Pervaporation of volatile organics from water: II. Influence of permeate pressure on partial fluxes

Journal of Membrane Science 186 (2001) 239–247

Pervaporation of volatile organics from waterII. Influence of permeate pressure on partial fluxes

Jenny Olsson∗, Gun Trägårdh, Christian TrägårdhDepartment of Food Engineering, Lund University, P.O. Box 124, SE-22100 Lund, Sweden

Accepted 4 December 2000

Abstract

Hydrophobic pervaporation is being developed within the area of separation of volatile organic compounds from diluteaqueous solutions. Optimisation of the pervaporation process for these types of applications is often very complex due tothe many different organic compounds which are to be separated simultaneously. The permeate pressure is one of the keyprocess parameters that has a considerable impact on both selectivities and partial fluxes. In this study, a model for predictingthe permeate pressure dependence of the partial fluxes of the organic compounds to be separated was developed. The modelincludes both the effect of external mass transfer and the effect of altered permeabilities due to membrane plasticisation forthe various permeants. Both these effects were proved to effect the partial fluxes to a significant extent. The model was shownto be applicable to organic permeants within the groups of alcohols, esters and aldehydes. Adequate information about themembrane separation factor and the overall separation factor together with the total flux at one specific permeate pressure isall that is needed for the application of this model. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: Hydrophobic pervaporation; Modelling; Permeate pressure; Concentration polarisation; Permeability

1. Introduction

Hydrophobic pervaporation is a membrane tech-nique used for the separation of either organic/wateror organic/organic liquid mixtures by means of par-tial vaporisation across a homogeneous permselectivemembrane. The permeate is then obtained as a liquidfollowing condensation. Hydrophobic pervaporationis being developed for applications related to wastewater treatment, industrial solvent recovery, aroma re-covery and the separation of products/inhibitors fromfermentation broths. In common for most of these

∗ Corresponding author. Tel.: +46-46-222-98-20;fax: +46-46-222-46-22.E-mail address: [email protected] (J. Olsson).

applications is the separation of volatile organic com-pounds from dilute aqueous solutions.

In order to optimise the pervaporation process, mod-els are required that can predict the influence of theprocess parameters on the performance of the process,expressed in terms of fluxes and separation factors.The key process parameters are the feed temperature,the feed crossflow velocity and the permeate pres-sure. In an earlier study by Olsson and Trägårdh [1],a model was developed which predicts the influenceof permeate pressure on the overall separation factorsof the pervaporation process for a system separatingvolatile organic compounds from a dilute aqueous so-lution. The model includes the effect of concentrationpolarisation from the bulk of the feed to the membranesurface, and its variation with permeate pressure. In

0376-7388/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S0 3 7 6 -7 3 88 (00 )00682 -7

240 J. Olsson et al. / Journal of Membrane Science 186 (2001) 239–247

Nomenclature

a activityc volume concentrationDAB diffusivity of a single particle A through

a stationary medium B (m2/s)D diffusion coefficient (m2/s)D mean or apparent diffusion coefficient

(m2/s)–D diffusion coefficient of the feed solution

(m2/s)F force (N)H Henry law coefficient (Pa)JV volume flux (m/s)JM molar flux (mole/m2 s)Ji partial fluxes (m/s), (mole/m2 s) or

(g/m2 h)kM molar mass transfer coefficient

(mole/m2 s Pa)kV volume mass transfer coefficient (m/s)l membrane thickness (m)L mobility (m2 mole/J s)N Avogadro’s number (mole−1)p pressure (Pa)Pi permeability (mole/m s) or (mole/m s Pa)R gas constant (J/mole K)SSS entropy (J/mole)S sorption coefficientT temperature (K)u velocity (m/s)up velocity of the fluid perpendicular to the

membrane surface (m/s)V partial molar volume (m3/mole)X molar fraction

Greek lettersαP relation between membrane mass transfer

coefficientsαPV overall selectivityδ thickness of the feed boundary layer (m)ε plasticisation factorφ volume fractionγ activity coefficientµ chemical potential (J/mole)Π driving force or (Pa)ρ total mole density (mole/m3)

