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Z. Phys. Chem.219 (2005) 1243–1259 by Oldenbourg Wissenschaftsverlag, München

Separation of Organic Compoundsfrom Surfactant Solutions by Pervaporation.The Influence of a Micellar Phaseon Mass Transfer

By Th. Gittel, Th. Hartwig, and K. Schaber∗

Institut für Technische Thermodynamik und Kältetechnik, Universität Karlsruhe,D-76128 Karlsruhe, Germany

Dedicated to the memory of Prof. Dr. Dr. h.c. Ernst Ulrich Franck

(Received March 31, 2005; accepted May 10, 2005)

Pervaporation / Surfactant / Mass Transfer / Micellar Phases

Volatile organic compounds (VOCs) can be separated from aqueous micellar surfactantsolutions with high efficiency by pervaporation processes using organophilic polymermembranes. This seems to be a surprising result because the transmembrane flux ofa VOC strongly depends on its volatility, which is rather low in the presence ofa surfactant at concentrations far above the critical micellar concentration.

Based on results of equilibrium measurements in micellar systems and pervaporationexperiments, a theoretical analysis of the mass transfer is given. It is shown that themass transfer for VOCs in the liquid boundary layer of a pervaporation membrane inthe presence of a micellar phase cannot be described by molecular diffusion processesalone. Obviously, the mass transfer is enhanced considerably by diffusing micelles whichtransport the solubilized VOC molecules in direction to the surface of the membrane.

1. Introduction

Pervaporation is a membrane separation process for liquid mixtures charac-terized by the selective mass transport through a non-porous polymeric mem-brane. The permeating compounds dissolve into the polymeric layer of themembrane, diffuse through it, and evaporate at the back of the membrane,mostly under vacuum conditions.

* Corresponding author. E-mail: [email protected]

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1244 Th. Gittelet al.

The term “pervaporation” has been introduced by Kober in 1917 [1]. Ac-tual overviews on membrane separation processes in general are given byRautenbach [2], Mulder [3] and Baker [4].

For pervaporation processes usually composite membranes are used whichconsist of a dense polymeric layer and a supporting porous sublayer. Thethickness of the active layer is between 5 and 20µm. The material of theactive layer is selected according to the compounds which have to be sepa-rated. Hydrophilic membranes (polyvinylalcohol, PVA; polyacrylnitrile, PAN)will preferentially transport water relative to organic compounds, andviceversa organophilic membranes (polydimethylsiloxane, PDMS; polyether-block-polyamide, PEBA) will enrich organic compounds in the permeate.

Pervaporation modules with composite membranes are commerciallyavailable in various configurations such as spiral wound, hollow fiber, and plateand frame (flat sheet) modules.

Pervaporation is applied in a variety of industrial separation processes.As examples water removal from ethanol and isopropanol [5], the separationof azeotropic organic mixtures [6], and the removal of volatile organic com-pounds (VOC) from water [7, 8] can be mentioned. Mainly pervaporation isused as a separation step in hybrid processes [9, 10].

Recently, pervaporation processes have been suggested for the separa-tion of volatile organic compounds (VOCs) from aqueous micellar surfactantsolutions. Such kind of process fluids stem, for example, from surfactant en-hanced soil remediation processes. Ithas been successfully demonstrated inpilot plants that pervaporation can be used to remove hazardous VOCs fromthese process fluids without affecting the surfactant permitting the recycling ofthe aqueous surfactant solution [11–15].

In principal, for the economic operation of pervaporation processes suffi-ciently high transmembrane fluxes (TMF) and selectivities must be achieved.

The driving force for the transmembrane flux of a permeating componentithrough the pervaporation membrane is adifference of chemical potentials onboth sides of the membrane,i.e. the feed side (F) and the permeate side (P).

