Effect of Salt Type on Mass Transfer in Reverse Osmosis Thin Film

Desalination 168 (2004) 383–390

0011-9164/04/$– See front matter © 2004 Elsevier B.V. All rights reserved

Presented at the EuroMed 2004 conference on Desalination Strategies in South Mediterranean Countries: Cooperationbetween Mediterranean Countries of Europe and the Southern Rim of the Mediterranean. Sponsored by the EuropeanDesalination Society and Office National de l’Eau Potable, Marrakech, Morocco, 30 May–2 June, 2004.

*Corresponding author.

Effect of salt type on mass transfer in reverse osmosis thin filmcomposite membranes

M. Khayet*, J.I. MengualDepartment of Applied Physics I, Faculty of Physics, University Complutense of Madrid

Av. Complutense s/n, 28040, Madrid, SpainTel./Fax +34 (91) 3945191; email: [email protected]

Received 30 January 2003; accepted 12 February 2004

Abstract

Reverse osmosis separation of inorganic salts in aqueous solutions has been studied using polyamide thin filmcomposite membrane, in spiral wound configuration. Various inorganic salts involving monovalent and divalentions have been studied. The solute transport through the membrane and the mass transfer coefficient at the highpressure feed side of the spiral wound module were determined for each type of salt. The mass transfer coefficientof each inorganic salt was predicted from the experimental data for the reverse osmosis separation of sodiumchloride as reference and the mass transfer empirical correlations. The values obtained were compared with theexperimental ones. The free energy parameters for monovalent cations, monovalent anions and divalent cationshave been calculated. These parameters were used to predict the reverse osmosis performance of inorganic salts inspiral wound reverse osmosis module. It was observed that the free energy values of the cations are negative whilethose of the anions are positive, suggesting that the surface of the membrane used is positively charged.

Keywords: Reverse osmosis; Inorganic salts; Desalination; Thin film composite membranes; Spiral wound module

1. Introduction

Aromatic polyamide membranes constituteone of the successful membranes developed for

desalination, while spiral wound modules arewidely used for commercial applications, rangingfrom reverse osmosis (RO) to ultrafiltration (UF).Therefore, the knowledge of the transport charac-teristics of such membranes and the predictability

384 M. Khayet and J.I. Mengual / Desalination 168 (2004) 383–390

of their mass transfer coefficient in spiral woundmodules are of practical interest.

In RO processes, preferential sorption at mem-brane–solution interface is one of the factorsgoverning solute separation. It is a function of themembrane material, solute and solvent inter-actions together with the experimental conditions.These interactions arise in general from the ionic,steric, polar, and/or non-polar character of eachone of the above three components of the systeminvolved. In fact, RO separations of inorganic saltsin aqueous solutions have been discussed fromdifferent points of view, including partitioncoefficient of solute between membrane and liquidphases, enthalpy of hydration of ions in the bulkphase solution, partial molar free energy ofhydration and entropy of ions in the bulk phasesolution, or relative free energy parameters forions and solutes [1]. The latter approach wasapplied in this study using various inorganic salttypes involving monovalent cations, monovalentanions and divalent cations.

On the other hand, it is well known that theRO transmembrane water flux leads to the appear-ance of the concentration polarization phenomenoneven when the separation of the solute from thesolvent is not perfect [2]. The solute concentrationat the membrane surface becomes higher than thatin the bulk phase. Most of the models used incharacterization of RO membranes make use ofmass transfer correlations in order to calculate thesolute concentration at the membrane surface [2].The most used correlations are those based on theChilton-Colburn and Deissler analogies betweenheat and mass transfer. In this study, the masstransfer coefficient in the feed side of spiral woundmodule, k, and the solute transport throughpolyamide thin film composite membrane (DK/δ) were evaluated based on RO transport equations[3]. The obtained value of k, for each inorganicsalt, was compared with the predicted one basedon the mass transfer empirical correlations [1,4].

The concept of free energy parameter govern-ing RO separations of ionic solutes in aqueous

solutes was established earlier and has been dis-cussed extensively with respect to inorganic ororganic solutes [4]. The approach is based on amodified form of the Born expression for freeenergy of ion-solvent interaction to both the bulksolution phase and the membrane-solutioninterface where water is preferentially sorbed. Theutility of the free energy of ions for predictingsolute separations in RO was illustrated withparticular reference to cellulose acetate mem-branes [4]. The object of this part of the work wasto obtain data on free energy for differentmonovalent and divalent ions in aqueous solutionswith respect to polyamide thin film compositemembrane used in spiral wound configuration andto compare such data with the corresponding onesapplicable for cellulose acetate and polyamidemembranes reported earlier [4–6]. The theoreticalapproach developed by Matsuura et al. [1,4], basedon free energy parameter, is applied in this studyto predict the RO solute separation of polyamidethin film composite membrane arranged in spiralwound module for inorganic salts in aqueoussolutions.

