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Journal of Membrane Science 289 (2007) 249–257

Study of mass and heat transfer in the osmotic evaporationprocess using hollow fibre membrane contactors

V.D. Alves, I.M. Coelhoso ∗REQUIMTE/CQFB, Departamento de Quımica, FCT, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

Received 13 July 2006; received in revised form 5 November 2006; accepted 4 December 2006Available online 9 December 2006

bstract

In this work, the mass and heat transfer in the osmotic evaporation process was studied using a hollow fibre membrane contactor. A calciumhloride dihydrate solution (2.8–6 M) was circulated in the fibres and a sucrose solution (20% and 45%, w/w) in the shell side of the module.he respective mass transfer correlations were determined using a single-step methodology involving the mass and heat transfer equations,imultaneously: Sht = 2.66Re0.25

t Sc0.33t (d/l)0.33 and Shs = 15.4Re0.92

s Sc0.33s (d/l). The correlations are valid for Reynolds numbers between 0.5 and

5 and are in agreement with that obtained for liquid–liquid extraction and gas absorption.It was observed that the mass transfer resistance in the fibres could be easily minimized, even when high driving forces are applied. Regarding

he shell side boundary layer mass transfer resistance, it can be significant when processing concentrated sucrose solutions (50% of the overallesistance for a 61% (w/w) sucrose concentration).

The temperature profile was calculated using a model, which combines the heat and mass transfer equations. Although the temperature gradienthrough the boundary layers was not significant, the temperature difference between the membrane interfaces can be important for high driving

◦

orces, it reached almost 3 C when using a 6 M CaCl2 solution.The mass and heat transfer model was also used to calculate the water flux and the overall mass transfer coefficient during the concentration

rocess of a sucrose solution. The values predicted are in agreement with the experimental results for the range of Reynolds and Schmidt numberstudied.

2006 Elsevier B.V. All rights reserved.

sfer c

attc

amatat

eywords: Osmotic evaporation; Hollow fibre membrane contactors; Mass tran

. Introduction

Membrane processes are especially interesting for the con-entration of heat sensitive aqueous solutions containing foodnd pharmaceutical products, since they can operate at ambientr moderate temperatures, avoiding any risk of quality reductiony overheating. Osmotic evaporation is an example of such pro-ess, which can be applied in the concentration of fruit juices [1].

In this process, a porous hydrophobic membrane separates theolution to be concentrated from an osmotic solution, usually aalt solution, with a low water activity. Due to the hydropho-

icity of the membrane, the aqueous solutions cannot enter theores, and a liquid–vapour interface is formed in each pore end.he water activity difference between the two solutions induces

∗ Corresponding author. Tel.: +351 212 948 303; fax: +351 212 948 385.E-mail address: irc@dq.fct.unl.pt (I.M. Coelhoso).

bufittot

376-7388/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.memsci.2006.12.005

orrelations; Heat transfer

water vapour pressure difference, which is the driving force tohe water flux. The water evaporates in the solution to be concen-rated and the vapour crosses the membrane pores before beingondensed in the osmotic solution [2].

Since the water fluxes obtained are low, usually between 0.2nd 3 l/m2 h (5.6 × 10−8 and 8.3 × 10−7 m3/m2 s), the use ofembrane contactors with high specific areas, between 1500

nd 6000 m2/m3, will make this technique very promising forhe concentration process at industrial scale. These contactorsre constituted by a group of capillary fibres (internal diame-er 0.3–0.6 mm) placed inside a shell [3]. The aqueous phase toe concentrated (juice) circulates in the shell side of the mod-le while the osmotic solution circulates in the lumen of thebres. This configuration will minimize the viscous effects due

o the increase of the viscosity of the juice during the concen-ration process (the viscosity of a 70 wt.% sugar solution is tworders of magnitude higher than the viscosity of water at roomemperature).

2 f Membrane Science 289 (2007) 249–257

vwqttopsfp

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tat

2

2

sipvitp

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wipttm

wmeo

t

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tm

50 V.D. Alves, I.M. Coelhoso / Journal o

Due to the concentration polarization phenomena, the waterapour pressure near the membrane is different from the bulkater vapour pressure, in both sides of the membrane. Conse-uently, there are three resistances to the water and heat fluxes:wo boundary layer resistances in each side of the membrane, andhe membrane resistance [4]. The membrane resistance dependsn the size and tortuosity of the membrane pores, and on theorosity and thickness of the membrane. The selection of auitable membrane is crucial because the overall mass trans-er of a contactor can be significantly affected by the membraneroperties.

