Facilitated Transport of Carbon Dioxide through Supported Liquid

Dec 15, 1995 - was a mixture of CO2 and CH4, and the CO2 partial pressure pCO2,F was in the range from 0.05 to 0.97 atm. Compared to the MEA ...
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Ind. Eng. Chem. Res. 1996, 35, 538-545

Facilitated Transport of Carbon Dioxide through Supported Liquid Membranes of Aqueous Amine Solutions Masaaki Teramoto,* Katsuya Nakai, Nobuaki Ohnishi, Qingfa Huang, Takashi Watari, and Hideto Matsuyama Department of Chemistry and Materials Technology, Faculty of Engineering and Design, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606, Japan

A series of experiments on the facilitated transport of CO2 through supported liquid membranes containing monoethanolamine (MEA) and diethanolamine (DEA) was performed. The feed gas was a mixture of CO2 and CH4, and the CO2 partial pressure pCO2,F was in the range from 0.05 to 0.97 atm. Compared to the MEA membranes, the DEA membranes showed a little higher permeation rate of CO2 since the equilibrium constant of the reaction between CO2 and MEA is too large for CO2 to be released to the receiving phase rapidly. When pCO2,F and the MEA concentration were 0.05 atm and 4 mol/dm3, respectively, the separation factor R(CO2/CH4) was about 2000. It was found that if the membrane thickness multiplied by the square root of the tortuosity factor of the microporous support membrane is used as the effective pore length, the experimentally observed permeation rates of CO2 can be satisfactorily simulated by the theory of facilitated transport of CO2 through aqueous amine membranes. A method for estimating the solubilities of CO2 in the membrane solutions from the permeation rates of CH4 was also proposed. It was also found that permeation rates of CO2 through aqueous DEA membranes reported by Guha et al. were quantitatively explained by the proposed theory. 1. Introduction Separation of CO2 is a very important gas separation process (Kohl and Riesenfeld, 1985). Recently, application of the membrane separation technique to the separation of CO2 has been attracting attention due to low energy consumption compared to traditional separation methods such as gas absorption and adsorption. Although many polymeric membranes have been developed for CO2 separation, the separation factor of CO2 over N2 and CH4 is rather low (Kesting and Fritzsche, 1993). To overcome the problem of low selectivity, use of facilitated transport membranes has been proposed (Ward and Robb, 1967; LeBlanc et al., 1980). As the carriers of CO2 which effectively enhance the permeation rate of CO2, amines such as monoethanolamine (MEA) (Smith and Quinn, 1979; Donaldson and Nguyen, 1980; Meldon et al., 1986) and diethanolamine (DEA) (Donaldson and Nguyen, 1980; Guha et al., 1990; Davis and Sandall, 1993) have been investigated. Smith and Quinn (1979) measured the tracer flux of 14CO2 through the membrane of aqueous MEA solution, which had been equilibrated with a known partial pressure of CO2 (“tracer transport”). Since the tracer concentration was negligibly small, this arrangement realized the uniform carrier concentration in the membrane and this made the differential mass balance equation linear. In addition, they performed the “net transport experiments” where the partial pressure of CO2 in the downstream side was kept lower than that in the upstream side. However, the permeation flux was discussed only qualitatively. In order to obtain the reaction rate constants of CO2 with various amines, Donaldson and Nguyen (1980) employed the tracer transport technique which was the same as that used by Smith and Quinn (1979). They reported that, for the CO2-MEA system, the measured rate constant was in agreement with previously reported values. However, they did not give a satisfactory interpretation for the permeation rates of CO2 through aqueous DEA membranes. Guha et al. (1990) performed the experiments on the net permeation of CO2 through an immobilized liquid membrane of 0888-5885/96/2635-0538$12.00/0

