Selective CO2 Separation from CO2−N2 Mixtures by Immobilized

(PVDF) substrate was experimentally studied for use as a venting membrane in space-walk applications. The effects of Na2CO3 concentration, CO2 partial...
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Ind. Eng. Chem. Res. 1999, 38, 3489-3498

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Selective CO2 Separation from CO2-N2 Mixtures by Immobilized Carbonate-Glycerol Membranes H. Chen, A. S. Kovvali, S. Majumdar, and K. K. Sirkar* Department of Chemical Engineering, Chemistry and Environmental Science, New Jersey Institute of Technology, Newark, New Jersey 07102

Separation of carbon dioxide from a humid mixture of CO2-N2 through membranes containing immobilized solutions of Na2CO3-glycerol in porous and hydrophilic poly(vinylidene fluoride) (PVDF) substrate was experimentally studied for use as a venting membrane in space-walk applications. The effects of Na2CO3 concentration, CO2 partial pressure, and feed stream relative humidity (RH) were investigated. The carbonate concentration was in the range of 0-4.0 mol/ dm3. The feed gas RH range was 49-100%; the sweep gas was dry helium. CO2 partial pressure (pCO2,f) range was 0.007-0.77 atm. Addition of Na2CO3 increased the CO2 permeability drastically at lower carbonate concentrations; at higher Na2CO3 concentrations, this permeability increase is partly compromised by increased solution viscosity and salting-out effect. N2 permeability coefficient decreased with an increase in Na2CO3 concentration. Very high CO2/N2 selectivities were observed at high Na2CO3 concentrations. Higher CO2/N2 selectivities were observed at lower CO2 partial pressure differentials. Steady-state water content in the hygroscopic immobilized liquid membrane (ILM) increases with an increase in feed stream RH. The water content in the ILM considerably affects its viscosity and the effective concentration of the carriers in the ILM; those factors determine the permeation performances of the ILM. Generally, lower permeances and greater CO2/N2 selectivity values were observed at lower feed stream RHs. When the feed RH ) 50.7%, pCO2,f ) 0.007 atm and the Na2CO3 concentration was 1.0 mol/dm3; the separation factor R(CO2/N2) observed was 3440. Prolonged runs lasting 14 days showed that the ILM permeation performances were quite stable. The ILMs were also found to be stable when challenged with feed streams of very low RHs. 1. Introduction Acid gases present in numerous industrial waste gas streams have caused increasing global environmental concerns. To alleviate the pollution problems, acid gases in such streams need to be removed. The increased demand for acid gas treating and the cost of purification by conventional processes suggest a need for energyefficient and selective gas-treating technology. Recent application of membrane separation of CO2 has been attracting attention due to its inherent simplicity, ease of control, compact modular nature, and great potential for lower cost and energy efficiency compared to traditional separation methods. These attractive features have stimulated significant research in gas separation using polymeric as well as liquid membranes. So far, commercially successful gas separation membranes are mainly thin nonporous polymeric membranes. In polymeric membrane-based gas permeation, separation of a gas mixture is achieved due to the differences in permeation rates through the thin separating layer. Although many polymeric membranes have been developed for CO2 separation, the separation factors of CO2 over N2 or CH4 are rather low.1 To overcome the problem of low CO2/N2 selectivity, use of facilitated transport membranes has been proposed.2,3 In facilitated transport membranes, the transport of CO2 is augmented by reversible reactions between CO2 and certain carriers in the membrane. Inert gases such as N2 and CH4 do not react with the carriers and can only * Corresponding author. Telephone: +1-973-596-8447. Fax: +1-973-642-4854. E-mail: [email protected].

permeate via the solution-diffusion mechanism. Therefore, selectivities significantly higher than those achievable with polymeric membranes can be expected. Facilitated transport of CO2 has been known for many years and widely researched;4,5 extensive mathematical models have also been developed.6-9 Facilitated transport membranes for CO2 separation reported in the literature include immobilized liquid membrane (ILM), solvent-swollen polymer membrane, and fixed carrier membranes.5 The ILM is generally considered to be the least stable configuration, and increasing its stability has been an important research topic. In ILMs, the liquid solution is physically trapped in but not chemically bonded to the support matrix. The low stability can be a result of the evaporation of the liquids into the gas phases during operation. To alleviate the problem of ILM drying out when aqueous solutions are used as the ILM fluid, the feed and sweep gas streams are always humidified. Another interesting alternative is to use low-volatility and hygroscopic liquids such as poly(ethylene glycol) (PEG)10-12 as the major component in the ILM fluid. Facilitated transport of CO2 has been investigated using various carrier species, e.g., monoethanolamine (MEA),12 diethanolamine (DEA),12-14 and ethylenediamine (EDA).15 Also, carbonate/bicarbonate aqueous solutions2,6 have shown quite high selectivities for CO2 separations. LeBlanc et al.3 and, later, Way et al.16 studied CO2 separation performance of ion-exchange membranes containing organic amine counterions. These membranes have the advantage that the carrier retained by strong electrostatic forces cannot easily be

10.1021/ie990045c CCC: $18.00 © 1999 American Chemical Society Published on Web 07/31/1999

