A theoretical study of dense gas extraction using a hollow fiber membrane contactor

J. of Supercritical Fluids 37 (2006) 157–172

A theoretical study of dense gas extraction usinga hollow fiber membrane contactor

Alan Gabelmana, Sun-Tak Hwangb,∗a Givaudan Flavors Corporation, Cincinnati OH 45216, USA

b Department of Chemical and Materials Engineering, University of Cincinnati, Cincinnati OH 45221-0171, USA

Received 2 April 2004; received in revised form 23 June 2005; accepted 26 August 2005

Abstract

Hollow fiber membrane contactors offer several advantages over dispersed phase contactors for extraction of aqueous feeds, including higherinterfacial area, absence of emulsions, no flooding at high flow rates, and no unloading at low ones. The use of these contactors with extractionsolvents near or above their critical points is of particular interest, because such fluids provide a favorable distribution of many solutes, high masstransfer rates, and easy recovery of extracted solutes.

In this paper, we describe a theoretical study of acetone extraction from aqueous solution into supercritical carbon dioxide, with tube side CO2

fl ) butn small. Thei convection.F igher thanw

ed. Ethanola ntactor, andt l contactors.I rrespondingt©

K itical fluid;E

1

toiwi

com

uidsd the

con-for a

en inlf a

tac-uper-ility

assrther-thatimplyed

0d

ow either with or opposed to the force of gravity. Buoyancy-induced flow in the CO2 phase was important for large (1.8 mm inside diameterot small (0.6 mm i.d.) fibers, consistent with our expectation that such flow is more difficult to achieve when the characteristic length is

mportance of buoyancy-induced flow decreased with increasing imposed fluid velocity, as forced convection masked the effects of freeor the range of conditions studied, the mass transfer coefficient obtained with flow in the direction of gravity was as much as 33% hith flow opposing gravity.A study comparing the performance of traditional mass transfer equipment and hollow fiber membrane contactors is also describ

nd isopropanol extractions performed by others using spray, sieve tray or packed columns were run on a simulated membrane cohe resulting values for the height equivalent to a theoretical stage (HETS) were compared to the reported values for the conventionan most instances the simulated membrane contactor offered a significantly (in some cases, substantially) lower HETS than the coraditional column, indicating that the membrane contactor was more efficient.

2005 Elsevier B.V. All rights reserved.

eywords: Mathematical model; Buoyancy-induced flow; Free convection; Natural convection; Hollow fiber; Membrane contactor; Dense gas; Supercrxtraction

. Introduction

For decades the chemical industry has used some type ofower or column to perform gas/liquid or liquid/liquid contactingperations. However, an important disadvantage of this approach

s the interdependence of the two fluid phases to be contacted,hich sometimes leads to difficulties such as emulsions, foam-

ng, unloading and flooding[1].As explained in our previous papers[2,3], non-dispersive

ontact via a microporous membrane is an alternative technol-gy that overcomes these problems and also offers substantiallyore interfacial area per unit volume than columns. Using a

∗ Corresponding author. Tel.: +1 513 556 2791; fax: +1 513 556 3473.E-mail address: [email protected] (S.-T. Hwang).

suitable membrane configuration such as a hollow fiber, flto be contacted flow on opposite sides of the membrane anfluid/fluid interface forms at the mouth of each pore. Suchtactors have been studied extensively since the mid-1980sdiverse range of applications; numerous examples are givour first paper[2], in Gabelman’s dissertation[4], and in severarecent review articles[5–11]. A schematic representation oparallel flow membrane contactor is shown inFig. 1.

A particularly interesting application of membrane contors is extraction with dense gases (i.e., near critical or scritical fluids). Like liquids, dense gases offer high solubof many solutes of interest, yet they also offer the high mtransfer rate and low pressure drop enjoyed with gases. Fumore, solubility is usually a strong function of density, sothe dense gas is easily separated from dissolved solutes sby reducing the pressure[12,13]. Carbon dioxide has the add

896-8446/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.supflu.2005.08.009

158 A. Gabelman, S.-T. Hwang / J. of Supercritical Fluids 37 (2006) 157–172

Nomenclature

a Interfacial area for mass transfer (cm2 cm−3)Cp Constant pressure heat capacity (cal mol−1 ◦K−1)d Diameter (cm)D Diffusivity (cm2 s−1)g Acceleration due to gravity (cm s−2)Gr Grashof number (L3gρ�ρ/µ2)Gz Graetz number (d2v/DL)HETS Height of an equivalent theoretical stage (cm)k Thermal conductivity (cal s−1 cm−1 ◦K−1)K Overall mass transfer coefficient (cm s−1)L Length (cm)Pr Prandtl number (Cpµ/k)Q Flow rate (cm3 s−1)r Radial coordinate (cm)R Radius (cm)Ra Rayleigh number (L3g�ρ/µD)Re Reynolds number (dρv/µ)Ri Richardson number (Gr/Re2)Sc Schmidt number (µ/Dρ)v Velocity (cm/s)V Module volume (cm3)z Axial coordinate (cm)

Greek lettersµ Viscosity (g cm−1 s−1)ρ Density (g cm−3)

SubscriptsA Component Ai Insidew Aqueous phasez Axial

Superscript* Denotes a dimensionless quantity

advantages of being inexpensive, non-toxic and non-flammableand for these reasons is often the solvent of choice in dense gaextraction. Propane is sometimes preferred because the solubity of many materials is higher, although the flammability ofpropane is a drawback.

Although extraction using hollow fiber contactors with tradi-tional solvents has been thoroughly investigated, only a handfuof reports on dense gas extraction using this technology haappeared in the recent literature[2–4,14–20]. Moreover, only

Fig. 1. A parallel flow hollow fiber membrane contactor. (Redrawn from[67].)

the work of Bothun and co-workers[14,15], Gabelman[4]and Gabelman and co-workers[2,3] can be considered an in-depth, quantitative study of mass transfer in these systems. Anabundance of such quantitative results with ordinary solvents isavailable, but those data are not necessarily applicable to densegases because dense gases possess unique properties, particu-larly near the critical point[21–23].

In our first paper[2], we developed a first principles math-ematical model that predicts the steady state velocity and con-centration profiles for dense gas extraction using a hollow fibercontactor. The model accounts for buoyancy-induced flow in thedense gas, because such flow can be significant in the near criticalor supercritical region[22]. The model was validated by show-ing that predicted Sherwood numbers for tube flow agree withthose obtained from the classical equations[24–26], which havebeen confirmed by many experiments over a period of decades.In [2] and our subsequent paper[3], model predictions for theextraction of a variety of solutes from water into dense CO2or propane were shown to agree reasonably well with experi-mental values, except for data obtained with a module that wasparticularly susceptible to non-uniform shell side flow and theassociated loss of efficiency[27–38].

Having validated the model as described above, one can gainconsiderable insight by using it to study mass transfer perfor-mance as a function of geometry and operating parameters. Theresults of such a study can be employed to assess the feasibil-i sivea dy isd ateri tione

effi-c trans-f trac-t Ou dt ranec

2

por-t osity.I pub-lp por-t eateri sti-g ularc atiles erea lutes . Leea lenei heyd ressest t and

,s

il-

ls

ty of a potential new extraction application, in lieu of expennd time-consuming laboratory experimentation. Such a stuescribed in this paper, i.e., the extraction of acetone from w

nto supercritical carbon dioxide. An analysis of free convecffects in the dense gas is included in this study.

The model is also useful to demonstrate the improvediency of membrane contactors versus conventional masser equipment. In this paper, results reported for the exion of ethanol or isopropanol from water into dense C2sing packed, spray or sieve tray towers[39–44]are compare

o those obtained using a simulated hollow fiber membontactor.

. Buoyancy effects

As mentioned above, buoyancy-induced flow can be imant in dense gases, as suggested by their low kinematic viscndeed, buoyancy-induced flow is frequently mentioned inished work with supercritical fluids. Debenedetti and Reid[22]ointed out that at a given Reynolds number, the relative im

ance of natural convection is two orders of magnitude grn a supercritical fluid than in a normal liquid. These inveators used a technique involving laminar flow in a rectanghannel to measure binary diffusion coefficients of nonvololutes in supercritical fluids. The diffusion coefficients wstrong function of the degree of inclination of the so

ource plane, an effect attributable to natural convectionnd Holder[45] studied mass transfer of toluene and naphtha

n supercritical carbon dioxide in a silica gel packed bed. Teveloped a generalized mass transfer correlation that exp

he Sherwood number as a function of the Reynolds, Schmid

A. Gabelman, S.-T. Hwang / J. of Supercritical Fluids 37 (2006) 157–172 159

Grashof numbers; the latter arises in buoyancy-induced flows,as explained below.

