Pervaporation of volatile organic compounds from water: I Influence of permeate pressure on selectivity

Journal of Membrane Science 187 (2001) 23–37

Pervaporation of volatile organic compounds from waterI Influence of permeate pressure on selectivity�

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

Received 22 March 2000; accepted 31 August 2000

Abstract

Hydrophobic pervaporation is developing within several interesting areas of application related to the recovery of volatileorganic compounds from dilute water solutions. So far this process has only been commercialised to a limited extent. Foroptimisation and scale-up, models are needed to predict the influence of key process parameters such as temperature, hy-drodynamic conditions on the feed side of the membrane and permeate pressure on the partial fluxes and the selectivity. Inthis study, pervaporation experiments were performed with multicomponent mixtures of five esters, one aldehyde and fouralcohols, all at ppm levels in aqueous solution. A model was developed for predictions of the influence of permeate pressure onthe overall separation factor. The model includes the effect of concentration polarisation on the feed side of the membrane andits dependence on permeate pressure, the variation in separation properties of the membrane with permeate pressure and theproperties of the individual permeants. The results support the theory that shrinking of modified silicone rubber membranesused for pervaporation reduces the separation ability of the membrane in terms of reduced hydrophobicity. In the case of veryhydrophobic permeants, this effect causes a considerable reduction in the selectivity. © 2001 Elsevier Science B.V. All rightsreserved.

Keywords: Pervaporation; Hydrophobic membrane; Permeate pressure; Selectivity; Concentration polarisation

1. Introduction

Pervaporation is a membrane technique used forthe separation of liquid mixtures by means of par-tial vaporisation across a permselective membrane.The permeate is then obtained as a liquid followingcondensation. Nowadays, hydrophilic pervaporationmay be considered a well established technology. Re-cently, hydrophobic pervaporation has also become

� The above article should have appeared before the article en-titled “Prevaporation of volalite organics from water II. Influenceof permeate pressure on partial fluxes”, which was published involume 186/2, pages 239–247.

∗ Corresponding author. Tel.: +46-46-222-98-20;fax: +46-46-222-46-22.

commercialised for applications in waste water treat-ment, industrial solvent recovery and aroma recovery[1]. Another area of potential application of hydropho-bic pervaporation is in the treatment of fermentationbroths, either the extraction of inhibitors to increasethe product yield or extraction of the products [2].What most of these applications have in commonis that they are based on the separation of volatileorganic compounds from dilute aqueous solutions.

In order to optimise the pervaporation process, mod-els are needed that can predict the influence of theprocess parameters on the performance of the pro-cess, expressed in terms of flux and separation factors.One of the most important process parameters is thepermeate pressure which, together with the operatingtemperature, determines the driving force of the whole

0376-7388/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S0 3 7 6 -7 3 88 (00 )00679 -7

24 J. Olsson, G. Trägårdh / Journal of Membrane Science 187 (2001) 23–37

Nomenclature

b constant (mbar−1)CPM concentration polarisation modulusD diffusion coefficient inside the membrane

(mol/m s mbar)D0 diffusion coefficient inside the membrane

at infinite permeant concentration(mol/m s mbar)

–D diffusion coefficient in thefluid (m2/s)

dh hydraulic diameter (m)H Henry law coefficient (mbar)J mole flux (mol/m2 s)k mass transfer coefficient

(mol/m2 s mbar)kv mass transfer coefficient (m/s)L length of the flow channel (m)l thickness of the active layer of the

membrane (m)p pressure (mbar)p0 equilibrium vapour pressure (mbar)P permeability coefficient

(mol/m s mbar)Re Reynolds numberS solubility coefficientSc Schmidt numberSh Sherwood numberVP velocity of the fluid perpendicular to the

membrane surface (m/s)X mole fractiony length coordinate (m)z length coordinate (m)

Greek lettersαP relation between the membrane mass

transfer coefficients for the componentsto be separated

αPV overall separation factorαVLE separation factor of the vapour liquid

equilibrium in the feed solutionγ activity coefficientδ thickness of the feed

boundary layer (m)ε plastication factorφ volume fraction inside the membraneρ mole density (mol/m3)

Subscriptsbl boundary layerf feed or feed sidei componentint intrinsicj componentm membranep permeate or permeate sidew water0 equilibrium

Superscriptsb bulkl permeate interfacem membrane0 feed interface

process. High fluxes and high separation factors aredesirable in order to minimise the membrane area re-quired to reduce both the capital costs and the cost ofreplacing the membranes. On the other hand, a largeflux requires both a low condensation temperature anda strong vacuum pump, which in turn results in a highenergy input into the process. Earlier studies on theeconomical optimisation of the pervaporation processfor the recovery of volatile organic compounds fromwater by Hickey and Gooding [3] and Wenchang et al.[4] applying spiral wound and hollow fiber modules,respectively, have shown that the optimum permeatepressure could be significantly >0. In order to estab-lish the economically optimum permeate pressure, itis necessary to be able to predict the influence ofpermeate pressure on both flux and selectivity.