2. Experimental

The experimental study was carried out usinga pilot plant ROI-2 provided by Osmonics [7]. Astainless steel spiral wound module S2521(Osmonics), containing polyamide thin filmcomposite membrane, was employed in this study.The effective membrane area of the membranemodule was 1.2 m2.

The inorganic solutes used are listed in Table 1,along with some relevant physiochemical data.In this study, prior to each salt aqueous solutiontest, the membrane module was initially subjectedfor pure water experiment to measure the purewater membrane permeability. All the experimentswere conducted at fixed feed flow rate of about(171 kg/h), feed pressure of 1378.9 kPa and feedtemperature of approximately 22ºC. The soluteconcentrations used were in the range of 0.09–

M. Khayet and J.I. Mengual / Desalination 168 (2004) 383–390 385

Table 1List of solutes used with some physicochemical and experimental dataa

aA ≈ 8.88×10–12 m/sPa; bCalculated from Eq. (8); cCalculated from Eq. (6).

Solute DS (10–11 m2/s)

Product flow rate (10–6 m/s)

f (%)

k (10–5 m/s)b

DK/δ (10–8m/s)c

Σ(∆∆G/RT)i

LiCl 136.67 7.72 99.17 3.92 5.32 –0.624 NaCl 161.10 7.95 98.70 4.25 8.71 –0.130 KCl 199.48 7.66 98.23 4.77 11.77 0.171 NaBr 162.63 7.89 98.20 4.17 11.96 0.187 NaI 161.59 7.66 97.55 4.29 16.14 0.487 LiBr 137.77 7.76 98.81 3.86 7.65 –0.3068 KBr 162.63 8.06 97.50 4.20 17.08 0.4877 MgCl2 125.02 5.98 99.76 3.66 1.21 –2.067 MnCl2 125.62 6.18 99.47 3.78 1.18 –1.137 CaCl2 133.55 6.42 98.67 3.80 1.18 –0.274 MgBr2 126.25 5.76 99.58 3.64 2.08 –1.4338

0.1 mol/l. The solute concentrations in the feedand product solutions were measured with a con-ductivimeter 712 ΩMetrohm and a 692 pH/Iono-meter ΩMetrohm with the corresponding ionselective electrode. In each experiment, the soluteseparation f, was calculated using the followingequation:

Solute conc. in feed Solute conc. in productSolute conc. in feed

f −= (1)

3. Theoretical approach

The following basic equations for RO transporthave been derived and discussed extensively withrespect to single solute aqueous solution systemsfor the case where water is preferentially sorbedat the membrane–solution interface [1]. Thesolvent flux is given as:

( ) ( )2 3 2 3sJ A P P= ⎡ − − π − π ⎤⎣ ⎦ (2)

where A is the pure water permeability constant,(P2 – P3) is the transmembrane hydrostatic pressuredifference, π2 and π3 are the osmotic pressures ofthe feed and the permeate solutions at the mem-brane surface, respectively. When the feed liquid

is pure water, both π2 and π3 are zero, and therefore

( )2 3sJ A P P= − (3)

The solute permeation flux, Jd, is written as:

( )2 2 3 3dDKJ c X c X= −δ

(4)

(DK/δ) is called the solute transport parameter,the quantity K is the equilibrium constant inde-pendent of salt concentration, X2 is the solute molefraction of the feed solution at the membranesurface, X3 is the solute mole fraction of permeatesolution, c2 and c3 are the total molar concentrationincluding solute and solvent in feed and permeate,respectively.

By using Eq. (4) and the following relation:

3d

d s

JXJ J

=+ (5)

the solute transport parameter can be calculatedas:

( ) 132 2 3 3

31sXDK J c X c X

X−= −

δ − (6)


The equation for the concentration polarizationis given by the film model [1,2]:

2 3

1 3 1

ln d sX X J JX X kc

⎡ ⎤− +=⎢ ⎥−⎣ ⎦(7)

where k is the mass transfer coefficient at the feedside of the membrane module.

Eq. (7) can be solved for k parameter, assuminga constant total molar concentration c = c1 = c2 = c3.

