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Membranes
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Numerical Modelling in Membrane Processes
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Numerical Modelling in Membrane Processes

A special issue of Membranes (ISSN 2077-0375). This special issue belongs to the section "Membrane Physics and Theory".

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 48612

Special Issue Editors

Dr. Sébastien Déon

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Guest Editor
Institut UTINAM (CNRS UMR 6213), Universite Bourgogne Franche-Comte, Besancon, France
Interests: membrane processes; transport modelling; electrokinetic characterization; surface modification; water treatment
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Patrick Dutournié

E-Mail Website
Guest Editor
Institut de Science des Matériaux de Mulhouse (IS2M-UMR CNRS 7361), Université de Haute-Alsace, 15 Rue Jean Starcky, BP 2488, 68057 Mulhouse CEDEX, France
Interests: numerical modelling; heat and mass transfer; zeolite films; membrane synthesis; ion separation

Special Issue Information

Dear Colleagues,

Membrane processes have demonstrated their enormous potential for water treatment by removing organic and mineral contaminants before permeating stream discharge or by concentrating high added-value compounds in retentate stream. Although the advantages and drawbacks of the various membrane processes are well known, the mechanisms governing their filtration performances are usually not fully understood and discussion is often still open. For this purpose, researchers develop numerical models for decades to describe the transport of species through membranes, in order to predict their performances for specific applications.

This Special Issue on “Numerical Modelling in Membrane Processes” seeks to collate original research studies which deal with the use of mathematical models to understand, describe, predict or optimize the performances of membrane processes. This Special Issue mainly focuses on the modelling of fluid flow or mass transfer, and especially the description of phenomena governing filtration performances such as transport mechanisms, exclusion phenomena, fouling, concentration polarization, surface charge regulation, etc. The numerical approaches proposed in submitted manuscripts can be applied to various membrane processes, such as pressure-driven (reverse osmosis, nanofiltration, ultrafiltration, microfiltration), concentration-driven (pervaporation, forward osmosis, pressure retarded osmosis), electrically driven (electrodialysis) or thermally driven (membrane distillation) processes.

As Guest Editors, we cordially invite you to submit a manuscript for publication in this Special Issue of the journal Membranes. Authors are invited to submit recent results in the form of either research papers or critical reviews of the state-of-the-art.

We are looking forward to receiving your valued contributions.

Dr. Sébastien Déon
Prof. Dr. Patrick Dutournié
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Membranes is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Membrane processes
  • Transport Modelling
  • Filtration performances
  • Fouling
  • Concentration polarization

Published Papers (18 papers)

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Editorial

Jump to: Research, Review

4 pages, 219 KiB  
Editorial
Numerical Modeling in Membrane Processes
by Sébastien Déon and Patrick Dutournié
Membranes 2022, 12(11), 1030; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes12111030 - 23 Oct 2022
Viewed by 888
Abstract
Membrane processes have demonstrated their enormous potential for water treatment, either by removing organic and mineral contaminants before permeating stream discharge, or by concentrating high added-value compounds in retentate stream [...] Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)

