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Review ArticleReview on Pervaporation Theory Membrane Performanceand Application to Intensification of Esterification Reaction

Ghoshna Jyoti Amit Keshav and J Anandkumar

Department of Chemical Engineering National Institute of Technology Raipur 492010 India

Correspondence should be addressed to Amit Keshav dramitkeshavgmailcom

Received 11 September 2015 Revised 17 November 2015 Accepted 26 November 2015

Academic Editor Georgiy B Shulrsquopin

Copyright copy 2015 Ghoshna Jyoti et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The esterification reaction is reversible and has low yield In order to increase the yield of reaction it is required to simultaneouslyremove the product of reaction For this membranes are the viable approach Pervaporation membranes have success in removalof components in dilute forms Membrane performance is represented in terms of flux sorption coefficient separation factor andpermeanceThese factors are related to the thickness of membrane temperature and feed concentration Higher flux is observed atlower membrane thickness and higher feed concentration of water and lower selectivity is observed at higher temperatures due toincreased free volume lower viscosity and higher feed side pressure Different factors affect the pervaporation aided esterificationreactor setup such as effect of initial molar ratios of the reactants effect of catalyst concentration effect ofmembrane area and effectof temperature Large membrane size could provide higher surface for the transfer of acid though the challenges of membranerupture do surround the studies In the present review work we tried to collaborate the works in totality of the pervaporationdesign starting from the membrane behavior to the process behavior Different prospective fields are also explored which needinvestigation

1 Introduction to Pervaporation

Separation of liquidmixtures by partial vaporization througha membrane (nonporous or porous) is the separation princi-ple in pervaporation This results in collection of permeatingcomponent in vapor form which may be either removed byflowing an inert medium or applying low pressure on thepermeant side The driving force for pervaporation processis the difference in chemical potential corresponding to theconcentration gradient between phases on the opposite sidesof the interfacial barrier Sorption diffusion model is usedto describe the transport on the basis of difference in themolecular size instead of volatility as in the case of distillationThus it could be effectively utilized as economical substituteazeotropic separations In addition to this the no use of thirdcomponent and requirement of low energy consumption (dueto energy integration) are the add-on benefits [1 2] In thelast two decades pervaporation is finding wide range of areasfor its application such as liquid hydrocarbons separations(petrochemical application alcoholether separations) [3ndash5]

removal of volatile organic compounds (VOCs) from water[6 7] removal of water from glycerin [8] and dehydration tointensify esterification reaction [9 10]

Pervaporation can be integrated with either distillationor a chemical production step to provide intensification andenergy integration Pervaporation-distillation hybrid systemleads to a clean technology and offer potential savings inenergy because of reduced thermal and pressure require-ments When integrated with reactions such as esterificationprocess it offers the opportunity to shift the chemical equi-librium by removing the product of the reaction Reactor-pervaporation hybrid method overcomes the inhibition ofthe chemical equilibriumof the process and therefore leads toan increased productivity This process also allows one to useheat of the chemical reaction to increase the efficiency of thepervaporation process and leads consequently to potentialsavings in energy costs

Membranes are successfully used in separation industriesas selective barriers to prevent unwanted solutes from perme-ating throughThus the impurity is separated from the target

Hindawi Publishing CorporationJournal of EngineeringVolume 2015 Article ID 927068 24 pageshttpdxdoiorg1011552015927068

2 Journal of Engineering

Reverse osmosis Ultrafiltration Particle filtration

NanofiltrationMicrofiltration

Dialysis

Gas separation

Pervaporation

Sorption diffusion Hydrodynamic sieving control

0000 0001 001 01 10 10 100 1000(120583m)

Figure 1 The choice of membrane with respect to the size of particles encountered

Separation is based on pore sizes and hence the membranesgot their characteristic names as microfiltration ultrafiltra-tion and nanofiltration membranes (Figure 1) Membranesare either porous or nonporous and in the separation basedon sizes usually porous membranes are used Pervaporationis the distinction class among above membranes as theseparation criteria are different Pervaporation membranesare nonporous and have been widely employed for sepa-rating liquid mixtures The separation feature is based onaffinity with membrane materials and hence the moleculehaving higher affinity is adsorbed and diffuses through themembranewhile themembrane retainsmolecules having lowaffinity

2 Membrane Materials for Pervaporation

For pervaporation the hydrophilic membranes were the firstone to achieve the industrial applications and were usedfor the organic solvent dehydration The main industrialapplications in pervaporation even today are almost the sameas before which is the dehydration of organic liquids Bymodifying the active layer of these membranes with differentchemical compositions and structures these membranesare enabled to extract water with broad ranges of fluxand selectivity [11 12] Commercially available hydrophilicmembranes are made of polymeric membranematerials suchas polyvinyl alcohol (PVA) polyimides polymaleimidesNafion and polyacrylonitrile (PAN)

Presently there have been a number of investigatorsconcerning RampD of the hydrophilic membrane which canbe cataloged into organic inorganic and organic-inorganichybridmembranes Inorganicmembranes such as zeolite andsilica are generally used [13 14] Inorganic membranes arevery suited for high temperature applications (harsh envi-ronments) and generally these membranes are prepared bysol-gel method which was appropriate to elaborate thin andporous layers with controllable porosity on a wide range ofchemically resistantmacroporous substrates [15]While theseinorganic membranes showed high dehydration efficiencytheir industrialization process may be slow-paced due to thecomplicated large-scale preparation and high manufacturingcost In addition to this several kinds of commercial organic

membranes including PERVAP 2201 [16 17] PERVAP 1005(GFT) [18] and GFT-1005 [19] have been introduced to thepervaporation-esterification coupling process Few studies oncross-linked poly(vinyl alcohol) membranes have also beeninvestigated such as PVA with catalyst Zr(SO

4)2sdot4H2O and

Amberlyst [20 21] cast on polyethersulfone [22 23] and onpoly(acrylonitrile) [24] However the inherent instabilities ofthese organic membranes severely limit their applications

Organic-inorganic hybrid materials have been proposedto be the best choice for having both the functionality of theorganic moiety and the stability of inorganic moiety Buddet al [25] employed zeolitepolyelectrolyte (chitosanpoly(4-styrene sulfonate)) multilayer pervaporation membranes toenhance the yield of ethyl lactate Adoor et al [26] pre-pared aluminum-rich zeolite beta incorporated sodium algi-nate pervaporation membranes Organic-inorganic hybridmembranes showed improved performance of pervaporativedehydration of solution with better flux and retention

Hydrophobic membranes used as pervaporation mem-branes are used to separate volatile organic compoundsfrom the body of water Hydrophobic membrane systemsutilize molecules made from proprietary polymeric hollowfiber membranes The membrane only permits the volatileorganic compound and rejects water molecule due to itshydrophobic nature Hence pervaporation integrated withmembrane separation technology serves as an interestingsubject for the separation of organic compounds such aspollutants and high-value products like aroma compoundsHere the membranes employed are polymeric in nature[27ndash29] Rarely ceramic membranes [30ndash34] can also beused However when it comes to recovering volatile polarorganics from their very dilute solutions in water [35] theselectivity exhibited by polymeric membranes as well asceramic membranes is not high [36ndash38]

One of the most applied polymeric materials for organicseparation is polydimethylsiloxane (PDMS) PDMS exhibitshigh selectivity and permeability towards organic substancesbecause of the flexible structure and therefore is preferredfor the removal of organic compounds from water [39]Organic liquid membranes of oleyl alcohol (OA) were foundto demonstrate high selectivity for recovering species liken-butanol and acetone [40] from simulated fermentation

Journal of Engineering 3

Membrane

Vacuum pumpFeed pump

Reactor

Condenser

Permeance

Retentate

Condenser

Figure 2 Schematic diagram of pervaporation-chemical reactor integrated system

broths Employing tri-n-octylamine (TOA) as a supportedliquid membrane (SLM) Thongsukmak and Sirkar [41]prepared liquid membrane of trioctylamine (TOA) in thecoated hollow fibers and demonstrated high selectivity of asmuch as 275 220 and 80 for n-butanol acetone and ethanolfrom a very dilute solution representative of an acetone-n butanol-ethanol (ABE) fermentation broth (15 wt n-butanol 08 wt acetone and 05 wt ethanol)

In hybrid configuration as the pervaporation membranereactor esterification is a typical example in which pervapo-ration is used for removal of the product or the byproductof a reaction (Figure 2) Esterification reactions are typi-cally reversible and equilibrium limited processes with esterand water as products Pervaporation-membrane reactors(PVMR) have a selective membrane for removal of waterfrom the esterification reaction mixtures and hence achieve ahigher yield of ester In pervaporation-esterification couplingsystems several types of commercial membranes are usedincluding GFT-1005 [19] polydimethylsiloxane [42] PER-VAP 2201 [16 43] and PERVAP 1005 [44 45] Table 1 showsthe various membranes employed for the pervaporation-esterification integrated system for the synthesis of severalesters such as methyl acetate ethyl acetate isobutyl acetateethyl acrylate and ethyl lactate

Zhang et al [46] employed three types of compositemembrane namely glutaral cross-linked chitosan (GCCS)carbomer (CP)polyacrylonitrile (PAN) glutaral cross-linked gelatin (GCGE)PAN and glutaral cross-linked hya-luronic acid (GCHA)hydrolysis modification- (HM-) PANto study esterification of lactic acid and ethanol In GCCSCPPAN composite membrane the content of the CP is05 wt and the molar ratio of the CS repeating unit to GA is60 For GCGEPAN composite membrane the content of theGE is 2 wt and the mass ratio of the GA to GE is 25 and inthe case of GCHAHM-PAN membrane the content of theHA is 08 wt and the cross-linking degree is 03 Korkmazet al [47] employed ester-permeable polydimethylsiloxane(PDMS) and the water-permeable poly(vinyl alcohol)membranes to study the esterification of acetic acid withisobutanol They prepared the membranes in laboratories

which are composed of the respective polymer and a cross-linking agent Zhang et al [48] employed a catalyticallyactive pervaporation membrane to enhance the conversionof esterification reaction of acetic acid and n-butanol Themembrane used consists of three layers a support layer(commercial PES porous membrane) a separation layer(PVA pervaporation membrane) and a porous catalytic layerwith the loading of catalysts

Currently it is great deal of interest in pervaporationassisted production of enzymatic esters by lipase-catalysedchemical esterification reaction because higher selectivitycan be achieved by the biotechnological way as milder reac-tion conditions should be applied thus energy demand costof production and byproduct formation can be simultane-ously reduced and the conversion or yield of biodiesels can beenhanced [49 50] Krishna et al [51] studied the esterificationof isoamyl alcohol with acetic acid in n-heptane solventusing immobilized lipase fromMucor mieheiThey presentedrelationship between esterification variables (substrate andenzyme concentrations and incubation period) and esteryield to determine optimum conditions for the synthesis ofisoamyl acetate catalyzed by Lipozyme IM-20 (immobilizedlipase from Mucor miehei) They observed that conversionover 95 achieved at even very low enzyme concentrationsZiobrowski et al [50] presented the enzymatic production ofglycerol monostearate in different high polar organic solventsto remove water produced during the esterification processusing pervaporation Shieh et al [49] investigated a commer-cial immobilized lipase from Rhizomucor miehei (LipozymeIM-77) to catalyze the transesterification of soybean oil andmethanol They developed relationships between the vari-ables (reaction time temperature enzyme amount substratemolar ratio and added water content) and the response(percent weight conversion) and obtained the optimumconditions for biodiesel synthesis using central compositerotatable design (CCRD) and RSM analysis Koszorz et al[45] studied the kinetics of enzymatic esterification of oleicacid and i-amyl-alcohol (main compound of fusel oil) In theexperiments an immobilized lipase enzyme Novozym 435(Novo Nordisk Denmark) which was taken as a catalyst and


Table 1 Pervaporation membranes employed for various esterification reactions

Membranes Nature of membrane Esterification reactions studied ReferenceChitosan-tetraethoxysilane hybridmembrane

Hydrophilic organic-inorganic hybridmembrane Lactic acid + ethanol [73]

Nafion membrane Hydrophilic catalytically active membrane Acetic acid + methanol [94]Acetic acid + butanol [94]

GFT-1005 and T1-b membrane Hydrophilic organic membrane Lactic acid + ethanol [19]Succinic acid + ethanol [19]

Polydimethylsiloxane membrane [PDMS] Hydrophobic cross-linked membrane Acetic acid + isobutanol [95]Acetic acid + ethanol [42]

PERVAP[2201]

Hydrophilic polymeric membrane

Lactic acid + ethanol [16][2201] Lactic acid + ethanol [9][2201] Lactic acid + ethanol [96][2216] Lactic acid + ethanol [96][1000] Acetic acid + ethanol [97][2201] Acetic acid + isopropanol [43][2201] Propionic acid + isopropanol [98][1005] Oleic acid + i-amyl alcohol [45][1005] Acetic acid + ethanol [18][1005] Acetic acid + benzyl alcohol [44]

Polyetherimide-120574 alumina compositemembrane

Hydrophilic composite polymeric-inorganicmembrane Acetic acid + ethanol [99]

Silica membrane [Pervatech BV] Hydrophilic inorganic membrane Lactic acid + ethanol [13]Polyetherimide composite membrane Polymericceramic membrane Acetic acid + ethanol [100]

PVA membrane Hydrophilic polymericceramic compositemembrane Acetic acid + n-butanol

[89][87][101]

PVAmembrane cross-linked with catalystZr[SO

4]2sdot4H2O Polymeric composite catalytic membrane Acetic acid + butanol [20]

PVA membrane [Amberlyst coated] Polymericceramic composite membrane Acetic acid + butanol [21]

PVA membrane [cast onpolyethersulfone]

Hydrophilic polymeric compositemembrane

Oleic acid + methanol [22]222Trifluoroethanol +methacrylic acid [23]

Zeolite membrane [aluminum rich zeolitebeta incorporated sodium alginate] Hydrophilic mixed matrix membrane Acetic acid + ethanol [26]

Zeolite T membrane Hydrophilic membrane Acetic acid + n-butanol [102]Acetic acid + ethanol [103]

Zeolite NaA membrane Hydrophilic membrane Lactic acid + ethanol [14]Propionic acid + isopropanol [98]

Poly[ether block amide] membrane Organophilic membrane Acetic acid + n-butanol [104]Poly[26-dimethyl-14-phenylene oxide][PPO] and thin layer fluoroplastic Hydrophobic composite membrane Acetic acid + methanol [105]

Tubular hydroxy sodalite [SOD]membrane Hydrophilic membrane Acetic acid + ethanol [106]

Acetic acid + butanol [106]HZSM-5 membrane Hydrophilic catalytic active membrane Acetic acid + ethanol [107]Poly[26-dimethyl-14-phenylene oxide][PPO] and fullerene C

60

Hydrophobic composite membrane Acetic acid + ethanol [108]


Membrane

1

2

3

4

Figure 3 Steps involved in transport of component through apervaporation membrane

proved to be very sensitive for the presence of water andalcohol in the reaction mixture

3 Theory of Pervaporation

The transport of component across the membrane in per-vaporation is described by solution desorption model thatresults from these processes in series (i) diffusion of thecomponent through the liquid boundary layer to the mem-brane surface (ii) sorptiondiffusion into the membrane(iii) transport through the membrane and (iv) diffusionthrough the vapor phase boundary layer into the bulk ofthe permeance (Figure 3) In modeling the transport modelfor pervaporation it is assumed that the resistance offeredby the boundary layer at the vapor phase is negligible andthat the concentration of the solute is zero at the permeantside since the permeant side is maintained at a low vacuumAt increased permeant pressure however the resistanceto transport on the vapor side will increase and becomesignificant

Transport through the boundary layer on the liquid feedside of the membrane is given by

119869

bl119886= 119896

119897120588 (119909

119891minus 119909

119894119897) (1)

where 119896119897is the boundary layermass transfer coefficient on the

liquid side and 119909119894119897and 119909119891are the organic concentration at the

liquid-membrane interface and feed side respectivelyMembrane transport is given by

119869

119898

119900= 119896

119894120588 (119909

119898119897minus 119909

119898119892) (2)

where 119896119894is membrane mass transfer coefficient 119905 is mem-

brane thickness and 119909

119898119897and 119909

119898119892are the organic concen-

tration at the membrane in liquid phase and vapor phaserespectively

Overall organic flux is described by

119869

119894= 119870ov120588 (119909119891 minus 119909119901) (3)

where the subscripts 119891 and 119901 refer to feed and permeanceIt can also be expressed in terms of partial vapor pressureconcentration of 119894 or fugacity as [52 53]

119869

119894= 119876ov119894119860(119901

119897119894minus 119901

119892119894) = 119870ov119897119860(119862

119897119894minus 119862

lowast

119892119894) (4)