( )1 3

3 2 3

ln1

sJ X Xkc X X X

⎛ ⎞−= ⎜ ⎟− −⎝ ⎠(8)

On the other hand, the mass transfer coefficientused in the concentration polarization equation[Eq. (7)] may be obtained from Sherwood corre-lation [2]

Sh Re Scβ γ= α (9)

where Sh, Re and Sc are the Sherwood, Reynoldsand Schmidt numbers, respectively and α, β andγ are characteristic constants, which depend onthe hydrodynamic conditions of each system. Forspiral wound modules, the following correlationhas been reported in [1].

1/ 2

1/ 2 1/3Sh 1.065 Re Sc2

f sp

sp sp

hL

⎛ ⎞η= ⎜ ⎟⎜ ⎟− η⎝ ⎠

(10)

where hf is the thickness of feed flow channel, ηspand Lsp are the mixing efficiency of spacer andthe spacer mesh width, respectively.

According to the above correlation, at a givenReynolds number, the quantity (Sh/Sc1/3) is a con-stant. Matsuura et al. [4], based on Eqs. (9) and(10), stated that when k for NaCl is known, k forother solutes in dilute solutions can be obtainedfrom the following relation:

2 / 3

NaCl,NaCl

S

S

Dk kD

⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠(11)

where DS and DS,NaCl represent the diffusivities ofthe solute under consideration and sodiumchloride solute in water, respectively.

The concept of free energy parameter govern-ing RO separations of ionic solutes in aqueoussolutions has been discussed previously [1,4]. Thefollowing relationships have been derived byMatsuura et al. [4] to calculate the free energyparameter of ions:

, ,

1

m i B i

i

m B

i m i B

G GGRT RT

E ERT r r

∆ − ∆∆∆⎛ ⎞− =⎜ ⎟⎝ ⎠

⎧ ⎫⎛ ⎞ ⎛ ⎞− ⎪ ⎪= −⎨ ⎬⎜ ⎟ ⎜ ⎟+ ∆ + ∆⎪ ⎪⎝ ⎠ ⎝ ⎠⎩ ⎭

(12)

where ∆G represents the free energy of solute–solvent interaction (i.e. the free energy of hyd-ration of solute in the present study), R is the gasconstant, T is the absolute temperature, the sub-scripts m and B the membrane solution interfaceand the bulk solution phase, respectively; thesubscript i refers to the particular ion under con-sideration and E is defined as:

( )20 11

2i

s

z eE N

⎛ ⎞= −⎜ ⎟ε⎝ ⎠

(13)

where N is the Avogadro number, zi is the valenceof the ion, e0 is the electronic charge, ri is the radiusof the ion and εs is the dielectric constant of solvent.

The free energy parameter is a function of thechemical nature of the solute, solvent, and mem-brane material. With respect to completely ionizedinorganic solutes in water, it has been shown thatthe solute transport parameter is related to the freeenergy parameter for the ions by the expression:

* exp cc a

DK G GC nRT RT

⎧ ⎫∆∆ ∆∆⎛ ⎞ ⎛ ⎞= +⎨ ⎬⎜ ⎟ ⎜ ⎟δ ⎝ ⎠ ⎝ ⎠⎩ ⎭(14)

where nc and na represent the number of moles ofcations and anions, respectively and C* dependsonly on the morphological structure of the membrane


and is independent of the nature of solute. If thefree energy parameters of the ions Na+ and Cl–

are known, the value of C* can be calculated fromEq. (13) using experimental data on solute trans-port parameter.

The calculated values of the solute transportparameter and the mass transfer coefficient in thefeed side of the membrane module for each solutemay then be used to obtain the solute separation,f, using the following expression [4]:

11 expd s d sJ J J JDK fS f Sk

−+ +− ⎡ ⎤= ⎢ ⎥δ ⎣ ⎦(15)

where S is the effective membrane area.

4. Results and discussion

The concentration of the solute at the mem-brane surface was calculated from Eqs. (1)–(3).Then, the mass transfer coefficient, k, wasevaluated from Eq. (8). The obtained valuestogether with the data involved in the calculationsare summarized in Table 1. The mass transfercoefficient is, in general, higher for the inorganicsalt having higher diffusion coefficient. Fig. 1shows the k values obtained as functions of the

y = 0.2658x0.5444

R2 = 0.9733

3.0

3.5

4.0

4.5

5.0

100 120 140 160 180 200 220

D s (10-11 m2/s)

k (

10-5

m/s

)

Eq. (8)

Eq. (11)

Fig. 1. Mass transfer coefficients calculated from Eqs. (8)and (9) vs. diffusion coefficient of the inorganic salts.The solid curve refers to the fitting of the k values obtainedfrom Eq. (8).

solute diffusivities. The pairs of values (k, DS)were fitted to a potential function by the leastsquares method. From Eq. (11), k was calculatedtaking sodium chloride as reference solute. Theresults are also presented in Fig. 1. The agreementbetween the mass transfer coefficients calculatedby Eq. (8) and Eq. (11) may be considered good(i.e. the discrepancy is less than 4.9%). However,for spiral wound modules the applicability of theempirical mass transfer correlations is notrecommended as both the membrane type and thespacer used in the high-pressure side of the mem-brane module may cause large errors.

