Carbon Dioxide Reaction Kinetics and Transport in Aqueous Amine

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Ind. Eng. Chem. Fundam. 1980, 19, 260-266

Carbon Dioxide Reaction Kinetics and Transport in Aqueous Amine Membranes Terrence L. Donaldson" and Yen N. Nguyen Depafiment of Chemical Engineering, University of Rochester, Rochester, New York 14627

Reaction kinetics of C02 with mono-, di-, and triethanolamine and triethylamine have been studied using a tracer 14C02membrane transport technique. At low concentrationsof mono- and diethanohmine the resutts are consistent with carbamate formation. At higher concentrationsthe chemistry appears to be more complex. Transport resutts are discussed in terms of various potential phenomena. Although triamines do not form carbamates with COB, both triethanolamine and triethylamine increased the membrane transport flux of COP. The only reasonable reaction mechanism for triethanolamine consistent with our data is base catalysis of C02 hydration. Triethylamine, on the other hand, appears to act only as a weak base to produce free OH- which reacts with COP.

Introduction Facilitated transport in liquid membranes offers an attractive technique for the study of reaction kinetics, as shown by Donaldson and Quinn (1974,1975) and Lander and Quinn (1978). Experimental conditions can easily be adjusted to give pseudo-steady-state membrane transport and true pseudo-first-order reaction kinetics for tracer species. The differential equations which govern the simultaneous reaction and diffusion process can be solved analytically in closed form and used to determine reaction kinetic parameters from experimental data. A unique aspect of the experimental method is the presence of equilibrium concentrations of all nontracer species. The method is somewhat analogous to relaxation techniques, in which the system is perturbed about an equilibrium state. Both the forward and reverse reactions of permeant and carrier are significant. The reactions specifically are not irreversible, and hence this method is complementary to techniques in which the reactions may be considered irreversible. This paper reports new information on the reaction kinetics and mechanisms for the reactions of COz and ethanolamines in aqueous solution. Amines are used for C 0 2 absorption in a variety of industrial processes (Danckwerts and Sharma, 1966). Reaction rates are faster than ordinary COPhydration rates and are comparable to arsenite-catalyzed hydration rates. However, the mechanisms of the amine reactions are not understood in a comprehensive sense. Our results provide additional insight into the kinetics and mechanisms, particularly for diethanolamine and triethanolamine. Results with monoethanolamine confirm existing reaction models and demonstrate the applicability of the experimental method to COP-amine reactions. C02-Amine Chemistry Danckwerts (1979) has noted that the reactions of COz with amines are generally more complicated than most investigators have presumed. The principal reaction of C02with mono- and disubstituted amines is the formation of carbamic acids, which dissociate completely. The proton is picked up by a second amine molecule. The reaction sequence is RzNH + COZ + R2NCOO- + H+ (1) RzNH

+ H+ + RzNHZ+

(2)

where R may be an H or other group. Reaction 1 is the rate-limiting step, and the kinetics are usually first order

in unprotonated amine and COz concentrations (Danckwerts and McNeil, 1967; Coldrey and Harris, 1976). Monoethanolamine (MEA) has been studied extensively a t concentrations less than 1 M, and the results have been generally consistent with reactions 1 and 2. Experiments with diethanolamine (DEA) have shown several types of deviation from this scheme. Most reports have indicated that the reaction rate is first order in DEA concentration a t low concentrations (Sada et al., 1976a; Jorgensen, 1956; Coldrey and Harris, 1976; Jensen et al., 1954; Sharma, 1965). However, Nunge and Gill (1963) obtained second-order kinetics in DEA concentration in pure DEA, and Hikita et al. (1977) also obtained secondorder kinetics in aqueous solutions of DEA. There is some evidence for second-order dependence on DEA concentration from the results of Jensen and Jorgensen (Danckwerts, 1979). Coldrey and Harris (1976) used a rapid flow thermal method and found evidence for a rapid exothermic reaction followed immediately by an endothermic reaction during the initial phase of the (presumed) formation of carbamate. (However,their results have been questioned (Dixon, 1977)). Various hydrogen bonding, dimerization, and catalysis phenomena have been offered to explain these effects. Danckwerts (1979) has proposed a reaction mechanism involving a carbamate zwitterion intermediate which is deprotonated by a base such as water or unprotonated DEA. This mechanism leads to an apparent DEA kinetic order from 1 to 2, depending on the relative magnitudes of the various rate constants and base concentrations. The tri-substituted amines, such as triethanolamine (TEA), do not form carbamates since there is no hydrogen atom to be displaced by the COP. However, amines are weak bases in aqueous solutions, and COP will combine directly with free OH- produced from protonation of the amines. When the R group of the amine is an alcohol, formation of monoalkyl carbonate will occur a t high pH. The reaction is believed to be NHzROH + OH- * NH2RO- + H2O (3) "PRO+ COZ + NHZROCOO(4) in which Reaction 4 is the rate-limiting step (Jorgensen et al., 1954; 1956). Sada et al. (1976a) and Hikita et al. (1977) have studied the C02-TEA system a t high pH by gas absorption and by rapid mixing and flow techniques, respectively. Their results appear to be consistent with monoalkyl carbonate formation, whereas our results indicate an additional re-