Recently, Albrecht et al. [5] showed that, membranes withltrafiltration porosity profile provide water vapour permeabili-ies at least at the same level as PP microfiltration membranes,hich are usually employed in contactor applications. For a

pecific membrane this resistance cannot be changed, so, inrder to maximize the water flux, it is necessary to determinehe hydrodynamic conditions that minimize the boundary layeresistances.

The objective of this work is to study the mass transfer processnd obtain mass transfer correlations for the osmotic evapora-ion process, and then, to compare them with the referred inhe literature. It should be pointed that the mass transfer cor-elations for hollow fibre membrane contactors published werebtained for different processes, namely liquid–liquid extractionnd gas absorption [6–10]. The very few works that use hol-ow fibre membrane contactors for osmotic evaporation eithero not refer any correlation or they use some of the literatureorrelations mentioned previously [11,12].

Although in the osmotic evaporation process both solutionsre maintained at the same temperature, there is a temperatureradient between the membrane interfaces due to the evapora-ion in one side of the membrane and the condensation in thether side. This temperature difference induces heat transfer byonduction through the membrane and heat is also transferred inhe boundary layers. Therefore, both the concentration and tem-erature profiles will be evaluated for the osmotic evaporationrocess using different operating conditions.

The mass and heat transfer correlations obtained will be usedo predict water fluxes for other experimental conditions andpplied in the simulation of the water flux and of the overall massransfer coefficient for the concentration of a sucrose solution.

. Theory

.1. Mass transfer

Due to the hydrophobicity of the membrane, the aqueousolutions cannot enter the pores and liquid–vapour equilibriums established in each pore entrance (Fig. 1). The water trans-ort involves water evaporation in the solution with higher water

apour pressure, followed by vapour transport in the gas phasemmobilised within the pores, and its condensation in the solu-ion with lower water vapour pressure. The water flow rate isroportional to the water vapour pressure difference between

astu

ig. 1. Water activity and temperature profiles in the osmotic evaporation pro-ess.

oth membrane interfaces:

dVw

dt= kmpAlm(pws − pwt) = kmpAlm(P∗

wsams − P∗wtamt)

(1)

here kmp is the membrane mass transfer coefficient and Alms the fibre logarithmic mean area. Due to the concentrationolarization phenomena, the effective driving force are lowerhan that calculated at bulk conditions. The water flow rate inhe boundary layers can be related to the respective individual

ass transfer coefficients ks and kt by

dVw

dt= ktAt(at − amt) = ksAs(ams − as) (2)

here ai is the bulk water activity, ami the water activity at theembrane interface, and At and As are the fibres internal and

xternal areas, respectively. Rearranging Eqs. (1) and (2) webtain:

dVw

dt= 1

(P∗ws/Asks) + (1/Almkmp) + (P∗

wt/Atkt)

× (asP∗ws − atP

∗wt) (3)

Expressing the water flux (Jw) using the logarithmic mean ofhe internal and external membrane area (Alm):

w = 1

Alm

dVw

dt(4)

he overall mass transfer coefficient Kp can be defined as

p = 1

(AlmP∗ws/Asks) + (1/kmp) + (AlmP∗

wt/Atkt)(5)

The membrane mass transfer coefficient is dependent onhe transport mechanisms of the water molecules across the

embrane pores. Since osmotic evaporation is carried out at

mbient temperature and pressure, using membranes with poreize usually ranging from 0.1 to 1 �m, it can be assumed thathe main transport mechanisms present are Knudsen and molec-lar diffusion. Therefore, according to the Dusty-gas model, the

f Mem

m

k

pomiwR[e

S

(

S

wre

(t

P

2

isfAiditttt

q

q

wficms

rbb

q

wmts

N

N

w

3

3

adecndi(a

3

wsddmeJlomhmaSa

V.D. Alves, I.M. Coelhoso / Journal o

embrane mass transfer coefficient can be estimated by

mp = 1.8 × 10−5

RTδ

(3τ

εdp(8RT/πMw)1/2 + τpair

εPDw−air

)−1

(6)