119869

119894= 119870ov119894 (119891

feed119894

minus 119891

permeate119894

) (5)

where 119869

119894is the flux of 119894 across the membrane 119876ov119894 is

the overall mass transfer coefficient of 119894 in terms of vaporpressure 119860 is the membrane area 119901

119897119894and 119901

119892119894are partial

vapor pressures of 119894 in the liquid side and in the permeant(or gas) side respectively 119870ov119897 is the overall mass transfercoefficient of 119894 in terms of liquid concentration 119862

119897119894is the

concentration of 119894 in the liquid and 119862lowast119892119894

is the concentrationof 119894 in the liquid which would be in equilibrium with the gasIn pervaporation the partial vapor pressure is preferred as ameasure of the driving force since the effects of temperatureon the driving force and on the mass transfer coefficients areseparated more clearly

The partial vapor pressure of 119894 in the liquid side is relatedto the concentration in the liquid side (119862

119897119894) by the expression

given by [54]

119901

119897119894=

119862

119897119894120574

119894119901

0

119894

120588

119897

(6)

where 120574

119894is the activity coefficient of 119894 in the liquid side

119901

0

119894is the saturation vapor pressure of pure 119894 at the liquid

temperature and 120588

119897is the molar density of the liquid The

partial vapor pressure of 119894 in the gas side is related to theconcentration in the gas side (119862


119901

119892119894=

119862

119892119894119901

119879

120588

119892

(7)

where 119901

119879is the total pressure in the gas side and 120588

119892is

the molar density of the gas 119870ov119894 in (5) is the apparentmass transfer coefficient and 119891

119894is fugacity The fugacity of

component in the feed and in permeance can be expressedas follows

119891

feed119894

= 120574

119894119909

feed119894

119901

119900

119894(119879

feed)

119891

permeate119894

= 120574

119894119875

119901

(8)

where 119901119900119894is the vapor pressure of compound 119894 120574

119894is activity

coefficient 119879feed is the feed temperature and 119901

119879is total

pressureThe membrane mass transfer coefficient (119896

119894) includes

sorption to diffusion through and desorption from themembrane It is equivalent to the relation between thepermeability coefficient (119875

119894) and the thickness of the active

layer of the membrane (119897) as shown in

119896

119894=

119875

119894

119897

(9)

119875

119894= 119878

119894119863

119894 (10)


where the permeability coefficient (119875119894) is equal to the product

of the solubility coefficient of the permeance in themembrane(119878119894) and the diffusion coefficient (119863

119894) of the permeance in the

membraneAs stated earlier for pervaporation the permeant con-

centration can be neglected when vacuum is used on thepermeant sideTherefore the overall mass transfer coefficientis estimated from the organic flux data obtained by varyingfeed concentration Combining the above equations resultsin the resistance-in-series model that is typically applied todescribe components transport by pervaporation [54 55]

1

119870ov=

1

119896

119897

+

119897

119875

119898

(11)

or

1

119876ov=

1

119876

119898

+

1

119876

119897

=

119897

119875

119898

+

120574119901

0

120588

119897119896

119897

(12)

It is assumed that the diffusion coefficient remainsconstant and that there is negligible resistance offered bythe vapor phase boundary layer It is generally known thatpermeant pressures of 1ndash15 Torr are a valid assumption Theliquid phase mass transfer coefficient for a driving forceexpressed in terms of vapor pressure (119876

119897) is related to the

liquid phase mass transfer coefficient for a driving force interms of concentration (119896

119897) as follows

119876

119897=

120588

119897

120574119901

0119896

119897 (13)

The factor 1205741199010120588119897is the conversion factor from a con-

centration driving force to a partial vapor pressure drivingforce It is useful to note this conversion factor since valuesfor119876119897are not generally available and it is 119896

119897which is normally

found in correlations which relate mass transfer coefficient tophysical and hydrodynamic conditions Similarly to convertthe overall mass transfer coefficient from a vapor pressuredriving force (119876ov) into a concentration driving force (119870ov)

119876ov =120588

119897

120574119901

0119870ov119897 (14)

Ganapathi-Desai and Sikdar [56] reported that fluxincreased linearly with increasing feed concentration asexpected from (3)The slope of the line yields the overallmasstransfer coefficient (119870ov) The determination of liquid sidemass transfer coefficient (119896

119897) is obtained using correlations

For laminar flow through a flat channel Levequersquos correlation(15) is used For turbulent flow (16) is used [57 58]

Levequersquos correlation for laminar flow in open channels isgiven as

119896

119897= 16 [

119863

119894

119889

ℎ

] [Re]13 [Sc]13 [119889

ℎ

119871

] (15)

For turbulent flow through open channels 119896119897may be pre-

dicted as

119896

119897= 0026 [

119863

119894

119889

ℎ

] [Re]08 [Sc]13 (16)

where Re = 119906120588119903119889

ℎ120578 is Reynolds number 119871 is length of

cell 119889ℎis hydraulic diameter 119860 is cross-sectional area 119906 is

velocity and119863119894is diffusivity

Upon determination of 119896

119897from correlations the

resistance-in-series model is applied to the data (119870ov and119896

119897) and membrane resistance (or permeability) is calculated

from the intercept of the plot of 1119870ov versus 1119896119897from

(11) This approach yields a quick measure of membranepermeability but cannot be relied upon if the 119896

119897estimates

are approximate Ganapathi-Desai and Sikdar [56] studiedthe separation of volatile organic compounds (VOCs) suchas 111-trichloroethane (TCA) and trichloroethylene (TCE)from dilute aqueous solutions using composite membraneand reported the permeability by the above method as57times10

minus9 and 11times10minus8m2s for TCA and TCE respectivelyThey reported the permeability values for other systems also

31 Solution DiffusionTheory The transport of gas vapor orliquid through a dense nonporous membrane is described as[59]

Permeability (119875) = solubility (119878) times diffusivity (119863) (17)

Solubility for gases is described by Henryrsquos law For idealsystems solubility is independent of concentration and hencesorption isotherm is linear and concentration inside thepolymer is proportional to applied pressure For liquids asthey are not ideal Henryrsquos law is not applicable In additionthe affinity between liquid and polymer is much greaterhence sometimes cross-linking is necessary to prevent poly-mer dissolution High solubility implies high permeabilityas this influences diffusivity by making the polymer chainsmore flexible Sorption isotherm is nonlinear and behavioris described by free volume models and Flory Hugginsthermodynamics Diffusion coefficients increase with thetemperature while sorption is usually exothermic [59ndash61]For the effect of temperature on the permeability of organiccompounds through a membrane different results havebeen reported in the literature in some cases permeabilitydecreases with temperature [60 61] in others permeabilityincreases with temperature [53] and for some cases perme-ability is unaffected by temperature within the range studied[52 55]

Diffusivity depends on geometry of penetrant (asmolecu-lar size increases diffusion coefficient decreases) and concen-tration Dependence on size is determined by Stokes-Einsteinequation which is the relation between frictional resistanceand the radius of the diffusing component

119891 = 6120587120578119903 (18)

And diffusion coefficient is inversely proportional to fric-tional resistance as

119863 =

119870119879

119891

(19)

Large molecules having ability to swell the polymer canhave large diffusion coefficient Diffusivity is determined by


permeation method or time lag method The amount ofpenetrant (119876

119897) passing through the membrane in time 119905 is

given by

119876

119897=

119863119888

119894

119897

[119905 minus

119897

2

2119863

] (20)

Instead of 119876119897 pressure (119901) can also be monitored and this

plot of 119901 versus time (119905) will give time lag as interceptand permeability as slope from the steady state part of thispermeation experiment Since 119875 = 119878 times 119863 hence 119878 can befound once119863 and 119875 are known

Alternatively keeping the polymer in closed volume andapplying pressure to the chamber can determine diffusivityDue to sorption the pressure decreases with time andequilibrium is reached

4 Parameters in Membrane Performance

The effectiveness of a pervaporation membrane can be deter-mined by mainly two parameters namely the separationfactor and the permeant flux The flux was determinedby weighing the permeant mass and then dividing by theproduct of the interval time and membrane area In dilutesolutions the fluxes are equal to the product of 119863

119894119878

119894for

each component where 119863119894is the diffusion coefficient in the

membrane material and 119878119894is the sorption coefficient defined

as

119878

119894=

119908

119894Memb

119908

119894Feed (21)

where 119908119894Memb and 119908119894Feed are the weight fractions of compo-

nent 119894 in the membrane material and the liquid feed solutionin solubility equilibrium with the membrane phase

The solubility of a compound is the amount sorbedby the membrane under equilibrium conditions and hencea thermodynamic parameter in contrast to the diffusivity(119863119894) which is a kinetic parameter quantifying the rate of

permeation through the membrane 119863119894is depended on the

geometry of themembrane as well as its state (glassy rubberyswollen etc) A small molecule will more easily diffusethrough a membrane than a larger one

Separation factor determines the overall separation per-formance of a membrane systemThe value of separation fac-tor may vary from unity to infinity High value of separationfactor specifies amplified selectivity The separation factor 120572

119894

for a given compound 119894 is defined as the follows

120572

119894=

119908

permeate119894

(1 minus 119908

permeate119894

)

119908

feed119894

(1 minus 119908

feed119894

)

(22)

where119908119894is the weight fraction of the compound 119894 in the feed

(119908feed119894

) and in the permeance (119908permeate119894

)Following the solution-diffusion mechanism the basic

transport equation for pervaporation can be written as

119869

119894= [

119875

119894

119897

] (119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901) (23)

where 119875119894is the membrane permeability which is a product

of diffusivity and solubility coefficients 119897 is the membranethickness 119910

119894is the permeant mole fraction and 119901

119901 is thepermeant pressure The term [119875

119894119897] is known as permeance

that can be determined by rearranging the above equation

[

119875

119894

119897

] =

119869

119894

(119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901)

(24)

The ideal membrane selectivity 120573 is defined as the ratio ofthe permeability coefficients or the permeances

120573

119894119895=

119875

119894

119875

119895

(25)

Overall performance of the membrane was evaluated interms of pervaporation separation index (PSI) as given in thefollowing [62]

PSI = 119869 (120572 minus 1) (26)

where 119869 is permeation flux (kgm2h) when 120572 = 1 noseparation occurs PSI of zero means either zero flux orzero separation Table 2 and Figures 4ndash6 summarize theperformance parameters of different types of membranesfor several systems obtained in the pervaporation studies ofresearch articles It presents the values of important param-eters including permeation flux and selectivity of membraneat different operating temperatures

41 Effect of Membrane Thickness According to Fickrsquos equa-tion and the solution-diffusion model permeability of apenetrant through a membrane should be independent ofmembrane thickness but the flux is inversely proportionalto membrane thickness [63] Hasanoglu et al [64] studiedhydrolysis reaction of ethyl acetate (ethyl acetate (EAc) waterethanol (EOH) and acetic acid (AsAc)) using polydimethyl-siloxane (PDMS) and discussed the effect of membranethickness 250120583m and 300 120583m membranes thickness wereemployed It was found that fluxes through 250120583m mem-branes are higher than those through the 300120583mmembranes

Hyder et al [65] studied the influence of selective layerthickness on separation factors of dehydration of ethanol-water mixture using poly(vinyl alcohol) and poly(sulfone)(PVA-PSf) cross-linked composite membrane with varyingselective PVA layer thickness and concluded that with achange in thickness from 52 to 4 120583m (92 decrease) theselectivity change was not significant (only 17 decrease)compared to the change in flux (193 increase) that wasdependent on the bulk thickness of the membrane

Raisi and Aroujalian [66] investigated the effect ofmembrane thickness on the performance behavior of thepervaporationmembrane PDMS (polydimethylsiloxane) andPOMS (polyoctylmethylsiloxane) in the binary and ternarymodel solution of pomegranate aroma compounds It wasobserved that results were in agreement with the fact that thepermeation rate is inversely proportional tomembrane thick-ness because permeation resistance enhances as membranethickness increases


Table 2 Overview of membrane performance parameters of different pervaporation systems

System MembraneParameters

ReferenceTemperature(∘C)

Flux(kgm2h) Selectivity

Waterisobutyl acetate PDMS 70 4429 1421 [47]Waterisobutyl acetate PERVAP 1201 70 0712 6865 [47]

Waterethyl acetate Hydrophilic 40 0448(molm2h) mdash [109]

Waterethyl acetate Hydrophobic 40 7505(molm2h) mdash [109]

Waterethyl lactate Glutaral cross-linked chitosan (GCCS)carbomer(CP)polyacrylonitrile (PAN) 80 1247 256 [46]

Waterethyl lactate Glutaral cross-linked gelatin (GCGE)PAN 80 108 298 [46]

Waterethyl lactate Glutaral cross-linked hyaluronic acid(GCHA)hydrolysis modification (HM)-PAN) 80 1634 233 [46]

Waterethyl oleate PERVAP 1000 25 0215 120 [110]Watern-butanol PVAPES 75 014 135 [48]n-Butyl acetatemethanol PERVAP 2255-50 41 mdash 35 [111]Isobutyl acetatewater Cross-linked PDMS 60 37 14 [95]Waterethanol Polyvinyl alcohol 90ndash100 0ndash2 50ndash2000 [112]Waterethanol Polyamide-6 80 115 2 [113]Waterdioxane Polyamide-6 35 004 45 [114]Wateracetic acid Polyamide-6PAA 15 0005 82 [115]Waterisopropanol PESS Li+ 25 0087 40 [116]Waterisopropanol PESS K+ 25 0026 60 [116]Acetonewater Polypropylene 116 01ndash12 3 [117]Isopropanolwater Silicone rubber 25 003ndash011 9ndash22 [118]Butanolwater Silicone rubber 30 lt0035 45ndash65 [119]Butyl acetatewater PDMS 50 055 370 [120]Ethanolwater Zeolite NaA 95 335 5100 [121]Wateracetic acid Pervatech 75 25 150 [122]Waterisopropanol Pervatech 100 40 250 [122]Ethanolwater Polyacrylonitrile 70 003 12500 [123]Ethanolwater Polyvinyl alcohol 70 038 140 [123]Ethanolwater Polyhydrazide 70 165 19 [123]Methanolisopropanol Polypyrrole 58 0004 2 [124]Watern-butanol PVA membrane 70ndash90 0154ndash0184 122ndash165 [125]Watern-butyl acetate PVA membrane 70ndash90 015ndash0196 432ndash441 [125]Wateracetic acid PVA membrane 70ndash90 0176ndash0192 90ndash108 [125]Watermethanol CS-TEOS 60ndash80 0005ndash029 450ndash1150 [73]Ethanolwater Tri-n-octylamine (liquid membrane) 54 00598 100 [75]Ethyl acetatewater Surface modified alumina membrane 40 0254 669ndash789 [76]Ethyl propionatewater Surface modified alumina membrane 40 0343 1065ndash973 [76]Ethyl butyratewater Surface modified alumina membrane 40 0377 1205ndash1228 [76]Waterethanol Modified porous glass 79 01 1630 [126]Waterethanol Polyimide 75 001 850 [127]

Journal of Engineering 9Fl

ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30

Adoor et al (2008)Domingues et al (1999)Ma et al (2009)

Guo et al (2004)Sarkar et al (2010)Zhang et al (2014)

Figure 4 Effect of feed water concentration (wt) on flux of water-organic pervaporation system

Ma et al (2009)Zhang et al (2014)

Sarkar et al (2010)Guo et al (2004)

Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0

Water in feed (wt)0 5 10 15 20

Figure 5 Effect of feed water concentration (wt) on separationfactor of water-organic pervaporation system

Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8

Khajavi et al (2010)Ameri et al (2010)Korkmaz et al (2009)

Figure 6 Obtained trend of flux with time for different pervapora-tion systems

42 Effect of Temperature Temperature has a significanteffect on the transportation rateThe effect of temperature canbe expressed by an Arrhenius type function Since 119875 = 119878times119863both 119878 and119863 contribute to the effect of temperature For smallnoninteractive gases 119863 is the more dominating as 119878 doesnot change much with temperature For the larger moleculesthe situation is more complex since two effects diffusion andsolubility are opposing and further both are concentrationdependent

119878 dependence on temperature can be described as

119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)

where 119878119900is the temperature-independent constant and Δ119867

119904

is heat of solution Similarly temperature effect on diffusionis described as

119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)

where119863119900is the temperature-independent constant and 119864

119889is

activation energy for diffusion or it is a preexponential factorUsing 119875 = 119878 times119863 and using the above expression for 119878 and119863we get

119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)

Chang et al [67] represent the temperature dependence offlux using the following relationship

119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875

119900) is the water flux measured at a feed side

temperature of 119879119900 and permeant side pressure of 119875119900The term on the influence of permeant pressure on water

flux in (30) is derived from the fact that the driving force fortransport originates from the difference in chemical potentialbetween feed and permeance in the pervaporation [68]The difference in chemical potential can be approximatedas a difference in partial vapor pressures of the permeatingcomponent in the liquid feed and the gaseous permeanceEmpirical equations for partial water permeation flux andpermeation water composition are given by the followingequations