0196-4313/80/1019-0260$01.00/0@ 1980 American Chemical Society

Ind. Eng. Chem. Fundam., Vol. 19, No. 3, 1980

action. More will be said later about their experiments. Experimental Procedures The tracer transport method for kinetic studies has been described by Donaldson and Quinn (1974, 1975) and Lander and Quinn (1978). The Millipore filter membrane containing the aqueous amine solution is placed in the diffusion cell, which is then equilibrated on both sides with identical partial pressures of untagged COz in N1. A very small amount of tracer 14C02is introduced on one side of the cell, and the flux and driving force for the tracer I4CO2 transport are recorded during the initial pseudo-steadystate period. The results are expressed as a dimensionless flux ratio 14C02flux in amine membrane (5) = 14C02flux in water membrane

'

5,

0

-.

1

I

I

I

2 NOMINAL

3

4

I

5

I 6

I

1

6

7

I

8

261 1

9

(MI

MEA CONCENTRATION x IOz

Figure 1. Transport results with MEA solutions. 30

I

I

I

I

The data have been corrected for the slightly different solubility and diffusivity of COz in water compared to amine solutions. Reproducible results were obtained with individual membranes, which indicates that the physical properties of the type BS (polyvinyl chloride) and type FALP (polytetrafluoroethylene) membranes are not altered by exposure to amine solutions. The mathematical model for the facilitated transport process is obtained from the solution to the steady-state species conservation equations of the form

where pi is the net rate of depletion of species i by chemical reaction. Since the sum of untagged and tagged COz concentration is effectively the same on both sides of the membrane, the system is at reaction equilibrium with respect to total carbon (although not at equilibrium with respect to tracer species). Hence, concentrations of all species not containing carbon are independent of position within the membrane, and reaction kinetics in eq 6 for tracer species are therefore truly pseudo first order (assuming mass action kinetics). (This mathematical simplification is one of the major advantages of this experimental technique. Kinetics generally are not pseudo first order in net transport systems.) The analytical solution for the flux ratio $ is l+F (7) = 1 + (F/$) tanh 4

'

where

and

The rate constant k is defined as k =~A~[R~NH] (10) where kAm is the second-order forward rate constant for reaction 1. The equilibrium constant KAmapplies to reaction 1, and L is the diffusional path length. Only carbamate carrier is considered in this analysis; it will be shown later that the rate of bicarbonate carrier formation from COz uncatalyzed hydration is negligible compared to carbamate formation. Concentrations of all nontracer species are calculated by solving the various reaction

UNPROTONATED MEA CONCENTRATION x 103 ( M )

Figure 2. Rate constants for MEA reaction with COBfrom data in Figure 1.

equilibrium expressions simultaneously with the known COz concentration, nominal amine concentration, and an electroneutrality equation. Equilibrium constants are shown in Table I and concentrations of the various species are shown in Table I1 for typical experimental conditions. Additional parameter values are also given in the Appendix.

Experimental Results Monoethanolamine. Transport experiments were done with type FALP membranes containing 0.0265 to 0.0828 M MEA, adjusted to 0.23 M ionic strength with NaCl. Experimental values of the flux ratio t) are shown in Figure 1. The rate constants determined from these flux ratios are shown in Figure 2 as a function of the unprotonated amine concentration. The second-order rate constant kAm is given by the slope, and is 6000 M-' s-l. Other reported values for this rate constant range from 5900 to 8400 M-' s-* a t 298 K (Clarke, 1964; Sharma, 1965; Sada et al., 1976a,b; Hikita et al., 1977). The excellent linear correlation of k with unprotonated MEA to give a second-order rate constant consistent with other reported values demonstrates the applicability of this facilitated transport technique to the C02-amine systems in a quantitative manner. Carbamate hydrolysis to produce bicarbonate has been proposed by Smith and Quinn (1979) to account for irregularities in their C 0 2 transport results in MEA. We have investigated the effect of bicarbonate by adding KHCOBto MEA solutions. If a bicarbonate reaction were involved in the facilitation process, then altering the bicarbonate concentration should affect the experimental facilitation. Our results are shown in Table 111. Also shown are predicted values oft) from eq 7 with the rate constant from

