Benito, J. M. Application of the Solution-Diffusion-Film Model for the Transfer of Electrolytes and Uncharged Compounds in a Nanofiltration Membrane. J Ind Eng Chem. 2017, 47, 368–74. https://doi.org/10.1016/j.jiec.2016.12.007

[47] Yonge, D.T.; Biscardi, P. G.; Duranceau, S. J. Modeling Ionic Strength Effects on Hollow-Fiber Nanofiltration Membrane Mass Transfer. Membranes 2018, 8, 37. https://doi.org/10.3390/membranes8030037

[48] Yaroshchuk, A.; Bruening, M. L. An analytical Solution of the Solution-Diffusion-Electromigration Equations Reproduces Trends in ion Rejections During Nanofiltration of Mixed Electrolytes. J. Membr. Sci. 2017, 523, 361–372.https://doi.org/10.1016/j.memsci.2016.09.046

[49] Madsen, H.T.; Søgaard, E.G. Applicability and Modelling of Nanofiltration and Reverse Osmosis for Remediation of Groundwa- ter Polluted with Pesticides and Pesticide Transformation Products. Sep. Purif. Technol. 2014, 125, 111–119. https://doi.org/10.1016/j.seppur.2014.01.038

[50] Liu, Y-l.; Wei, W.; Wang, X-m.; Yang, H-w.; Xie, Y.F. Relat- ing the Rejections of Oligomeric Ethylene Glycols and Saccharides by Nanofiltration: Implication for Membrane Pore Size Determina- tion. Sep. Purif. Technol. 2018, 205, 151–158. https://doi.org/10.1016/j.seppur.2018.05.042

[51] Xu, R.; Zhou, M.; Wang, H.; Wang, X.; Wen, X. Influences of Temperature on the Retention of PPCPs by Nanofiltration Mem- branes: Experiments and Modeling Assessment. J. Membr. Sci.2020, 599, 117817. https://doi.org/10.1016/j.memsci.2020.117817

[52] Kong, F.-x.; Yang, H.-w.; Wang, X.-m.; Xie, Y. F. Assessment of the Hindered Transport Model in Predicting the Rejection of Trace Organic Compounds by Nanofiltration. J. Membr. Sci. 2016, 498, 57–66. https://doi.org/10.1016/j.memsci.2015.09.062

[53] Aguirre Montesdeoca, V.; Van der Padt, A., Boom, R.M., Janssen, A.E.M. Modelling of Membrane Cascades for the Purifica- tion of Oligosaccharides. J. Membr. Sci. 2016, 520, 712–722. https://doi.org/10.1016/j.memsci.2016.08.031

[54] Darvishmanesh, S.; Van der Bruggen, B. Mass Transport through Nanostructured Membranes: Towards a Predictive Tool. Membranes 2016, 6, 49. https://doi.org/10.3390/membranes6040049

[55] Labban, O.; Chong, T. H.; Lienhard, V J. H. Design and Mod- eling of Novel Low-Pressure Nanofiltration Hollow Fiber Modules for Water Softening and Desalination Pretreatment. Desalination 2018, 439, 58–72. https://doi.org/10.1016/j.desal.2018.04.002

[56] Déon, S.; Escoda, A.; Fievet, P.; Dutournié, P.; Bourseau P. How to Use a Multi-Ionic Transport Model to Fully Predict Rejec- tion of Mineral Salts by Nanofiltration Membranes. Chem. Eng. J. 2012, 189–190, 24–31. https://doi.org/10.1016/j.cej.2012.02.014

[57] Thibault, K.; Zhu, H.; Szymczyk, A.; Li, G. The Averaged Potential Gradient Approach to Model the Rejection of Electrolyte Solutions Using Nanofiltration: Model Development and Assess- ment for Highly Concentrated Feed Solutions. Sep. Purif. Technol. 2015, 153, 126–37. https://doi.org/10.1016/j.seppur.2015.08.041

[58] Blumenschein, S.; Böcking, A.; Kätzel, U.; Postel, S.; Wess- ling, M. Rejection Modeling of Ceramic Membranes in Organic Solvent Nanofiltration. J. Membr. Sci. 2016, 510, 191–200. https://doi.org/10.1016/j.memsci.2016.02.042