Research

Jump to: Editorial, Review

28 pages, 1289 KiB  
Article
Geometrical Influence on Particle Transport in Cross-Flow Ultrafiltration: Cylindrical and Flat Sheet Membranes
by Gun Woo Park and Gerhard Nägele
Membranes 2021, 11(12), 960; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11120960 - 06 Dec 2021
Cited by 1 | Viewed by 2546
Abstract
Cross-flow membrane ultrafiltration (UF) is used for the enrichment and purification of small colloidal particles and proteins. We explore the influence of different membrane geometries on the particle transport in, and the efficiency of, inside-out cross-flow UF. For this purpose, we generalize the [...] Read more.
Cross-flow membrane ultrafiltration (UF) is used for the enrichment and purification of small colloidal particles and proteins. We explore the influence of different membrane geometries on the particle transport in, and the efficiency of, inside-out cross-flow UF. For this purpose, we generalize the accurate and numerically efficient modified boundary layer approximation (mBLA) method, developed in recent work by us for a hollow cylindrical membrane, to parallel flat sheet geometries with one or two solvent-permeable membrane sheets. Considering a reference dispersion of Brownian hard spheres where accurate expressions for its transport properties are available, the generalized mBLA method is used to analyze how particle transport and global UF process indicators are affected by varying operating parameters and the membrane geometry. We show that global process indicators including the mean permeate flux, the solvent recovery indicator, and the concentration factor are strongly dependent on the membrane geometry. A key finding is that irrespective of the many input parameters characterizing an UF experiment and its membrane geometry, the process indicators are determined by three independent dimensionless variables only. This finding can be very useful in the design, optimization, and scale-up of UF processes. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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13 pages, 1322 KiB  
Article
A Novel Numerical Procedure to Estimate the Electric Charge in the Pore from Filtration of Single-Salt Solutions
by Patrick Dutournié, T. Jean Daou and Sébastien Déon
Membranes 2021, 11(10), 726; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11100726 - 23 Sep 2021
Cited by 2 | Viewed by 1422
Abstract
The assessment of physicochemical parameters governing the transport of ions through nanoporous membranes is a major challenge due to the difficulty in experimental estimation of the dielectric constant of the solution confined in nanopores and the volumetric membrane charge. Numerical identification by adjusting [...] Read more.
The assessment of physicochemical parameters governing the transport of ions through nanoporous membranes is a major challenge due to the difficulty in experimental estimation of the dielectric constant of the solution confined in nanopores and the volumetric membrane charge. Numerical identification by adjusting their values to fit experimental data is a potential solution, but this method is complicated for single-salt solutions due to the infinite number of couples that can describe a rejection curve. In this study, a novel procedure based on physical simplifications which allows the estimation of a range of values for these two parameters is proposed. It is shown here that the evolution of the interval of membrane charge with salt concentration can be described in all the experimental conditions by the Langmuir–Freundlich hybrid adsorption isotherm. Finally, it is highlighted that considering the mean dielectric constant and the adsorption isotherms assessed from a range of concentrations allowed a good prediction of rejection curves, irrespective of the salt and membrane considered. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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19 pages, 7580 KiB  
Article
Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface
by Kyung Tae Kim, Jo Eun Park, Seon Yeop Jung and Tae Gon Kang
Membranes 2021, 11(10), 724; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11100724 - 23 Sep 2021
Cited by 6 | Viewed by 1958
Abstract
Fouling mitigation using chaotic advection caused by herringbone-shaped grooves in a flat membrane module is numerically investigated. The feed flow is laminar with the Reynolds number (Re) ranging from 50 to 500. In addition, we assume a constant permeate flux on [...] Read more.
Fouling mitigation using chaotic advection caused by herringbone-shaped grooves in a flat membrane module is numerically investigated. The feed flow is laminar with the Reynolds number (Re) ranging from 50 to 500. In addition, we assume a constant permeate flux on the membrane surface. Typical flow characteristics include two counter-rotating flows and downwelling flows, which are highly influenced by the groove depth at each Re. Poincaré sections are plotted to represent the dynamical systems of the flows and to analyze mixing. The flow systems become globally chaotic as the groove depth increases above a threshold value. Fouling mitigation via chaotic advection is demonstrated using the dimensionless average concentration (c¯w*) on the membrane and its growth rate. When the flow system is chaotic, the growth rate of c¯w* drops significantly compared to that predicted from the film theory, demonstrating that chaotic advection is an attractive hydrodynamic technique that mitigates membrane fouling. At each Re, there exists an optimal groove depth minimizing c¯w* and the growth rate of c¯w*. Under the optimum groove geometry, foulants near the membrane are transported back to the bulk flow via the downwelling flows, distributed uniformly in the entire channel via chaotic advection. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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13 pages, 4171 KiB  