3490 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999

forced out of the support matrix. A new kind of fixed carrier type membrane is based on the polyelectrolyte, poly((vinylbenzyl)trimethylammonium fluoride) (PVBTAF).17 The permselectivity of the PVBTAF membrane is dependent on the hydration state of the membrane and is optimal when the feed stream relative humidity is in the range 0.25-0.50. Recently, Ho18 disclosed another kind of facilitated transport membrane based on a hydrophilic polymer and amino acid salts. Like the PVBTAF membranes, this membrane preferentially permeates CO2 and is potentially useful for CO2/H2 separation. In ILMs, the increased CO2 transport rate and CO2/ N2 selectivity are derived from the reversible reactions between CO2 and the carrier species. Theoretically, to observe greater extents of facilitation, higher carrier concentrations in ILM and faster CO2-carrier reaction kinetics as well as appropriate reaction reversibility are desired.2,6,7 Also, to further increase CO2 permeance, thinner ILMs are preferred, although decreasing ILM thickness may undermine its stability and decrease CO2/ N2 selectivity. To increase CO2/N2 selectivity, N2 permeance through the ILM should be as low as possible. Reduced N2 permeances can be achieved by decreasing N2 solubility and/or diffusion coefficient in the ILM fluid, which also helps to promote the relative contribution of reaction-augmented transport of CO2 and increase the CO2/N2 selectivity. In this work, glycerol is used as the ILM liquid and Na2CO3 as the carrier. We focus on the expected high selectivity and much improved stability. The general objective is to experimentally investigate CO2 permeation characteristics through immobilized carbonate-glycerol membranes from humid CO2-N2 mixtures. The specific objective of the present work is to examine the possibility of using this ILM for CO2 separation from gas streams containing lower CO2 partial pressures, e.g., venting membranes for spacewalk applications where the breathing mixtures will always have a humidity between 30 and 70% and moisture recovery is not practiced. Detailed analysis and modeling of facilitated CO2 transport through aqueous ILMs containing NaHCO3 have been reported in the literature.6,7 In this work, the ILM fluid consists of glycerol, carbonate, and moisture (water) picked up from the feed stream. Dry helium is introduced as a sweep gas on the permeate side since it is more useful for simulating the space-walk situations where space vacuum will be applied to the permeate side. As a result, there is a gradient of moisture concentration along the membrane length as well as along the membrane thickness. These two gradients of water concentration introduce extraordinary variations in ILM viscosity, species diffusivity, and CO2, N2, and Na2CO3 solubilities along and across the membrane. Rigorous modeling of the facilitated CO2 transport for the present system requires information on the physicochemical data on viscosity and gas solubility for the carbonate-glycerol-water system. Since they are not readily available in the literature, the present work is confined mainly to experimental investigation. 2. Literature Review 2.1. Glycerol Membrane. Glycerol is a viscous liquid having an extremely low volatility and high hygroscopicity. It has much higher viscosity than PEG 400 at ambient temperatures (Table 1). While PEG 400 has been studied as an ILM liquid,10,11 use of glycerol as the

Table 1. Comparison of Physical Properties of Glycerol and PEG 400 at 20 °C

glycerol PEG 400

MW (g/mol)

density (g/cm3)

viscosity, cP

vapor pressure, mmHg

92.09 380-420

1.25 1.124

1412 19 100

7.15 × 10-5 22 -

Figure 1. Diffusion and reaction of CO2 across an immobilized liquid membrane of a carbonate-water mixture in glycerol.

liquid in the ILM has not been reported in open literature. Although the viscosity of pure glycerol is very high, the viscosity of its aqueous solution decreases rapidly with an increase of the water content. For example, at 20 °C, the viscosity of aqueous glycerol solution containing 30 wt % water is about 1.59% of that of pure glycerol.19 Since glycerol is very hygroscopic, it tends to absorb moisture from the surroundings. This property is useful for maintaining the water content in the ILM. Another attractive property of glycerol is that it is generally recognized as safe for living organisms.20 Therefore, compared with PEG or other amine-based ILMs, glycerol-based ILMs are environmentally friendly and can be used for CO2 removal from closed space for human activities. Moreover, salts such as carbonate/ bicarbonate are reasonably soluble in glycerol at room temperature (e.g., Na2CO3 has a solubility of 1.2 M in glycerol at 25 °C). The carbonate solubility in glycerol can however be enhanced by the absorbed moisture with which the salts can exist as ionized species. On the other hand, as the relative humidity decreases, the carbonate solubility is drastically reduced to the level of that in pure glycerol. Since gas diffusivity in a liquid is inversely related to the liquid viscosity,21 a high viscosity of glycerol could introduce both advantages and disadvantages as an ILM liquid. The advantage is that inert gases, such as nitrogen, can have quite low permeability through glycerol ILMs. This means that CO2/N2 selectivity can be quite high if CO2 transport is augmented by reversible reactions. On the other hand, a disadvantage of the high viscosity is that the transport rates of carriers for facilitated transport, such as CO32- and/or HCO3-, will also be retarded. As a result, lower permeability for CO2 through the ILM can be expected. This can be partly overcome by preparing ILMs with reduced thicknesses. 2.2. Description of the Facilitation Mechanism. Figure 1 depicts the transport of carbon dioxide. Carbon dioxide dissolves into the ILM liquid at the feed side boundary and reacts with carbonate ions in the presence of water. The flux of the solute carbon dioxide from the high to the low partial pressure side of the membrane is enhanced by the additional flux of the reaction products. At the low partial pressure side of the film, the reaction is reversed and carbon dioxide is released from the liquid where it is swept away by a receiving

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helium gas stream and the carrier species diffuses back to the high-pressure side of the membrane. To maintain zero current flow, the flux of bicarbonate must be twice the absolute value of the flux of carbonate. 2.3. CO2 and Carbonate Chemistry. The chemistry of the CO2-carbonate/bicarbonate system has been investigated and reviewed by many authors.2,4 The ratecontrolling reactions for the process are:

CO2 + H2O h H2CO3

(1)

OH- + CO2 h HCO3-

(2)

The following very fast reactions can be assumed to be at equilibrium: +

H +

CO32-

h

HCO3-

H2O h H+ + OH-

(3) (4)

The hydration reactions produce a bicarbonate ion concentration gradient which parallels that of the physically dissolved CO2. The presence of Na2CO3 leads to the appearance of carbonate ions which associate with H+ according to reaction 3 and diffuse counter to the bicarbonate ions. The overall reaction is thus written as

CO2 + H2O + CO32- h 2HCO3-

(5)

The CO32- generated at the lower pressure side of the membrane from the reverse reaction of eq 3 diffuses counter to the bicarbonate ions to satisfy the restriction of electroneutrality in the membrane. 3. Experimental Section 3.1. Materials. The liquid membrane was supported by flat sheets of hydrophilic poly(vinylidine fluoride) (PVDF) microporous membranes (Millipore, Bedford, MA) (thickness, ca. 100 µm; pore size, 0.1 µm; porosity, 0.7). Glycerol of 99% purity was purchased from Sigma (St. Louis, MO) and used without further purification. Sodium carbonate was obtained from Mallinckrodt Chemical Co. (St. Louis, MO). Na2CO3-glycerol solutions were prepared by dissolving the desired amount of Na2CO3 in known volumes of glycerol. Deionized water was obtained using a Barnstead E-Pure system (Model D4641, Dubuque, IA). All gas mixtures and pure gases used for the experiments were obtained from Matheson (East Rutherford, NJ). 3.2. Preparation of ILMs. The most commonly used method for preparing immobilized liquid membranes is to impregnate the pores of a porous polymer membrane with the solvent-carrier solution.5 By soaking a porous substrate in the solvent, films can be impregnated with the liquid or liquid mixtures. Porous hydrophilic PVDF films were used as substrates in this work because of their high porosity and favorable wetting properties. The ILM is prepared readily by the immersion technique. After immersing the substrate in carbonateglycerol solution for a predetermined period of time, it was removed from the liquid, and the extra fluid was wiped from the surfaces; the ILM was ready for test. If the immersion time is long enough, the ILMs thus prepared can be 100% wetted and translucent, which is a good indication that the pores are filled with the carbonate-glycerol solution. ILMs prepared by the