[59] Fadaei, F.; Shirazian, S.; Ashrafizadeh, S. N. Mass Transfer Modeling of ion Transport through Nanoporous Media. Desalina- tion 2011, 281, 325–333.https://doi.org/10.1016/j.desal.2011.08.025

[60] Dey, P.; Linnanen, L.; Pal, P. Separation of Lactic Acid from Fermentation Broth by Cross Flow Nanofiltration: Membrane Char- acterization and Transport Modelling. Desalination 2012, 288, 47–57. https://doi.org/10.1016/j.desal.2011.12.009

[61] Farsi, A.; Boffa, V.; Qureshi, H. F.; Nijmeijer, A.; Winnubst, L.; Christensen, M. L. Modeling Water Flux and Salt Rejection of Mesoporous γ-Alumina and Microporous Organosilica Membranes. J. Membr. Sci. 2014, 470, 307–315.https://doi.org/10.1016/j.memsci.2014.07.038

[62] Pal, P.; Das, P.; Chakrabortty, S.; Thakura, R. Dynamic Model- ling of a Forward Osmosis-Nanofiltration Integrated Process for Treating Hazardous Wastewater. Environ. Sci. Pollut. Res. 2016, 23, 21604–21618. https://doi.org/10.1007/s11356-016-7392-8

[63] Silva, V.; Martın, A.; Martınez, F.; Malfeito, J.; Pradanos, P.; Palacio, L.; Hernandez, A. Electrical Characterization of NF Mem- branes. A Modified Model with Charge Variation along the Pores. Chem. Eng. Sci. 2011, 66, 2898–2911.https://doi.org/10.1016/j.ces.2011.03.025

[64] Zerafat, M.M.; Shariati-Niassar, M.; Hashemi, S.J.; Sabbaghi, S.; Ismail, A.F.; Matsuura, T. Mathematical Modeling of Nanofiltra- tion for Concentrated Electrolyte Solutions. Desalination 2013, 320, 17–23. https://doi.org/10.1016/j.desal.2013.04.015

[65] Pal, P.; Sardar, M.; Pal, M.; Chakrabortty, S.; Nayak, J. Model- ling Forward Osmosis-Nanofiltration Integrated Process for Treat- ment and Recirculation of Leather Industry Wastewater. Comput Chem Eng. 2019, 127, 99–110.https://doi.org/10.1016/j.compchemeng.2019.05.018

[66] Kumar, R.; Chakrabortty, S.; Pal, P. Membrane-Integrated Physico-Chemical Treatment of Coke-Oven Wastewater: Transport Modelling and Economic Evaluation. Environ. Sci. Pollut. Res.2015, 22, 6010–6023. https://doi.org/10.1007/s11356-014-3787-6

[67] Luo, J.; Wan, Y. Effect of highly Concentrated Salt on Reten- tion of Organic Solutes by Nanofiltration Polymeric Membranes. J. Membr. Sci. 2011, 372, 145–153.https://doi.org/10.1016/j.memsci.2011.01.066

[68] Chakrabortty, S.; Sen, M.; Pal, P. Arsenic Removal from Con- taminated Groundwater by Membrane-Integrated Hybrid Plant: Optimization and Control Using Visual Basic Platform. Environ. Sci. Pollut. Res. 2014, 21, 3840–3857.https://doi.org/10.1007/s11356-013-2382-6

[69] Chakrabortty, S.; Roy, M.; Pal, P. Removal of Fluoride from Contaminated Groundwater by Cross Flow Nanofiltration: Trans- port Modeling and Economic Evaluation. Desalination 2013, 313, 115–124. https://doi.org/10.1016/j.desal.2012.12.021

[70] Oatley-Radcliffe, D. L.; Williams, S. R.; Barrow, M. S.; Wil- liams, P. M. Critical Appraisal of Current Nanofiltration Modelling Strategies for Seawater Desalination and Further Insights on Dielec- tric Exclusion. Desalination 2014, 343, 154–161. https://doi.org/10.1016/j.desal.2013.10.001