SubscriptsA componentB componentbl feed boundary layeri componentint intrinsicj componentl permeatem membraneov overallref reference statetot totalw water0 feed

Superscriptsb bulkl permeate sidesat equilibrium state+ inside the membrane∞ infinite dilution0 feed side

addition, the model can predict the variation in perme-abilities with the permeate pressure for the various or-ganic compounds. This variation in permeabilities wasrelated to a shrinking behaviour of the membrane. Theonly experimental data required for application of themodel are the intrinsic and overall separation factorsand the total flux at one specified permeate pressure.The model was found to predict the separation factorssatisfactorily for the compounds studied, i.e. for fivealcohols, four esters and one aldehyde.

The aim of this study was to develop a comple-mentary model for prediction of influence of permeatepressure on partial fluxes using the model developedby Olsson & Trägårdh [1].

2. Derivation of the solution–diffusion model forthe application of pervaporation

Binning et al. (1961) were the first to propose asolution–diffusion mechanism for the transport of liq-uids through homogeneous membranes [2]. Perme-ation through the membrane during liquid permeation,which was later named pervaporation, was divided

J. Olsson et al. / Journal of Membrane Science 186 (2001) 239–247 241

into three consecutive steps, i.e. sorption into the feedside of the membrane, diffusion through the mem-brane and, finally, desorption into the vapour phaseat the permeate side of the membrane. Binning et al.also stated that transport through the membrane is therate-determining step in pervaporation, i.e. the diffu-sion process through the membrane is slow in com-parison with the sorption rate and the desorption rate.The original solution–diffusion model proposed byLonsdale et al. (1965), described the flux of a compo-nent i through the membrane as the product of the con-centration (ci) the mobility (Li) and the driving force[3]. An assumption neglecting the convective contribu-tion to the flux has thus been made. This assumption isjustified when homogeneous membranes or very densetop layers of asymmetric or composite membranes areused, since the Peclét number �1 [4]. According to ir-reversible thermodynamics, the driving force for masstransfer is given by the gradient in chemical poten-tial. The effect of flow coupling can be neglected inthe case of pervaporation of very dilute aqueous so-lutions of volatile organic compounds. Hence, the ef-fect of flow coupling is not included here. Assumingone-dimensional, steady-state diffusion flow throughthe membrane, the flux of component i, Ji is given by

JVi = −ciLi

dµi

dz(1)

where µi denotes the chemical potential and z is thelength coordinate according to Fig. 1. As Mulder andSmolders pointed out, the assumption of steady-stateflow through the membrane does not allow the mem-brane to undergo any structural changes [4].

Fig. 1. Profile of the water concentration across the membraneand its dependence on permeate pressure, according to the modelderived in Eqs. (30)–(31).

The chemical potential of a component i is ex-pressed as

µi(z) = µi,ref + RT ln ai(z) +∫ p(z)

pref

Vi dp

−∫ T (z)

Tref

SSSi dp (2)

where µi,ref is the chemical potential at the referencestate, ai the activity, Vi denotes the partial molar vol-ume, p the pressure and SSSi is the entropy of com-ponent i. Neglecting any temperature drop across themembrane and considering the pervaporation processto be an isothermal process leads to the fourth termin Eq. (2) becoming zero. Combining Eqs. (1) and (2)with these assumptions gives

JVi = −ciLi

(RT

d ln ai

dz+ Vi

dp

dz

)T

(3)

As the solution–diffusion model involves the assump-tion that the nonporous part of the membrane is en-tirely at the feed pressure, Eq. (3) reverts to

JVi = −ciLiRT

d ln ai

dz(4)

The hydrodynamical theory takes as its starting pointthe Nernst–Einstein equation, which states that thediffusivity of a single particle or solute molecule Athrough a stationary medium B, DAB, is

DAB = RT

N× uA

FA(5)

in which uA/FA denotes the mobility of the single par-ticle A, i.e. the steady-state velocity attained by theparticle under the action of unit force, R is the gasconstant, T represents the temperature and N repre-sents Avogadro’s number [5]. The difference betweenthe mobility defined in Eq. (1), i.e. Li , and ui /Fi issimply a factor of N , i.e.