Figure 2. Schematic of the experimental setup.

immersion technique normally have thicknesses comparable to the PVDF substrates. To maximize gas fluxes, the ILM fluid can be immobilized in a thin section of the substrate. ILMs with reduced thicknesses can be prepared by the coating technique. In this technique, the porous substrates are carefully laid on top of the coating solution. The wicking rate of the liquid into the substrate pores is dependent on the viscosity of the liquid, surface properties of the substrate, and the coating time.23 After a predetermined period of coating time, the substrate is removed from the solution and the extra liquid on the coating surface is carefully wiped out with a tissue paper. The average thickness of the ILM, δ, can be estimated gravimetrically:

δ)

W1 - W0 AtFm

(6)

where W0 and W1 refer to the weights of the substrate and the prepared ILM, respectively, At is the total substrate area, F is the density of the Na2CO3-glycerol solution, and m is the porosity of the substrate. This coating technique can lead to ILMs with average thicknesses considerably less than that of the substrate. 3.3. Flow Cell Technique. The CO2/N2 permeation performances through the carbonate-glycerol membranes were measured by the flow cell technique,24 which involves passing a sweep gas on the permeate side whose flow rate and compositions were continuously recorded. Only a small fraction of the feed gas diffuses across the membrane and is carried away by the sweep stream. The sweep gas is essentially an inert gas which lowers the partial pressures of the permeating species in the sweep chamber. A schematic diagram of the experimental setup is shown in Figure 2. A circular piece of PVDF substrate (nominal diameter, 47 mm) impregnated with the Na2CO3-glycerol solution was housed in a cell designed to allow a feed stream and a sweep stream to pass on opposite sides of the film. The film was supported by a porous 152 µm thick fine circular stainless steel screen (Pall Trinity Micro, Cortland, NY) and sealed by a 4.0 cm diameter O-ring. The total exposed membrane area on each surface was 12.5 cm2. The feed gas stream was humidified with water before passing into the cell. Unless otherwise stated, the sweep gas was dry helium. Feed streams with relative humidities (RHs) less than 100% were obtained by the blending of dry and humidified gases. For this purpose, the feed source was split into two streams. One stream was passed through a water bubbler, while the other was left dry. The two streams were blended prior to contacting the membrane.

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The RH of the resulting stream was determined using a humidity probe (Model HMP 31UT, Vaisala, Woburn, MA). The gas flow rates were controlled using mass flow controllers (Matheson, Horsham, PA). The feed side pressure was controlled using a pressure regulator (Fairchild Model 10182 BP, Towaco, NJ). All connecting lines were 1/8 in. soft copper tubing. Inlet feed gas pressure and permeate side pressure were measured with pressure gauges (Matheson). The sweep gas line was connected to a Hewlett-Packard 5890 gas chromatograph (GC) for analysis of the exiting sweep gas samples containing the permeating species. A Porapak column (Alltech, Deerfield, IL) was used for all the analyses. All experiments were carried out at room temperature (23 ( 2 °C). The experimental procedure consisted of setting the feed gas flow rate such that the partial pressure of CO2 remained essentially constant along the feed side of the membrane. The sweep flow rate was set to keep the partial pressure of CO2 in the permeate relatively small, yet high enough for accurate determination. The permeation rates of CO2 and N2 were obtained from their concentrations in sweep gas and the sweep gas flow rate. Due to the small membrane area, the change in CO2 or N2 partial pressure along the feed side due to permeation was negligible. 3.4. Measurement of Equilibrium Water Concentration in Glycerol. Glycerol is strongly hygroscopic and 100% miscible with water. When the Na2CO3glycerol ILM is exposed to feed streams with high RHs, it could pick up considerable amount of water from the feed stream even though some amount of water will be lost in the permeate. The water content in glycerol has significant effects on its viscosity as well as gas solubility and diffusivity through it. Since such data were not directly available in the literature, experiments were conducted to determine how much water is absorbed in glycerol when exposed to environments of known RHs at a given temperature. Due to its hygroscopic nature, “fresh” glycerol starts absorbing water from the air immediately when exposed to it. If the contact time is long enough (e.g., overnight), the water content in glycerol will be in equilibrium with the water vapor pressure (which corresponds to a certain RH at a given temperature) in the air. The weight change of glycerol + water under different relative humidities was recorded using an electronic balance (Model PB 303, Mettler-Toledo). Repeated measurements showed that this simple technique can give reasonably reproducible results. 4. Analysis of Experimental Data The effective permeance of a species i, (Qi/tm)eff, through a homogeneous membrane of thickness tm is calculated as follows:

(Qi/tm)eff ) Vi/At∆pi

(7)

where At is the total membrane area and Vi and ∆pi are the volumetric permeation rate and the partial pressure differential of species i across the membrane, respectively. Equation 7 can be easily adapted for the case of transport through an ILM consisting of a microporous polymer support and a liquid phase constrained in the pores of the support. A voidage balance in the membrane leads to the following equation:11

Attmm ) τmtmAm

(8)

where m and τm are the substrate porosity and tortuosity, respectively. Thus the wetted membrane area, Am, can be found from

Am ) Atm/τm

(9)

The true permeance of species i through the liquid membrane can be written now as

(Qi/tm) ) Viτm/Atm∆pi

(10)

Since m < 1 and τm > 1, the true permeance value calculated from eq 10 is always greater than the effective permeance from eq 7. The permeability coefficient of species i is given by

Qi ) Vitmτm/Atm∆pi

(11)

The ideal separation factor Ri-j for two gas species i and j is defined by

Ri-j ) Qi/Qj

(12)