[71] Roy, Y.; Sharqawy, M. H.; Lienhard, J. H. Modeling of Flat- Sheet and Spiral-Wound Nanofiltration Configurations and its Application in Seawater Nanofiltration. J. Membr. Sci. 2015, 493, 360–372. https://doi.org/10.1016/j.memsci.2015.06.030

[72] Bonner, R.; Germishuizen, Ch.; Franzsen, S. Prediction of Nanofiltration Rejection Performance in Brackish Water Reverse Osmosis Brine Treatment Processes. J. Water Process. Eng. 2019, 32, 100900. https://doi.org/10.1016/j.jwpe.2019.100900

[73] Labban, O.; Liu, Ch.; Chong, T. H.; Lienhard, J. H. Fundamen- tals of Low-Pressure Nanofiltration: Membrane Characterization, Modeling, and Understanding the Multi-Ionic Interactions in Water Softening. J. Membr. Sci. 2017, 521, 18–32. https://doi.org/10.1016/j.memsci.2016.08.062

[74] Chakrabortty, S.; Nayak, J.; Pal, P.; Kumar, R.; Chakraborty, P. Separation of COD, Sulphate and Chloride from Pharmaceutical Wastewater Using Membrane Integrated System: Transport Model- ing Towards Scale-Up. J. Environ. Chem. Eng. 2020, 8, 104275. https://doi.org/10.1016/j.jece.2020.104275

[75] Pal, P.; Thakura, R., Chakrabortty S. Performance Analysis and Optimization of an Advanced Pharmaceutical Wastewater Treat- ment Plant Through a Visual Basic Software Tool (PWWT.VB).Environ. Sci. Pollut. Res. 2016, 23, 9901–9917. https://doi.org/10.1007/s11356-016-6238-8

[76] Roy, Y.; Warsinger, D. M.; Lienhard, J. H. Effect of Tempera- ture on Ion Transport in Nanofiltration Membranes: Diffusion, Convection and Electromigration. Desalination 2017, 420, 241–257. https://doi.org/10.1016/j.desal.2017.07.020

[77] Déon, S.; Escoda, A.; Fievet, P. A Transport Model Consider- ing Charge Adsorption Inside Pores to Describe Salts Rejection by Nanofiltration Membranes. Chem. Eng. Sci. 2011, 66, 2823–2832. https://doi.org/10.1016/j.ces.2011.03.043

[78] Bajpai, Sh.; Rajendran, R. M.; Hooda, S. Modeling the Per- formance of HPA Membrane for Sulfate Ion Removal from Ternary Ion System. Korean J. Chem. Eng. 2019, 36, 1648–1656. https://doi.org/10.1007/s11814-019-0357-0

[79] Fang, J.; Deng, B. Rejection and Modeling of Arsenate by Nanofiltration: Contributions of Convection, Diffusion and Elec- tromigration to Arsenic Transport. J. Membr. Sci. 2014, 453, 42–51. https://doi.org/10.1016/j.memsci.2013.10.056

[80] Cathie Lee, W.P.; Mah, Sh.-K.; Leo, C.P.; Wu, T. Y.; Chai, S.-P. Phosphorus Removal by NF90 Membrane: Optimisation Using Central Composite Design. J. Taiwan Inst. Chem. Eng. 2014, 45, 1260–1269. https://doi.org/10.1016/j.jtice.2014.02.011

[81] Bandini, S.; Morelli, V. Effect of Temperature, pH and Com- position on Nanofiltration of Mono/Disaccharides: Experiments and Modeling Assessment. J. Membr. Sci. 2017, 533, 57–74. https://doi.org/10.1016/j.memsci.2017.03.021

[82] Liu, H.; Zhao, L.; Fan, L.; Jiang, L.; Qiu, Y.; Xia, Q.; Zhou J. Establishment of a Nanofiltration Rejection Sequence and Calcu- lated Rejections of Available Monosaccharides. Sep. Purif. Technol. 2016, 163, 319–330. https://doi.org/10.1016/j.seppur.2016.03.016

