Ind. E n g . Chem. Res. 1988,27, 1895-1900
1895
Pervaporation of Methanol-Ethylene Glycol with Cellophane Membrane: Some Mechanistic Aspects? Indrani Ghosh, Shyamal K. Sanyal, and Ram N. Mukherjea* Chemical Engineering Department, Jadavpur University, Calcutta 700032, India
The effect of different parameters on the separation by pervaporation of a methanol-ethylene glycol mixture with cellophane membrane, at 1.01 X lo5 P a upstream pressure and 13.3-Pa downstream pressure, was investigated. Although total permeation rates increased with increasing methanol content in feed and with increasing temperature, selectivities decreased, the effect of agitation being negligible. The results indicated the importance of sorption and diffusion behavior of the permeants on the pervaporation mechanism, and an anomalous sorption-permeation behavior was presumably caused by polymer-liquid interactions in the membrane and the intrachain hydrogen bonding of the ethylene glycol. However, above 60% methanol content in feed, the effect of diffusion was much less pronounced, and selective separation of methanol was attributed to the preferential sorption of methanol at the upstream side of the membrane. The permselective behavior of dense polymeric membranes, displaying a preferential affinity for one of the components in a mixture of liquids, is the basis of separation in the pervaporation process. The mechanism of pervaporation of binary mixtures is complicated by the affinities which relate to thermodynamic liquid-liquid interactions of the permeating mixtures and the polymer-liquid interactions, thus resulting in nonlinear transport with respect to the permeant concentration. Fels and Huang (1971) developed a model which was based on single-component permeation and on an extension of the free-volume theory for diffusion of organic substances in polymers. I t provided an insight into the effect of one permeating component on another. However, by using concentration-dependent diffusion coefficients based on Fick's law, Greenlaw et al. (1977) developed more appropriate correlations of the interactions between membrane and permeants that were capable of describing coupled transport behavior in swollen membranes. In light of the three-step solution-diffusion theory of mass transport through the membrane, consisting of sorption, diffusion, and desorption from the membrane (Binning et al., 1961), and on assuming that sorption increased the diffusivities of penetrants through the membrane due to substantial swelling of the membrane matrix, Rautenbach and Albrecht (1980) and Brun et al. (1985) developed models for the prediction of flux and selectivities of pervaporation of binary mixtures. The mechanistic aspects of pervaporation of binary mixtures were studied by several workers. Suzuki et al. (1981, 1987) and Suzuki and Onozato (1983) investigated the pervaporation of different liquid mixtures and analyzed the transport phenomena with regard to the effect of mixing of liquids on solubility and diffusivity of permeants. They suggested that, if the liquid component had a plasticizing effect on the polymer membrane, a synergetic effect of liquid mixtures on the diffusion rate would be observed. Larchet et al. (1983) studied the effect of different operating parameters on membrane performance and emphasized the importance of the thermodynamic interactions within the system and the role of sorption and diffusion in the separation mechanism. The physicochemical parameters like molar volume, polarities, solubilities in the membrane, and membrane morphology were also found to be important in the pervaporation mecha'Dedicated to Prof. W. Funke, Institute fur Technische Chemie der Universitaet Stuttgart, West Germany, on the occasion of his 60th birthday. 0888-5885/88/262~-1895$01.50/0
nism as shown by Itoh et al. (1985). Thus, prediction of the separation mechanism of pervaporation appears to be quite complex, especially when some of the properties of the permeants have close similarities with those of the membrane (Table I), as in the case of the present study of the separation of methanol and ethylene glycol through a cellophane membrane. It may be mentioned here that this separation is industrially important in the manufacture of poly(ethy1ene terephthalate), in the polyester industry. The present investigation is aimed at establishing the effect of parameters like feed composition, temperature, and agitation on permeation rates and selectivities. Binary sorption measurements were made in order to determine any permeant-membrane interactions. Finally, apparent activation energies and integral diffusivities were calculated in order to make an interpretation of the mechanistic aspects of the pervaporation process. Experimental Section Materials. The membrane used was commercially available cellophane film (PT 300 of Kesoram Rayon Ltd., India; thickness, 0.025 mm; density, 1.41 g/cm3). Thickness uniformity was checked by a micrometer caliper. Total membrane area was 0.0038 m2. Methanol and ethylene glycol (AR grade, E. Merck) were used without further purification. Analysis. The