Li = ui

FiN(6)

By applying the hydrodynamical theory, as suggestedby Lee (1975), by combination of Eqs. (4), (5) and(6), the following relationship is obtained [6]:

JVi = −ciDi

d ln ai

dz(7)


where Di is the diffusion coefficient of component ithrough the membrane polymer. The activity insidethe membrane can be described as the product of theactivity coefficient, γ+

i , and the molar fraction, Xi , i.e.

a+i = γ+

i Xi (8)

If z ∈ ]0, l[ the activity coefficient can be consideredto be constant with respect to the concentration of thecomponent, where l is defined as the membrane thick-ness. At low concentrations, this is a valid assump-tion. Inserting this expression for the activity insidethe membrane into Eq. (7) gives

JVi = −ciDi

Xi

× dXi

dz(9)

which can be reduced to

JMi = −ρDi

dXi

dz(10)

where JMi is the molar flux expressed in mole/m2 s.

Integration across the membrane gives

JMi = −ρ

Di

l(X+

i,l − X+i,0) (11)

where Di is the mean or apparent diffusion coefficient[4]. To include the sorption and the desorption stepsinto the model, the solution–diffusion model assumesthat equilibrium is established at the membrane inter-faces on both the feed and the permeate sides. At equi-librium, the chemical potential outside the membraneis equal to the chemical potential inside the membrane.Applying Eq. (2) at the interfaces and neglecting thepressure term and the entropy term leads to the con-clusion that the activities must also be equal at bothsides of the interfaces, i.e.

µi,0 = µ+i,0 => ai,0 = a+

i,0 (12)

µi,l = µ+i,l => ai,l = a+

i,l (13)

The activity of component i in the feed under liquidconditions and in the permeate under gaseous condi-tions can be expressed as

ai,0 = γi,0Xi,0 (14)

and

ai,l = γi,lpl

psati

Xi,l (15)

where pl denotes the permeate pressure and psati is the

equilibrium vapour pressure of component i. The con-centrations inside the membrane at the two interfacescan be obtained by combination of Eqs. (8), (12), (13),(14) and (15):

X+i,0 = γi,0

γ+i

Xi,0 (16)

X+i,l = γi,lpl

γ+i psat

i

Xi,l (17)

The molar flux is then obtained by inserting Eqs. (16)and (17) into Eq. (11), according to

JMi = ρDi

lγ+i

(γi,0Xi,0 − γi,l

pl

psati

Xi,l

)(18)

In Eq. (18), the driving force is expressed as a differ-ence in activity and it can easily be converted into adifference in partial pressure, according to

JMi = ρDi

lγ+i psat

i

(γi,0Xi,0psati − γi,lplXi,l) (19)

Eq. (19) can also be converted to a form in whichthe gradient is expressed as an apparent difference inconcentration, according to

JMi = ρDiγi,0

lγ+i

(Xi,0 − γi,lpl

γi,0psati

Xi,l

)(20)

Derived expressions for permeabilities togetherwith the corresponding driving forces are given inTable 1. As Eq. (20) shows, this apparent concen-tration difference is not equal to the true concen-tration difference. As a consequence, although theresulting membrane mass transfer coefficient will

Table 1The table gives different expressions for the driving force and thecorresponding permeabilitya

Driving force, �Πi Pi

�ai = γi,0Xi,0 − γi,lXi,l

pl

psati

(–)ρDi

γ+i

(mole/m s)

�pi = γi,0Xi,0psati − γi,lXi,lpl (Pa)

ρDi

γ+i psat

i

(mole/m s Pa)

�Xi = Xi,0 − γi,lpl

γi,0psati

Xi,l (–)ρDiγi,0

γ+i

(mole/m s)

a The molar flux is obtained from JMi = (Pi �Πi)/ l.


have the dimensions of velocity, this will only repre-sent an apparent velocity and can not be used whenapplying the resistance-in-series theory. For thesereasons, it is not meaningful to express the drivingforce for the pervaporation process as a difference inconcentration.