5. Results and Discussion ILMs having average thicknesses ranging from 30 to 100 µm were prepared from Na2CO3-glycerol solutions using the immersion or coating techniques. The concentration of Na2CO3 examined ranged from 0 to 4.0 mol/dm3. On a weight basis this represents 0-0.51 g of Na2CO3/(g of glycerol). While 1.0 M solution is clear and stable, higher carbonate concentrations in glycerol lead to turbid solutions at room temperature. Therefore, most of the ILMs used in this work were prepared with 1.0 M solution. Membranes examined visually after permeation tests showed no sign of salt crystallization. The experimental results on the tortuosity of the substrate are presented first. Then, the effects of Na2CO3 concentration, CO2 partial pressure differential, and feed stream relative humidity on ILM permeation performances will be reported, followed by results of the ILM stability tests. 5.1. Tortuosity Factor of the Support Membrane. The tortuosity factor τm is introduced to allow for both varying direction of diffusion and varying pore crosssection of a porous substrate.25 In this work, the tortuosity of the PVDF substrate was determined from the permeation rate of nitrogen through a supported liquid membrane of pure water. For this particular set of permeation experiments, both the feed and the sweep streams were saturated with water vapor. The value of τm can be estimated from the following equation:

τm )

()

Qi m∆piAt tm Vi

(13)

which is a variation of eq 11. The value of QN2 at the appropriate N2 partial pressure differential is based on the product of N2 diffusivity through water, DN2, and N2 solubility in water, SN2:

QN2 ) DN2SN2

(14)

There is considerable discrepancy regarding DN2 in the literature. In a particular source,26 it is given as 1.9 × 10-5 cm2/s at 25 °C, but, in another source,27 it is

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3493

Figure 3. Effect of Na2CO3 concentration on the CO2-N2 separation and CO2/N2 permeability coefficients (feed, humidified 0.52% CO2-balance N2 gas mixture; sweep, dry helium; CO2 partial pressure differential, 0.55 cmHg; the ILM thickness from low to high Na2CO3 concentrations, 99, 87, 77, 96, 98, and 100 µm, respectively).

reported to increase from 2.6 × 10-5 cm2/s at 20 °C to 3.5 × 10-5 cm2/s at 30 °C. In this work, the experimental result of DN2 in water27 was used for the determination of τm. The Henry’s constant for nitrogen solubility in water can be found from the literature.28 For example, at 23.5 °C, H ) 8.87 × 104 atm. When pN2 ) 90.40 cmHg ) 1.190 atm, equilibrium nitrogen mole fraction in water is 1.34 × 10-5. Therefore, nitrogen solubility in water under the above conditions is 1.84 × 10-4 cm3/ (cm3 cmHg). As noted in the previous section, the substrate porosity m and the thickness of the film tm were taken to be 0.70 and 100 µm, respectively (as specified by the manufacturer). From the above data and the permeation results, the average value of τm calculated was 2.58. 5.2. Effect of Initial Na2CO3 Concentration in ILM. Figure 3 illustrates the pronounced effects of adding Na2CO3 to glycerol membranes on CO2-N2 permeabilities and CO2/N2 selectivity. The data points in this figure were obtained under similar CO2 partial pressures with a feed gas containing 0.52% CO2 in N2. The ILMs had thicknesses from 77 to 100 µm as determined gravimetrically. With a Na2CO3 concentration of 0.1 M, the CO2 permeability coefficient increased by a factor of nearly 100 compared to that through pure glycerol. It is also seen from Figure 3 that, at similar CO2 partial pressure differentials, QCO2 increased with an increase of Na2CO3 concentration, presumably because more carriers are available for the facilitated transport of CO2. It can be noted from the figure that, in the higher carbonate concentration range, QCO2 did not increase proportionally with an increase in Na2CO3 concentration. Possibly, this is because the favorable facilitation effect in the higher carrier concentration

Figure 4. Effect of CO2 partial pressure differential on ILM performances (1.0 M Na2CO3-glycerol ILM; feed RH ) 100%).

range is, to some extent, compromised by the decreases in both the solubility of CO2 and the diffusivities of the chemical species in the ILM for the high Na2CO3 concentration range. It can be noted from Figure 3 that the permeability coefficient of N2, which is transported via the simple solution-diffusion mechanism, decreased with an increase in Na2CO3 concentration in the ILM over the concentration region investigated. Theoretically, the ILM viscosity and the ionic strength of the membrane solution should increase with the increase in Na2CO3 concentration. As a result, both the solubility and the diffusivity of N2 in the ILM would decrease. Therefore, the observed decreasing trend of QN2 with the increase in Na2CO3 concentration is not unexpected. From the above discussion, it is clear that, at similar CO2 partial pressure differentials, CO2/N2 selectivity increases with an increase in Na2CO3 concentration. 5.3. Effect of Feed Partial Pressure of Carbon Dioxide. The effects of CO2 partial pressure difference across the ILM, which is essentially equal to pCO2,f (the feed partial pressure of CO2), on CO2-N2 permeances and the separation factor are shown in Figure 4. As can be seen from the figure, at the Na2CO3 concentration of 1.0 M and feed RH of 100%, CO2 permeance decreased significantly with an increase of pCO2,f, although N2 permeance did not change appreciably. This characteristic, known as “carrier saturation”, is intrinsic to facilitated transport systems.4,5 The total flux of CO2 is composed of two parts, that of physically dissolved carbon dioxide plus that of the bicarbonate ion.2 The relative proportion of CO2 transported in physically dissolved form and in chemically combined form is dependent on, among others, the carriers available for facilitation reaction. The higher the concentration of dissolved CO2, the greater is the

3494 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 Table 2. Comparison of CO2 Permeation Performances of Different Facilitated Transport Membranes membrane composition

membrane type

∆pCO2, cmHg

(Q/tm)CO2 × 106, cm3(STP)/(cm2 s cmHg)

selectivity

ref

1 M Na2CO3-glycerol 1 M DEA-PEG 400 1 M MEA-water polyelectrolyte-salt blend (PVBTAF) hydrophilic polymer + amino acid salt plasma-grafted membrane containing ethylenediamine

ILM ILM ILM fixed-site carrier membrane fixed-site carrier membrane ion-exchange membrane

0.51-58.7 1.984-14.98 3.8-74 17.3-84.8 ∼57 3.6

30 to 2.5 6.932 to 2.523 50 to 5 11.3 to 7.17 ∼10b ∼100

3440 to 100 a (CO2/N2) 145 to 20 (CO2/C2H6) 2000 to 200 (CO2/CH4) 983 to 629 (CO2/N2) 30 to 15 (CO2/H2) 4700 (CO2/N2)

this work 11 13 17 18 15

a Higher selectivities are observed at reduced feed relative humidities; see Table 3 of this work. b Estimated assuming the dense layer thickness is 20 µm.