aqueous DEA solution. Although they tried to simulate the permeation rates by solving the diffusion equations in the membrane numerically, their computed values were considerably higher than the experimental results as will be described later. Davis and Sandall (1993) reported that the permeation rate of CO2 through the membranes of DEA-poly(ethylene glycol) mixture and also of diisopropanolamine-poly(ethylene glycol) mixture could be successfully simulated by their permeation model. As was described above, the permeation rates of CO2 through aqueous MEA and DEA membranes under the condition of unequal partial pressure of CO2 across the membrane have not yet been quantitatively simulated by the theory of facilitated transport. In this study, a series of experiments on the simultaneous permeation of CO2 and CH4 through aqueous MEA and DEA membranes was performed and the permeation rates of CO2 were quantitatively discussed on the basis of the approximate solution of facilitated transport which had been proposed by Teramoto (1995). A method for applying the facilitated transport theory developed for a liquid membrane consisting of a liquid membrane phase alone to the analysis of facilitated transport through a supported liquid membrane prepared by impregnating a microporous polymer support having tortuous pore structure with a carrier solution is also proposed. 2. Theory 2.1. Approximate Solution of Facilitated Transport of CO2 through Aqueous Amine Membranes. It was reported that the reaction of CO2 with primary amine and secondary amine RR′NH (R, R′; functional group or hydrogen) such as monoethanolamine and diethanolamine is expressed as follows (Danckwerts, 1979):

CO2 (A) + 2RR′NH (B) h RR′NCOO- (E) + RR′NH2+ (F) (a) © 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996 539

The reaction rate is generally expressed by

r ) -(dCA/dt) ) k1{CACB - CECF/(KeqCB)}/{1 + k2/(k3CB)} (1) For the CO2-MEA system, the relation k2/(k3CB) , 1 holds while for the CO2-DEA system the term k2/(k3CB) cannot be neglected when CB is low. The differential mass balance equations of the present facilitated transport system are

DA d2CA/dx2 ) r

(2)

DB d2CB/dx2 ) 2r

(3)

DE d2CE/dx2 ) -r

(4)

DF d2CF/dx2 ) -r

(5)

subject to the boundary conditions

x ) 0: CA ) CA0, dCB/dx ) dCE/dx ) dCF/dx ) 0 (6)

equations numerically to simulate the permeation rate of CO2 through liquid membranes consisting of the secondary amines, diethanolamine, and diisopropanolamine in poly(ethylene glycol). Guha et al. (1990) obtained numerical solutions of the basic equations for the case of k2/k3 ) 0. Recently, Teramoto (1994) developed an approximate solution for the facilitation factor in the facilitated transport membranes where a reaction A (permeate) + B (carrier) h C (complex) occurs. Very recently, this approximation method was extended to the facilitated transport system where reaction a occurs in the membrane (Teramoto, 1995). It was confirmed that the approximate solutions agree with the numerical solutions reported by Davis and Sandall (1993) and by Guha et al. (1990), and also that this approximation method provides sufficiently accurate facilitation factors over the entire range from the physical diffusion region to the chemical equilibrium region. According to this approximation method, the facilitation factor F can be calculated by solving the following simultaneous algebraic equations. F)

(

x ) L: CA ) CAL, dCB/dx ) dCE/dx ) dCF/dx ) 0 (7) The conservation of the carrier B in the membrane is expressed as

∫0

L

(CB + CE + CF) dx ) CBTL

(8)

The above equations and the boundary conditions are transformed in a dimensionless form:

γ0

(

γL

)

f0

2

rEqKb0

(

(1 - aL) + (cosh γ0 - 1) 1 -

e0f0

)

Kb02

)

2

sinh γ0 + γ0f0/(rEqKb0 ) 1+

fL

)

2

rEqKbL

(

(1 - aL) + (cosh γL - 1)

eLfL

KbL2

)

- aL

2

)

sinh γL + γLfL/(rEqKbL ) 1 - aL - q(b0 - bL)/2 ) 1 - aL + rEq(e0 - eL) ) 1 - aL + rFq(f0 - fL) (17)

ab - ef/(Kb) d2a ) δ2 2 1 + m/b dy

(9)

d2b 2δ2 ab - ef/(Kb) ) q 1 + m/b dy2

(10)

δ2 ab - ef/(Kb) d2e )2 rEq 1 + m/b dy

(11)

d 2f δ2 ab - ef/(Kb) ) rFq 1 + m/b dy2

(12)

y ) 0:

a ) 1, db/dy ) de/dy ) df/dy ) 0

(13)

y ) 1:

a ) aL, db/dy ) de/dy ) df/dy ) 0

(14)

∫01 (b + e + f) dy ) 1

1+

(15)