Article
Numerical Simulation of Continuous Extraction of Li+ from High Mg2+/Li+ Ratio Brines Based on Free Flow Ion Concentration Polarization Microfluidic System
by Dongxiang Zhang, Xianglei Zhang, Leilei Xing and Zirui Li
Membranes 2021, 11(9), 697; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11090697 - 10 Sep 2021
Cited by 5 | Viewed by 2538
Abstract
Ion concentration polarization (ICP) is a promising mechanism for concentrating and/or separating charged molecules. This work simulates the extraction of Li+ ions in a diluted high Mg2+/Li+ ratio salt lake brines based on free flow ICP focusing (FF-ICPF). The [...] Read more.
Ion concentration polarization (ICP) is a promising mechanism for concentrating and/or separating charged molecules. This work simulates the extraction of Li+ ions in a diluted high Mg2+/Li+ ratio salt lake brines based on free flow ICP focusing (FF-ICPF). The model solution of diluted brine continuously flows through the system with Li+ slightly concentrated and Mg2+ significantly removed by ICP driven by external pressure and perpendicular electric field. In a typical case, our results showed that this system could focus Li+ concentration by ~1.28 times while decreasing the Mg2+/Li+ ratio by about 85% (from 40 to 5.85). Although Li+ and Mg2+ ions are not separated as an end product, which is preferably required by the lithium industry, this method is capable of decreasing the Mg2+/Li+ ratio significantly and has great potential as a preprocessing technology for lithium extraction from salt lake brines. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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25 pages, 7476 KiB  
Article
Effect of Modifying the Membrane Surface with Microcapsules on the Flow Field for a Cross-Flow Membrane Setup: A CFD Study
by Sebastian Osterroth, Christian Neumann, Michael Weiß, Uwe Maurieschat, Alexandra Latnikova and Stefan Rief
Membranes 2021, 11(8), 555; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11080555 - 22 Jul 2021
Cited by 2 | Viewed by 2163
Abstract
In this study, the attachment of microcapsules on the membrane surface and its influence on the flow field for a cross-flow membrane setup are investigated. The microcapsules were placed on the top layer of the membrane. The overall purpose of this modification was [...] Read more.
In this study, the attachment of microcapsules on the membrane surface and its influence on the flow field for a cross-flow membrane setup are investigated. The microcapsules were placed on the top layer of the membrane. The overall purpose of this modification was the prevention of membrane biofouling. Therefore, in a first step, the influence of such a combination on the fluid flow was investigated using computational fluid dynamics (CFD). Here, different properties, which are discussed as indicators for biofouling in the literature, were considered. In parallel, different fixation strategies for the microcapsules were experimentally tested. Two different methods to add the microcapsules were identified and further investigated. In the first method, the microcapsules are glued to the membrane surface, whereas in the second method, the microcapsules are added during the membrane fabrication. The different membrane modifications were studied and compared using CFD. Therefore, virtual geometries mimicking the real ones were created. An idealized virtual geometry was added to the comparison. Results from the simulation were fed back to the experiments to optimize the combined membrane. For the presented setup, it is shown that the glued configuration provides a lower transmembrane pressure than the configuration where microcapsules are added during fabrication. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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15 pages, 1366 KiB  
Article
Exergy Analysis of a Direct Contact Membrane Distillation (DCMD) System Based on Computational Fluid Dynamics (CFD)
by Jihyeok Choi, Yongjun Choi, Juyoung Lee, Yusik Kim and Sangho Lee
Membranes 2021, 11(7), 525; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11070525 - 13 Jul 2021
Cited by 5 | Viewed by 3225
Abstract
Understanding the energy efficiency of direct contact membrane distillation (DCMD) is important for the widespread application and practical implementation of the process. This study analyzed the available energy, known as exergy, in a DCMD system using computational fluid dynamics (CFD). A CFD model [...] Read more.
Understanding the energy efficiency of direct contact membrane distillation (DCMD) is important for the widespread application and practical implementation of the process. This study analyzed the available energy, known as exergy, in a DCMD system using computational fluid dynamics (CFD). A CFD model was developed to investigate the hydrodynamic and thermal conditions in a DCMD module. After the CFD model was verified, it was used to calculate the temperature polarization coefficient (TPC) and exergy destruction magnitudes under various operating conditions. The results revealed that slight decreases and increases in the TPC occurred with distance from the inlet in the module. The TPC was found to increase as the feed temperature was reduced and the feed and permeate flow rates were increased. The exergy destruction phenomenon was more significant under higher feed temperatures and higher flux conditions. Although the most significant exergy destruction in the permeate occurred near the feed inlet, the effect became less influential closer to the feed outlet. An analysis of exergy flows revealed that the efficiency loss in the permeate side corresponded to 32.9–45.3% of total exergy destruction. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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14 pages, 3992 KiB  