[83] Shah, A. D.; Huang, Ch.-H.; Kim, J.-H. Mechanisms of Antibi- otic Removal by Nanofiltration Membranes: Model Development and Application. J. Membr. Sci. 2012, 389, 234–244. https://doi.org/10.1016/j.memsci.2011.10.034

[84] Balannec, B.; Ghoufi, A.; Szymczyk, A. Nanofiltration Per- formance of Conical and Hourglass Nanopores. J. Membr. Sci. 2018, 552, 336–340. https://doi.org/10.1016/j.memsci.2018.02.026

[85] Fadaei, F.; Hoshyargar, V.; Shirazian, S.; Ashrafizadeh S. Mass Transfer Simulation of Ion Separation by Nanofiltration Consider- ing Electrical and Dielectrical Effects. Desalination 2012, 284, 316–323. https://doi.org/10.1016/j.desal.2011.09.018

[86] Fridman-Bishop, N.; Tankus, K. A.; Freger, V. Permeation Mechanism and Interplay between Ions in Nanofiltration. J. Membr. Sci. 2018, 548, 449–458.https://doi.org/10.1016/j.memsci.2017.11.050

[87] Zhu, Y.; Zhu, H.; Li, G.; Mai, Zh.; Gu, Y. The Effect of Dielec- tric Exclusion on the Rejection Performance of Inhomogeneously Charged Polyamide Nanofiltration Membranes. J Nanopart Res.2019, 21, 217. https://doi.org/10.1007/s11051-019-4665-4

[88] Marecka-Migacz, A.; Mitkowski, P. T.; Nedzarek, A., Rózan- ski, J.; Szaferski, W. Effect of pH on Total Volume Membrane Charge Density in the Nanofiltration of Aqueous Solutions of Ni- trate Salts of Heavy Metals. Membranes 2020, 10, 235. https://doi.org/10.3390/membranes10090235

[89] Ortiz-Albo, P.; Ibañez R.; Urtiaga A.; Ortiz I. Phenomenologi- cal Prediction of Desalination Brines Nanofiltration through the Indirect Determination of Zeta Potential. Sep. Purif. Technol. 2019, 210, 746–753. https://doi.org/10.1016/j.seppur.2018.08.066

[90] Marecka-Migacz, A.; Mitkowski, P. T.; Antczak, J.; Rózanski, J.; Prochaska K. Assessment of the Total Volume Membrane Charge Density through Mathematical Modeling for Separation of Succinic Acid Aqueous Solutions on Ceramic Nanofiltration Mem- brane. Processes 2019, 7, 559. https://doi.org/10.3390/pr7090559

[91] Micari, M.; Diamantidou, D.; Heijman, B.; Moser, M.; Haidari A., Spanjers, H.; Bertsch V. Experimental and Theoretical Charac- terization of Commercial Nanofiltration Membranes for the Treat- ment of Ion Exchange Spent Regenerant. J. Membr. Sci. 2020, 606, 118117. https://doi.org/10.1016/j.memsci.2020.118117

[92] Wang, X.; Li B.; Zhang, T.; Li, X. Performance of Nanofiltra- tion Membrane in Rejecting Trace Organic Compounds: Experi- ment and Model Prediction. Desalination 2015, 370, 7–16. https://doi.org/10.1016/j.desal.2015.05.010

[93] Kumar, V. S.; Hariharan, K. S.; Mayya, K. S.; Han, S. Volume Averaged Reduced Order Donnan Steric Pore Model for Nanofiltra- tion Membranes. Desalination 2013, 322, 21–28. https://doi.org/10.1016/j.desal.2013.04.030

[94] Wang, Zh.; Xiao, K.; Wang, X. Role of Coexistence of Nega- tive and Positive Membrane Surface Charges in Electrostatic Effect for Salt Rejection by Nanofiltration. Desalination 2018, 444, 75–83. https://doi.org/10.1016/j.desal.2018.07.010

[95] Escoda, A.; Déon, S.; Fievet, P. Assessment of Dielectric Con- tribution in the Modeling of Multi-Ionic Transport Through Nanofil- tration Membranes. J. Membr. Sci. 2011, 378, 214–223. https://doi.org/10.1016/j.memsci.2011.05.004

