computational fluid dynamics applied to membranes state of the art and opportunities

Chemical Engineering and Processing 45 (2006) 437–454

Computational fluid dynamics applied to membranes:State of the art and opportunities

R. Ghidossia, D. Veyreta, P. Moulinb,∗a Institut Universitaire des Systemes Thermiques Industriels (IUSTI CNRS-UMR 6595), Technopole de Chateau Gombert,

5 rue Enrico Fermi, 13453 Marseille Cedex 13, Franceb Laboratoire d’Etudes et d’Applications des Procedes Separatifs (LPPE CNRS-UMR 6181), Universite Paul Cezanne d’Aix Marseille,

Europole de l’Arbois, Batiment Laennec, Hall C, BP 80, 13545 Aix en Provence Cedex 04, France

Received 5 July 2005; received in revised form 3 November 2005; accepted 3 November 2005Available online 13 December 2005

Abstract

Membrane filtration has become firmly established as a primary technology for ensuring the purity, safety and/or efficiency of the treatmentof water or effluents. In this paper, we review the improvements that have been achieved concerning the membranes used for microfiltration,u tational flud rane process.B utational fluidd hich CFDm©

K

1

hsmsmctmrdsitq

gy towidef thislved

theseg andiatediques. Theaneand

sedthods

tionscribeore

rans-ed toerentthe

rane

0d

ltrafiltration, nanofiltration/reverse osmosis processes during the last decades. More especially, we review the state of the art compuidynamics (CFD) methods applied to membranes processes. Many studies have focused on the best ways of using a particular membut, the design of new membrane systems requires a considerable amount of process development as well as robust methods. Compynamics may provide a lot of interesting information for the development of membrane processes. We review the different ways in wethods are used to improve membrane performance.2005 Elsevier B.V. All rights reserved.

eywords: Computational fluid dynamics; Membrane; Review; Opportunities; Flow

. Introduction

Over the past two decades, membrane filtration processesave played a more and more important role in industrialeparation. A number of studies have focused on enhancingicrofiltration, ultrafiltration, nanofiltration and reverse osmo-

is processes. These include: (i) testing of new membraneaterials; (ii) use of different pore sizes; (iii) determination of

onditions for optimal selectivity; (iv) attempts to determinehe optimum trans-membrane pressure or permeate flux toinimize fouling. The design of a new membrane typically

equires a considerable amount of process development. Theefinition of a generic model with applicability to membraneystems requires rigorous and robust methods. Numerousmprovements of the technology have allowed membrane selec-ion for a particular process to be done more easily and moreuickly. Typically, the development of the membrane is done

∗ Corresponding author. Tel.: +33 4 42 90 85 05; fax: +33 4 42 90 85 15.E-mail address: [email protected] (P. Moulin).

sequentially, with the use of a statistical design methodolominimize the number of experiments needed to explore arange of variables. However, there are several aspects oconstantly evolving technology that have not yet been resoand still pose an obstacle toward its development. One ofimportant aspects is the understanding of membrane foulinsubsequent permeate flux decline, which is inevitably assocwith these processes. In this review, we describe the technthat are available for the optimization of these processesmodelling of flow and concentration polarisation in membrsystems or thin channels with permeable walls is not newcomputational fluid dynamics (CFD) is an important tool uto develop membrane processes. We summarise the meused to enhance microfiltration, ultrafiltration, nanofiltraand reverse osmosis processes. In the first part, we dethe CFD results for laminar and turbulent conditions and mespecially for the different models used to describe mass tfer. In the second part, we study the CFD approaches usunderstand the decrease in membrane fouling by using diffinstabilities or turbulence promoters. We try to describeopportunities that can be used for the optimization of memb

255-2701/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2005.11.002

438 R. Ghidossi et al. / Chemical Engineering and Processing 45 (2006) 437–454

processes. For the sake of clarity, this review will not detail allthe assumptions made and the equations used in each study.

2. CFD and membrane models

2.1. Computational fluids dynamics

The development of this technology is due to the increas-ing number of different types of applications of these processesin different domains, particularly in the industrial sector. Mem-brane filtration can be used in a broad range of applications[1]. Amembrane is a permselective barrier of a few hundred nanome-ters to a few millimetres in thickness, which under the effectof a transfer force, will allow or prohibit the passage of cer-tain components between two separate mediums. There are twomain models making it possible to better comprehend this phe-nomenon. The first model, developed by Kadem and Katchalsky,is a solubilization-diffusion model based on the concept of capil-larity. The second one is the model of polarization that results in aprogressive accumulation of species (particles, molecules, etc.)stopped on the surface of the membrane. Considerable debateexists regarding the suitable theoretical work to describe thisphenomenon. The theoretical work describing the phenomenonhas been the subject of much controversy. The effects of vari-ous parameters on permeate flux decline and the mechanismsof membrane fouling have been investigated. However, littlep meca madt n asw unc-t byu ld ab p mii hab esigm entsi menio athe ntas ativei andf techn ed tb . Ther ces-s rlyinp ons,p portp ratios nisma em-b fromt entlyl s itsg tionT of

the module, the boundary layer transport, the diffusive trans-port and the separation activity driven by the surface wet-ability,as well as the electrostatic, chemical and physical interactionsat the membrane surface. All these processes are interdepen-dent and non-linear. A CFD approach is suitable for combiningthem into a numerical simulation. Commercial CFD packagesare often used to make such numerical studies. The attraction ofthese methods is that they make it possible to see the effects ofdifferent parameters on the system performance. Models existwhich allow the analysis of the effects of the variable permeation,rejection changes, variable physical properties of the solutionbeing processed and gravitational influence. Many of the mod-els, although simplified, have proved to be remarkably accurateat predicting membrane performance over some limited ranges.

2.2. CFD equations under laminar conditions

The basic transport equations that govern the flow of a viscousfluid are mathematical representations of conservation princi-ples under laminar or turbulent conditions. Specifically, theyrepresent the conservation of three physical quantities: mass,momentum and energy. The principle ofmass conservationapplied to a flowing fluid result in the equation:

∂ρ

w ftm

ws

nderl e tou urbu-l n thes fes-t alesi e notf capac-i ulentm nt eses h dis-c Event tionst tioni ltingd , ande od ist e sumo rying

rogress has been made in understanding the fundamentalnisms of membrane fouling. Therefore, efforts have been

owards the theoretical modelling of the fouling phenomenoell as towards the prediction of flux and rejection as a f

ion of time. The complexity of these models is reducedsing numerical simulations. These CFD simulations yieetter understanding of these complex processes and hel

mize the number of experiments. As a consequence, CFDecome an effective tool to achieve the goal of a better dore rapidly and cost effectively. The impressive improvem

n computer performance have been matched by developn numerical and mathematical methods[2]. As computationpens new application areas, it stimulates new ideas for mmatical and physical modelling and algorithms. Experimetudies provided only qualitative or perhaps semi-quantitnformation on concentration polarization, cake formationouling phenomena. Several techniques in the fields of nanoology, microfluidics, optics, spectroscopy and sensors nee refined in order to improve their accuracy and resolutionelative complexity of these flow problems highlights the neity to understand the physics and mathematics of the underoblems. CFD offers the possibility to model many situatirovided suitable computing power is available. Fluid transhenomena are of great importance for membrane sepaystems. They occur while the various separation mechare at work. A membrane module is the housing for a mrane that physically seals and isolates the feed stream

he permeate flux. The performance of a module is inherinked to the fluid movement through its volume, and thueometrical configuration is an important design considerahe system will take into account the flow, the bulk region

h-e

n-sn

ts

-l

-o

g

ns

.

∂t+ div(ρυ) = 0 (1)

hereρ (kg m−3) is the density andυ is thex component ohe velocity (m s−1). The principle ofconservation of linearomentum dictates that, for any fluid element:

∂(ρυ)

∂t+ div(ρυu) = −∂P

∂y+ div(µ gradυ) + SMy (2)

hereP is the pressure (Pa),µ the viscosity (Pa s) and SMy theource term in they direction.

All these equations are solved by different programs uaminar and turbulent conditions. It is theoretically feasiblse the governing equations described in this section for t

ent as well as laminar flows. The major difference betweeimulations of turbulent flows and laminar flows is the maniation of eddy motions with an extensive range of length scn the turbulent flow regime. However, today’s computers arast enough and they do not possess the required storagety to solve these equations directly. The reason is that turb

otion contains scales that are typically 103 times smaller thahe extent of the flow domain. To resolve the motion on thcales by means of a numerical procedure requires a mesretization beyond the capabilities of modern computers.hough it is unreasonably hard to apply the governing equao turbulent flows, it is possible to describe turbulent mon terms of time-averaged quantities and to use the resuescriptions in the conservation laws for mass, momentumnergy. The main consideration of the time-averaged meth

hat time dependent flow properties can be described as thf a time-averaged steady mean component and a time-va

R. Ghidossi et al. / Chemical Engineering and Processing 45 (2006) 437–454 439

fluctuating component. These equations could be written as

∂ρ

∂t+ div(ρU) = 0 (3)

whereU is the averagex component of velocity (m s−1):

∂(ρU)

∂t+ div(ρUU)

= −∂P

∂y+ div(µ gradU) +

[−∂(ρu′2)

∂x− ∂(ρu′υ′)

∂y

]+ SMx

(4)

where U is the average velocity vector (m s−1), u′ the time-averaged fluctuatingx direction velocity (m s−1), v′ the time-averaged fluctuatingy direction velocity (m s−1) and SMx isthe source term in thex direction. All of these equations repre-sent the laminar and the turbulent conditions. There are severalturbulence models that could be used to solve these equations.Conventional models include the mixing length,k–ε, RNGk–ε,Reynolds stress and algebraic stress models. Recent modelsinclude the LED (large eddy) method which is based on space-filtered equations.

