analysis of caso4 scale formation mechanism in various

Journal of Membrane Science 163 (1999) 63–74

Analysis of CaSO4 scale formation mechanism in variousnanofiltration modules

Sangho Lee, Jaehong Kim, Chung-Hak Lee∗School of Chemical Engineering, College of Engineering, Seoul National University, Seoul 151-742, South Korea

Received 15 July 1998; accepted 12 April 1999

Abstract

Scale formation of sparingly soluble salts has a significant effect on flux decline in nanofiltration (NF) system. This studyfocuses on the elucidation of the different mechanisms of scale formation according to membrane modules in NF system.

In unstirred batch NF, flux decline was mainly due to surface (heterogeneous) crystallization, while in crossflow NF,fouling was attributed to both surface and bulk crystallization. However, the extent of contribution of each crystallizationto the fouling depended on the NF modules. The bulk (homogeneous) crystallization followed by crystal deposition on thesurface of the nanofilter played a major role in flux decline in the spiral wound module whereas surface blockage due to thesurface crystallization does in the tubular module. When an on-line microfiler was introduced to prevent crystal depositionduring the concentration run, flux improvement was pronounced only in case of the spiral wound module, whereas it wasnegligible in case of the tubular module. This was because the microfilter could only remove crystals formed in the retentatethrough the bulk crystallization which is the dominant fouling mechanism in the spiral wound module.

A modified resistance-in-series model was applied to assess the fouling characteristics of each NF module based on thebulk and the surface crystallization. The greatest extent of the fouling due to surface crystallization in tubular module wasattributed to its highest concentration polarization modulus compared with the other two modules at the same crossflow rate.©1999 Elsevier Science B.V. All rights reserved.

Keywords:Nanofiltration; Calcium sulfate; Crystallization; Membrane fouling; Membrane module

1. Introduction

In recent years, nanofiltration (NF) technology hasbeen widely applied to water purification, municipaland industrial wastewater treatment and reuse, etc.One of the most promising applications of NF may bewater softening. Selective retention characteristics inNF make it possible to economically remove multiva-

∗ Corresponding author. Tel.: +82-2-880-7075; fax:+82-2-888-1604E-mail address:[email protected] (C.-H. Lee)

lent ions from water. However, in water softening, aserious problem to overcome is the membrane foulingdue to scale formation. Controlling of the membranefouling due to the scale formation is a major expensein designing and operation of practical NF membraneplant. Sparingly soluble salts such as CaCO3, CaSO4and SiO2 could precipitate on the membrane surfacewhen their concentration exceeds the solubility lim-its and subsequently decrease the product flow ratethrough the membrane. Various means have been pro-posed to address the scale formation control, but nonehave solved this problem with satisfactory results.

0376-7388/99/$ – see front matter ©1999 Elsevier Science B.V. All rights reserved.PII: S0376-7388(99)00156-8

64 S. Lee et al. / Journal of Membrane Science 163 (1999) 63–74

Several recent publications have dealt with themechanisms of calcium sulfate scale formation onmembranes: Okazaki and Kimura [1] used basic con-cepts from nucleation and crystallization kinetics inconjunction with a cake filtration model to interpretflux decline curves and assumed that crystal nucle-ation occurred on the membrane surface and nucleiformation rate is dependent on the degree of the su-persaturation. Gilron and Hasson [2] considered thatthe flux decline was due to the blockage of the mem-brane surface by lateral growth of the deposit (surfaceor heterogeneous crystallization). On the other hand,Pervov [3] suggested that crystal formation took placein the bulk solution due to strong oversaturation in thedeadlocks (bulk or homogeneous crystallization) andthen the crystals came out of the sites sediment on themembrane surface, which led to the flux decline. Sev-eral other researchers attempted to model the foulingprocess [4–6]. However, few studies have been doneon the crystal formation mechanisms according to thetypes of the membrane modules.

The purpose of this study was to elucidate the dif-ferent pathways toward the membrane fouling dur-ing the NF of calcium sulfate solution. Special effortswere made to examine the effect of the types of theNF modules on membrane fouling. A new approachfor flux enhancement was also attempted based on thedifferent scale formation mechanisms.