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Ind. Eng. Chem. Fundam., Vol. 19, No. 3, 1980

Table I. Equilibrium Constants reaction equilib const

amine

[R,NCOO‘] [H’] 1

2

KAm =

Kb =

[R2”1

value

sourceb

MEA

1.8x 10-5

DEA

2.5

MEA

5.2 x 10-5 M

DEA

1.67 x 10-5 M

TEA triethylamine

1.26 X M 5.65 x 10-4 ~a

Danckwerts and Sharma (1966) Danckwerts and Sharma (1966)

[CO,l

[R,NH*] [OH-] [R,NI

X

Danckwerts and Sharma (1966); Union Carbide Danckwerts and Sharma (1966); Union Carbide Nguyen (1978) Handbook of Chemistry and Phvsics 11962) I

K , = [ H 4 [ OH -1

,

4.47 x 10-7 M Q

Edsall(l969)

4.67 x 10.” Ma

Edsall(l969)

1.0x 10-14 M Z Q

Edsall(l969)

At infinite dilution. Adjusted for ionic strength effects using Debye-Huckel theory only for 1 M ionic strength applications. Values for Kb for all four amines are in good agreement with measurements in our laboratory by a titration metho d a t the ionic strengths in our membranes. Table 11. Typical Equilibrium Concentrations of Nontracer Species in mol/L; 1% CO, in t h e Gas Phase

co,2-

nominal concn

OH-

x

lo6

HCO; x 10,

x 10’

R3N

x 10,

R,NH’ x 102

R,NCOO-

amine MEA MEAa DEA TEA triethylamine

0.0828 0.0265 0.088 1.0 0.50

3.59 11.0 3.87 8.73 27.8

5.46 16.8 5.87 11.2 38.6

0.147 1.39 0.170 0.73 5.03

0.468 0.213 1.56 87.4 1.35

6.78 1.00 6.73 12.6 48.65

1.03 1.44 0.512

x

lo2

Plus 0.20 M KHCO,.

Table 111. Transport Results with Bicarbonate Solutions Containing 0.0265 M MEA bicarbonate concn, M

predicted flux ratio

exptl flux ratio

0.025 0.10 0.20

2.35 3.49 3.82

2.27 3.30 3.70

the MEA experiments above (Figure 2). The maximum expected bicarbonate contribution to the flux ratio from non-amine reactions is only 0.06 at the highest KHC03. Agreement between model and experiments is within experimental reproducibility. These data give k~~ = 5350 M-ls-l when analyzed in the manner of Figure 2. These results are good evidence that bicarbonate plays no role in the transport process other than influencing the overall species distribution. This conclusion is consistent with the generally accepted description of the “final” equilibrium in transient C 0 2 absorption. As C02 is hydrated slowly to form bicarbonate and carbonate, reaction 1 is shifted to the left with no direct hydrolysis of carbamate to produce bicarbonate (Danckwerts and McNeil, 1967; Astarita e t al., 1964; Emmert and Pigford, 1962). Diethanolamine. Experiments were done with type BS membranes containing 0.031 to 0.088 M DEA, also adjusted to 0.23 M ionic strength with NaC1. The flux ratios are shown in Figure 3, and the pseudo-first-order rate constants are shown in Figure 4 as a function of unprotonated amine concentration. The results indicate that this system is more complex than the MEA system since a linear relationship between k and unprotonated DEA is not obtained. We do not yet have a satisfactory interpretation for these data with DEA. However, the experiments were identical

I 0

1

I

I

I

2 3 4 5 6 7 NOMINAL DEA CONCENTRATION x IO2 IM)

8

I

I

I

I

J

9

Figure 3. Transport results with DEA solutions.

“I

0

i

I

i

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I

1

I

1

I

1

2

4

6

8

10

12

UNPROTONATED

DEA CONCENTRATION x IO’

I 14

I 16

18

(MI

Figure 4. Rate constants for DEA reaction with C 0 2 from data in Figure 3, assuming carbamate carrier.