Article
A Simple 1D Convection-Diffusion Model of Oxalic Acid Oxidation Using Reactive Electrochemical Membrane
by Ekaterina Skolotneva, Marc Cretin and Semyon Mareev
Membranes 2021, 11(6), 431; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11060431 - 07 Jun 2021
Cited by 4 | Viewed by 2299
Abstract
In recent years, electrochemical methods utilizing reactive electrochemical membranes (REM) have been recognized as the most promising technologies for the removal of organic pollutants from water. In this paper, we propose a 1D convection-diffusion-reaction model concerning the transport and oxidation of oxalic acid [...] Read more.
In recent years, electrochemical methods utilizing reactive electrochemical membranes (REM) have been recognized as the most promising technologies for the removal of organic pollutants from water. In this paper, we propose a 1D convection-diffusion-reaction model concerning the transport and oxidation of oxalic acid (OA) and oxygen evolution in the flow-through electrochemical oxidation system with REM. It allows the determination of unknown parameters of the system by treatment of experimental data and predicts the behavior of the electrolysis setup. There is a good agreement in calculated and experimental data at different transmembrane pressures and initial concentrations of OA. The model provides an understanding of the processes occurring in the system and gives the concentration, current density, potential, and overpotential distributions in REM. The dispersion coefficient was determined as a fitting parameter and it is in good agreement with literary data for similar REMs. It is shown that the oxygen evolution reaction plays an important role in the process even under the kinetic limit, and its contribution decreases with increasing total organic carbon flux through the REM. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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23 pages, 9467 KiB  
Article
Water as a Blood Model for Determination of CO2 Removal Performance of Membrane Oxygenators
by Benjamin Lukitsch, Raffael Koller, Paul Ecker, Martin Elenkov, Christoph Janeczek, Markus Pekovits, Bahram Haddadi, Christian Jordan, Margit Gfoehler and Michael Harasek
Membranes 2021, 11(5), 356; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11050356 - 12 May 2021
Cited by 1 | Viewed by 2995
Abstract
CO2 removal via membrane oxygenators has become an important and reliable clinical technique. Nevertheless, oxygenators must be further optimized to increase CO2 removal performance and to reduce severe side effects. Here, in vitro tests with water can significantly reduce costs and [...] Read more.
CO2 removal via membrane oxygenators has become an important and reliable clinical technique. Nevertheless, oxygenators must be further optimized to increase CO2 removal performance and to reduce severe side effects. Here, in vitro tests with water can significantly reduce costs and effort during development. However, they must be able to reasonably represent the CO2 removal performance observed with blood. In this study, the deviation between the CO2 removal rate determined in vivo with porcine blood from that determined in vitro with water is quantified. The magnitude of this deviation (approx. 10%) is consistent with results reported in the literature. To better understand the remaining difference in CO2 removal rate and in order to assess the application limits of in vitro water tests, CFD simulations were conducted. They allow to quantify and investigate the influences of the differing fluid properties of blood and water on the CO2 removal rate. The CFD results indicate that the main CO2 transport resistance, the diffusional boundary layer, behaves generally differently in blood and water. Hence, studies of the CO2 boundary layer should be preferably conducted with blood. In contrast, water tests can be considered suitable for reliable determination of the total CO2 removal performance of oxygenators. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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19 pages, 3113 KiB  
Article
Correlations for Concentration Polarization and Pressure Drop in Spacer-Filled RO Membrane Modules Based on CFD Simulations
by Boram Gu, Claire S. Adjiman and Xiao Yun Xu
Membranes 2021, 11(5), 338; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11050338 - 01 May 2021
Cited by 18 | Viewed by 4103
Abstract
Empirical correlations for mass transfer coefficient and friction factor are often used in process models for reverse osmosis (RO) membrane systems. These usually involve four dimensionless groups, namely Reynolds number (Re), Sherwood number (Sh), friction factor (f), and Schmidt number (Sc), [...] Read more.