Here, a ) CA/CA0, b ) CB/CBT, e ) CE/CBT, f ) CF/CBT, y ) x/L, aL ) CAL/CA0, K ) KeqCA0, m ) k2/(k3CBT), q ) (DB/DA)(CBT/CA0), rE ) DE/DB, rF ) DF/DB, and δ ) L(kCBT/DA)1/2. The facilitation factor F is defined as the ratio of the permeation flux in the presence of carrier to that of physical permeation in the absence of carrier, and is expressed as follows:

F ) {-DA(dCA/dx)x)0,L}/(DACA0/L) ) -(da/dy)y)0,1 (16) Davis and Sandall (1993) solved the above differential

(b0 + bL + e0 + eL + f0 + fL)/2 ) 1

(18)

e0 ) f0

(19)

eL ) fL

(20)

Equations 19 and 20 represent electrical neutrality in the membrane. Here, aL, b0, bL, e0, eL, f0, and fL are the dimensionless concentrations at the boundaries of the membrane, and γ0 and γL are defined as follows:

γ0 ) δ[{b0 + (f0/rEqKb0)}/(1 + m/b0)]1/2

(21)

γL ) δ[{bL + (fL/rEqKbL)}/(1 + m/bL)]1/2

(22)

where δ is defined as

δ ) L(k1CBT/DA)1/2

(23)

The six unknown concentrations at the two boundaries of the membrane can be determined from eqs 17-23 for the given values of dimensionless parameters aL ) CAL/ CA0, K ) KeqCA0, m ) k2/(k3CBT), q ) DBCBT/(DACA0), rE ) DE/DB, rF ) DF/DB, and δ ) L(k1CBT/DA)1/2. Then the facilitation factor F can be calculated from these concentrations. 2.2. Application of Approximate Solution to Supported Liquid Membranes. The above approximate solution was developed for the facilitated transport membrane comprising a liquid phase alone. This solu-

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Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996

tion can be easily applied to the analysis of the facilitated transport through a supported liquid membrane consisting of a microporous polymer support and a liquid membrane phase constrained in the pores of the support. In this case, the differential mass balance equations are expressed as follows:

The diffusive flux without chemical reaction is given by

Ji ) nπr02Di∆Ci/Le

(35)

DeA d2CA/dx2 ) r

(24)

DeB d2CB/dx2 ) 2r

(25)

DeE d2CE/dx2 ) -r

(26)

where Ji represents the flux through unit area of the porous membrane, n is the number of pores per unit membrane area, r0 is the pore radius, and ∆Ci is the concentration difference between the two boundaries of the membrane. Le is the actual diffusional path length, i.e., the effective pore length. Due to the tortuous pore structure, Le is longer than the membrane thickness L, the straight line distance through the membrane. Combining eqs 34 and 35 gives

DeF d2CF/dx2 ) -r

(27)

Ji ) Di(∆Ci/L)/(Le/L)2

Here  is the porosity of the support membrane and Dei is the effective diffusivity defined by the following equation.

Ji ) Dei(dCi/dx)

Dei ) Di/τ

(29)

Here, the tortuosity factor τ is introduced to allow for both varying direction of diffusion and varying pore cross section (Satterfield, 1970). The value of τ can be experimentally determined by the experiments on the physical permeation of gases through supported liquid membranes as will be described later. The dimensionless form of eq 24 is expressed by the following equation. 2

ab - ef/(Kb) da ) τL2(kCBT/DA) 2 1 + m/b dy

(30)

(31)

should be used in calculating the facilitation factor by using eqs 17-23. This indicates that the effective diffusional path length Le is expressed by the following equation using the membrane thickness L and τ.

Le ) τ1/2L

(37)

This equation is equivalent to eq 28. Then, from eqs 36 and 37, we can see that τ based on the parallel pore model is interpreted as (Le/L)2. This relation is the same as eq 32 although only the effect of varying direction of diffusion is considered in the parallel pore model. The diffusion equation of A in a cylindrical pore of the facilitated transport membrane is the same as eq 9, and the boundary condition for A is expressed by

x ) 0:

CA ) CA0;

x ) Le: CA ) CAL

(38)

Then, the dimensionless diffusion equation is represented by

ab - ef/(Kb) d2a ) δ′ 2 2 1 + m/b dy′

y′ ) 0: a ) 1;

(39)