Ind. Eng. Chem. Fundam., Vol. 19, No. 3, 1980

with the MEA experiments described above, and we have no reason to doubt the flux measurements. We wish to report our preliminary transport results and make several comments concerning their possible interpretation and significance. (1)Various physicochemical parameters are needed in order to calculate the rate constants from eq 7-9 and the reaction scheme in reactions 1 and 2. These values have been documented in the Appendix. The equilibrium constants KAm and Kb were obtained at 293 K from Danckwerts and Sharma (1966), who reported that the temperature and ionic strength dependence are not known. We are not aware of other published values of KAm. Measurements of Kb in our laboratory by a titration method at 298 K and 0.23 M ionic strength are in good agreement with the values in Table I. The rate constants from our flux data can be fit to a fiist-order kinetic model by doubling Kb. However, the resulting value of kb is about 400 M-’ s-l, which is significantly smaller than other reported values. Minor changes in the diffusivities or membrane thickness do not influence the functional behavior seen in Figure 4. (2) It may be argued that there is sufficient uncertainty in the flux measurements to account for the unusual kinetics suggested by Figure 4, especially since the fluxes are near the reaction equilibrium limit at lower DEA concentrations. Based on our considerable experience with this experimental method, we do not believe that the qualitative behavior seen in Figure 4 is due to experimental uncertainty in the flux measurements. We do not claim that Figure 4 is a true representation of the kinetics, but rather that the situation may be more complicated than our reaction and transport model presumes. We have done transport experiments at much higher concentrations of DEA and MEA. Transport rates were very slow compared to expected values based on the model and results at lower amine concentrations. Similar phenomena were observed in another laboratory (D. R. Smith, private communication) and reported by Smith and Quinn (1979), who show that the tracer flux decreases as the MEA concentration is increased above 1 M. Clearly these observations are inconsistent with simple carbamate formation and suggest more complex chemical equilibria or kinetics. (3) It does not seem likely that catalysis phenomena are responsible for these effects. The experimental observation is an apparent decrease in the reaction rate as all species concentrations increase (except H+). However, it is conceivable that the speciation model is incomplete. It is well known t h a t carboxylic acids form dimers, “homoconjugated’ complexes, and ion pairs (Eberson, 1969). Reports of association in polar solvents are inconclusive, and apparently the extent of association in aqueous media has not been determined. It can be shown that in our system the amount of carbamate increases very rapidly with increasing amine concentration, while the other species increase approximately linearly over this concentration range. Any type of association phenomena could alter the speciation significantly and hence alter the pseudo-firstorder rate constants and the reaction equilibrium limit, 1 + F. If the present data analysis is based on incorrect values of F , then the calculated rate constants will be incorrect also. The relative amount of association would be expected to be larger at higher concentrations and negligible at lower concentrations. In this regard it is interesting to note that the apparent limiting slope in Figure 4 at lower concentrations of DEA gives kAm = 1400

5

I

/

I

1

I 0

263

I

02 04 06 08 10 N O M I N A L TEA CONCENTRATION ( M )

1

Figure 5. Transport results with TEA solutions. I

-

I

I

I 1

1 I 0

01

I

I

02 03 04 05 06 UNPROTONATED TEA CONCENTRATION I M )

07

08

I

09

Figure 6. Rate constants for TEA reaction with COZ from data in Figure 5, assuming bicarbonate carrier.

M-’ s-l, which is in the range of values for lzAm reported by other investigators who found first-order behavior at low concentrations (Sharma, 1965; Sada et al., 1976a; Jorgensen, 1956; Jensen et al., 1954). There is no experimental evidence for anomalous behavior of MEA at the low concentrations shown in Figures 1 and 2. However, association phenomena might also occur at higher concentrations. In addition, it should be remembered that other investigators generally have studied only the forward reaction in the absence of significant carbamate product. Hence, association phenomena involving the carbamate species would not be present. In summary, we do not have compelling evidence to favor a particular interpretation at this time. However, the preceding discussion serves to emphasize features of our experimental method which are distinctly different from unsteady-state gas absorption and/or reaction methods. The correct description of the DEA-CO2 system must be consistent with results from both types of experiments, as is the case with MEA at low concentrations. Triethanolamine. Transport experiments were done with 0.1 to 1.0 M triethanolamine solutions and BS membranes. Significant facilitation was observed despite the absence of a carbamate carrier. The experimental flux results are shown in Figure 5. To evaluate the rate constant, it is first necessary to know F,which means that the overall chemical reaction and the carrier species must be known. We suggest that unprotonated TEA is a base catalyst for hydration of carbon dioxide to bicarbonate. The transport data will be analyzed on this basis, and then supporting evidence for this interpretation will be discussed. If our hypothesis of base catalysis by TEA is correct, then the pseudo-first-order rate constant should be linear with unprotonated TEA, regardless of the total nominal