∆µi = µiF −µiP (1)

Assuming isothermal conditions across the membrane∆µi can be written as

∆µi = RT lnf iF

f iP

. (2)

f iF and fiP are the fugacities of componenti in the bulk phases on both sides ofthe membrane. The fugacityf iF is that of a component in a liquid mixture L.For low pressures the extended Raoult’s law with the activity coefficientγi ,the mole fractionxi, and the pure component vapor pressurepois(T ) can beapplied.

f iF = f LiF = xiγi pois(T ) (3)

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Separation of Organic Compounds from Surfactant Solutions. . . 1245

The fugacity f LiF is equal to the equilibrium partial pressurepiF in a (non ex-

isting) gas phase on the feed side of the membrane. The fugacityfi p can bereplaced by the partial pressurepiP on the permeate side assuming an ideal gasphase. Consequently Eq. (2) can be transformed to

∆µi = RT lnpiF

piP

. (4)

Permeation takes place if the potential difference∆µi is positive, i.e. forpiF > piP.

For constant values of the permeate partial pressurepiP the transmembraneflux (TMF), which is approximately proportional to∆µi, can be increased byincreasing the temperature and thus the vapor pressurepois(T ), or by increas-ing xi.

At small mole fractionsxi , the partial pressurepiF becomes low and thetransmembrane flux tends to very low values.

Considering that in the presence of a micellar phase at relatively highsurfactant concentrations the extramicellar mole fractionsxi,ex of permeatingVOCs are rather low, the good performance of such kind of pervaporationprocesses resulting from obviously high VOC transmembrane fluxes is a sur-prising result.

The present paper elucidates this special mass transfer effect in micellarsolutions.

At first equilibrium vapor pressure data of aqueous VOC-surfactant solu-tions and typical results of permeation experiments are presented. Afterwards,based on these data, a theoretical analysis of the mass transfer is given.

2. Experimental2.1 Material

The membrane used in the experiments is a composite membrane type CMX-GF-010-D (CM-CELFA) consisting of two layers. The active layer made ofpoly-dimethyl-siloxane (PDMS) is about 10µm in thickness. The porous sup-porting layer is made of polyether-copolymer. Its influence on the separationperformance can be neglected.

Lutensol FSA10 (BASF AG) is a non-ionic surfactant with 10 ethylenoxidegroups. The critical micellar concentration is 0.01 g/l in water at ambient con-ditions. Normally it is usede.g. in aqueous subsurface remediation or industrialdegreasing process steps.

As an ionic surfactant Hexadecyl-trimethylammoniumbromide (CTAB,Merck) was used. CTAB is a cationic surfactant with a critical micellar concen-tration of 0.29 g/l in water at ambient conditions.

As volatile organic compounds (VOCs)p-xylene and naphthalene, whichare nearly unsoluble in water, were dissolved in aqueous solutions of Luten-

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Fig. 1. Flow sheet of the laboratory installation for pervaporation experiments.

sol FSA10 and CTAB, respectively. The normal boiling temperature (p =1013 mbar) ofp-xylene is 138.35 ◦C, that of naphthalene 217.95 ◦C. Bothproducts were provided by Merck with a purity of≥ 99%.

For the analysis of the liquid mixtures, a HPLC device was used (HewlettPackard 1100). Separations were performed on a Nucleosil 100-5 RP 18 (125×4 mm ID) column protected by a Nucleosil 100-5 RP 18 (4×4 mm ID) columnby Hewlett Packard. The samples of feed solution taken during the experimentwere stored in a cool place and analysed within 36 hours.

2.2 Equipment

Fig. 1 shows a scheme of the laboratory installation for pervaporation experi-ments. The feed tank is 1 liter of volume and made of glass. A gear type pump(V = 100. . . 300 l/h) is used to circulate the feed solution to the membrane celland back to the feed tank. The volumetric flow is measured by a rotameter andthe temperature of the feed is controlled by a resistance thermometer Pt 100.A rotary vane pump is keeping a constant vacuum at the permeate side. Thepermeate is collected in cooled traps, filled with liquid nitrogen. Two traps areinstalled in parallel and can be operated alternately. The tubes on the permeateside between membrane cell and cooling traps are heated to avoid condensationof gaseous permeate. All tubes on feed and permeate side are made of stainlesssteel or PFA, respectively, to minimize adsorption of organic compounds.