The aim of this study was to develop a generalmodel for predicting the influence of permeate pres-sure on the overall separation factor in pervaporativerecovery of volatile organic components from diluteaqueous solutions. The model should include the in-fluence of permeate pressure on both the external masstransfer from the bulk of the feed to the membranesurface and the separation properties of the membranematerial. An earlier study by Baker et al. [5] impliesthat both of these parameters may have a significantinfluence on the overall selectivity of the pervapora-tion process. Such a model, would for instance allowpredictions of the variation in the permeate composi-tion with permeate pressure. This would be especially

J. Olsson, G. Trägårdh / Journal of Membrane Science 187 (2001) 23–37 25

interesting for applications where the composition ofthe permeate is of importance which, for instance, isthe case in aroma recovery from beverages. Obtaininga concentrate with an optimal aroma profile is crucialin this application and such a model would make itpossible to predict the process conditions at which apermeate with the optimum aroma profile is produced.

2. Theory

The flux of component i, Ji , is proportional to thedifference in partial pressure according to

Ji = kov,i (pbf,i − pb

p,i ) (1)

where kov,i is the overall mass transfer coefficient, pbf,i

the partial pressure of the bulk of the feed solution andpb

p,i the partial pressure of the bulk of the permeatevapour for component i. According to Raoult’s law,which is a model assumption, the partial pressure ofcomponent i in the bulk of the feed can be expressedas follows:

pbf,i = γiX

bf,ip0,i (2)

where γ i is the activity coefficient, Xbf,i the mole frac-

tion in the bulk of the feed and p0,i the equilibriumvapour pressure of the pure component i. Accordingto Dalton’s law, the partial pressure of component iin the permeate, pb

p,i , is assumed to be the permeatepressure, pp, multiplied by the mole fraction of com-ponent i of the permeate, Xb

p,i , i.e.

pbp,i = Xb

p,ipp (3)

According to the resistance-in-series theory andthe solution diffusion theory, the overall resistance tomass transfer from the bulk of the feed to the bulkof the permeate can be divided into several consecu-tive steps: diffusion through the liquid feed boundarylayer, sorption into the membrane, diffusion throughthe membrane, desorption into the vapour phase onthe permeate side of the membrane and diffusioninto the bulk of the permeate. The fundamental as-sumption that the flux through all the mass transferresistances is equal yields

Ji = kov,i (pbf,i − pb

p,i ) = kbl,i (pbf,i − pm

f,i )

= km,i (pmf,i − pm

p,i ) = kp,i (pmp,i − pb

p,i ) (4)

where kbl,i , km,i and kp,i are the mass transfer coef-ficients for component i of the liquid feed boundarylayer, the membrane and the vapour permeate bound-ary layer, respectively [6]. Since the diffusivities ofthe permeants on the permeate side of the membraneare considerably higher than the total flux, the bound-ary layer effect on the permeate side of the membranevanishes [7]. The relationship of the mass transfercoefficients can thus be written as follows:

1

kov,i= 1

km,i

+ 1

kbl,i(5)

The mass transfer coefficient of the membrane in-cludes sorption to, diffusion through and desorptionfrom the membrane. It is equivalent to the relationbetween the permeability coefficient, Pi , and the thick-ness of the active layer of the membrane, l, accordingto

km,i = Pi

l(6)

where the permeability coefficient is equal to the prod-uct of the solubility coefficient of the permeant in themembrane polymer, Si , and the diffusion coefficient,Di , of the permeant in the membrane polymer [8,9],i.e.

Pi = SiDi (7)

The sorption step can be considered as a mixingprocess between the liquid and the polymer of theactive layer. The mixing of liquids and polymers of-ten results in non-linear sorption isotherms due to in-teractions between the components. However, in thecase of sorption of dilute organic–water mixtures inhydrophobic membranes, these interactions are oftensmall, resulting in linear sorption [10–12]. The dif-fusion coefficient of a permeant is generally concen-tration dependent. In addition, it is affected by othercompounds present in the membrane. In the case ofpervaporation of dilute aqueous solutions of organiccompounds, the concentration of the organic perme-ants in the membrane will be very low, causing only aslight plasticisation of the polymer. Therefore, it canbe assumed that the transport properties of the organicpermeants through the membrane will not vary withtheir concentration [13].

At steady state, a mass balance of the processyields that the sum of convective and diffusive


transport through the feed boundary layer is equal tothe amount permeated through the membrane [14]

VPXf,i − –Di

dXf,i

dy= VPXp,i (8)

where VP is the velocity of the fluid perpendicular tothe membrane surface, –Di the diffusion coefficient ofthe component in the fluid and y the length coordinate.After integration with the boundary conditions,

y = 0 Xf,i = Xbf,i

y = δi Xf,i = Xmf,i

and combination with the equation

kvbl,i = –Di

δi(9)

the relationship between the concentration of the com-ponent at the membrane interface and the concentra-tion of the component in the bulk of the feed solution,i.e. the concentration polarisation modulus, CPMi , isobtained [14]

CPMi = Xmf,i

Xbf,i

= (Xbf,i − Xp,i ) exp(VP/k

vbl,i ) + Xp,i

Xbf,i

(10)

According to Eq. (9), the mass transfer coefficientof the feed boundary layer is determined by the hydro-dynamic conditions in the feed channel and the diffu-sion coefficient of the component in the feed solution.It is thus independent of the permeate pressure andhas been treated as a constant in this study. The masstransfer coefficient of the feed boundary layer can beestimated using semi-empirical Sherwood correlationsfor laminar flow and crossflow operation, according to