3. Prediction of the pressure dependence onpartial fluxes

In a previous study, a model for the pressure de-pendence of the selectivity in hydrophobic pervapora-tion was developed for the application of recovery ofvolatile organic compounds from dilute aqueous so-lutions [1]. When the solution–diffusion theory wasdeveloped for pervaporation, it was assumed that theoverall resistance to mass transfer was dominated bythe membrane resistance. Later it has been shown thatthe transport of mass often is effected by and some-times even limited by concentration polarisation in thefeed boundary layer. Therefore, the model includesboth the external mass transfer from the bulk of thefeed to the membrane surface and the separation prop-erties of the membrane material. The model is sum-marised in Eqs. (22), (24) and (25). It was derivedfrom the resistance-in-series theory combined withsolution–diffusion theory, and the mass transfer in thefeed boundary layer was assumed to be Fickian. De-tails of the derivation are given in [1]. The selectivity,αPVi , is defined according to

αPVi = (Xb

i,l/Xbi,0)

(Xbj,l/X

bj,0)

≈ Xi,l

Xbi,0

(21)

where the superscript b represents the bulk concentra-tion. Concentration polarisation at the permeate sideis neglected due to the high diffusivities of the per-meants in comparison to the total flux [7]. The modeldescribes the pressure dependence of the selectivity as

αPVi = e(up/k

Vbl,i )

Hw+(αPi −1)p1

HiαPi

− 1 + e(up/k

Vbl,i )

(22)

where up denotes the velocity of the feed perpendicu-lar to the membrane surface, which can be obtained asthe total flux divided by the density of the feed solu-tion. αP

i is defined as the ratio between the membrane

mass transfer coefficient of the organic compound andwater, according to

αPi = kM

m,i

kMm,w

(23)

Hi and Hw are the Henry law coefficients of the or-ganic and water, respectively, defined as the productof the activity coefficient and the equilibrium vapourpressure of the component. Due to the very low con-centration of organics, the water concentration in boththe feed and the permeate is close to unity and hence,the total flux is close to the water flux. In the casewhere water only plasticises the membrane to a limitedextent, the water permeability can be assumed to beindependent of permeate pressure. The validity of thisassumption has been demonstrated for silicone rubbermembranes [8]. Consequently, up will vary with per-meate pressure according to

up = JMtot(0)

ρ′

(1 − pl

p0

)(24)

The mass transfer coefficient of the feed boundarylayer, kVbl,i , is treated as a constant in this study sincethere was no change in the hydrodynamic conditionsof the feed. The mass transfer coefficient of the bound-ary layer, defined as the relation between the diffu-sion coefficient of the liquid (–Di) and the thicknessof the boundary layer (δi) can be obtained from amass balance of the feed boundary layer at steady-stateconditions with the assumption of Fickian diffusion,according to

kVbl,i = –Di

δi= up

ln

(αPVi (pl)−αPV

int,i (pl)

αPVint,i (pl)−αPV

i (pl)αPVint,i (pl)

) (25)

where αPVint,i is the intrinsic selectivity defined accord-

ing to

αPVint,i = (Xi,l/Xi,0)

(Xj,l/Xj,0)≈ Xi,l

Xi,0(26)

According to the resistance-in-series theory, the masstransfer coefficients are related according to

1

kMov,i

= 1

kMbl,i

+ 1

kMm,i

(27)

where kMov,i is the overall mass transfer coeffi-

cient. As explained in the section in which the


solution–diffusion model is derived, it is importantnot to use the volume-based mass transfer coeffi-cients when combining the mass transfer through themembrane with the external mass transfer. Conver-sion between the volume and the molar-based masstransfer coefficient of the boundary layer is given bythe relation

kMbl,i = ρ

γ0,ipsati

kVbl,i (28)

Combining Eqs. (19), (21), (23), (27) and (28) togetherwith the assumption that γ i ,l is close to unity, due tovery low permeate pressures, gives