The solute transport parameter (DK/δ) wascalculated from Eq. (6). The results are also shownin Table 1. It can be observed that the solutetransport parameters of the salt involving divalentions are lower than those of the monovalent ions.Ghiu et al. [6] studied the importance of para-meters like ionic size, ionic hydrated size, diffus-ivity in solution, enthalpy and entropy of hydrationon salt permeation. It was reported that thecrystallographic radii cannot explain the order ofsalt type permeation and the hydrated radii mustbe considered instead of the crystallographic radii.In fact, the enthalpy of hydration (∆H) as well asthe entropy of hydration (∆S) represent moreprecise quantification of the degree of hydration.Both thermodynamic parameters ∆H and ∆S areintegrated in the bulk Gibbs free energy (∆G).Furthermore, the interaction ion-solvent must betaken not only in the bulk feed solution but alsoat the membrane surface. All these observationswere considered by the free energy parameterdefined in Eq. (12).

In this study, values of EB, ∆B, Em and ∆m weredetermined as stated earlier in [4]. The calculatedvalues of EB and ∆B were respectively182.0 kcal Å/mol and 0.86 Å for monovalentcations, 120.5 kcal Å/mol and –0.20 Å for mono-valent anions and 746.3 kcal Å/mol and 1.03 Å fordivalent cations. Em and ∆m were 181.8 kcal Å/moland 0.90 Å for monovalent cations,126.6 kcal Å/mol and –0.13 for monovalent anions


and 750.5 kcal Å/mol and 1.05 Å for divalentcations, respectively. These data were used tocalculate the free energy of solute-solventinteraction ∆G at the membrane solution interfaceand at the bulk solution phase of ionic solutes,together with the free energy parameter of eachion type. The results are shown in Table 2.

Using the experimental data (DK/δ) for NaClgiven in Table 1 and the data on (–∆∆G/RT)i forNa+ and Cl– ions given in Table 2, the value of C*

was calculated from Eq. (14). A value of9.92×10–8 m/s was obtained. It can be observedthat the quantity (∆∆G/RT)i is negative for allcations and positive for all anions. This indicatesthat the anion is attracted and the cation is repelledby the membrane surface which means that themembrane surface is positively charged and henceit acts as an acid (proton donor). This resultconfirms the observation made earlier forpolyamide material [5,6]. In contrast, an oppositesign of (∆∆G/RT)i was observed for celluloseacetate membranes used in RO [4]. Furthermore,it was found that the values of the ionic parameterfor divalent cations are lower than those for themonovalent cations. This results in lower valuesfor (DK/δ) and hence higher values for soluteseparations with respect to solutes involving

Table 2Free energy parameters for some monovalent cations, monovalent anions and divalent cations

Ions Ionic radius (Å)

∆GB,i (kcal/mol)

∆Gm,i (kcal/mol)

∆∆G (kcal/mol)

(∆∆G/RT)i

Monovalent cations Li+ 0.60 –123.5 –121.2 0.907 –1.5463 Na+ 0.95 –98.3 –98.3 0.617 –1.0527 K+ 1.33 –80.8 –81.5 0.441 –0.7518 Monovalent anions Cl– 1.81 –75.8 –75.4 –0.541 0.9228 Br– 1.95 –72.5 –69.6 –0.727 1.2395 I– 2.16 –61.4 –62.4 –0.903 1.5396 Divalent cations Mg++ 0.65 –455.5 –441.9 2.295 –3.9129 Mn++ 0.80 –370.1 –406.1 1.749 –2.9827 Ca++ 0.99 –380.8 –368.2 1.243 –2.1195

divalent cations. Also, Table 2 shows that thevalues of (∆∆G/RT)i for the halide anions increasewith the increase in ionic radius. This means thatwith respect to solutes involving halide anions,(DK/δ) increases, and hence solute separationdecreases, with the increase of the ionic radius(Table 1).