119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)

The data on saturation vapor pressure required for calcu-lating (32) were obtained by using the coefficients as tabulatedby Daubert and Danner [69] and the activity coefficient byusing the coefficients for the Van Laar equation as tabulatedby Gmehling and Onken [70] The equations and coefficientsare given in the following equations


119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)

119860 = 73649 times 10 119861 = minus72582 times 10

3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574

119908are the saturated vapor pressure and the

activity coefficient of water respectively and 119909119908is the mole

fraction of water in an ethanolwater mixtureEffect of temperature on membrane mass transfer coef-

ficient (119896119897) can be derived from changes in the physical

properties of the solution mainly its viscosity For thesame flow rate the Reynolds number increases sharply withtemperature From 30∘C at a constant liquid flow rate theReynolds number increased from 7930 to 11469 at 50∘C andto 15573 at 70∘C in the studies by Oliveira et al [54] Theirstudies were on monochlorobenzene (MCB) transport usingsilicone rubber (70 polydimethylsiloxane (PDMS) + 30silica filler) tubing as membrane

Burshe et al [71] studied the effect of temperature onflux and selectivity of water in glycerine-water mixturesusing Nafion (NA) cellulose triacetate (CA) carboxylatedpolyvinyl chloride (CPVC) and polyimide and polyethersul-fone (PES) membranes Temperature was varied from 30∘Cto 70∘C Increasing temperature was found to increase fluxThough amount sorbed decreased with temperature yet thisis offset by an increase in the diffusion coefficient of the solutebecause of increased temperature NA has the lowest energyof activation for diffusion and hence efficiently transportswater through it Increasing temperature however decreasesselectivity The reason behind this is that the thermal motionof polymer chains randomly produces free volumes throughwhich permeating molecules can diffuse With increasingtemperature thermal agitation increases thus enlarging thediffusive free volume Thus more solute can diffuse throughthe membrane At water content gt 60 very little differencein selectivity was observed at all temperatures

Domingues et al [44] pointed out that the flux ispractically linear for small variations in the water concen-tration and that it increases with an increase in temperatureand membrane selectivity for water remains constant andequal to 96 Guo et al [72] reported that water fluxincreases with an increase in temperature The reason isthat increase in motions of the polymer chains thermallyinduced and the expansion of the free volume In additionthe increased thermal motions of the permeant moleculesalso promote their diffusion However water permeance doesnot increase with an increase in temperature The relativelynegative dependence of water permeances on temperaturemay arise from the fact that permeance is defined as per-meant flux divided by permeant driving force The drivingforce combines two temperature-dependent factors 120574

119894and

119901sat119894 which are external factors outside the membrane Thevalues of water activity coefficients of different butanol watersystems (1-butanolwater 2-butanolwater isobutanolwater

and tert-butanolwater) are quite close at different tempera-tures for each of four butanol systemsThus119901sat119894 plays amoreimportant role than the water activity coefficient in these foursystems The higher temperature results in a higher 119901sat119894 alarger denominator and consequently a smaller permeance

Ma et al [73] presented the effect of operating tem-perature ranging from 60∘C to 80∘C on the pervaporationproperties of the CS-TEOS membrane The reaction systemwas lactic acid-ethanol and Amberlyst 15 ion exchange resinwas used as a catalyst Total flux increased notably whilethe separation factor decreased with increasing temperatureWhen operating temperature is increased vapor pressureof permeating components in the upstream side of themembrane increases Vapor pressure difference between theupstream and downstream side of the membrane enhancedthe transport driving forceMoreover increasing temperaturebrought about higher molecular diffusivity [74] thereforethe mass transport was faster and the total flux increased Inaddition as temperature is increased polymer chains becamemore flexible and accommodated larger available free volumeof the polymer matrix for diffusion which allowed easierwater and ethanol transfer across membrane and eventuallythe selectivity decreased

Thongsukmak and Sirkar [75] studied alcohol-waterseparation for feed alcohol concentrations of 5ndash10 in thepresence of a small amount of n-butanol in the feed varyingbetween 05 and 25 wt over a feed temperature range of 30ndash54∘C In single organic solvent species in solution three feedconcentration levels the values for 15 5 and 10wt weretaken As the temperature was increased from 25 to 54∘Cthe n-butanol-water selectivity went up from 60 to as highas 162 at 54∘C the permeant mass flux of n-butanol reached110 g(m2h) at 54∘C (for a n-butanol wt of 15 in feed)In mixtures of n-butanol and ethanol the selectivity andmass flux of solvents were increased significantly at elevatedtemperatures For a constant air flow rate the beneficialeffect of increasing temperature on the mass transfer ofmonochlorobenzene (MCB) across the membrane siliconerubber (70 polydimethylsiloxane (PDMS) + 30 silicafiller) tubing (30mm id with 1mm wall thickness) wasreflected in an increase of the MCB concentration in the airstream leaving the membrane module [54] For an increasein temperature from 30∘C to 50∘C the MCB concentrationin the gas outlet of the membrane module (at standardtemperature and pressure) increased by a factor of 13 from32 to 42 gmminus3 From 30 to 60∘C the increase was by a factorof 16

Song et al [76] studied the pervaporation of ester (ethylacetate EA ethyl propionate EP ethyl butyrate EB) with


hydrophobicmembranes Effect of temperature (30ndash50∘C) ondifferent esters (ethyl acetate EA ethyl propionate EP andethyl butyrate EB) was studied For EB andwater permeationthrough a hydrophobic aluminamembrane the 119864

119886values are

341 and 457 kJmol for EB and water respectively whereastheir corresponding 119864

119901values are minus22 and minus51 kJmol The

negative value of 119864119901for EB means that the increasing rate

of ester flux reduces with increasing temperature Activationenergy of penetrant increased as the penetrant size increasedin the order EA lt EP lt EB Activation energy (119864

119886) is the sum

of the activation energy of diffusion (119864119863) and the enthalpy of

sorption (Δ119867) While 119864119863is usually positive Δ119867 is negative

for the exothermic sorption process When the positive119864

119863dominates over the negative Δ119867 the positive value

of 119864119886occurs indicating that the membrane permeability

coefficient increases with increasing temperature [60] In thisstudy the activation energy (119864

119901) of esters was negative and

that of water was positive values The ester flux decreasedand water flux increased with increasing temperature whichshows that the activation energy of sorption (Δ119867) dominatesover diffusion The activation energy of EB was greater thanEA and EP which means that permeation flux of EB wasmost sensitive to the temperature change It was observed thatall ester compound and water fluxes increased exponentiallywith temperature The reason for this is the flux expressionwhich is expressed as follows

119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)

Since vapor pressure (119901119900119894) increases with increasing

temperature this results in the increase of flux (119869119894) The

fluxes of EB increased with increasing temperature and theconcentration of EB in permeance decreased with increasingtemperature This result might be explained by the negativevalue of 119864

119901for ester as described earlier All esters (EA

EP and EB) exhibited similar behavior regarding permeantconcentration with feed temperature

Transport of volatile organic compounds (VOCs) suchas 111-trichloroethane (TCA) and trichloroethylene (TCE)from dilute aqueous solutions through composite mem-brane constructed on a porous ceramic support from ablock copolymer of styrene and butadiene (SBS) was stud-ied by Ganapathi-Desai and Sikdar [56] An increase infeed temperature causes changes in the feed viscosity andVOC diffusion coefficients and yields higher fluxes for allcomponents Arrhenius plot of flux versus temperature wasused to calculate the activation energy for the transportof the VOCs through the SBS composite membrane Theseactivation energies for TCA and TCE were found to be 44and 53 kcalmol respectively In an earlier work byDutta andSikdar [77] activation energy of 56 kcalmolwas reported forTCA transport through the SBS membrane

43 Effect of Feed Concentration 119863 can be related as anexponential function of volume fraction of penetrant as

119863 = 119863

119900exp (120574120601) (36)

where 120601 is the volume fraction of penetrant 120574 is exponentialconstant (plasticizing constant indicating the plasticizing

action of the penetrant on segmental motion) and 119863119900is the

diffusion concentration at zero concentration119863119900is related to

molecule size and 119863119900is large for small molecules and small

for large molecules However 120601 and 120574 are greatly dominatingfactors as they are in exponential terms For gases that hardlyshow any interaction with polymer 120574 = 0 hence119863 = 119863

119900

Free volume theory describes the concentration depen-dence of the diffusion coefficient Polymer has two statesnamely glass and rubber Below glass transition temperaturethere is glassy state and mobility of chain segment is limitedAbove 119879

119892 mobility increases frozen microvoids no longer

exist and the number of the parameters changes one ofwhich is the specific volume expressed as

119881

119891= 119881

119879minus 119881

119900 (37)

where 119881

119900is the volume occupied by molecules at 0 K

(estimated by group contribution method)Fractional volume is defined as

V119891=

119881

119891

119881

119879

(38)

where V119891or 119881119879is obtained from polymer density For glass

polymer the fractional free volume is 0025 and hence below119879

119892it is constant and is equal to V

119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)

where Δ120572 is the difference between the value of thermalexpansion coefficient above 119879

119892and below 119879

119892 Molecule can

diffuse only if there is sufficient space or free volume If thepenetrant size increases the amount of free volume must alsoincrease The probability of finding hole whose size exceedsthe critical value is proportional to exp(minus119861V

119891) 119861 is local

free volume needed for a given penetrant V119891is fractional

free volume Thus the mobility of penetrant depends on theprobability of finding a hole of appropriate size Mobility canbe related to thermodynamic diffusion coefficient

119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860

119891is dependent on the size and shape of pene-

trant molecule and 119861 is in relation to minimum local freevolume necessary to allow a displacement Thus from theabove equation 119863 increases as temperature increases and 119863decreases as the size of penetrant molecule increases since 119861increases

For noninteracting systems119860119891and 119861 are independent of

the polymer type hence diffusivity of given gas molecule canbe determined from density measurement alone If 119860

119891and

119861 are function of the polymer type V119891as function of both

temperature and concentration in needed

V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)

where V119891(0 119879) is the free volume of the polymer at tem-

perature 119879 in the absence of penetrant 120573(119879) is constant


characterizing the extent to which the penetrant contributesto the free volume and 120601 is the volume fraction of penetrant

Diffusion coefficient at zero penetrant concentration canbe given as

119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)

Combining the equations

ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)

Thus the LHS is related linearly to 120601

minus1 The relationshipbetween measured diffusion coefficient (119863) and thermody-namic diffusion coefficient (119863

119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)

The factor in bracket is obtained fromFloryHuggins thermo-dynamics The activity of penetrant inside the polymer is

ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)

where 120594 is the interaction parameter if 120594 is greater than 2the interaction is small if 120594 lies between 05 and 2 stronginteraction exists and high permeability is expected Thus

[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)

Component diffuses not a single molecule but in dimmer ortrimmer form Size of diffusing component increases withthe diffusion coefficient decreases The presence of clusteredcomponent can be determined by the cluster integral 119866

11

(Zimm Lindbergh theory)

119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881

1is the molar volume For an ideal system

[119889 ln 119886119894119889 ln120601

119894] = 1 hence LHS of the above equation is 1

and hence no clustering is there If LHS is greater than minus1clustering will occur

Chang et al [67] studied the pervaporation of ethanolin the pilot plant and found that the water content inpermeance is still high even with low water content in thefeed Membrane selectivity was found to be hardly alteredby permeant pressure change Permeation fluxes increaselinearly with the water content in the feed and decrease withpermeant pressure Temperature influence is described byArrhenius law and activation energy was found to be 119864

119908=

784 kcalmol

Burshe et al [71] studied the effect of water concentrationon flux and selectivity of water in glycerine-water mixturesusing Nafion (NA) cellulose triacetate (CA) carboxylatedpolyvinyl chloride (CPVC) polyimide (PI) and polyether-sulfone (PES) membranes Increasing water in feed increasesflux of water and following trend was observed NA gt CA gt

PES gt CPVC gt PI The reason for this is the plasticizationof NA membrane because of increased water concentrationin the membrane phase which increases the free volume andresults in increasing the sorption Selectivity decreases withan increase of water in the feed in the trend PES gt PI gtNA gt

CA gt CPVCGuo and Hu [78] studied on ethanol-water transport in

novel silicone copolymer consisting of PDMS segments andladder-like phenylsilsesquioxane segments and found thatthe concentration of ethanol in the permeance is alwayshigher than that in the corresponding feed The separa-tion factor decreases as the ethanol concentration in feedincreases High separation factor can be obtained for theseparation of dilute aqueous solution of ethanol through themembrane The flux of ethanol increases proportionally withincreasing ethanol concentration in the feed whereas the fluxof water is almost constant for various feed compositionsThemagnitude of separation factor and flux for the pervaporationincreases in the following order methanol lt ethanol lt 2-propanol lt acetone lt THF This order just corresponds withthe decreasing order of the solubility parameters of theseorganic components

Wolinska-Grabczyk et al [79] employed three types ofmembranes PUU-PEs-1 PUU-PEs-2 and PU-PEt-1 for sep-aration of both high and low concentrations of benzene inbenzenecyclohexane mixture Polyester-based polyuretha-nes (PUU-PEs-1 PUU-PEs-2) exhibited an acceptable selec-tivity and permeability and excellent stability to separatebenzenecyclohexane azeotropic mixture Replacement ofthe polyester macrodiol with the polyether one (PU-PEt-1)resulted in a membrane material with a much higher perme-ability accompanied still by a lower selectivity The increasein the flux value is commonly accompanied by the loss of themembrane selectivity For the separation of MTBEMeOHmodel mixture containing 15 mass of MeOH the obtainedmembranes were preferentially permeable to MeOH overMTBE Excellent separation capability (100 of MeOHin permeance) is shown by PU-PEt membrane preparedfrom polyether-based polyurethane The substitution of thepolyether in a polyurethane soft segment by the polyesterresulted in more permeable membrane with slightly lessseparation ability For the removal of benzene and chloroformfrom water PU-PD-1 polyurethanes exhibit excellent selec-tivity Structural modifications concerning the application ofthe polyether rather than the polydiene macrodiol (PU-PEt-1versus PU-PD-2) led to some improvement of the membranepermeability however at the expense of its selectivity

Guo et al [72] found that the partial water flux increasesrapidly with feed water concentration The selective layerof the composite membrane is made of polyvinyl alcohol(PVA) with hydroxyl substituted groups Thus it has a highpolarity and experiences a strong interaction with water


through hydrogen bonding At higher feed water concen-trations there are greater numbers of water molecules incontact with the selective layer of the membrane Thereforemore water molecules are sorbed into the membrane whichcauses a greater degree of swelling in the top layer of themembrane Consequently more water molecules can passthrough the water-swollen membrane and water permeationflux increases as the feed water content increases The per-centage of increment for water permeance with increasingfeed water content is slightly lower than that of water fluxPresence exhibits more accurate permeant-specific transportproperties with feed concentration because it has significantlydecoupled the effect of fugacity difference as the drivingforce from the overall membrane transport Butanol con-centration in the permeance decreases with an increase infeed water concentration for the 2-butanol isobutanol andtert-butanolwater systems while the trend is opposite to the1-butanolwater system 1-Butanol presents the highest fluxcomparedwith other alcohols because of the strongest affinitybetween 1-butanol andmembrane and the highest linearity of1-butanol molecular structure

Ma et al [73] studied the effect of water content in the feedvarying from 2wt to 15wt in the esterification studies onlactic acid ethanol system using Amberlyst 15 ion exchangeresin With the increase of water content in the feed thetotal flux increased from 271 g(m2h) to 352 g(m2h) whilethe separation factor decreased from 1380 to 268 Degreeof swelling value of the CS-TEOS membrane increased withincreasing water content in the feed leading to the reductionof mass transfer resistance and the acceleration of diffusionvelocity for components in the membrane Meanwhile thesize of voids in the membrane became larger and larger withincreasing 119863119878 value ethanol molecules won more chance topass through these voids which resulted in the decrease ofseparation factor

In the hydrolysis reaction of ethyl acetate (ethyl acetate(EAc) water ethanol (EOH) and acetic acid (AsAc)) usingpolydimethylsiloxane (PDMS) membrane Hasanoglu et al[64] found that with the increase in the ethyl acetateconcentration in the feed the ethyl acetate fluxes increaseWhile the ethyl acetate concentrations increase from 1 to3wt total fluxes (summation of partial fluxes) change inthe range of 79ndash307 gm2h for the quaternary mixtures Thisphenomenon was explained related to the plasticizing effectof the organicmolecules As the EAc concentration in the feedincreases membrane swells more and the polymer chainsbecome more flexible thus decreasing the energy requiredfor the diffusive transport through the membrane Aceticacid and ethanol permeate through the PDMS membrane invery small quantities For the mixtures which have the sameEAc concentrations an increase in ethanol concentration infeed yields higher partial fluxes of ethanol while the aceticacid flux is not much affected by feed concentration of aceticacid The reason for this is that the three different feedmixtures having 3 EAc concentrations have different partialfluxes of EAc indicating the effects of mutual interactionsof each component on the fluxes The total fluxes increasewith increasing EAcwater ratio due to the hydrophobicity of

the membrane and the affinity of the membrane to the EAcmolecules An increase in EAcorganic ratio in feed yields adecrease in EAcorganic selectivity This is due to the reasonthat increases of ethyl acetate amount in the feed mixturein which PDMS is more permeable causes the membraneto swell Therefore the amount of other soluble componentsdissolved in the membrane increases due to the presence ofethyl acetate