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TEA concentration. The rate constant is shown in Figure 6 as a function of unprotonated TEA concentration; the relationship is linear, and the second-order catalytic rate constant is 2.7 M-ls-l. To alter the concentration of unprotonated TEA relative to total TEA in the membrane, several experiments were done with 100% COz in the gas phase instead of 1%,using the same TEA concentrations. These solutions were more acidic, and consequently the fraction of unprotonated amine was about 0.3, compared to 0.9 for the 1% COP experiments (at 1.0 M nominal amine). Total ionic strength was 1.0 M, compared to 0.23 M for the 1% experiments. A value of 2.0 M-' s-l was obtained for the second-order rate constant, which agrees reasonably well with the result from the 1% experiments and is strong evidence in favor of unprotonated amine as the reactive species. Bicarbonate carrier is also produced via COP + OH-, since TEA is a weak base which produces OH- from water. However, it can be shown quite easily that the pseudofirst-order rate constants for this mechanism are an order of magnitude smaller than the rate constants shown in Figure 6. For example, et 1.0 M nominal TEA, the pH is about 9.0, and k should be about 0.12 s-l from the known uncatalyzed hydration rate constants. However, the experimental value of k, presuming that the carrier is bicarbonate, is 2.4 s-l. An alternative hypothesis is that TEA monoalkyl carbonate is the carrier in our membrane transport experiments. Jorgensen and Faurholt (1954) and Jorgensen (1956) studied the kinetics and equilibria of TEA monoalkyl carbonate formation at 273 and 291 K. From their results an estimate can be made for the kinetics and equilibria at our operating temperature of 298 K. An Arrhenius extrapolation gives a value of 1.53 X lo4 M-2 s-l for the third-order rate constant k3 for the overall reaction COP

+ OH- + RzNCHzCHzOH

ka

R2NCHZOCH2COO- + HzO (11)

Based on this rate data, the rate constant in our transport system should be 0.13 s-' for 1.0 M nominal TEA. This prediction is 20 times smaller than our experimental value of 2.4 s-l. In addition, the pseudo-first-order rate constant according to reaction 11 would be proportional to the product [R3N][OH-]rather than to [R3N] alone, as was found experimentally. These characteristics indicate that monoalkyl carbonate carrier is not responsible for the facilitation in our experiments. This conclusion is independent of the value of the equilibrium constant for reaction 11. Base Catalysis. The only reasonable reaction mechanism which is consistent with our experimental results is base catalysis of the COz hydration reaction. The pair of unshared electrons on the nitrogen atom enables amines to act as general base catalysts for other reactions; for example, the imidazole catalyzed hydrolysis of acetylimidazole (Jencks, 1969). The mechanism for COz hydration catalysis is presumably hydrogen bonding between amine and water, which weakens the H-0 bond and increases the nucleophilic reactivity of the water toward COz. Free hydroxide is never actually formed. This mechanism is shown in eq 12. R~N-H-O-H

i c o 2

-

R3"+

+

HCoi

(12)

This interpretation is supported indirectly by our experimental results. The good correlation of k with unprotonated TEA, rather than with total amine or total