The boundary layer mass transfer coefficients depend on theroperties of the solutions and on the hydrodynamic conditionsf the system. These coefficients are generally obtained using theass transfer correlations referred in the literature, the major-

ty having the same form: the Sherwood number (Sh = kd/D),hich contains the mass transfer coefficient, as a function of theeynolds number (Re = ud/ν) and Schmidt number (Sc = ν/D)

6–10]. In this work, a general form based on the Levequequation [13] will be used for the tube side:

ht = αtReβtt Sc

1/3t

(di

l

)1/3

(7)

For the shell side, an exponent of 1 will be used for the termd/l), as considered by several authors [14–16]:

hs = αsReβss Sc1/3

s

(dh

l

)(8)

here the subscripts t and s refer to the tube and shell sides,espectively, di the fibre internal diameter, dh the hydraulic diam-ter and α and β are constants to determine.

The pure water vapour pressure at both membrane interfacesP∗

wi) can be correlated to the respective temperatures (Tmi) usinghe Antoine equation for water:

∗wi (Pa) = exp

[23.2 − 3816.4

Tmi (K) − 46.1

](9)

.2. Heat transfer

Although osmotic evaporation is usually considered as ansothermal process, since both solutions are maintained at theame temperature, the temperatures at the two membrane inter-aces are different due to heat transfer across the membrane.

temperature difference is created between both membranenterfaces due to the water evaporation in one side (coolingown the solution to be concentrated) and further condensationn the other side (heating up the osmotic solution) [17]. Thisemperature difference induces heat transfer by conduction inhe opposite direction (Fig. 1). In addition, there are also twohermal boundary layers adjoining the membrane and the heatransfer equations are as follows:

= NwHv + hmAlm(Tms − Tmt) (10)

= hsAs(Ts − Tms) = htAt(Tmt − Tt) (11)

here q is the heat flow rate, hs and ht the heat transfer coef-

cients in the boundary layers, hm the membrane heat transferoefficient, Ti the bulk temperature, Tmi the temperature at theembrane interface and Hv is the water latent heat of vapori-

ation. From Eqs. (10) and (11), an expression for the heat flow

3

p

brane Science 289 (2007) 249–257 251

ate as a function of the water molar flux through the mem-rane (Nw) and of the individual heat transfer coefficients, cane obtained:

= TbhmAlm + NwHv

1 + (hmAlm/Ashs) + (hmAlm/Atht)(12)

here Tb is the bulk temperature difference. In analogy toass transfer, the following equations will be used to describe

he boundary layer heat transfer coefficients in the tube and shellide, respectively:

ut = αtReβtt Pr

1/3t

(di

l

)1/3

(13)

us = αsReβss Pr1/3

s

(dh

l

)(14)

here Nu is the Nusselt number and Pr is the Prandtl number.

. Experimental

.1. Materials

The solutions were prepared with calcium chloride dihydratend sucrose pro-analysis grade (Riedel-deHaen, Germany), andeionised water. A hollow fibre membrane contactor with anffective internal area of 0.16 m2 was used. This contactorontains 400 polypropylene fibres (Accurel® PP Q3/2) with aominal pore size of 0.2 �m, 70% porosity, 20 cm long, internaliameter of 600 �m and a thickness of 200 �m. The tortuos-ty factor for this membrane can vary from 1.4 (τ = 1/ε) to 2.4τ = (2 − ε)2/ε) according to the most used tortuosity modelsvailable in the literature [10].

.2. Experimental set-up

The experimental set-up is presented in Fig. 2. The solutionsere pumped through the shell side of the module (water or

ucrose solution) and lumen of the fibres (calcium chloride dihy-rate solution), in a counter current mode, using magneticallyriven gear pumps (Ismatec, Switzerland). The temperature wasaintained constant at the inlet (T = 25 ± 0.1 ◦C) with two heat

xchangers, and was measured at the inlet and outlet with typethermocouples. In order to evaluate the water flux, the weight

oss of the water or sucrose solution reservoir, was acquiredver time using a technical balance (Sartorius BL3100, Ger-any) during 1 h. The volume of the salt solution used (6 l) was

igh enough to minimize the dilution effects during the experi-ents. The sucrose solution concentration was determined using

n Abbe refractometer, and, a water activity meter (Aqualaberies 3, Decagon Devices, USA) was used to measure the waterctivity of the solutions.