[96] Karakhim, S. O.; Zhuk, P. F.; Kosterin, S. O. Kinetics Simula- tion of Transmembrane Transport of Ions and Molecules Through a Semipermeable Membrane. J. Bioenerg. Biomembr. 2020, 52, 47–60. https://doi.org/10.1007/s10863-019-09821-8

[97] Hoshyargar, V.; Fadaei, F.; Ashrafizadeh, S. N. Mass Transfer Simulation of Nanofiltration Membranes for Electrolyte Solutions through Generalized Maxwell-Stefan Approach. Korean J. Chem. Eng. 2015, 32, 1388–1404. https://doi.org/10.1007/s11814-014-0329-3

[98] Saeed, A.; Vuthaluru, R.; Vuthaluru, H. B. Investigations into the Effects of Mass Transport and Flow Dynamics of Spacer Filled Membrane Modules Using CFD. Chem. Eng. Res. Des. 2015, 93, 79–99. https://doi.org/10.1016/j.cherd.2014.07.002

[99] Kaufman, Y.; Kasher, R.; Lammertink, R. G. H.; Freger, V. Microfluidic NF/RO Separation: Cell Design, Performance and Application. J. Membr. Sci. 2012, 396, 67–73. https://doi.org/10.1016/j.memsci.2011.12.052

[100] Asefi, H.; Alighardashi, A.; Fazeli, M., Fouladitajar A. CFD Modeling and Simulation of Concentration Polarization Reduction by Gas Sparging Cross-flow Nanofiltration. J. Environ. Chem. Eng. 2019, 7, 103275. https://doi.org/10.1016/j.jece.2019.103275

[101] Cao, H.; O'Rourke, M.; Habimana, O.; Casey, E. Analysis of Surrogate Bacterial Cell Transport to Nanofiltration Membranes: Effect of Salt Concentration and Hydrodynamics. Sep. Purif. Tech- nol. 2018, 207, 498–505.https://doi.org/10.1016/j.seppur.2018.06.072

[102] Onorato, C.; Gaedtke, M.; Kespe, M.; Nirschl, H.; Schäfer, A.I. Renewable Energy Powered Membrane Technology: Computa- tional Fluid Dynamics Evaluation of System Performance with Variable Module Size and Fluctuating Energy. Sep. Purif. Technol. 2019, 220, 206–216. https://doi.org/10.1016/j.seppur.2019.02.041

[103] Kostoglou, M.; Karabelas, A. J. Comprehensive Simulation of Flat-Sheet Membrane Element Performance in Steady State Desali- nation. Desalination 2013, 316, 91–102. https://doi.org/10.1016/j.desal.2013.01.033

[104] Naskar, M.; Rana, K.; Chatterjee, D.; Dhara, T.; Sultana, R.; Sarkar, D. Design, Performance Characterization and Hydrody- namic Modeling of Intermeshed Spinning Basket Membrane (ISBM) Module. Chem. Eng. Sci. 2019, 206, 446–462.https://doi.org/10.1016/j.ces.2019.05.049

[105] Dzhonova-Atanasova, D. B.; Tsibranska, I. H.; Paniovska, S.P. CFD Simulation of Cross-Flow Filtration. Chem. Eng. Trans.2018, 70, 2041–2046. https://doi.org/10.3303/CET1870341

[106] Trojanowska, A.; Tsibranska, I.; Dzhonova, D.; Wroblewska, M.; Haponska, M.; Jovancic, P.; Marturano, V.; Tylkowski, B. Ultrasound-Assisted Extraction of Biologically Active Compounds and Their Successive Concentration by Using Membrane Processes. Chem. Eng. Res. Des. 2019, 147, 378–389.https://doi.org/10.1016/j.cherd.2019.05.018

[107] Kerdi, S.; Qamar, A.; Alpatova, A.; Vrouwenvelder, J. S.; Ghaffour, N. Membrane Filtration Performance Enhancement and Biofouling Mitigation Using Symmetric Spacers with Helical Fila- ments. Desalination 2020, 484, 114454. https://doi.org/10.1016/j.desal.2020.114454