Fig. 2 shows the cross-section of the membrane cell, which is designed fora flat sheet membrane. The effective membrane surface which is in contact withthe feed solution is about 40 cm2. The inlet is above the center of the membraneand the feed channel is forcing the liquid on a spiral way to the outlet. Therectangular cross section has a width and height of 5 and 1.5 mm, respectively.The membrane itself is supported by a porous metal plate. This membrane cellconfiguration allows an operation at well defined flow conditions (Reynoldsnumbers) along the membrane surface. A more detailed description of the ex-perimental setup is given elsewhere [15].

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Fig. 2. Cross section of the membrane cell.

2.3 Vapor–liquid equilibria in micellar solutions

The partition of the organic compound between micelle and continuous phaseis an important property of the feed solution, but not easy to determine. Gossettand Lincoff have published a method to find out how much is in and outsidethe micelle at equilibrium [16, 17]. The method is called equilibrium partition-ing in closed systems (epics) and based on determining Henry’s law constantsby a GC-Headspace procedure for solutions with and without the presence ofsurfactant. The advantage of the procedure is that no absolute concentrationshave to be measured. The determination of relative concentrations is sufficient.A detailed description of theory and the way the procedure is adapted in thiswork is given in [15–17].

Vapour–liquid equilibria in highly diluted solutions – as used in the presentinvestigation – can be described by Henry’s law:

cGi = Hccc

Li . (5)

With surfactant, the expression changes to

cGi = Hccc

Li f . (6)

cLi is the overall concentration of the volatile organic compoundi in the liquid

phase, which includes the extramicellar concentrationci,ex and the concentra-tion ci,m of moleculesi which are solubilized in micelles.

With (5) and (6), the dimensionless extramicellar fractionf is given as

f = ci,ex

cLi

= ci,ex

ci,ex+ ci,m

. (7)

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Fig. 3. Extramicellar fraction ofp-xylene over surfactant concentration at different tem-peratures.

Fig. 3 presents results of measurements with the epics method for thep-xylene–Lutensol FSA10 system at different temperatures and concentrationsof Lutensol FSA10. Starting from a pure aqueous solution where the valueof the extramicellar fraction ofp-xylene is f = 1.0 the fraction is decreas-ing considerably with increasing concentration of surfactant. At a surfactantconcentration of 1% more than 80% ofp-xylene is inside the micelles andhas no influence on the partial pressure ofp-xylene. The influence of thetemperature is only small compared tothe effect of the increasing concentra-tion.

At temperatures higher than 42◦C a phase separation could be observed.Two phases are formed, one phase with a high, the other with a low surfactantconcentration. As the curve at 50◦C shows, the phase separation has no im-pact on the (overall) Henry coefficients or the (overall) extramicellar fractions,respectively.

Nevertheless, in order to exclude any effects of phase separation on themass transfer in the liquid boundary layer, all pervaporation experiments havebeen performed at a temperature of 40◦C.

In literature, similar experimental results for systems with non-ionic surfac-tants and chlorinated hydrocarbons are published [18].

Data of partitioning coefficients for the CTAB–naphthalene system meas-ured by fluorescence quenching are given in [19]. The partitioning coefficient

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K is defined as

K = xi,m

ci,ex

= 1− f

f

1

S − SCMC

. (8)

whereS represents the surfactant concentration. The extramicellar fractionffor the CTAB–naphthalene system was calculated with Eq. (8), using data fromliterature [19].

2.4 Results of permeation experiments

The first important result of the experiments carried out at the laboratory instal-lation described above is the fact that the surfactant molecule could not pass themembrane. The transmembrane flux consists only of water and the volatile or-ganic compound. In the analysis of permeate samples of different experimentsno surfactant could be identified in the chromatogram. Based on this, a seriesof experiments was performed to investigate the influence of the surfactant onthe mass transfer of the volatile organic compound [15].