JA ) -DeA(dCA/dx)x)0,L ) -(/τ)(DACA0/L)(da/dy)y)0,1 ) (/τ)(DACA0/L)F (33) Here, F is the facilitation factor corresponding to the value of δ′ expressed by eq 31. The same equation can be derived on the basis of the parallel pore model which pictures transport as occurring through a number of parallel capillaries of the same size (Youngquist, 1970). According to this model, the porosity of the membrane  is expressed as follows:

(34)

y′ ) 1: a ) aL

(40)

Here, y′ ) x/Le and δ′ is defined by eq 31. The permeation flux is given by

JA ) -nπr02DA(dCA/dx)x)0,Le ) -(L/Le)(DACA0/Le)(da/dy′)y′)0,1 ) (/τ)(DACA0/L)F (41)

(32)

Then, the permeation flux of A is expressed by the following equation.

 ) nπr02Le/L

Ji ) (/τ)Di(∆Ci/L)

with the following boundary condition

Comparison of eq 9 with eq 30 or eq 23 suggests that the parameter δ′ defined by

δ′ ) τ1/2L(k1CBT/DA)1/2

Here, the tortuosity factor is generally defined by the following equation.

(28)

The effective diffusivity is related to the molecular diffusivity using the porosity and the tortuosity factor of the support membrane τ as follows:

(36)

where F is defined by

F ) {-DA(dCA/dx)x)0,Le}/(DACA0/Le) ) -(da/dy′)y′)0,1 (42) In deriving eq 41, eq 34 was used. Thus, eq 41 derived on the basis of the parallel pore model is exactly the same as eq 33 although the physical meaning of τ is different for these two equations. It is noted again that in evaluating the facilitation factor F using eqs 17-23, δ′ should be used instead of δ. It is also noted that when the permeation occurs in the physical diffusion region (δ f 0) or in the chemical equilibrium region (δ f ∞), the facilitation factor F does not depend on δ or δ′. In other words, F is determined independently of the effective diffusional path length in these regions. The

Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996 541

Figure 1. Schematic diagram of experimental apparatus.

Figure 2. Effects of pCO2,F and monoethanolamine concentration on the permeation rates of CO2 and CH4 and separation factor.

validity of the present model where τ1/2L is taken as the effective pore length will be discussed later.

4. Results

3. Experimental Section The experimental apparatus used in this study was the same as used in a previous study (Matsuyama et al., 1994). The schematic diagram of the experimental apparatus is shown in Figure 1. The permeation cell consisted of two compartments (thickness 3.7 mm, membrane area 7.92 cm2) for a feed and a sweep gas. Durapore VVLP poly(vinylidene difluoride) hydrophilic microporous membranes supplied from Millipore (thickness ca. 100 µm, pore size 0.1 µm, porosity 0.70) were used as the supports of the liquid membranes. The membrane thickness was measured by a micrometer. Monoethanolamine (MEA) and diethanolamine (DEA) were purchased from Wako Pure Chemical Industries, Ltd., Osaka, Japan. The support membrane was soaked in an aqueous amine solution for more than 2 h, and the solution on the surface of the support was blotted by a cellulose filter paper and used for the permeation experiment. The supported liquid membrane was sandwiched between the two compartments. The feed gas was a mixture of CO2 and CH4, and the sweep gas was helium. Both gas streams were supplied to the permeation cell at atmospheric pressure after presaturation with water. The partial pressure of CO2 in the feed gas was changed from 0.05 to 0.97 atm, the flow rate of the feed gas was in the range from 200 to 300 cm3/min, and that of the sweep gas was 50 cm3/min at 298 K and 1 atm. The partial pressure of CO2 in the sweep gas was less than 2% of that in the feed gas. The sweep gas from the cell was analyzed by a gas chromatograph equipped with a thermal conductivity detector (Shimadzu, GC-8APT, column activated carbon). The permeation rates of CO2 and CH4 were obtained from the partial pressures in the feed and the sweep gases and the sweep gas flow rate. Due to the small membrane area, the compositions of the feed gas and the retentate were almost the same. The temperature was 298 K.

4.1. Determination of Tortuosity Factor of Support Membrane. The tortuosity factor of the support membrane was determined from the permeation rate of pure CO2 through a supported liquid membrane of pure water. The permeation rate RCO2 is expressed by the following equation.