Sh = 1.62 ×(

Re Scdh

L

)0.33

(11)

where Sh is the Sherwood number, Re the Reynoldsnumber, dh the hydraulic diameter and L the length ofthe flow channel [15,16]. However, an earlier studyon the effect of concentration polarisation on perva-porative aroma recovery, showed that this Sherwoodcorrelation gives a poor estimate of the mass trans-fer coefficient of the boundary layer, especially incases of extensive concentration polarisation. It is,therefore, better to use experimental results for the

membrane mass transfer coefficient and then to obtainthe mass transfer coefficient of the boundary layerthrough Eq. (5) [17].

The velocity of the fluid perpendicular to the mem-brane surface is equal to the total mole flux, Jtot,divided by the mole density of the fluid, ρ

VP = Jtot

ρ(12)

If the membrane mass transfer coefficient for wa-ter is independent of permeate pressure, the water fluxwill decrease linearly with increasing permeate pres-sure and reach zero as the permeate pressure becomesequal to the partial pressure of the feed solution. Thisassumption is valid, since water plasticises hydropho-bic silicone rubber polymers to a limited extent [18].Due to the very low concentration of aroma com-pounds in the feed solution, the total flux is very closeto the water flux, Jw, and can be assumed to varywith the permeate pressure in the same way as the wa-ter flux. Thus, the velocity of the fluid perpendicularto the membrane surface will vary with the permeatepressure according to

VP(pp) = Jtot(0)

ρ

(1 − pp

pf

)(13)

The concentration polarisation is, thus, dependenton the permeate pressure. The concentration polarisa-tion modulus will increase with increasing permeatepressure until it reaches unity at the point where thepermeate pressure becomes equal to the partial pres-sure of the feed solution (see Eq. (10)).

The separation factor, αPVi/j , determines the ability of

the pervaporation process to separate the substancesi and j and it is calculated from the concentrationsof the components in the bulk of the feed and in thecondensed permeate according to

αPVi/j

= Xp,i/Xbf,i

Xp,j /Xbf,j

(14)

The intrinsic separation factor, αPVint,i/j , is a measure

of the ability of the membrane to separate the sub-stances i and j and it is, in analogy with αPV

i/j , calcu-lated from

αPVint,i/j

= Xp,i/Xmf,i

Xp,j /Xmf,j

(15)


A mass balance over the membrane at steady stateleads to the conclusion that the relation between theflux of the organic compound and the water flux isequivalent to the relation between the permeate con-centration of the organic compounds and the permeateconcentration of water

Ji

Jw= km,i

km,w

(pmf,i − pp,i )

(pmf,w − pp,w)

= Xp,i

Xp,w(16)

Combining Eqs. (15) and (16), and introducing αPi as

the membrane mass transfer coefficient of the organiccompounds divided by the membrane mass transfercoefficient of water, gives the following relation:

αPVi = Xb

f,w

Xbf,i

αPi

(pmf,i − pp,i )

(pmf,w − pp,w)

(17)

where

αPi = km,i

km,w(18)

For practical reasons, αPVi/w will be denoted αPV

i as wa-ter is always the second component. Due to the verylow concentration of aroma compounds, the water con-centration in the bulk of the feed solution, in the feedsolution at the membrane interface and in the perme-ate is assumed to be unity. If Eqs. (2) and (3) and thedefinition of the concentration polarisation moduluswith the assumption above are combined, the follow-ing relation is obtained:

αPVi = Hiα

Pi

Hw + (αPi − 1)pp

CPMi (19)

where

Hi = γip0,i , Hw = γwp0,w (20)

Eqs. (19) and (10) yield

αPVi = exp(VP/k

vbl,i )

(Hw + (αPi − 1)pp)/(Hiα

Pi ) − 1

+exp(VP/kvbl,i )

(21)

In the case of no concentration polarisation and apermeate pressure of 0, Eq. (21) reduces to

αPVi (0) = αVLE

i αPi (0) (22)

where

αVLEi = Hi

Hw(23)

Thus, the separation factor for the whole process thensimply becomes the product of the separation factorfor the vapour liquid equilibrium, αVLE

i , and αPi (0),

which is in accordance with the findings of Blumeet al. [19] Wijmans and Baker [20] and Baudot et al.[21]. According to Eq. (21), the separation factor forthe pervaporation process is independent of the feedcomposition at very low concentrations of the organiccompound. The parameters influencing the separationperformance of the process are the Henry law coeffi-cients of the permeants, the mass transfer coefficientof the feed boundary layer (which depends on thehydrodynamic conditions in the flow channel and thediffusivities of the permeants in the feed solution) themass transfer properties of the membrane polymer(through αP

i ) and the permeate pressure. The Henrylaw coefficients and the mass transfer coefficient of thefeed boundary layer are independent of the permeatepressure. The dependence of permeate pressure on thevelocity of the fluid perpendicular to the membranesurface is described in Eq. (13). The ability of themembrane polymer to separate the components, αP

i ,may also be a function of the permeate pressure.Greenlaw et al. [22] studied the effect of permeatepressure on hexane removal from water and the re-sults confirmed that the separation properties of themembrane were indeed dependent on the perme-ate pressure. Wijmans and Baker [18] explained theresults as being a consequence of the permeant plasti-cising the membrane. To construct a complete modelfor the prediction of the influence of the permeatepressure on the separation factor, a model that pre-dicts the influence of permeate pressure on the masstransfer properties of the permeants in the membranepolymer is also needed.

