Rate of Generation of Ions H<Superscript>+</Superscript> and OH<Superscript>−</Superscript> at the Ion-Exchange Membrane/Dilute Solution Interface as a Function of the Current Density

Partial currents of water dissociation products through cation- and anion-exchange membranes that form thin desalination channels in electrodialyzers are measured. The investigations are performed in a broad interval of flow rates during desalination of dilute sodium chloride solutions at overlimiting currents. A water dissociation theory, which was developed for bipolar membranes, and a mass transfer theory that allows for the space charge formation at overlimiting currents are used to derive an expression, according to which the rate of generation of the H⁺ and OH^? ions is defined by the ratio of the current density to its critical value at which water starts undergoing discernible dissociation.     

Prediction of permeate flux during osmotic pressure-controlled electric field-enhanced cross-flow ultrafiltration

Electric field-enhanced cross-flow ultrafiltration has been carried out to separate protein, bovine serum albumin, from aqueous solution using a 30,000 molecular weight cutoff membrane. A theoretical model is developed to predict permeate flux under a laminar flow regime including the effects of external d.c. electric field and suction through the membrane for osmotic pressure-controlled ultrafiltration. The governing equations of the concentration profile in the developing mass transfer boundary layer in a rectangular channel are solved using a similarity solution method. The effect of d.c. electric field on the variation of membrane surface concentration and permeate flux along the length of the channel is quantified using this model. The expression of Sherwood number relation for estimation of mass transfer coefficient is derived. The analysis revealed that there is a significant effect of electric field on the mass transfer coefficient. A detailed parametric study has been carried out to observe the effect of feed concentration, electric field, cross-flow velocity, and pressure on the permeate flux. For 1 kg/m3 BSA solution, by applying a d.c. electric field of 1000 V/m, the permeate flux increases from 42 to 98 L/m2 h compared to that with zero electric field. The experimental results are successfully compared with the model predicted results.     

Study of the mass transfer phenomena involved in an electrophoretic membrane contactor

Electrophoretic separators, in which a porous membrane is used as a contactor, offer the possibility to scale up electrophoresis as well as to extend the field of application of electrodialysis to fractionate polyamino acids, peptides or small proteins for instance. This paper deals with the study of the mass transfer mechanisms involved in such electroseparation processes. On one hand, a theoretical approach is carried out. The different contributions to the mass transfer are considered in order to establish a relationship providing the solute concentration as function of the main parameters of the system, i.e. the operating conditions and the membrane, buffer and solute characteristics. In this expression, a partition coefficient is used to represent the interactions taking place at the membrane–solution interface. Then, an experimental study is performed with different representative solutes using a prototype apparatus in order to determine the dependence of the solvent and solute transfer with respect to the operating and physicochemical parameters of the system. The experimental results show the existence of a limiting electro-osmotic flux, the origin of which is explained. Then the partition coefficient is determined for any set of conditions by fitting the variations of the solute concentration calculated by the model with experimental ones. The dependence of the partition coefficient with respect to the solute and buffer characteristics, together with that of the transmission coefficient obtained during filtration experiments, shows that the main limitation with respect to the mass transfer is due to electrostatic interactions taking place at the membrane–solution interface.     

On modeling incipient crystallization of sparingly soluble salts in frontal membrane filtration

Modeling incipient crystallization ("scaling") in desalination membrane modules is a very difficult task due to several complications arising from the interplay of physico-chemical solution conditions (leading to supersaturation) with the flow field and related transport processes, including solid phase generation phenomena and membrane surface geometrical changes caused by the developing discrete particles. Although eventually all these aspects must be included in a comprehensive process model, it is fruitful to isolate and tackle them separately, thereby improving our understanding and developing techniques which will facilitate the ensuing synthesis of an integrated modeling framework. The focus in this work is on solid phase generation phenomena accounting for the membrane surface geometrical changes. A mean field model is developed that includes bulk and surface particle nucleation and growth processes. The relative importance of the two types of processes is analyzed. It is shown that, if thick concentration boundary layers exist around surface particles, the mean field theory--although not strictly valid--can be approximately used to estimate the transport coefficients, in conjunction with a unit cell problem for transport processes around a single surface particle. The unit cell problem is formulated and typical results for the flow and concentration field therein are presented as well as the corresponding mass transfer coefficients.     