JCO2 ) DCO2,WHCO2,W(pCO2,F - pCO2,S)/(τL) (43) Here, DCO2,W is the diffusivity of CO2 in water (1.97 × 10-5 cm2/s (Peaceman, 1951)), HCO2,W is the Henry constant of the CO2-water system (3.40 × 10-2 mol/ (dm3‚atm), (Morrison and Billett, 1952)), and  is the porosity (0.7, the value reported by Millipore Ltd.). The value of τ calculated from eq 43 was 3.23. A similar experiment was performed with pure methane as the feed gas. Using the values of DCH4,W ) 1.70 × 10-5 cm2/s (Witherspoon and Bonoli, 1969) and HCH4,W ) 1.34 × 10-3 mol/(dm3‚atm) (Morrison and Billett, 1952), the value of τ was obtained as 3.35, which is close to the value obtained with the CO2 permeation experiment. 4.2. Permeation Rates of CO2 and CH4 through Aqueous MEA and DEA Membranes. The effect of the partial pressure of CO2 in the feed gas, pCO2,F, on the permeation rates of CO2 and CH4 and the separation factor R(CO2/CH4) is shown in Figure 2 for aqueous MEA membranes of various concentrations. It is seen that for each MEA concentration the permeation rate of CH4 which is transported by the simple solutiondiffusion mechanism is almost constant irrespective of pCH4,F ()1 - water vapor pressure (0.03 atm) - pCO2,F). It is also seen that RCH4 decreases considerably as the MEA concentration increases. One reason for this is that, with increasing MEA concentration, the diffusivity of CH4 in the membrane solution decreases due to the increase in the viscosity. Another reason is that, as the MEA concentration increases, the solubility of CH4 in the membrane solution decreases since the ionic strength

542

Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996 Table 1. Estimated Values of Diffusivities and Solubilities of CO2 in Liquid Membrane Solutions and Chemical Equilibrium Constants Keq CBT RCH4,M/ µAm/ µM/ DCO2,M/ HCH4,M/ HCO2,M/ carrier (mol/dm3) RCH4,W µW µW DCO2,W HCH4,W HCO2,W (dm3/mol) MEA MEA MEA DEA DEA DEA

1 2 4 1 2 4

0.530 0.265 0.172 0.591 0.419 0.197

1.19 1.42 2.14 1.42 2.12 5.73

1.29 1.67 2.98 1.50 2.39 7.80

0.844 0.709 0.482 0.763 0.559 0.254

0.628 0.373 0.356 0.775 0.749 0.775

0.659 0.410 0.430 0.812 0.823 0.936

5.0 × 104 1.1 × 105 1.5 × 105 2.5 × 103 4.4 × 103 4.4 × 103

solutions of various amine concentrations were estimated from the values in water using the following equation (Hikita et al., 1980).

Di,M/Di,W ) (µM/µW)-2/3

Figure 3. Effects of pCO2,F and diethanolamine concentration on the permeation rates of CO2 and CH4 and separation factor.

of the membrane solution increases with an increase in the MEA concentration due to the formation of ionic species, e.g., carbamate ion and protonated MEA, as will be described later. On the other hand, the permeation rate of CO2 decreases with an increase in pCO2,F since CO2 is transported by the carrier-mediated transport mechanism. RCO2 does not increase appreciably with increasing MEA concentration because the favorable facilitation effect of high carrier concentration is compensated by the decreases in both the solubility of CO2 and the diffusivities of the chemical species in the solution of high MEA concentration. Therefore, a higher separation factor R(CO2/CH4) was obtained at lower CO2 partial pressure and higher MEA concentration. The value of R at [MEA]T ) 4 mol/dm3 and pCO2,F ) 0.046 atm was about 2000. The separation factor for pure water membrane was 29.9. This value agreed with 30.5, which was calculated from the solubilities and the diffusivities of these gases in water described in section 4.1 by the following equation.