The permeant concentration profile inside the mem-brane is a function of the permeate pressure, as shownschematically in Fig. 1. With increasing permeatepressure, a larger fraction of the membrane will beplasticised until the whole membrane is plasticised asthe permeate pressure reaches the equilibrium vapourpressure of the feed solution.

From Eqs. (6), (7) and (18), it can be seen that αPi is

the relation between the solubility coefficients and the


Fig. 1. A schematic drawing of the influence of permeate pressureon the concentration profile across the membrane. The grey scaleindicates the concentration, i.e. the darker the colour, the higherthe concentration. In (a), the permeate pressure is close to unityand only a thin segment of the membrane is plasticised; in (b),the permeate pressure has been increased; and in (c), the permeatepressure is equal to the equilibrium vapour pressure of the feedsolution which causes the whole membrane to become plasticised.

diffusion coefficients of the organic component andwater respectively, according to

αPi = SiDi

SwDw(24)

The sorption behaviour is known to be dependenton the concentrations in the feed solution. However,the water concentration in the feed solution is close tounity and will thus not vary with permeate pressure.Therefore, the solubility coefficient of water can beassumed to be independent of the permeate pressure.

The concentrations of the organic compounds nearthe membrane surface are, on the other hand, expectedto vary with permeate pressure as the concentration po-larisation varies with permeate pressure. With increas-ing permeate pressure, the feed concentrations near themembrane surface, of those organic compounds thatsuffer from concentration polarisation, increase withincreasing permeate pressure. However, they will notexceed the bulk concentration and thus the assumptionof linear sorption isotherms at low concentrations isstill valid. Thus, the solubility coefficients for the or-ganic compounds can be assumed to be independentof permeate pressure.

The diffusion coefficients are also known to beconcentration dependent. Both linear and exponen-tial relationships have been proposed, depending onhow strongly the concentration influences diffusion[23,24]. For a binary mixture of an organic compoundand water, the exponential relationship is expressed

according to

Di = D0,i exp(εiiφi + εwiφw),

Dw = D0,w exp(εwiφi + εwwφw) (25)

where D0 denotes the diffusion coefficient at infi-nite concentration, ε the plastication factor and φ

the volume fraction. As the concentrations of the or-ganic components are very low, the plastication effectof these compounds is neglected. Thus, Eq. (25) isreduced to

Di = D0,i exp(εwiφw),

Dw = D0,w exp(εwwφw) (26)

The volume fraction of water inside the membraneis a function of both the distance through the mem-brane and the permeate pressure. A linear water con-centration profile across the membrane is assumed dueto only slight plastication of the membrane by wa-ter. At zero permeate pressure, the solution–diffusionmodel assumes that the volume fraction of water atthe permeate side of the membrane, φl

w, is close to0. When the permeate pressure becomes equal to theequilibrium vapour pressure of the feed solution, thedriving force disappears and the water concentrationwill be constant throughout the membrane. Thus, theboundary conditions for φl

w are

φlw(0) = 0, φl

w(Pf) = φ0w (27)

In addition, φlw can be assumed to be linearly propor-

tional to the permeate pressure as long as the masstransfer is not controlled by desorption, which togetherwith the boundary conditions gives

φlw(pp) = pp

pfφ0

w (28)

The resulting concentration profile and its pressuredependence are shown in Fig. 2. With the stated as-sumptions, the volume fraction of water inside themembrane can be described by the relation

φzw(pp, z) = φ0

w

[1 −

(1 − pp

pf

)z

l

](29)

As the aim was to predict the net permeability foreach permeant, the integral mean value of the water


Fig. 2. The model concentration profile and its permeate pressuredependence.

volume fraction at any permeate pressure, φ̄w, wasderived according to

φ̄w = 1

l

∫ l

0ϕz

w(pp, z) dz = φ0w

2

(1 + pp

pf

)(30)

and the resulting function will replace Eq. (29) inthe subsequent derivation of αP

i . Combination ofEqs. (24), (26) and (30) together with the above statedassumptions gives

αPi = SiD0,i

SwD0,wexp

[φ0

w

2(εwi−εww)

(1+pp

pf

)](31)

This equation can be rearranged into

αPi = αP

i (0) exp

[φ0

w(εwi − εww)

2pfpp

](32)

where

αPi (0) = SiD0,i

SwD0,wexp

[φ0

w

2(εwi − εww)

](33)

According to Eq. (33), αPi (0) is a constant and equal

to the relation between the net organic permeabilityand the net water permeability at zero permeate pres-sure. The permeate pressure dependence of αP

i is de-scribed by the exponent in Eq. (32). The volume frac-tion of water in the selective layer at equilibrium, φ0

w,is a membrane property which can be determined ex-perimentally. According to Wijmans and Baker [18],the permeability coefficient of water is expected to beconstant with respect to the permeate pressure due toonly moderate plasticising by the permeant in perva-poration systems in which the membrane material is

made of a hydrophobic rubbery polymer such as sil-icone rubber. This has been confirmed by several ex-perimental studies [5,18,21,25]. For this reason, theplastication factor for water, εww, could be assumedto be close to 0 in this study. However, the plastica-tion factors for the organic permeants, εwi , have to befound from pervaporation experiments, or estimatedusing an empirical relationship.