Thongsukmak and Sirkar [75] studied alcohol-waterseparation for feed alcohol concentrations of 5ndash10 in thepresence of a small amount of n-butanol in the feed varyingbetween 05 and 25 wt over a feed temperature range of30ndash54∘C In single organic solvent species in solution threefeed concentration levels the values for 15 5 and 10wtare taken The selectivity of ethanol goes up to 38 at a feedtemperature of 54∘C and 100 wt ethanol in feed Higherfeed ethanol concentration results in a higher selectivity andmass flux due to a higher driving force for the pervaporationof ethanol through the liquid membrane In the studies onmixtures of n-butanol and ethanol the selectivity and massflux of ethanol got higher when the concentration of ethanolwas higher in the feedThis is due to the higher concentrationin the feed that provided a higher driving force via theincrease in the ethanol effective partial pressure The massflux of ethanol obtained for 10wt ethanol in feed obtainedwas 162 g(m2h) which is considerably higher than the fluxfor the experiment without n-butanol added to the feed(by 73) The selectivity of ethanol went up to 66 for themixture of 10 wt ethanol with 1 wt n-butanol in the feed at54∘C this is much higher than the highest ethanol selectivityobtained with single species solution of ethanol at 54∘C

Pervaporation of esters with hydrophobic membrane wasstudied by Song et al [76] Permeation fluxes of esters werefound to increase linearly as feed concentration increasedwhile the permeation flux of the water was not affected byester concentration in the feed The fluxes can be expressedas follows

119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)

At a given temperature the permeation flux of esteris a function of 119896

119894 saturation pressure of ester (119901119900

119894) and

molar fraction of ester (119909feed119894

) 119896119894increases with the feed

concentration owing to the increasing solubility coefficient(119878119894) and diffusion coefficient (119863

119894) As expected from the

above equation ester flux increased relatively linearly withincreasing molar fraction in feed (119909feed

119894) In the case of water

flux however it might be inferred from the equation thatwater flux at a given temperature did not depend on esterconcentration in the feed because the molar fraction of waterin the feed (119909feed

119908) remained virtually constant in the range of

dilute ester concentrationThat is why the permeation flux ofwater was not affected by ester concentration The total fluxincreased with increasing ester concentration in the feed dueto the high flux of ester

As the feed ester concentration was increased from 015to 060wt the separation factor of EA at 40∘C increasedfrom 669 to 789 However the separation factors of EP andEB were not much affected by feed concentration which was


in the range of 1065ndash973 and 1205ndash1228 respectively Theseparation factors of PDMSmembrane are higher than thoseof this study separation factor of EAwith PDMSGFT is 850ndash1450 PDMS GFTz 2540 PDMS DC 3680 Those of EP andEB with PDMS are 790ndash1712 and 96ndash1963 respectively

Ganapathi-Desai and Sikdar [56] in their studies on SBSpolymer membrane single VOC tests and ceramic bilayermembrane for TCA and TCE transport reported that fluxincreased linearly with increasing feed concentration Waterflux stayed relatively constant over the range of concentration119870ov increases with flow rate proving the domination ofboundary layer resistance in the overall transport of TCAacross the membrane Selectivity was found to increase withflow rate

5 Intensification of the Esterification ReactionUsing Pervaporation

Esterification is one of the most important chemical reac-tions in the chemical industry Esters are derived fromcarboxylic acid by the replacement of hydrogen in the ndashCOOH group of acid by the hydrocarbon group of alcoholEsterification reaction is a slow reaction and is reversible innature The reaction is carried out in the presence of thecatalyst Homogeneous catalysts such as H

2SO4 HCl [80]

and p-toluenesulfonic acid [14] are frequently employed toesterification process However these catalysts have beenfound to attack membranes as well as the devices and aredifficult to be separated from the products As a result thereis an increasing effect on heterogeneous catalysts such as ion-exchange resin [81] zeolite [82] and solid super acid [83]Ion-exchange resin has displayed comprehensive superiorityin many situations [84] Amberlyst 15 ion-exchange resinpossesses distinct advantages including being environmen-tally benign being nontoxic being long-term chemically andphysically stable [85] and being easily recyclable [43 84 86]and has been successfully explored as a powerful catalyst forthe esterification reaction

Since the reaction is a reversible reaction and is equi-librium limited the yield of ester is generally small It isrecommended that the ester be distilled off as soon as itis formed so that the reverse reaction does not happen Toimprove the yield it is customary to drive the position ofthe equilibrium to the ester side by either using excess ofone of reactants (usually alcohol) or removal of the productof the reaction However there are challenges involved suchthat using excess of reactant would result in increased cost ofthe subsequent separation as the product stream is obtainedin diluted form in the excess reactant Subsequent removalof the product of the reaction via processes such as reactivedistillation required that the difference in the volatility ofproduct and reactants be sufficiently large This is usuallynot the case in many processes and in addition formationsof azeotropes were noted The mismatching of the reactionand distillation temperature is an additional complicationand in many cases the process performance and energyconsumption in reactive distillation are the major cost factorin the manufacturing of esters

6 Comparison of Esterificationwith and without Pervaporation

The integration of esterification reactor with a pervaporationpilot plant via hybrid reactor permits the selective permeationof the component (water) from the mixture Hence theconversion of thermally limited esterification reaction isenhanced through controlled removal of one of the productspecies from the reaction mixture Pervaporation is a ratecontrolled separation process and the separation efficiencyis not limited by relative volatility In pervaporation processonly water is permeated by membrane and accomplishesphase change Hence the energy required is comparativelylower In addition to this the temperature of operation of per-vaporation setup matches with the temperature of reactionand hence could be advantageously used for enzymatic ester-ification due to temperature constraints normally imposedby enzyme stability Different factors affect the pervaporationaided esterification reactor setup such as effect of initialmolarratios of the reactants effect of catalyst concentration effectof membrane area and effect of temperature Large mem-brane size could provide higher surface for the transfer of acidthough the challenges of membrane rupture do surround thestudies An increase in temperature catalyst concentrationand initial molar ratios of the reactants induces not onlyan acceleration of esterification but also acceleration inpervaporation

The combination of pervaporation with the chemicalreaction is very attractive system nowadays The couplingof pervaporation separation process into conventional ester-ification processes with suitable membranes enhances theyield of the esters and conversion of acids [16 44 73]Intensification of esterification of acetic acid and n-butylalcohol using Zr(SO

4)2sdot4H2O using PVAceramic composite

membrane was studied by Liu and Chen [87] PV enhancedthe conversion and it was higher for the PV-aided esterifica-tion than for the reaction without PV Water content for thereaction without PV was higher than that for the PV-aidedreaction due to water removal by PV Table 3 and Figures 7and 8 list comparative study of esterification reaction systemwithout and with incorporated with pervaporation sepa-ration process It summarizes the results of pervaporationesterification integrated system in terms of conversion whencompared to a nonintegrated system

7 Effect of OperatingConditions on Esterification CoupledPervaporation Process

Operating parameters were classified in three groups [88]

(1) Factors which influence directly the esterificationkinetics catalyst concentration and initial reactantmolar ratio (alcoholacid)

(2) Factors that influence directly pervaporation kineticsratio of membrane area to initial reaction volume(119860119881119900)


Table 3 Comparison of results of esterification reaction with and without pervaporation

Esterification system Catalystmembrane Withoutpervaporation With pervaporation Reference

Benzyl alcohol andacetic acid

p-Toluenesulfonic acid GFTmembrane (GFT PERVAP 1005)

Conversion of aceticacid = 045

Conversion of aceticacid = 06 [44]

Ethanol and acetic acid HCl hydrophilic membrane Equilibriumconversion = 06

Equilibriumconversion = 082 [128]

Ethanol and lactic acid Amberlyst 15 PERVAP 2201 Conversion of lacticacid = 021

Conversion of lacticacid = 088 [16]

Lactic acid and ethanol Amberlyst 15 ion exchange resinorganic-inorganic hybrid membrane

Yield of ethyl lactate =66 [wt]

Yield of ethyl lactate =80 [wt] [73]

Acetic acid and n-butylalcohol

Zr[SO4]2sdot4H2O PVAceramic

composite membraneConversion ofn-butanol = 065

Conversion ofn-butanol = 089 [87]

Acrylic acid andn-butanol Amberlyst 131 PERVAP 2201 Conversion of acrylic

acid = 068Conversion of acrylicacid = 096 [129]

Oleic acid and ethanol Amberlyst 15 hydrophilicpoly[vinyl alcohol]

Yield of ethyl oleate =23

Yield of ethyl oleate =50 [130]

Acetic acid withisopropanol

Amberlyst 15 PVA membranePERVAP 2201

Mole fraction ofisopropyl acetate = 03

Mole fraction ofisopropyl acetate =061

[38]

Lactic acid with ethanol Amberlyst XN-1010 water selectivemembrane

Conversion of lacticacid = 05


Acetic acid and ethanol Sulfuric acid polymericceramiccomposite membrane



Lactic acid with ethanol Amberlyst XN-1010 GFT-1005 Conversion of lacticacid = 0522


Lactic acid withisopropanol

Sulfuric acid PVA-PES compositemembrane



Lactic acid withn-butanol




Acetic acid and ethanol Dowex50 PVA-PVP incorporatingPMAmixed matrix membrane



Acetic acid with ethanol

Amberlyst 15 polydimethylsiloxanemembrane



[42]Sulfuric acid polydimethylsiloxanemembrane



Rathod et al (2013)Wasewar et al (2009)

Ma et al (2009)Korkmaz et al (2004)

Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10

Figure 7 Different trends of conversion of acid with time foresterification without pervaporation system

(3) Factors that influence simultaneously the esterifica-tion and pervaporation kinetics temperature



Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100

Figure 8 Different trends of conversion of acid with time foresterification with pervaporation system

71 Effect of Initial Reactant Ratio Delgado et al [16] studiedeffect of ethanol lactic acid initial feed molar ratio (119877) over


a range of 1 1 to 3 1 catalyst (Amberlyst 15) loading 2ratio membrane (PERVAP 2201) area to initial volume ofreaction 119878119881

119900= 23mminus1 and reaction and pervaporation

temperature 34815 K It was found that at the beginning ofthe process the higher the initial reactant molar ratio thehigher the reaction rate However as the reaction proceedsit was found that higher ester formation was obtained whenworking in stoichiometric proportionThismay be due to thedilution effect of ethanol In simple esterification reactionshigher equilibrium conversions were obtained by increasingthe initial reactant molar ratio but the limited reactantwill never react completely In esterification-pervaporationreactors a complete conversion of one reactant is obtainablewhen the other reactant is in excess no matter how small theexcess is Conversion in this kind of integrated process can gobeyond the equilibrium conversion which is the maximumconversion reached in a conventional reactor

In pervaporation aided esterification of acetic acid andn-butyl alcohol using catalyst p-toluenesulfonic acid andsolid super acid and membrane phosphatic poly(vinyl alco-hol)poly acrylonitrile (PPVAPAN) composite membraneXuehui and Lefu [90] found that higher ester formationoccurs at higher 119877 for fixed time (where 119877 is ratio of initialmolar quantity of alcohol to acid) Maxima in water concen-tration also obtained at lower timeswhenhigher119877 is used Liuet al [89] reported the result of esterification of acetic acid +n-butyl alcohol + Zr(SO

4)2sdot4H2O + PVAceramic composite

membrane in the form of dimensionless parameter 119865that stands for the interaction between water removal andwater production during the coupling process Conversionwas increased and water production rate decreases with 119877

119900

increasing Maximum in water content in the mixture hadhigher amplitude at a lower 119877

119900

Ma et al [73] reported that the yield of ethyl lactate usingAmberlyst 15 ion exchange resin did not remarkably increasewith the initial molar ratio of ethanol to lactic acid from 2 to4 119877119900played a part in reaction rate but exerted no effect on

kinetics of PV Water production rate is decreased with theincrease of 119877

119900and caused the maximum amplitude in water

content lower at a higher 119877119900

72 Effect of Catalyst Concentration In the esterification ofbenzyl alcohol and acetic acid using p-toluenesulfonic acidand employing commercial GFT membrane (GFT PERVAP1005) Domingues et al [44] found that increase in theamount of catalyst leads to an increase in the reaction ratehowever beyond 41molm3 there is no significant increaseLiu et al [89] (system acetic acid + n-butyl alcohol +Zr(SO

4)2sdot4H2O + PVAceramic composite membrane)

found that water production rate was proportional to andincreased with the increase of catalyst concentration Whenthe catalyst concentration was increased the maximumin water content in the mixture was increased and shiftedto shorter time and the final water content decreased Maet al [73] varied Amberlyst 15 from 05 wt to 30 wtin esterification of lactic acid + ethanol in pervaporationstudied in organic-inorganic hybrid membrane preparedby in site hydrolysis and condensation of tetraethoxysilane

with chitosan aqueous solution Yield of ethyl lactate wasimproved with the increase of catalyst loading The reasonfor this is increasing catalyst active sites and decreasing ofreaction activation energy which could obviously acceleratereaction rate The water contents in the reactor had highermaximum amplitude for a higher catalyst concentrationduring the reaction Delgado et al [16] studied effect ofcatalyst (Amberlyst 15) concentration (2 35 and 55 wtof total initial solution) in esterification of ethanol + lacticusing PERVAP 2201 Increase in the amount of catalyst leadsto an increase in the reaction rate In the studies on diluteacid the effect is not higher due to the high initial amount ofwater in the reactor

73 Effect of Membrane Area to Initial Reaction Volume RatioDelgado et al [16] varied the membrane area to initialreaction volume ratio for 12ndash46mminus1 in the esterification ofethanol and lactic acid using Amberlyst 15 and PERVAP2201 It was found that the higher the value of this ratio thehigher the ethyl lactate concentration in the reactor thereforehigher conversions are reached This result is obvious sincewater concentration in the reactor will decrease faster whenthe membrane area per unit of reaction volume is largerDomingues et al [44] found that in the esterification studieson benzyl alcohol and acetic acid using p-toluenesulfonicacid as catalyst and GFT PERVAP 1005 membrane to obtain60 conversion of AA increase in membrane surface area (119878)leads to less operating time to reach the conversion level Inaddition the 100 percent conversion of alcohol was achieved

To measure the capacity of membrane unit membraneparameter 120596 (characterizing membrane permeability) andoperating parameters 119878 and 119881

119900are combined as a single vari-

able 120596119878119881 (permeability lowast surface areavolume of reactionmixture) [60] It was found that conversion of the membranereactor can go beyond the equilibrium conversion Gapbetween the two limits that is 120596119878119881 varies from 0 to infinitybecomes larger as the reaction time increases indicatingthat the reaction is increasingly facilitated by membranepervaporation The higher the value of 120596119878119881 the higher theconversionWhenmembrane is used to enhance the reactionwater concentration (119862

119908119862

119900119862

119908is water concentration and

119862

119900is the water concentration that would be obtained at

complete conversion) undergoes a maximum as reactionproceeds in time The larger the value of 120596119878119881 the shorterthe time required for water to reach maximum concentrationand the smaller the magnitude of the maximum waterconcentration As reaction proceeds reaction rate decreasesSuch a decrease in reaction rate is however slowed downby the use of a membrane because selective removal ofwater further concentrates the reactants Despite the fact thatpervaporation can shift the equilibrium toward the ester sideand go beyond equilibrium conversion it cannot drive thereaction to completion that is 119883 = 1 in a finite time scaleno matter how large the value of 120596119878119881 is When one of thereactant species is used in excess a complete conversion ofthe other is achievable

The result was explained in theway that the concentrationof water in the reactor will be reduced more rapidly when themembrane is more permeable andor when the membrane


area per unit reaction volume is larger so higher is theconversion During the early period of reaction the rate ofchemical reaction is high whereas water concentration islow and so is the rate of water removal from the reactorConsequently water concentration gradually increases untilit reaches maximum when its formation rate and removalrate become equalThereafter the water removal is faster thanformation resulting in depletion of water in the reactor

Liu et al [89] (system acetic acid + n-butyl alcohol +Zr(SO

4)2sdot4H2O+PVAceramic compositemembrane) stated

that rate of water removal was reduced with the decrease of119878119881 Further liquid had higher amplitude at a lower 119878119881 Maet al [73] (system lactic acid + ethanol + Amberlyst 15 +organic-inorganic hybridmembrane) found that 119878119881 exertedno influence on reactive kinetics but caused the variation ofthe water extraction rate Water production rate is decreasedwith the increase of 119878119881