.3. Calculation methods

The fitting calculations were carried out using the softwareackage ScientistTM, from MicroMath®. The errors associated

252 V.D. Alves, I.M. Coelhoso / Journal of Membrane Science 289 (2007) 249–257

Fig. 2. Experimental set-up: (1) membrane contactor; (2) calcium chloride dihy-dp(

wd

4

4

cpcaTnfltfla

ttt2iRiFrs

u

Fd

epK

rac

cnitrit(Itused. However, with a sucrose concentration of 20% (w/w) themass transfer resistance in the boundary layers is negligible,since the water flux remains practically constant in the range of

rate solution reservoir; (3) water/sucrose solution reservoir; (4) balance; (5)ump; (6) heat exchanger; (7) computer; (8) flow meter; (9) pressure gauge;10) thermocouple.

ith the determined parameters were calculated within a confi-ence interval of 95%.

. Results and discussion

.1. Mass transfer correlations

The mass transfer resistance inside the fibres was studied byarrying out a set of experiments, in which deionised water wasumped through the shell of the membrane contactor to avoidoncentration polarization in that side of the membrane, andcalcium chloride dihydrate solution flowed inside the fibres.he water flux was measured maintaining constant the Reynoldsumber in the shell side (Re = 82.5), which corresponds to aow rate of 1680 ml/min and varying the Reynolds number of

he calcium chloride dihydrate solution (0.35 ≤ Re ≤ 41.9). Theow rate varied in this case from 23 to 1300 ml/min. The resultsre presented in Fig. 3.

As expected, the water flux increases with the increase ofhe calcium chloride dihydrate solution concentration, due tohe raise of the driving force. However, its value seems noto be affected by the Reynolds number, especially when the.8 and 3.5 M solutions were used. For these solutions theres a negligible concentration polarization for all the range ofeynolds number studied. Only with the 6 M solution a decrease

n the water flux was detected for Reynolds numbers below 7.5.rom these results, it can be concluded that the mass transfer

esistance in the fibres is easily minimized for the conditionstudied.

The overall mass transfer coefficient (K′P) was determined

sing Eq. (5) assuming negligible temperature polarization

Ftd

ig. 3. Water flux as a function of the Reynolds number in the fibres, for threeifferent CaCl2 solutions (shell side: deionised water, Res = 82.5).

ffects, i.e., P∗ws and P∗

wt were calculated using the bulk tem-erature. The results, represented in Fig. 4, show an increase of′P with the increase of the Reynolds number until a plateau is

eached, meaning that the mass transfer resistance in the bound-ry layers is negligible. The value of the plateau is certainly verylose to the membrane mass transfer coefficient.

A second set of experiments was carried out to study the con-entration polarization in the shell side. In this case, the Reynoldsumber of the calcium chloride dihydrate solution (3.5 M) flow-ng inside the fibres was maintained constant, at a value for whichhe mass transfer resistance is negligible (Ret = 57.1) and flowate of 1490 ml/min chosen taking into account the results shownn Fig. 4. In addition, a sucrose solution was pumped throughhe shell at different flow rates, ranging from 95 to 1490 ml/min0.7 ≤ Res ≤ 45.0). The results obtained are presented in Fig. 5.t can be observed that the water flux is highly dependent onhe Reynolds number when a 45% (w/w) sucrose solution is

ig. 4. Overall mass transfer coefficient for the experiments carried out varyinghe Reynolds number in the fibres, for three different CaCl2 solutions (shell side:eionised water, Res = 82.5).

V.D. Alves, I.M. Coelhoso / Journal of Membrane Science 289 (2007) 249–257 253

Fm

RK

htvs

wcmfWt

V

ic

Fts

Table 1Constants of the mass transfer correlations and the membrane mass transfercoefficient obtained

Parameter Value

αt 2.66 ± 0.27βt 0.25 ± 0.04αs 15.4 ± 0.5β

k

ricacs1rksamoott

9mtdα

[a

ig. 5. Water flux as a function of the Reynolds number in the shell side of theodule, for two different sucrose solutions (fibres: CaCl2 = 3.5 M, Ret = 57.1).

eynolds number studied. The overall mass transfer coefficient,′P, represented in Fig. 6, shows for this set of experiments a

igh dependence on the Reynolds number due to the high massransfer resistance of the shell side of the membrane, but thealue of the plateau is similar to the one obtained in the previouset (with a deviation of about 11%).