2.3. CFD for laminar conditions

Many authors are interested in the simulation of laminarc ndert -b nnelsw rsta dmane pu-t h thei alls ofm ntd e fil-t ala s wea

d too e[ gu-l edt edict wasw acyo ricalp ion.T in thc res-s ure,t rmeam undm roum ion o

Fig. 1. Velocity field in a shell and tube system with inner tube wall permeabilityin the radial direction[14].

the results presented revealed the importance of this completestudy. This new CFD approach was verified by application togas separation, pervaporation and reverse osmosis case studies.Their work is to be distinguished from most existing models,which are usually process specific and are only applicable withina restricted operating range. Simulation results for these sys-tems agreed with experimental data. Their very interesting paperdemonstrated the generality of the detailed model by consider-ing a range of different membrane systems. Moreover, sincethese early works, better performing solvers have been devel-oped to improve computational fluid dynamics. They use moreequations, as they use both the Navier–Stokes and Darcy’s equa-tions. The Darcy equation is

J = Lp(TMP − σ�π) (5)

where TMP is the transmembrane pressure (Pa),J the permeateflux (m s−l ),�π the osmotic pressure difference across the mem-brane (Pa),σ the Stavermann reflection coefficient,Lp the per-meability (m s−1 Pa−1). Nassehi et al.[14] used Darcy’s equa-tion to represent the porous wall conditions. The flow tangentialto the porous tube surface was modelled by the Navier–Stokesequations. They developed a new method for the imposition ofpermeable wall conditions in viscous flow domains. It was basedon the finite element method and was more robust because theyadded more complex governing equations and boundary condi-t owsm oughp tech-n e fluxi of ac am-p moree bec odel.T ossi-b ont em-b ationp ibitedb d thev thism deld masst and

onditions since most of the filtration processes work uhese conditions[3–37]. The first simulations of flow in a memrane were undertaken under laminar conditions in chaith porous walls[3,4]. Laminar conditions were studied fis it is easier to generate flow in the membrane. Later, Friet al. [5] considered the effect of the viscosity in their com

ation. The enhancement of these models culminated witnvestigation of laminar flow in a porous pipe with variable wuction or variable radial mass flux or numerical solutionicropolar fluid in porous wall[6,7]. A summary of the receevelopments on the role of fluid mechanics in membran

ration was made by Belfort et al.[8,9]. They described severttempts to model both steady one and two-phase flows as unsteady flows.

Many authors are very interested in using this methoptimize membrane processes[11–16]. For example, Karod

11] studied the pressure drop for a fluid flow in a rectanar slit and cylindrical tube with porous walls. They assumhe wall permeability to be constant. The pressure drop prion using their expression for constant wall permeabilityithin 2–10% of the numerical CFD solution. The accurf the numerical routine was verified by comparing numeredictions for constant wall velocity using Berman’s soluthe agreement was best for low recoveries. For example,ase of ultrafiltration–microfiltration, where the channel pure drop would be a significant fraction of the inlet presshe expressions presented in their work for constant wall pebility could be more accurate. Marriot et al.[12,13]worked on aore general approach to model hollow-fibre and spiral-woembrane modules. The model was developed from rigoass, momentum and energy balances. The high precis

ll

-

e

-

sf

ions. This method offers a means of linking of the free flodelled by the Navier–Stokes equations to the flows thrermeable walls described by the Darcy equation. Thisique was applied to model the feed stream and permeat

n an axisymmetric case. The results allowed visualizationomplex flow in a porous tube. Since this work, we can for exle visualize and evaluate the pressure loss in a porous tubeasily (Fig. 1). Thus, this model for crossflow filtration canonsidered as the first step towards creating a complete mhe attraction of these semi-analytical models is that it is ple to tailor them for relatively quick and easy investigation

he effect of different parameters on the performance of a mrane system. Accurate modelling of the flow and concentrolarisation in pressure-driven membrane processes is inhy the complex couplings between the flow equations anariable solution properties. Das et al. went on developingodel a few years later[15]. Their results showed that the moeveloped can predict the patterns expected for flow and

ransport systems involving a porous wall. The velocity field


Fig. 2. Representation of laminar flow in a tubular membrane with a cylindricalcoordinate system[16].

the flow circulation near the interface for different permeabilitywere described. Their model provides a robust mean of analy-sis of the flow hydrodynamics. Another very interesting studywas performed by Damak et al.[16]. They worked on a laminar,incompressible and isothermal flow in a cylindrical tube witha permeable wall. They assumed the flow to be axisymmetric.As Das et al. did, they used the Navier–Stokes equations andDarcy’s law to explain the transfer in the tube and in the porouswall. Moreover, with an adequately long entrance region with-out upstream suction, the tube was considered to generate a flowthat is fully developed at the porous tube entrance. Furthermore,the classical assumption of constant physical properties of thesystem, such as density, viscosity and porosity of the wall wasmade in order to simplify the problem (Fig. 2). The flow in thefree fluid region and in the porous medium in the radial directionwas described by the Navier–Stokes equations and Darcy’s law,respectively. First, the model was carefully verified. Then, vari-ous simulations based on different axial Reynolds numbers andfiltration numbers were presented. The results were discussed tostudy the validity of classical assumptions made in simplifiedmodels. Moreover, the relative divergence between the axialvelocity profile with and without wall suction was character-ized. Therefore, the development of mathematical models haoffered a theoretical structure for the understanding of the phenomenon responsible for flux decline. All the recently reportedworks regarding the simulation of filtration processes are baseo allt a bet r thm ami-n inac entm

2con

c sicoc layeo flect ssurm direv ando set filtra

Fig. 3. Geometry of a crossflow unit[18].

tion, the investigations available are quite limited in scope. Thestudies published provided only qualitative or perhaps semi-quantitative information on concentration polarization, cake for-mation and fouling phenomena. Several of these methods needrefinements to improve accuracy and resolution. This is thereason why computational fluid dynamics is so often used todevelop and understand these processes. Simulations are moreprecise and easier to perform than experimental studies butrequire the input of suitable constitutive relations for quan-tities such as viscosity, diffusivity, rejection coefficient, etc.,which are not always known to estimate the cake thickness, therejection or the profile of the flow. For example, Geissler et al.[18] developed a dynamic model of crossflow microfiltration inflat channel systems under laminar flow conditions, often usedin bio-technological processes. The model was based on thedescription of the hydrodynamics in channels with rectangularcross section, permeable walls and some empirical parameters.This kind of simulation is suitable for estimating the necessarymembrane area for the filtration process (Fig. 3). Their numer-ical code is based on a finite volume method, which solves theNavier–Stokes equations. The authors’ theoretical predictionswere verified by measuring the local permeate flux and localcake height during the non-stationary phase of crossflow filtra-tion. They verified their computation with experimental results.The module was made of Plexiglas, which allowed visualisationof the mechanism of particle deposition and measurement of thefi de ins te sta-t entalr nsions earlys flatc quitew andC forc n ofm owingt resis-t by theK asingt whichi rite al ranep y. Then pers ed infl en-s the

n these models. This gives the opportunity of simplifyinghe existing theories and of understanding these phenomener. We consider that these works are a good beginning foodelling of fluid flows in membrane processes under lar conditions. Many specific cases could be treated in lamonditions. Progress could be made towards the developmore accurate models.

.3.1. Cake and polarisation–concentration modelsSeveral methods have been used for in situ monitoring of

entration polarization in order to better appreciate the phyhemical processes governing the growth of a polarizedf solutes near a membrane surface. They include light de

ion techniques, magnetic resonance imaging, direct preeasurements, direct observation through the membrane,

isualization above the membrane, laser triangulometryptical laser sensors[17]. But, despite the potential of the

echniques to advance the understanding of membrane

s-

d

t-e

rof

--r-ect

-

lter cake height with a camera. The simulations were maeveral cases and the authors concluded that for absoluionary values the computation agreed with the experimesults within a range of 15% for all parameters and suspeystems studied. The model developed in their paper is nuitable to predict the course of a filtration process in ahannel crossflow unit and to estimate the cake thicknessell. A more precise model was then developed by Leelark[19] who worked with a standard type of channel usedrossflow ultrafiltration. From the study of dead-end filtratioonodisperse colloidal suspensions, they succeeded in sh

hat when the particle size decreased, the specific cakeance increased. However, it did not increase as predictedozeny–Carman equation. They also showed that an incre

ransmembrane pressure resulted in a denser cake layer,ncreased the specific cake resistance. Their goal was to waw that could be applied to describe the effect of transmembressure on the specific cake resistance more accuratelumerical model of cross flow filtration developed in their pauccessfully explained the fundamental mechanisms involvux decline during crossflow ultrafiltration of colloidal suspions. The model provided a useful tool for investigating


effect of various operating parameters, such as the particle size,feed concentration, axial velocity, and membrane dimensions.That study was made possible by the numerical simulations,which allowed a reduced number of experiments. The modelrequired the specific cake resistance as an input parameter,which was obtained independently from the dead end filtrationtests. The simulations showed that the model predictions werein good agreement with crossflow experimental results. Carroll[20] developed a model to demonstrate these mechanisms fortypical hollow-fibre membranes during the dead-end microfiltra-tion of particulate suspensions. The model accommodated bothcompressible and incompressible cakes, and predicted highlylocalised fluxes, which are completely absent in planar mem-branes. These localised fluxes combined with transmembranepressure gradients to produce non-uniform cake growth pat-terns and non-uniform cake resistance profiles. The role of cakeproperties and operating conditions in determining the permeateflux decline mechanism was established from the evolution ofthe flux profiles. The author deduced from simulations a fluxdecline model incorporating cake compressibility for microfil-tration through a hollow-fibre membrane. This new localisedflux decline mechanism in hollow fibres has a number of impor-tant consequences. Firstly, it is important for establishing the roleplayed by hollow fibre properties in the fouling of hollow fibremembranes. The rate of flux decline with throughput dependsupon the properties of the fibres and of the cake. Secondly, them resf sen-t n ofm ns ofp ec-t on ins CFDc atedp entp , axialv tion.H usedo ismsa case( on-d ount.T r thes tions,t xist-i usingt tion.T ntingt

2rou

m leteb matr etteu raneM ass

Fig. 4. Mesh generation in the normalized fluid flow channel[21].

transfer equation are very difficult to obtain. Several attemptshave been made to solve this problem numerically by finitedifference methods to predict the concentration profile withinthe flow channel. Under an applied pressure, water penetratesthrough the membrane pores and the solute is rejected by themembrane. As a result, a thin concentration boundary layer iscreated near the membrane surface and the flux declines. Huangand Morrissey[21] tried to better understand this phenomenonof polarization. The purpose of their work was to use a numeri-cal model to reproduce the process of concentration polarizationand to model the solute concentrations on the membrane surface.They aimed to create a method that could be used in the engineer-ing analysis and design of crossflow ultrafiltration processes.They used a finite element method and meshed the surface ofthe membrane with a very fine mesh to capture the importantphysical processes (Fig. 4). Specifically, when a very small dif-fusion coefficient is examined, substantially finer meshes mustbe used in the vicinity of the membrane surface to cope with thesteep concentration gradient. Using CFD, the authors illustratedthe way in which the diffusion coefficient influences the thick-ness of the concentration boundary layer. They showed that for agiven permeate flux, there was a linear relationship between dif-fusion coefficient and thickness of the concentration boundarylayer, which is in agreement with classical theory. This modelcan be used to predict the mass transfer coefficient, which isan important parameter in the creation and analysis of a mem-b d fore e theb

edo ents qua-t alls.T cingc ins

odel facilitates predictions of flux decline for hollow fibrom the flux decline for planar membranes. Finally, it is esial to consider this localised performance in the situatioore complex crossflow systems. The non-uniform patterarticle deposition in hollow fibres and local variation in conv

ive forces could also influence the rate of cake accumulatiuch systems. All these studies show the important role thatan play in understanding cake formation. The models crerovide a useful instrument for studying the effect of differarameters, such as the particle size, feed concentrationelocity and membrane dimensions in many types of filtraowever, all of the studies developed in these papers focn particular cases. We consider that the fouling mechanre too complicated to be simulated successfully for eachdifferent type of membrane, solution, filtration, operating citions, etc.). Many parameters have to be taken into acche model has to solve the Navier–Stokes equations fouspension flows as well as the convection diffusion equaaking into account the effect of the shear rate. Moreover, eng models consider the pressure loss along the membranehe Hagen Poiseuille law, which is an important approximaherefore, the determination of a general model represe

hese phenomena seems difficult to achieve.