R(CO2/CH4)W ) (HCO2,WDCO2,W)/(HCH4,WDCH4,W) (44) The effect of pCO2,F on RCO2, RCH4, and R(CO2/CH4) obtained with DEA membranes is shown in Figure 3. While the tendency of this figure is very similar to that shown in Figure 2 for the MEA membranes, the permeation rates of CO2 through the DEA membrane are a little higher than those through the MEA membrane. The separation factors obtained with the MEA and DEA membranes are similar. 5. Comparison of Experimental Data with Computed Results 5.1. Physicochemical Properties of Facilitated Transport Systems. (a) Diffusivity of CO2 and Amines. The diffusivities of CO2, MEA, and DEA in pure water have been reported as follows: DCO2,W ) 1.97 × 10-5 (Peaceman, 1951), DMEA,W ) 1.12 × 10-5 (Hikita et al., 1980), and DDEA,W ) 8.20 × 10-6 cm2/s (Hikita et al., 1980). The diffusivities in the liquid membrane

(45)

The viscosity of the membrane solution in the pores of the support, µM, cannot be measured. Here, the viscosities of amine solutions saturated with CO2 at 1 atm were measured by an Ostwald viscometer and these values were taken as the viscosities of the membrane solutions. The viscosities are listed in Table 1. This approximation may be reasonable since in the simulation of the permeation rates of CO2 the MEA and DEA concentrations in the membrane calculated by the present approximation method were found to be less than 15% of the initial amine concentration CBT. As shown in Table 1, these viscosities are higher than µAm, the corresponding values of the aqueous amine solutions reported in the literature (Hikita et al., 1980). The diffusivities of carbamate ion and protonated amine were assumed to be equal to that of amine. (b) Solubilities of CO2 in Membrane Solutions. The solubility of CO2 in the liquid membrane solutions was estimated as follows. Since CH4 permeates through the membrane by the simple solution-diffusion mechanism, its permeation rate is proportional to both the solubility and the diffusivity in the membrane solution. Therefore, the following equation holds for the ratio of the permeation rate through the aqueous membrane solution to that through pure water membrane.

RCH4,M/RCH4,W ) (HCH4,M/HCH4,W)(DCH4,M/DCH4,W) ) (HCH4,M/HCH4,W)(µM/µW)-2/3 (46) Here, eq 45 was used. Then, the solubility ratio HCH4,M/ HCH4,W can be calculated from the experimentally measured permeation rates of CH4 and the viscosities of the aqueous membrane solutions using eq 46. It should be noted that HCH4,M is not the Henry constant of CH4 for the aqueous amine solution but that for the aqueous membrane solution which is in contact with CO2 and contains unreacted amine and reaction products, i.e., carbamate ion and protonated amine. The solubility ratio HCO2,M/HCO2,W does not necessarily equal HCH4,M/HCH4,W. The solubilities of gases in electrolyte solutions could be estimated by the following equation (van Krevelen and Hoftijzer, 1948).

log(HM/HW) ) -(ig + i+ + i-)I

(47)

Here, ig, i+, and i- are the constants specific to the gaseous, cationic, and anionic species, respectively, and I is the ionic strength. Since these values for the present system are not available, these were estimated from the solubility data of CO2 and CH4 in aqueous NaCl and KI solutions (Morrison and Billett, 1952). By

Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996 543

Figure 4. Effects of pCO2,F and Keq on RCO2 through the MEA membranes.

using their data, the following relation was obtained.

iCO2 ) iCH4 - 0.041

(48)

As has been already described, more than 85% of the amine initially incorporated in the membrane was converted to ionic species, i.e., carbamate E and protonated amine F. Therefore, the ionic strength of the membrane solution in contact with CO2 was about half the initial amine concentration. Then, the following relation holds between the solubilities of CO2 and CH4 in the membrane solution.

HCO2,M/HCO2,W ) (HCH4,M/HCH4,W)(100.041I)

(49)

Then, from eqs 46 and 49, we obtain

HCO2,M/HCO2,W ) (µM/µW)2/3(RCH4,M/RCH4,W)(100.041I) (50) From the observed values of RCH4,M/RCH4,W and the viscosity ratios shown in Table 1, the values of HCO2,M/ HCO2,W were estimated and are also shown in Table 1. (c) Chemical Equilibrium Constants and Reaction Rate Constants. The chemical equilibrium constants Keq at about 293 K were reported to be 1.1 × 105 and 4.38 × 103 dm3/mol for MEA and DEA, respectively (Danckwerts and Sharma, 1966). The chemical equilibrium constant depends on the temperature and the ionic strength of the solution. However, no information on this is available. The reaction rate constants for CO2-MEA and CO2-DEA systems used in the simulation were 5920 dm3/(mol‚s) (Hikita et al., 1977) and 1410 dm3/(mol‚s) (Laddha and Danckwerts, 1981), respectively. The value of k2/k3 for DEA was 1.18 mol/dm3 (Laddha and Danckwerts, 1981). 5.2. Simulation of the Experimental Data. Figure 4 shows the comparison between the experimentally observed permeation rates of CO2 through the aqueous

Figure 5. Effects of pCO2,F and Keq on RCO2 through the DEA membranes.

