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Modified solution-diffusion model Incorporating Rotational Kinetic Energy in Pressure Retarded Osmosis

APPLIED SCIENCES-BASEL 2025年第3期15卷 1312-1312页

作者： Ruiz-Navas, Daniel Quinones-Bolanos, Edgar Sharqawy, Mostafa H. Univ Guelph Sch Engn Guelph ON N1G 2W1 Canada Univ Cartagena Fac Engn Cartagena 131001 Colombia

Pressure-retarded osmosis (PRO) is a process that allows the production of mechanical energy from the chemical potential difference between two solutions of different concentrations separated by a semi-permeable membrane. One of the main obstacles for this technology to be commercially competitive is the difference between the theoretical power density and the experimental power density due to negative factors like ICP. Analytical models facilitate the analysis of the relationships between system parameters and thus facilitate the optimization of components. In general, PRO has traditionally been explained through the solution-diffusion model, where the flow of water through the membrane depends on a diffusivity factor, the concentration gradient, and the hydraulic pressure gradient. This paper focuses on developing a modified solution-diffusion model that includes means to control the ICP through rotational kinetic energy. An energy balance method for obtaining a solution diffusion-based model is explained, and an analytical model is obtained. Finally, said model is verified through simulations with parameters reported in the literature to obtain insight on the required dimensions for a prototype. It was found that a turning radius of 0.5 m and an angular speed of less than 3000 rev/min could generate enough kinetic energy to compensate for ICP losses in a PRO scenario. Also, the results suggest that bigger concentration differences could benefit more of this technology, as they require almost the same energy as smaller concentration differences but allow for more energy extraction.

关键词： pressure-retarded osmosis solution-diffusion model rotational kinetic energy

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Salt and Water Transport in Reverse Osmosis Membranes: Beyond the solution-diffusion model

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ENVIRONMENTAL SCIENCE & TECHNOLOGY 2021年第24期55卷 16665-16675页

作者： Wang, Li Cao, Tianchi Dykstra, Jouke E. Porada, Slawomir Biesheuvel, P. M. Elimelech, Menachem Yale Univ Dept Chem & Environm Engn New Haven CT 06520 USA Wageningen Univ Environm Technol NL-6708 WG Wageningen Netherlands Wetsus European Ctr Excellence Sustainable Water Technol NL-8911 MA Leeuwarden Netherlands

Understanding the salt-water separation mechanisms of reverse osmosis (RO) membranes is critical for the further development and optimization of RO technology. The solution-diffusion (SD) model is widely used to describe water and salt transport in RO, but it does not describe the intricate transport mechanisms of water molecules and ions through the membrane. In this study, we develop an ion transport model for RO, referred to as the solution-friction model, by rigorously considering the mechanisms of partitioning and the interactions among water, salt ions, and the membrane. Ion transport through the membrane is described by the extended Nernst-Planck equation, with the consideration of frictions between the species (i.e., ion, water, and membrane matrix). Water flow through the membrane is governed by the hydraulic pressure gradient and the friction between the water and membrane matrix as well as the friction between water and ions. The model is validated using experimental measurements of salt rejection and permeate water flux in a lab-scale, cross-flow RO setup. We then investigate the effects of feed salt concentration and hydraulic pressure on salt permeability, demonstrating strong dependence of salt permeability on feed salt concentration and applied pressure, starkly disparate from the SD model. Lastly, we develop a framework to analyze the pressure drop distribution across the membrane, demonstrating that cross-membrane transport dominates the overall pressure drop in RO, in marked contrast to the SD model that assumes no pressure drop across the membrane.

关键词： reverse osmosis salt permeability water permeability ion transport solution-friction model solution-diffusion model

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Modification to solution-diffusion model for performance prediction of nanofiltration of long-alkyl-chain ionic liquids aqueous solutions based on ion cluster

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Green Energy & Environment 2020年第1期5卷 105-113页

作者： Jianguo Qian Ruiyi Yan Xiaomin Liu Chunshan Li Xiangping Zhang Key Laboratory of Green Process and Engineering Beijing Key Laboratory of Ionic Liquids Clean ProcessState Key Laboratory of Multiphase Complex SystemsInstitute of Process EngineeringChinese Academy of SciencesBeijing 100190China College of Chemistry and Chemical Engineering University of Chinese Academy of SciencesBeijing100049China

Mathematical modeling for nanofiltration of ionic liquids(ILs) solutions could assist to understand transfer mechanism and predict experimental values. In this work, modeling by solution-diffusion model for nanofiltration of long-alkyl-chain ILs aqueous solutions was proposed. Molecular simulations were performed to validate the existence of ion cluster in long-alkyl-chain ILs aqueous solution. Based on the results of simulations, parameters used in the solution-diffusion model were modified, such as concentration of ILs and diameter of ion *** modeling process was developed for three long-alkyl-chain ILs aqueous solutions with different concentrations(1-alkyl-3-methylimidazolium chloride: [C6 mim]Cl, [C8 mim]Cl, [C10 mim]Cl). The calculated values obtained from modified solution-diffusion model could well match the experimental values.