74 Effect of Temperature of Reaction and PervaporationDelgado et al [16] in the esterification of ethanol and lacticacid using Amberlyst 15 and PERVAP 2201 found that watercontent in the reaction medium decreased rapidly whenmembrane permeation flux increased as a consequence ofan increase in pervaporation temperature (33815 34815and 35815 K) As a result the esterification rate increasesXuehui and Lefu [90] (system acetic acid + n-butyl alcohol +p-toluenesulfonic acid and solid super acid + PPVAPANcomposite membrane) reported that higher ester is formedat higher temperature for fixed time Maxima in waterconcentration also obtained at lower times when highertemperature is used



found that dimensionless parameter 119865 that stands for theinteraction between water removal and water increaseswith increasing temperature indicating that the accelerationof the rate of water extraction is faster than that of waterproduction rate This is due to the reason that both the waterproduction rate and permeability coefficient are higher at ahigher temperature Maximum in water concentration wasincreased with temperature but shifted to a shorter timedue to the higher water production rate Before the watercontent went through its maximum value the rate of waterproduction was larger than that of water removal afterwater content attained the maximum value the rate of waterproduction was less than that of water removal

Ma et al [73] studied the effect of temperature from50∘C to 80∘C in the esterification of lactic acid + ethanolusing Amberlyst 15 ion exchange resin and organic-inorganichybrid membrane Esterification of lactic acid and ethanolwas an endothermic reaction (based on Arrhenius plot)accordingly the yield of ethyl lactate increased with increas-ing reaction temperature in pervaporation assisted esteri-fication Liu and Chen [87] (system acetic acid + n-butylalcohol + Zr(SO

4)2sdot4H2O + PVAceramic composite mem-

brane) found that reaction rate constants for the esterificationare a function of process temperature andwere increasedwiththe increase of the temperature (70ndash90∘C)The accelerating ofthe reaction rate constantwith the increase of the temperature

for the forward reactionwas faster than the backward processSo water production rate was higher in a higher temperaturethan in a lower temperature Meanwhile the permeationparameter for water is also varied with the temperatureand was increased with the increase of the temperatureAs a result water permeation flux was increased with theincrease of the process temperatureWater concentration hada higher maximum value for a higher process temperatureThis may be explained by the fact that the accelerationfor water production rate had a higher value at a highertemperature so water content increased faster during theearlier reaction stage due to a slower backward reaction ratewhile it decreased faster later due to a higher backwardreaction rate

Grob and Heintz [91] studied isotherms of aromaticcompounds in organophilic polymer membranes (polyether-polyamide block-copolymer (PEBA)) used in pervaporationand found that sorption of phenol aniline 2-chlorophenol 4-nitrophenol 24-dinitrophenol 441015840-isopropylidenediphenol(bisphenol A) and pyridine decreases with temperatureSorption coefficients are obtained as slopes of the straightlines The number of the free hydroxyl groups plays acertain role for the affinity of the aromatic compoundsfor the membrane material PEBA The sorption process oftransferring aromatics from aqueous solution to the mem-brane is exothermic Values of calculated sorption enthalpiesΔℎinfinity range between minus25 and minus12 kJmol The sorption ofboth aniline and phenol in the membrane material was notaffected by the presence of the second aromatic compoundThe system phenolbisphenol A shows a certain synergisticsolubility effect The solubility of phenol is enhanced by thepresence of bisphenol A but the phenol has no influenceon the solubility of bisphenol A Burshe et al [71] studieddehydration of glycerine-water mixtures by pervaporationusing membranes such as Nafion (NA) cellulose triacetate(CA) polyimide carboxylated polyvinyl chloride (CPVC)and polyethersulfone (PES) Temperature was varied from30 to 70∘C It was found that increased feed temperaturedecreased the sorption of water and heat of sorption (Δ119867

119904)

is negative

75 Other Factors

751 Effect of Downstream Pressure on Various Terms Gen-erally downstream pressure is less than 1mmHg If down-stream pressure increases at membrane permeant interfacedesorption slows down thus downstream pressure becomesthe rate controlling Increase in pressure increases the activityof both permeances dissolved in the downstream layer ofthe working membrane If pressure increases and exceedsthe saturated vapor pressure of permeance selectivity fallsAt low downstream pressure desorption is rapid thus dif-fusion becomes the rate controlling Beyond the transitionpressure desorption slows down and progressively governsthe selectivity of pervaporation transport In this regimeselectivity is determined by the relative volatilities of the feedcomponents If the more rapid permeating species is alsothe more volatile selectivity increases as the downstreampressure is raised In the opposite case a steep decrease in


selectivity is observed For ideal gasmixtures with permeancecontaining no significant amount of noncondensable gas thepermeant composition (1198831015840

119860 mole fraction) depends on the

downstream pressure (119875)

119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)

where 119860 and 119861 are the fast and slow permeancesDerivation gives

119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)

If 119860 is less volatile 119875lowast119860minus 119875

lowast

119861lt 0 and selectivity decreases as

119875 increasesBurshe et al [71] in the dehydration studies on glycerine-

water mixture using various membranes found the effectof downstream pressure on the dehydration Pressure wasvaried from 1 to 20mmHg It was found that higher thedownstream pressure lower in water flux Selectivity is notaffected by downstream pressure change It is recommendedthat it is better to use 20mmHg downstream pressures asthis reduces the load on the refrigeration unit supplying thecooling medium for condensing the water issuing from theequipment

752 Effect of Molecule Size on the Permeability of DifferentCompounds Song et al [76] studied the permeation of dif-ferent ester compounds (ethyl acetate EA ethyl propionateEP ethyl butyrate EB) through surface-modified aluminamembrane (Al

2O3) Ester (EA EP and EB) concentrations

in permeance increased almost linearly with increasing esterconcentrations in the feedThe ester concentration in perme-ance increased in the order of EB gt EP gt EA as well as esterflux even though molecular weight and molar volume of EBare greater than EP and EA This may be attributed to thelowest solubility of EB in water since the low solubility relatesto the high hydrophobicity Due to the lowest solubilityEB has highest affinity to the hydrophobic surface of themembraneThis is aswould be expected since organic specieshave a stronger affinity to the organophilic membrane thanwater-soluble solutes Although the concentration of esters(EA EP and EB) was only 015ndash060wt in the feed EAEP and EB in permeance were concentrated up to 913ndash3226 1379ndash370 and 1533ndash4257wt respectively Phaseseparation occurred in permeant stream because the esterconcentration in permeance was much above the saturationlimit

Thedifference in the flux andpermeance of different com-ponent in a particular membrane is explained in terms of dif-ference in affinity between the component and themembranefor the different components A simple approach to describ-ing the affinity between materials is the solubility parameterGuo et al [72] in the studies of dehydration of butanolmixtures found that the solubility parameters 120575sp (MPa 12)of PVA (the selective layer of membrane) and water are391 and 479 respectively The difference between solubilityparameters for each pair of butanolmembrane is in the order

of 1-butanolmembrane (16)lt isobutanolmembrane (164)lt2-butanolmembrane (17) lt tert-butanolmembrane (174)The solubility parameter theory proposes that the materialswill have strong interaction when their respective solubilityparameters are close to each other Therefore based on thistheory the affinity between the butanol and the membraneis in the order of 1-butanol gt isobutanol gt 2-butanol gt tert-butanol Accordingly the butanol fluxes present the sameorder so do the butanol permeances

Hasanoglu et al [64] studied hydrolysis reaction ofethyl acetate (ethyl acetate (EAc) water ethanol (EOH)and acetic acid (AsAc)) using polydimethylsiloxane (PDMS)PDMS membrane permeates EAc much more than the othercomponents This is not unexpected because the solubilityparameter of PDMS is closer to ethyl acetate than the othercomponents (120575PDMS = 81 (calcm3)05) [92] Thus PDMSis more selective to ethyl acetate than other componentsThe solubility parameter is a measure of the affinity betweenpolymer and penetrant and can give qualitative informationabout interaction between polymer and penetrant As theaffinity between permeant and polymer increases the amountof liquid inside the polymer increases and consequently theflux through the membrane increases [93]

8 Conclusion

Membranes both hydrophilic and hydrophobic are widelyused in industries for both product recovery and wastetreatment Nowadays it is widely used in industries fordehydrating solvents such as ethanol and isopropanol Aspervaporation is independent of vaporliquid equilibria itcan preferentially remove water from a stream irrespec-tive of the other components present Therefore it can beconsidered as a substitute where distillation is difficult orcostly Moreover pervaporation can be used progressivelyto improve reactor performance by either purifying feedsor separating reaction products Since pervaporation is amembrane process these separations can be combined withthe reaction step resulting in substantial improvements inreaction efficiencies yields and process economics In thisregard lots of scope exists for separation of esterificationproduct or the byproduct Research is going on to developnew and better membranes that is with higher fluxesbetter selectivity and broader chemical resistance which willexpand the areas where pervaporation-esterification hybridis feasible

Nomenclature

119896

119897 Boundary layer mass transfer coefficient

on the liquid side119909

119894119897 Organic concentration at the

liquid-membrane interface119870

119894 Membrane mass transfer coefficient

119905 Membrane thickness119909

119891 119909

119892 Concentration of component in feed andpermeance

119869

119894 Flux of 119894 across the membrane


119876ov119894 The overall mass transfer coefficientof 119894 in terms of vapor pressure

119860 Membrane area119901

119897119894 119901

119892119894 Partial vapor pressures of 119894 in the

liquid side and in the permeance (orgas) side respectively

119870ov119894 Overall mass transfer coefficient of 119894in terms of liquid concentration

119862

119897119894 Concentration of 119894 in the liquid

119862

lowast


119901

119897119894 Partial vapor pressure of 119894 in the

liquid side119901

119892119894 Partial vapor pressure of 119894 in the gas

side119862

119892119894 Concentration in the gas side

120574

119894 Activity coefficient of 119894 in the liquid

side119901

0

119894 Saturation vapor pressure of pure 119894

at the liquid temperature120588

119897 Molar density of the liquid

119901

119879 Total pressure in the gas side

120588

119892 Molar density of the gas

119870ov119894 Apparent mass transfer coefficient119891

119894 Fugacity of component 119894

119875

119894 Permeability coefficient

119897 Thickness of the active layer of themembrane

119878

119894 Solubility coefficient of the in the

membrane119863

119894 Diffusion coefficient of the in the

membrane120574119901

0120588

119897 Conversion factor from a

concentration driving force to apartial vapor pressure driving force

119876ov Overall mass transfer coefficient (interms of vapor pressure drivingforce)

119870ov Overall mass transfer coefficient (interms of concentration drivingforce)

119876

119897 Liquid phase mass transfer

coefficient (in terms of vaporpressure driving force)

119870


coefficient (in terms ofconcentration driving force)

Re Reynolds number = 120588119906119889ℎ120583

Sc Schmidt number = 120583120588119863119871 Length of the system119889

ℎ Hydraulic diameter of the system

119908

119894PEBA (iemembrane)119908

119894Feed

Weight fractions of component 119894 inthe PEBA material and the liquidfeed solution in solubilityequilibrium with the PEBA phaserespectively

119910 119909 Weight fractions of components inthe permeance and feedrespectively

119908

119894 Weight fraction of the compound 119894

in the feed (119908feed119894

) and in thepermeance (119908permeate

119894)

119901

119901 Permeant pressure120573 Ideal membrane selectivity119862

119901water 119862119891water Water concentrations in thepermeance and feed respectively

119869

119901 Permeation flux (kgm2h)

119878

119900 Temperature-independent

constantΔ119867

119904 Heat of solution

119863


constant in (33)119864

119889 Activation energy for diffusion or

it is a preexponential factor119875

119900

119908 120574

119908 The saturated vapor pressure and

the activity coefficient of waterrespectively

119909

119908 Mole fraction of water in an

ethanolwater mixture120601 Volume fraction of penetrant120574 Exponential constant (plasticizing

constant indicating theplasticizing action of the penetranton segmental motion)

119863

119900 Diffusion concentration at zero

concentration in (41)119886

119894 Activity of penetrant inside the

polymer119881

119900 Volume occupied by molecules at

0 K119863

119879 Thermodynamic diffusion

coefficient120594 Interaction parameter is molar

volume119889 Volume fraction of penetrant119869

119908(119879

119900 119875

119900) Water flux measured at a feed side

temperature of 119879119900 and permeantside pressure of 119875119900

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work was supported by the DSTMinistry of Science andTechnology New Delhi India (SBFTPETA-972012)

References

[1] J G Crespo and C Brazinha ldquoFundamentals of pervaporationrdquoin Pervaporation Vapour Permeation and Membrane Distilla-tion A Basile A Figoli and M Khayet Eds chapter 1 Wood-head Publishing Elsevier Amsterdam The Netherlands 1stedition 2015


[2] B V Bruggen and P Luis ldquoPervaporationrdquo in Progress inFiltration and Separation R J Wakeman Ed chapter 4Elsevier Scientific 1979 University of California 2015

[3] L Aouinti D Roizard and M Belbachir ldquoPVCndashactivated car-bonbasedmatrices a promising combination for pervaporationmembranes useful for aromaticndashalkane separationsrdquo Separationand Purification Technology vol 147 pp 51ndash61 2015

[4] C P Ribeiro B D Freeman D S Kalika and S KalakkunnathldquoAromatic polyimide and polybenzoxazole membranes for thefractionation of aromaticaliphatic hydrocarbons by pervapo-rationrdquo Journal of Membrane Science vol 390-391 pp 182ndash1932012

[5] Z Li B Zhang L Qu J Ren and Y Li ldquoA novel atmosphericdielectric barrier discharge (DBD) plasma graft-filling tech-nique to fabricate the composite membranes for pervaporationof aromaticaliphatic hydrocarbonsrdquo Journal of Membrane Sci-ence vol 371 no 1-2 pp 163ndash170 2011

[6] J Kujawa S Cerneaux and W Kujawski ldquoHighly hydrophobicceramic membranes applied to the removal of volatile organiccompounds in pervaporationrdquo Chemical Engineering Journalvol 260 pp 43ndash54 2015

[7] A A Ghoreyshi H Sadeghifar and F Entezarion ldquoEfficiencyassessment of air stripping packed towers for removal of VOCs(volatile organic compounds) from industrial and drinkingwatersrdquo Energy vol 73 pp 838ndash843 2014

[8] S-K Mah S-P Chai and T Y Wu ldquoDehydration of glycerinsolution using pervaporation HybSi and polydimethylsiloxanemembranesrdquo Journal of Membrane Science vol 450 pp 440ndash446 2014

[9] P Delgado M T Sanz and S Beltran ldquoPervaporation of thequaternary mixture present during the esterification of lacticacid with ethanolrdquo Journal of Membrane Science vol 332 no1-2 pp 113ndash120 2009

[10] M-H Zhu I Kumakiri K Tanaka and H Kita ldquoDehydrationof acetic acid and esterification product by acid-stable ZSM-5membranerdquoMicroporous andMesoporousMaterials vol 181 pp47ndash53 2013

[11] W Zhang Z Yu Q Qian Z Zhang and X Wang ldquoImprov-ing the pervaporation performance of the glutaraldehydecrosslinked chitosan membrane by simultaneously changing itssurface and bulk structurerdquo Journal of Membrane Science vol348 no 1-2 pp 213ndash223 2010

[12] C Zhao H Wu X Li et al ldquoHigh performance compositemembranes with a polycarbophil calcium transition layer forpervaporation dehydration of ethanolrdquo Journal of MembraneScience vol 429 pp 409ndash417 2013

[13] C S M Pereira V M T M Silva S P Pinho and A ERodrigues ldquoBatch and continuous studies for ethyl lactatesynthesis in a pervaporation membrane reactorrdquo Journal ofMembrane Science vol 361 no 1-2 pp 43ndash55 2010

[14] J J Jafar P M Budd and R Hughes ldquoEnhancement ofesterification reaction yield using zeolite A vapour permeationmembranerdquo Journal ofMembrane Science vol 199 no 1 pp 117ndash123 2002

[15] N Agoudjil S Kermadi and A Larbot ldquoSynthesis of inorganicmembrane by solndashgel processrdquo Desalination vol 223 no 1ndash3pp 417ndash424 2008

[16] P Delgado M T Sanz S Beltran and L A Nunez ldquoEthyllactate production via esterification of lactic acid with ethanolcombined with pervaporationrdquo Chemical Engineering Journalvol 165 no 2 pp 693ndash700 2010

[17] S Assabumrungrat J Phongpatthanapanich P PraserthdamT Tagawa and S Goto ldquoTheoretical study on the synthesis ofmethyl acetate from methanol and acetic acid in pervaporationmembrane reactors effect of continuous-flowmodesrdquoChemicalEngineering Journal vol 95 no 1 pp 57ndash65 2003