.3.2. CFD and models of flow through the porous materialThere have been many studies on flow through a po

embrane[21–28]. Experimental studies cannot be compecause sensors cannot be installed inside the porousial. Therefore, computation is an attractive approach to bnderstand the behaviour of the liquid through the memboreover, analytical solutions to the convection–diffusion m

s

e-r.

rane filtration process. Their work also highlights the neextremely high resolution near the membrane surface sincoundary layer is very thin.

Richardson and Nassehi[22] developed an algorithm basn the Streamline Upwind Petrov Galerkin finite elemcheme for the solution of flow and convective dispersion eions in two-dimensional domains with solid and porous wheir approach was shown to provide a method for reproduoncentration profiles within geometrically complex doma


Fig. 5. Solution domain with a flat porous wall opposite a curved porous wall[22].

(Fig. 5). The characteristic of this approach was the constructionof a simple technique for the treatment of concentration bound-ary conditions along the porous walls. Therefore this modeloffered a useful step towards the development of a fast engineer-ing technique for the quantitative analysis of crossflow filters.The applicability of the model was established in a large rangeof domains comprising both flat and curved porous walls. More-over, an important step was made because they showed that themodel was able to take into account the link between the phys-ical and rheological factors and the fouling on the permeablesegment, and thus the process performance[23–25]. Chatterjeeet al. [26] developed a numerical solution, based on the finitedifference method, for modelling the performance of a radialflow hollow fibre reverse osmosis module. The three-parameterSpiegler Kedem model was used to describe the mass transportthrough the membrane. The membrane performance factors asdescribed by the three-parameter Spiegler Kedem model werapproximated from experimental data.Fig. 6shows how both theretentate and the permeate flows pass through a module and hothe finite difference grid is used. By comparing these results fodifferent NaCl concentrations, they considered the solution dif-fusion model adequate for describing the mass transport acrosthe membrane, the parameters evaluated from the present modbeing not very different from the results obtained by the modelSekino et al.[27,28]. More experimental data for phenol sepa-ration were obtained on a hollow fibre module and the modew lears et am ans stim

F

tion program can also be used for developing the mass transfercorrelation in the radial flow hollow fibre modules. These stud-ies show that models can be created to predict the operations forultrafiltration, microfiltration, nanofiltration and reverse osmosiswith good accuracy. Moreover, the CFD models do not neglectthe physical and rheological factors nor the properties of thefoulant on the permeable wall. Very fine meshes seem neces-sary to achieve high accuracy. This requires great computerpower and long calculation times, which could be a handicapin enhancing membrane processes.

2.3.3. CFD and osmotic pressure: nanofiltration andreverse osmosis

Advances in the understanding of membrane transfer pro-cesses and their optimisation require models that can simulateall the important physical processes occurring in membrane sys-tems[29–37]. The operating osmotic pressure is a basic param-eter governing the design and evaluation of a membrane separa-tion system. For example, the performance of a spiral-woundmodule can be improved by optimizing some key geometri-cal parameters for given operating conditions. Many authorsare interested in this application. For example, Ben-Boudinaret al.[29] made numerical simulations of a spiral wound mod-ule. The investigation covered a wide range of feed conditionsby using experimental data provided from two different typeso theirp res-s at anyp itht umd con-c lationc asst sumet andr sion ofc asicm opti-ma s tola thes vel-ol anceo con-s ayer.

F iformi

as used to analyse the data. Moreover, the CFD results chowed that the two parameters model used by Sekinoay not be sufficient for accurate design and analysis of m

olute–membrane systems. Furthermore, this parameter e

ig. 6. Finite difference meshes construction for a hollow fibre module[26].

e

wr

sel

llyl.ya-

f modules. In the case of the desalination of sea water,rogram facilitated the evaluation of the concentrations, pures and flow rates in the feed and permeate channelsoint in the module. For illustration, they decided to work w

wo typical modules. The results were obtained with maximeviations of about 10% and 15% for the permeate flow andentration, respectively. They suggested that a better calcuould be achieved if a more precise relationship for the mransfer coefficient could be established. Many authors ashat spiral-wound modules typically used in nanofiltrationeverse osmosis systems can be considered as a succeshannel slits. This slit-type configuration represents the bodel to be studied and characterised for the design andisation of such industrial membrane modules[30–35]. Suchconfiguration strongly restricts the circulating flow rate

ow values, typically giving rise to laminar flows.Fig. 7showstypical geometry used in this modelling approach. When

lit is an open channel, the laminar flow becomes fully deped in its first stages, as concluded by Geraldes et al.[32],

eading to a very high value of the mass transfer resistr to severe problems of concentration polarisation, as aequence of the growth of the concentration boundary l

ig. 7. Scheme of the NF slit used for the numerical predictions, with unnlet velocity and inlet solute concentration profiles[31,32].


Overcoming these effects is important for the optimisation ofmass transfer. In fact, mass transfer in slit-type channels can beimproved by modifying the hydrodynamic parameters and thedesign and by decreasing the concentration at the boundary layer.Moreover, the feed flow influences the growth of the bound-ary layer and its mixing with the main stream. As a result, thedesign of membrane modules needs accurate analysis of the con-centration polarisation phenomenon. Nanofiltration membraneperformance can be predicted in terms of either apparent rejec-tion coefficients or permeate fluxes resulting from CFD or amass transfer model using boundary conditions that take intoaccount solute–solvent–membrane interactions. For the CFDpredictions, the variation of the solution properties of density,viscosity and diffusivity with the solute concentrations were con-sidered. The previous mathematical model described the flowand mass transfer in the feed near the membrane, which acts asa selective barrier. The effect of concentration polarisation onthe decline of the permeate fluxes was also taken into accountin the predictions of these fluxes. A correlation for the ratiobetween the concentration and the hydrodynamic boundary layerthickness was then obtained, being valid for the ranges of inter-est in nanofiltration and excellent agreement was obtained withexperimental values. Such a correlation gave some insight intothe different mechanisms involved in the growth rates of thoseboundary layers. The use of CFD for the modelling of transportprocesses occurring at the fluid phase adjacent to a nanofiltrationm rizat tionc isticsa press ilea on-c gonee finem emee veryfi te hic self-c CFDm ionsa ent ov hefl eu tionw odelw in thsc ditioc wah aledt owr is syt nsitd t ths ance owt clud

the variable fluid properties but also explicit the modelling of themembrane, making CFD an increasingly powerful tool. Thesesimulations represent a powerful tool for enhancing nanofiltra-tion and reverse osmosis processes and the models become moreand more precise.

2.4. CFD under turbulent conditions

Most studies have been done for laminar conditions but forsome researchers it proved necessary to work under turbulentconditions[38–42]. For example, ultrafiltration modules operatein turbulent regime and the mixing properties of the turbu-lence are very important to minimize solute concentrating in thenear wall region. Pellerin et al. studied the turbulent transportin membrane modules by CFD simulation in two dimensions[39]. The CFD package used was suitable to incorporate sepa-ration models based on the chemical and physical interactionsbetween specific membranes and feed solutions for compari-son with experimental results. The pressure-related boundarycondition for permeate velocity is an essential characteristicfor enlarging the model to multi-component systems where themembrane separation performance would be modeled. To thiseffect the convection–diffusion equation for solute transport wasadded and the effect of inlet concentrations and diffusion coef-ficients were studied. Using CFD, they demonstrated that themost important parameters were the Reynolds and Schmidt num-b keyr por-t andd rtedb t ofr suredb onlyw olubil-i itedl layerw he cakei , thet samet thec ationw vari-a anda mainp bilityc e thep andt pti-m ulsed itivet inedw imew thec alln rovet f at still

embrane allowed the evaluation of the concentration polaion effect. Furthermore, the calculation of intrinsic rejecoefficients, which are linked to the membrane characternd to the operating conditions in terms of transmembraneure and feed solute, concentration could be determining. Wnd Fletcher[36] proposed a general purpose CFD model of centration polarisation and fluid flow. The model has underxtensive verification and highlights also the need for veryeshes near the wall and suitable high order numerical schspecially when the polarisation is high. The problem is thatne meshes necessitate powerful computer and necessitaost investment in term of time calculation. The need foronsistent physical property models was highlighted. Theodel developed used explicit equations for property variatnd it can now be easily adapted to include any arrangemariation in wall flux, rejection, viscosity and diffusivity. Texibility of this model was only limited by the ability of thser to correctly describe the physical properties. The equaere solved using the finite volume code CFX4. The mas extended to examine the consequence of buoyancyalt water system under reverse osmosis conditions[37]. In thisase the need to choose the location of the boundary conarefully to ensure that it does not cause non-physical flowighlighted. Application of the model to brackish water reve

hat gravitational effects are only significant at very low flates. The authors also showed that in the reverse osmosem the extraction rates are not sufficient to generate deifferences between the feed concentration and the fluid aurface of the membrane, which can cause significant buoyffects in horizontal flat channel systems. These models sh

rend towards greater completeness, as not only do they in

-

-y

s,

gh

,f

s

e

ns

s-yeyae

ers. Both dimensionless numbers were found to play aole in controlling the solute concentration gradients. An imant work regarding modelling of concentration polarisationepolarisation with high frequency backpulsing was repoy Redkar et al.[42]. In this study, a turbulent back transporejected solutes from the deposited layer to the bulk was eny the action of stirring. In fact, the gel started appearinghen the membrane surface concentration exceeded the s

ty limit of the solutes in the solvent. Therefore, this deposayer was not a true gel layer but may be called a gel-typehose properties are supposed to be the same as those of t

n filtration equipment. As the membrane rejects the soluteshickness of this deposited gel layer increases. But at theime, due to the stirring, some solutes are removed fromake surface and go into the bulk. The Kozeny Carman equas used to relate the permeate flux with other operatingbles. So this work was a combination of the filtration theorygel polarisation model. This model depended on three

arameters, namely the back transport coefficient, permeaoefficient and membrane hydraulic resistance. They gavredicted and experimental values of the maximum fluxes

he corresponding optimal forward filtration times. The oal forward filtration time increased with increasing backpuration, whereas the maximum flux was relatively insens

o the backpulse duration. Most importantly, the fluxes obtaith backpulsing theory predicted that the forward filtration thich maximizes the flux is, in general, slightly longer thanritical value which leads to cake or gel formation. The smumber of papers focusing on turbulent conditions tends to p

hat modelling in turbulent conditions is difficult. The lack ourbulent model is significant in this case and researchers


do not agree on the validity of the current commercial modelsproposed. In fact, it requires the resolution of more compli-cated equations and very fine meshes. Consequently, the use ofmore powerful computers is necessary and the computing timesshould be longer. However, many authors are getting attractedto model turbulent conditions because many membrane pro-cesses work under high Reynolds numbers. Several papers haverecently been published on this subject and referenced in thispart, which could lead to opportunities in membrane processesdevelopment.