2. Theory

2.1. Concentration polarization

In pressure-driven membrane process concentrationpolarization arises when solute is largely rejected bythe membrane. Due to this phenomenon, the concen-tration of soluble salts easily become supersaturated atthe NF membrane surface even though the bulk con-centration is still undersaturated. In the NF of the feedsolution containing mainly divalent ions, the concen-tration of salt in the permeate is negligible with re-spect to concentration (Cm) at membrane surface andbulk concentration (Cb). Therefore, the concentrationpolarization modulus, which is defined by the ratioCmandCb (Cm/Cb), is given as the Eq. (1) [7]:

Cm

Cb= exp

(Jδ

D

)(1)

where,J is the permeation flux,δ the characteristicboundary layer thickness andD the diffusivity ofsolute.

Since the hydrodynamic conditions of membranemodules are different, the extent of concentrationpolarization may be different from one another evenat the same crossflow velocity. For instance, the con-centration polarization is less severe in spiral woundmodule than in plate-and-frame module since the feedspacer in spiral wound module promotes turbulentflow. Table 1 summarizes the concentration polariza-tion modulus in spiral wound, plate-and-frame, andtubular modules.

2.2. Mechanisms for the scale formation

There are two ways for explaining flux declinemechanisms due to scale formation in RO/NF mem-branes; cake formation and surface blockage mecha-nism [2,3].

In cake formation mechanism, crystal particleswhich are formed in bulk phase through bulk (homo-geneous) or secondary crystallization deposit on themembrane to form a layer. Therefore, the flux de-cline comes up with the accumulation of the porouslayer of precipitate and could be described by aresistance-in-series model:

J = 1P − π

η (Rm + Rc)(2)

where1P is the transmembrane pressure,π the os-motic pressure,η the permeate viscosity,Rm the mem-brane resistance andRc the resistance due to cake for-mation.

On the other hand, in surface blockage mechanismscale formation may occur due to surface (heteroge-neous) crystallization on membrane surface and themembrane surface becomes blocked by the lateralgrowth of crystals. Assuming the areas occupied bycrystals are completely impermeable, the flux in theabsence of the cake formation could be expressed asfollows:

J = 1P − π

ηRm

Afree

At(3)

where At is the total membrane area andAfree themembrane area unoccupied by surface (heteroge-neous) crystallization

S. Lee et al. / Journal of Membrane Science 163 (1999) 63–74 65

Table 1Equations for concentration polarization modulusa [8–11]

Type Concentration polarization modulus Flow condition

Spiral wound exp

(17Jν0.625h0.875

u0.875D0.75

)Turbulent

Plate-and-frame exp

(Jd 0.33

h L0.33

1.86u0.33D0.67

)Laminar

Tubular exp

(Jd0.11

t ν0.56

0.023u0.89D0.67

)Turbulent

a J: flux, ν: kinematic viscosity,h: channel height,u: crossflow velocity,D: diffusion coefficient,dt : tube diameter,dh: hydraulic diameter.

Fig. 1. Scale formation mechanisms in NF membrane.

The two different schemes are depicted in Fig. 1.When the bulk phase becomes supersaturated due

to increasing concentration, it is possible that bothmechanisms of crystallization simultaneously occur inNF system. In this case the flux may be representedby combining Eqs. (2) and (3);

J = 1P − π

η (Rm + Rc)

Afree

At(4)

Assuming that the thickness of crystal layer formedon the membrane surface is constant [6],Afree couldbe defined as follows:

Afree = At − βms (5)

whereβ is the area occupied per unit mass andmsthe weight of scale which is crystallized on membranesurface

If the crystal slurry is incompressible, cake resis-tanceRc can be calculated based on a conventionalcake filtration theory:

Rc = αmc

At(6)

whereα is the specific cake resistance factor per unitweight of cake,mc the accumulated weight of precip-itated scale

Based on these equations, the most predominantmechanism may be determined if the relationship be-tween flux and precipitated mass is identified. A lin-ear relationship betweenJ and surface crystal mass msshould be obtained when the surface blockage mech-anism is predominant whereasJ−1 should be pro-portional to cake massmc when the cake formationmechanism is predominant. The total mass of crystalsformed both on membrane surface and in bulk phasecan be calculated through the following mass balance.

mt = ms + mc = cf Vf − crVr − cpVp (7)

wheremt is the total mass of crystals;cf , cr, cp thesolute concentrations of feed, retentate and permeate,respectively andVf , Vr, Vp the volumes of feed, re-tentate and permeate, respectively.