关键词： solution-diffusion model Nanofiltration Long-alkyl-chain ionic liquid Molecular dynamic simulation Ion cluster

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Optimizing Reverse Osmosis Membrane Parameters through the Use of the solution-diffusion model: A Review

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Engineering（科研） 2022年第1期14卷 9-32页

作者： Farah Z. Najdawi Kaleb T. Neptune Department of Material Science Engineering and Commercialization Texas State University San Marcos TX USA

When designing and building an optimal reverse osmosis (RO) desalination plant, it is important that engineers select effective membrane parameters for optimal application performance. The membrane selection can determine the success or failure of the entire desalination operation. The objective of this work is to review available membrane types and design parameters that can be selected for optimal application to yield the highest potential for plant operations. Factors such as osmotic pressure, water flux values, and membrane resistance will all be evaluated as functions of membrane parameters. The optimization of these parameters will be determined through the deployment of the solution-diffusion model devolved from the Maxwell Stephan Equation. When applying the solution-diffusion model to evaluate RO membranes, the Maxwell Stephan Equation provides mathematical analysis through which the steps for mass transfer through a RO membrane may be observed and calculated. A practical study of the use of the solution-diffusion model will be discussed. This study uses the diffusion-solution model to evaluate the effectiveness of a variety of Toray RO membranes. This practical application confirms two principal hypotheses when using the diffusion-solution model for membrane evaluation. First, there is an inverse relationship between membrane and water flux rate. Second, there is a proportional linear relationship between overall water flux rate and the applied pressure across a membrane.

关键词： Reverse Osmosis Membrane solution-diffusion model Maxwell Stephan Equation Desalination Plants Membrane Optimization

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Rejection of pharmaceuticals during forward osmosis and prediction by using the solution-diffusion model

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JOURNAL OF MEMBRANE SCIENCE 2015年 476卷 410-420页

作者： Kong, Fan-xin Yang, Hong-wei Wu, Yu-qiao Wang, Xiao-mao Xie, Yuefeng F. Tsinghua Univ Sch Environm State Key Joint Lab Environm Simulat & Pollut Con Beijing 100084 Peoples R China Penn State Univ Environm Engn Programs Middletown PA 17057 USA

Two commercial forward osmosis (FO) membranes (HTI-ES and HTI-NW) were employed to study the rejection performance of 24 pharmaceuticals (PhACs) using NaCI as the draw solute. The PhAC permeability coefficient (B value) was determined for each PhAC by using both the reverse osmosis (RO) mode method and the diffusion cell method. The B values were used to predict the rejection ratios in the FO mode. The rejection ratio increased with the increase of draw solute (NaCI) concentration for each PhAC. Under a NaCI concentration of 1 mol/L, all PhACs were highly rejected by > 90%, except for a Few including nalidixic acid, gemfibrozil, carbamazepine and sulfamethoxazole, which were rejected by 80-90% when HTI-ES membrane was used The HTI-NW membrane could reject PhACs better than the HTI-ES membrane;however, the PhACs followed almost an identical sequence in terms of the rejection raLios. Results showed that the B values for several charged PhACs of relatively low molecular weight obtained by the diffusion cell method could be substantially larger than that determined by the RO mode method. In comparison with the experimental data, the B values obtained by the diffusion cell method were more appropriate to be used to predict the rejection ratios of the PhACs by the solution-diffusion model during FO operation. The underestimation of the B values by using the RO mode method might be primarily due to the ion exchange mechanism caused by reverse draw solute permeation during FO operation. Compared with he hydrophobicity and he charge properties, the molecular weight of PhAC was a more important factor in determining its B value. Very low B value is expected if the molecular weight is higher than 300 Da. Exceptions, however, were found including clofibric acid, gemfibrozil and sulfadiazine. The solute-membrane affinity should also be taken into consideration when trying to link the B values with physicochemical properties of the PhACs. (C) 2014 Elsevier B.V. All rights reserve

关键词： Pharmaceuticals (PhACs) Forward osmosis (FO) solution-diffusion model Permeability coefficient diffusion cell