3. CFD and hydrodynamic conditions

The use of CFD allows us to determine, describe and optimizethe complex hydrodynamics generated by pulsatile flow and gassparging[43–53], spacers[54–65], Dean and Taylor vortices[66–79] and geometry[80–84]. The performance of pressure-driven membrane processes is limited by factors like concen-tration polarisation, cake-layer growth and fouling, resultingin low volumetric permeation rates. In recent years extensivestudies have been performed – modification of the membranesurface, optimization of scouring and hydrodynamic methods– for cancelling or reducing these limitations and thus improv-ing membrane processes. In fact, an increase in the shear stressinduces a decrease in the cake layer thickness and generallycreates a greater permeate flow. Various approaches, includingg nel,c havb iclesf e, tol useb n thafl tinga olar-i hess flowa y laya nott ch-n scribt ly thp

3

tud-i sidet tos rateI pus iclesa bablm rovet tionl ento easeo the

membrane. This theory has been demonstrated in several stud-ies [43–51]. This way of creating turbulence by injecting gasallows creation of a gas liquid two-phase crossflow operationthat can significantly increase the permeate flux and, moreover,can improve the membrane rejection characteristics. This ideawas developed by Stanton et al.[52]. In fact, injecting air bub-bles into the liquid feed to generate a two phase flow streamhas proved to be an effective, simple and low cost techniquefor enhancing ultrafiltration processes and has allowed betterrejection. Previous studies had been based on the analysis of theexperimental data and mass transfer correlations. The authorsattempted to model the slug flow ultrafiltration process usingthe volume of fluid method with the aim of understanding andquantifying the details of the permeate flux enhancement result-ing from gas sparging. For this numerical study, the commercialCFD package FLUENT was used. This CFD was used to simu-late the motion of a single Taylor bubble rising in a liquid flowingthrough a circular cross-section tube. In vertical pipes, Taylorbubbles are axisymmetric and have round noses, while their tailis generally assumed to be nearly flat. The Taylor bubble occu-pies most of the cross-sectional area of the tube. When the bubblerises through a moving liquid, the liquid that is flowing aheadof the nose of the bubble is displaced as a liquid film. It startsflowing downwards in the annular space between the tube walland the bubble surface. Alongside the bubble, the liquid filmaccelerates until it reaches its terminal velocity, provided theb filmp es ah allyb hisr ance-ma antifyt t onu thatp exam-i thei nt canb t. Thet r filmfl iv-o anes.F argedu rea-sT dule.T e sur-f amicra lcu-l ragedp modelr oret-i medt e fluxd e dis-t lling

enerating turbulent flows, placing inserts in the flow chanreating turbulence promoters and pulsations of feed flow,een used to improve the migration of the solute or part

rom the membrane surface to the bulk flow. For examplimit the particle layer growth, high shear rates can be cay rotating parts of the module. Several studies have showuid instabilities like Taylor vortices, established in a rotannular filter, are very effective in reducing concentration p

sation and particle deposition due to high shear rates. Thear rates increase rapidly with the increasing axial feednd lead to enhanced mass transfer between the boundarnd the bulk phase. But, this way of optimizing the flow is

he only one. We will make a state of the art of all the teology developed to enhance these processes. We will de

he gas sparging and Dean vortices to illustrate respectiveulse-gas sparging and Dean and Taylor vortices.

.1. Pulses and gas sparging

The improvement of crossflow ultrafiltration has been sed by many authors who injected air in the concentrate inhe membrane[43–53]. The use of unsteady flow can leadignificant benefits by increasing heat and mass transfert was demonstrated that the permeate flux increased withatile flow and that the accumulation of the retained partt the membrane surface was reduced very effectively, proainly through the increased shear. It has already been p

hat injecting air could diminish the concentration polarisaayer during ultrafiltration of macromolecules. The developmf the filtration flux was supposed to be due to an incrf the turbulence and also of the crossflow velocity inside

e

dt

e

er

ee

s.l-

yd

ubble is long enough. At the rear of that bubble the liquidlunges into the liquid plug as a circular wall jet and producighly agitated mixing zone in the bubble wake. It is generelieved that a kind of vortex exists in this mixing zone. Tegion is believed to be responsible for mass transfer enhent due to the increase in the wall shear stress (Fig. 8). Theuthors thought that it is essential to understand and qu

he details of slug flow dynamics and to identify their effecltrafiltration performance. In their paper, they explainedermeate flux enhancement was due to gas sparging by

ning the hydrodynamics of gas–liquid two-phase flow andncrease in mass transfer. They showed that the enhancemee explained by the increase in the mass-transfer coefficien

urbulence just behind the air bubble, caused by the annulaowing downward, is of significant intensity, and plays a ptal role in permeate flux enhancement in tubular membrurthermore, the permeate flux enhancement due to gas spltrafiltration with tubular membranes can be predicted withonable accuracy. Taha et al. also worked on this subject[53].hey tried to develop a model using a tubular membrane moheir representation was based on dividing the membran

ace area into various regions depending on the hydrodynegime in the vicinity of the membrane, as shown inFig. 9. Bynalysing the fluid flow in these regions, it is possible to ca

ate the mass transfer coefficients for each region. The aveermeate flux for the membrane can be assessed. Theesults were compared with experimental data and with thecally calculated data. Simulation studies were also perforo check the effects of some process factors on permeatevelopment. The authors succeeded in determining thre

inct mass transfer zones in the slug flow regime called fa


Fig. 8. Simulation of slug flow[52].

film zone, wake zone and liquid slug zone. The mass transfecoefficients for each of these zones were determined. With thesvalues, the averaged permeate flux for gas-sparged ultrafiltratiowas determined. There was reasonably good agreement betweexperimental data and theoretically predicted data. The results osimulation studies show that gas sparging can be greater at highfeed concentration and transmembrane pressure. Also, increaing liquid flow rate has contradictory effects in single phase flowas well as in gas sparged ultrafiltration. These studies show thpotential of computational fluid dynamics in this domain. Thelarge numbers of papers published shows how attractive thi

domain is for researchers. This method of enhancing membraneprocess performance is easy to use and this was true for eachcase studied, as shown by the number of papers. Furthermore, thelack of recent papers tends to prove that this method cannot beoptimized any further. Many improvements have already beenmade to enhance microfiltration, ultrafiltration, nanofiltration,reverse osmosis processes and to lead to a better understandingof these phenomena with the help of CFD.

3.2. Spacers

The term “turbulence promoters” is nowadays accepted inthe literature, although the stable flows may not necessarilyexhibit the characteristics of fully developed turbulence. Thepresence of spacers leads to increased pressure drop, as well asto the formation of localized stagnation or dead zones, wherethe above phenomena may be increased. Thus, the importantrole of membrane spacers has been recognized in the past years,and several experimental and theoretical studies have aimed atunderstanding the underlying phenomena and optimizing spacerconfigurations[54–65]. Thus, although it is common knowledgethat the presence of a spacer can greatly improve the membranemass transfer, detailed understanding of fluid dynamics in thechannel has not been developed because of experimental andnumerical complexities. The spiral wound membrane modulec ura-t piralw e walls wallc flowp com-p n, iti istri-b itht t hasb anya flowag in an LU-E in as were

Fig. 9. Flow regimes for

renenf

ers-

e

s

onfiguration is one of the most common membrane configions in the field of membrane technology applications. In sound membrane modules, spacers are used to enhanchear stress and to promote eddy mixing, thereby reducingoncentration and fouling. The effect of spacer filaments onatterns in narrow channels can just be quantified usingutational fluid dynamics. To find an optimal spacer desig

s essential to determine the flow pattern and turbulence dution in a spacer filled channel or spiral wound module. Whe development of more powerful computing techniques, iecome possible to simulate flow in spacer-filled channels. Muthors have experimentally and numerically investigatedround a cylinder between two walls. Cao et al.[54] investi-ated CFD simulations of net-type turbulence promotersarrow channel. They ran simulations in two dimensions. FNT was used as the CFD package to simulate the flowpacer-filled channel. The general governing equations

two-phase flow[53].


applied on a curvilinear grid to enable computations in com-plex or irregular geometries. Several turbulence models couldbe used to solve the Navier–Stockes equations. In the turbulentregime, the RNGk–ε model used by the authors was first used inquantum field theory. They investigated the effects of differentarrangements of turbulence promoters. Spacers come in variousforms that are composed of a net-like arrangement of filamentsaligned parallel, transverse or at an angle to the module axis.The spacer causes flow disturbance before and after the trans-verse filaments. In order to elucidate the likely extent of theflow disturbance, the CFD simulations were directed towardsthe effect of cylindrical objects positioned normal to the flow.The simulations revealed the detailed flow patterns, velocitydistributions, and turbulent kinetic energy distributions in thespacer-filled channel. It was found that the location of the highshear stress region and of the eddies was closely related to thespacer cylinder geometry and their position in the channel. Bycomparing simulation results, it can be concluded that carefulselection of the location of the transverse filaments and of thedistances between them is very important in spacer optimisation.It was found that the mass transfer differences between the topand bottom membrane surfaces could be equalised by placingthe transverse spacer cylinders alternately on the top and bottomwall or suspending them in the middle of the channel. The sim-ulation suggested that suspending transverse spacer cylinders inthe channel is more desirable. The simulation also suggestedt cylid peaa ovem estal versc ssurd selet esec als eri-o n am nnei rdert inanf ristio nders whef ctert ationp eome hicha lencp su rang