Empirical correlations for mass transfer coefficient and friction factor are often used in process models for reverse osmosis (RO) membrane systems. These usually involve four dimensionless groups, namely Reynolds number (Re), Sherwood number (Sh), friction factor (f), and Schmidt number (Sc), with the associated coefficients and exponents being obtained by fitting to experimental data. However, the range of geometric and operating conditions covered by the experiments is often limited. In this study, new dimensionless correlations for concentration polarization (CP) modulus and friction factor are presented, which are obtained by dimensional analysis and using simulation data from computational fluid dynamics (CFD). Two-dimensional CFD simulations are performed on three configurations of spacer-filled channels with 76 combinations of operating and geometric conditions for each configuration, covering a broad range of conditions encountered in RO membrane systems. Results obtained with the new correlations are compared with those from existing correlations in the literature. There is good consistency in the predicted CP with mean discrepancies less than 6%, but larger discrepancies for pressure gradient are found among the various friction factor correlations. Furthermore, the new correlations are implemented in a process model with six spiral wound modules in series and the predicted recovery, pressure drop, and specific energy consumption are compared with a reference case obtained by ROSA (Reverse Osmosis System Analysis, The Dow Chemical Company). Differences in predicted recovery and pressure drop are up to 5% and 83%, respectively, highlighting the need for careful selection of correlations when using predictive models in process design. Compared to existing mass transfer correlations, a distinct advantage of our correlations for CP modulus is that they can be directly used to estimate the impact of permeate flux on CP at a membrane surface without having to resort to the film theory. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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31 pages, 3109 KiB  
Article
Theoretical Analysis of a Mathematical Relation between Driving Pressures in Membrane-Based Desalting Processes
by Sung Ho Chae and Joon Ha Kim
Membranes 2021, 11(3), 220; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11030220 - 19 Mar 2021
Cited by 3 | Viewed by 1859
Abstract
Osmotic and hydraulic pressures are both indispensable for operating membrane-based desalting processes, such as forward osmosis (FO), pressure-retarded osmosis (PRO), and reverse osmosis (RO). However, a clear relation between these driving pressures has not thus far been identified; hence, the effect of change [...] Read more.
Osmotic and hydraulic pressures are both indispensable for operating membrane-based desalting processes, such as forward osmosis (FO), pressure-retarded osmosis (PRO), and reverse osmosis (RO). However, a clear relation between these driving pressures has not thus far been identified; hence, the effect of change in driving pressures on systems has not yet been sufficiently analyzed. In this context, this study formulates an actual mathematical relation between the driving pressures of membrane-based desalting processes by taking into consideration the presence of energy loss in each driving pressure. To do so, this study defines the pseudo-driving pressures representing the water transport direction of a system and the similarity coefficients that quantify the energy conservation rule. Consequently, this study finds three other theoretical constraints that are required to operate membrane-based desalting processes. Furthermore, along with the features of the similarity coefficients, this study diagnoses the commercial advantage of RO over FO/PRO and suggests desirable optimization sequences applicable to each process. Since this study provides researchers with guidelines regarding optimization sequences between membrane parameters and operational parameters for membrane-based desalting processes, it is expected that detailed optimization strategies for the processes could be established. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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35 pages, 6419 KiB  
Article
The Need for Accurate Osmotic Pressure and Mass Transfer Resistances in Modeling Osmotically Driven Membrane Processes
by Endre Nagy, Imre Hegedüs, Danyal Rehman, Quantum J. Wei, Yvana D. Ahdab and John H. Lienhard
Membranes 2021, 11(2), 128; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11020128 - 14 Feb 2021
Cited by 14 | Viewed by 3302
Abstract
The widely used van ’t Hoff linear relation for predicting the osmotic pressure of NaCl solutions may result in errors in the evaluation of key system parameters, which depend on osmotic pressure, in pressure-retarded osmosis and forward osmosis. In this paper, the linear [...] Read more.
The widely used van ’t Hoff linear relation for predicting the osmotic pressure of NaCl solutions may result in errors in the evaluation of key system parameters, which depend on osmotic pressure, in pressure-retarded osmosis and forward osmosis. In this paper, the linear van ’t Hoff approach is compared to the solutions using OLI Stream Analyzer, which gives the real osmotic pressure values. Various dilutions of NaCl solutions, including the lower solute concentrations typical of river water, are considered. Our results indicate that the disparity in the predicted osmotic pressure of the two considered methods can reach 30%, depending on the solute concentration, while that in the predicted power density can exceed over 50%. New experimental results are obtained for NanoH2O and Porifera membranes, and theoretical equations are also developed. Results show that discrepancies arise when using the van ’t Hoff equation, compared to the OLI method. At higher NaCl concentrations (C > 1.5 M), the deviation between the linear approach and the real values increases gradually, likely indicative of a larger error in van ’t Hoff predictions. The difference in structural parameter values predicted by the two evaluation methods is also significant; it can exceed the typical 50–70% range, depending on the operating conditions. We find that the external mass transfer coefficients should be considered in the evaluation of the structural parameter in order to avoid overestimating its value. Consequently, measured water flux and predicted structural parameter values from our own and literature measurements are recalculated with the OLI software to account for external mass transfer coefficients. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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19 pages, 4559 KiB  
Article
Removal of Sulfadiazine by Polyamide Nanofiltration Membranes: Measurement, Modeling, and Mechanisms
by Haochen Zhu, Bo Hu and Fengrui Yang
Membranes 2021, 11(2), 104; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11020104 - 02 Feb 2021
Cited by 5 | Viewed by 2606
Abstract
In this study, a complete steric, electrostatic, and dielectric mass transfer model is applied to investigate the separation mechanism of typical antibiotic sulfadiazine by NF90, NF270, VNF-8040 and TMN20H-400 nanofiltration membranes. FTIR and XPS analysis clearly indicate that the membranes we used possess [...] Read more.
In this study, a complete steric, electrostatic, and dielectric mass transfer model is applied to investigate the separation mechanism of typical antibiotic sulfadiazine by NF90, NF270, VNF-8040 and TMN20H-400 nanofiltration membranes. FTIR and XPS analysis clearly indicate that the membranes we used possess skin layers containing both amine and carboxylic acid groups that can be distributed in an inhomogeneous fashion, leading to a bipolar fixed charge distribution. We compare the theoretical and experimental rejection rate of the sulfadiazine as a function of the pressure difference across the nanopore for the four polyamide membranes of inhomogeneously charged nanopores. It is shown that the rejection rate of sulfadiazine obtained by the solute transport model has similar qualitative results with that of experiments and follows the sequence: RNF90>RVNF2−8040>RNF270>RTMN20H−400. The physical explanation can be attributed to the influence of the inhomogeneous charge distribution on the electric field that arises spontaneously so as to maintain the electroneutrality within the nanopore. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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20 pages, 5786 KiB  
Article
Mass Transport in Osmotically Driven Membrane Processes
by Peng Xie, Tzahi Y. Cath and David A. Ladner
Membranes 2021, 11(1), 29; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11010029 - 01 Jan 2021
Cited by 7 | Viewed by 2017
Abstract
Forward osmosis (FO) and pressure retarded osmosis (PRO) are the two operational modes for osmotically driven membrane processes (ODMPs). ODMPs have gained increasing popularity in the laboratory over the years; however, OMDPs have not been applied in very many cases at full scale [...] Read more.
Forward osmosis (FO) and pressure retarded osmosis (PRO) are the two operational modes for osmotically driven membrane processes (ODMPs). ODMPs have gained increasing popularity in the laboratory over the years; however, OMDPs have not been applied in very many cases at full scale because they are still emerging technologies that require further development. Computational fluid dynamics (CFD) modeling coupled with solute transport evaluation provides a tool to study hydrodynamics and concentration polarization in FO and PRO. In this study a series of models were developed to predict water flux. The simulation results of empty-channel (with no feed spacer) membrane cells were verified by comparison with experimental results, showing that CFD simulation with solute transport is a reliable tool. Ensuing 2D and 3D models were built to study the impact of feed spacers on the velocity and concentration distribution inside the flow channels, and investigate whether the presence of spacers would enable enhancement of water flux. The results showed that spacers could change the concentration and velocity profile and they could reduce or enhance water flux depending on the inlet flow velocity and distance between the membrane and spacer. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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20 pages, 4685 KiB  
Article
Gas Permeation Model of Mixed-Matrix Membranes with Embedded Impermeable Cuboid Nanoparticles
by Haoyu Wu, Maryam Zamanian, Boguslaw Kruczek and Jules Thibault
Membranes 2020, 10(12), 422; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes10120422 - 15 Dec 2020
Cited by 16 | Viewed by 2315
Abstract
In the packaging industry, the barrier property of packaging materials is of paramount importance. The enhancement of barrier properties of materials can be achieved by adding impermeable nanoparticles into thin polymeric films, known as mixed-matrix membranes (MMMs). Three-dimensional numerical simulations were performed to [...] Read more.