Taking into account the experimental conditions used, inhich either the water diffusion coefficient or the kinematic vis-

osity of the solutions varied between experiments, a single-stepethodology was applied in the determination of the mass trans-

er correlations [4,16], instead of using the method proposed byilson. By integration of Eq. (3), an expression for the water

ransported through the membrane over time (Vw) is obtained:

w = V0 + 1

(P∗ws/Asks) + (1/Almkmp) + (P∗

wt/Atkt)

× (asP∗ws − atP

∗wt)(t − t0) (15)

n which V0 and t0 represent the initial conditions. The modelomposed by Eqs. (1)–(15) was adjusted to the experimental

ig. 6. Overall mass transfer coefficient for the experiments carried out varyinghe Reynolds number in the shell side of the module, for two different sucroseolutions (fibres: CaCl2 = 3.5 M, Ret = 57.1).

ed

avcdri[β

fit(o

4b

b

s 0.92 ± 0.03

mp (10−10 m s−1 Pa−1) 2.84 ± 0.06

esults (water volume transferred over time of both sets of exper-ments), in order to evaluate the constants of the mass transferorrelations and the membrane mass transfer coefficient, insingle-step calculation. The values of the water diffusion

oefficients in calcium chloride dihydrate (3.9 × 10−10 m2

−1 ≤ Dw ≤ 1.3 × 10−9 m2 s−1) and sucrose solutions (7.1 ×0−10 m2 s−1 ≤ Dw ≤ 1.7 × 10−9 m2 s−1) used were thateferred in the literature [18,19], as well as the values of theinematic viscosity (1.62 × 10−6 m2 s−1 ≤ ν ≤ 7.2 × 10−6 m2

−1), specific heat (1690 J kg−1 K−1 ≤ cp ≤ 3700 J kg−1 K−1)nd thermal conductivity (0.494 W m−1 K−1 ≤ kT ≤ 0.559 W−1 K−1) of the calcium chloride dihydrate solutions [20] and

f the sucrose solutions [21,22]. It was observed a variationf the temperature and concentration of the solutions fromhe entrance to the exit of the module during the experiments;herefore, the average value was used in the calculations.

The parameter values and errors, for a confidence interval of5%, are presented in Table 1. The values of the constants deter-ined for the tube side mass transfer correlation are similar to

he majority referred in the literature for laminar flow in cylin-rical tubes, namely that presented by Leveque [13] in whicht = 1.62 and βt = 0.33 (Gz ≥ 25). Viegas et al. [16], Tong et al.23] and Cooney and Poufos [24] presented correlations withn exponent of the Reynolds number equal to 1; however, thosequations were obtained for a range of Graetz number (Gz ≤ 65)ifferent from that of this work (53 ≤ Gzt ≤ 580).

The shell side mass transfer correlation obtained is also ingreement with the literature. Viegas et al. [16] obtained thealues of αt = 8.71 and βt = 0.74 using a hollow fibre membraneontactor with a packing density of 30%, similar to the packingensity of the module used in this work (φ = 0.37), and for aange of Reynolds number (Re < 34) compatible with that stud-ed here (0.7 ≤ Res ≤ 45.0). In addition, Dahuron and Cussler14] correlated their data on protein extraction with αt = 8.8 andt = 1, for identical hydrodynamic conditions.

Regarding the value of the membrane mass transfer coef-cient obtained (kmp = 2.84 × 10−10 m s−1 Pa−1), it is similar

o that predicted by the Dusty-gas model using Eq. (6)kmp = 2.20 × 10−10 m s−1 Pa−1), considering the contributionf both molecular and Knudsen diffusion mechanisms.

.2. Water activity and temperature profiles in the

oundary layers

After the calculation of the parameters, the model composedy Eqs. (1)–(15) was used to estimate the water activity and