of Reynolds numbers typical of such membrane modules. ACFD code, based on the finite-volume method, was used. Duringeach simulation the governing equations were integrated in timeby imposing a constant mean pressure gradient until the flowreached a statistically steady state. Above a critical Reynoldsnumber of 60 the flow became unstable due to mechanisms sim-ilar to those operating in the case of a cylinder in unboundedflow. Above a Reynolds number of 78 walls eddies appeared.This characteristic of the flow in the channel wall was due tothe interaction of the vortices shed by the cylinders with thevortices layers created on the channel walls. Three-dimensionaleffects were not considered in that study. This approach, which iscommon practice in turbulent flow numerical simulations, mayalso be useful to solve the mass transfer problem in order toobtain local mass transfer. The understanding achieved in thatstudy is expected to facilitate optimization studies of membranespacer configurations. Schwinge et al.[62] studied an unsteadyflow in narrow spacer-filled channels for spiral-wound mem-brane modules. They inspected the subcritical and supercriticalflow patterns in narrow two-dimensional channels for single andmultiple filaments. As the cylindrical spacer filaments were ori-ented transverse to the main flow direction, two-dimensionalCFD simulations could be used. These two-dimensional calcu-lations are an excellent viewing device for future estimation ofmore complex spacer geometries. The fluid used was water ata temperature of 293 K. This fluid was supposed to be incom-p . Thefl tions.T , butu sid-e weres eree nss intro-d in an rreda freefl equa-t uired.T accu-r tionst dicali t al.[ l ofp lectivet pas-

hat reducing the distance between the transverse spacerers could reduce the distance between the shear stressnd produce more efficient eddy activity, which may imprass transfer at the membrane surfaces. However, it was

ished that the reduction in the distance between transylinders could also significantly increase the channel prerop and consequently increase the operating costs. The

ion of optimum geometry involves a trade-off between thompeting effects. Koutsou et al.[56] carried out the numericimulation of the flow in a plane-channel containing a pdic array of cylindrical turbulence promoters. The flow iodel two-dimensional geometry, consisting of a plane-cha

n which an array of cylinders is located, was studied in oo obtain a better understanding of the behaviour, the domeatures and structures, as well as the statistical charactef the spacers. This work was intended to get a better utanding of transport phenomena in membrane elements,eed flow spacers tend to enhance mass transport charaics, possibly decreasing fouling and concentration polarizhenomena while increasing pressure drop. Model flow gtry was considered, consisting of a plane-channel, in wregular array of cylinders was inserted, acting as turbu

romoters, as shown inFig. 10. Direct numerical simulationsing the Navier–Stokes equations were performed over a

Fig. 10. Schematic of flow geometry[54].

n-ks

b-eec-

l

tcs-reis-

-

e

e

ressible, isothermal and to have constant fluid propertiesuid movement was governed by the Navier–Stokes equahese equations were suitable for all Reynolds numbersnder laminar conditions they could be solved without conring the resolution of turbulent eddies. These equationsolved using a CFD code. Five filament configurations wxamined (Fig. 11). Computational fluid dynamics calculatiohowed complex interaction between all the parametersuced in the numerical simulation. For a single filamentarrow channel the wall reduced the transition, which occut slightly higher Reynolds numbers than for a cylinder in aow channel. However, the authors showed that a good adion between process parameters and fine meshes is reqhis increases the computational cost but enhances theacy of the results. Therefore, they suggested that calculao three dimensions would necessitate careful and methodentification of appropriate modelling procedures. Wiley e63] explained the interest of a numerical simulation moderessure driven membrane processes describing the se

rapping of certain particles in the feed channel and the

Fig. 11. Different configurations developed[62].


Fig. 12. The basic shapes of commercial net spacers[64].

sage of others to the permeate channel. The effects of changesin rejection, wall permeation rates and solution properties onflow rate and concentration profiles are presented for emptychannels and channels with turbulence promoters. Therefore,the authors decided to use CFD because this method can inte-grate the modelling of a flow in complex geometries whichincludes the recirculation and the difference in fluid proper-ties between the bulk solution and the membrane wall. Thefinite volume code CFX4 was used to solve the continuationequations. The flow was also assumed to be steady, incompress-ible and laminar but the viscosity and diffusivity were likelyto change. The model was confirmed with a high number ofsemi-analytical solutions. While the model developed has beencorroborated for a series of situations, it can readily be adaptedfor other conditions of physical properties and of permeationrates. The advantage of the model is that it may help to estimatethe effect of various assumptions on concentration polarisation.This kind of information is essential to use membrane systemsproperly. Moreover, their paper revealed that it was necessary toimprove the CFD package used for the representation of mem-brane systems by including a model allowing the descriptionof selective component exclusion. The modular nature of thisvalidated CFD model makes it a powerful tool for the design ofmembrane systems. Li et al. optimized commercial net spacersin spiral wound membrane modules[64]. They decided to com-pare the two main types of commercial net spacers frequentlyun rs: thedts fil-a ef nt am fromC n

Fig. 14. CFD fluid flow results[65].

two neighbouring filaments consists mainly of one “dead eddy”,which does not contribute much to mass transfer. If the value ofl/h is very highl/h = 10, shedding of vortices will only enhancemass transfer in the direct neighbourhood of the filaments, result-ing in lower average mass transfer. This means that an optimumvalue ofl/h exists. The geometric parametersα andβ also playan important role in enhancing mass transfer. It was found thatthe spacer geometry is optimal forl/h = 4, α = 30 andβ = 120over a large range of power number values. The results of theCFD simulations were validated using a few experimental data.The experiments confirmed that the geometric parameters ofspacers have a considerable influence on mass transfer for agiven crossflow power consumption. Comparison of the exper-iments carried out with different non-woven spacers showedthat there is an optimal spacer geometry, which agrees with theoptimal geometry obtained by CFD simulations. On the otherhand, Karode et al.[65] reported results from a computationalfluid dynamics study performed to visualize the steady statefluid flow structure through spacer filled channels in flat sheetform. A commercially available CFD routine called PHOENICSwas used to implement the fluid flow equations. The simulationwas done with a rectangular test cell showing spacer filamentsand a typical grid (Fig. 14). Water was taken as the bulk fluidfor all CFD simulations. These simulations were run for inletvelocities ranging from 0.25 to 1.0 m s−1, which encompassedtypical cross flow velocities in commercial membrane modules.C eralc ss ofs ss. Them highw mentd d thea r is ani thefi etera Theo ar ratewi h casea there

sed—woven and non-woven spacers, as shown inFig. 12. Aon-woven spacer can be characterized by four parameteistance between spacer filamentsl1 andl2, the angleβ between

he spacer filaments and the flow attack angleα (Fig. 13). Thistudy focused on cylindrical filaments. The diameter of thements (d) was half the channel height (h). The influence of th

our geometric parameters on mass transfer enhancemeechanical energy dissipation were investigated. ResultsFD simulations indicated that ifl/h is small, the flow betwee

Fig. 13. Geometric characterisation of a nonwoven spacer[64].

ndomputational fluid dynamics simulations were run on sevommercially available spacers to evaluate the effectivenepacers in terms of pressure drop and average shear streain factors influencing the design of an effective spacer (all shear and low pressure drop) seem to be the ratio of filaiameter to inter-filament distance, the filament diameter anngle between the spacer filaments. The filament diamete

mportant parameter since it limits the packing density innal membrane module. The ratio between filament diamnd inter-filament spacing influences the bulk flow pattern.rder of spacers when arranged in increasing average sheas found to be different for high (1 m s−1) and low (0.25 m s−1)

nlet velocities. The authors compared each spacer for eacnd gave advice on the choice of the spacer. Therefore,


Fig. 15. Representation of Dean vortices in coiled pipe[74].

seems to be important characteristics to take into account beforechoosing a spacer. Spacer development is a typical applicationusing CFD because flow or pressure sensors are impossible toinsert in such a process. However, it seems that the latest stud-ies performed in this way give the finest spacer optimizationand that further progress would be difficult to achieve. In manycases, energy consumption considerations should also be takinto account in deciding on the best spacer geometry.

3.3. Dean vortices

It is possible to make these vortices visible in a helicallycoiled membrane (Fig. 15). Experimental results show anenhanced filtrate flux and improved filtration process. Theeffect of Dean vortices on the filtration flux and efficiency ofmembrane processes in sinusoidal curved and helically coiletubular membranes has been investigated by several researgroups[66–79]. The Dean number is the ratio of the centrifugalforce to the viscous force. The Dean number in a curved pipeis defined as this dimensionless parameter:

De = Re

√di

dc(6)

tart h

where Re is the Reynolds number (dimensionless),di theinternal diameter anddc the curve diameter (m):

Re = ρυdi

µ(7)

Experimental studies have shown that the efficiency of cross-flow filtration in curved membranes can be much higher thanin straight membranes.

CFD simulations were run, illuminating two important effectsof secondary flow: an increase in the wall shear stress causinga reduced particle deposition and an enhanced mass transfer atthe boundary layer.

In addition, a detailed study of the performance of helicalscrew thread inserts in tubular membranes was carried out byBellhouse et al.[66]. This study was designed to examine thecomplete fluid dynamic processes contributing to flux enhance-ment when screw thread inserts are used with tubular mem-branes. The computational fluid dynamics code FLUENT wasused to predict the behaviour of membranes fitted with inserts.The design combined a mainly helical flow, in which Dean vor-tices are engendered, with an approximately axial flow, whichmodifies the Dean vortices into a continuous corkscrew vortex.This support created an excellent adjustment of the feed fluidand minimized concentration polarisation effects. The inserts(Fig. 16) were tested under microfiltration conditions using yeastsolutions, under ultrafiltration conditions using reconstitutedp ionsu sig-n thep ranesu theire wasf sure-m ula-t ce oft orus,h int tionsf nianfl istedi rann besa terial.T veral

Fig. 16. Single and three s

en

dch

elical screw-thread inserts[66].

owdered milk solutions, and under nanofiltration conditsing synthetic dyes. The authors succeeded in showingificant boost (by factors of 6–10) of the filtration fluxes inresence of inserts compared to the classical tubular membnder the same operational conditions. They comparedxperimental results with CFD results and good conformityound between the CFD calculations and experimental meaents. Moulin et al. wrote a paper in which a numerical sim

ion of shear stress was proposed to determine the influenhe geometric parameters in four different tubes—straight, telical and woven[68]. The mathematical model consisted

he resolution of the Navier–Stokes and continuity equaor a 3D steady, laminar flow of an incompressible Newtouid with constant physical properties. This method consn creating vortices in modules without moving parts. Theyumerical simulations with nonporous cylindrical straight tund compared the wall shear stress at the surface of the mahey worked under laminar conditions and established se


Fig. 17. Representation of the secondary velocity vectors made[74] (heli-cal tubeRe = 1, De = 0.4,θ = 520◦, di = 3:2 mm,dc = 20 mm,b = 30 mm, water,ρ = 1000 kg m−3, µ = 10−3 Pa s).