In the packaging industry, the barrier property of packaging materials is of paramount importance. The enhancement of barrier properties of materials can be achieved by adding impermeable nanoparticles into thin polymeric films, known as mixed-matrix membranes (MMMs). Three-dimensional numerical simulations were performed to study the barrier property of these MMMs and to estimate the effective membrane gas permeability. Results show that horizontally-aligned thin cuboid nanoparticles offer far superior barrier properties than spherical nanoparticles for an identical solid volume fraction. Maxwell’s model predicts very well the relative permeability of spherical and cubic nanoparticles over a wide range of the solid volume fraction. However, Maxwell’s model shows an increasingly poor prediction of the relative permeability of MMM as the aspect ratio of cuboid nanoparticles tends to zero or infinity. An artificial neural network (ANN) model was developed successfully to predict the relative permeability of MMMs as a function of the relative thickness and the relative projected area of the embedded nanoparticles. However, since an ANN model does not provide an explicit form of the relation of the relative permeability with the physical characteristics of the MMM, a new model based on multivariable regression analysis is introduced to represent the relative permeability in a MMM with impermeable cuboid nanoparticles. The new model possesses a simple explicit form and can predict, very well, the relative permeability over an extensive range of the solid volume fraction and aspect ratio, compared with many existing models. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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14 pages, 1525 KiB  
Article
Dynamic Modeling Using Artificial Neural Network of Bacillus Velezensis Broth Cross-Flow Microfiltration Enhanced by Air-Sparging and Turbulence Promoter
by Aleksandar Jokić, Ivana Pajčin, Jovana Grahovac, Nataša Lukić, Bojana Ikonić, Nevenka Nikolić and Vanja Vlajkov
Membranes 2020, 10(12), 372; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes10120372 - 27 Nov 2020
Cited by 5 | Viewed by 2194
Abstract
Cross-flow microfiltration is a broadly accepted technique for separation of microbial biomass after the cultivation process. However, membrane fouling emerges as the main problem affecting permeate flux decline and separation process efficiency. Hydrodynamic methods, such as turbulence promoters and air sparging, were tested [...] Read more.
Cross-flow microfiltration is a broadly accepted technique for separation of microbial biomass after the cultivation process. However, membrane fouling emerges as the main problem affecting permeate flux decline and separation process efficiency. Hydrodynamic methods, such as turbulence promoters and air sparging, were tested to improve permeate flux during microfiltration. In this study, a non-recurrent feed-forward artificial neural network (ANN) with one hidden layer was examined as a tool for microfiltration modeling using Bacillus velezensis cultivation broth as the feed mixture, while the Kenics static mixer and two-phase flow, as well as their combination, were used to improve permeate flux in microfiltration experiments. The results of this study have confirmed successful application of the ANN model for prediction of permeate flux during microfiltration of Bacillus velezensis cultivation broth with a coefficient of determination of 99.23% and absolute relative error less than 20% for over 95% of the predicted data. The optimal ANN topology was 5-13-1, trained by the Levenberg–Marquardt training algorithm and with hyperbolic sigmoid transfer function between the input and the hidden layer. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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21 pages, 23659 KiB  
Article
Impact of Permeable Membrane on the Hydrocyclone Separation Performance for Oily Water Treatment
by Sirlene A. Nunes, Hortência L. F. Magalhães, Severino R. de Farias Neto, Antonio G. B. Lima, Lucas P. C. Nascimento, Fabiana P. M. Farias and Elisiane S. Lima
Membranes 2020, 10(11), 350; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes10110350 - 18 Nov 2020
Cited by 11 | Viewed by 2082
Abstract
In the oil industry and academy, the treatment of water contaminated with oil using conventional hydrocyclones and membranes has been an alternative to meet the requirements established by environmental control agencies. However, such equipment is not fully efficient in the treatment of much [...] Read more.
In the oil industry and academy, the treatment of water contaminated with oil using conventional hydrocyclones and membranes has been an alternative to meet the requirements established by environmental control agencies. However, such equipment is not fully efficient in the treatment of much diluted oily water, with both presenting restrictions in their performance. In this sense, the present work proposes to study the separation process of oily water using a new configuration of hydrocyclone, equipped with a porous ceramic membrane in the conical part’s wall (filtering hydrocyclone). For the theoretical study, a Eulerian–Eulerian approach was applied to solve the mass and momentum conservation equations, and the turbulence model, using the computational fluid dynamics technique. The results of the velocity, pressure and volumetric fraction of the involved phases, and the separation performance of the hydrocyclone, are presented, analyzed, and compared with those obtained with a conventional hydrocyclone. The results confirmed the high potential of the proposed equipment to be used in the separation of the water and oil mixture. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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Review