Lim and co-workers[46,47]passed supercritical carbon diox-ide through a column packed with pelletized naphthalene orbenzoic acid. They observed a marked difference in mass trans-fer between gravity-assisted and gravity-opposed flow, and theymentioned that such natural convection effects were particularlyimportant near the critical point. Knaff and Schlunder[48] stud-ied solid/dense gas mass transfer by passing supercritical CO2through the annular space surrounding a solid rod of naphtha-lene or caffeine. They observed free convection effects with theformer but not the latter, because only naphthalene was suffi-ciently soluble in CO2 to provide a significant density gradientin the boundary layer next to the rod. Other examples of freeconvections in dense gases are found in the work of Puiggene etal. [49], Sovova et al.[50], and Stuber et al.[51].

For flows where buoyancy is important,Gr1/2 arises in placeof the Reynolds number[52]. Here the Grashof numberGr isgiven by:

Gr = L3gρ�ρ

µ2 . (1)

In Eq.(1), L is the characteristic length for mass transfer,g isthe acceleration due to gravity,ρ is the density,�ρ is the char-acteristic density difference, andµ is the viscosity. The Grashofnumber can be considered the ratio of the buoyancy force tot shofn odue

oldnv r ther iplea ectb itioni onls ri ratioi restii atioi area yt ingt lativi lkaa

theR theS

R

ratioo tuma rati

of buoyancy velocity to diffusion velocity[55,56]. As before,the average values were obtained by integrating over the lengthof the module; alternatively, the average Grashof number wassimply multiplied by the Schmidt number. Again a detailedexplanation of the calculation method used here is available inGabelman’s dissertation[4].

Buoyancy-induced flows arising from heat transfer have beenstudied extensively; much of this work has been with plumes andother external flows, but a substantial amount of information isalso available on enclosed flows of interest here. For example,Marner and McMillan[57] calculated the axial velocity profilesfor mixed convective flow in a vertical isothermal tube, wherethe fluid enters the bottom of the tube with a fully developedparabolic velocity profile. That parabolic profile was distortedin a manner consistent with the presence of buoyancy-drivensecondary flows.

Metais and Eckert[58] presented available heat transfer dataon flow through vertical and horizontal tubes as plots of theReynolds number versus the parameterGrPr(di/L). The data,applicable for 0.01 < Pr(di/L) < 1.0, had been obtained ateither constant wall temperature or uniform wall heat flux. Sixflow regimes were apparent; these were characterized as forcedlaminar, forced turbulent, free laminar, free turbulent, mixedlaminar and mixed turbulent.

In general, for laminar flow in vertical tubes, heat and masstransfer rates increase when buoyancy forces are in the direc-t ow[ ucedflK

3m

ticalc withta om-m wasut , andmw ed inT poresw

low-i sayst nsferc ncen-t

Q

en-t dule,r nt te

he viscous force[53]. In the present paper the average Graumber was obtained by integrating over the length of the mle. Please refer to Gabelman’s dissertation[4] for a detailedxplanation of the calculation ofGr for this work.

The ratio of the Grashof number to the square of the Reynumber (Gr/Re2, known as the Richardson number,Ri) can beiewed as the ratio of the buoyancy to the inertial force, oelative importance of free versus forced convection. In princll systems that undergo heat or mass transfer are subjuoyancy-induced flows because density is a function of pos

n these systems. However, for heat transfer such flows areignificant in systems whereGr/Re2 � 1 if the Prandtl numbes small, while for large Prandtl numbers the appropriates Gr/Re2Pr1/3. Both forced and free convection are of inten the mixed convection region, whereGr/Re2 (or Gr/Re2Pr1/3)s of order unity, and forced convection is dominant if the rs much less than one[53–55]. Presumably these guidelineslso applicable to mass transfer problems ifPr is replaced b

he Schmidt number,Sc. A mathematical argument supporthe use of the Richardson number as an indicator of the remportance of free versus forced convection is given by Shirand Griffith[23].

Analysis of free convection systems also gives rise toayleigh number, which is the product of the Grashof andchmidt numbers:

a = L3g�ρ

µD. (2)

Physically, the Rayleigh number can be viewed as thef buoyancy forces tending to cause flow to other momennd mass transfer effects tending to resist flow, or as the

-

s

to

y

er

o

ion of flow; interestingly, the opposite is true for turbulent fl55,59]. Other authors who have reported on buoyancy-indow in enclosed geometries include Brown and Gauvin[60] anduehn and Goldstein[61,62].

. Effect of operating parameters and geometry onass transfer—a theoretical study

Simulated extraction of acetone from water into supercriarbon dioxide was conducted using countercurrent flow,he module oriented vertically and CO2 flowing either with orgainst gravity. The two fibers chosen for this study are cercially available from Membrana GmbH; the smaller onesed for the experimental work described previously[2–4]. The

emperature, pressure, feed concentration, module lengthembrane porosity were all kept constant at 32◦C, 135 bar, 5%/w, 41.6 cm and 0.75, respectively. Modules are describable 1; because the membranes were hydrophobic, theere wetted by the CO2.Mass transfer coefficients were calculated using the fol

ng form of the governing equation for mass transfer, whichhat the mass flux is equal to the product of the mass traoefficient, the interfacial area for mass transfer and the coration driving force:

w(ρAw,in − ρAw,out) = Kw,avgaV�ρAw,avg. (3)

Here,ρAw, in andρAw, out are the solute densities (i.e., concrations) of the aqueous phase entering and leaving the moespectively. The mass transfer coefficientKw, avg is based ohe aqueous phase log mean driving force, and the flow raQw


Table 1Modules used for theoretical study of acetone extraction into supercritical carbondioxide

Small fibers (Table 2) Large fibers (Table 3)

Nature of membranematerial

Hydrophobic Hydrophobic

Fiber i.d. (cm) 0.06 0.18Fiber o.d. (cm) 0.10 0.24Equivalent shell side

radiusa(cm) 0.22 0.52

Length (cm) 41.6 41.6Packing density 0.21 0.21Porosity 0.75 0.75Tortuosity 1.3 1.3Flow pattern Parallelb Parallelb

a Defined in Gabelman’s dissertation[4].b SeeFig. 1.

can be taken as constant because the amount of mass transferredis assumed to be small. Additional details are available in ourprevious paper[2] and in Gabelman’s dissertation[4]. Yield anddistribution of mass transfer resistance were also determinedas explained in[2] and [4]. The mass transfer resistance wasassumed to be distributed among three resistances in series, i.e.,the tube side fluid boundary layer, the membrane and the shellside fluid boundary layer. Fluid physical properties were esti-mated as described in[4].

Placement of the aqueous fluid on the tube or shell side eachoffers an advantage. Aqueous flow through the shell may bechosen because that is usually the preferred location for the fluidwith the higher viscosity, so that the pressure drop is minimized.On the other hand, dense gas flow through the shell may reduceshell side bypassing, because the lower viscosity of the densegas allows it to penetrate the shell space more quickly[16]. Here,we placed the dense gas in the tubes because of our interest inbuoyancy-induced flow. That is, more information on buoyancy-induced flow is available for tube versus shell flow (e.g.,[58]),and with the dense gas in the tubes, that information may enhanceour understanding of natural convection there.

The results inTable 2are for a fiber inside radius of 0.3 mm,outside radius of 0.5 mm, and a shell side equivalent radius(defined in[4]) of 1.1 mm, for which the packing density is0.21. (Predictions for the larger fiber are presented inTable 3and discussed later.) The Grashof numbers given inTable 2w slicea ngtht berw Onlt ts fob Sucfl , ass at ot

var-it ro-fi do oun

Fig. 2. Concentration profiles for simulated acetone extraction run 2 ofTable 2,with dimensionless lengthz* as the parameter. Dimensionless radii of 0, 1, 1.67and 3.67 correspond to the tube center, the tube side membrane surface, the shellside membrane surface, and the shell side equivalent radius, respectively.

ary layer just barely penetrates to the shell side equivalentradius.

At the lowest aqueous Graetz number studied in thissequence, the aqueous phase boundary layer resistance was 77%of the total, somewhat close to the relative resistance obtainedin the acetone extraction results obtained previously[2] at asimilar Graetz number. On the other hand, the aqueous phaseresistance dropped to 29% of the total when the Graetz numberwas increased by a factor of 1000. The overall mass transfercoefficient increased with increasing fluid velocity, as expectedfor this range of Graetz numbers. The concomitant decrease inyield is also not surprising.

A log–log plot of the overall and shell side (aqueous phase)mass transfer coefficients versus aqueous phase Graetz numberis shown inFig. 3. The variation in the shell side coefficient isqualitatively similar in shape to the results from the classicalequations for tube flow (see[2,4]), i.e., the plot is linear at highGraetz numbers, then begins to level with decreasingGz. As theaqueous phase resistance increases with decreasing shell sideGraetz number, that resistance becomes increasingly important

F shells cetonef s was0 eoa

ere obtained by calculating the values at successive axiallong the length of the module, then integrating over the le

o obtain the average. The Rayleigh and Richardson numere then calculated from the average Grashof number.

he CO2 phase values are given because the model accounuoyancy-induced flow there and not in the aqueous fluid.ow is likely to be much less important in the aqueous fluiduggested by its high kinematic viscosity compared to thhe CO2 phase[22].