MEA membranes of various concentrations and the computed results (solid and dotted lines) obtained by the approximation method described in section 2.2. The reported value of Keq at 293 K and 2 mol/dm3 MEA concentration is 1.1 × 105 dm3/mol (Danckwerts and Sharma, 1966). Solid lines are the computed results using this value as Keq. It is seen that the computed results agree with the experimental data when [MEA]T was 2 and 4 mol/dm3. However, when [MEA]T was 1 mol/dm3, the computed results are a little lower than the experimental data. It can also be seen in Figure 4 that the value of Keq which gives the best fit between the calculated and the experimental results changes with the MEA concentration. This may be explained as follows. As has been already described, MEA initially incorporated in the support membrane is almost converted to carbamate ion and protonated MEA by the reaction with CO2. This means that the ionic strength of the membrane solution changes with the initial amine concentration. Since the activity coefficients of the chemical species change with the ionic strength, it seems reasonable that Keq which gives the best fit between the computed and the experimental results changes with [MEA]T. It is also seen in Figure 4 that the computed permeation rate of CO2 decreases with an increase in Keq since a too large value of Keq makes the releasing rate of CO2 at the sweep side of the membrane slow. In Figure 5, permeation rates of CO2 through the DEA membranes are compared with the computed results for several values of Keq. The diffusivity and the solubility of CO2 shown in Table 1 were used in the calculation. As in the case of the MEA membranes, a higher value of Keq gives a lower computed permeation rate. The solid lines represent the computed results using 4380 dm3/mol (Danckwerts and Sharma, 1966) as Keq. Agreement between the computed and the experimental results is fairly good. Although the reaction rate of CO2 with DEA is lower than that with MEA, the DEA membrane showed a little higher permeation rate of

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Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996

been reported (Suchdeo and Schultz, 1974; Smith and Quinn, 1980; Davis and Sandall, 1993). In these studies, τL was used as the effective diffusional path length without giving any rational explanation for this. As far as we know, the present study is the first one where τ1/2L is taken as the effective diffusional path length. Recently, facilitated transport in porous media has been analyzed more rigorously for the CO2-HCO3- system using the method of volume averaging (Ochoa-Tapia et al., 1991). Their mathematical treatment is much more complicated than ours based on the very simple model. The present study demonstrates that even such a simple model can be used in interpreting facilitated transport in porous membranes. 6. Conclusion Figure 6. Simulation of the permeation rate of CO2 reported by Guha et al. Carrier: DEA, [DEA]T ) 1.94 mol/dm3.

CO2 than the MEA membrane. This is because the lower chemical equilibrium constant of the reaction of CO2 with DEA is favorable for rapid release of CO2 to the receiving side. 5.3. Simulation of the Permeation Rates of CO2 Reported in the Literature. Guha et al. (1990) reported the permeation rates of CO2 through the supported liquid membranes containing an aqueous DEA solution ([DEA]T ) 1.94 mol/dm3). The support membrane was a microporous polypropylene membrane Celgard 2400 (thickness 25.4 µm, porosity 0.38, tortuosity 5.0, average effective pore size 0.02 µm). The permeation rates of CO2 were calculated from the data shown in Table 2 of their paper using the following relation and are shown in Figure 6.