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An Improved Permeation model for solution-diffusion-Based Hollow Fiber Gas Separation Membrane: Implementation and Analysis

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ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING 2024年第0期

作者： Almarjeh, Rama Alqassar Bani Yeo, Jason Yi Juang Atassi, Yomen Hosseini, Seyed Saeid Sunarso, Jaka Higher Inst Appl Sci & Technol Dept Appl Phys Damascus Syria Swinburne Univ Technol Fac Engn Comp & Sci Res Ctr Sustainable Technol Kuching Sarawak Malaysia Univ South Africa Inst Nanotechnol & Water Sustainabil Coll Sci Engn & Technol Johannesburg South Africa

Dense polymeric hollow fiber membrane-based gas separation modules are becoming increasingly important in various industrial fields due to their higher efficiency compared to other gas separation processes. modeling the membranes gas separation process and analyzing the governing mathematical equations such as the solution-diffusion model are crucial for optimizing module performance and making the process cost-effective. Herein, we introduce an improved methodology for solving the mathematical model of polymeric hollow fiber gas separation membranes focusing on a simpler and more accurate solution strategy. Unlike previous solving methods, the model characteristic functions (feed flow, permeate flow, feed composition, permeate composition within the porous support layer, and bulk permeate composition) better adhere to boundary conditions at the module inlet and closed-end. The improved solving algorithm provides a more accurate solution, with a maximum mean squared error of 7.3441 x 10-5 and minimum R2$$ {R}<^>2 $$ of 0.8853, outperforming previous complex methods. The corrected algorithm also features improved speed, completing calculations in under 0.015 s, faster than any reported values. The model's response to changes in geometric and operating conditions is evaluated through an extensive sensitivity test, which is conducted by statistical analysis and numerical solutions. Numerical solution approach allows for a wider range of possibilities of interactions compared to statistical analysis and enables inspection of a wider response surface. Additionally, the response equation is estimated for permeate purity, stagecut, and retentate purity, and the process is optimized for different goals. Performance of membrane gas separation is highly sensitive to the membrane sizing and feed concentration, as these factors significantly influence the separation driving force. Therefore, this study presents an improved solving strategy and a detailed description of the effe

关键词： gas separation hollow fiber membrane numerical methods process optimization sensitivity analysis solution-diffusion model

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Development of a generalized mathematical model for two-stage reverse osmosis desalination systems

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COMPUTERS & CHEMICAL ENGINEERING 2024年 182卷

作者： Mehrizi, Reihaneh Abouei Mirbagheri, Seyyed Ahmad Shams, Amin KN Toosi Univ Technol Dept Civil & Environm Engn 1346 Vali Asr St Tehran Iran Semnan Univ Fac Civil Engn Dept Civil Engn Semnan *** Iran

This study presented a generalized mathematical model for a two-stage reverse osmosis (RO) system based on mass balance, the solution-diffusion model, and film theory. The model is user-friendly and can be customized for any membrane regardless of the manufacturer. A set of non-linear equations was solved in MATLAB to calculate the system arrangement, performance parameters, and the required feed pressure for the desired recovery ratio by incorporating membrane characteristics and design parameters. Actual data from a two-stage RO system were employed for model validation against ROSA software results. To optimize energy conservation, equal recovery rates are applied to both stages, resulting in lower calculated feed pressures than those obtained using ROSA software. The study reveals a strong agreement between the simulation results and those obtained from the ROSA software and alignment with the membrane manufacturer's recommendations, making the model a reliable tool for evaluating the system before implementation.

关键词： Mathematical modeling Reverse osmosis Desalination solution-diffusion model Concentration polarization

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solution-diffusion with defects model for pressure-assisted forward osmosis

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JOURNAL OF MEMBRANE SCIENCE 2014年 470卷 323-333页

作者： Duan, Jintang Litwiller, Eric Pinnau, Ingo King Abdullah Univ Sci & Technol Div Phys Sci & Engn Adv Membranes & Porous Mat Ctr Thuwal 239556900 Saudi Arabia