feed and permeate compositions were analyzed at 30 "C by measuring the refractive indices with an Abbey-type refractometer (Erma, Japan). Pervaporation Apparatus. The batch steady-state pervaporation runs were carried out in a permeation cell as shown in Figure 1. The cell was made from two 12.25-cm-0.d. and 8.8-cm-i.d. aluminum flanges. The membrane was supported by a porous aluminum disk of sufficient porosity to avoid disturbing the equlibrium at the downstream interface. The upstream side was provided with a hot water circulating coil, an agitator, and a capillary tube to measure the permeation rates. Figure 2 shows a schematic diagram of the pervaporation setup. Procedure. At first, the membrane was placed over the porous disk, and the cell was bolted together. It was then evacuated for an hour to 13.3 Pa and the feed was introduced at the upper compartment. When the rate of fall in the capillary tube became constant, a steady-state permeation was assumed. Approximately 1-2 h was required to reach the steady state of permeation, depending on the feed composition and temperature, and hence a membrane was used only once for one such run. The 0 1988 American Chemical Society
1896 Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988 Table I. Froperties of System Components
system components ethylene glycol methanol cellophane (regenerated cellulose)
dielectric const
solubility parameter, 6, (cal/cm3)'I2
37 32.63 6.7-7.7
14.6 14.5 15.65
molar vol 55.6 40.2
hydrogen bonding group strongstrong strong
solubility in cellopharde, S, g/g of dry membrane at 30 "C at 40 "C 0.31 0.45
I
0.33 0.48
p
50'C
Figure 3. Dependence of total permeation rate, Jp,on the methanol concentration in the feed at 30, 35, 40, 45, and 50 "C. Figure 1. Schematic diagram of the permeation cell: (a) feed chamber, (b) condenser, (c) variable-speed motor, (d) hot-water circulation coil, (e) thermowell, (0 precision bore capillary tube, (9) rubber gasket, (h) wheel stirrer, (i) vapor removal tube, (j) porous aluminum disk, (k)membrane.
r---
1
2000 electrobalance (Cahn Instruments, Inc., Cerrites, CA). I t required about 2 h for complete desorption of the membrane. Membrane Performance and Separation Characteristics. The performance of pervaporation membranes used for fractionating a given liquid mixture is characterized by the total permeation rate, Jpin kg/(m2h), and the membrane selectivity or separation factor, a,which was determined by the weight fraction of methanol in the feed, X, and in the pervaporate, Y , measured at 30 "C. It is expressed with respect to the preferentially transferred species, in this case, methanol, as v I
1-Y
ff=-/--
Figure 2. Schematic diagram of permeation setup: (a) permeation cell, (b) constant-temperature bath, (c) feed point, (d) variable-range McLeod gauge, (e) cold traps for collection of vapor, (0 vacuum Pump.
permeation rate was measured by weighing the amount collected over a given period. The permeate was analyzed and returned to the feed compartment from time to time in order to maintain a constant composition of the feed. Reproducibility was good when the membrane was desorbed for 1 h before the start of the experiment. Sorption Measurement. The cellophane membrane was allowed to equilibrate in mixtures of various compositions at 30 "C. The swollen membranes were then desorbed under vacuum. The amounts sorbed were determined from the refractive indices of the sorbate which were collected in traps immersed in liquid nitrogen. The solubilities of methanol and ethylene glycol at 30 and 40 "C, in the cellophane membrane, as determined by similar experiments, are given in Table I. Diffusivity at Zero Concentration. The diffusivity at zero concentration, Do,at 30 "C, of methanol and ethylene glycol was measured by desorption experiments as described by Rogers et al. (1976). The equipment used to measure desorption as a function of time was a Cahn
/
v
A
1--x
Results and Discussion Steady-State Permeation and Separation. Steadystate permeabilities and separation factors of methanol and ethylene glycol through cellophane, at 1.01 X lo6 Pa upstream prssure and 13.3-Pa downstream pressure, are shown in Figures 3-6 and Figures 8-10, which indicated that both the permeabilities and separation factors were functions of feed composition and temperature. Effect of Feed Composition. Figure 3 shows the concentration dependence of the total permeation rates over the range of temperatures studied. Although the total permeation rates remained below the ideal flow rates (curve A, dotted lines), it increased with increasing methanol content in the feed. The individual permeation rates of the permeants at 30 and 40 OC were calculated from their total permeation rates and selectivities by
(3)
The plot of the individual permeation rates of methanol and that of the total permeation rates, with respect to methanol content in the feed (Figures 3 and 4),were found
Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988 1897 /
IL
t
/
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ea
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a'
zc
p/o
- .