[18] R Krupiczka and Z Koszorz ldquoActivity-based model of thehybrid process of an esterification reaction coupled with per-vaporationrdquo Separation and Purification Technology vol 16 no1 pp 55ndash59 1999

[19] D J Benedict S J Parulekar and S-P Tsai ldquoPervaporation-assisted esterification of lactic and succinic acids with down-stream ester recoveryrdquo Journal of Membrane Science vol 281no 1-2 pp 435ndash445 2006

[20] Y Zhu and H F Chen ldquoPervaporation separation andpervaporation-esterification coupling using crosslinked PVAcomposite catalytic membranes on porous ceramic platerdquo Jour-nal of Membrane Science vol 138 no 1 pp 123ndash134 1998

[21] T A Peters N E Benes and J T F Keurentjes ldquoPreparationofAmberlyst-coated pervaporationmembranes and their appli-cation in the esterification of acetic acid and butanolrdquo AppliedCatalysis A General vol 317 no 1 pp 113ndash119 2007

[22] B Sarkar S Sridhar K Saravanan and V Kale ldquoPreparationof fatty acid methyl ester through temperature gradient drivenpervaporation processrdquo Chemical Engineering Journal vol 162no 2 pp 609ndash615 2010

[23] S-M Ahn J-W Ha J-H Kim Y-T Lee and S-B Lee ldquoPer-vaporation of fluoroethanolwater and methacrylic acidwatermixtures through PVA composite membranesrdquo Journal ofMembrane Science vol 247 no 1-2 pp 51ndash57 2005

[24] J M L Neel Q T Nguyen and H Bruschke ldquoCompositemembrane for separating water from fluids containing organiccomponents by means of pervaporationrdquo US Patent 5 3343141994

[25] P M Budd N M P S Ricardo J J Jafar B Stephenson andR Hughes ldquoZeolitepolyelectrolyte multilayer pervaporationmembranes for enhanced reaction yieldrdquo Industrial and Engi-neering Chemistry Research vol 43 no 8 pp 1863ndash1867 2004

[26] SGAdoor L SManjeshwar SD Bhat andTMAminabhavildquoAluminum-rich zeolite beta incorporated sodium alginatemixed matrix membranes for pervaporation dehydration andesterification of ethanol and acetic acidrdquo Journal of MembraneScience vol 318 no 1-2 pp 233ndash246 2008

[27] L M Vane ldquoA review of pervaporation for product recoveryfrom biomass fermentation processesrdquo Journal of ChemicalTechnology and Biotechnology vol 80 no 6 pp 603ndash629 2005

[28] Y Mori and T Inaba ldquoEthanol production from starch in apervaporation membrane bioreactor using Clostridium ther-mohydrosulfuricumrdquoBiotechnology and Bioengineering vol 36no 8 pp 849ndash853 1990

[29] M She and S-T Hwang ldquoConcentration of dilute flavorcompounds by pervaporation permeate pressure effect andboundary layer resistance modelingrdquo Journal of MembraneScience vol 236 no 1-2 pp 193ndash202 2004

[30] N Qureshi M M Meagher J Huang and R W HutkinsldquoAcetone butanol ethanol (ABE) recovery by pervaporationusing silicalite-silicone composite membrane from fed-batchreactor of Clostridium acetobutylicumrdquo Journal of MembraneScience vol 187 no 1-2 pp 93ndash102 2001

[31] H Matsuda H Yanagishita H Negishi et al ldquoImprovement ofethanol selectivity of silicalite membrane in pervaporation bysilicone rubber coatingrdquo Journal of Membrane Science vol 210no 2 pp 433ndash437 2002


[32] H Yanagishita C Maejima D Kitamoto and T NakaneldquoPreparation of asymmetric polyimide membrane for waterethanol separation in pervaporation by the phase inversionprocessrdquo Journal of Membrane Science vol 86 no 3 pp 231ndash240 1994

[33] T Sano N Yamashita Y Iwami K Takeda and Y KawakamildquoEstimation of dealumination rate of ZSM-5 zeolite by adsorp-tion of water vaporrdquo Zeolites vol 16 no 4 pp 258ndash264 1996

[34] T Sano S Ejiri K Yamada Y Kawakami and H YanagishitaldquoSeparation of acetic acid-water mixtures by pervaporationthrough silicalite membranerdquo Journal of Membrane Science vol123 no 2 pp 225ndash233 1997

[35] B Smitha D Suhanya S Sridhar and M RamakrishnaldquoSeparation of organicmdashorganic mixtures by pervaporationmdasha reviewrdquo Journal of Membrane Science vol 241 no 1 pp 1ndash212004

[36] C-L Chang and M-S Chang ldquoPreparation of compositemembranes of functionalised silicone polymers and PVDF forpervaporation of ethanol-water mixturerdquoDesalination vol 148no 1ndash3 pp 39ndash42 2002

[37] J R Gonzalez-Velasco J A Gonzalez-Marcos and C Lopez-Dehesa ldquoPervaporation of ethanolmdashwater mixtures throughpoly(1-trimethylsilyl-1-propyne) (PTMSP)membranesrdquoDesali-nation vol 149 no 1ndash3 pp 61ndash65 2002

[38] M Krea D Roizard N Moulai-Mustefa and D Sacco ldquoSyn-thesis of polysiloxanendashimide membranesmdashapplication to theextraction of organics from water mixturesrdquo Desalination vol163 no 1ndash3 pp 203ndash206 2004

[39] M K Djebbar Q T Nguyen R Clement and Y GermainldquoPervaporation of aqueous ester solutions through hydrophobicpoly (ether-block-amide) copolymer membranesrdquo Journal ofMembrane Science vol 146 no 1 pp 125ndash133 1998

[40] M Matsumura and H Kataoka ldquoSeparation of dilute aqueousbutanol and acetone solutions by pervaporation through liquidmembranesrdquo Biotechnology and Bioengineering vol 30 no 7pp 887ndash895 1987

[41] A Thongsukmak and K K Sirkar ldquoPervaporation membraneshighly selective for solvents present in fermentation brothsrdquoJournal of Membrane Science vol 302 no 1-2 pp 45ndash58 2007

[42] A Hasanoglu Y Salt S Keleser and S Dincer ldquoThe esterifica-tion of acetic acid with ethanol in a pervaporation membranereactorrdquo Desalination vol 245 no 1ndash3 pp 662ndash669 2009

[43] M T Sanz and J Gmehling ldquoEsterification of acetic acid withisopropanol coupled with pervaporation part I kinetics andpervaporation studiesrdquo Chemical Engineering Journal vol 123no 1-2 pp 1ndash8 2006

[44] L Domingues F Recasens and M A Larrayoz ldquoStudies of apervaporation reactor kinetics and equilibrium shift in benzylalcohol acetylationrdquo Chemical Engineering Science vol 54 no10 pp 1461ndash1465 1999

[45] Z Koszorz N Nemestothy Z Ziobrowski K Belafi-Bako andR Krupiczka ldquoInfluence of pervaporation process parameterson enzymatic catalyst deactivationrdquo Desalination vol 162 no1ndash3 pp 307ndash313 2004

[46] M Zhang L Chen Z Jiang and J Ma ldquoEffects of dehydrationrate on the yield of ethyl lactate in a pervaporation-assistedesterification processrdquo Industrial amp Engineering ChemistryResearch vol 54 no 26 pp 6669ndash6676 2015

[47] S Korkmaz Y Salt and S Dincer ldquoEsterification of acetic acidand isobutanol in a pervaporation membrane reactor usingdifferent membranesrdquo Industrial and Engineering ChemistryResearch vol 50 no 20 pp 11657ndash11666 2011

[48] W Zhang W Qing N Chen Z Ren J Chen and W SunldquoEnhancement of esterification conversion using novel com-posite catalytically active pervaporationmembranesrdquo Journal ofMembrane Science vol 451 pp 285ndash292 2014

[49] C-J Shieh H-F Liao and C-C Lee ldquoOptimization of lipase-catalyzed biodiesel by response surface methodologyrdquo Biore-source Technology vol 88 no 2 pp 103ndash106 2003

[50] Z Ziobrowski K Kiss A Rotkegel N Nemestothy RKrupiczka and L Gubicza ldquoPervaporation aided enzymaticproduction of glycerol monostearate in organic solventsrdquoDesalination vol 241 no 1ndash3 pp 212ndash217 2009

[51] S H Krishna B Manohar S Divakar S G Prapulla and N GKaranth ldquoOptimization of isoamyl acetate production by usingimmobilized lipase from Mucor miehei by response surfacemethodologyrdquo Enzyme and Microbial Technology vol 26 no2-4 pp 131ndash136 2000

[52] A Baudot andMMarin ldquoPervaporation of aroma compoundscomparison of membrane performances with vapour-liquidequilibria and engineering aspects of process improvementrdquoFood and Bioproducts Processing vol 75 no 2 pp 117ndash142 1997

[53] D Beaumelle M Marin and H Gibert ldquoPervaporation withorganophilic membranes state of the artrdquo Transactions of theInstitution of Chemical Engineers C vol 71 no 2 pp 77ndash89 1993

[54] T A C Oliveira J T Scarpello and A G LivingstonldquoPervaporation-biological oxidation hybrid process for removalof volatile organic compounds from wastewatersrdquo Journal ofMembrane Science vol 195 no 1 pp 75ndash88 2002

[55] J G Wijmans A L Athayde R Daniels J H Ly H DKamaruddin and I Pinnau ldquoThe role of boundary layers inthe removal of volatile organic compounds from water bypervaporationrdquo Journal of Membrane Science vol 109 no 1 pp135ndash146 1996

[56] S Ganapathi-Desai and S K Sikdar ldquoA polymer-ceramic com-posite membrane for recovering volatile organic compoundsfrom wastewaters by pervaporationrdquo Clean Products and Pro-cesses vol 2 no 3 pp 140ndash148 2000

[57] P Cote and C Lipski ldquoMass transfer in pervaporation forwater and wastewater treatmentrdquo in Proceedings of the 3rd Inter-national Conference on Pervaporation Processes and ChemicalIndustry R A Bakish Ed pp 449ndash462 1988

[58] Z Qi and E L Cussler ldquoMembrane separation of potassiumnitrate from mixed brinesrdquo Journal of Membrane Science vol19 no 3 pp 259ndash272 1984

[59] J G Wijmans and R W Baker ldquoThe solution-diffusion modela reviewrdquo Journal of Membrane Science vol 107 no 1-2 pp 1ndash271995

[60] X Feng and R Y M Huang ldquoEstimation of activation energyfor permeation in pervaporation processesrdquo Journal of Mem-brane Science vol 118 no 1 pp 127ndash131 1996

[61] A Hillaire and E Favre ldquoIsothermal and non-isothermalpermeation of an organic vapor through a dense polymermembranerdquo Industrial and Engineering Chemistry Research vol38 no 1 pp 211ndash217 1999

[62] P Sampranpiboon R Jiraratananon D Uttapap X Feng andR YMHuang ldquoPervaporation separation of ethyl butyrate andisopropanol with polyether block amide (PEBA) membranesrdquoJournal of Membrane Science vol 173 no 1 pp 53ndash59 2000

[63] C K Yeom and K-H Lee ldquoA study on desorption resistance inpervaporation of single component through densemembranesrdquoJournal of Applied Polymer Science vol 63 no 2 pp 221ndash2321997


[64] A Hasanoglu Y Salt S Keleser S Ozkan and S DincerldquoPervaporation separation of organics from multicomponentaqueous mixturesrdquo Chemical Engineering and Processing Pro-cess Intensification vol 46 no 4 pp 300ndash306 2007

[65] M N Hyder R Y M Huang and P Chen ldquoEffect of selec-tive layer thickness on pervaporation of composite poly(vinylalcohol)ndashpoly(sulfone) membranesrdquo Journal of Membrane Sci-ence vol 318 no 1-2 pp 387ndash396 2008

[66] A Raisi and A Aroujalian ldquoAroma compound recovery byhydrophobic pervaporation the effect of membrane thicknessand coupling phenomenardquo Separation and Purification Technol-ogy vol 82 no 1 pp 53ndash62 2011

[67] J-H Chang J-K Yoo S-H Ahn K-H Lee and S-M KoldquoSimulation of pervaporation process for ethanol dehydrationby using pilot test resultsrdquoKorean Journal of Chemical Engineer-ing vol 15 no 1 pp 28ndash36 1998

[68] M H V Mulder and C A Smolders ldquoOn the mechanismof separation of ethanolwater mixtures by pervaporation ICalculations of concentration profilesrdquo Journal of MembraneScience vol 17 no 3 pp 289ndash307 1984

[69] D E Daubert and R P Danner Physical and ThermodynamicProperties of Pure Chemicals Data Compilation Design Insti-tute for Physical Property Data AIChE Hemisphere PublishingCorporation 1991

[70] J Gmehling andU OnkenVapor-Liquid EquilibriumData Col-lection Aqueous-Organic Systems vol 1 of Dechema ChemistryData Series part 1 DECHEMA Frankfurt Germany 1977

[71] M C Burshe S B Sawant and V G Pangarkar ldquoDehydrationof glycerine-water mixtures by pervaporationrdquo Journal of theAmerican Oil Chemistsrsquo Society vol 76 no 2 pp 209ndash214 1999

[72] W F Guo T-S Chung and T Matsuura ldquoPervaporation studyon the dehydration of aqueous butanol solutions a comparisonof flux vs permeance separation factor vs selectivityrdquo Journalof Membrane Science vol 245 no 1-2 pp 199ndash210 2004

[73] J Ma M Zhang L Lu X Yin J Chen and Z JiangldquoIntensifying esterification reaction between lactic acid andethanol by pervaporation dehydration using chitosan-TEOShybrid membranesrdquo Chemical Engineering Journal vol 155 no3 pp 800ndash809 2009

[74] A Svang-Ariyaskul R Y M Huang P L Douglas et alldquoBlended chitosan and polyvinyl alcohol membranes for thepervaporation dehydration of isopropanolrdquo Journal of Mem-brane Science vol 280 no 1-2 pp 815ndash823 2006

[75] AThongsukmak and K K Sirkar ldquoExtractive pervaporation toseparate ethanol from its dilute aqueous solutions characteristicof ethanol-producing fermentation processesrdquo Journal of Mem-brane Science vol 329 no 1-2 pp 119ndash129 2009

[76] K-H Song K-R Lee and J-M Rim ldquoPervaporation of esterswith hydrophobic membranerdquo Korean Journal of ChemicalEngineering vol 21 no 3 pp 693ndash698 2004

[77] B K Dutta and S K Sikdar ldquoSeparation of volatile organiccompounds from aqueous solutions by pervaporation using S-B-S block copolymer membranesrdquo Environmental Science andTechnology vol 33 no 10 pp 1709ndash1716 1999

[78] Z Guo and C Hu ldquoPervaporation of organic liquidwater mix-tures through a novel silicone copolymer membranerdquo ChineseScience Bulletin vol 43 no 6 pp 487ndash490 1998

[79] AWolinska-Grabczyk J Muszynski and A Jankowski ldquoAppli-cations of polyurethane-based membranes in pervaporationseparationsrdquo Chemical Papers vol 54 no 6 pp 389ndash392 2000

[80] P Maeki-Arvelaa T Salmia M Sundellb K Ekmanb R Pelto-nenb and J Lehtonen ldquoComparison of polyvinylbenzene andpolyolen supported sulphonic acid catalysts in the esterificationof acetic acidrdquo Applied Catalysis A General vol 184 pp 25ndash321999

[81] A Izci and F Bodur ldquoLiquid-phase esterification of acetic acidwith isobutanol catalyzed by ion-exchange resinsrdquo Reactive andFunctional Polymers vol 67 no 12 pp 1458ndash1464 2007

[82] S R KirumakkiNNagaraju and SNarayanan ldquoA comparativeesterification of benzyl alcohol with acetic acid over zeolitesH120573HY and HZSM5rdquo Applied Catalysis A General vol 273 no 1-2pp 1ndash9 2004

[83] F Omota A C Dimian and A Bliek ldquoFatty acid esterificationby reactive distillation part 2mdashkinetics-based design for sul-phated zirconia catalystsrdquoChemical Engineering Science vol 58no 14 pp 3175ndash3185 2003

[84] T A Peters N E Benes A Holmen and J T F KeurentjesldquoComparison of commercial solid acid catalysts for the esterifi-cation of acetic acid with butanolrdquoApplied Catalysis A Generalvol 297 no 2 pp 182ndash188 2006

[85] Y-H Liu Q-S Liu and Z-H Zhang ldquoAmberlyst-15 as a newand reusable catalyst for regioselective ring-opening reactionsof epoxides to 120573-alkoxy alcoholsrdquo Journal of Molecular CatalysisA Chemical vol 296 no 1-2 pp 42ndash46 2008