To assess the impact of the concentration of the permeating component onthe VOC depletion in the feed vessel aset of experiments were carried out,where only the initial concentration of the organic compound was varied. Thetemperature of the feed solution, the volumetric flow, the surfactant concentra-tion and the permeate pressure were kept constant.

Fig. 4 shows the experimental results forp-xylene. The data for variousinitial concentrations have been fitted by a least square minimization method.The concentration ofp-xylene is standardised with the initial concentrationand plottedversus the time the solution was treated. Nearly no difference canbe seen in depletion between different initial concentrations within the inves-tigated concentration range. Obviously, the concentration ofp-xylene has noinfluence on the course of the depletion curve and the mass transfer velocityitself, respectively.

In Fig. 5 four experiments withp-xylene are compared which are carriedout at different volumetric flow rates through the membrane cell, but otherwiseunchanged conditions. The volumetric flow can be expressed as a Reynoldsnumber Re, because of the constant cross section and viscosity. Increasing theRe number, which means increasing volumetric flow, has a positive influenceon the depletion ofp-xylene. The mass transfer coefficient within the mem-brane and the permeate is the same at all experiments, only the flow conditionson the feed side are changed. The thickness of the liquid boundary layer onthe surface of the membrane changes with the turbulence of the feed stream.A higher Reynolds number means a thinner boundary layer, and consequentlya lower mass transfer resistance for the volatile organic compound. This is thereason why the concentration is decreasing faster.

Fig. 6 shows a set of experiments where only the concentration of the sur-factant was varied and the other parameters were kept constant.

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Fig. 4. Depletion of p-xylene from surfactant solutions starting at different initial concen-trations.

Fig. 5. Influence of Re-number on depletion ofp-xylene from surfactant solutions.

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Fig. 6. Influence of surfactant concentration on depletion ofp-xylene.

Treating the binary mixture of water andp-xylene without surfactant theinitial concentration could be reduced to less than 10% within 300 min.

In the presence of surfactant Lutensol FSA10 thep-xylene concentrationdrops less rapidly because of the solubilization of the VOC in micelles and thehigher viscosity of surfactant solutions.

For thep-xylene–Lutensol FSA10 system the depletion curves for variousLutensol FSA10 concentrations are nearly identical within the accuracy of themeasurements.

The naphthalene–CTAB system exhibits a qualitative similar depletion be-haviour, as shown in Fig. 7, but the depletion of naphthalene happens slowlierthan that of xylene. Furthermore, a higher impact of the surfactant on the de-pletion velocity was observed. With an extramicellar fractionf of 15%, thenaphthalene concentration was reduced to 50% of its initial value whereasp-xylene could be reduced to 20% under the same conditions.

This can be explained with the lower saturation vapor pressure of naphtha-lene compared top-xylene, leading to a lower gradient of chemical potentialsaccording to Eqs. (3) and (4) and thus to lower transmembrane fluxes.

Fig. 8 gives an impression of the transmembrane fluxes ofp-xylene andnaphthalene at various feed concentrations. The concentrations of the VOCsin permeate samples taken from the cooling traps in well defined intervals andanalysed at the HPLC system, were used to calculate the partial fluxes of theVOCs from the total.

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Fig. 7. Influence of surfactant concentration on depletion of naphthalene.

Fig. 8. Transmembrane fluxes ofp-xylene and naphthaleneversus VOC feed concentra-tion.

In a first approach a linear dependency between flux and feed concentrationcan be assumed. The mass fraction ofp-xylene of the total flux is lower than

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10% under all conditions investigated. In case of naphthalene, the mass fractionis less then 5%. More than 90% of the flux is water.

3. Theory

Based on the experimental results, the mass transfer mechanisms were ana-lysed, with the focus on the liquid boundary layer on the feed side of themembrane. The analysis is performed forp-xylene at a temperature of 40◦C.