2 f Membrane Science 289 (2007) 249–257

tawca(vcecrRslsuTtss

ttteTttfsttte

fl

Fdfi

Ftd

4c

efttctTts

54 V.D. Alves, I.M. Coelhoso / Journal o

emperature profiles in the system. The ratio of the waterctivity at the bulk to the water activity at the interface (at/amt)as calculated for both sets of experiments. In the experiments

arried out varying the Reynolds number in the fibres (Fig. 3),t/amt was higher than 0.96 for the 2.8 M (at = 0.750) and 3.5 Mat = 0.635) calcium chloride dihydrate solution, confirming aery low mass transfer resistance. When the 6 M (at = 0.277)alcium chloride dihydrate solution was used, a higher differ-nce between amt and at was obtained (at/amt = 0.840). In thisase, the contribution of the tube side boundary layer to overallesistance varies from 10% (Ret = 13.6) up to 17% (Ret = 0.85).egarding the experiments in which the water flux was mea-

ured varying the Reynolds number in the shell (Fig. 5), theowest value of the ratio ams/as was 0.84 (45% (w/w) sucroseolution (as = 0.948) and Re = 0.7), which increased practicallyp to one when the 20% sucrose solution (as = 0.987) was used.he contribution of the shell side boundary layer resistance

o the overall resistance varies from 4%, achieved with 20%ucrose solution, to 50% for the lowest Reynolds numbertudied (Res = 0.7) and the 45% sucrose solution.

Concerning the temperature profile, the calculations revealedhat, in both sets of experiments, the temperature gradient inhe boundary layers is not significant. In Fig. 7 is representedhe temperature profile for the experiment in which the high-st temperature gradient was observed in the boundary layers.he values presented in Fig. 7 are the arithmetic mean of the

emperatures at the inlet and outlet of the module. However,he temperature difference created between the membrane inter-aces (Tm) reached almost 3 ◦C when using the 6 M CaCl2olution (Fig. 8). The increase of Tm from 2.5 to 3 ◦C is dueo an increase of the water flux (see Fig. 3). Beyond that value,he water flux does not change significantly with the increase ofhe Reynolds number, which causes a decrease of T . For the

mxperiments varying the Reynolds number in the shell side, theTm estimated is always below 1 ◦C (Fig. 9), due to the loweruxes obtained (Fig. 5).

ig. 7. Temperature profile of the experiment with the highest temperature gra-ient observed in the boundary layers (shell side: deionised water Res = 82.5,bres: CaCl2 = 6 M, Ret = 0.85).

im

Ftt

ig. 8. Temperature difference created between both membrane interfaces forhe experiments carried out varying the Reynolds number in the fibres, for threeifferent CaCl2 solutions (shell side: deionised water, Res = 82.5).

.3. Prediction of water fluxes for different experimentalonditions

The model can also be used to predict the water flux forxperimental conditions different from that studied. However,or those conditions, even though the temperature of the solu-ions can be specified at the inlet of the shell and fibres, theemperature at the outlet is not known. That value is needed toalculate the bulk temperature in each side of the membrane,aken as the average between the inlet and the outlet values.he outlet temperatures can be calculated taking into account

hat the heat released by the solution circulating in the shellide of the module, and that received by the solution circulatingn the fibres, is equal to the overall heat transferred across the

embrane:

mscps(Tins − T out

s ) = mtcpt(Toutt − T in

t )

= nwHv − hm(Tmt − Tms) (16)

ig. 9. Temperature difference created between both membrane interfaces forhe experiments carried out varying the Reynolds number in the shell side, forwo different sucrose solutions (fibres: CaCl2 = 3.5 M, Ret = 57.1).

f Membrane Science 289 (2007) 249–257 255

wrb

T

T

caa

T

T

ahtcsaflcawcsautRa

FiR

FsC

IfloeRFFndbhum

V.D. Alves, I.M. Coelhoso / Journal o

here m is the mass flow rate and the superscripts in and outefer to the inlet and outlet, respectively. The equation above cane expressed as a function of T out

s and T outt :

outs = T in

s − nwHv − hm(Tmt − Tms)

mscps(17)

outt = T in

t + nwHv − hm(Tmt − Tms)

mtcps(18)

The temperature values at the membrane interface can bealculated using Eqs. (10) and (11). However, since the temper-ture gradient in the boundary layers can be neglected, it can bessumed that Tms ≈ Ts and Tmt ≈ Tt leading to

ms = 1

2(T in

s + T outs ) (19)

mt = 1

2(T in

t + T outt ) (20)