In runs 1–4, the aqueous (shell side) flow rate wased while the CO2 flow was held constant, with CO2 flow inhe direction of the force of gravity. The concentration ples for run 2 are shown inFig. 2. With the geometry anperating conditions employed here, the aqueous phase b

s

syr

h

f

d-

ig. 3. Effect of aqueous (shell side) flow rate (i.e., Graetz number) on theide and overall mass transfer coefficients for the simulated extraction of arom aqueous solution into supercritical carbon dioxide. Fiber inner radiu.3 mm, flow was countercurrent, CO2 flow was in the direction of the forcf gravity, and CO2 phase Graetz number was 0.5. See text andTable 2fordditional details.

A.G

abelman,S.-T.H

wang

/J.ofSupercriticalFluids

37(2006)

157–172161

Table 2Theoretical study of acetone extraction from aqueous solution into supercritical carbon dioxide using small fibersa

Runnumber

Aqueous phaseGraetz number

CO2 phaseGraetz number

CO2 flow direction vs.gravityb

Mass transfercoefficientc

(cm/s× 104)

Distribution of masstransfer resistanced

CO2 phaseGrashof numbere

CO2 phaseRayleighnumbere

CO2 phaseRichardsonnumber

Yieldf (%)

Tube (%) Pore (%) Shell (%)

1 2.3 0.51 Same 5.2 7.8 15.3 76.9 224 1133 0.05 48.22 23 0.51 Same 7.3 10.9 21.6 67.6 259 1312 0.05 5.73 231 0.51 Same 11.5 17.5 34.2 48.2 262 1328 0.05 0.64 2308 0.51 Same 15.7 24.5 47.0 28.5 260 1314 0.05 0.15 23 0.13 Same 9.4 15.3 27.4 57.3 61 307 0.2 1.56 23 0.25 Same 8.3 12.5 24.3 63.2 129 653 0.1 3.02 23 0.51 Same 7.3 10.9 21.6 67.6 259 1312 0.05 5.77 23 5.1 Same 6.2 8.4 18.1 73.5 639 3233 0.001 14.58 23 13 Same 6.1 7.6 18.0 74.5 623 3155 0.0002 15.69 5.8 0.13 Same 7.0 10.7 20.6 68.7 62 314 0.2 6.02 23 0.51 Same 7.3 10.9 21.6 67.6 259 1312 0.05 5.7

10 231 5.1 Same 9.4 13.2 27.9 58.9 974 4932 0.002 2.211 577 13 Same 10.9 14.1 32.5 53.4 1179 5969 0.0004 1.212 5.8 0.13 Opposing 7.0 10.9 20.6 68.6 66 336 0.2 6.013 23 0.51 Opposing 7.3 11.0 21.5 67.4 267 1352 0.05 5.714 231 5.1 Opposing 9.4 13.3 27.9 58.8 980 4964 0.002 2.215 577 13 Opposing 10.9 14.1 32.5 53.3 1182 5985 0.0004 1.2

a The module is described inTable 1. Tube side fluid: carbon dioxide; fluid direction: countercurrent; temperature: 32◦C; pressure: 135 bar; fluid velocity: 0.25–25 cm/s. The partition coefficient was 0.9(g/cm3)solvent/(g/cm3)aqueous, estimated by Brignole[65] using a group contribution-associating equation of state[66]. For all runs the overall and solute mass balances (calculated as described in[4]) closed to 100%.

b Either in the same direction as the force of gravity or opposing gravity.c Calculated as described in[2], using the aqueous phase log mean driving force.d Calculated as described in[2]. The sum may not be 100 because of rounding.e Average over the length of the module.f The percentage of incoming solute appearing in the extract (calculated as described in[2]).

162A

.Gabelm

an,S.-T.Hw

ang/J.ofSupercriticalF

luids37

(2006)157–172

Table 3Theoretical study of acetone extraction from aqueous solution into supercritical carbon dioxide using large fibersa

Runnumber

Aqueous phaseGraetz number

CO2 phaseGraetz number

CO2 flow directionvs. gravityb

Mass transfercoefficientc

(cm/s× 104)

Distribution of masstransfer resistanced

CO2 phase Grashofnumbere (× 10−3)

CO2 phase Rayleighnumbere (× 10−3)

CO2 phaseRichardsonnumber

Yieldf (%) Flowregimeg

Tube (%) Pore (%) Shell (%)

1 13 0.46 Same 3.2 8.1 12.8 79.2 4 19 9 9.0 ML2 66 2.3 Same 3.7 9.2 14.9 76.0 14 72 1 5.7 Borderlineh

3 133 4.6 Same 4.1 10.8 16.5 72.7 21 105 0.5 3.8 FL4 452 16 Same 5.1 13.9 20.6 65.4 32 160 0.06 1.6 FL5 1329 46 Same 6.5 14.7 26.0 59.3 36 181 0.01 0.8 FLi6 13 0.46 Opposing 2.4 28.1 9.5 62.4 29 145 65 8.3 ML7 66 2.3 Opposing 2.9 29.9 11.5 58.6 47 240 4 4.8 ML8 133 4.6 Opposing 3.5 24.3 14.2 61.5 46 231 1 3.4 ML9 452 16 Opposing 5.0 16.8 20.0 63.2 38 194 0.08 1.6 FL

10 1329 46 Opposing 6.4 15.5 25.8 58.7 38 190 0.01 0.8 FLi

a The module is described inTable 1. Tube side fluid: carbon dioxide; fluid direction: countercurrent; temperature: 32◦C; pressure: 135 bar; fluid velocity: 0.1–10 cm/s. The partition coefficient was 0.9(g/cm3)solvent/(g/cm3)aqueous, estimated by Brignole[65] using a group contribution-associating equation of state[66]. For all runs the overall and solute mass balances (calculated as described in[4]) closed to 100%.

b Either in the same direction as the force of gravity or opposing gravity.c Calculated as described in[2], using the aqueous phase log mean driving force.d Calculated as described in[2]. The sum may not be 100 because of rounding.e Average over the length of the module.f The percentage of incoming solute appearing in the extract (calculated as described in[2]).g After Metais and Eckert[58]; see text. ML: mixed laminar; FL: forced laminar.h Near border between forced and mixed laminar regimes.i Near transition to forced turbulent regime.


in determining the value of the overall mass transfer coefficient.For this reason the shell side coefficient approaches the overallone as the shell side flow rate decreases.

In runs 2 and 5–8, the CO2 phase (tube side) flow rate wasvaried while the shell side flow was held constant, again withCO2 flow in the direction of the force of gravity. (Note that therow in Table 2that describes run 2 is repeated so that all resultsfrom this sequence can be viewed together.) Most of the masstransfer resistance was in the aqueous phase boundary layer overthe entire range of CO2 phase Graetz numbers studied. The tubeside resistance decreased with increasing flow rate as expected,but these changes were not particularly important because thatresistance was small. The relative pore resistance also decreasedwith increasing flow rate, and the relative aqueous phase resis-tance increased. Yield increased with increasing solvent flowrate as expected.

The effect of CO2 (tube side) flow rate on the overall and tubeside mass transfer coefficients is shown inFig. 4. As explainedabove, the coefficients change little with flow rate because mostof the mass transfer resistance is in the aqueous phase boundarylayer. Note that the tube side coefficient is substantially largerthan the overall one because of the effect of the aqueous phaseresistance on the latter. The tube side coefficient does trendupward slightly with increasing flow rate; however, the over-all coefficient actually decreases with increasing flow. This mustresult from a corresponding decrease in the aqueous phase (shells t doen t, ths es it ougt latet ence

F tubes etonf s was0 ofga

between the wall and bulk fluid concentrations[2,4], all of whichare affected by changes on the tube side.

Runs 2 and 9–15 ofTable 2were conducted at a constant sol-vent/aqueous volumetric ratio of 1/1. (Again the row inTable 2that describes run 2 is repeated so that all results from thissequence can be viewed together.) The portion of the mass trans-fer resistance in the aqueous phase boundary layer decreasedwith increasing flow rate as expected. Still, the aqueous phaseremained the primary resistance even at the highest flow ratestudied. The mass transfer coefficient increased with increasingflow rate, a result that is attributable primarily to the correspond-ing reduction in the aqueous resistance. The yield decreasedwith increasing flow rate, even though the solvent/aqueous ratioremained unchanged, a consequence of the decrease in residencetime.

Runs 12–15 were performed at the same conditions as runs2 and 9–11, except CO2 flow was against and with the force ofgravity, respectively. All results were nearly identical for bothsets, indicating that buoyancy effects were insignificant. More-over, the highest Richardson number for these runs (as well asthe other runs described inTable 2) was only 0.2, providingfurther evidence that buoyancy was not important. This is theexpected conclusion for the small fiber diameter used here.