RCO2 (this work, cm3(STP)/(cm2‚s‚cmHg)) ) QCO2 (Guha et al., cm3(STP)‚cm/(cm2‚s‚cmHg))(/τL) (51) They tried to simulate their data by the numerical solutions of the basic equations assuming that the reaction rate is expressed by eq 1 with k2/k3 ) 0 and the effective pore length is τL. Their computed results for two different sets of physicochemical properties, which are listed in Table 3 of their paper, are shown by the dashed lines in Figure 6. These results are considerably higher than the experimental data. This may be due to the following two reasons. One is that they used the physicochemical properties such as the diffusivities and the solubility of CO2 for the CO2-aqueous DEA solution system. However, since the value of Keq is very large and the reaction rate is fast in this system, most of DEA in the membrane is considered to be consumed even at low partial pressures of CO2. Therefore, the physicochemical properties for the system of CO2-aqueous solution containing DEA, carbamate ion, and protonated DEA should have been used in the simulation. Another reason is that they used τL instead of τ1/2L as the effective pore length. The results calculated by using the solubility and the diffusivity listed in Table 1 ([DEA]T ) 2 mol/dm3) and by assuming that the effective diffusional path length is τ1/2L are shown by the solid line. It is seen that the present computed results are in good agreement with the experimental data. Many studies on the analysis of the facilitated transport of various gases through porous membranes have

Experiments on the separation of CO2 from CH4 by supported liquid membranes containing aqueous monoethanolamine or diethanolamine solutions were performed, and the data were discussed quantitatively on the basis of the approximate solution of the facilitated transport which had been presented by one of the present authors. It was found that the experimentally observed permeation rates of CO2 and those available in the literature could be simulated fairly well by taking account of the following. 1. In the analysis, the solubilities of CO2 in the membrane solutions containing not only the unreacted amine but also the reaction products, e.g., carbamate ion and protonated amine, should be used. The permeation rates of CH4 provide useful information for evaluating the solubilities of CO2 in the membrane solutions. 2. It is recommended to use τ1/2L as the effective diffusional path length where L is the membrane thickness and τ is the tortuosity factor of the microporous support membrane defined by eq 29. Nomenclature a ) CA/CA0 b ) CB/CBT C ) concentration (mol/m3) CBT ) total carrier concentration (mol/m3) D ) diffusivity (m2/s) De ) effective diffusivity (m2/s) e ) CE/CBT F ) facilitation factor f ) CF/CBT HCO2 ) Henry constant of CO2 (mol/(m3‚atm)) I ) ionic strength (mol/dm3) ig, i+, i- ) salting-out parameter (dm3/mol) J ) permeation flux (mol/(m2‚s)) K ) KeqCA0 Keq ) equilibrium constant of reaction a (m3/mol) k1 ) forward reaction rate constant (m3/(mol‚s)) k2/k3 ) reaction rate parameter (mol/m3) L ) membrane thickness (m) Le ) effective diffusional path length (m) m ) k2/(k3CBT) n ) number of pores per unit membrane area (1/m2) p ) partial pressure (atm) q ) (DB/DA)(CBT/CA0) R ) permeation rate (cm3(STP)/(cm2‚s‚cmHg)) r ) reaction rate (mol/(m3‚s)) r0 ) radius of capillary pore (m) rJ ) DJ/DB (J ) E, F) x ) distance (m) y ) x/L

Ind. Eng. Chem. Res., Vol. 35, No. 2, 1996 545 y′ ) x/Le Subscripts A ) CO2 Am ) aqueous amine solution B ) amine (MEA or DEA) E ) carbamate ion (RR′NCOO-) F ) protonated amine (RR′H2+) F ) feed gas L ) value at x ) L or y ) 1 (receiving side interface) M ) membrane solution S ) sweep gas (receiving side) T ) total value W ) water 0 ) value at x ) 0 (feed side interface) Greek Letters γ0 ) L[{(k1CB0/DA) + (k1CF0/DEKeqCB0)}/{1 + k2/(k3CB0)}]1/2 ) δ[{b0 + (f0/rEqKb0)}/(1 + m/b0)]1/2 γL ) L[{(k1CBL/DA) + (k1CFL/DEKeqCBL)}/{1 + k2/(k3CBL)}]1/2 ) δ[{bL + (fL/rEqKbL)}/(1 + m/bL)]1/2 δ ) L(k1CBT/DA)1/2 δ′ ) Lτ1/2(k1CBT/DA)1/2 or Le(k1CBT/DA)1/2  ) porosity of support membrane µ ) viscosity (Pa‚s) τ ) tortuosity factor of support membrane

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Received for review July 5, 1995 Accepted October 23, 1995X IE950112C X Abstract published in Advance ACS Abstracts, December 15, 1995.