In order to predict the water flux, an iterative method waspplied due to the interdependence between the water flux andeat transfer. An initial water flux was assumed, followed byhe estimation of the interface temperatures, which allowed thealculation of a new value of the water flux. The process wastopped when the deviation between the calculated water fluxnd the initial water flux was less than 0.1%. In Fig. 10 the waterux predictions are presented for experiments where water is cir-ulating in the shell side of the membrane contactor (Res = 82.5)nd the Reynolds number in the fibres is varied using solutionsith different concentrations of CaCl2. An operation in a counter

urrent mode was considered with an inlet temperature of botholutions equal to 25 ◦C. The experimental results, presentedlready in Fig. 3, are also shown. It can be concluded that,

sing a calcium chloride dihydrate solution with a concentra-ion up to 6 M, the mass transfer resistance can be neglected foreynolds numbers above 20, since the water flux estimated islways constant above that value.

ig. 10. Prediction of the water flux as a function of the Reynolds numbern the fibres (lines) for different CaCl2 solutions (shell side: deionised water,es = 82.5). Symbols—experimental results of Fig. 3.

atft

4cs

eatt(ctfle

wtt

ig. 11. Prediction of the water flux as a function of the Reynolds number in thehell side of the module (lines), using a 45% sucrose solution (fibres: differentaCl2 solutions, Ret = 20.) Symbols—experimental results of Fig. 5.

A similar set of predictions was carried out for the shell side.n this case a 45% (w/w) sucrose solution was considered toow in the shell side of the module and different solutionsf CaCl2 in the fibres. Maintaining constant the flow rate forach CaCl2 solution, the water flux was calculated varying theeynolds number in the shell. The results are presented inig. 11, along with the experimental results shown already inig. 5. As expected, the water flux increases as the Reynoldsumber becomes higher, reaching a different plateau for eachriving force applied. However, as the water activity differenceetween the two solutions increases, the plateau is reached atigher Reynolds numbers. Since the same sucrose solution issed in the shell side of the module, the respective boundary layerass transfer coefficient is equal at a given Reynolds number, for

ll driving forces used. In this way, the higher water fluxes leado a larger difference between the bulk and the membrane inter-ace water activity, according to Eq. (2), which is more difficulto cancel.

.4. Simulation of the water flux and overall mass transferoefficient for the concentration process of a sucroseolution

The best hydrodynamic conditions were then used in anxperiment for the concentration of a sucrose solution, taken asmodel fruit juice. This experiment was carried out circulating

he sucrose solution in the shell side of the membrane contac-or (Reinitial = 47) and a CaCl2 solution (C = 5 M) in the fibresRet = 19). The concentration of the salt solution was maintainedonstant by adding calcium chloride dihydrate in order to main-ain the driving force constant during the experiment. The waterux and the sucrose concentration were measured during thexperiment, and the results are presented in Fig. 12.

It can be seen that a final concentration of about 60% (w/w)as achieved. The water flux was practically constant during

he first part of the experiment, decreasing only at the end, dueo the effect of the sucrose solution viscosity, which increased

256 V.D. Alves, I.M. Coelhoso / Journal of Mem

Ftfi

sflurcataetrtptl

tl

FacR

Ectwifiib

5

ocadp

fiwts

mtfisAwmw

ig. 12. Water flux and sucrose concentration over time, during the concentra-ion process of a sucrose solution (shell side: sucrose solution, initial Res = 47,bres: CaCl2 = 5 M, Ret = 19).

ignificantly for concentrations above 47% (w/w). The waterux and the overall mass transfer coefficient were predictedsing the mass transfer correlations obtained, and the seriesesistance model previously presented. These predictions werearried out for the period of the experiment where the Reynoldsnd the Schmidt numbers were in the range for which the massransfer correlations were obtained. The calculated water fluxnd overall mass transfer coefficient are in agreement with thexperimental results (Fig. 13). In addition, the overall massransfer coefficient predicted (K′

P = 2.57 × 10−10 ms−1 Pa−1)emained constant throughout almost all the experiment and nearhe value of the membrane mass transfer coefficient calculatedreviously (kmp = 2.84 × 10−10 m s−1 Pa−1), confirming thathe mass transfer resistance in both boundary layers was quiteow.

Using the water flux obtained experimentally, and neglectinghe mass transfer resistance in the fibres, the shell side boundaryayer resistance was calculated during all the experiment, with

ig. 13. Experimental water flux and overall mass transfer coefficient (symbols),nd the values predicted using the mass transfer correlations (lines), for theoncentration process of a sucrose solution (shell side: sucrose solution, initiales = 47, fibres: CaCl2 = 5 M, Ret = 19).