For these two sets as well as runs 2 and 5–8 (conductedat a constant aqueous phase velocity), the Richardson numberdecreased with increasing COphase velocity, an indication oft rest-i asedw stentw ofilesb res-i at thecR m-b r withd

eri shells sityw d con-c l keptc ec-t etricr tyi shofn btaint onn ers.

hoseo ).T n thea thered asedw n inr

ideG r

ide) mass transfer coefficient, because the pore coefficienot change. Even though the shell side flow rate is constanhell side mass transfer coefficient is influenced by changhe tube side flow rate because the fluids communicate thrhe membrane pores. That is, the shell side coefficient is reo the concentration gradient at the outer wall and the differ

ig. 4. Effect of CO2 (tube side) flow rate (i.e., Graetz number) on theide and overall mass transfer coefficients for simulated extraction of acrom aqueous solution into supercritical carbon dioxide. Fiber inner radiu.3 mm, flow was countercurrent, CO2 flow was in the direction of the forceravity, and the aqueous phase Graetz number was 23. See text andTable 2fordditional details.

senhd

e

2he increased masking of free by forced convection. Intengly, the Grashof and Rayleigh numbers generally increith increasing velocity. Although this does not seem consiith the decreasing Richardson numbers, concentration precame increasingly flat with decreasing flow rate (as the

dence time available for mass transfer increases), so thorresponding decrease in�ρ led to smaller values ofGr anda (Eqs.(1) and (2)). However, the square of the Reynolds nuer apparently decreased faster than the Grashof numbeecreasing flow rate, hence the increase inRi (i.e.,Gr/Re2).

The results given inTable 3were generated using a fibnside radius of 0.9 mm, outside radius of 1.2 mm, and aide equivalent radius of 2.6 mm, for which the packing denas again 0.21. As before, the temperature, pressure, feeentration, module length, and membrane porosity were alonstant at 32◦C, 135 bar, 5% w/w, 41.6 cm and 0.75, respively. All runs were performed at a solvent/aqueous volumatio of 1/1, with CO2 flow in the direction of the force of gravin runs 1–5 and against gravity in 6–10. Again the local Graumbers were averaged over the length of the module to o

he values shown inTable 3, and the Rayleigh and Richardsumbers were calculated from the average Grashof numb

Not surprisingly, the trends observed here are similar to tbtained with the smaller fibers (Table 2, runs 2 and 9–15hat is, the majority of the mass transfer resistance was oqueous side, and in general the portion of the resistanceecreased with increasing flow rate. Again the yield decreith increasing flow rate, a consequence of the reductio

esidence time.The variation in mass transfer coefficient with tube s

raetz number for all 10 runs is shown inFig. 5. Results fo


Fig. 5. Effect of CO2 (tube side) flow rate (i.e., Graetz number) on the overallmass transfer coefficient for simulated extraction of acetone from aqueous solu-tion into supercritical carbon dioxide, with a fiber inner radius of 0.3 or 0.9 mm,countercurrent flow, and CO2 flow either with or opposed to the force of gravity.See text andTables 2 and 3for additional details.

the smaller fibers discussed above (Table 2) are also shown forcomparison. All four curves are qualitatively similar, i.e., themass transfer coefficient is less sensitive to flow rate at low versus high Graetz numbers. Again the increase in mass transfcoefficient with increasingGz reflects the decrease in the majorresistance to mass transfer (i.e., the shell side, aqueous phaboundary layer) with increasing flow rate. Moreover, the shapeof the curves is consistent with our expectation, based on thclassical results for tube flow discussed previously[2,4]. Themass transfer coefficients for the smaller fiber are substantiallhigher than those for the larger one, because the wall is thinneand the boundary layers are also not as thick in the former.

As discussed above, buoyancy-induced flows were not important for the smaller fibers, and it is no surprise that the curves foflow with and opposing the force of gravity are nearly coincident.However, it is clear fromFig. 5 that buoyancy-induced flow issignificant with the larger fibers, particularly as the imposed flowrate decreases. Because the tube side concentration is highesthe wall, and the density increases with concentration under thconditions used here, the fluid density is also highest at the walThis means that the fluid near the wall tends to fall, which addsto the imposed velocity when the CO2 flow is in the directionof gravity (i.e.,aiding), and detracts from it when the imposedvelocity opposes gravity. This leads to a lower relative CO2phase resistance to mass transfer for aiding versus opposing flo(Table 3), and a corresponding shift in the relative pore and aqueo loca COfl sd ce od n.

The Grashof, Rayleigh and Richardson numbers given inTable 3are much larger than those obtained with the smallerfibers (Table 2), consistent with the observation fromFig. 5thatbuoyancy-induced flow is more important with the larger fibers.(Note that the values ofGr and Ra in Table 3are expressedin thousands.) The impact of fiber diameter is not surprisingbecause the Grashof and Rayleigh numbers are proportional tothe cube of the characteristic length, and the Richardson numbervaries linearly with length. Intuitively it seems reasonable that abuoyancy-induced flow is more likely to occur in a larger fluidspace, where the influence of the walls is reduced.

The Richardson numbers indicate that buoyancy-inducedflow was indeed important at the lower flow rates and insignifi-cant at the higher ones. Moreover, buoyancy-induced flow wasmore important for opposing versus aiding flow; a possibleexplanation is proposed below. As with the smaller fibers, in gen-eral the decrease in�ρ values caused the Grashof and Rayleighnumbers to increase with increasing flow rate, even thoughthe significance of buoyancy-induced flow clearly diminished(Fig. 5). Again the square of the Reynolds number increased evenfaster, so that the Richardson number decreased with increasingflow rate, consistent with the reduced effect of flow directionon the mass transfer coefficient, yield and distribution of masstransfer resistance.

A plot of the Richardson versus the CO2 phase Graetz numberis presented inFig. 6; again the results for the smaller fibers( wst r thel thel therew rfi

di erep orceo

FR lutioni mm,c ity.S

us phase resistances. The buoyancy-driven changes in velso lead to higher mass transfer coefficients and yields for2ow with gravity. As seen inFig. 5andTable 3, these differenceecrease with increasing flow rate, which is a consequenecreased masking of free convection by forced convectio

-er

se

e

yr

-r

t atel.

w-ity

f

Table 2) are included for comparison. The plot clearly shohat (a) the Richardson numbers are substantially higher foarger fibers, (b) the impact of buoyancy-induced flow inarger fibers decrease with increasing flow rate, and (c)as no significant effect of flow direction onRi for the smallebers.

Buoyancy effects in runs 1 and 6 ofTable 3are discussen more detail in the following paragraphs. These runs werformed with the solvent flow with and opposed to the ff gravity, respectively. Concentration profiles (Figs. 7 and 8)

ig. 6. Effect of CO2 (tube side) flow rate (i.e., Graetz number) on the CO2 phaseichardson number for simulated extraction of acetone from aqueous so

nto supercritical carbon dioxide, with a fiber inner radius of 0.3 or 0.9ountercurrent flow, and CO2 flow either with or opposed to the force of gravee text andTables 2 and 3for additional details.


Fig. 7. Concentration profiles for simulated acetone extraction into supercriticalCO2, with CO2 flowing with the force of gravity. The parameter is dimensionlesslengthz* . Dimensionless radii of 0, 1, 1.33 and 2.93 correspond to the tube center,the tube side membrane surface, the shell side membrane surface, and the shellside equivalent radius, respectively. See text and run 1 ofTable 3for details.

become increasingly steep with increasing length, except nearthe Co2 entrance (z* = 1). As with the smaller fibers (Fig. 2),the conditions and geometry employed here allow the aqueousphase boundary layer to just barely reach the shell side equivalentradius.

Because buoyancy-induced flow is driven by a change indensity (i.e., concentration), we expect the importance of buoy-ancy to follow the concentration gradient. That is, we expectbuoyancy-induced flow to be most prominent near the solvententrance, where the concentration profiles are most steep. Wefurther expect buoyancy to be more important for opposing thanfor aiding flow, because the profiles for the latter are less steep.The distortion of the profiles for opposing flow near the solvententrance (seeFig. 8) suggests that buoyancy-induced flow isindeed important there. For other indications of the significanceof buoyancy along the length of the module, we look at thedistortion of the axial velocity profile, the magnitude and direc-tion of the radial velocity, and the magnitude of the Richardsonnumber.

Tube side (CO2) axial velocity profiles for runs 1 and 6of Table 3are presented inFigs. 9–12. For clarity, the pro-files for each run are divided between two figures. Profilesfor 0≤ z* ≤ 0.75 are given inFigs. 9 and 11for runs 1 and

F riticalC en-s o thet surface,af

Fig. 9. Tube side (CO2) axial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing with the force of gravity. Profilesare shown for 0≤ z* ≤ 0.75, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 1 ofTable 3for details.

Fig. 10. Tube side (CO2) axial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing with the force of gravity. Profilesare shown for 0.85≤ z* ≤ 1.0, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 1 ofTable 3for details.

6, respectively; similarly, results for 0.85≤ z* ≤ 1.0 are shownin Figs. 10 and 12.