-OH groups, is evidence in favor of catalysis by the unprotonated nitrogen atom. An alternate site for base catalysis is the ionized base -CH20- from the alcohol group. However, its concentration would be about 10-fold higher at 1% COP than at 100% COP Hence, the experimental first-order rate constant should be roughly 10-fold greater for the 1% experiments than for the 100% experiments. This difference is not seen. The same argument may be used to rule out monoalkyl carbonate formation. Base catalysis of COz hydration by anions of weak acids is well known (Sharma and Danckwerts, 1963). Bicarbonate and carbonate are not catalysts. Several nitrogen compounds were studied by Dennard and Williams (1966). Imidazole was a very weak catalyst, while various substituted pyridines had no catalytic activity. Although base catalysis could be present in MEA and DEA solutions, it was mentioned earlier that no bicarbonate carrier facilitation could be detected experimentally. If the catalytic rate constant were about 3 M-' s-l, the maximum pseudo-first-order rate constant would be about 0.015 s-l for MEA and 0.05 s-l for DEA for the amine concentrations in Figures 1 and 3. These rate constants are comparable to the uncatalyzed hydration rate constants, which produce negligible bicarbonate carrier facilitation under these conditions in our membranes. The efficiency of amines as general base catalysts is usually primary < secondary < tertiary (Jencks, 1969), so COPhydration catalysis by MEA and DEA is probably less than by TEA. There are two other reports of studies on the COZ-TEA system. Sada et al. (1976a) used a wetted wall column for COz absorption. They presented evidence for two reactions, one of which was presumed to be COz + OH- at long contact times. However, their proposed initial reaction of COPwith TEA is nothing more than COz reacting with the OH- produced from protonation of TEA by water (their eq 5 through 7). It is not clear how the same reaction could appear as two distinct rate-limiting steps with different rate constants. An interpretation which is more consistent with their data is to consider the initial reaction to be monoalkyl carbonate formation, followed at longer times by COz + OH-. The rate constant for this initial reaction was found to be 16.8 M-' s-l based on a pseudo-first-order reaction model in which TEA was assumed constant. Although unprotonated TEA would be nearly constant, the reactive species for monoalkyl carbonate formation is undoubtedly the -CHzO- anion, whose concentration is proportional to OH- (see reactions 3 and 4). It is not obvious that OHshould be constant in their experiments. Hence, it seems possible that their reported rate constant is actually some sort of average value from their pseudo-first-order model. If we assume for the moment that OH- was in fact constant, then the maximum combined rate constant may be estimated for the monoalkyl carbonate formation and the COz + OH- reaction. The pH of 1 M TEA is about 11 and virtually all of the amine is unprotonated. Based on our estimated value of k3 for reaction 11,the maximum rate constant for monoalkyl carbonate formation is 15 M-' s-l. Similarly, the known rate constant for the C02+ OHreaction (8500 M-' 9-l) leads to an apparent TEA rate constant of 8.5 M-' s-l at 1 M TEA. The combined maximum rate constant for an apparent COP+ TEA reaction is thus 23.5 M-ls-I, which exceeds their result of 16.8 M-ls-'. These calculations certainly suggest that the initial reaction was monoalkyl carbonate formation in their experiments. However, it would be difficult to deduce the true k3 rate constant from this data of Sada et al. since it

Ind. Eng.

Table IV. Transport Results with Triethylamine Solutions. One percent CO, in the gas phase, 1.0M total ionic strength exptl predicteda nominal exptl amine flux rate con- rate conconcn, M ratio stant, s-l stant, s - l 1.22 1.26 1.37

0.30 0.395 0.50

Given by 0.037

+

0.14

0.19

0.16

0.23 0.27

0.24

8500 [OH-] (Edsall, 1 9 6 9 ) .

is probable that the OH-. concentration was decreasing. Another study of the C0,-TEA system was reported by Hikita et al. (19771, who used a rapid mixing method followed by an observation tube in which the extent of reaction was determined from the change in temperature. They also argue that the reaction should be pseudo first order with respect to C02since the change in TEA is small, and claim that the data were consistent with these assumptions. Monoalkyl carbonate formation is the presumed reaction. As in the case of Sada et al., the reactive species is undoubtedly -CH20-, which is proportional to OH-, and it is not obvious that OH- should be constant. Their rate constant at 1M TEA is about 50 M-' s-l. Again, a maximum value of about 25 M-' s-l would be predicted as described previously. This discrepancy may mean that our extrapolated value of k3 is somewhat too small, or it might be related to their corrections for viscous heating. The results of Sada et al. and Hikita et al. may now be compared to our results. It has already been shown that kinetic parameters for monoalkyl carbonate formation which can account for the former's results are too small to account for our results. On the other hand, catalysis of the CO, hydration reaction by TEA would contribute only 3 M-l s-l to the total rate constant a t 1 M TEA in their experiments. This contribution is small relative to the total rate constant and would decrease linearly with decreasing TEA. The principal reason that our experiments feature hydration catalysis and their experiments feature monoalkyl carbonate is the pH difference of 2 units. Triethylamine. Several membrane transport experiments were done with triethylamine, which has no alcohol groups and is a stronger base than the ethanolamines. Ionic strength was 1 M. Facilitation was obtained, but the rate constants were comparable to values for the COz OH- reaction. Typical results are shown in Table IV. The small variation between the experimental rate constants and the predicted rate constants for the OH- reaction is probably due to inaccuracies in the corrected equilibrium constants at this high ionic strength. If there were a base catalysis contribution with a rate constant of 3 M-' s-l comparable to triethanolamine, the apparent rate constant would be only 0.04 at 0.5 M amine. Thus, it appears that the dominant reaction under our conditions is COP + OH-. It is probable that triethylamine has less catalytic activity than TEA since the former is a stronger base. Summary Our results for the kinetics of the CO, reaction with MEA and DEA a t low concentrations agree with results of other investigators and validate the experimental method for the study of CO, + amine reactions. No evidence was found for bicarbonate carrier transport in MEA solutions, which indicates that there is no significant hydrolysis of MEA carbamate to bicarbonate under our experimental conditions. A t higher concentrations the transport results indicate that both the MEA and DEA systems are more complex.