(dsoooao

tcw

A

tMamara

brane Science 289 (2007) 249–257

qs. (1)–(5). It was noticed that, in the last hour of operation, itsontribution to the overall resistance increased from 13.5% whenhe sucrose concentration was 47% (w/w), up to 50% at the endhen a 61% (w/w) sucrose concentration was achieved. This fact

s due to the raise of the sucrose solution viscosity (μ = 9.4 mPa sor C = 47%, w/w and μ = 54.1 mPa s for C = 61%, w/w). Thencrease of the viscosity led to a decrease of the Reynolds numbern the shell side of the module, and the hydrodynamic conditionsecame less favourable.

. Conclusions

The resistance to mass and heat transfer in the osmotic evap-ration process was studied using a hollow fibre membraneontactor. In addition, the mass transfer correlations for the shellnd tube sides were obtained, which are in agreement with thoseetermined in the liquid–liquid extraction and gas absorptionrocesses.

It was observed that the boundary layer resistance in thebres was easily minimized, even when high driving forcesere applied. Regarding the shell side boundary layer mass

ransfer resistance, it can be significant when processing sucroseolutions with concentrations of 45% (w/w) and above.

Heat transfer correlations were obtained by analogy withass transfer. Using a model, which combines the heat and mass

ransfer equations, was possible to estimate the temperature pro-le created in the system, due to the water evaporation in oneide of the membrane followed by condensation in the other side.lthough the temperature gradient through the boundary layersas negligible, the temperature difference created between theembrane interfaces can be significant (it reached almost 3 ◦Chen using the 6 M CaCl2 solution).The concentration process of a sucrose solution, from 12%

w/w) up to 60% (w/w), was also studied. The flux slowlyecreased during the first 7 h of the experiment and then, aharp decrease was observed in the last hour, due to the effectf increasing viscosity of the sucrose solution. Thus, it wasbserved a negligible concentration polarization in both sidesf the membrane during almost all the experiment. A consider-ble mass transfer resistance in the shell side of the module wasnly detected for sucrose concentrations above 47% (w/w).

The mass and heat transfer model was also used to calculatehe water flux and the overall mass transfer coefficient during theoncentration process. The values predicted were in agreementith the experimental results.

cknowledgements

The authors acknowledge Prof. Alberto Sereno, FEUP, Por-ugal, for his support on the water activity measurements, Dr

ario Eusebio, FCT/UNL, for the data acquisition software,nd Balasz Koroknai for his collaboration in some of the experi-

ents performed during his stay in the Biochemical Engineering

nd Process Group at FCT/UNL. V.D. Alves acknowledges theesearch grant PRAXIS XXI/BD/18300/98 from Fundacao paraCiencia e a Tecnologia.

V.D. Alves, I.M. Coelhoso / Journal of Mem

Nomenclature

a water activity (dimensionless)A membrane area (m2)cp specific heat (J mol−1 K−1)Dw water diffusion coefficient in the aqueous solu-

tions (m2 s−1)dp membrane pore diameter (m)Hv water latent heat of vaporisation (J mol−1)h heat transfer coefficient (W m−2 K−1)Jw water flux (m3 m−2 s−1)Kp overall mass transfer coefficient (m s−1)k individual mass transfer coefficient (m s−1)kmp membrane mass transfer coefficient (m s−1 Pa−1)Mw water molar mass (kg mol−1)m mass flow rate (kg s−1)Nu Nusselt number (dimensionless)Nw water flux (mol m−2 s−1)P total pressure (Pa)pw partial pressure (Pa)Pr Prandtl number (dimensionless)P∗

w pure water vapour pressure (Pa)q heat flow rate (W)R gas constant (J K−1 mol−1)Re Reynolds number (dimensionless)Sc Schmidt number (dimensionless)Sh Sherwood number (dimensionless)T temperature (K)Vw water volume (m3)

Greek symbolsα constant (dimensionless)β constant (dimensionless)δ membrane thickness (m)ε membrane porosity (dimensionless)μ absolute viscosity (N s m−2)ν kinematic viscosity (m2/s)τ membrane tortuosity (dimensionless)

Subscriptsm membranes shell

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[F. Nakashio, T. Hano, Extractive recovery of lactic acid with hollow fiber

t fibreslm logarithmic mean

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