As explained previously, because buoyancy-induced flow isaiding for CO2 flow in the direction of the force of gravity, theaxial velocity should increase near the tube wall and decrease

Fig. 11. Tube side (CO2) axial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing against the force of gravity. Profilesare shown for 0≤ z* ≤ 0.75, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 6 ofTable 3for details.

ig. 8. Concentration profiles for simulated acetone extraction into supercO2, with CO2 flowing against the force of gravity. The parameter is dimionless lengthz* . Dimensionless radii of 0, 1, 1.33 and 2.93 correspond tube center, the tube side membrane surface, the shell side membranend the shell side equivalent radius, respectively. See text and run 6 ofTable 3

or details.


Fig. 12. Tube side (CO2) axial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing against the force of gravity. Profilesare shown for 0.85≤ z* ≤ 1.0, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 6 ofTable 3for details.

farther away. These deviations from the usual parabolic profileare clearly seen inFigs. 9 and 10. After moving slightly closerto the undistorted profile with increasing length near the outlet(z* = 0), in general the profiles become increasingly distortedwith increasingz* . There is even enough distortion to cause areversal of flow near the solvent inlet, as indicated by the neg-ative velocities there. The amount of distortion decreases closeto the CO2 inlet (z* = 1), and at the inlet the parabolic profileis recovered, as it must be to satisfy the boundary conditionthere. This behavior is consistent with the tube side concentra-tion profiles given inFig. 7. That is, after becoming slightly moreshallow with increasing length near the solvent outlet, thoseprofiles become increasingly steep with increasing length up toaboutz* = 0.98. At that point the profiles begin to decrease inslope, becoming flat at the CO2 inlet, where the concentrationis zero.

For CO2 flow opposed to the force of gravity, the axialvelocity profiles are distorted in the opposite direction. Thatis, velocity decreases near the tube wall and increases fartheraway, as shown inFigs. 11 and 12. Again the distortion gen-erally increases with increasingz* until the parabolic profile isrecovered at the CO2 inlet. As with aiding flow, this behavioris consistent with the concentration profiles shown inFig. 8.ComparingFigs. 11 and 12to Figs. 9 and 10, we see that thedistortion in the axial velocity profiles is greater for opposingversus aiding flow, suggesting that buoyancy-induced flow ism pro-fiv

zeror ag-n rfacea id inf omt wardt

a0 oreda t

Fig. 13. Tube side (CO2) radial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing with the force of gravity. Profilesare shown for 0≤ z* ≤ 0.75, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 1 ofTable 3for details.

Fig. 14. Tube side (CO2) radial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing with the force of gravity. Profilesare shown for 0.85≤ z* ≤ 1.0, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 1 ofTable 3for details.

the membrane surface (r* = 1), as required by the boundary con-ditions (see[2,4]). For aiding flow (Figs. 13 and 14), the radialvelocity nearr* = 0.5 is negative at the solvent exit, goes to zeroa small distance away, then increases a small amount in the

Fig. 15. Tube side (CO2) radial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing against the force of gravity. Profilesare shown for 0≤ z* ≤ 0.75, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 6 ofTable 3for details.

ore prominent in the former. Similarly, the concentrationles near the solvent entrance are steeper for opposing (Fig. 8)ersus aiding (Fig. 7) flow.

Buoyancy-induced flow is also characterized by non-adial velocity. As explained previously, for aiding flow the mitude of the axial velocity increases near the membrane sund decreases farther away. To prevent formation of a vo

ront of the decelerating fluid, we expect radial flow away frhe membrane surface. Conversely, we expect radial flow tohe surface when the imposed flow opposes gravity.

Tube side radial velocity profiles for runs 1 and 6 ofTable 3re given inFigs. 13–16; again, profiles for 0≤ z* ≤ 0.75 and.85≤ z* ≤ 1.0 are separated for clarity. Each profile is ancht a radial velocity of zero at the center of the tube (r* = 0) and a


Fig. 16. Tube side (CO2) radial velocity profiles for simulated acetone extractioninto supercritical CO2, with CO2 flowing against the force of gravity. Profilesare shown for 0.85≤ z* ≤ 1.0, where the parameterz* is dimensionless length.Dimensionless radii of 0 and 1 correspond to the tube center and the tube sidemembrane surface, respectively. See text and run 6 ofTable 3for details.

positive direction with increasing length untilz* is about 0.75.Afterward the magnitude decreases, then it increases quickly inthe negative direction, reaching a maximum of 13 atz* = 0.98.At that point the magnitude begins to decrease, until finally theboundary condition atz* = 1.0 forces the radial velocity to zero.Profiles for flow against gravity (Figs. 15 and 16) are similar,except the directions are opposite and the magnitudes are greater.These changes generally follow those in the tube side concen-tration gradients seen inFigs. 7 and 8. Interestingly, the maximaof the profiles for opposing flow move closer to the center of thetube with increasing length for 0.95≤ z* ≤ 0.99 (Fig. 16).

The changes in the magnitude and direction of the radiavelocity are shown more clearly inFig. 17, which indicates thehighest (or most negative) velocity for each of the profiles givenin Figs. 13–16as a function of dimensionless length. Again theradial velocity is highest (or most negative) near the solvent inletwhere buoyancy is most important. Moreover, the directions ofthe radial velocity in this high-buoyancy region are negative andpositive for aiding and opposing flow, respectively, to fill thevoid in front of the decelerating fluid as explained above.

While the dimensionless radial velocities shown inFigs. 13–17are significant, it is worth noting that they are stillconsiderably smaller than the axial velocities. The largest dimensionless radial velocity is 81, which occurs for opposing flow at

F ofiless

z* = 0.98 andr* = 0.33 (Figs. 16 and 17). The correspondingdimensional radial velocity is obtained after multiplying by thebulk axial velocity (0.1 cm/s) andRi /L (0.002)[2,4]; the result is0.02 cm/s. At the same point the dimensionless axial velocity is5; the dimensional value, obtained after multiplying by the bulkaxial velocity [2,4], is 0.5 cm/s, an order of magnitude higherthan the radial velocity. On the other hand, the characteristiclength in the radial direction is two orders of magnitude smallerthan the one in the axial direction, i.e., 0.09 cm (the fiber insideradius) versus 41.6 cm (the module length). This suggests thatradial flow may be more important than one might infer fromthe magnitudes of the radial and axial velocities alone.

In summary, the axial and radial velocity profiles for runs 1and 6 ofTable 3(Figs. 9–17) all suggest that buoyancy-inducedflow is most prominent near the solvent inlet (z* = 1), and thatbuoyancy is more important for opposing versus aiding flow.This is consistent with the values of the dimensionless num-bers that characterize buoyancy-induced flow.Fig. 18 showsthe local Richardson number as a function of dimensionlesslength for both aiding and opposing flow. TheRi values increasesteadily with increasing length until very close to the solventinlet, except for a small decrease nearz* = 0 andz* = 0.9. Thelatter may be attributable to the inherent instability of buoyancy-induced flow. The former corresponds to the slight decreasein concentration gradient with increasing length near the sol-v ar.A ntiret ob

n inF mucha witht eaterd desas

l-a plot

F onee orwd

ig. 17. Maximum (or most negative) dimensionless radial velocities for prhown inFigs. 13–16.

l

,

-

ent outlet (Figs. 7 and 8); the reason this occurs is not clet the solvent inlet the concentration is zero across the e

ube cross-section, soGr (and consequentlyRi) must go to zerecause there is no concentration gradient (see Eq.(1)).

The corresponding plot for opposing flow is also showig. 18. The magnitudes of the Richardson numbers are ass seven times higher for opposing flow, which is consistent

he higher magnitudes of the radial velocities and the gristortion of the axial velocity profiles. Although the magniture different, the general shapes of the two curves inFig. 18areimilar.

As explained above, Metais and Eckert[58] presented avaible heat transfer data on flow through vertical tubes as a

ig. 18. Tube side (CO2) local Richardson numbers for simulated acetxtraction into supercritical CO2, with CO2 flowing against (upper curve)ith (lower curve) the force of gravity. See text and runs 1 and 6 ofTable 3foretails.


of the Reynolds number versusGrPr(di/L), and identified sixflow regimes. (Presumably their plot is also applicable to masstransfer ifPr is replaced bySc.) Three of the five runs inTable 3conducted with CO2 flow in the direction of the force of gravity(runs 3–5) fell clearly into the forced laminar regime. Run 2,performed at the second lowest fluid velocity, was on the bor-der between forced and mixed laminar. Only run 1, conductedat the lowest velocity studied, was plainly in the mixed lam-inar regime. On the other hand, three of the five runs carriedout with the solvent flow opposed to the force of gravity (runs6–8) were characterized as mixed laminar; only the runs con-ducted at the two highest velocities (runs 9 and 10) were in theforced laminar regime. Consistent with the above discussion,these results indicate that the importance of buoyancy-inducedflow decreased with increasing fluid velocity, and that buoyancyhad a greater impact with opposing versus aiding flow. However,inferences from the plot of Metais and Eckert[58] must be madewith caution. That is, the data they used had been obtained ateither constant wall temperature or uniform heat flux, and thecorresponding boundary conditions for mass transfer were notsatisfied in the extractions described inTable 3. Fortunately,scrutiny of the model results suggests that they were sufficientlyclose to the uniform wall flux condition to render the aboveinferences valid.