[108] Koutsou, C. P.; Karabelas, A. J. A Novel Retentate Spacer Geometry for Improved Spiral Wound Membrane (SWM) Module Performance. J. Membr. Sci. 2015, 488, 129–142. https://doi.org/10.1016/j.memsci.2015.03.064

[109] Lim, K. B.; Wang, P. Ch.; An, H.; Yu, S. C. M. Computa-tional Studies for the Design Parameters of Hollow Fibre Membrane Modules. J. Membr. Sci. 2017, 529, 263–273. https://doi.org/10.1016/j.memsci.2017.01.053

[110] Min, J.; Zhang, B. Convective Mass Transfer Enhancement in a Membrane Channel by Delta Winglets and Their Comparison with Rectangular Winglets. Chin. J. Chem. Eng. 2015, 23, 1755–1762. https://doi.org/10.1016/j.cjche.2015.09.006

[111] Qamar, A.; Bucs, S.; Picioreanu, C.; Vrouwenvelder, J.; Ghaf- four, N. Hydrodynamic Flow Transition Dynamics in a Spacer Filled Filtration Channel Using Direct Numerical Simulation. J. Membr. Sci. 2019, 590, 117264.https://doi.org/10.1016/j.memsci.2019.117264

[112] Tonova, K.; Lazarova, M.; Dencheva-Zarkova, M.; Pan- iovska, S.; Tsibranska, I.; Stanoev, V.; Dzhonova, D.; Genova, J. Separation of Glucose, other Reducing Sugars and Phenolics from Natural Extract by Nanofiltration: Effect of Pressure and Cross- Flow Velocity. Chem. Eng. Res. Des. 2020, 162, 107–116. https://doi.org/10.1016/j.cherd.2020.07.030

[113] Yang, Zh.; Cheng, J.; Yang, Ch.; Liang, B. CFD-based Opti- mization and Design of Multi-Channel Inorganic Membrane Tubes. Chin. J. Chem. Eng. 2016, 24, 1375–1385.https://doi.org/10.1016/j.cjche.2016.05.044

[114] Al-Rudainy, B.; Galbe, M.; Wallberg O. From Lab-Scale to On-Site Pilot Trials for the Recovery of Hemicellulose by Ultrafil- tration: Experimental and Theoretical Evaluations. Sep. Purif. Tech- nol. 2020, 250, 117187 https://doi.org/10.1016/j.seppur.2020.117187

[115] Cortés-Juan, F.; Balannec, B.; Renouard, T. CFD-assisted Design Improvement of a Bench-Scale Nanofiltration Cell. Sep. Purif. Technol. 2011, 82, 177–184. https://doi.org/10.1016/j.seppur.2011.09.010

[116] Lee, Y. K.; Won, Y.-J.; Yoo, J. H.; Ahn, K. H.; Lee, Ch.-H.Flow Analysis and Fouling on the Patterned Membrane Surface. J. Membr. Sci. 2013, 427, 320–325. https://doi.org/10.1016/j.memsci.2012.10.010

[117] Ronen, A.; Lerman, S.; Ramon, G. Z.; Dosoretz, C. G. Ex- perimental Characterization and Numerical Simulation of the Anti- Biofuling Activity of Nanosilver-Modified Feed Spacers in Mem- brane Filtration. J. Membr. Sci. 2015, 475, 320–329. https://doi.org/10.1016/j.memsci.2014.10.042

[118] Koutsou, C.P.; Karabelas, A.J.; Kostoglou, M. Membrane Desalination under Constant Water Recovery – The Effect of Mod- ule Design Parameters on System Performance. Sep. Purif. Technol. 2015, 147, 90–113. https://doi.org/10.1016/j.seppur.2015.04.012

[119] Yao, L.; Qin, Zh.; Chen, Q.; Zhao, M.; Zhao, H.; Ahmad, W.; Fan, L.; Zhao, L. Insights Into the Nanofiltration Separation Mecha- nism of Monosaccharides by Molecular Dynamics Simulation. Sep. Purif. Technol. 2018, 205, 48–57. https://doi.org/10.1016/j.seppur.2018.04.056

[120] Suk, M. E. Single-File Water Flux Through Two-Dimensional Nanoporous Membranes. Nanoscale Res. Lett. 2020, 15, 204. https://doi.org/10.1186/s11671-020-03436-4