2.3. Analysis of each resistance term

In the NF of CaSO4 solution with three kinds of NFmodules (tubular, plate-and-frame, spiral wound, re-spectively), the boundary layer thicknesses were cal-culated using the equations shown in Table 1. As theirvalues were only around 10mm for all the tested mod-ules, we assumed that the bulk crystallization withinthe boundry layer is negligible [2]. Since the cake re-sistance,Rc is directly related to the amount of thecrystals formed in bulk phase,Rc could be eliminatedfrom Eq. (4) if the retentate is continuously prefilteredon-line by 0.45mm microfilter in order to remove thesuspended crystals.


In this context, the following procedure was adoptedto evaluate each resistance term and fraction of freearea,Afree/At for each NF module:1. Membrane resistance (Rm) is obtained from

pure water flux. In our cases the osmotic pres-sure was calculated from Gibbs equation. Itwas small enough (about 0.7 kgf/cm2) to be ne-glected compared with the operation pressure forNF(10 kgf/cm2).

2. According to Eq. (3),Afree/At is estimated fromthe steady-state flux of NF with a microfilter sincethe cake resistance (Rc) is removed in this case.

3. The cake resistance (Rc) is the difference in resis-tance between the case with and without microfil-ter and thus,Rc is calculated based on the Eq. (4).

3. Experimental

3.1. Batch nanofiltration cell experiments

The dead end filtration cell(volume capacity;100 ml) was pressurized at 10 bar by N2 gas. Themembrane used was NF-45(Filmtech) and the effec-tive membrane area was 22.1 cm2. The feed solutionwas 2000 ppm of CaSO4. In all the experiments, thefeed solution temperature was kept between 20 and25◦C, and all the flux data were corrected at 25◦C bythe following equation:

Flux at 25◦C

= Flux atT ◦C × Viscocity atT ◦C

Viscocity at 25◦C(8)

3.2. Crossflow filtration

Fig. 2 shows a schematic diagram of the crossflowNF system combined with on-line microfiltration. Thesystem with a total working volume of 4–8 l consistedof a feed vessel, temperature controller, high pressurepump, MF and NF module. Three kinds of mem-brane modules were tested to investigate the effect ofmodule type on fouling phenomena: plate-and-frame,spiral wound and tubular modules. The membraneshaving similar ion rejection characteristics were usedin each module. Table 2 summarizes the modulesand membranes tested in the experiments. The cross-flow velocity was fixed at 0.6 m/sec and the feed

Fig. 2. Schematic diagram of crossflow NF equipment.

solution was 2000 ppm of CaSO4 for all the threemodules.

The crossflow experiments were carried out in bothcontinuous concentration(Fig. 3(a)) and total recyclemodes(Fig. 3(b)). At the start of each run, the waterflux was measured with ultra pure water (a resistiv-ity ; ca. 18 M Ohm cm). In the concentration runs, theequipment was operated with and without a micro-filter by recirculating only the retentate and continu-ously collecting the permeate. In total recycle runs,both the retentate at the supersaturation degree (SD)of 2.5 and the permeate were recycled with and with-out a microfilter in order to study the fouling mecha-nisms in depth. The microfilter was a polypropylenecartridge filter (Osmonics, Hydrex II) with a pore sizeof 0.45mm.

3.3. Analytical methods

The analytical methods from Standard Methods[12] were adopted for measurement of feed, retentateand permeate ion concentration: an ion chromatog-raphy (DIONEX 4000I) and an atomic absorptionspectroscopy(NIPPON jarrell Ash, AA-880 mark II).A conductivity cell (ATI Orion, Model 170) was


Table 2Specifications of NF membranes

Membrane Surface area (m2) Hydraulic radius (mm) Channel length (mm) Rejection of inorganic salts

Plate-and-frame NF-45 0.018 0.5 50 MgSO4 2000 ppm : 99%Spiral wound NF-40 0.3 0.25 350 NaCl 2000 ppm : 45%Tubular MPT-34A 0.024 6.35 600 NaCl 50,000 ppm : 35%

Fig. 3. Schematics of NF operation mode; (a) concentration runs(b) total recycle runs.

installed on-line for the continuous monitoring oftotal soluble ion concentrations. The supersaturationdegree (SD) of CaSO4 in retentate was evaluated bythe ratio of the retentate concentration to the saturatedone (Cb/Cs) which is proportional to the solutionconductivity. The turbidity was measured by a neph-elometer (HF DRT-100B turbidimeter). The meansize and size distribution of crystal particles in theretentate were evaluated using a laser light scatteringinstrument(Malvern Mastersizer/E).