relationships. They concluded that Dean vortices increase theshear stress to the same extent as they enhance permeate fluxin pervaporation process. They also showed that the simulationallows analysis of the flow behaviour from the laminar to theturbulent regime. Moreover, any geometry design may be sim-ulated so that the influence of Dean vortices in straight, helicaltubes as well as woven fibres can be predicted with the use ofCFD. The simulations may be used to visualize the Dean vor-tices: their location in the flow, their centre and their rotationcan be determined as shown inFig. 17. The results obtainedwere in good conformity with published results obtained usingimaging methods. Moll et al. developed this first concept[72].They supposed the effect of the feed concentration was notcompletely understood. Their goal was to give new insight bycomparing laser visualisation results with CFD results. Theyalso used a mathematical model that consisted in solving theNavier–Stokes and continuity equations for a 3D steady, laminarflow of an incompressible homogeneous and Newtonian fluid.The algorithm which was based on the finite element methodused a projection method in order to approximate the solutionof the equations. In the case studied, attention was restrictedto rigid, nonpermeable bounded walls. The authors comparedtheir results with several experimental techniques of visualisa-tion that had previously been used to reveal secondary flows.For example, Winzeler et al.[75] had used a fine aluminiumsuspension in a methylene blue solution and Bolinder et al.[76]h n ino wase lopeb ntar ev-e ricalt tionr andf tionsi ticlei froma toryc ds tfi vesn ent

Fig. 18. Projected trajectories of numerical tracers in a half section made byMoll et al. (helical tube,Re = 1627,di = 3.2 mm,dc = 20 mm,b = 30 mm, water,ρ = 1000 kg m−3, µ = 10−3 Pa s, particle diameter = 0.5 m)[72].

caused by Dean vortices. As the Reynolds number increases,due to the centrifugal force, the maximum of the axial flow istransferred to the opposite of the membrane. A wide range ofReynolds numbers was treated and we can see that the axial flowwas closer to the wall, which is in accord with laser visualisation.In some cases, the enhancement of mass transfer can be totallyexplained by the wall shear stress augmentation due to the Deanvortices. Considering this paper, when particles such as those ofthe baker’s yeast were present in the solution, a second effect ofDean vortices was noticeable which can be understood by con-sidering swirling motion effects. In fact, at low concentrations,the regions where accumulation of retained matter occurs remainvery thin whatever the geometry. Thus, this distribution of theaccumulation is similar in straight and helical tubes. In thesecases, the main mass transfer improvement is due to the aver-aged wall shear stress improvement. When the concentrationincreases significantly, gradients of retained matter are modi-fied and the influence of the channel geometry is more and morenoticeable. Therefore, in this case due to the curved pathlines,the mass transfer mechanism is different from that observed ina straight membrane: this might suggest that accumulation ofretained matter occurs in a thinner zone in the helical geometry,which provides a kind of recirculation effect. These studies showthe importance of numerical simulation in membrane processesto better understand these complex phenomena. Even with themost powerful sensors, we could not have obtained such pre-c ed too cha-n lboze li-c rvedt werec bet-t tingc ysis,t alcu-l in at con-t eda solu-

ad used laser Doppler velocimetry and laser visualisatiorder to visualize the vortices. The numerical simulationasy to apply and more precise than all the methods deveefore. Therefore, it allowed comparison of the experimeesults with the CFD simulations. Moll et al. worked at sral Reynolds numbers and examined two different cylind

ubes, straight and helical, for numerical tracers. Simulaesults were considered for expanded velocity distributionsor different Reynolds numbers. They chose different secn the channel and they obtained the positions of the parn those consecutive sections. A trajectory was deducedll the successive positions of a given particle. This trajecan be anticipated in local coordinate systems, which leagures likeFig. 18. Considering all the results, this paper giew insight into the effects involved in the flux enhancem

dl

s

o

ise results with experiments. Another study was performptimize the module design and in order to inspect the meisms influencing membrane filtration performance, by But al. [77]. They focused on crossflow microfiltration in heally coiled membranes, and specifically in sinusoidal cuubular membranes. Experimental and theoretical studiesarried out. Numerical calculations were performed to get aer perception of why Dean vortices are so efficient in limiake layer growth. At the beginning of the theoretical analhe three-dimensional velocity and pressure field were cated by solving the Navier–Stokes equations numericallyhree-dimensional Cartesian coordinate system with a finiterol volume method for laminar fluid flow in a helically coilnd a sinusoidal curved tube with impermeable walls. The


Fig. 19. Geometry of the sinusoidal curved tube and streamlines of the velocityfield in the cross-section after three 180◦ curvatures developed[77]: (a)De = 100,Re = 500; (b)De = 400,Re = 2000; (c)De = 600,Re = 3000.

tion of the governing equations was achieved for the case ofan incompressible, isothermal, fully developed and steady stateNewtonian fluid flow. The geometry of the tube is describedin Fig. 19. This simulation allows using different crossflowvelocities for different solute concentrations, Dean numbers andReynolds numbers. The beneficial effect of a curved membranecan be explained by an increase of the particle lift force, whichcan be correlated with the wall shear stress. The rapid mixingbetween boundary layer and bulk phase, results in an improvemass transfer in the cross section. Further progress in modelling the filtration process should be made to reach a betteunderstanding of the flow and mass transfer in curved membranes. Based on these results and on future results, the desiof new optimized crossflow microfiltration modules could beproposed. The authors also can suggest optimum parametefor the filtration of a latex and yeast suspension solution. Theresults of these simulations corresponded to the results of thexperimental investigation, which showed that the highest fluximprovement occurred for Reynolds numbers about 2000 anDean number about 400. They also demonstrated that curvemembranes are more effective than straight membranes. Thewere able to design a new type of optimized membrane moreeffective than a straight membrane. All these developments inmodelling the filtration process allow a better understanding offlow and mass transfer in curved membranes. The efficiency othis approach for enhancing membrane processes is evident fl cture thesfi

3

ranp hans inorg tubul cove para

ing barrier. The performance of a membrane separation processcan be characterised by the product of the permeate flux and thetotal filtration area. These kind of developments interest manyresearchers[80–84]. A very interesting paper was written byTarabara et al.[81]. This paper showed that the geometry has animportant place in the membrane enhancement. They presentedresults of computational fluid dynamics modelling of the flowwithin a crossflow membrane filtration cell whose dimensionsreplicated those of the SEPA CF. They used a commercial CFDpackage FLUENT based on the finite-volume method. Flow fieldwas characterized in terms of velocity, pressure, and shear stress.Flow was found to be unidirectional over the greatest part of thechannel area with the exception of the corners of the channel.Stagnation areas were observed in dead ends at the inlet andoutlet of the channels. The relation between the highest shearrate created in this geometry and the average inlet velocity wasgiven. This paper showed that it was highly possible to enhancemembrane geometry by using CFD. Dolecek et al. carried outmany studies in this domain[82,83]. Their first study dealtwith the modelling of permeates flow in a multichannel ceramicmembrane. The aim was to simulate numerically the permeateflow in porous body of a multichannel membrane element andto estimate the effect of the element configuration on the fluxperformance. It was limited to pure permeate flow simulation,leaving the simultaneous filtration for future work. Permeateflow in the porous body of a multichannel membrane elementw d. As effecto y of ac of thep ura-t adeb thei ce thep rme-a ssure,

F wc

arge numbers of papers published. Unfortunately, manufars do not use this approach to improve the performance ofltration processes.

.4. Geometry

One of the most important characteristics of these membrocesses is the compactness of the membrane. The excurface is large, which enhances filtration. For example,anic membranes are manufactured especially in flat-disc,

ar or multichannel configurations. The channel surface isred with a skin layer which has small pores and acts as a se

d-r-gn

rs

e

ddy

for-e

ege

--

-t-

as replicated numerically using the finite element methoimple honeycomb configuration was chosen to reveal thef geometry parameters on the performance. The geometreramic membrane element was chosen for the simulationermeate flow. This simple rectangular honeycomb config

ion is used, for example, in ceramic membrane monoliths my CeraMem Corp (Fig. 20). The authors wanted to check

nfluence of many parameters. The parameters that influenerformance of a membrane element are: permeability, pete viscosity, flow channel pressure, permeate conduit pre

ig. 20. A repeating section of the element[81]: (1) permeate conduits; (2) flohannels; (3) repeating section.


distance between permeate conduits, number of flow channelsbetween two adjacent layers of permeate conduits, porous wallthickness and flow channel width. When the permeability ofthe membrane element porous body is very high compared topermeability of the active membrane layer the permeate flux iscontrolled by the latter and the flux performance is proportionalto the membrane packing density. When the permeability of theactive membrane increases the effect of the membrane elementconfiguration becomes significant. Generally, for a given valueof the permeability the maximum permeate flux per unit vol-ume of a membrane element can be found. When the distancebetween permeate conduits decreases the active membrane sur-face increases, which affects flux performance positively. On theother hand, for very short distances, the cross section availableto the permeate flow decreases, affecting the permeate flux neg-atively. When the number of channels increases, the membranesurface increases but at the same time the permeate from innerchannels must travel a longer distance to reach a permeate con-duit. Thus the contribution to the overall flux is relatively smallfrom the inner channels for high numbers of channels. There aredead zones of small pressure gradient around the inner channels.This work can help to develop new membrane geometry. A morecomplex study was performed by the same authors two yearslater. Their goal was to develop configurations with the highestpossible filtration area per unit of membrane volume. The filtra-tion area packing density of inorganic multichannel membranesc ndt sup-p mostu ores ults.T raneg ilityw usedb undt io oft ssere at thee is notg kingd atert thel dis-t totap aned portp met( w isg of at branp ighv surf ionso thant brap eforem duc

Fig. 21. Membrane geometry[82].