An osmosis transport model is presented that combines the standard internal and external concentration polarization equations in the forward osmosis (FO) held with the selective layer transport equations first proposed by Sherwood in 1967. The Sherwood model describes water flux as the sum of a solute-selective, diffusive component driven by the sum of osmotic pressure and hydraulic pressure differences, and a nonselective, convective component driven by hydraulic pressure difference only. This solution-diffusion with detects (SDWD) model and the solution-diffusion (SD) model were compared against data collected using polyamide thin-film-composite (PA-TFC) and integrally-skinned asymmetric cellulose triacetate (CTA) membranes, evaluated in various configurations. When tested with pure water on the porous support side and 1.5 M (pi=72.7 bar) sodium chloride solution on the selective layer side, applying 1.25 bar of hydraulic pressure to the porous support side increased water flux by an order of magnitude for PA-TFC membranes, but had negligible effect on CTA membrane flux. These large flux variations can be explained by the SDWD model, but not the SD model. To confirm the existence of defects, a PA-TFC membrane was coated with a uniform, highly water-permeable, nonselective polymer. After coating to block convection through defects, the influence of hydraulic pressure on water flux through this membrane essentially disappeared. Water flux through these defects is low (< 1% of total water flux for PA-TFC membranes) and of little consequence in practical FO or reverse osmosis (RO) applications. But in pressure-assisted forward osmosis (PAFO) or pressure-retarded osmosis (PRO), convective transport through defects affects the solute concentration difference across the membrane selective layer, increasing or decreasing water flux through defect-free regions. The presence of defects may explain why membrane power density in PRO is lower than that predicted based on FO an

关键词： Forward osmosis solution-diffusion model Concentration polarization Pressure Defect

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Molecular insights into butane isomer separation by MFI zeolite membrane: Intersection channel effect on the orientation of fluid molecules

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SEPARATION AND PURIFICATION TECHNOLOGY 2025年 361卷

作者： Wang, Wenqiang Niu, Mengfei Ma, Rugang Qin, Yao Feng, Xin Zhou, Rongfei Lu, Xiaohua Zhu, Yudan Nanjing Tech Univ Coll Chem Engn State Key Lab Mat Oriented Chem Engn 30 Puzhu South Rd Nanjing 211816 Peoples R China Suzhou Lab Suzhou 215125 Peoples R China

MFI zeolite membranes are widely used for separating butane isomers, however, MFI zeolite membranes show significantly different separation performance in butane isomers under different conditions. In this study, molecular simulation combined with the solution-diffusion model is used to study the mechanism of MFI zeolite membrane separation on butane isomer. Results demonstrate that the n/i-butane selectivity along the zig-zag channel of MFI zeolite membranes is higher than that along the straight channel and separation performance difference is mainly due to the diffusion contribution. Intersection channel plays an important role in butane isomer diffusion selectivity. The integration of the unfavorable molecular orientation of i-butane at intersections can reflect the change of diffusion coefficient. The diffusion coefficient containing molecular microstructural information combined with the solution-diffusion model is further extended to understand the selectivity by highly oriented MFI zeolite membranes under different temperatures (298-373 K) and feed side pressures (101-201 kPa).

关键词： MFI zeolite channel Molecular simulation solution-diffusion model Molecular orientation N/i-butane

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Rejection of trace organic compounds by membrane processes: mechanisms, challenges, and opportunities

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REVIEWS IN CHEMICAL ENGINEERING 2023年第5期39卷 875-910页

作者： Mahlangu, Oranso T. Motsa, Machawe M. Nkambule, Thabo, I Mamba, Bhekie B. Univ South Africa Coll Engn Sci & Technol Inst Nanotechnol & Water Sustainabil Florida Sci Campus ZA-1709 Roodepoort South Africa

This work critically reviews the application of various membrane separation processes (MSPs) in treating water polluted with trace organic compounds (TOrCs) paying attention to nanofiltration (NF), reverse osmosis (RO), membrane bioreactor (MBR), forward osmosis (FO), and membrane distillation (MD). Furthermore, the focus is on loopholes that exist when investigating mechanisms through which membranes reject/retain TOrCs, with the emphasis on the characteristics of the model TOrCs which would facilitate the identification of all the potential mechanisms of rejection. An explanation is also given as to why it is important to investigate rejection using real water samples, especially when aiming for industrial application of membranes with novel materials. MSPs such as NF and RO are prone to fouling which often leads to lower permeate flux and solute rejection, presumably due to cake-enhanced concentration polarisation (CECP) effects. This review demonstrates why CECP effects are not always the reason behind the observed decline in the rejection of TOrCs by fouled membranes. To mitigate for fouling, researchers have often modified the membrane surfaces by incorporating nanoparticles. This review also attempts to explain why nano-engineered membranes have not seen a breakthrough at industrial scale. Finally, insight is provided into the possibility of harnessing solar and wind energy to drive energy intensive MSPs. Focus is also paid into how low-grade energy could be stored and applied to recover diluted draw solutions in FO mode.

关键词： cake-enhanced concentration polarisation membrane fouling solution-diffusion model trace organic compounds

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