4. Results and discussion

4.1. Crystal formation and flux decline in unstirredbatch nanofiltration

The variation of flux during the NF of CaSO4 so-lution was illustrated as a function of CF in Fig. 4.Rapid and continuous flux decline was observed fromthe first stage, even though the SD of less than 1.1was maintained and the turbidity of bulk phase wasquite low(less than 1 NTU) throughout the NF. It sug-gested that no significant bulk crystallization occurredin the bulk phase, but fast crystallization occurred atthe membrane surface. The concentration polarizationis not increasing with time due to the continuous crys-tal formation near membrane surface [5], so the effectof osmotic pressure on flux decline with time couldbe neglected.

Fig. 4. Flux decline in dead-end NF.


Fig. 5. Estimation of mass of crystal grown on the membranesurface in case of dead-end NF.

The amount of the CaSO4 crystals which formed onthe membrane surface was estimated to be 11.3 g/m2 ofmembrane from the mass balance Eq. (8) for CaSO4.A linear relationship was observed between the massof CaSO4 crystals and flux as depicted in Fig. 5, whichindicates that flux decline was mainly due to the sur-face crystallization on the membrane surface, as de-scribed in Section 2. This is what one would expectsince, in unstirred batch filtration, surface crystalliza-tion could be dominant due to the severe concentra-tion polarization at the membrane surface. This resultcoincides with some previous studies [2].

4.2. Comparison of flux and supersaturationdegree between nanofiltration modules in crossflownanofiltration

Fig. 6 illustrates the results of crossflow NF of satu-rated calcium sulfate solution of 2000 ppm with threekinds of NF modules. The permeate flux and super-saturation degree (SD) of CaSO4 in the retentate areshown as a function of CF. In contrast to the dead-endfiltration, the permeate flux was maintained at rela-tively high initial value below the CF of 2 regardlessof the membrane modules. The SD continuously in-creased with the CF before reaching a certain point(SD = 2.7), but after that it abruptly decreased.

From this result, three distinct periods of behav-ior could be identified as shown in Fig. 6. During theearly phase of the run (Period 1), no significant fluxdecline is observed for all the three modules (Fig.6(a–c)). Even though the bulk and membrane wallconcentration exceed the CaSO4 saturation concentra-tion, neither bulk nor surface crystallization occurs inthis period since the concentration is less than a crit-ical supersaturation level that needs to initiate crystalnucleation. In contrast to the dead-end mode(Fig. 4),even the surface crystallization did not occur on themembrane surface in the crossflow mode. It could beattributed to the fact that the concentration polariza-tion modulus in crossflow mode should be less thanthat in a dead-end mode.

During Period 2, the ionic concentrations withinthe boundary layer exceeds the critical value so thatthe surface crystallization begins. The crystal layeron the membrane surface blocks the membrane andsubsequently decreases the permeate flux. Since themembrane wall concentration is always higher thanthe bulk concentration, the bulk crystallization in thebulk retentate does not occur yet. No crystal forma-tion was observed in the retentate and the turbidity ofthe retentate solution was as low as the initial feedsolution.

As the fluid is removed through the membrane inconcentration run, the ionic concentrations in the bulksolution increase and approach the critical value atwhich bulk crystallization starts (Period 3). DuringPeriod 3, the SD is abruptly decreased and the bulkturbidity is increased due to the formation of crystalparticles in the retentate. From this point the retentatebecame very turbid, and simultaneously the averageparticle size of crystal formed in retentate increasedup to about 100mm. As shown in Fig. 6(a–c), the in-tensive bulk crystallization started mostly at SD = 2.7and progressed thereafter regardless of the membranemodules. During this period, flux decline is attributedto both surface and bulk crystallization.

However, it is worth noting that the length of Period2 is quite different from module to module. The lengthof Period 2 is shortest in spiral wound module (Fig.6(a)) whereas it is longest in tubular module (Fig.6(b)). The plate-and-frame module takes intermediatelength (Fig. 6(c)). As the intensive bulk crystallizationstarts at Period 3, the shortest length of Period 2 meansthat the bulk crystallization contributes little to flux


Fig. 6. Flux SD and retentate turbidity vs. concentration factor according to membrane module type; Crossflow velocity for all the threemodules = 0.6 m/s; (a) spiral wound (b) tubular (c) plate-and-frame.

decline. On the other hand, the longest length of Period2 means that the flux decline results mostly from thesurface crystallization. It is very important factor todesign a hybrid NF system to enhance the permeate

flux. This will be discussed in more detail in Section4.3.