Membrane extraction through cross-flow rectangular modules

The mass transfer for membrane extraction through a cross-flow parallel-plate module has been studied both theoretically and experimentally. Theoretical analysis of mass transfer in cross-flow membrane extractors was analogous to heat transfer in cross-flow heat exchangers with the assumption that the concentration variation in the cross-sections of flow channel was negligible. Experiments were carried out with the use of membrane sheet made of microporous polypropylene coated with polytetrafluoroethylene as a permeable barrier to extract acetic acid from aqueous solution by methyl isobutyl ketone. Theoretical predictions are in agreement with the experimental results. The simpler but still precise equation for predicting the total mass transfer rate might be more powerful than the exact solution obtained in the previous work to overcome the mathematical difficulties in device design.     

苦咸水反渗透淡化中膜面结垢预测及防垢进展

苦咸水反渗透（BWRO）中的防垢过程,首先取决于给水水质,而根据水质条件和垢在膜面的形成机理采取相应的防垢措施是非常重要的。 显然,有效地管控膜面无机结垢及抑制膜面污染需要开展无机结垢趋势的预测、防垢措施和非破坏性无机垢监控等方面的技术研究。 一系列传统和新兴的分析技术,包括摩尔比率法、直接目测法和光谱法等已应用于BWRO过程中膜面防垢研究。 本文详细综述了该过程中无机结垢趋势的预测、防垢方法和非破坏性无机垢监控技术等方面的研究进展。 此外,针对目前的研究方向提出了建议。     

Solvent extraction through a double-pass parallel-plate membrane channel with recycle

The reflux indeed has much influence on the heat and mass transfer, which in turn plays a significant role on the design, calculation, and operation of the equipment. The effects of recycle on membrane extraction through a double-pass parallel-plate channel have been studied both theoretically and experimentally. Theoretical analysis of mass transfer in multipass membrane extractors was analogous to heat transfer in multipass heat exchangers. Experiments were carried out with the use of a membrane sheet made of microporous polypropylene coated with polytetrafluoroethylene as a permeable barrier to extract acetic acid from aqueous solution by methyl isobutyl ketone. Theoretical predictions are in qualitative agreement with the experimental results. Contrast a single-pass parallel-plate membrane channel without recycle, considerable improvement in mass transfer is obtainable if membrane extraction is operated in a double-pass device of same size with recycle which provides the increase of fluid velocity and pre-extraction (or pre-mixing) effect. It is found that recycle can enhance mass transfer, especially for operations with higher inlet volume rate or shorter conduit length.     

Mass transfer performance for hollow fibre modules with shell-side axial feed flow: using an engineering approach to develop a framework

For several membrane separation processes, hollow fibre modules are either an already established or a promising type of module. Based on the analogy between mass and heat transfer, an engineering approach is proposed to estimate the shell-side mass transfer coefficient for axial flow in hollow fibre modules with due allowance for the void fraction. The approach enables one to take the entrance effects of the hydrodynamic and concentration profile into account. The trends obtained by this generalised approach are similar to those of empirical correlations found in the literature over a wide range of Reynolds numbers and module packing densities. The empirical correlations differ significantly one from the other. The differences between the mass transfer coefficients obtained by the empirical correlations compared to those obtained following the approach proposed in this study are discussed. The different effects influencing mass transfer in hollow fibre modules are identified and discussed as a function of void fraction. Further, an approach to reflect the influence of maldistribution on mass transfer performance is provided.     

Model verification of limiting concentration by electrodialysis of an electrolyte solution

The concentration of LiCl in brine and brine volume are obtained as functions of current density by the method of limiting concentration by electrodialysis. These relationships are used for model calculations of current efficiency, the diffusion, osmotic, and electroosmotic permeability of an MK-40/MA-40 membrane pair, and also salt hydration numbers. These theoretical values of water transport numbers and LiCl hydration numbers are compared with corresponding experimental and literature data. It is shown that the model adequately describes the phenomena of the mass electrotransport occurring in electrodialyzers with noncirculating concentration compartments, and it can be successfully applied in calculating the technological parameters of the process, finding the transport properties of ion-exchange membranes, and determining salt hydration numbers in aqueous electrolyte solutions.     