Table 3. Effect of Feed Stream RH on ILM Permeation Performancesa

c

(Q/tm)N2 × 109, cm3(STP)/(cm2 s cmHg)

(Q/tm)CO2 × 105, cm3(STP)/(cm2 s cmHg)

CO2-N2 selectivity

water vapor permeation rate, cm3(STP)/(min cm2)

feed-in RH, %

feed-out RH, %

50.7 56.9 66.0b 67.9 76.7 78.0b 87.0b 88.3 93.9b 95.4b

29.1 30.7 nac 39.2 41.4 na na 46.3 na 62.0

Feed, 0.52% CO2-N2; Retentate Pressure, 7.5 psig 4.38 1.51 4.81 1.64 5.05 1.57 7.03 2.23 7.88 2.17 6.56 1.88 10.9 2.50 12.0 2.02 14.5 2.74 22.5 3.10

3440 3420 3120 3180 2760 2850 2290 1680 1890 1380

0.00697 0.00826 na 0.00845 0.00973 na na 0.0110 na 0.00777

49.4 57.9 67.8 77.8 83.3 92.3 94.2

29.5 33.4 42.0 35.7 48.2 50.1 51.9

Feed, 1.98% CO2-N2; Retentate Pressure, 7.0 psig 4.28 0.634 4.87 0.862 4.87 0.851 6.60 1.22 9.99 1.51 15.2 1.92 18.4 1.94

1480 1770 1750 1840 1500 1260 1050

0.00554 0.00695 0.00618 0.00602 0.00964 0.00968 0.0114

a t ) 100 µm; A ) 25.1 cm2; PVDF-based 1.0 M carbonate-glycerol ILM; sweep gas, dry helium. b Retentate pressure ) 6.1 psig. m m Not available.

formation of the HCO3-. Thus, at greater pCO2,f, the membrane tends to get saturated with HCO3-. This lowers the concentration of CO32- available for further CO2 uptake, thereby decreasing the rate of flux variation with pCO2,f, as detailed in the literature for other facilitated transport systems.11-14 Since the ILMs display the pressure-dependent CO2 permeances, high separation factors were obtained at lower CO2 partial pressures and at higher Na2CO3 concentrations. The value of R observed at [Na2CO3] ) 3.0 M, pCO2,f ) 0.55 cmHg and RH ) 100% was 1140. It is relevant to compare the CO2 permeance of the current ILM with those of other facilitated transport membranes in the literature (Table 2). As can be noted from the table, at lower CO2 partial pressures, the CO2 permeance of the current ILM is greater than that of DEA-PEG 400 ILM 11 but lower than that of MEAwater ILM.12 Of all the membranes listed in Table 2, the functional cation exchange substrate based ethylenediamine (EDA) membrane 15 has the greatest CO2 permeance and CO2/N2 selectivity at low CO2 partial pressures. However, because of the toxic nature and high volatility29 of EDA, the membrane is not environmentally friendly and its stability remains to be demonstrated. At higher CO2 partial pressures, fixed-carrier membranes17,18 give better CO2 permeances than the ILMs. It should be noted that the carbonate-glycerol ILM in this work does not need humidified sweep gas. This means vacuum can be used instead of the sweep gas at the permeate side. Note that carbonate-glycerol ILMs can have a very high CO2/N2 selectivity of around 3440 (for conditions of this high selectivity, see Table 3 of this work).

Figure 5. CO2 permeance for different transmembrane pressure differentials and RHs (1.0 M Na2CO3-glycerol ILM; feed, 0.46% CO2-balance N2).

ILMs consist of liquids immobilized in the capillarylike pore structures of the substrates. The maximum transmembrane pressure (TMP) differential an ILM can handle depends on, among others, the pore size of the substrate and the surface tension of the ILM fluid. To justify their practical use, ILMs should be able to hold TMPs reasonably greater than those for intended applications. The PVDF film used in the present work has a water bubble point pressure of 4.8 atm 30 (i.e., 360 cmHg). To test the integrity of the carbonate-glycerol ILM under different TMPs, permeation runs were carried out under varying feed side pressures and RHs. The results are shown in Figure 5. The ILMs were stable up to a TMP of 120 cmHg (i.e., 1.58 atm). The ILMs did not leak and showed consistent CO2/N2 selectivities. Because carbon dioxide partial pressure differential across the ILM increases with the increase in TMP differential, the observed decrease in CO2

Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 3495

Figure 6. Equilibrium water content in glycerol (T ) 21.0-24.0 °C).

permeance with an increase in the TMP differential is expected. It can also be noted from Figure 5 that higher feed RHs can lead to greater CO2 permeances. This will be studied in more detail in the next section. 5.4. Effects of Feed Stream Humidity. 5.4.1. Equilibrium Water Concentration in Glycerol. The experimentally determined equilibrium water content in pure glycerol is shown in Figure 6. The equilibrium water concentration in glycerol increases monotonically with an increase of ambient relative humidity. In the ambient RH range of 75-80% (typical range of the RH of the exiting sweep/permeate stream in this work), the equilibrium water content is approximately in the range 0.4-0.6 g of water/(g of glycerol). This corresponds to a water mole fraction of 0.67-0.75. The actual water concentration in the ILM is difficult to determine experimentally. This is partially because, in most of our permeation experiments, the feed stream was completely humidified and the sweep gas stream was dry before contacting the ILM. Therefore, the two sides of the ILM were faced with gas streams with significantly different RHs. The RH of the retentate stream was somehow reduced to around 70%, depending on the operating conditions; correspondingly the RH of the sweep-out stream (helium + permeated gases) was generally between 75 and 80%. As a result, water concentration in the ILM may decrease considerably from the upstream side to the downstream side. Because of the high RHs of the feed stream, the actual water concentrations at the upstream side of and within the ILM are expected to be greater than the above estimates which are based on the RH of the permeate stream. Also from Figure 6, it can be inferred that the relative humidities of the feed and/or sweep streams can have significant effects on the permeation performances of the ILM. Since the water content is an important parameter in determining the ILM’s viscosity and ionic strength which are critical to both the diffusivity and the solubility of the permeating species in the ILM, it provides an additional dimension for adjusting and finetuning the permeation properties of the ILM. Moreover, the water content may affect the diffusivities and the solubilities of N2 and CO2 to different extents. Therefore, the feed stream RH is likely to affect the permselectivity of the ILM.