[86] G D Yadav and M B Thathagar ldquoEsterification of maleic acidwith ethanol over cation-exchange resin catalystsrdquo Reactive andFunctional Polymers vol 52 no 2 pp 99ndash100 2002

[87] Q L Liu and H F Chen ldquoModeling of esterification of aceticacid with n-butanol in the presence of Zr(SO

4)2∙4H2O coupled

pervaporationrdquo Journal of Membrane Science vol 196 no 2 pp171ndash178 2002

[88] M O David T Q Nguyen and J Neel ldquoPervaporationesterification coupling part I Basic kineticmodelrdquoTransactionsof the Institution of Chemical Engineers vol 69 p 341 1991

[89] Q Liu Z Zhang and H F Chen ldquoStudy on the coupling ofesterificationwith pervaporationrdquo Journal ofMembrane Sciencevol 182 no 1-2 pp 173ndash181 2001

[90] L Xuehui andW Lefu ldquoKinetic model for an esterification pro-cess coupled by pervaporationrdquo Journal of Membrane Sciencevol 186 no 1 pp 19ndash24 2001

[91] A Grob and A Heintz ldquoSorption isotherms of aromaticcompounds in organophilic polymer membranes used in per-vaporationrdquo Journal of Solution Chemistry vol 28 no 10 pp1159ndash1174 1999

[92] J Brandrup and E H Immergut Polymer Handbook JohnWiley amp Sons New York NY USA 1975

[93] M H V Mulder Thermodynamic Principles of PervaporationPervaporation Membrane Separation Processes Elsevier Ams-terdam The Netherlands 1991

[94] L Bagnell K Cavell A M Hodges A W-H Mau and A JSeen ldquoThe use of catalytically active pervaporation membranesin esterification reactions to simultaneously increase productyield membrane permselectivity and fluxrdquo Journal of Mem-brane Science vol 85 no 3 pp 291ndash299 1993

[95] S Korkmaz Y Salt A Hasanoglu S Ozkan I Salt and SDincer ldquoPervaporationmembrane reactor study for the esterifi-cation of acetic acid and isobutanol using polydimethylsiloxanemembranerdquoAppliedCatalysis AGeneral vol 366 no 1 pp 102ndash107 2009

[96] P Delgado M T Sanz and S Beltran ldquoPervaporation study fordifferent binary mixtures in the esterification system of lactic


acid with ethanolrdquo Separation and Purification Technology vol64 no 1 pp 78ndash87 2008

[97] K C S Figueiredo V M M Salim and C P Borges ldquoSyn-thesis and characterization of a catalytic membrane for perva-poration-assisted esterification reactorsrdquo Catalysis Today vol133-135 no 1ndash4 pp 809ndash814 2008

[98] E Ameri A Moheb and S Roodpeyma ldquoVapor-permeation-aided esterification of isopropanolpropionic acid using NaAand PERVAP 2201 membranesrdquo Chemical Engineering Journalvol 162 no 1 pp 355ndash363 2010

[99] B-G Park and T T Tsotsis ldquoModels and experiments withpervaporationmembrane reactors integratedwith an adsorbentsystemrdquo Chemical Engineering and Processing Process Intensifi-cation vol 43 no 9 pp 1171ndash1180 2004

[100] Y Zhu R G Minet and T T Tsotsis ldquoA continuous pervapora-tion membrane reactor for the study of esterification reactionsusing a composite polymericceramic membranerdquo ChemicalEngineering Science vol 51 no 17 pp 4103ndash4113 1996

[101] Y Zou Z Tong K Liu and X Feng ldquoModeling of esterificationin a batch reactor coupled with pervaporation for production ofn-butyl acetaterdquo Chinese Journal of Catalysis vol 31 no 8 pp999ndash1005 2010

[102] H Zhou Y Li G Zhu J Liu L Lin and W Yang ldquoMicrowavesynthesis of aampb-oriented zeolite T membranes and theirapplication in pervaporation-assisted esterificationrdquo ChineseJournal of Catalysis vol 29 no 7 pp 592ndash594 2008

[103] K Tanaka R Yoshikawa C Ying H Kita and K-I OkamotoldquoApplication of zeolite membranes to esterification reactionsrdquoCatalysis Today vol 67 no 1ndash3 pp 121ndash125 2001

[104] K Liu Z Tong L Liu and X Feng ldquoSeparation of organiccompounds from water by pervaporation in the production ofn-butyl acetate via esterification by reactive distillationrdquo Journalof Membrane Science vol 256 no 1-2 pp 193ndash201 2005

[105] A V Penkova G A Polotskaya and A M Toikka ldquoSeparationof acetic acid-methanol-methyl acetate-water reactivemixturerdquoChemical Engineering Science vol 101 pp 586ndash592 2013

[106] S Khajavi J C Jansen and F Kapteijn ldquoApplication of asodalite membrane reactor in esterificationmdashcoupling reactionand separationrdquo Catalysis Today vol 156 no 3-4 pp 132ndash1392010

[107] M P Bernal J Coronas M Menendez and J SantamarıaldquoCoupling of reaction and separation at the microscopic levelesterification processes in a H-ZSM-5 membrane reactorrdquoChemical Engineering Science vol 57 no 9 pp 1557ndash1562 2002

[108] A Penkova G Polotskaya and A Toikka ldquoPervaporationcomposite membranes for ethyl acetate productionrdquo ChemicalEngineering and Processing Process Intensification vol 87 pp81ndash87 2015

[109] L Gubicza K Belafi-Bako E Feher and T Frater ldquoWaste-freeprocess for continuous flow enzymatic esterification using adouble pervaporation systemrdquo Green Chemistry vol 10 no 12pp 1284ndash1287 2008

[110] K C S Figueiredo V M M Salim and C P Borges ldquoEthyloleate production by means of pervaporation-assisted ester-ification using heterogeneous catalysisrdquo Brazilian Journal ofChemical Engineering vol 27 no 4 pp 609ndash617 2010

[111] P Luis J Degreve and B V Bruggen ldquoSeparation of methanol-n-butyl acetate mixtures by pervaporation potential of 10commercialmembranesrdquo Journal ofMembrane Science vol 429pp 1ndash12 2013

[112] U Sander and P Soukup ldquoDesign and operation of a perva-poration plant for ethanol dehydrationrdquo Journal of MembraneScience vol 36 pp 463ndash475 1988

[113] W Kujawski M Waczynski and M Lasota ldquoPervaporationproperties of dense polyamide-6 membranes in separation ofwater-ethanol mixturesrdquo Separation Science and Technologyvol 31 no 7 pp 953ndash963 1996

[114] R W Tock J Y Cheung and R L Cook ldquoDioxane-watertransport through nylon 6 membranesrdquo Separation Science vol9 no 5 pp 361ndash379 1974

[115] R Y M Huang Y Xu Y Jin and C Lipski ldquoNovel blendednylon membranes for the pervaporation separation of aceticacid-water and ethanol-water liquid mixture water systemsrdquo inProceedings of the 2nd International Conference on Pervapora-tion Processes in the Chemical Industry R Bakish Ed pp 225ndash239Materials Corporation SanAntonio TexUSAMarch 1987

[116] WKujawski Q TNguyen and JNeel ldquoPervaporation ofwater-alcohols mixtures through nafion 117 and poly(ethylene-co-styrene sulfonate) interpolymer membranesrdquo in Proc Ill IntConf on PV Proc in the Chem Ind Nancy France 1988 RBakish Ed p 355 Bakish Materials Corporation EnglewoodNJ USA 1988

[117] W Featherstone and T Cox ldquoSeparation of aqueous-organicmixtures by pervaporationrdquo British Chemical Engineering andProcess Technology vol 16 pp 817ndash819 1971

[118] S Kimura and T Nomura ldquoPervaporation of organic substancewater system with silicon rubber membranerdquoMaku vol 8 pp177ndash183 1983

[119] W J Groot R G M Van Der Lans and K C A M LuybenldquoPervaporation of fermentation productsrdquo inProc 3rd Int Confon PV Proc in the Chem Ind Nancy France 1988 R BakishEd p 398 BakishMaterials Corporation EnglewoodNJ USA1988

[120] W Kujawski ldquoPervaporative removal of organics from waterusing hydrophobic membranes Binary mixturesrdquo SeparationScience and Technology vol 35 no 1 pp 89ndash108 1999

[121] M Kondo M Komori H Kita and K-I Okamoto ldquoTubulartype pervaporation module with zeolite NaA membranerdquo Jour-nal of Membrane Science vol 133 no 1 pp 133ndash141 1997

[122] F M Velterop Pervatech Selective Ceramic Membranes Infor-mation Leaflet Pervatech Rijssen The Netherlands 1999

[123] H L Fleming and C S Slater ldquoPervaporationrdquo in MembraneHandbook W S W Ho and K K Sirkar Eds chapter 10 p 105Van Nostrand Reinhold New York NY USA 1992

[124] M Zhou M Persin W Kujawski and J Sarrazin ldquoElectro-chemically synthesised polypyrrole membranes for the sepa-ration of organic mixtures by pervaporationrdquo in Proc 7th IntConf on Pervaporation (Reno Nevada USA 1995) R BakishEd p 193 BakishMaterials Corporation Englewood NJ USA1995

[125] Z Yun T Zhangfa L Kun and F Xianshe ldquoModeling ofesterification in a batch reactor coupled with pervaporation forproduction of n-butyl acetaterdquo Chinese Journal of Catalysis vol31 no 8 pp 999ndash1005 2010

[126] A Ishikawa T H Chiang and F Toda ldquoSeparation of waterndashalcohol mixtures by permeation through a zeolite membraneon porous glassrdquo Journal of the Chemical Society ChemicalCommunications vol 12 pp 764ndash765 1989

[127] K Okamoto N Tanihara H Watanabe et al ldquoVapor perme-ation and pervaporation separation of water-ethanol mixturesthrough polyimide membranesrdquo Journal of Membrane Sciencevol 68 no 1-2 pp 53ndash63 1992


[128] X Feng and R Y M Huang ldquoStudies of a membrane reactoresterification facilitated by pervaporationrdquo Chemical Engineer-ing Science vol 51 no 20 pp 4673ndash4679 1996

[129] E Sert and F S Atalay ldquon-Butyl acrylate production byesterification of acrylic acid with n-butanol combined withpervaporationrdquo Chemical Engineering and Processing ProcessIntensification vol 81 pp 41ndash47 2014


[131] K Wasewar S Patidar and V K Agarwal ldquoEsterification oflactic acid with ethanol in a pervaporation reactor modelingand performance studyrdquoDesalination vol 243 no 1ndash3 pp 305ndash313 2009

[132] A P RathodK LWasewar and S S Sonawane ldquoIntensificationof esterification reaction of lactic acid with iso-propanol usingpervaporation reactorrdquo Procedia Engineering vol 51 pp 456ndash460 2013

[133] A P Rathod K LWasewar and S S Sonawane ldquoEnhancementof esterification reaction by pervaporation reactor an intensify-ing approachrdquo Procedia Engineering vol 51 pp 330ndash334 2013

[134] G S Gokavi M G Mali U V Desai and T M AminabhavildquoHighly water selective mixed matrix blend membranes ofpoly(vinyl alcohol)ndashpoly(vinyl pyrolidone) incarporating phos-phomolybdic acid for application in pervaporation assistedesterification of acetic acid with ethanolrdquo Procedia Engineeringvol 44 pp 845ndash846 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Reverse osmosis Ultrafiltration Particle filtration

NanofiltrationMicrofiltration

Dialysis

Gas separation

Pervaporation

Sorption diffusion Hydrodynamic sieving control

0000 0001 001 01 10 10 100 1000(120583m)

Figure 1 The choice of membrane with respect to the size of particles encountered

Separation is based on pore sizes and hence the membranesgot their characteristic names as microfiltration ultrafiltra-tion and nanofiltration membranes (Figure 1) Membranesare either porous or nonporous and in the separation basedon sizes usually porous membranes are used Pervaporationis the distinction class among above membranes as theseparation criteria are different Pervaporation membranesare nonporous and have been widely employed for sepa-rating liquid mixtures The separation feature is based onaffinity with membrane materials and hence the moleculehaving higher affinity is adsorbed and diffuses through themembranewhile themembrane retainsmolecules having lowaffinity

2 Membrane Materials for Pervaporation

For pervaporation the hydrophilic membranes were the firstone to achieve the industrial applications and were usedfor the organic solvent dehydration The main industrialapplications in pervaporation even today are almost the sameas before which is the dehydration of organic liquids Bymodifying the active layer of these membranes with differentchemical compositions and structures these membranesare enabled to extract water with broad ranges of fluxand selectivity [11 12] Commercially available hydrophilicmembranes are made of polymeric membranematerials suchas polyvinyl alcohol (PVA) polyimides polymaleimidesNafion and polyacrylonitrile (PAN)

Presently there have been a number of investigatorsconcerning RampD of the hydrophilic membrane which canbe cataloged into organic inorganic and organic-inorganichybridmembranes Inorganicmembranes such as zeolite andsilica are generally used [13 14] Inorganic membranes arevery suited for high temperature applications (harsh envi-ronments) and generally these membranes are prepared bysol-gel method which was appropriate to elaborate thin andporous layers with controllable porosity on a wide range ofchemically resistantmacroporous substrates [15]While theseinorganic membranes showed high dehydration efficiencytheir industrialization process may be slow-paced due to thecomplicated large-scale preparation and high manufacturingcost In addition to this several kinds of commercial organic

membranes including PERVAP 2201 [16 17] PERVAP 1005(GFT) [18] and GFT-1005 [19] have been introduced to thepervaporation-esterification coupling process Few studies oncross-linked poly(vinyl alcohol) membranes have also beeninvestigated such as PVA with catalyst Zr(SO

4)2sdot4H2O and

Amberlyst [20 21] cast on polyethersulfone [22 23] and onpoly(acrylonitrile) [24] However the inherent instabilities ofthese organic membranes severely limit their applications

Organic-inorganic hybrid materials have been proposedto be the best choice for having both the functionality of theorganic moiety and the stability of inorganic moiety Buddet al [25] employed zeolitepolyelectrolyte (chitosanpoly(4-styrene sulfonate)) multilayer pervaporation membranes toenhance the yield of ethyl lactate Adoor et al [26] pre-pared aluminum-rich zeolite beta incorporated sodium algi-nate pervaporation membranes Organic-inorganic hybridmembranes showed improved performance of pervaporativedehydration of solution with better flux and retention

Hydrophobic membranes used as pervaporation mem-branes are used to separate volatile organic compoundsfrom the body of water Hydrophobic membrane systemsutilize molecules made from proprietary polymeric hollowfiber membranes The membrane only permits the volatileorganic compound and rejects water molecule due to itshydrophobic nature Hence pervaporation integrated withmembrane separation technology serves as an interestingsubject for the separation of organic compounds such aspollutants and high-value products like aroma compoundsHere the membranes employed are polymeric in nature[27ndash29] Rarely ceramic membranes [30ndash34] can also beused However when it comes to recovering volatile polarorganics from their very dilute solutions in water [35] theselectivity exhibited by polymeric membranes as well asceramic membranes is not high [36ndash38]

One of the most applied polymeric materials for organicseparation is polydimethylsiloxane (PDMS) PDMS exhibitshigh selectivity and permeability towards organic substancesbecause of the flexible structure and therefore is preferredfor the removal of organic compounds from water [39]Organic liquid membranes of oleyl alcohol (OA) were foundto demonstrate high selectivity for recovering species liken-butanol and acetone [40] from simulated fermentation


Membrane


Reactor

Condenser

Permeance

Retentate

Condenser














PERVAP[2201]







[89][87][101]













60



Membrane

1

2

3

4






119869

bl119886= 119896

119897120588 (119909

119891minus 119909

119894119897) (1)




119869

119898

119900= 119896

119894120588 (119909

119898119897minus 119909

119898119892) (2)



119898119897and 119909




119869

119894= 119870ov120588 (119909119891 minus 119909119901) (3)


119869

119894= 119876ov119894119860(119901

119897119894minus 119901

119892119894) = 119870ov119897119860(119862

119897119894minus 119862

lowast

119892119894) (4)

119869

119894= 119870ov119894 (119891

feed119894

minus 119891

permeate119894

) (5)

where 119869



119897119894and 119901



119897119894is the





given by [54]

119901

119897119894=

119862

119897119894120574

119894119901

0

119894

120588

119897

(6)

where 120574


119901

0






119901

119892119894=

119862

119892119894119901

119879

120588

119892

(7)

where 119901


119892is




119891

feed119894

= 120574

119894119909

feed119894

119901

119900

119894(119879

feed)

119891

permeate119894

= 120574

119894119875

119901

(8)


119894is activity


119879is total


119894) includes




119896

119894=

119875

119894

119897

(9)

119875

119894= 119878

119894119863

119894 (10)