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37 pages, 2405 KiB  
Review
Prediction of Permeate Flux in Ultrafiltration Processes: A Review of Modeling Approaches
by Carolina Quezada, Humberto Estay, Alfredo Cassano, Elizabeth Troncoso and René Ruby-Figueroa
Membranes 2021, 11(5), 368; https://0-doi-org.brum.beds.ac.uk/10.3390/membranes11050368 - 18 May 2021
Cited by 21 | Viewed by 6510
Abstract
In any membrane filtration, the prediction of permeate flux is critical to calculate the membrane surface required, which is an essential parameter for scaling-up, equipment sizing, and cost determination. For this reason, several models based on phenomenological or theoretical derivation (such as gel-polarization, [...] Read more.
In any membrane filtration, the prediction of permeate flux is critical to calculate the membrane surface required, which is an essential parameter for scaling-up, equipment sizing, and cost determination. For this reason, several models based on phenomenological or theoretical derivation (such as gel-polarization, osmotic pressure, resistance-in-series, and fouling models) and non-phenomenological models have been developed and widely used to describe the limiting phenomena as well as to predict the permeate flux. In general, the development of models or their modifications is done for a particular synthetic model solution and membrane system that shows a good capacity of prediction. However, in more complex matrices, such as fruit juices, those models might not have the same performance. In this context, the present work shows a review of different phenomenological and non-phenomenological models for permeate flux prediction in UF, and a comparison, between selected models, of the permeate flux predictive capacity. Selected models were tested with data from our previous work reported for three fruit juices (bergamot, kiwi, and pomegranate) processed in a cross-flow system for 10 h. The validation of each selected model’s capacity of prediction was performed through a robust statistical examination, including a residual analysis. The results obtained, within the statistically validated models, showed that phenomenological models present a high variability of prediction (values of R-square in the range of 75.91–99.78%), Mean Absolute Percentage Error (MAPE) in the range of 3.14–51.69, and Root Mean Square Error (RMSE) in the range of 0.22–2.01 among the investigated juices. The non-phenomenological models showed a great capacity to predict permeate flux with R-squares higher than 97% and lower MAPE (0.25–2.03) and RMSE (3.74–28.91). Even though the estimated parameters have no physical meaning and do not shed light into the fundamental mechanistic principles that govern these processes, these results suggest that non-phenomenological models are a useful tool from a practical point of view to predict the permeate flux, under defined operating conditions, in membrane separation processes. However, the phenomenological models are still a proper tool for scaling-up and for an understanding the UF process. Full article
(This article belongs to the Special Issue Numerical Modelling in Membrane Processes)
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