5.4.2. Water Transport Across the ILM. As shown in reactions 1 and 2, water is a reactant in the CO2 hydration reactions. Therefore, as experimentally confirmed later, water must be present in the ILM and/or in the feed gas stream in order to observe any facilitation effect. In this work, since the feed stream was humidified and the sweep stream was dry, water transport from the feed side to the permeate side could occur via two distinct paths: (a) transport via the solution-diffusion mechanism driven by its partial pressure differential and (b) transport via the reversible reactions. It is apparent from reaction 5 that the molar flux of water transported via path (b) is equal to the molar flux of CO2 transported via the facilitation reaction. Simple calculations based on feed side RHs and flow rate suggested that water transport via path (a) was dominant under our experimental conditions. In this work, initially a solution of sodium carbonate in glycerol has been used as ILM in the porous PVDF substrate. Water, which is necessary for the facilitation reactions, is supplied from the feed gas stream that is humidified before entering the permeation cell. As discussed above, if the feed stream is saturated with water vapor, steady-state water concentration in the ILM is much greater than that of carbonate or CO2. As a result, a water concentration change in the ILM due to the hydration reactions should be insignificant. This suggests that the feed gas stream need not be completely saturated with water vapor to observe the desired facilitated transport. 5.4.3. Effects of Feed Gas Humidity. Feed streams with RHs of less than 100% were obtained by blending a dry gas stream with a water vapor saturated stream. The RH range of the feed stream investigated was from about 49 to 95%. Table 3 lists the permeation performances of 1 M Na2CO3-glycerol ILMs at different feed stream RHs and CO2 levels. In this set of experiments, two permeation cells were connected in series (total membrane area, 25.1 cm2) to increase N2 and CO2 concentrations in the sweep stream and ensure that the N2 peak was above the GC detection limit. As a result, significant RH changes between feed-in and feed-out streams were observed. As can be seen from Table 3, both CO2 and N2 permeances decreased with a decrease in feed stream RH. This is expected because the water content in ILMs decreases significantly with a decrease in feed RH. The decreased water concentration in the ILM will drastically increase the liquid-phase viscosity which can be responsible for the observed decreases in CO2 and N2 permeances. Another factor responsible for the decreased permeances for low-RH feed streams is the “salting-out” effect. At low RHs, the water content in the ILM is much lower and the effective carbonate concentration is greater. This could considerably decrease the gas solubilities in and diffusivities through the ILM. Also from Table 3, it can be noted that the feed stream RH significantly affects the CO2/N2 selectivity of the ILM. For the feed RH range 50.7-95.4%, the observed selectivity for 1 M carbonate-glycerol ILM for the feed gas of 0.52% CO2-balance N2 was between 3440 and 1380. Those data are 305-62% greater than 850, the selectivity observed for 1 M Na2CO3-glycerol ILM under similar CO2 partial pressure differential and 100% feed RH as shown in Figure 3. For the feed gas of 1.98% CO2-balance N2, the observed selectivity as listed

3496 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999 Table 4. Comparison of Na2CO3-Glycerol ILM Permeation Preformances with Dry and 100% Humidified Feed Streamsa feed RH ) 0% ILM liquid glycerolc

Na2CO3-glycerold watere

QN2

b

10-10

QCO2

b

10-10

feed RH ) 100% QCO2/QN2

3.79 × 5.62 × 1.48 1.24 × 10-10 2.79 × 10-10 2.25 unstable because of evaporation

QN2

b

10-10

2.85 × 1.56 × 10-10 5.01 × 10-9

QCO2b

QCO2/QN2

1.11 × 10-8 1.77 × 10-7 2.09 × 10-7

38.9 1140 41.7

a Unless otherwise noted, the feed gas was 0.55% CO -balance N and the sweep gas was dry helium. The feed side pressure was 2 2 generally in the range of 6.5-9.5 psig (i.e., 109-125 cmHg). b Qi, in the unit of (cm3(STP) cm)/(cm2 s cmHg). c For RH ) 100%, the feed gas was 10.6% CO2-balance N2. d For RH ) 0%, the Na2CO3 concentration in glycerol was 0.6 M and the feed gas was 10.6% CO2balance N2; for RH ) 100%, the Na2CO3 concentration in glycerol was 3.0 M. e Sweep gas helium was completely humidified.

in the table for the feed RH range 49.4-94.2% was also considerably greater than 300-350, the normal selectivity range observed for 1 M Na2CO3-glycerol ILM under similar CO2 partial pressure differential and 100% feed RH. In summary, with a decrease in feed stream RH, significantly greater selectivity and somewhat decreased permeances can be expected. The last column of Table 3 lists water vapor permeation rates through the ILMs calculated from the feed inlet, feed outlet RH values and the feed outlet flow rate. Water vapor permeation rate generally increased with an increase in feed side RH, presumably because of the increased water vapor partial pressure differential across the ILMs. Like most polymeric membranes, the carbonate-glycerol ILM of this work has very high water vapor permeabilities under the experimental conditions. With completely dry feed streams (RH ) 0%), we were able to determine the “true” permeability coefficients of the gas species through glycerol and carbonateglycerol ILMs. The experimental results are listed in Table 4. For the purpose of comparison, the permeability coefficients obtained using feed streams with RH ) 100% are also listed in the table. Table 4 shows the importance of the presence of water and carbonate for the facilitated transport of CO2 through the ILM. First, pure glycerol has an extremely low CO2/N2 selectivity. The increased selectivity of 38.9 with the feed stream RH of 100% could be the result of the presence of a significant amount of water in the ILM. As listed in the last row of the table, pure water ILM shows a selectivity of 41.7 under the experimental conditions. Second, significant facilitated transport of CO2 was observed only in the presence of both water and carbonate. No facilitation would be possible if water or carbonate is absent in the ILM. Also from the table, it can be noted that the presence of carbonate in the ILM can significantly decrease N2 permeability coefficient, which contributes to the observed high CO2/N2 selectivities. As noted earlier, the decreased N2 permeability coefficient could come from the decreased N2 diffusivity and solubility in the ILM as a result of the increased liquid-phase viscosity and salting-out effect. 5.5. ILM Stability. The stability of the Na2CO3glycerol ILMs in terms of CO2 flux and CO2/N2 selectivity were examined in 14-day long permeation runs with various CO2-N2 gas mixtures. The thicknesses of the ILMs were in the range of 50-100 µm. In the stability runs, the total retentate pressure was around 1.5 atm. Figure 7 shows the stability test results for a 90 µm thick, 1.0 M Na2CO3-glycerol ILM. As shown in the figure, the separation factor and CO2/N2 permeances were reasonably constant throughout the experimental period. An important characteristic of the Na2CO3-glycerol ILM is that it is not prone to drying up. In this work,

Figure 7. ILM performances versus time (tm ) 90 µm; 0.9 M carbonate-glycerol ILM; feed, 0.55% CO2-balance N2 with RH ) 100%; retentate pressure, 1.50 atm).