1

119870ov=

1

119896

119897

+

119897

119875

119898

(11)

or

1

119876ov=

1

119876

119898

+

1

119876

119897

=

119897

119875

119898

+

120574119901

0

120588

119897119896

119897

(12)




119897) as follows

119876

119897=

120588

119897

120574119901

0119896

119897 (13)





119876ov =120588

119897

120574119901

0119870ov119897 (14)





119896

119897= 16 [

119863

119894

119889

ℎ

] [Re]13 [Sc]13 [119889

ℎ

119871

] (15)


dicted as

119896

119897= 0026 [

119863

119894

119889

ℎ

] [Re]08 [Sc]13 (16)

where Re = 119906120588119903119889










119897estimates







119891 = 6120587120578119903 (18)


119863 =

119870119879

119891

(19)





given by

119876

119897=

119863119888

119894

119897

[119905 minus

119897

2

2119863

] (20)






119894119878

119894for



as

119878

119894=

119908

119894Memb

119908

119894Feed (21)







119894


120572

119894=

119908

permeate119894

(1 minus 119908

permeate119894

)

119908

feed119894

(1 minus 119908

feed119894

)

(22)


(119908feed119894




119869

119894= [

119875

119894

119897

] (119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901) (23)







[

119875

119894

119897

] =

119869

119894

(119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901)

(24)


120573

119894119895=

119875

119894

119875

119895

(25)


PSI = 119869 (120572 minus 1) (26)


















ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30






Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0



Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8





119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)


119904


119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)


119889is


119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)


119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875




119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)



119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Membrane


Reactor

Condenser

Permeance

Retentate

Condenser














PERVAP[2201]







[89][87][101]













60



Membrane

1

2

3

4






119869

bl119886= 119896

119897120588 (119909

119891minus 119909

119894119897) (1)




119869

119898

119900= 119896

119894120588 (119909

119898119897minus 119909

119898119892) (2)



119898119897and 119909




119869

119894= 119870ov120588 (119909119891 minus 119909119901) (3)


119869

119894= 119876ov119894119860(119901

119897119894minus 119901

119892119894) = 119870ov119897119860(119862

119897119894minus 119862

lowast

119892119894) (4)

119869

119894= 119870ov119894 (119891

feed119894

minus 119891

permeate119894

) (5)

where 119869



119897119894and 119901



119897119894is the





given by [54]

119901

119897119894=

119862

119897119894120574

119894119901

0

119894

120588

119897

(6)

where 120574


119901

0






119901

119892119894=

119862

119892119894119901

119879

120588

119892

(7)

where 119901


119892is




119891

feed119894

= 120574

119894119909

feed119894

119901

119900

119894(119879

feed)

119891

permeate119894

= 120574

119894119875

119901

(8)


119894is activity


119879is total


119894) includes




119896

119894=

119875

119894

119897

(9)

119875

119894= 119878

119894119863

119894 (10)







1

119870ov=

1

119896

119897

+

119897

119875

119898

(11)

or

1

119876ov=

1

119876

119898

+

1

119876

119897

=

119897

119875

119898

+

120574119901

0

120588

119897119896

119897

(12)




119897) as follows

119876

119897=

120588

119897

120574119901

0119896

119897 (13)





119876ov =120588

119897

120574119901

0119870ov119897 (14)





119896

119897= 16 [

119863

119894

119889

ℎ

] [Re]13 [Sc]13 [119889

ℎ

119871

] (15)


dicted as

119896

119897= 0026 [

119863

119894

119889

ℎ

] [Re]08 [Sc]13 (16)

where Re = 119906120588119903119889










119897estimates







119891 = 6120587120578119903 (18)


119863 =

119870119879

119891

(19)





given by

119876

119897=

119863119888

119894

119897

[119905 minus

119897

2

2119863

] (20)






119894119878

119894for



as

119878

119894=

119908

119894Memb

119908

119894Feed (21)







119894


120572

119894=

119908

permeate119894

(1 minus 119908

permeate119894

)

119908

feed119894

(1 minus 119908

feed119894

)

(22)


(119908feed119894




119869

119894= [

119875

119894

119897

] (119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901) (23)







[

119875

119894

119897

] =

119869

119894

(119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901)

(24)


120573

119894119895=

119875

119894

119875

119895

(25)


PSI = 119869 (120572 minus 1) (26)


















ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30






Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0



Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8





119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)


119904


119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)


119889is


119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)


119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875




119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)



119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















PERVAP[2201]







[89][87][101]













60



Membrane

1

2

3

4






119869

bl119886= 119896

119897120588 (119909

119891minus 119909

119894119897) (1)




119869

119898

119900= 119896

119894120588 (119909

119898119897minus 119909

119898119892) (2)



119898119897and 119909




119869

119894= 119870ov120588 (119909119891 minus 119909119901) (3)


119869

119894= 119876ov119894119860(119901

119897119894minus 119901

119892119894) = 119870ov119897119860(119862

119897119894minus 119862

lowast

119892119894) (4)

119869

119894= 119870ov119894 (119891

feed119894

minus 119891

permeate119894

) (5)

where 119869



119897119894and 119901



119897119894is the





given by [54]

119901

119897119894=

119862

119897119894120574

119894119901

0

119894

120588

119897

(6)

where 120574


119901

0






119901

119892119894=

119862

119892119894119901

119879

120588

119892

(7)

where 119901


119892is




119891

feed119894

= 120574

119894119909

feed119894

119901

119900

119894(119879

feed)

119891

permeate119894

= 120574

119894119875

119901

(8)


119894is activity


119879is total


119894) includes




119896

119894=

119875

119894

119897

(9)

119875

119894= 119878

119894119863

119894 (10)







1

119870ov=

1

119896

119897

+

119897

119875

119898

(11)

or

1

119876ov=

1

119876

119898

+

1

119876

119897

=

119897

119875

119898

+

120574119901

0

120588

119897119896

119897

(12)




119897) as follows

119876

119897=

120588

119897

120574119901

0119896

119897 (13)





119876ov =120588

119897

120574119901

0119870ov119897 (14)





119896

119897= 16 [

119863

119894

119889

ℎ

] [Re]13 [Sc]13 [119889

ℎ

119871

] (15)


dicted as

119896

119897= 0026 [

119863

119894

119889

ℎ

] [Re]08 [Sc]13 (16)

where Re = 119906120588119903119889










119897estimates







119891 = 6120587120578119903 (18)


119863 =

119870119879

119891

(19)





given by

119876

119897=

119863119888

119894

119897

[119905 minus

119897

2

2119863

] (20)






119894119878

119894for



as

119878

119894=

119908

119894Memb

119908

119894Feed (21)







119894


120572

119894=

119908

permeate119894

(1 minus 119908

permeate119894

)

119908

feed119894

(1 minus 119908

feed119894

)

(22)


(119908feed119894




119869

119894= [

119875

119894

119897

] (119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901) (23)







[

119875

119894

119897

] =

119869

119894

(119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901)

(24)


120573

119894119895=

119875

119894

119875

119895

(25)


PSI = 119869 (120572 minus 1) (26)


















ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30






Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0



Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8





119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)


119904


119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)


119889is


119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)


119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875




119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)



119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Membrane

1

2

3

4






119869

bl119886= 119896

119897120588 (119909

119891minus 119909

119894119897) (1)




119869

119898

119900= 119896

119894120588 (119909

119898119897minus 119909

119898119892) (2)



119898119897and 119909




119869

119894= 119870ov120588 (119909119891 minus 119909119901) (3)


119869

119894= 119876ov119894119860(119901

119897119894minus 119901

119892119894) = 119870ov119897119860(119862

119897119894minus 119862

lowast

119892119894) (4)

119869

119894= 119870ov119894 (119891

feed119894

minus 119891

permeate119894

) (5)

where 119869



119897119894and 119901



119897119894is the





given by [54]

119901

119897119894=

119862

119897119894120574

119894119901

0

119894

120588

119897

(6)

where 120574


119901

0






119901

119892119894=

119862

119892119894119901

119879

120588

119892

(7)

where 119901


119892is




119891

feed119894

= 120574

119894119909

feed119894

119901

119900

119894(119879

feed)

119891

permeate119894

= 120574

119894119875

119901

(8)


119894is activity


119879is total


119894) includes




119896

119894=

119875

119894

119897

(9)

119875

119894= 119878

119894119863

119894 (10)







1

119870ov=

1

119896

119897

+

119897

119875

119898

(11)

or

1

119876ov=

1

119876

119898

+

1

119876

119897

=

119897

119875

119898

+

120574119901

0

120588

119897119896

119897

(12)




119897) as follows

119876

119897=

120588

119897

120574119901

0119896

119897 (13)





119876ov =120588

119897

120574119901

0119870ov119897 (14)





119896

119897= 16 [

119863

119894

119889

ℎ

] [Re]13 [Sc]13 [119889

ℎ

119871

] (15)


dicted as

119896

119897= 0026 [

119863

119894

119889

ℎ

] [Re]08 [Sc]13 (16)

where Re = 119906120588119903119889










119897estimates







119891 = 6120587120578119903 (18)


119863 =

119870119879

119891

(19)





given by

119876

119897=

119863119888

119894

119897

[119905 minus

119897

2

2119863

] (20)






119894119878

119894for



as

119878

119894=

119908

119894Memb

119908

119894Feed (21)







119894


120572

119894=

119908

permeate119894

(1 minus 119908

permeate119894

)

119908

feed119894

(1 minus 119908

feed119894

)

(22)


(119908feed119894




119869

119894= [

119875

119894

119897

] (119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901) (23)







[

119875

119894

119897

] =

119869

119894

(119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901)

(24)


120573

119894119895=

119875

119894

119875

119895

(25)


PSI = 119869 (120572 minus 1) (26)


















ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30






Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0



Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8





119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)


119904


119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)


119889is


119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)


119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875




119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)



119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















1

119870ov=

1

119896

119897

+

119897

119875

119898

(11)

or

1

119876ov=

1

119876

119898

+

1

119876

119897

=

119897

119875

119898

+

120574119901

0

120588

119897119896

119897

(12)




119897) as follows

119876

119897=

120588

119897

120574119901

0119896

119897 (13)





119876ov =120588

119897

120574119901

0119870ov119897 (14)





119896

119897= 16 [

119863

119894

119889

ℎ

] [Re]13 [Sc]13 [119889

ℎ

119871

] (15)


dicted as

119896

119897= 0026 [

119863

119894

119889

ℎ

] [Re]08 [Sc]13 (16)

where Re = 119906120588119903119889










119897estimates







119891 = 6120587120578119903 (18)


119863 =

119870119879

119891

(19)





given by

119876

119897=

119863119888

119894

119897

[119905 minus

119897

2

2119863

] (20)






119894119878

119894for



as

119878

119894=

119908

119894Memb

119908

119894Feed (21)







119894


120572

119894=

119908

permeate119894

(1 minus 119908

permeate119894

)

119908

feed119894

(1 minus 119908

feed119894

)

(22)


(119908feed119894




119869

119894= [

119875

119894

119897

] (119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901) (23)







[

119875

119894

119897

] =

119869

119894

(119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901)

(24)


120573

119894119895=

119875

119894

119875

119895

(25)


PSI = 119869 (120572 minus 1) (26)


















ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30






Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0



Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8





119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)


119904


119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)


119889is


119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)


119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875




119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)



119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












given by

119876

119897=

119863119888

119894

119897

[119905 minus

119897

2

2119863

] (20)






119894119878

119894for



as

119878

119894=

119908

119894Memb

119908

119894Feed (21)







119894


120572

119894=

119908

permeate119894

(1 minus 119908

permeate119894

)

119908

feed119894

(1 minus 119908

feed119894

)

(22)


(119908feed119894




119869

119894= [

119875

119894

119897

] (119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901) (23)







[

119875

119894

119897

] =

119869

119894

(119909

119894120574

119894119901

sat119894minus 119910

119894119901

119901)

(24)


120573

119894119895=

119875

119894

119875

119895

(25)


PSI = 119869 (120572 minus 1) (26)


















ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30






Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0



Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8





119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)


119904


119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)


119889is


119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)


119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875




119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)



119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















ux J

(kg

m2 middot

h)

16

14

12

1

08

06

04

02

0

Water in feed (wt)0 5 10 15 20 25 30






Sepa

ratio

n fa

ctor

500

450

400

350

300

250

200

150

100

50

0



Flux

(kg

m2 middot

h)

045

04

035

03

025

02

015

01

005

0

Time (hr)0 2 4 6 8





119878 = 119878

119900exp(minus

Δ119867

119904

119877119879

) (27)


119904


119863 = 119863

119900exp (minus

119864

119889

119877119879

) (28)


119889is


119875 = 119863

119900119878

119900expminus(

Δ119867

119904+ 119864

119889

119877119879

) = 119875

119900expminus(

119864

119901

119877119879

) (29)


119869

119908(119879 119875) = 119869

119908(119879

119900 119875

119900) exp [(

119864

119908

119877

)(

1

119879

119900minus

1

119879

)]

sdot

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875)

119877119879 ln (119909119908120574

119908119875

119900

119908119910

119908119875

119900)

(30)

where 119869119908(119879

119900 119875




119869

119908= 3935119862

119891

119908

(31)

119862

119901

119908=

12119862

119891

119908

0055 + 1284119862

119891

119908 minus 77119862119891

119908

2 (32)



119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119875

119900

119908= exp (119860 +

119861

119879

+ 119862 ln119879 + 119863119879

119864)


3 119862 = minus73037 119863 = 41653 times 10

minus6 119864 = 2

(33)

ln 120574119908= 119860

12[

119860

21(1 minus 119909

119908)

119860

12119909

119908+ 119860

21(1 minus 119909

119908)

]

2

119860

12= 17769 119860

21= 094

(34)

where 119875119900119908and 120574








119894and








119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119886values are





119886) is the sum









119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) 119862

2) (35)








119863 = 119863

119900exp (120574120601) (36)






119900




119881

119891= 119881

119879minus 119881

119900 (37)

where 119881



V119891=

119881

119891

119881

119879

(38)




119891119879119892 Above 119879

119892

V119891= V119891119879119892

+ Δ120572 (119879 minus 119879

119892) (39)


119892and below 119879

119892 Molecule can


119891) 119861 is local



119863

119879= 119877119879119860

119891exp[minus 119861

V119891

] (40)

where 119860





119891and



V119891(120601 119879) = V

119891(0 119879) + 120573 (119879) 120601 (41)






119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119863

0= 119877119879119860

119891exp[minus 119861

V119891(0 119879)

] (42)


ln 119863119879119863

0

= [

119861

V119891(0 119879)

minus

119861

V119891(120601 119879)

] (43)

or

[ln 119863119879119863

0

]

minus1

= [

V119891(0 119879)

119861

minus

V119891(0 119879)

2

119861 (119879) 119861 sdot 120601

] (44)



119879) is

119863

119894= 119863

119879[

119889 ln 119886119894

119889 ln120601119894

] (45)


ln 119886119894= ln(

119901

119894

119901

119900

) = ln120601119894+ (1 minus

V119894

V119901

)120601

119901+ 120594120601

2

119901 (46)


[

119889 ln 119886119894

119889 ln120601119894

] = 1 minus (2120594 + 1 minus

V119894

V119901

)120601 + 2120594120601

2

119901 (47)


11


119866

11

119881

1

= (

1

120601

1

minus 1) [

119889 ln 119886119894

119889 ln120601119894

] minus

1

120601

1

(48)

where 119881


[119889 ln 119886119894119889 ln120601




119908=

784 kcalmol














119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119869

119894= 119870

119894(119862

119894119909

feed119894

119901

119900

119894(119879

feed) minus 119862

2) (49)



119894) and
















2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














2SO4 HCl [80]







































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




































[38]





























Con

vers

ion

()

70605040302010

0

Time (hr)0 2 4 6 8 10





Time (hr)0 2 4 6 8 10

Con

vers

ion

()

1009080706050403020100










119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119900


119900













119908119862

119900119862


119862


















119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























119904)

is negative

75 Other Factors






119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119883

1015840

119860=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

1

119875

minus

119875

119860

119875

lowast

119861minus 119875

lowast

119860

(50)


119889119883

119860

119889119875

=

119875

119860119875

119861

119875

lowast

119861minus 119875

lowast

119860

times

1

119875

2 (51)


lowast










8 Conclusion


Nomenclature

119896







119891 119909


119869





119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119897119894 119901




119862


119862

lowast


119901


liquid side119901


side119862


120574


side119901

0




119901


120588




119875



119878


membrane119863



0120588





119876



119870






119908


119894Feed



119908




119894)

119901



119869


119878


constantΔ119867


119863





119900

119908 120574



119909




119863




polymer119881


0 K119863




119908(119879

119900 119875





Acknowledgment


References



























































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


































































































4)2∙4H2O coupled






















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Download - Review Article Review on Pervaporation: Theory, …downloads.hindawi.com/journals/je/2015/927068.pdf · Review Article Review on Pervaporation: Theory, Membrane Performance, and Application

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