new membranes. There is no use in placing a lot of channels inthe membrane to increase its surface if the inner channels do notwork. On the other hand, if the permeability of the skin layeris high or if the channels are not covered with the skin layerat all, then the channels near the membrane surface contributesignificantly to the total permeate flux while the contributionsof the inner channels are negligible (Fig. 22). In this case, thepermeate flow is controlled predominantly by the porous sup-port permeability. Moreover, another parameter is to be takeninto account: the authors called it coefficientα. In fact, thisparameter represents the ratio between the flow channel widthand the inter channel wall thickness. This review is very impor-tant and shows that it is essential to respect a minimum widthbetween two channels. This minimum width allows a minimumof transmembrane pressure and thus the permeate in the porouscan be ejected more easily. They also insisted on the fact thatthe larger the number of channels, the larger the surface, but atthe same time the permeate from inner channels must travel alonger distance to reach a permeate conduit. Thus the contribu-tion of the inner channels to the overall flux is relatively smallfor large numbers of channels. Darcovich et al.[84] proposed anew approach to develop these processes. The objective was todesign a thin channel membrane module with very uniform flowproperties, to use a statistical experimental design approach todetermine the module parameters and to select module param-eters which give uniform flow conditions over a broad rangeo dulec com-p bovem hichu theirs odulew a. At asd es. At sign.T erfor-m oundt citya worst

an reach 400 m2/m3. The purpose of this study was to extehe results to the simulation of permeate flow in the porousort of inorganic 19 channel membranes—probably thesed multichannel configuration. This configuration is also muitable for an experimental verification of numerical reshe effects on the permeate flow distribution of the membeometry and of the ratio of skin layer to support permeabere studied. The results of numerical simulations can beoth for filtration and backflush operating modes. It was fo

hat channel contributions depend significantly on the rathe skin layer to porous support permeabilities and to a lextent, on the membrane geometry. The authors proved thnhancement of the multichannel membrane performanceenerally proportional to the increase in filtration area pacensity. If the permeability of the porous support is much gre

han that of the skin layer the permeate flow is controlled byatter and the contributions of all the channels are uniformlyributed. This study showed that channel contributions toermeate flux in inorganic 19 hexagonal channel membrepend significantly on the ratio of skin layer to porous supermeabilities and to a less extent, on the membrane geoFig. 21). For low values of the permeability, the permeate flooverned by the skin layer resistance and the contributions

he channels are nearly equivalent; in this case, the memerformance is proportional to the filtration surface. For halues of the permeability, a region of nearly constant presormed in the internal part of the membrane and contributf middle and central channels were significantly smaller

hose of corner and wall channels because the transmemressure was lower in the middle of the membrane. Theranufacturers have to take this into account when they pro

ls

ry

lle

e

ne

e

f practical operating conditions. The flow through the mohannel was simulated using a finite difference code. Theutational fluid dynamics scheme which calculated the aodule characteristics was a turbulent transport model wsed the finite difference method. Therefore, the aim oftudy was to design for research purposes a membrane mith uniform flow characteristics over the permeating are

hin channel cross flow module with a uniform flow field wesigned for the characterization of flat ceramic membran

otal of ten variables were considered for the module dehis design was used to evaluate the predicted module pance for each combination of the design variables. It was f

hat running the simulation at the highest cross flow velond the lowest module pressure always resulted in the


Fig. 22. CFD results: isobars and streamlines in the porous media[82].

performance for a given module design. All these observationswere made inside the porous material. With experiments, wecould not have observed all of these characteristics and couldnot have progressed in the design of new membrane geome-tries. Therefore, computational fluid dynamics is an essentialtool to progress in this field. Moreover, enhancing membraneprocesses by modifying the geometry characteristics seems aninteresting approach. In these studies, the goal generally reachedis to increase the wall shear stress at the membrane surface tolimit the polarisation–concentration phenomenon.

4. Conclusion

This review shows the interest of coupling numerical simula-tion and membrane processes. The large number of publicationssuggests the high potential of this approach for enhancing mem-brane processes. The increasing number of studies is clearlyrelated to the recent developments in computer power and tothe use of finer grid meshes in the vicinity of the membrane.This review shows that two approaches have been particularlyconsidered: the comprehension of the hydrodynamics and ofthe mass transfer. The hydrodynamics allows the increase ofthe shear stress near the wall, thus allowing the enhancement ofmembrane processes. Commonly, the first simplifying assump-tions can be summarized by: the stronger the shear stress, thew ate tt omet . Ths ndi-t er, im proi es thm andt e pef donu studi raneS fican

number of turbulence models in numerical simulations and theircomparison with experimental results in the case of membraneprocesses is not excellent, which limits the use of CFD in tur-bulent regime. The understanding of the phenomena involved inmass transfer is without any doubt a very attractive approach ofmembrane processes. The hydrodynamic approach in complexgeometries makes it possible to predict the shear stress nearthe wall. The latest publications show however that couplingthese two approaches leads to difficulties. Thus, CFD is withoutany doubt an important tool for understanding mass transfer inmembrane processes. Opportunities for the development of newmembrane geometries are numerous. The latest studies seem toshow the importance of the comprehension of the mass transferin the development of a membrane. Such a membrane shouldexhibit the largest specific surface, the highest shear rate at itssurface and the lowest dead volume.

Acknowledgements

The authors wish to thank David FLETCHER [Computa-tional Fluid Dynamics Research and Consultancy, Departmentof Chemical Engineering, University of Sydney, NSW 2006,Australia] for many helpful discussions.

References

amic

ics,4-6).ppl.

ical

, J.

tube

ous

eaker the fouling. Therefore, a large number of studies relhe diphasic flows, the turbulence promoters, and to the geries of membranes capable of generating secondary flowstudy of hydrodynamics reveals the optimum operating coions and the most suitable geometry characteristics. Howevost cases, the membranes are created with the aim of im

ng the transfer of solvent. The second approach associatodels of mass transfer in the vicinity of the membrane

he hydrodynamic models. In most cases, the studies werormed under laminar conditions. Several studies weresing the models of concentration of polarization, and other

es were carried out inside the porous matrix of the membome recent studies consider turbulent flows, but the signi

o-e

nv-e

r-e-.t

[1] R. Sondhi, R. Bhave, G. Jung, Applications and benefits of cermembranes, Membr. Technol. 2003 (2003) 5–8.

[2] J.H. Ferziger, M. Peric, Computational Methods for Fluid Dynam2nd ed., Springer Publisher, NY, 2002, 423 pp. (ISBN: 3-540-4207

[3] A.S. Berman, Laminar flow in channels with porous walls, J. APhys. 24 (1953) 1232–1235.

[4] R.M. Terrill, Laminar flow in a uniformly porous channel, Aeronaut15 (1964) 299–310.

[5] M. Friedman, J. Gillis, Viscous flow in a pipe with absorbing wallsAppl. Mech. 34 (1967) 819–827.

[6] T. Mizushina, S. Takeshita, G. Unno, Study of flow in a porouswith radial mass flux, J. Chem. Eng. 4 (1971) 135–142.

[7] L.S. Galowin, M.J. De Santis, Investigation of laminar flow in a porpipe with variable wall suction, AIAA 12 (1974) 1585–1594.


[8] G. Belfort, N. Nagata, Fluid mechanics and cross-flow filtration: somethoughts, Desalination 53 (1985) 57–79.

[9] G. Belfort, Fluid mechanics in membrane filtration: recent developments,J. Membr. Sci. 40 (1989) 123–147.

[10] C. Hirsch, Numerical Computation of Internal and External Flows,Volume 2: Computational methods for inviscid and viscous flows, Engi-neering Analysis with Boundary Elements, 3 (1992) 277.

[11] S.K. Karode, Laminar flow in channels with porous walls, revisited, J.Membr. Sci. 191 (2001) 237–241.

[12] J. Marriott, E. Sorensen, I.D.L. Bogle, Detailed mathematical modellingof membrane modules, Comput. Chem. Eng. 25 (2001) 693–700.

[13] J. Marriott, E. Sorensen, A general approach to modelling membranemodules, Chem. Eng. Sci. 58 (2003) 4975–4990.

[14] V. Nassehi, Modelling of combined Navier–Stokes and Darcy flowsin crossflow membrane filtration, Chem. Eng. Sci. 53 (1998) 1253–1265.

[15] D.B. Das, V. Nassehi, R.J. Wakeman, A finite volume model for thehydrodynamics of combined free and porous flow in sub-surface regions,Adv. Environ. Res. 7 (2002) 35–58.

[16] K. Damak, A. Ayadi, B. Zeghmati, P. Schmitz, A new Navier–Stokesand Darcy’s law combined model for fluid flow in crossflow filtrationtubular membranes, Desalination 161 (2004) 67–77.

[17] J. Chen, Q. Li, In situ monitoring techniques for concentration polariza-tion and fouling phenomena in membrane filtration, Adv. Colloid Interf.Sci. 107 (2004) 83–108.

[18] S. Geissler, U. Werner, Dynamic model of crossflow microfiltration inflat-channel systems under laminar flow conditions, Filtration Separat.32 (1995) 533–537.

[19] Y. Lee, M. Clark, Modeling of flux decline during crossflow ultrafiltra-tion of colloidal suspensions, J. Membr. Sci. 149 (1998) 181–202.

[20] T. Carroll, The effect of cake and fibre properties on flux declines01)

[ flow

[ ationEng.

[ ng ofmbr.

[ rafil-nsfer

[ jan,. Eng

[ lingters

[ osis

[ osis

[ and290.

[ fer998)

[ nsfer

[ nsferregio002)

[ ranerical

[34] V. Magueijo, M.N. de Pinho, V.M. Geraldes, Numerical and experimen-tal study of mass transfer in lysozyme ultrafiltration, Desalination 145(2002) 193–199.

[35] M.N. De Pinho, V. Semiao, V.M. Geraldes, Integrated modelling oftransport processes in fluid/nanofiltration membrane systems, J. Membr.Sci. 206 (2002) 189–200.

[36] D.E. Wiley, D.F. Fletcher, Techniques for computational fluid dynamicsmodelling of flow in membrane channels, J. Membr. Sci. 211 (2003)127–137.

[37] D.F. Fletcher, D.E. Wiley, A computational fluids dynamics study ofbuoyancy effects in reverse osmosis, J. Membr. Sci. 245 (2004) 175–181.

[38] D.C. Wilcox, Turbulence Modelling for CFD, DCW Industries, LaCanada, California, 1998.

[39] E. Pellerin, E. Michelitsch, K. Darcovich, S. Lin, C.M. Tam, Turbulenttransport in membrane modules by CFD simulation in two dimensions,J. Membr. Sci. 100 (1995) 139–153.

[40] Y. Miyake, K. Tsujimoto, H. Beppu, Direct numerical simulation of aturbulent flow in a channel having periodic pressure gradient, Int. J.Heat Fluid Flow 16 (1995) 333–340.

[41] T. Kotzev, Numerical study of the fluid dynamics and mass transfer ofan ultrafiltration performance in a tube membrane module, Int. J. Eng.Sci. 32 (1994) 359–368.

[42] S. Redkar, V. Kuberkar, R.H. Davis, Modeling of concentration polar-ization and depolarization with high-frequency backpulsing, J. Membr.Sci. 121 (1996) 229–242.

[43] Y. Wang, J.A. Howell, R.W. Field, D. Wu, Simulation of cross-flowfiltration for baffled tubular channels and pulsatile flow, J. Membr. Sci.95 (1994) 243–258.

[44] C. Cabassud, S. Laborie, J.M. Lain, How slug flow can enhance theultrafiltration flux in organic hollow fibres, J. Membr. Sci. 128 (1997)93–101.

[ owSci.