By adding Eqs. (32) and (33) to Eq. (21), a com-plete model for predicting the influence of permeatepressure on the separation factor is obtained.

3. Materials and methods

3.1. Feed solution

A previously developed model solution of applejuice aromas was used as the feed solution [26]. Tenaroma compounds, all of which were identified inapple juice from Spanish Granny Smith’s apples,were selected for inclusion in the feed solution.Four of the selected aroma compounds were alco-hols, i.e. iso-butanol, n-butanol, iso-amyl alcohol andn-hexanol, one was an aldehyde, i.e. trans-2-hexenal,and five were esters, i.e. ethyl acetate, ethyl bu-tanoate, ethyl-2-methyl butanoate and hexyl acetate.Each aroma compound was used at a concentrationof 10 ppm (w/w). Demineralised and distilled Milli-Qwater, with a resistance greater than 18 M� cm, wasused as the solvent. The aroma compounds used toprepare the solution had a purity of about 99%.

3.2. 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/m2h.

3.3. Pervaporation apparatus

The experimental set-up is shown in Fig. 3. Aplate-and-frame module with a membrane area of184 cm2 was used. The dimensions were 0.75 mm


Fig. 3. Experimental set-up of the pervaporation apparatus.

× 20 mm and the hydraulic diameter was 1.45 mm.An accurate gear pump was used to recirculate theretentate to the temperature-controlled feed vessel(10 l). The permeate was collected in cold traps bycondensation, either with liquid nitrogen at −196◦Cor with dry ice at −56◦C. Vacuum was achieved witha vacuum pump, which also separated inert gasesfrom the permeate. The vacuum controller measuredthe permeate pressure and controlled opening andclosing of the magnetic valve (see Fig. 3). The vac-uum controller was adjusted to allow the permeatepressure was to vary within a range of 1 mbar.

3.4. Experimental procedures

The membrane was conditioned for 12–16 h withMilli-Q water before each experiment. The feedtemperature was 20.0◦C and the feed flow velocitycorresponded to a Reynolds number of 415. The per-meate pressure was varied in the range 0–16 mbar.During conditioning, dry ice was used for condensa-tion, whereas during the experiments liquid nitrogenwas used. About 3 h after starting the pervapora-tion process, the feed temperature was stable and amass transfer equilibrium was deemed to have beenestablished. The cold trap was exchanged every hour

and the permeate was thawed and poured back intothe feed tank to limit the loss of aroma compoundsfrom the feed. During the fourth hour, permeate wascollected and samples from the feed tank were takenfor analysis. The total flux was determined gravimet-rically with an experimental error of 1–2%.

3.5. Analysis

The aroma compound concentrations in both thefeed and the permeate were analysed with a VarianVista 6000 gas chromatograph (Varian Associates,Sunnyvale, CA, USA). The gas chromatograph wasequipped with a fused silica capillary GC column(NB-351, 25 m, 0.32 mm, Nordion Instruments OyLtd., Helsinki, Finland). The temperature change wasprogrammed from 55 to 93◦C at a rate of 6◦C/min,and then from 93 to 110◦C at a rate of 30◦C/min, withan initial holding period of 1 min and a final holdingperiod of 9 min. The injector and detector were setto 180 and 190◦C, respectively. The carrier gas wasnitrogen at a flow rate of 1.22 ml/min, and the samplewas split 1:70 in the injector. As internal standard1-pentanol was used. Each concentration determina-tion was based on three or four different injections.The values of aroma concentrations varied by 5–10%.


4. Results and discussion

4.1. Modelling the influence of permeatepressure on αP

i

In an earlier study, it has been shown that perva-poration of the alcohols iso-butanol, n-butanol andiso-amyl alcohol under the present operating condi-tions did not cause concentration polarisation [17]. Forthese components αP

i could be obtained from the ex-perimental results as the relation between the overallmass transfer coefficient for the alcohols and water, as-suming that the overall mass transfer coefficients wereequal to the membrane mass transfer coefficients. InFig. 4, the values of αP

i are plotted versus the permeatepressure for these alcohols. The experimental resultsshow that αP

i strictly decreases with increasing per-meate pressure. The first approach to modelling wasto fit the data to a simple linear polynomial functionand the agreement between the linear fit and the datawas indeed very good, with standard deviations of 4%for iso-butanol and 6% for butanol and iso-amyl al-cohol. In addition, the αP

i values of the fitted linearcurves were equal to 0 at permeate pressures closeto the equilibrium vapour pressure of the feed. Foriso-butanol, n-butanol and iso-amyl alcohol the per-meate pressure was 24, 28 and 31 mbar, respectively,at this point, which should be compared with the equi-librium vapour pressure of the feed solution which was23 mbar. Based on the assumption that αP

i (pf) = 0,the following model was suggested:

αPi (pp) = αP

i (0)

(1 − pp

pf

)(34)

The second approach to finding a model with whichto predict αP

i was to fit the data to the exponentialmodel, which was derived from theory (see Eqs. (32)and (33)).