Fig. 2 shows the plot of ln(DK/δ) as functionof Σ(∆∆G/RT)i. A straight line can be plottedbetween the two parameters which indicates thatthe procedure used can be applied also for spiralwound configuration. It must be mentioned here

Fig. 2. Correlation of ln(DK/δ) vs. Σ(∆∆G/RT)i.

y = 1.0496x - 16.126

R2 = 0.9971

-18.5

-18

-17.5

-17

-16.5

-16

-15.5

-15

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Σ(∆∆G /RT )i

ln (D

K/ δ

)


that, for a given membrane, a lower value forΣ(∆∆G/RT)i may result in a lower value for (DK/δ)and better solute separation can be obtained.

In addition, by using the value of C* and thedata on (–∆∆G/RT)i for different ions given inTable 2, the values of (DK/δ) for the differentinorganic solutes were calculated from Eq. (14).The results are presented in Fig. 3 as a functionof the previously obtained values determined fromEq. (6). Good agreement can be observed betweenboth values, which indicates that the procedureused is adequate.

The values of (DK/δ) calculated from Eq. (14)were used to obtain data on solute separation, f,using Eq. (15) and the applicable value of masstransfer coefficient, k, on the high-pressure sideof the membrane obtained from the straight line

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16

DK /δ (10-8 m/s) from Eq. (6)

DK

/ δ (

10-8

m/s

) fro

m E

q. (1

4)

Monovalent cations

Monovalent anions

Divalent cations

97

97.5

98

98.5

99

99.5

100

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Σ(∆∆G /RT )i

f (%

)

Experimental

Predicted

Fig. 3. Comparison of the calculated solutetransport parameters from Eq. (14) and theones calculated from Eq. (6).

Fig. 4. Theoretical and experimental soluteseparation vs. Σ(∆∆G/RT)i . The solid curverefers to the predicted values.

in Fig. 1. Fig. 4 shows the variation of both theexperimental and the calculated solute separationwith the algebraic sum Σ(∆∆G/RT)i. The predictedsolute separation (solid line) did not differsignificantly from the experimental one. Thehighest difference in data on solute separationswas within 0.2% for CaCl2. The agreement betweenthe calculated and experimental results confirmsthe practical validity of the prediction techniqueand the numerical values of the free energy usedin this study.

5. Conclusions

The transport of various inorganic salts inaqueous solutions through polyamide thin filmcomposite membrane in spiral wound


configuration has been studied using reverseosmosis process. The mass transfer coefficient ofeach inorganic salt at the high pressure feed sideof the spiral wound module was determined bymeans of two methods and little discrepancybetween them was detected. In general, it wasfound that the mass transfer coefficient is higherfor the inorganic salt having higher diffusioncoefficient.

It was also observed that the solute transportparameter of the salt involving divalent ions islower than that of the monovalent ions. The freeenergy parameters for monovalent cations,monovalent anions and divalent cations have beencalculated and the obtained values were employedto predict the reverse osmosis performance of eachinorganic salt. The free energy values of thecations are negative while those of the anions arepositive, suggesting that the surface of thin filmcomposite membrane used in this study ispositively charged. Good agreement between thepredicted reverse osmosis solute separation andthe experimental one was obtained.

Acknowledgement

The authors of this work gratefully acknow-ledge the financial support of the “Comunidad deMadrid” through its project Nº 07M/0059/2002.

References[1] T. Matsuura, Synthetic Membranes and Membrane

Separation Processes, CRC Press, Boca Raton, 1994.[2] V. Gekas and B. Hallström, Mass transfer in the

membrane concentration polarization layer underturbulent cross flow. I. Critical literature review andadaptation of existing Sherwood correlations tomembrane operations, J. Membr. Sci., 30 (1987)153–170.

[3] S. Sourirajan, Reverse Osmosis, Academic Press,London, 1970.

[4] T. Matsuura, L. Pageau and S. Sourirajan, Reverseosmosis separation of inorganic solutes in aqueoussolutions using porous cellulose acetate membranes,J. Appl. Polym. Sci., 19 (1975) 179–198.

[5] J.M. Dickson, T. Matsuura, P. Blais and S.Sourirajan, Reverse osmosis separations of someorganic and inorganic solutes in aqueous solutionsusing aromatic polyamide membranes, J. Appl.Polym. Sci., 19 (1975) 801–819.

[6] S.M.S. Ghiu, R.P. Carnahan and M. Barger, Masstransfer in RO TFC membranes — dependence onthe salt physical and thermodynamic parameters,Desalination, 157 (2003) 385–393.

[7] http://www.gewater.com/equipment/membraneequip/41_E2_Series.jsp

Documents

Effect of Salt Type on Mass Transfer in Reverse Osmosis Thin Film