[121] Liu, J.; Xu, Q.; Jiang, J. A Molecular Simulation Protocol for Swelling and Organic Solvent Nanofiltration of Polymer Mem- branes. J. Membr. Sci. 2019, 573, 639–646. https://doi.org/10.1016/j.memsci.2018.12.035

[122] Teng, X.; Fang, W.; Liang, Y.; Lin, Sh.; Lin, H.; Liu, Sh.; Wang, Zh.; Zhu, Y.; Jin, J. High-Performance Polyamide Nanofil- tration Membrane with Arch-Bridge Structure on a Highly Hydrated Cellulose Nanofiber Support. Sci. China Mater. 2020, 63, 2570–2581. https://doi.org/10.1007/s40843-020-1335-x

[123] Xu, Q.; Jiang, J. Effects of Functionalization on the Nanofil- tration Performance of PIM-1: Molecular Simulation Investigation. J. Membr. Sci. 2019, 591, 117357.https://doi.org/10.1016/j.memsci.2019.117357

[124] Liu, J.; Kong, X.; Jiang, J. Solvent Nanofiltration through Polybenzimidazole Membranes: Unravelling the Role of Pore Size from Molecular Simulations. J. Membr. Sci. 2018, 564, 782–787. https://doi.org/10.1016/j.memsci.2018.07.086

[125] Azamat, J.; Baghbani, N. B.; Erfan-Niya, H. Atomistic Under- standing of Functionalized γ-graphyne-1 Nanosheet Membranes for Water Desalination. J. Membr. Sci. 2020, 604, 118079. https://doi.org/10.1016/j.memsci.2020.118079

[126] Cong, W.; Gao, W.; Garvey, Ch. J.; Dumée, L. F.; Zhang, J.; Kent, B.; Wang, G.; She, F.; Kong, L. In Situ SAXS Measurement and Molecular Dynamics Simulation of Magnetic Alignment of Hexagonal LLC Nanostructures. Membranes 2018, 8, 123. https://doi.org/10.3390/membranes8040123

[127] Zhang, X.; Liu, Ch.; Yang, J.; Zhu, Ch.-Y.; Zhang, L.; Xu, Zh.-K. Nanofiltration Membranes with Hydrophobic Microfiltration Substrates for Robust Structure Stability and High Water Permea- tion Flux. J. Membr. Sci. 2020, 593, 117444. https://doi.org/10.1016/j.memsci.2019.117444

[128] Calabrò, F. Modeling the Effects of Material Chemistry on Water Flow Enhancement in Nanotube Membranes. MRS Bull. 2017, 42, 289–293. https://doi.org/10.1557/mrs.2017.58

[129] da Silva Arouche, T.; dos Santos Cavaleiro, R. M.; Tanoue, P. S. M.; Sousa de Sa Pereira, T.; Filho, T. A.; de Jesus Chaves Neto, A. M. Heavy Metals Nanofiltration Using Nanotube and Electric Field by Molecular Dynamics. J. Nanomater. 2020, 2020, 4063201. https://doi.org/10.1155/2020/4063201

[130] Calo, V. M.; Iliev, O.; Lakdawala, Z.; Leonard, K. H. L.; Printsypar, G. Pore-Scale Modeling and Simulation of Flow, Trans- port, and Adsorptive or Osmotic Effects in Membranes: The Influ- ence of Membrane Microstructure. Int J Adv Eng Sci Appl Math.2015, 7, 2–13. https://doi.org/10.1007/s12572-015-0132-3

[131] Sofos, F.; Karakasidis, Th. E.; Giannakopoulos, A. E.; Lia- kopoulos, A. Molecular Dynamics Simulation on Flows in Nano- Ribbed and Nano-Grooved Channels. Heat Mass Transf. 2016, 52, 153–162. https://doi.org/10.1007/s00231-015-1601-8

[132] Xu, Q.; Jiang, J. Molecular Simulations of Liquid Separations in Polymer Membranes. Curr. Opin. Chem. Eng. 2020, 28, 66–74. https://doi.org/10.1016/j.coche.2020.02.001