For iso-butanol, n-butanol and iso-amyl alcohol, thestandard deviations from the fitted curves were com-parable to those obtained for the linear fit (see Fig. 4).Due to the small differences in standard deviations forthe two proposed models, it is so far not possible todeduce which one is preferable. However, by perform-ing a series expansion of the exponential model, i.e.on Eq. (32), according to McLaurin’s formula

f (x) = f (0) + f ′(0)x + f ′′(0)2!

x2 + · · · (35)

Fig. 4. The experimentally obtained values of αPi for the alcohols

iso-butanol, n-butanol and iso-amyl alcohol vs. the permeate pres-sure. The solid lines correspond to curves obtained from the linearmodel, according to Eq. (34), and the dashed lines correspond tocurves fitted to an exponential function by regression, accordingto Eq. (32). The equations of the fitted curves and their standarddeviations are also given.

combined with the assumption that there is no des-orption of organic compounds at a permeate pres-sure equal to the equilibrium vapour pressure of thefeed solution, the initial linear polynomial model, i.e.


Fig. 5. The experimentally obtained values for VP vs. the permeatepressure. The function VP(pp) according to Eq. (13), with anexperimentally obtained value of Jtot(0), is represented by the solidline.

Eq. (34), is obtained if second-order terms and higherare neglected. The linear model is consequently a goodapproximation of the exponential model in the caseof small negative values of the exponent constant, b,defined as b = φ0

w(εwi − εww)/2pf (compare withEq. (32)).

4.2. Modelling the influence of permeate pressureon αPV

i

From the experimental results, the velocity of thefluid perpendicular to the membrane surface, VP, can

Table 1Some properties of the permeants studieda

Permeant γ∞i p0,i (mbar) αPV

int,i (0) CPM(0)i b (mbar−1)

iso-Butanol 55.5 [29] 11.84 [27] 39 1 −0.06n-Butanol 55.5 [29] 6.11 [28] 40 1 −0.05iso-Amyl alcohol 153 [29] 2.99 [28] 54 1 −0.05n-Hexanol 426 [29] 0.89 [27] 171 [26] 0.615 −0.05trans-2-Hexenal 400 [29] 8.12 [29] 701 [26] 0.405 −0.170Ethyl acetate 153 [29] 98.44 [27] 404 [26] 0.536 −0.127Ethyl butanoate 1860 [29] 17.46 [28] 2220 [26] 0.157 −0.203Ethyl-2-methyl butanoate 5640 [29] 25.88 [28] 3710 [26] 0.087 −0.23iso-Amyl acetate 3830 [29] 5.95 [28] 3220 [26] 0.115 −0.22Hexyl acetate 11300 [29] 1.34 [30] 3810 [26] 0.102 −0.26Water 1 23.37 [27] 1 1 –

a The activity coefficients at infinite dilution in water, γ∞i were estimated using a UNIFAC method. The equilibrium vapour pressures,

p0,i , were obtained through Antoine’s constants from the literature, for all compounds except trans-2-hexenal. In this case, Antoine’sconstants were estimated through a method based on the Clausius–Clayperon equation. The intrinsic separation factor at zero permeatepressure, αPV

int,i (0), the concentration polarisation modulus at zero permeate pressure, CPM(0)i and the adjusted values of b, according toEqs. (21) and (32), for the permeants are also presented.

be obtained as the total flux divided by the densityof the feed solution. In Fig. 5, the experimentally ob-tained values of VP are plotted versus the permeatepressure. In addition, the function VP(pp) according toEq. (13) is presented in the same graph.

The agreement between the model and the exper-imental data is satisfactory and the model is deemedto be valid for predictions of VP. There is, however,a small deviation of the results from the model as thepermeate pressure approaches 15 mbar. This devia-tion could be explained by the presence of a smallleakage of air into the vacuum chamber during theexperiments. An air leakage into the system woulddilute the permeate vapour and thus improve the driv-ing force of the process. This effect caused slightlyhigher fluxes than expected at high permeate pres-sures. In addition, the linear relationship between VPand permeate pressure found experimentally verifiesthe assumption that the water permeability is inde-pendent of permeate pressure. Consequently, it ispossible to assume that εww is close to 0.

Apart from VP and αPi , the mass transfer coefficient

of the feed boundary layer, kvbl,i , is also required to ob-

tain the separation factor of the process from Eq. (21).Applying Eqs. (10) and (14) at a permeate pressure of0 mbar, kv

bl,i can be calculated according to

kvbl,i = VP(0)

ln[(CPM(0)i−αPVi (0))/(1−αPV

i (0))](36)


Fig. 6. The separation factors, αPVi , for the alcohols studied are

plotted vs. the permeate pressure. The experimentally obtainedresults are presented as solid symbols, the solid line correspondsto the simple model according to Eqs. (21) and (34), and thedashed line corresponds to the model according to Eqs. (21) and(32) with the adjusted value of b given in Table 1.