The driving force for the transmembrane flux of a componenti is the dif-ference of the chemical potentials on both sides of the membrane, as alreadypointed out.

But most of all common mass transfer relationships in chemical engin-eering are formulated with concentration based properties instead of chemicalpotentials. Following this classical approach the area related mass transfer vel-ocity for low mass fluxes can be written:

n i = Ni

AM

= k(ciF − ciP) . (9)

The overall mass transfer coefficientk can be expressed with a resistance inseries model of the single resistancesof liquid boundary layer, membrane andpermeate space:

1

k= 1

k l

+ 1

km

+ 1

kp

. (10)

When aqueous diluted systems at low permeate pressure are investigated, thepermeate concentrationciP in Eq. (9) is normally neglected [20–22].

In this work another approach was made to describe the mass transport.The concentration in the permeate side was not simply neglected, but usingHenry’s law and assuming ideal gas behaviour the following expression wasderived [15]:

n i = 1(1kl

+ 1km

+ pnwRTHCC

)ciF . (11)

To make Eq. (11) more handy an overall mass transfer coefficientkov is intro-duced.

n i = kovciF (12)

The mass balance around the membrane cell with the assumption of a plugflow in the feed channel gives the following expression in terms of the con-centration of the compoundi entering the membrane cell (index “M” for

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membrane cell) with the active membrane surfaceAM:

cMi,out = cM

i,in exp(

−kovAM

V

). (13)

The behaviour of the feed vessel can be expressed as a continuous stirredtank reactor (index “T” for tank):

VdcT

i

dt= V

(cT

i,in − cTi

). (14)

Combining the balance for the membrane cell and the feed vessel gives thefollowing equation

ln

(cT

i

cTi,0

)= t

τ

[exp

(−kovAM

V

)−1

], (15)

with cTi,0 as the initial feed concentration of the compoundi and the residence

time τ = V/V . Eq. (15) is used to estimatekov from the measured depletioncurves by fitting the measuring points to a curve of an exponential type.

The valuekov takes into account the liquid boundary layer, the membraneand the permeate concentration in terms of the permeate pressure. To find outthe fraction of the mass transfer resistances of these three parameters, they haveto be separated.

A well-known method to determine the fraction of the single parameters isthe so called Wilson plot [19, 23].

Fig. 9 shows a Wilson plot, based on results ofkov calculated from fittedcurves in the way presented above, all at same conditions of permeate pressure,surfactant concentration and feed temperature. 1/kov is plotted over the recipro-cal volumetric flow to the power ofb. The value ofb is normally between zeroand one and fitted to give a straight line. Extrapolating the line to infinite highflow (1/V b → 0) the resistance of the membrane and the permeate pressure canbe read on the ordinate:

1

kM

+ p

nWRTHCC

= 1661s

m. (16)

Using this valuekov can be separated and the desired value ofk l is avail-able. It has to be emphasized that this value is only valid for fixed conditionsof permeate pressure, temperature and membrane properties. If one of theseparameters would change a new Wilson plot is needed.

In relation to the total mass transfer resistance the fraction of the membraneand the permeate space is small. Depending on the feed flow it is only between4 and 6% of the total value at given conditions.

Fig. 10 shows some values fork l calculated from experiments in the pre-sented way for different surfactant concentrations (filled circles) and for thep-xylene–water system, too (k l = 7×10−5 m/s).

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Fig. 9. Wilson plot for experiments carried out at 40◦C and 30 mbar for thep-xylene-Lutensol FSA10 system. The dotted line represents the extrapolated part of the regressionline.

Fig. 10. Mass transfer coefficientkl of the liquid boundary layer over surfactant concentra-tion for the p-xylene-Lutensol FSA10 system. Experimental results and theoretical masstransfer coefficients based on diffusion of VOC molecules.