+

Chem. Fundam., Vol. 19, No. 3,

1980

265

Base catalysis of C 0 2 hydration by TEA is the only reasonable mechanism which is consistent with our data for the C02-TEA system. This reaction pathway is observable when the pH is 5 9 such that monoalkyl carbonate formation and the CO, + OH- reaction are suppressed. On the other hand, triethylamine appears to have less (if any) catalytic activity and acts only as a weak base to produce free OH- for reaction with CO, in our membrane system. Acknowledgment Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. Support was also provided by Xerox Corporation, Hooker Chemical Company, and E. I. du Pont de Nemours & Co., Inc. We also thank Harvey Palmer, Department of Chemical Engineering, and George McLendon, Department of Chemistry, for very helpful discussions. Appendix The equilibrium concentrations of all nontracer species in the membrane are calculated by solving the various equilibrium relationships, the total amine balance [Am] = [R3NH+]+ [R3N] + [R2NCOO-] (Al) and the electroneutrality equation [R3NH+]+ [H+] + [K'] = [R2NCOO-] + [OH-] + [HCOB-] + 2[CO:-] (A2) The potassium ion concentration is zero except for the experiments in which KHC03 was added. [H+]and [OH-] are negligible compared to the other species. Equilibrium constants are given in Table I and typical species concentrations are shown in Table 11. All experiments are carried out at 298 f 0.5 K. The gas phase contained 1% COP in Nz unless otherwise noted. The CO, solubility and diffusivity in water were 3.38 X g-mol L atm (International Critical Tables, 1928) and 1.97 X 10- cm2/s (Otto and Quinn, 1971). The C02solubility in amine solutions relative to water was taken from Sada et al. (1976a) and Clarke (1964). Viscosities of amine solutions were determined experimentally. Variation of D, with viscosity was estimated from the Stokes-Einstein approximation. The diffusivities of bicarbonate, monoethanolamine, and diethanolamine relative to C 0 2 were taken to be 0.58 (Donaldson and Quinn, 1975), 0.56, and 0.35 (Ibrahim and Kerloor, 1962), respectively. Diffusivities of the carbamates were assumed equal to the corresponding amine values. The diffusion path length L was determined from experiments with acidified water in which there is no facilitation. For BS membranes and FALP membranes, L was found to be 200 and 105 pm, respectively. Nomenclature C = concentration, mol cm-3 D = diffusion coefficient, cmPs-l F = dimensionless facilitation factor, defined in eq 8 K,, = reaction equilibrium constant for reaction 1, dimensionless k = reaction rate constant; pseudo-first-order rate constant,

h

S-1

k b = forward rate constant for reaction 1, M-' s-l k3 = forward rate constant for reaction 11, M-2

L = diffusional path length through membrane, cm R = functional groups of amines x = coordinate in direction of transport Greek Letters p = net rate of consumption by chemical reaction, mol cm-3 S-1