In conclusion, unlike the smaller fibers discussed above, theeffects of buoyancy with the larger fibers are significant. Thosee omt rtiono bersF t thh thei wheb lvene ondi , thee hapb e form hterfl

restf actoi comp wita herc oy-a nsfi g flo[

t highe liversa overo sameo rate.A pre-f een

mass transfer coefficient and yield. Such a study would requirefurther examination of the effects of solvent/feed ratio, fiber andmodule dimensions, membrane properties, and fluid bulk veloc-ities, as well as knowledge of the capital and operating costs andproduct value.

4. Extraction using membrane versus traditionalcontactors

A number of investigators have reported on extraction ofvarious solutes from water into dense CO2 using traditional con-tacting equipment. To assess the value of membrane contactorsas an alternative technology, membrane contactor performancefor the same extractions was modeled, and the results were com-pared to the published data. The study looked at extraction ofethanol and isopropanol because much of the available datawere obtained with these two solutes. The simulated module,described inTable 4, was similar to the Liqui-Cel® Extra-Flow(2.5× 8) module offered by Celgard LLC. That product wasemulated because it is currently the most widely used commer-cially available membrane contactor, with a design that has beenoptimized for a variety of applications. The central baffle usedin the Celgard module was not considered in the simulations, sothat parallel flow could be assumed.

TM em-b

FFSLVPPTNF

TC branec

Cn

7 Packed, Raschig rings 2.5 122 0.628 Packed, Sulzer EX 2.5 400 2.09 Spray 9.9 168 13

10 Sieve tray 9.9 168 1311 Packed, Raschig rings 9.9 168 1312 Packed, IMTP 9.9 168 13

a Comparison is given inTable 6.

ffects include distortion of the axial velocity profiles frhe usual parabolic shape, non-zero radial velocities, distof the concentration profiles and higher Richardson numor the system studied here, buoyancy was insignificant aighest solvent flow rates (i.e., Graetz numbers) tested,

ncreased with decreasing flow rate as expected. For casesuoyancy was important, the impact was small near the soxit, then increased steadily with increasing length, corresp

ng to the increase in concentration gradient. Moreoverffects were greater for opposing versus aiding flow, perecause the heavier fluid opposed the imposed flow in ther, but in aiding flow the forced flow was opposed by the lig

uid.While these results are intellectually of considerable inte

rom a practical point of view the important issue is the impf buoyancy on the mass transfer coefficient.Table 3andFig. 8

ndicate that the effect can be appreciable. For example,aring runs 1 and 6, the mass transfer coefficient obtainediding flow was 33% higher than with opposing flow, all otonditions being identical. As mentioned above under “Buncy Effects,” others have also observed improved mass tra

n dense gas systems operated in aiding versus opposin50,51].

For the extraction problems like the one considered inTable 3,he preferred set of operating conditions is the one with thest mass transfer coefficient and throughput rate that still den acceptable yield. Clearly aiding (runs 1–5) is preferredpposing (runs 6–10) flow, because the former offers ther higher mass transfer coefficient and yield at a given flown optimization study would be needed to determine the

erred tradeoff between throughput rate and yield, or betw

.enret-

s-

,

-h

erw

-

able 4odule details used in the comparison of performance of traditional to mrane contactorsa

iber i.d. (cm) 0.024iber o.d. (cm) 0.030hell diameter (cm) 6.3ength (cm) 15.6olume (l) 0.49acking density 0.25orosity 0.4ortuosity 2.5umber of fibers 10812low pattern Parallel (seeFig. 1)

a Comparison is given inTable 6.

able 5olumns used in the comparison of performance of traditional to memontactorsa

olumnumber

Type Diameter(cm)

Active length(cm)

Volume (l)

1 Packed, Sulzer BX64 5.4 140 3.22 Spray 2.5 51 0.253 Spray 2.5 76 0.374 Sieve tray 2.5 122 0.375 Spray 2.3 87 0.356 Spray 2.5 122 0.62

A.G

abelman,S.-T.H

wang

/J.ofSupercriticalFluids

37(2006)

157–172169

Table 6Comparison of traditional to membrane contactors for dense CO2 extraction of isopropanol or ethanol from water

Solute Temperature (◦C) Pressure(MPa)

Experimental results for traditional contactor Results for simulated membrane contactora

Columnnumberb

Velocity (cm/s) HETSc (cm) Aqueous flowrate (cm3/s)

Reference Velocity (cm/s) HETSc,d (cm) Aqueous flowrate (cm3/s)

Solute mass balanceclosuree (%)

Aqueous CO2 Aqueous CO2

EtOH 40 10.0 1f 0.049 0.62 55 1.1 [39] 0.22 2.8 6 1.1 101EtOH 40 10.0 1g 0.087 0.66 83 2.0 [39] 0.41 3.1 8 2.0 100EtOH 35 10.3 2 0.048 1.0 18 0.24 [41] 0.5 10.4 18 2.4 100IPA 40 10.3 3 0.048 0.44 35 0.24 [41] 0.5 4.6 9 2.4 102IPA 40 10.3 4 0.048 0.40 19 0.24 [41] 0.5 4.2 9 2.4 102IPA 25 8.3 4 0.048 0.41 19 0.24 [41,64] 0.41 3.5 9 2.0 101EtOH 35 10.3 4 0.047 1.4 15 0.23 [64] 0.50 14.5 21 2.4 100EtOH 35 10.3 5 0.045 0.49 49 0.18 [40] 0.37 4.0 10 1.8 100IPA 35 10.3 5 0.045 0.45 36 0.18 [40] 0.37 3.7 7 1.8 103IPA 40 10.3 6 0.036 0.12 16 0.18 [43] 0.37 1.2 4 1.8 102IPA 40 10.3 7 0.019 0.26 11 0.10 [43] 0.20 2.7 4 1.0 103EtOH 60 10.0 8 0.009 1.7 100 0.04 [44] 0.09 17.1 10 0.4 102IPA 24 8.2 9 0.048 1.6 80 3.7 [63] 0.76 25.2 26 3.7 101IPA 40 10.3 9 0.048 2.5 88 3.7 [63] 0.76 39.4 24 3.7 102IPA 24 8.2 10 0.048 0.6 31 3.7 [63] 0.76 9.5 19 3.7 101IPA 40 10.3 10 0.048 0.45 39 3.7 [63] 0.76 7.1 14 3.7 101IPA 24 8.2 11 0.048 0.37 42 3.7 [63] 0.76 5.8 15 3.7 101IPA 40 10.3 11 0.048 0.65 44 3.7 [63] 0.76 10.2 16 3.7 102IPA 24 8.2 12 0.048 0.44 50 3.7 [63] 0.76 6.9 16 3.7 101IPA 40 10.3 12 0.048 0.65 61 3.7 [63] 0.76 10.2 16 3.7 102

a SeeTable 4for description of contactor. All runs were countercurrent. Orientation was vertical, with the aqueous fluid flowing upward through the tubes. Partition coefficients used in the simulations wereestimated from the data of Chun et al.[40], Lahiere[64], or Budich and Brunner[44].

b FromTable 5.c Height equivalent to a theoretical stage.d Calculated as described in[4]. The mass transfer coefficient used in this calculation was determined as described in[2], using the aqueous phase log mean driving force.e Calculated as described in[4]. For all simulations the overall mass balance (see[4]) closed to 100%.f Operated in bubble flow.g Operated in trickling flow.


The traditional columns used by the various researchers aredescribed inTable 5, and the results of the study are presented inTable 6. The performance indicator was the height of an equiv-alent theoretical stage (HETS). For the extractions of Seibertand Moosberg[63] and Bernad et al.[39], the conditions usedwith the conventional equipment that gave the lowest HETSvalues were used in the simulations. However, all other dataused in the study were obtained at throughput rates that werefar below the recommended operating range for the Liqui-Cel®

module (seewww.liqui-cel.com). For this reason, for each con-ventional contactor run the aqueous fluid flow rate used to obtainthe lowest HETS value was increased by a factor of 10 for thesimulation, then the CO2 velocity was set by maintaining thesame solvent/feed ratio. Membrane contactor HETS values werecalculated as explained in Gabelman’s dissertation[4]. For allsimulations the overall and solute mass balances closed to 100and 100–103%, respectively.

The HETS obtained with the membrane was the same as orlower than for the traditional contactor in all but one of the casesstudied. In some instances the value for the membrane contactorwas an order of magnitude lower. For example, Bernad et al.[39] obtained HETS values of 55 or 83 cm upon extraction ofethanol in a packed column operated in bubble or trickling flow,respectively. The corresponding values for the simulated mem-brane contactor were only six and eight cm. Performance wasalso considerably better for ethanol extraction with the mem-bH menw putr

L them arly,t la fact actorv ands r thes para -folh thesr ranec

ers edc thec meno ETSv dingr

ntact werH runt eratea nsfed ione

in the Introduction, these results make a strong case for the ben-efits of membrane contactors over conventional mass transferequipment for supercritical fluid extraction.