JMi = αP

i kMbl,i

αPi + (kM

bl,i/kMm,w)

Xb0,i (Hi − αPV

i pl) (29)

In addition, to predict the variation in partial fluxeswith permeate pressure, relationships describing thepermeate pressure dependence of the membrane plas-tication, i.e. αP

i , are required. If the organic permeantcan form hydrogen bonds with water, the water sol-ubility will be improved considerably. An increase inwater concentration inside the membrane, due to in-creased permeate pressure, is, therefore, expected toreduce αP

i for the less water-soluble permeant muchmore rapidly than for the more water-soluble perme-ant. As significantly different behaviour of αP

i as afunction of permeate pressure is expected dependingon the presence of hydroxyl groups on the organic per-meant, models which can be applied to both types oforganic permeants must be found.

In an earlier study, the following relationship wasderived between αP

i and the permeate pressure:

αPi (pl) = αP

i (0) exp

(φ0i (εwi − εww)

2p0pl

)(30)

where

αPi (0) = SiD0,i

SwD0,wexp

(φ0

w

2(εwi − εww)

)(31)

D0 denotes the diffusion coefficient at infinite con-centration, ε the plasticisation factor and φ is the vol-ume fraction. The derivation of Eqs. (30) and (31) isbased on the assumption of an exponential concentra-tion dependency of the diffusion coefficients and theassumption of a linear concentration profile for wa-ter across the membrane. The boundary conditions are

given in Fig. 1. The detailed derivation of Eqs. (30)and (31) can be found in [1]. According to Eq. (31),αPi (0) is constant and equal to the relation between

the net organic permeability and the net water per-meability at zero permeate pressure. The exponentφ0

l (εwi − εww)/2p0 is a constant, which is related tothe effect of membrane plasticisation on the perme-ation of the organic compound. An empirical relationbetween the exponent and the activity coefficient foran organic compound in water solution at infinite di-lution (γ∞

i ) was also found in [1], i.e.

φ0l (εwi − εww)

2p0= 0.0099 − 0.0284 ln(γ∞

i ) (32)

This relation was found to be valid for the all the or-ganic permeants that can not form hydrogen bondswith water, i.e. the esters and the aldehyde. As ex-pected, the membrane plasticisation did not reduce αP

i

for the organic permeants that could form hydrogenbonds with water, i.e. the alcohols, as rapidly with in-creasing permeate pressure as predicted by Eq. (32).However, by linearisation according to MacLaurinsformula combined with the boundary condition thatαPi (p0) = 0, the following relation could be derived

from Eq. (30), [1]:

αPi (pl) = αP

i (0)

(1 − pl

p0

)(33)

This model was found to be applicable for all thealcohols studied for values of pl up to 2/3 of p0.Eq. (29) can be used to predict the partial fluxesof organic compounds in dilute aqueous solutionstogether with Eqs. (22), (24), (25) and, for organicpermeants containing hydroxyl groups, Eqs. (30) and(32), whereas for organic permeants lacking hydroxylgroups, Eq. (33) must be employed. The only datarequired to predict the influence of permeate pressureon partial fluxes of organic compounds for a specificmembrane are

• the total flux, which is close to the water flux fordilute systems,

• the intrinsic selectivity, i.e. the selectivity obtainedin the case of no concentration polarisation,

• the overall selectivity at one specific permeate pres-sure.


Table 2Some properties of the permeants studieda

Permeant γ∞i

(–) psati (mbar) αPV

int,i (0) (–) αPVi (0) (–)