In an earlier study, the intrinsic separation factors forthe POMS-PEI membrane with an active layer of thesame thickness, αPV

int,i (0), were determined at 20◦C[26] (see Table 1). According to the definition of theconcentration polarisation modulus, CPM(0)i can beobtained as the relation between αPV

int,i (0) and αPVi (0)

and thus, kvbl,i can be calculated from Eq. (36). Eq. (21)

was then combined either with Eq. (34), for applica-tion of the linear model, or with Eq. (32), for applica-tion of the exponential model, in order to include thepressure dependence of αP

i in the model. In addition,the resulting equation obtained from the exponentialmodel had to be fitted to the experimentally obtainedseparation factors by adjusting the value of the expo-nent b. The adjusted values of b are listed in Table 1.

The final models predicting the pressure depen-dence of αPV

i for the various components are shownin Figs. 6 and 7 as dashed curves for the linear modeland as solid curves for the exponential model.

Fig. 7. The separation factors, αPVi , for the esters and the aldehyde

studied are plotted vs. the permeate pressure. The experimentallyobtained results are presented as solid symbols, the solid linecorresponds to the simple model according to Eqs. (21) and (34),the dashed line corresponds to the model according to Eqs. (21)and (32) with the adjusted value of b given in Table 1.

It can be seen that there is very good agreementfor all the compounds studied between the separationfactors obtained from the exponential model and thecorresponding experimental results. In the case of lowvalues of the exponent b, which is the case for all thealcohols studied, the functions of the separation fac-tors obtained from the exponential model, as expectedalmost overlap the corresponding function obtainedfrom the linear polynomial model, as can be seen inFig. 6. The values of b for the aldehyde and the estersare significantly higher than for the alcohols, whichexplains the large deviation of the separation factorsobtained from the linear polynomial model from the


experimental results in Fig. 7. With the exponentialmodel it can be seen in Fig. 7 that it is possible toadjust the value of b such that the separation factorsobtained for all the components studied are in agree-ment with the experimental results. Efforts were alsomade to fit the separation factors of the esters and thealdehyde obtained from the linear polynomial modelsuch that they would approach the corresponding ex-perimental results. This was done by adjusting the val-ues of Pf , Hi and αP

i in Eqs. (21) and (34). However, itwas not possible in any of these cases to obtain a rea-sonable agreement between the predicted separationfactor and the experimental results since the shape ofthe theoretical functions deviated considerably fromthat of the experimental results. For this reason, itcould be concluded that the linear polynomial modelfor the estimation of αP

i can only be applied in thecase of low values of b, whereas the exponential decaymodel can be applied in all cases.

For four of the esters, i.e. ethyl butanoate,ethyl-2-methyl butanoate, iso-amyl acetate and hexylacetate, the shape of the curves differed from thatof the others. For these components, the processseparation factors were almost constant with respectto permeate pressure at low permeate pressures. Athigher permeate pressures, the separation factors be-gan to decrease with increasing permeate pressure.Several other researchers have earlier reported thistype of plateau behaviour of the separation factor asa function of the permeate pressure [5,25,31–33].

This plateau behaviour could be explained as a bal-ance between the effect of decreasing concentrationpolarisation due to decreasing total flux, which causesan improvement in the separation factor, and theeffect of poorer separation properties of the selectivelayer with increasing permeate pressure. This expla-nation is supported by the experimental results, sincethe behaviour was observed for components causingthe most severe concentration polarisation. This is inagreement with the reported concentration polarisa-tion modulus at zero permeate pressure for the variouscomponents in Table 1.

As can be seen in Figs. 6 and 7, the process sep-aration factors decreased with increasing permeatepressure for all the permeants studied with the ex-ception of four esters, which gave rise to consid-erable concentration polarisation. According to thediscussion above, the effect of decreased concentra-

tion polarisation and reduced membrane separationproperties with increasing permeate pressure, at lowpermeate pressures, cancel out, resulting in an almostpressure-independent separation factor.

4.3. Prediction and interpretation of membraneplastication

Hydrophobic pervaporation membranes generallydo not swell as much as hydrophilic ones, but someplastication of hydrophobic silicone rubber mem-branes has been observed [18]. As can be seen fromTable 1, negative values of the exponent b were ob-tained for all organic compounds studied, indicatingplastication. Since εww could be assumed to be closeto 0, and both φ0

w and pf have positive values, εwi ,could be concluded to have a negative value. Thephysical interpretation of a negative plastication fac-tor is polymer shrinking. The authors suggest that theshrinking mechanism could be explained by phaseseparation on a very small scale inside the polymerlayer. Small domains of water are formed due to itsvery low solubility in the polymer. These domainswould then exert pressure on the polymer chains,which would bring them closer together, i.e. shrink.Such a mechanism would cause a reduction in thediffusion rate of the hydrophobic permeants for tworeasons. The mobility of the permeants would de-crease due to shorter distances between the polymerchains. In addition, the length of the diffusion pathswould increase as these permeants would, to someextent, be hindered from diffusing through the waterdomains. Thus, the suggested shrinking mechanismpredicts reduced membrane selectivity. This mecha-nism would also predict decreased membrane selec-tivity with increasing permeate pressure. Plasticationof the membrane is dependent on the permeate pres-sure, since the local permeate concentration insidethe membrane increases with increasing permeatepressure. At zero permeate pressure, only a thin layerof the active membrane layer close to the feed isplasticised, whereas at a permeate pressure close tothe equilibrium vapour pressure of the feed the ma-jor part of the active layer is plasticised. Accordingto Nguyen, reduced membrane selectivities are ex-pected in cases of membrane plastication; the morehydrophobic the permeant, the larger the decrease inmembrane selectivity [34]. In the proposed exponen-