5. Conclusions

A theoretical study of acetone extraction from aqueous solu-tion into supercritical CO2 was performed, using countercurrentflow with CO2 flowing through the tubes, with or against theforce of gravity. Fibers with inside radii of 0.3 and 0.9 mm wereincluded in the study. Buoyancy-induced flow was important forthe large but not the small fibers, consistent with our expectationthat such flow is more difficult to achieve when the character-istic length is small. Free convection in the large fibers wascharacterized by velocity profiles that were distorted from theusual parabolic shape, non-zero radial velocities, distortion ofthe concentration profiles, and Richardson numbers that weresubstantially greater than one. These effects were more pro-nounced for opposing versuss aiding flow. Buoyancy was mostimportant near the solvent inlet, where the concentration gra-dients were highest. The importance of buoyancy-induced flowdecreased with increasing imposed fluid velocity, as forced con-vection masked the effects of free convection. For the range ofconditions studied, the mass transfer coefficient obtained withaiding flow was as much as 33% higher than with opposing flow.

Ethanol and isopropanol extractions performed by othersu imu-l werec ctors.TF tralb ctor.I a sig-n thec

branec nsferd ighlye e ofe tech-n sucha entedh ancy-i hesee ore-o nt ino non-a adingmc ientsa ancy-i

A

ngr o have

rane contactor versus a column packed with Sulzer EX[44]; theETS values were 100 and 10 cm. In this case the improveas even more striking in light of the 10-fold higher through

ate used in the membrane contactor simulation.For the three isopropanol extractions of Lahiere[64] and

ahiere and Fair[41], the corresponding HETS values forembrane contactor were lower by a factor of 2–4. Simil

he HETS values obtained by Chun et al.[40] for isopropanond ethanol extraction using a spray column each was a

or of five higher than the corresponding membrane contesult. Lahiere and Fair[41] and Lahiere[64] reported HETSalues of 18 and 15 cm for ethanol extraction using sprayieve tray columns, respectively; corresponding results foimulated membrane contactor (18 and 21 cm) did not coms favorably as others reported here. However, given the 10igher throughput rate used in these simulations, both ofesults still point to the superior performance of the membontactor.

Seibert and Moosberg[63] extracted isopropanol into eithupercritical or liquid CO2 using a spray, sieve tray or packolumn. Their equipment was considerably larger thanolumns used by others cited in this study, so no adjustf the throughput rate was needed for the simulations. Halues were all a factor of 2–4 higher than the corresponesults obtained with the membrane contactor.

In summary, in most cases the simulated membrane coor offered a significantly (in some cases, substantially) loETS than the corresponding traditional column. For some

his occurred even when the membrane contactor was opt 10 times the throughput rate of the traditional mass traevice. When considered along with the advantages ment

t

-r

ede

t

-

sd

rd

sing spray, sieve tray or packed columns were run on a sated membrane contactor, and the resulting HETS valuesompared to the reported values for the conventional contahe simulated contactor was similar to the Liqui-Cel® Extra-low module offered by Celgard LLC (but without the cenaffle), the most widely used commercially available conta

n most cases the simulated membrane contactor offeredificantly (in some cases, substantially) lower HETS thanorresponding traditional column.

These results strongly support the conclusion that memontactors are more effective than conventional mass traevices for dense gas extraction of aqueous feeds. The hfficient mass transfer (i.e., low HETS), along with absencmulsions, foaming, flooding and unloading, renders theology an attractive alternative to traditional approachess packed, spray or sieve tray columns. The work presere demonstrates that engineers should consider buoy

nduced flow when designing membrane contactors for txtractions, because such flow can indeed be significant. Mver, buoyancy-induced flow may be even more importather applications of interest, e.g., dense gas extraction ofqueous feeds such as vegetable oils. There the solvent loay be much higher than with the water/acetone/CO2 system

onsidered here, possibly leading to higher density gradnd a corresponding increase in the significance of buoy

nduced flow.

cknowledgments

Professor Bill Krantz (University of Cincinnati) is a leadiesearcher in membrane science, and we were fortunate t

http://www.liqui-cel.com/


the benefit of his guidance. Professor Glenn Lipscomb (Uni-versity of Toledo) kindly shared his expertise in the modelingof hollow fiber membrane contactors. The advice of ProfessorGranville Sewell (University of Texas at El Paso) on the use ofthe modeling software employed in our work was instrumental.Dr. Robert Eilerman (Givaudan Flavors) generously providedthe time and resources necessary to carry out this research.

References

[1] Z. Qi, E.L. Cussler, Microporous hollow fibers for gas absorption. II.Mass transfer across the membrane, J. Membr. Sci. 23 (1985) 333–345.

[2] A. Gabelman, S.-T. Hwang, W.B. Krantz, Dense gas extraction usinga hollow fiber membrane contactor: experimental results versus modelpredictions, J. Membr. Sci. 257 (2005) 11–36.

[3] A. Gabelman, S.-T. Hwang, Experimental results versus model predic-tions for dense gas extraction using a hollow fiber membrane contactor,J. Supercrit. Fluids 35 (2005) 26–39.

[4] A. Gabelman, Mass Transfer in Dense Gas Extraction Using a HollowFiber Membrane Contactor, Ph.D. Dissertation, University of Cincinnati,2003.

[5] E.L. Cussler, Hollow fiber contactors, in: J.G. Crespo, K.W. Boddeker(Eds.), Membrane Processes in Separation and Purification, Kluwer Aca-demic Publishers, Netherlands, 1994, pp. 375–394.

[6] A. Gabelman, S.-T. Hwang, Hollow fiber membrane contactors, J.Membr. Sci. 159 (1999) 61–106.

[7] R. Prasad, K.K. Sirkar, Membrane-based solvent extraction, in: W.S.W.Ho, K.K. Sirkar (Eds.), Membrane Handbook, Chapman & Hall, New

: R.Dciples

irkarpp.

[ ationstion6.

[ ents

[ Ind.,

[ sen-85)

[ er inembr

[ , S.ducts003)

[ olute5,49

[ tion:ticalngi-

[ pli-withate-998.

[ crit-ryluids:

Chemistry and Materials, International Society for the Advancement ofSupercritical Fluids, Nottingham, United Kingdom, 10–13 April, 1999.

[20] M.J. Yang, J. Pawliszyn, Supercritical fluid extraction of trace organiccompounds from aqueous media using a hollow fiber membrane module,presented at the American Chemical Society National Meeting, Chicago,22–27 August, 1993.

[21] G. Brunner, Gas Extraction, Springer, New York, 1994.[22] P.G. Debenedetti, R.C. Reid, Diffusion and mass transfer in supercritical

fluids, AIChE J. 32 (12) (1986) 2034–2045.[23] B.S. Shiralkar, P. Griffith, Deterioration in heat transfer to fluids at

supercritical pressure and high heat fluxes, J. Heat Transfer 91 (1969)27–36.

[24] L. Graetz,Uber die warmeleitungsfahigkeit von flussigkeiten, Ann. Phys.Chem. 18 (1883) 79–94.

[25] L. Graetz,Uber die warmeleitungsfahigkeit von flussigkeiten, Ann. Phys.Chem. 25 (1885) 337–357.

[26] M.A. Leveque, Les lois de la transmission de chaleur par convection,Ann. Mines 13 (1928) 201–299.

[27] V. Chen, M. Hlavacek, Application of Voronoi tessellation for model-ing randomly packed hollow-fiber bundles, AIChE J. 40 (1994) 606–612.

[28] M.J. Costello, A.G. Fane, P.A. Hogan, R.W. Schofield, The effect ofshell side hydrodynamics on the performance of axial flow hollow fibremodules, J. Membr. Sci. 80 (1993) 1–11.

[29] J. Lemanski, G.G. Lipscomb, Effect of shell-side flows on hollow-fiber membrane device performance, AIChE J. 41 (10) (1995) 2322–2326.

[30] J. Lemanski, G.G. Lipscomb, Effect of shell-side flows on the per-formance of hollow-fiber gas separation modules, J. Membr. Sci. 195(2002) 215–228.

[31] J.D. Rogers, R.L. Long Jr., Modeling hollow fiber membrane contac-for

.[ . Sci.

[ rans-t. Sci.

[ omly

[ E J.

[ od-ch to

[ low

[ ingribed

[ solu-tions

[ in ahem.

[ ntac-987)

[ tray,sis, in:luids,

[ umns987)

[ om

York, 1992.[8] B.W. Reed, M.J. Semmens, E.L. Cussler, Membrane contractors, in

Nobel, S.A. Stern (Eds.), Membrane Separations Technology. Prinand Applications, Elsevier, Amsterdam, 1995, pp. 467–497.

[9] K.K. Sirkar, Other new membrane processes, in: W.S.W. Ho, K.K. S(Eds.), Membrane Handbook, Chapman & Hall, New York, 1992,904–909.