Isobutanol 55.5 [11] 11.84 [9] 41.5 38.9n-Butanol 55.5 [11] 6.11 [10] 44.4 39.6Isoamyl alcohol 153 [11] 2.99 [10] 81.2 64.7n-Hexanol 426 [11] 0.89 [9] 171 105trans-2-Hexenal 400 [11] 8.12 [10] 701 284Ethyl acetate 153 [11] 98.44 [9] 404 217Ethyl butanoate 1860 [11] 17.46 [10] 2220 349Ethyl-2-methyl butanoate 5640 [11] 25.88 [10] 3710 323Isoamyl acetate 3830 [11] 5.95 [10] 3220 370Hexyl acetate 11300 [11] 1.34 [12] 3810 389Water 1 23.37 [9] 1 1

a The activity coefficients at infinite dilution in water, γ∞i

were estimated using a UNIFAC method. The equilibrium vapour pressures,psati , were obtained through Antoine’s constants taken from the literature, for all compounds except trans-2-hexenal. In this case, Antoine’s

constants were estimated through a method based on the Clausius–Clayperon equation. The intrinsic selectivities at zero permeate pressure,αPV

int,i (0), were obtained from [13], and the selectivities at zero permeate pressure, αPVi (0), were obtained from [1].

4. Materials and methods

4.1. Feed solution

Volatile organic compounds (10) were selected forinclusion in the feed solution and these are presentedin Table 2. Four of the selected compounds werealcohols: isobutanol, n-butanol, isoamyl alcohol andn-hexanol, one was an aldehyde: trans-2-hexenal,and five were esters: ethyl acetate, ethyl butanoate,ethyl-2-methyl butanoate, isoamyl acetate and hexylacetate. Each organic compound was used at a con-centration of 10 ppm (w/w). Demineralised and dis-tilled Milli-Q water, with a resistance greater than18 M% cm, was used as the solvent. The organic com-pounds used to prepare the solution had a purity ofabout 99%.

4.2. Pervaporation membrane

The membrane used was a POMS-PEI membrane;a poly-octyl-methyl siloxane membrane, manufac-tured by the GKSS Forschungzentrum, Geesthacht,Germany. Scanning electron microscopy photographswere taken of the cross-section of the membrane andthe thickness of the active layer was determined to be5 �m. The water flux at 20◦C and a permeate pressureclose to 0 mbar was 62.5 g/m2 h.

4.3. Experimental

A plate-and-frame module with a membrane areaof 184 cm2 and a hydraulic diameter of 1.45 mm wasused. The feed temperature was 20.0◦C and the feedflow velocity corresponded to a Reynolds number of415. The permeate pressure was varied in the range0–16 mbar and the condensation temperature was−196◦C. Details of the pervaporation apparatus andthe experimental procedures are described in [1].

4.4. Analysis

The aroma compound concentrations in both thefeed and the permeate were analysed with gas chro-matography. Details of the analysis are given in [1].The values of aroma concentrations varied by 5–10%.

5. Results

In Figs. 2 and 3, both the experimentally obtainedpartial fluxes of the organic compounds and the par-tial fluxes of the organic compounds predicted by themodel are presented as a function of the permeate pres-sure. For organic permeants with the ability to formhydrogen bonds with water, values of αP

i (pl) werepredicted by the linear model described by Eq. (33),whereas for organic permeants lacking the ability to


Fig. 2. The partial fluxes of the alcohols studied are plotted vs.the permeate pressure. The filled circles indicate the experimentalresults and the curves correspond to the partial fluxes predictedby the model. αP

i (pl) was predicted by Eq. (33).

form hydrogen bonds with water, values of αPi (pl)

were predicted by the exponential model described byEqs. (30)–(32). The equilibrium vapour pressures andthe activity coefficients in water at infinite dilution ofthe permeants are required to predict the partial fluxesand these are given in Table 2. The data for the equi-librium vapour pressures are based on experimentalresults. However, the activity coefficients at infinite di-lution in water had to be estimated using the UNIFACgroup contribution method. Both the intrinsic selec-tivities and the overall selectivities at zero permeatepressure have been experimentally determined in ear-lier studies and they are also presented in Table 2[1,13]. The total flux at zero permeate pressure wasdetermined to be 62.5 g/m2 h.