Since the surface crystallization on the membranewas in close relationship with concentration polariza-


Fig. 7. Effects of flow rate on flux decline in plate-and-framemodule.

tion, the rate of flux decline was expected to be af-fected by the crossflow recirculation rate. Fig. 7 showsthat in plate-and-frame module the higher the cross-flow rate, the longer the non-fouling region (Period 1).As the wall shear rate would increase with the cross-flow rate, it would be reasonable to assume that theincrease in the crossflow rate would lower the solutewall concentration and thus make the condition un-favorable for the surface crystallization on the mem-brane surface by increasing the wall shear rate. Butthe flux improvement by increasing flow rate was notso effective beyond the CF of 3.0 even at the high-est crossflow rate (0.76 m/sec) since the bulk crystal-lization in the retentate became important beyond thispoint due to the great extent of SD.

4.3. Flux enhancement by introducing microfiltrationon-line to the nanofiltration

In order to verify the dominant crystal formationmechanism for each module described in the previoussection, a microfilter (0.45mm) was inserted on-lineto NF as shown in Fig. 4. The role of the microfilterwas to continuously remove crystals formed in theretentate through the bulk crystallization during theconcentration run.

Fig. 8(a) shows the effect of 0.45mm MF on the fluxin spiral wound module. Below the CF of 2.0 (Period1, non-fouling region), any significant change was notobserved with the on-line microfiltration. However,beyond the CF of 2.5 (Period 3), the flux improvementwas much more pronounced compared with the fluxwithout the microfilter. It is because most of the crys-tals formed in the retentate through the bulk crystal-lization were removed by the on-line microfilter andconsequently their deposition on the membrane sur-face was prevented. It supports the fact that in spiralwound module, the bulk crystallization in the reten-tate is more important mechanism of the membranefouling and flux decline than surface crystallization.

In contrast, the efficiency of the on-line microfil-ter in tubular module was negligible during the entireperiods, as shown in Fig. 8(b). This result confirmedthat the flux decline in tubular module has nothing todo with the crystals formed in the bulk retentate so-lution but the dominant fouling mechanism is the sur-face blockage caused by the surface crystallization. Inplate-and-frame module (Fig. 8(c)) the prefilter had alittle effect on flux increment, but it was much lessthan that in spiral wound module. It is because boththe bulk and surface crystallization contribute to thefouling in this module.

In summary, flux enhancement could be achievedby eliminating crystals suspended in recirculation loopbut the efficiency is greatly different from module tomodule. Similar results were observed in some previ-ous studies [13].

4.4. Analysis of resistances in three modules

To further investigate the fouling mechanism indepth, the modified resistance-in-series model basedon Eqs. (1)–(8) was applied to quantitatively analyzethe characteristics of membrane fouling for each mod-ule. Since the osmotic pressure effect on the flux wasnegligible in this study,Rc was experimentally deter-mined to be the portion of the total resistance whichcan be eliminated when the on-line microfilter is used,while the fraction of free area,Afree/At is calculatedfrom the ratio of pure water flux to the steady-stateflux in the presence of the on-line microfilter. Whenthe steady state flux were obtained after 5 h NF opera-tion of supersaturated CaSO4 solution (SD = 2.5), the


Fig. 8. Effect of membrane module type on the efficiency of on-line microfilter; (a) spiral wound (b) tubular (c) plate-and-frame.

flux data (J1, J2) for three modules were measuredunder the crossflow velocity of 0.6 m/sec (Table 3).

These equations and the flux data were used toquantitatively evaluate various resistance terms, andthe fraction of free area for each module under thesame crossflow velocity of 0.6 m/sec (Table 3). These

data could be useful to find out which resistance dom-inantly affects the permeation flux for each module.

The Afree/At with spiral wound module was thehighest (0.507) whereas the magnitude of the fractionof free area is the least in tubular module (0.062). Itclearly illustrates that the fouling due to the surface


Table 3Composition of resistances, concentration polarization modulus and fraction of free membrane area in various membrane modulesd

Module type Jwa (l m2/h) J1

b (l m2/h) J2c (l m2/h) Rm (m−1) Rc (m−1) Afree/At Cm/Cb

Spiral wound 35.0 4.9 17.7 1.03× 1014 2.64× 1014 0.507 1.13Plate-and-frame 40.0 7.5 16.0 0.90× 1014 1.02× 1014 0.400 1.29Tubular 40.0 2.0 2.5 0.90× 1014 0.23× 1014 0.062 1.90

a Jw: water flux.b J1: steady-state flux without microfilter after 5 h operation under the total recycle run.c J2: steady-state flux with microfilter after 5 h operation under the total recycle run.d All values were calculated at the following conditions: the crossflow velocity of 0.6 m/sec, SD 2.5; the steady-state flux was measuredafter 5 h.