[ for80)

[ es:ylor990)

[ rmeate121

[ wn-mbr.

[ y onanes,

[ ward91–

[ sing

[ ular

[ rbu-157–

[ und

[ n ofrical

[ nofil-. Sci.

in hollow-fibre microfiltration membranes, J. Membr. Sci. 189 (20167–178.

21] L. Huang, M.T. Morrissey, Finite element analysis as a tool for crossmembrane filter simulation, J. Membr. Sci. 155 (1999) 19–30.

22] C.J. Richardson, V. Nassehi, Finite element modelling of concentrprofiles in flow domains with curved porous boundaries, Chem.Sci. 58 (2003) 2491–2503.

23] C.R. Bouchard, P.J. Carreau, T. Matsuura, S. Sourirajan, Modeliultrafiltration: prediction of concentration polarization effects, J. MeSci. 97 (1994) 215–229.

24] R.L. Singh, Influence of slip velocity at membrane surface on ulttration performance. I. Channel flow system, Int. J. Heat Mass Tra22 (1979) 721–729.

25] R.E. Lebrun, C.R. Bouchard, A.L. Rollin, T. Matsuura, S. SouriraComputer simulation of membrane separation processes, ChemSci. 44 (1989) 313–320.

26] A. Chatterjee, A. Ahluwalia, S. Senthilmurugan, S.K. Gupta, Modeof a radial flow hollow fiber module and estimation of model parameusing numerical techniques, J. Membr. Sci. 236 (2004) 1–16.

27] M. Sekino, Precise analytical model of hollow fibre reverse osmmodules, J. Membr. Sci. 85 (1993) 241–252.

28] M. Sekino, Study of an analytical model for hollow fiber reverse osmmodule systems, Desalination 100 (1996) 85–97.

29] M. Ben-Boudinar, W.T. Hanbury, S. Avlonitis, Numerical simulationoptimization of spiral wound modules, Desalination 86 (1992) 273–

30] V.M. Geraldes, V. Semiao, M.N. de Pinho, Nanofiltration mass transat the entrance region of a slit laminar flow, Ind. Eng. Chem. 37 (187–96.

31] V.M. Geraldes, V. Semiao, M.N. de Pinho, Flow and mass tramodelling of nanofiltration, J. Membr. Sci. 191 (2001) 109–128.

32] V.M. Geraldes, V. Semiao, M.N. de Pinho, The effect on mass traof momentum and concentration boundary layers at the entranceof a slit with a nanofiltration membrane wall, Chem. Eng. Sci. 57 (2735–748.

33] J.M. Miranda, J.B. Campos, Concentration polarization in a membplaced under an impinging jet confined by a conical wall, a numeapproach, J. Membr. Sci. 182 (2001) 257–270.

.

n

45] Y. Wang, J.A. Howell, R.W. Field, D. Wu, Simulation of crossflfiltration for baffled tubular channels and pulsatile flow, J. Membr.95 (1994) 243–251.

46] Y. Taitel, D. Barnea, A.E. Duckler, Modeling flow pattern transitionsteady upward gas-liquid flow in vertical tubes, AIChE J. 26 (19345–353.

47] Z.S. Mao, A.E. Duckler, The motion of Taylor bubbles in vertical tuba numerical simulation for the shape and the rise velocity of Tabubbles in stagnant and flowing liquids, J. Comput. Phys. 91 (1132–160.

48] S.R. Bellara, Z.F. Cui, D.S. Pepper, Gas sparging to enhance peflux in ultrafiltration using hollow fibre membranes, J. Membr. Sci.(1996) 175–184.

49] Z.F. Cui, K.I.T. Wright, Flux enhancements with gas sparging in dowards crossflow ultrafiltration: performance and mechanism, J. MeSci. 117 (1996) 109–116.

50] Q.Y. Li, Z.F. Cui, D.S. Pepper, Effect of bubble size and frequencthe permeate flux of gas-sparged ultrafiltration with tubular membrJ. Membr. Sci. 67 (1997) 71–75.

51] R. Ghosh, Z.F. Cui, Mass-transfer in gas-sparged ultrafiltration upslug flow in tubular membranes, J. Membr. Sci. 162 (1999)102.

52] S. Stanton, T. Taha, Z. Cui, Enhancing hollow fibre ultrafiltration uslug-flow a hydrodynamic study, Desalination 146 (2002) 69–74.

53] T. Taha, Z.F. Cui, Hydrodynamic analysis of upward slug flow in tubmembranes, Desalination 145 (2002) 179–182.

54] Z. Cao, D.E. Wiley, A.G. Fane, CFD simulations of net-type tulence promoters in a narrow channel, J. Membr. Sci. 185 (2001)176.

55] S.G. Chatterjee, G. Belfort, Fluid flow in an idealized spiral womembrane module, J. Membr. Sci. 28 (1986) 191–208.

56] C.P. Koutsou, S.G. Yiantsios, A.J. Karabelas, Numerical simulatiothe flow in a plane-channel containing a periodic array of cylindturbulence promoters, J. Membr. Sci. 231 (2004) 81–90.

57] V.M. Geraldes, V. Semiao, M.N. de Pinho, Flow management in natration spiral wound modules with ladder-type spacers, J. Membr203 (2002) 87–102.


[58] F. Li, W. Meindersma, A.B. de Haan, T. Reith, Optimization of com-mercial net spacers in spiral wound membrane modules, J. Membr. Sci.208 (2002) 289–302.

[59] V.M. Geraldes, V. Semiao, M.N. de Pinho, The effect of the ladder-typespacers configuration in NF spiral-wound modules on the concentrationboundary layers disruption, Desalination 146 (2002) 187–194.

[60] G. Costigan, B.J. Bellhouse, C. Picard, Flux enhancement in microfiltra-tion by corkscrew vortices formed in helical flow passages, J. Membr.Sci. 206 (2002) 179–188.

[61] V.M. Geraldes, V. Semiao, M.N. de Pinho, Hydrodynamics and concen-tration polarization in NF/RO spiral-wound modules with ladder-typespacers, Desalination 157 (2003) 395–402.

[62] J. Schwinge, D.E. Wiley, D.F. Fletcher, A CFD study of unsteady flowin narrow spacer-filled channels for spiral-wound membrane modules,Desalination 146 (2002) 195–201.

[63] D.E. Wiley, D.F. Fletcher, Computational fluid dynamics modelling offlow and permeation for pressure-driven membrane processes, Desalina-tion 145 (2002) 183–186.

[64] F. Li, W. Meindersma, A.B. de Haan, T. Reith, Experimental validationof CFD mass transfer simulations in flat channels with non-woven netspacers, J. Membr. Sci. 232 (2004) 19–30.

[65] S.K. Karode, Ashwani Kumar, Flow visualization through spacer filledchannels by computational fluid dynamics: pressure drop and shear ratecalculations for flat sheet geometry, J. Membr. Sci. 193 (2001) 69–84.

[66] B.J. Bellhouse, G. Costigan, K. Abhinava, A. Merry, The performanceof helical screw-thread inserts in tubular membranes, Separat. Purific.Technol. 22 (2001) 89–113.

[67] W.R. Dean, Fluid motion in a curved channel, Proc. R. Soc., LondonSer. 121 (1928) 402–406.

[68] P. Moulin, D. Veyret, F. Charbit, Dean vortices: comparison of numericalsimulation of shear stress and improvement of mass transfer in mem-

2001

[ uxbran

[ texlysis

[71] J. Wakeman, C.J. Williams, Additional techniques to improve microfil-tration, Separat. Purific. Technol. 26 (2002) 3–18.

[72] R. Moll, P. Moulin, D. Veyret, F. Charbit, Numerical simulation of Deanvortices: fluid trajectories, J. Membr. Sci. 197 (2002) 157–172.

[73] S. Agrawal, G. Jayaraman, Numerical simulation of dispersion in theflow of power law fluids in curved tubes, Appl. Math. Model. 18 (1994)504–512.

[74] D.N. Kuakuvi, P. Moulin, D. Veyret, P. Guichardon, F. Charbit, DeanVortices: Numerical simulation of shear stress and experimental improve-ment of mass transfer in ultrafiltration process, International Congresson Membranes (ICOM’99), Toronto, Canada, 1999.

[75] H.B. Winzeler, G. Belfort, Enhanced performance for pressure-drivenmembrane processes: the argument for fluid instabilities, J. Membr. Sci.80 (1993) 35–47.

[76] C.J. Bolinder, B. Sunden, Flow visualization and LDV measurementsof laminar flow in a helical square duct with finite pitch, Exp. ThermalFluid Sci. 11 (1995) 348–363.

[77] M. Bubolz, M. Wille, G. Langer, U. Werner, The use of dean vorticesfor crossflow microfiltration: basic principles and further investigation,Separat. Purific. Technol. 26 (2002) 81–89.

[78] T.T. Chandratilleke, Nursubyakto, Numerical prediction of secondaryflow and convective heat transfer in externally heated curved rectangularducts, Int. J. Thermal Sci., 42 (2003) 187–198.

[79] S. Ookawara, R. Higashi, D. Street, K. Ogawa, Feasibility study onconcentration of slurry and classification of contained particles bymicrochannel, Chem. Eng. J. 101 (2004) 171–178.

[80] G. Belfort, Membrane modules: comparison of different configurationsusing fluid mechanics, J. Membr. Sci. 35 (1988) 245–270.

[81] V.V. Tarabara, M.R. Wiesner, Computational fluid dynamics modelingof the flow in a laboratory membrane filtration cell operated at lowrecoveries, Chem. Eng. Sci. 58 (2003) 239–246.

[ nnel

[ ganicembr.

[ tedr. Sci.

brane processes at low permeation fluxes, J. Membr. Sci. 183 (149–162.

69] M.E. Brewster, K.Y. Chung, G. Belfort, Dean vortices with wall flin a curved channel membrane system: a new approach to memmodule design, J. Membr. Sci. 81 (1993) 127–137.

70] H. Mallubhotla, G. Belfort, W.A. Edelstein, T.A. Early, Dean vorstability using magnetic resonance flow imaging and numerical anaAIChE J. 47 (2001) 1126–1140.

)

e

,

82] P. Dolecek, Mathematical modelling of permeate flow in multichaceramic membrane, J. Membr. Sci. 100 (1995) 111–119.

83] P. Dolecek, J. Cakl, Permeate flow in hexagonal 19-channel inormembrane under filtration and backflush operating modes, J. MSci. 149 (1998) 171–179.

84] K. Darcovich, M.M. Dal-Cin, S. Ballevre, J.P. Wavelet, CFD-assisthin channel membrane characterization module design, J. Memb124 (1997) 181–193.

computational fluid dynamics applied to membranes state of the art and opportunities

Documents