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The decreasing mass transfer coefficientsk l with increasing surfactant con-centrations can be explained by two mechanisms which can be quantified asfollows:– As shown in Fig. 3 the extramicellar fraction decreases with increasing sur-

factant concentration. Established mass transfer approaches take only thefree p-xylene molecules into account, because only these would have animpact on the partial pressure of the organic component in the feed so-lution, and only these molecules play an active role in the mass transferprocess. ConsequentlyciF in Eq. (11) has to be multiplied by the extrami-cellar fraction f and thusn i or the mass transfer coefficient, respectively,decreases by a factorf .

– Another effect of the surfactant is the increasing viscosity of the feed so-lution with increasing concentration. The influence of the viscosity on themass transfer can be estimated with a typical Leveque correlation whichallows to calculate the dimensionless Sherwood number for laminar or tur-bulent flow, respectively, and various geometries [24]:

Sh∼ Re0.33Sc0.33 f(geometry) (17)

with Sh= kl dD

, Re= wdν

, Sc= ν

d.

The Reynolds number has been kept constant for all experiments consid-ered for this mass transfer analysis, so the Leveque correlation can bereduced to

k ld

D∼

( ν

D

)0.33

.

The characteristic diameterd has a constant value and the diffusion coef-ficient D is proportional to the viscosity. Using the method of Hayduk andLaudie [25] to estimate the diffusion coefficientD gives a proportionalityof

D ∼ 1

ν1.14.

Thus the dependency ofk l from the viscosity can be estimated with

k l ∼ ν−0.4 . (18)

The viscosity of aqueous Lutensol FSA10 solutions has been measured forvarious temperatures with a falling sphere viscosimeter [15].

Comprising both effects, vapor pressuredepression due to micellar formation,and increasing viscosity with increasing surfactant concentration, one obtainsthe theoretical mass transfer coefficients plotted with the empty squares inFig. 10.

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Obviously the mass transfer in a liquid boundary layer containing a micel-lar phase cannot be explained by diffusion of molecules alone. The moleculardiffusion model including the viscosity effect underestimates the transmem-brane flux by about factor 3 if the surfactant concentration is higher than 0.8%or the extramicellar fraction is lower than 0.21, respectively.

4. ConclusionMass transfer coefficients of organic compounds in liquid boundary layers dropto lower values if the organic compounds are partly solubilized in surfactantmicelles.

But the degree of reduction of mass transfer fluxes in such kind of boundarylayers is considerably lower than could be expected if the diffusion of extrami-cellar molecules is assumed as dominating mass transfer mechanism.

Thus it can be concluded that mass transfer of VOCs in micellar surfactantsolutions within the liquid boundary layer of a pervaporation membrane takesplace not only by diffusion of extramicellar molecules but also by the diffu-sion of micelles, which transport solubilized VOC molecules in direction to themembrane surface. There the micelles release the included VOC molecules anddiffuse back to the bulk phase as micelles or surfactant molecules.

A detailed description of the relevant transport and decay mechanisms ofmicelles at the surface of a membrane is under investigation.

Acknowledgement

The authors would like to thank the Deutsche Forschungsgemeinschaft (DFG)for the financial support of this project.

Nomenclature

AM [m2] membrane surface areac [mol/l] concentrationD [m2/s] diffusion coefficentf [−] extramicellar fractionfi [bar] fugacity of componentiHcc [−] Henry coefficientK [l/mol] partitioning coefficientk [m/s] mass transfer coefficentN [mol/s] molar flown [mol/m2 s] area related mass transfer velocityp [mbar] pressurepois [mbar] vapor saturation pressure of componenti

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R [J/mol K] gas constantS [mol/l] surfactant concentrationT [K] temperaturet [s] timeV [l] volumeV [l/s] volumetric floww [m/s] velocityx [−] molar fraction

γi [−] activity coefficientν [m2/s] kinematic viscosityµi [J/mol] chemical potential of componentiτ [1/s] time of residence

subscripts

0 initial valueCMC critical micellar concentrationex extramicellarF feedi compoundiin incoming (in feed tank)L liquidm micellarout outgoing (out of feed tank)ov overallP permeateW water

superscripts

G gasL liquidM membraneT feed tank

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