the sweep gas was dry helium and the hydrophilic PVDF-based ILMs remained leak-free and stable after exposure to the humidified feed streams for up to 350 h. The ILMs’ nitrogen permeance during this period was essentially constant. This confirmed our understanding that ILMs prepared with hydrophilic substrates and glycerol, which is hygroscopic and has very low vapor pressures at operating temperatures, can have good stability. The superior stability of the Na2CO3-glycerol ILM is further demonstrated in Figure 8, which shows the variations of feed stream RH and CO2 permeance through and the separation factor of a 0.6 M Na2CO3glycerol ILM vs time. The feed stream was a 10.6% CO2-balance N2 gas mixture. The feed RH was 100% for the first 48 h. Then, it was decreased to 13% and maintained at that level for 100 h. Finally, it was increased to 100% again. From the figure, it is clear that the ILM was not damaged by the 100 h exposure to the very low RH feed stream. Because of the very low RH, CO2 permeance decreased to very low levels and N2 permeance was too low to be determined accurately.

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tration of sodium carbonate, among others. Whereas the solubility of Na2CO3 in dry glycerol is around 1.2 M, the solubility is increased considerably in the presence of RH-induced moisture to levels of 3-4 M or even higher. Thus as the RH changes, especially, along the membrane thickness, the salt concentration changes, and so does the solubility of Na2CO3. In fact, with somewhat lower RHs, ILMs which have been prepared by us at the higher Na2CO3 concentrations may have local precipitations of Na2CO3. Thus physicochemical data on effective Na2CO3 concentration at saturation in a glycerol membrane exposed to moisture are needed. Correspondingly, the solubilities of N2 and CO2 in a glycerol-carbonate ILM membrane containing RHinduced moisture need to be determined. Useful theoretical predictions for the current ILM system can be implemented only if the above-mentioned parameters can be ascertained. 6. Concluding Remarks Figure 8. ILM stability test with changing feed RHs (tm ) 95 µm, 0.6 M carbonate--glycerol ILM; feed, 10.6% CO2-balance N2; retentate pressure, 1.54 atm).

However, after the feed RH was increased to 100% again, CO2 and N2 permeances also increased to approximately the initial levels and the CO2/N2 separation factor was not affected. As noted earlier, the low volatility and highly hygroscopic nature of glycerol are responsible for the observed stability. 5.6. Theoretical Modeling of the Observed Behavior. Detailed analysis and modeling of facilitated CO2 transport through aqueous ILMs containing NaHCO3 have been reported.6,7 However, in the present work, the ILM contains glycerol, sodium carbonate, and moisture. The latter would be picked up from the humidified feed stream. The sweep gas is dry helium, and it picks up moisture along its path. Most of the experiments have been carried out with the feed gas RH being 100%. As this gas exits, its RH is reduced to a lower level of around 70%. The RH of the exiting sweep gas correspondingly will generally be in the range of 70-80%, depending on the operating conditions. Thus there exists a sharp gradient of RH along the membrane length as well as along the membrane thickness. Figure 6 shows the strong relationship between the gas-phase RH and the water content in glycerol. As indicated earlier, the viscosity of glycerol is changed by orders of magnitude on addition of water. For example, pure glycerol viscosity at 20 °C is 1412 cp.19 Whereas for water contents of 0.75, 0.25, and 0.19 g of water/(g of glycerol), the viscosities at 23 °C are respectively 8, 50, and 90 cP (interpolated from ref 19). The corresponding gas-phase RHs are respectively 85, 60, and 48% (from Figure 6). The diffusivity of any ionic species is therefore going to be drastically affected by the RH and the water content both along the membrane as well as across the membrane. Research by previous investigators used aqueous ILMs that are not influenced by this novel dimension. To obtain the complete picture of the ILM behavior, additional equations describing the moisture distribution and transport along the membrane length as well as along the membrane thickness have to be solved in addition to conventional facilitated transport equations. There is an additional problem. Solubilities of CO2 and N2 in the carbonate-glycerol ILM have to be estimated. They are influenced strongly by the concen-

From the results of this work, the following conclusions can be drawn: (a) The addition of Na2CO3 drastically increased the permeation rate of CO2 through a glycerol-based liquid membrane. CO2 permeability generally increased with an increase in carbonate concentration; in higher Na2CO3 concentration ranges, this permeability increase is partially compromised by the combination of increased solution viscosity and salting-out effect. N2 permeability through the ILM decreased with an increase in Na2CO3 concentration. Therefore, very high CO2/N2 selectivities were observed at higher Na2CO3 concentrations. (b) An increase in CO2 partial pressure differential across the membrane resulted in partial saturation of the carbonate carrier; higher CO2/N2 selectivities were observed at lower CO2 partial pressure differentials. (c) Because of the hygroscopic nature of the liquid membrane, the steady-state water content in the ILM increases with an increase of feed stream relative humidity. The water content in the ILM drastically affects the ILM viscosity and the effective concentration of the carriers in the ILM, which are important factors determining the permeation performances of the ILM. Generally, lower permeances and greater CO2/N2 selectivity values were observed at lower feed stream humidities. When the feed RH ) 50.7%, pCO2,f ) 0.007 atm and the Na2CO3 concentration in glycerol was 1.0 mol/ dm3, the separation factor R(CO2/N2) observed was around 3440. (d) The stability of the Na2CO3-glycerol ILM in terms of flux, selectivity, and longevity was examined. Prolonged runs lasting 14 days showed that the ILM permeation performances were quite stable. The ILMs were also found to be stable when challenged with feed streams of very low relative humidities. The hydrophilized PVDF-based Na2CO3-glycerol ILM showed good stability and very high CO2/N2 selectivity at reduced feed stream RHs. However, it is desirable to increase the CO2 permeance still further. Possible reasons for the observed low permeance include (1) the ILM is relatively thick, (2) the ILM fluid is quite viscous, and (3) carbonate solubility in glycerol is limited. To increase the CO2 permeance, a promising strategy is to prepare thin ILMs with thinner hydrophilic substrates. To increase carrier concentration in the ILM, salts more soluble in glycerol should be explored. Also, because hollow fiber ILM is preferred for practical applications,