Local Mass Transfer during Electrodialysis with Ion-Exchange Membranes and Spacers

Mass transfer during electrodialysis with ion-conducting spacers in the intermembrane gap is modeled experimentally using a local-distribution analysis of solutions. Due to emergence of back-flow regions near the spacers, local quantities (diffusion layer thicknesses, surface concentrations, Sherwood numbers) are distributed nonuniformly over the channel length. In a smooth channel, due to concentration polarization, local mass transfer rates steadily decrease along the solution supply coordinate, but introducing ion-conducting spacers into the channel intensifies mass transfer because of periodic interruption of diffusion layers and formation of recirculation zones. Effect of geometrical size of spacers on the mass transfer is studied. It is found that the mass transfer rate is maximum for ion-conducting spacers with the ratio 3.5 < l/h< 4.0.     

The desalination of a mixed solution of an amino acid and an inorganic salt by means of electrodialysis with charge-mosaic membranes

A new electrodialysis with charge-mosaic membranes was proposed to achieve efficient desalination of a mixed solution of an amino acid and an inorganic salt. For such a mixed solution, the conventional electrodialytic desalination with both cation-and anion-exchange membranes had resulted in a considerable loss of the amino acid through the membranes. In this method, however, the amino acid in the desalination channel of the electrodialyzer migrates away from the membranes so that the permeation loss of the amino acid through the membrane can be prevented.

Batchwise desalination experiments by this method were carried out with a glutamic acid or arginine solution including NaCl under the condition of constant electric current density. Similar experiments by the conventional method were also carried out. As a result of comparing both methods, the amino acid loss in this method became much smaller than that in the conventional one. It was confirmed that this method was very useful for the desalination of an amino acid solution. The effects of operating conditions on the desalination process are also discussed.     

高回收率膜法苦咸水淡化工艺的应用研究进展

膜法苦咸水淡化过程中,符合环境保护要求的浓排水处理方法成本高昂,所以只有当回收率达到较高值时,在实际运行中才具有经济可行性。目前,在不加剧膜污染的条件下进一步提高苦咸水淡化系统回收率的方法已成为该领域研究热点。本文详细综述了高回收率膜法苦咸水淡化工艺的应用研究进展,包括基于反渗透、纳滤、正渗透、膜蒸馏、电渗析和电容去离子化淡化工艺过程,以及这些过程面临的热点问题,并对此提出了建议。     

The effect of ion-conducting spacers on mass transfer — numerical analysis and concentration field visualization by means of laser interferometry

Mathematical model is developed for the study of mass transfer processes under the laminar stationary flow in the channels of electromembrane system formed by alternating cation- and anion-exchange membranes at whose surfaces the ion-conducting spacers are fixed. The results of calculations are given of velocity and concentration fields, of current density distribution along the channel length for some values of Reynolds number and the values of the applied voltage. The comparison is made between the calculated mass transfer characteristics and the experimental data obtained by means of laser interferometry.     

Optimum design of reverse osmosis system under different feed concentration and product specification

The design of various multistage RO systems under different feed concentration and product specification is presented in this work. An optimization method using the process synthesis approach to design an RO system has been developed. First, a simplified superstructure that contains all the feasible design in present desalination process has been presented. It offers extensive flexibility towards optimizing various types of RO system and thus may be used for the selection of the optimal structural and operating schemes. A pressure vessel model that takes into account the pressure drop and concentration changes in the membrane channel has also been given to simulate multi-element performance in the pressure vessel. Then the cost equation relating the capital and operating cost to the design variables, as well as the structural variables of the designed system have been introduced in the objective function. Finally the optimum design problem can be formulated as a mixed-integer nonlinear programming (MINLP) problem, which minimizes the total annualized cost. The solution to the problem includes optimal arrangement of the RO modules, pumps, energy recovery devices, the optimal operating conditions, and the optimal selection of types and number of membrane elements. The effectiveness of this design methodology has been demonstrated by solving several seawater desalination cases. Some of the trends of the optimum RO system design have been presented.     

Modeling and analytical simulation of rotating disk ultrafiltration module

An unsteady state mass transfer model has been developed for rotating disk ultrafiltration module. Starting from the basic physics of the system, analytical expression of back transport flux generated due to rotation-induced shear field is determined, which is subsequently incorporated in the fundamental material balance equation. In order to get an analytical solution of governing partial differential equation via Laplace transformation, pseudo steady state consideration is imposed both on permeate as well as back transport flux. Once the analytical form of concentration field is obtained using the expression permeate flux, membrane surface concentration are evaluated using polymer solution theory and irreversible thermodynamics. Finally an iterative scheme is designed to simulate the permeate flux and membrane surface concentration under specified set of operating parameters. The prediction from this model is found to be in good agreement with experimental data obtained from PEG-6000/water system using cellulose acetate membrane of 5000 Da molecular weight cut-off.     