10] K.K. Sirkar, Membrane separations: newer concepts and applicfor the food industry, in: R.K. Singh, S.S.H. Rizvi (Eds.), BioseparaProcesses in Foods, Marcel Dekker, New York, 1995, pp. 353–35

11] K.K. Sirkar, Membrane separation technologies: current developmChem. Eng. Comm. 157 (1997) 145–184.

12] H. Brogle, CO2 as a solvent: its properties and applications, Chem.19 February 1982.

13] E. Stahl, D. Gerard, Solubility behaviour and fractionation of estial oils in dense carbon dioxide, Perfum. Flavor. 10 (April/May 1929–36.

14] G.D. Bothun, B.L. Knutson, H.J. Strobel, S.E. Nokes, Mass transfhollow fiber contactor extraction using compressed solvents, J. MSci. 227 (2003) 183–196.

15] G.D. Bothun, B.L. Knutson, H.J. Strobel, S.E. Nokes, E.A. BrignoleDıaz, Compressed solvents for the extraction of fermentation prowithin a hollow fiber membrane contactor, J. Supercrit. Fluids 25 (2119–134.

16] J.R. Robinson, M.J. Sims, Method and system for extracting a sfrom a fluid using dense gas and a porous membrane, US Patent884, 13 February 1996.

17] M.J. Sims, J.R. Robinson, A.J. Dennis, Porocritical fluid extraca new technique for continuous extraction of liquids with near-crifluids, in: P.R. von Rohr, C. Trepp (Eds.), High Pressure Chemical Eneering, Elsevier, Amsterdam, 1996, pp. 205–209.

18] M. Sims, W. McGovern, J. Robinson, Porocritical fluid extraction apcation: continuous pilot extraction of natural products from liquidsnear-critical fluids, in: ISASF 5th Meeting on Supercritical Fluids, Mrials and Natural Processing Proceedings, Nice, France, March, 1

19] R.W. Towsley, J. Turpin, M. Sims, J. Robinson, W. McGovern, Poroical fluid extraction using CO2 for industrial organic solvent recoveand recycle, in: Proceedings of the 6th Meeting on Supercritical F

.

,

.

0,

tors using film theory, Voronoi tessellations, and facilitation factorssystems with interface reactions, J. Membr. Sci. 134 (1997) 1–17

32] A.F. Seibert, J.R. Fair, Scale-up of hollow fiber extractors, SeparatTechnol. 32 (1–4) (1997) 573–583.

33] A.F. Seibert, X. Py, M. Mshewa, J.R. Fair, Hydraulics and mass tfer efficiency of a commercial-scale membrane extractor, SeparaTechnol. 28 (1–3) (1993) 343–359.

34] J. Wu, V. Chen, Shell-side mass transfer performance of randpacked hollow fiber modules, J. Membr. Sci. 172 (2000) 59.

35] M.-C. Yang, E.L. Cussler, Designing hollow-fiber contactors, AICh32 (11) (1986) 1910–1916.

36] F. Lipnizki, R. Field, Mass transfer performance for hollow fibre mules with shell-side axial feed flow: using an engineering approadevelop a framework, J. Membr. Sci. 193 (2001) 195.

37] J. Zheng, Y. Xu, Z. Xu, Flow distribution in a randomly packed holfiber membrane module, J. Membr. Sci. 211 (2003) 263–269.

38] Y. Wang, F. Chen, Y. Wang, G. Luo, Y. Dai, Effect of random packon shell-side flow and mass transfer in hollow fiber module descby normal distribution function, J. Membr. Sci. 216 (2003) 81–93.

39] L. Bernad, A. Keller, D. Barth, Separation of ethanol from aqueoustions by supercritical carbon dioxide – comparison between simulaand experiments, J. Supercrit. Fluids 6 (1993) 9–14.

40] B.-S. Chun, H.-G. Lee, J.-K. Cheon, G. Wilkinson, Mass transfercountercurrent spray column at supercritical conditions, Korean J. CEng. 13 (1996) 234–241.

41] R.J. Lahiere, J.R. Fair, Mass-transfer efficiencies of column cotors in supercritical extraction service, Ind. Eng. Chem. Res. 26 (12086–2092.

42] A.F. Seibert, D.G. Moosberg, J.L. Bravo, K.P. Johnston, Spray, sieveand packed high pressure extraction columns – design and analyProceedings of the 1st International Symposium on Supercritical FNice, France, October, 1988, pp. 561–570.

43] P.J. Rathkamp, J.L. Bravo, J.R. Fair, Evaluation of packed colin supercritical extraction processes, Solvent Extr. Ion Exc. 5 (1367–391.

44] M. Budich, G. Brunner, Supercritical fluid extraction of ethanol fraqueous solutions, J. Supercrit. Fluids 25 (2003) 45–55.


[45] C.H. Lee, G.D. Holder, Use of supercritical fluid chromatography forobtaining mass transfer coefficients in fluid-solid systems at supercriticalconditions, Ind. Eng. Chem. Res. 34 (1995) 906–914.

[46] G.-B. Lim, G.D. Holder, Y.T. Shah, Mass transfer in gas-solid systemsat supercritical conditions, J. Supercrit. Fluids 3 (1990) 186–197.

[47] G.-B. Lim, H.Y. Shin, M.J. Noh, K.P. Yoo, H. Lee, Subcritical tosupercritical mass transfer in gas–solid system, in: Proceedings of theInternational Symposium on Supercritical Fluids, Strasbourg, France 2,October, 1994, pp. 141–146.

[48] G. Knaff, E.U. Schlunder, Mass transfer for dissolving solids in super-critical carbon dioxide. Part I: Resistance of the boundary layer, Chem.Eng. Processes 21 (1987) 151.

[49] J. Puiggene, M.A. Larrayoz, F. Recasens, Free liquid-to-supercriticalfluid mass transfer in packed beds, Chem. Eng. Sci. 52 (1997) 195–212.

[50] H. Sovova, J. Kucera, J. Jez, Rate of the vegetable oil extraction withsupercritical CO2 – II. Extraction of grape oil, Chem. Eng. Sci. 49(1994) 415–420.

[51] F. Stuber, A.M. Vasquez, M.A. Larrayoz, F. Recasens, Supercriti-cal fluid extraction of packed beds: external mass transfer in upflowand downflow operation, Ind. Eng. Chem. Res. 35 (1996) 3618–3628.

[52] W.M. Deen, Analysis of Transport Phenomena, Oxford University Press,New York, 1998.

[53] L.E. Sissom, D.R. Pitts, Elements of Transport Phenomena, McGraw-Hill, New York, 1972.

[54] S.W. Churchill, A comprehensive correlating equation for laminar, assist-ing, forced and free convection, AIChE J. 23 (1977) 10–16.

[55] L.C. Thomas, Heat Transfer, second ed., Capstone Publishing Corpora-tion, Tulsa, OK, 2000.

[56] E.L. Cussler, Diffusion. Mass Transfer in Fluid Systems, second ed.,Cambridge University Press, New York, 1997.

[57] W.J. Marner, H.K. McMillan, Combined free and forced laminar convec-tion in a vertical tube with constant wall temperature, J. Heat Transfer92 (1970) 559.

[58] B. Metais, E.R.G. Eckert, Forced, mixed and free convection regimes,J. Heat Transfer 86 (1964) 295–296.

[59] B. Gebhart, Y. Jaluria, R.L. Mahajan, B. Sammamkia, Buoyancy-InducedFlows and Transport, Springer-Verlag, Berlin, 1988.

[60] C.K. Brown, W.H. Gauvin, Combined free and forced convection, I, II,Can. J. Chem. Eng. 43 (1965) 306–313.

[61] T.H. Kuehn, R.J. Goldstein, An experimental study of natural convectionheat transfer in concentric and eccentric horizontal cylindrical annuli, Int.J. Heat Mass Transfer 19 (1976) 1127.

[62] T.H. Kuehn, R.J. Goldstein, Correlating equations for natural convectionheat transfer between horizontal circular cylinders, J. Heat Transfer 100(1978) 635.

[63] A.F. Seibert, D.G. Moosberg, Performance of spray, sieve tray, andpacked contactors for high pressure extraction, Separat. Sci. Technol.23 (1988) 2049–2063.

[64] R.J. Lahiere, Mass Transfer and Hydraulic Characteristics of a Supercrit-ical Fluid Sieve Tray Extractor, Ph.D. Dissertation, University of Texasat Austin, 1986.

[65] E.A. Brignole, PLAPIQUI/UNS-CONICET, Bahıa Blanca, Argentina,personal communication, 6 June 2002.

[66] H.P. Gros, S.B. Bottini, E.A. Brignole, High pressure phase equilibriummodeling of mixtures containing associating compounds and gases, FluidPhase Equilib. 139 (1997) 75.

[67] K.L. Wang, E.L. Cussler, Baffled membrane modules made with hollowfiber fabric, J. Membr. Sci. 85 (1993) 265–278.

Documents

A theoretical study of dense gas extraction using a hollow fiber membrane contactor