tial model, the value of exponent b determines the rateat which the selectivity of the membrane decreaseswith increasing permeate pressure. Since the goalwas to obtain a complete model for the predictionof the influence of permeate pressure on the processseparation factor, some way of predicting the valuesof b for the various permeants must also be found.If the hypothesis that the value of b corresponds tothe plastication effect is correct, it would be possibleto find a relation between the value of b and the hy-drophobicity of the permeant, which increases withincreasing hydrophobicity. According to Lamer et al.[35] the activity coefficient at infinite dilution in wa-ter, γ∞

i, can be considered to be a measure of the

hydrophobicity of the molecule. In Fig. 8, the valuesof b obtained for the esters and the aldehyde studiedare plotted versus γ∞

i. The activity coefficients at

infinite dilution in water at 20◦C and 1 atm pressurewere estimated using a UNIFAC method [26], the val-ues obtained are presented in Table 1. As can be seenin Fig. 8, a relation exists between the two parameterswhich is in agreement with the hypothesis. A linearrelation between the value of b for the aldehyde andthe esters studied and the natural logarithm of γ∞

i

was obtained with a standard deviation of only 1%

b = 0.0099 − 0.0284 ln(γ∞i ) (37)

Fig. 8. The adjusted values of b for the esters and the aldehyde studied, obtained by fitting the experimental data to the model expressedin Eqs. (21) and (32), are plotted vs. the activity coefficient at infinite dilution in water for the permeants studied (see Table 1). The solidcurve was obtained by linear regression of the value of b vs. ln γ i .

Consequently, these results imply that it is possibleto predict the value of the exponent b for any per-meant within the chemical groups of aldehydes andesters, and that the plastication of the active layerseverely decreases the selectivity of the membranewith increasing permeate pressure, especially for veryhydrophobic permeants.

In addition, the very low values of b of about −0.05obtained for the alcohols studied (see Table 1), implythat the selectivity for alcohols is not substantially in-fluenced by the plastication of the membrane in com-parison with the esters and the aldehydes. Thus, theresults imply that the linear polynomial model for pre-dicting the pressure dependence of αP

i could be appliedto alcohols. The shrinking mechanism predicts the di-vergent behaviour of the alcohols compared with theother permeants studied. The water solubility of thealcohols is considerably higher than for the aldehydesand the esters, as they can form hydrogen bonds withboth water and with other alcohol molecules, whereasaldehydes and esters can only form hydrogen bondswith water. The alcohols would thus not be preventedfrom diffusing through the water region to the sameextent as the esters and aldehydes. Consequently, anincreased water content in the membrane would notdecrease the permeation rate of the alcohols as drasti-cally as the aldehydes or the esters.


4.4. Applicability of the model

One limitation of the model is that it can only beapplied at permeate pressures within the pressure re-gion studied, i.e. at permeate pressures no higher thantwo-thirds of the value of the equilibrium vapour pres-sure of the feed. At permeate pressures closer to theequilibrium vapour pressure of the feed solution, theseparation factor starts to increase. According to themodel, the process separation factor becomes equal tothe separation factor of the vapour liquid equilibriumin the feed solution at zero driving force. In reality, thismight not be the case at all. However, this limitationof the model is not crucial, since the model works verywell within the whole region of commercial interest.

The model was developed for dilute solutions ofvolatile organic compounds, and therefore, it does nottake the influence of flow coupling into consideration.The model is consequently only applicable for perva-poration of dilute solutions.

So far, the model has proved to be valid when per-vaporation is performed with a POMS-PEI membrane.Further studies are needed in order to extend the modelto other types of membranes.

The model has proved to be valid for permeantswithin the chemical groups of alcohols, aldehydes andesters. Investigations are required to validate the modelfor other chemical groups of permeants.

5. Conclusions

The model developed in this work allows the pre-diction of the influence of permeate pressure on thepervaporation process separation factor. The model in-cludes both the effect of external mass transfer andthe effect of altered membrane separation propertiesfor the various permeants. In addition, the experimen-tal results showed that it is important to consider bothof these effects when predicting the permeate pressuredependence of the process.

The results also support the theory that shrinkingof modified silicone rubber membranes for perva-poration reduces the selectivity of the membrane interms of reduced hydrophobicity. This effect causesa considerable reduction in the process separationfactors, especially in the case of very hydrophobicpermeants.

Acknowledgements

This work was supported by the European Com-mission through the AAIR project PL 94 1931. Theauthors wish to acknowledge GKSS Forschungzen-trum for generously supplying the pervaporation mem-branes. The authors also wish to thank Professor Vas-silis Gekas for valuable opinions on the theory of masstransfer.

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Documents

Pervaporation of volatile organic compounds from water: I Influence of permeate pressure on selectivity