3498 Ind. Eng. Chem. Res., Vol. 38, No. 9, 1999

suitable hollow fiber substrates are needed to prepare hollow fiber modules for future studies. Acknowledgment This work was primarily supported by the New Jersey Institute of Technology. Partial support was also received near the end of the work from Hamilton Standard, Windsor Locks, CT, as a subcontract from the main NASA contract. We acknowledge considerable discussions with Karen E. Murdoch of Hamilton Standard regarding their earlier NASA-sponsored work. H. Chen acknowledges support from the Chinese Academy of Sciences during October 1997 to March 1998. Nomenclature At ) total membrane area (m2) Am ) wetted membrane area (m2) Di ) diffusivity of species i (m2/s) pi ) partial pressure of component i (kPa) Qi ) permeability coefficient of species i ((cm3(STP) cm)/ (cm2 s cmHg)) Si ) solubility of species i (mol/(m3 kPa)) Vi ) volumetric permeation rate of species i (cm3(STP)/s) RH ) relative humidity (%) T ) temperature (K) tm ) liquid membrane thickness (m) Greek Letters R ) separation factor δ ) average ILM thickness (m) m ) porosity of substrate τm ) tortuosity of substrate µ ) viscosity ((N s)/m2) F ) density of the ILM liquid (g/cm3)

Literature Cited (1) Koros, W. J.; Fleming, G. K. Membrane-based Gas Separation. J. Membr. Sci. 1993, 83, 1. (2) Ward, W. J.; Robb, W. L. Carbon Dioxide-Oxygen Separation: Facilitated Transport of Carbon Dioxide across a Liquid Film. Science 1967, 156, 1481. (3) LeBlanc, O. H.; Ward, W. J.; Matson, S. L.; Kimura, S. G. Facilitated Transport in Ion-Exchange Membranes. J. Membr. Sci. 1980, 6, 339. (4) Meldon, J. H.; Stroeve, P.; Gregoire, C. E. Facilitated Transport of Carbon Dioxide: A Review. Chem. Eng. Commun. 1982, 16, 263. (5) Way, J. D.; Noble, R. D. Facilitated Transport. In Membrane Handbook; Ho, W. S. W., Sirkar, K. K., Eds.; Chapman and Hall: New York, 1992. (6) Otto, N. C.; Quinn, J. A. The Facilitated Transport of Carbon Dioxide through Bicarbonate Solutions. Chem. Eng. Sci. 1971, 26, 949. (7) Suchdeo, S. R.; Schultz J. S. The Permeability of Gases through Reacting Solutions: The Carbon Dioxide-Bicarbonate Membrane System. Chem. Eng. Sci. 1974, 29, 13. (8) Olander, D. R. Simultaneous Mass Transfer and Equilibrium Chemical Reaction. AIChE J. 1960, 6, 233.

(9) Teramoto, M. Approximate Solution of Facilitation Factors in Facilitated Transport. Ind. Eng. Chem. Res. 1994, 33, 2161. (10) Meldon, J.; Paboojian, A.; Rajangam, G. Selective CO2 Permeation in Immobilized Liquid Membranes. AIChE Symp. Ser. 1986, 248, 114. (11) Saha, S.; Chakma, A. Selective CO2 Separation from CO2/ C2H6 Mixtures by Immobilized Diethanolamine/PEG Membranes. J. Membr. Sci. 1995, 98, 157. (12) Davis, R. A.; Sandall, O. C. CO2/CH4 Separation by Facilitated Transport in Amine-Polyethylene Glycol Mixtures. AIChE J. 1993, 39, 1135. (13) Teramoto, M.; Nakai, K.; Ohnishi, N.; Huang, Q.; Watari, T.; Matsuyama, H. Facilitated Transport of Carbon Dioxide through Supported Liquid Membrane of Aqueous Amine Solutions. Ind. Eng. Chem. Res. 1996, 35, 538. (14) Guha, A. K.; Majumdar, S.; Sirkar, K. K. Facilitated Transport of CO2 through an Immobilized Liquid Membrane of Aqueous Diethanolamine. Ind. Eng. Chem. Res. 1990, 29, 2093. (15) Matsuyama, H.; Teramoto, M.; Iwai, K. Development of a New Functional Cation-Exchange Membrane and Its Application to Facilitated Transport of CO2. J. Membr. Sci. 1994, 93, 237. (16) Way, J. D.; Noble, R. D.; Reed, D. L.; Ginley, G. M.; Jarr, L. A. Facilitated Transport of CO2 in Ion Exchange Membranes. AIChE J. 1987, 33, 480. (17) Quinn, R.; Laciak, D. V. Polyelectrolyte Membranes for Acid Gas Separations. J. Membr. Sci. 1997, 131, 49. (18) Ho, W. S. W. Membranes comprising salts of amino acids in hydrophilic polymers. U.S. Patent 5,611,843, 1997. (19) Segru, J. B.; Oberstar, H. E. Viscosity of Glycerol and Its Aqueous Solutions. Ind. Eng. Chem. 1951, 43, 2117. (20) Morrison, L. R. Glycerol. In Encyclopedia of Chemical Technology, 4th ed.; Kroschwitz, J. I., Howe-Grant, M., Eds.; John Wiley & Sons: New York. 1991; Vol. 12, p 682. (21) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill Book Co.: New York, 1977. (22) Cammenga, H. K.; Schulze, F. W.; Theuerl, W. Vapor Pressure and Evaporation Coefficient of Glycerol. J. Chem. Eng. Data 1977, 22, 131. (23) Chibowaki, E.; Gonzalez-Caballero, F. Theory and Practice of Thin-layer Wicking. Langmuir 1993, 9, 330. (24) Bhave, R. R.; Sirkar, K. K. Gas Permeation and Separation by Aqueous Membranes Immobilized across the Whole Thickness or in a Thin Section of the Hydrophobic Microporous Celgard Films. J. Membr. Sci. 1986, 27, 41. (25) Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1970. (26) Perry R. H. Chemical Engineer’s Handbook, 4th ed.; McGraw-Hill Book Co.: New York, 1973; Vol. 3, p 224. (27) Wise, D. L.; Houghton, G. The Diffusion Coefficients of Ten Slightly Soluble Gases in Water at 10-60 °C. Chem. Eng. Sci. 1966, 21, 999. (28) Perry, R. H.; Green, D. W.; Maloney, J. O. Chemical Engineer’s Handbook, 6th ed.; McGraw-Hill Book Co.: New York, 1984; Vol. 3, p 103. (29) Stephenson, R. M.; Malanowski, S. Handbook of the Thermodynamics of Organic Compounds; Elsevier: New York. 1987. (30) Millipore Laboratory Catalogue; Millipore 1997.

Received for review January 19, 1999 Revised manuscript received June 9, 1999 Accepted June 16, 1999 IE990045C