266

Ind. Eng. Chem. Fundam. lB80, 19, 266-275

4 = dimensionless modulus, defined in eq 9 J. = dimensionless flux ratio, defined in eq 5 and 7 Subscripts Am = amine species i = chemical species i Literature Cited Astarita. G., Marrucci, G., Giola, F., Chem. Eng. Sci., 19, 95 (1964). Clarke, J. K. A., Ind. Eng. Chern. Fundam., 3, 239 (1964). Coldrey, P. W., Harris, 1. J., Can. J. Chem. Eng., 54, 566 (1976). Danckwerts. P. V., Chem. Eng. Sci., 34, 443 (1979). Danckwerts. P. V., McNeil, K. M., Chem. Eng. Sci., 22, 925 (1967). Danckwerts, P. V., Sharma, M. M., 7% Chem. Eng., CE244 (Oct 1966). Dennard, A. E., Williams, R. J. P., J. Chem. Soc. A , 812 (1986). Dixon. D. C., Can. J. Chem. Eng., 55, 487 (1977). Donaidson, T. L., Quinn, J. A., Roc. Mtl. Acad. Sci. USA, 71, 4995 (1974). Donaldson, T. L., Quinn, J. A., Chem. Eng. Sci., 30, 103 (1975). Eberson, L., Chapter 6, "Acidity and Hydrogen Bonding of Carboxyl Groups", in "The Chemistry of Carboxylic Acids and Esters", S. Patai, Ed., Intersclence, New York, 1969. Edsaii, J. T.. "Carbon Dioxide, Carbonic Acid, and Bicarbonate Ion: Physical Propertiesand Kinetics of Interm-", in "CO,: Chemical, Bbchemkxi, and physiological Aspects", R. E. Forster, J. T. Edsall, A. B. Otis, and F. J. W. Roughton,.Ed., NASA SP-188, Washington, D.C., pp 15-27 1969. Emmert, R. E., Pigford, R. L., AIChE J., 8, 171 (1962).

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Received for review June 28, 1979 Accepted April 14, 1980

Postwithdrawal Drainage of a Viscoelastic Separan Solution Kartlc C. Khllar, Charles B. Welnberger, and John A. Tallmadge' Department of Chemical Engineering, Drexel University, Philadelphia, Pennsylvania 79 104

The transient profiles of draining films, formed initially by vertical withdrawal of a flat plate, were studied experimentally for a viscoelastic liquid. In comparison with Newtonian and relatively inelastic power-law liquids, the viscoelastic liquid initially produced a thinner and more slowly draining film. In addition, the viscoelastic coating film was found to have a more uniform thickness during the initial period of drainage. As expected, elastic responses appeared to be significant during withdrawal and negllgible at long drain times. Logarithmic plots of thickness vs. drain time were found to be approximated by two straight lines of different slope. Hence these plots were characterized by three parameters, which were the short-time slope, the long-time slope, and a transition time, at which time the change in slope occurs. The long-time slope agreed with that predicted using a purely viscous, power-law liquid model.

Introduction Drainage represents a situation where a film of liquid, adhering to a solid surface, drains down the solid and thus thins with time. Here the solid is stationary and liquid flows downward mainly due to gravity. Under many drainage conditions, the behavior of the draining film is affected by the film profile prior to drainage. There are many methods of obtaining a draining film, some of which involve liquid lowering, in which a liquid is moved down along a solid surface (Satterly and Givens, 1933; Deryagin, 1964; problem 2R in Bird et al., 1960). Others involve complete removal of the solid from a liquid bath (White and Tallmadge, 1965) or rotation to vertical of a horizontal surface containing a sessile drop (Denson, 1970). In this work, we form the draining film by partial withdrawal of a flat plate from a liquid bath. This withdrawal is partial because complete removal does not occur. This results in the two step process shown in Figure 1. Drainage of this type has been called postwithdrawal drainage (Lang and Tallmadge, 1971). Specifically the phrase "postwithdrawal drainage" designates the situation in which a finite object, initially immersed in a bath of 0196-4313/80/1019-0266$01.OO/O

wetting fluid, is withdrawn at constant speed from the bath but not completely removed (Figure lA), brought to rest, and the resultant fluid coating then allowed to drain down into the bath (Figure 1B). The solid lifting process is called unsteady withdrawal, during which the initial film profile is established, and the downward flow process occurring along the stationary solid is called postwithdrawal drainage. Film drainage after withdrawal occurs in dip coating processes, in measuring contact angle, and in rinsing electroplated parts and brass mill tubes. Other practical applications of film drainage and the interrelationships among drainage, withdrawal, and removal are discussed in a review article by Tallmadge and Gutfinger (1967). Most of the work on drainage has been done with Newtonian liquids. However, some industrial processes involve viscoelastic liquids, such as dip coating with paints or polymer melts. Postwithdrawal drainage with such fluids involves a complex case of transient flow of nonNewtonian liquids where both shear and elongation effects are important. Thus, for both application and scientific reasons, the authors are interested in studying postwithdrawal drainage of viscoelastic liquids. 0 1980 American Chemical Society