Fig. 9. Theoretical estimation of concentration modulus with re-spect to various membrane modules.

crystallization was the most important in tubular mod-ule. It may be the reason why the removal of suspendedcrystals in the retentate was useless in enhancing theflux in tubular module as shown in Fig. 8(b).

It is interesting to note that the cake resistance inspiral wound module was almost 11 times greater thanthat in tubular module and 2.5 times greater than thatin plate-and-frame module. One possible explanationis that feed spacers in spiral wound module play a sig-nificant role in cake formation on NF membrane; sincethe flow through the spacer under pressure createsa greater turbulence, secondary nucleation is greatlypromoted by turbulent motion of fluids and thus mem-brane fouling due to bulk crystallization becomesimportant.

Fig. 9 shows the theoretical concentration polariza-tion modulus versus the crossflow velocity in all thethree modules calculated based on the equations inTable 1. The flow regimes in all the modules wereturbulent at this interval of the crossflow velocity.The order of the concentration polarization moduluswas always spiral wound< plate-and-frame< tubularmodule and coincides well with the trend ofAfree/Atin Table 3. This result indicates that the fouling due tosurface crystallization should depend on the concen-tration polarization modulus.

A plot of calculated SD at membrane surface versussteady-state flux with total recycle runs clearly demon-strates the effect of concentration polarization on sur-face crystallization (Fig. 10). A linear relationship

Fig. 10. Effect of SD at membrane wall on permeate flux duringtotal recycle runs.


between SD at membrane surface and flux was ob-served regardless of module types when an on-line mi-crofilter was used. This fact also supports that the dif-ferences in the scale formation mechanisms betweenthe three modules can be attributed to the wall con-centration.

5. Conclusions

The scale formation mechanisms in NF of CaSO4were examined with different NF modules both exper-imentally and theoretically. The following conclusionswere withdrawn:1. Permeation flux in unstirred batch NF was

exponentially decreased even though the reten-tate concentration was almost unchanged. Thelinear relationship between flux and depositedmass indicates that the NF fouling results fromthe surface (heterogeneous) crystallization.

2. In crossflow NF, flux decline was due to not onlysurface (heterogeneous) crystallization but alsodue to bulk (homogeneous) crystallization. Thesurface crystallization played the smaller role inmembrane fouling of spiral wound module incomparison to the other modules, but it was stillsignificant.

3. The flux enhancement was attempted through thehybrid system of the NF with an on-line microfil-ter by continuously eliminating crystals suspendedin recirculation loop. The greatest flux improve-ment was more pronounced in spiral wound mod-ule among the three modules. This is because thefouling due to surface crystallization, which can-not be prevented by on-line microfilter, was lessdominant in spiral wound than in plate-and-frameand tubular module.

4. Analysis of resistances in three types of modulesindicates that the extent of surface fouling in spiralwound module is smaller than in other modules.The lowest value ofAfree/At for the tubular modulewas attributed to higher concentration polarizationmodulus under the same flow condition.

6. List of symbols

At membrane area (m2)Afree membrane area unoccupied by precipitation

(m2)Afree/At the fraction of free areacf , cr, cp solute concentrations of feed, retentate and

permeate, respectively (mg/l)Cm solute concentration at membrane surfaceCs saturation concentration of CaSO4 (mg/l)D diffusion coefficient (m2/sec)J flux (l/m2/h)L channel length (m)Rc resistance due to cake formation (m−1)Rm membrane resistance (m−1)Vf , Vr, Vp volumes of feed, retentate and permeate,

respectively (l)dh hydraulic diameter (m)dt tube diameter (m)h channel height (m)mc accumulated weight of precipitated scale

(kg)ms weight of scale which is crystallized on

membrane surface (kg)mt total mass of crystals (kg)rh hydraulic resistance (m−1)u crossflow velocity (m/sec)1P transmembrane pressure (Pa)α specific cake resistance factor per unit

weight of cake (kg−1m−1)β blocking coefficient (m2/kg)π osmotic pressure (Pa)ν kinematic viscosity (m2/sec)

Acknowledgements

This work was financially supported as a HANproject by Ministry of Environment in Korea. Theauthors are grateful to Mr J.S. Yum and Mrs H.S.Lee for their assistance during the experiments at theInstitute of Environmental Science & Technology,Seoul National University.

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analysis of caso4 scale formation mechanism in various

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