膜接触器 复合有机胺溶液捕集CO2(英文）

本文提出一种基于氨基酸盐的CO₂复合吸收剂,采用膜接触器 复合溶液耦合技术研究了吸收CO₂的性能,并与单一氨基酸盐溶液吸收性能进行了比较,讨论了气液流速等因素对气液出口CO₂浓度、捕集效率和总传质系数的影响,开发了一个阻力层模型预测膜接触器的总传质系数。结果表明：复合溶液的性能明显好于单一氨基酸盐溶液;与单一溶液比较,使用复合溶液,气相出口CO₂浓度较低,液相出口CO₂浓度较高,捕集效率也较高;复合溶液的总传质系数明显高于单一溶液。可以证实,在膜吸收过程中氨基酸盐基复合溶液是一高效的CO₂吸收剂。模型的预测值符合实验值。     

Theoretical Analysis of the Effect of Ion Concentration in Solution Bulk and at Membrane Surface on the Mass Transfer at Overlimiting Currents

Overlimiting current modes are of considerable interest for the practice of electrodialysis (ED). However, the economical expedience of such ED modes is evident only for desalination of dilute solutions. Here, we show the theoretical analysis of the effect of concentration on the behavior of an ED cell with homogeneous ion-exchange membranes. The study is based on numerical solution of the two-dimensional system of coupled equations of Nernst–Planck–Poisson–Navier–Stokes. It is shown that as the electrolyte concentration in solution that enters the ED desalination chamber increases, the intensity of electroconvection decreases, which induces a decrease in the relative mass-transfer rate (the decrease in the ratio of current density to its limiting value). This effect is stronger in the region of high potential differences where the electroconvective instability of Rubinstein–Zaltzman is realized under the conditions of a nonuniform concentration field caused by solution desalination. In contrast, the increase in the counterion concentration at the membrane surface (associated with the increase in the surface charge) intensifies the electroconvection.     

Finite element analysis as a tool for crossflow membrane filter simulation

Finite element analysis (FEA) is a very powerful tool in analyzing many engineering problems. In this study, FEA was used to simulate the development of concentration polarization in ultrafiltration of protein solutions. A miniature crossflow membrane filter was developed to verify the FEA models. Polysulfone membrane disks (47 mm) were used in this study. Bovine serum albumin (BSA) solutions of different concentrations were pumped across the membrane flow channel. The crossflow velocity of the feed solution was carefully controlled at the laminar region. With the flow velocities within the flow channel estimated by a perturbation solution, the protein concentration on the membrane surface and the mass transfer coefficient were accurately predicted by FEA. This simulation method may provide a useful tool in engineering analysis and design of a membrane filtration process.     

Interaction of dispersed phase with concentration polarization

The effect of a dispersed phase in reducing the concentration polarization in a membrane tube has been studied. The presence of a dispersed phase seems to have an effect in controlling the size of eddy formation and the rate of energy dissipation in the fluid medium. The role of eddy length and the energy dissipation rate on the mass transfer coefficient is discussed. Theoretical results obtained for the mass transfer coefficient and for the concentration polarization in the case of gelatin ultrafiltration are compared with the existing experimental results. The theoretical predictions seem to be in good agreement with the experimentally observed results.     

CFD simulations of net-type turbulence promoters in a narrow channel

The most common spacers or turbulence promoters for membrane processes are net-like materials which enhance mass transfer as well as provide passage for feed solutions. The enhanced membrane performance of spacer-filled channels is determined by the fluid flow patterns induced by the spacer filaments. Insight into the effect of spacer characteristics can be obtained by computational fluid dynamics. In this research, the commercial finite volume package FLUENT was used to visualise the flow pattern in a rectangular membrane channel. Three transverse filament arrangements were simulated. The results show that both high shear stress regions and eddies are present in the channel due to the spacer cylinders. The mass transfer enhancement on the wall/membrane surface is directly related to the high shear stress value, velocity fluctuation, and eddy formation. The peak shear stress and velocity fluctuation are repeated after each spacer cylinder, while the eddies are generally found before and after each cylinder. The CFD simulation also suggests that reducing the transverse filament distance will reduce the distance between shear stress peaks and consequently introduce larger shear stress regions near the wall region and increase the number of eddies, which will benefit membrane mass transfer. However, the penalty for this is that energy losses will also be significantly increased. The selection of optimum spacer geometry design involves a trade-off between these competing effects.