6. Discussion

As expected, the partial fluxes of the organic com-pounds varied considerably with permeate pressure.From the experimental results, see Figs. 2 and 3, it canbe seen that for all cases, the fluxes strictly decreasedwith increasing permeate pressure. However, for fourof the esters, i.e. ethyl butanoate, ethyl-2-methyl

Fig. 3. The partial fluxes of the aldehyde and the esters studied areplotted versus the permeate pressure. The filled circles indicate theexperimental results and the curves correspond to the partial fluxespredicted by the model. αP

i (pl) was predicted by Eqs. (30)–(32).

butanoate, isoamyl acetate and hexyl acetate, initiallythe partial fluxes did not decrease as rapidly withincreasing permeate pressure as for the other com-pounds studied. At higher permeate pressures, thepartial fluxes decreased more rapidly with increasingpermeate pressure. This plateau behaviour could beexplained by the fact that these four esters suffer fromsevere concentration polarisation. As the effects ofdecreased concentration polarisation and decreaseddriving force with increasing permeate pressure atlow permeate pressures influence the partial fluxes inopposite directions, the net result will be an almostpermeate-pressure-independent partial flux. The sameeffect could be seen in the permeate pressure depen-dence of the separation factors for these esters [1].

For all the compounds studied, the model for pre-dicting the influence of permeate pressure on partialfluxes is in very good agreement with the experimental


results, see Figs. 2 and 3. It is thus possible to predictthe influence of permeate pressure on partial fluxes oforganic compounds from dilute aqueous solutions toa satisfactory degree of accuracy within the permeatepressure region of commercial interest.

Further studies are needed to confirm that the modelis applicable not only to the pervaporation of alco-hols, aldehydes and esters, but also to other groups oforganic compounds and to extend the model to othertypes of membranes.

7. Conclusions

The model developed in this study allows the pre-diction of the influence of permeate pressure on thepartial fluxes of organic compounds from dilute aque-ous solutions. The model includes both the effect ofexternal mass transfer and the effect of altered perme-abilities due to membrane plasticisation for the vari-ous permeants. Both of these effects were proved toeffect the partial fluxes to a significant extent. Ade-quate information about the membrane separation fac-tor and the overall separation factor together with thetotal flux at one specific permeate pressure, is all thatis needed for the application of this model. In ad-dition, when combining the solution–diffusion modelwith the resistance-in-series theory, it is important toapply an appropriate driving force.

Acknowledgements

This work was supported by the Swedish NationalBoard for Industrial and Technical Developmentthrough the Swedish Foundation for Membrane Tech-nology. The authors wish to acknowledge the GKSS

Forschungzentrum for generously supplying the per-vaporation membranes.

References

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[3] H.K. Lonsdale, U. Merten, R.L. Riley, Transport propertiesof cellulose acetate osmotic membranes, J. Appl. Polym. Sci.9 (1965) 1341–1362.

[4] M.H.V. Mulder, C.A. Smolders, On the mechanism ofseparation of ethanol/water mixtures by pervaporation. I.Calculations of concentration profiles, J. Membr. Sci. 17(1984) 289–307.

[5] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Diffusivity and themechanisms of mass transport, in: Transport Phenomena,Wiley, New York, 1960.

[6] C.H. Lee, Theory of reverse osmosis and some othermembrane permeation operations, J. Appl. Polym. Sci. 19(1975) 83–95.

[7] J.G.A. Bitter, J.P. Haan, Effect of concentration polarizationon membrane separation of gas mixtures, in: Proceedings ofthe 1987 Congress on Membranes and Membrane Processes,Tokyo, Japan, 8–12 June 1987, pp. 506–507.

[8] J.G. Wijmans, R.W. Baker, The solution–diffusion model: areview, J. Membr. Sci. 107 (1995) 1–21.

[9] J. Gmehling, U. Onken, Vapour–liquid equilibrium datacollection, Dechema Data Series Collection, 1913–1995.

[10] S. One, Computer Aided Data Book Of Vapour Pressure.Data Book Publishing Company, Tokyo, Japan, 1976.

[11] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties ofGases and Liquids, 4th Edition, McGraw-Hill, New York,USA, 1987.

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Documents

Pervaporation of volatile organics from water: II. Influence of permeate pressure on partial fluxes