a 0
30-
10
20
30 WT.1.
100-0
LO METHANOL
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60 FEED
70
80
90
100
Figure 4. Dependence of individual permeation rates of (A)methethylene glycol at 40, (0) methanol at 30, and ( 0 ) anol at 40, (0) ethylene glycol at 30 O C , on methanol concentration in feed.
to be similar in nature, while that of glycol showed a positive deviation from ideal. This suggests an enhanced permeation of glycol in the presence of methanol due to the plasticizing effect of methanol on the membrane. Inversely, the negative deviation of the permeation rate of methanol indicates a retarding effect of glycol on methanol permeation. A lowering of selectivities is thus expected with increasing methanol content in the feed. This is in agreement with our experimental results, as shown in Figure 5. High selectivities were evident up to low methanol contents (15%) for all the operating tempertures studied. Selectivitiesthereafter dropped rapidly until 60% methanol content in the feed, above which its fall was marginal. Figure 6 also shows the separation characteristics of the system, which indicates a selective permeation of methanol. The curve was somewhat similar to the vapor-liquid equilibrium diagram of methanol-ethylene glycol (Baker et al., 1964). It appears that, in the pervaporation process, an increased swelling with higher methanol content destroys the interchain hydrogen bonding within the cellophane structure (Mark et al., 1965) and increases the fractional free volume of the polymer. However, the membrane seems to attain a state of saturated plasticization around 60% methanol content in the feed, thereby allowing both of the permeants to diffuse out in the same manner. This phenomenon possibly accounts for the marked decrease in concentration dependence of selectivities at higher concentrations of methanol. Sorption Behavior of Binary Mixtures. Figure 7 shows the amounts of methanol and ethylene glycol sorbed at equilibrium into the membrane from different mixture compositions at 30 "C. Single-component methanol sorption was found to be higher than that of glycol, which also showed substantial sorption capacity into the membrane. Preferential sorption of methanol from its mixtures with glycol is probably due to its polarity being close to that of the membrane and its lower molar volume (Table
10
20
30 WT
'/a
I I LO 50 60 M E T H A N O L IN FEED
I L '0
80
Figure 5. Dependence of separation factor of methanol, a, on methanol concentration in the feed at ( 9 ) 30, (0) 35, (0) 40, ( 0 )45, and (v)50 O C .
Figure 6. Variation of methanol concentration in product with 30, (A) 40, and ( 0 )50 OC. methanol concentration in the feed at (0)
I). Here, it would be interesting to note that the nature of the plot of permeation ratios at 30 "C, with respect to methanol content in the feed (Figure 8), given by expressions 4 and 5, was similar to the sorption curves JrM
=
JiM/JiG
(4)
1898 Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988
W T '1. HEltlWOL IN F E E D
Figure 7. Dependence of sorption at 30 O C of ( 0 )methanol and (A) ethylene glycol on methanol concentration in the feed.
01 33
I
35
I
I
LO
i 5
50
7EMPERAlCLRE ' C
10-
0
t',
36-
Figure 9. Dependence of separation factor of methanol, a,on temperature at (a) 7.31%, (b) 15%, (c) 23%, (d) 32%, (e) 42%, (f) 52%, ( 9 ) 62%, (h) 74%, and (i) 86% methanol concentration in feed.
I
'$,
32
@ = I
\
WT % METHANOL IN
FEED
\
Figure 8. Dependence of permeation ratios at 30 "C of (0) methanol and ( 0 )ethylene glycol on methanol content in the feed.
(Figure 7 ) . This indicates a strong influence of the sorption of permeants on their permeation ratios. However, the sorption of ethylene glycol in the membrane was found to increase with the increase in glycol concentration in the feed, while its permeation rates were found to decrease (Figures 4 and 7). Thermodynamically the liquid mixture of methanol and ethylene glycol may be assumed to be almost ideal (Baker et al., 1964). Hence, liquid-liquid interactions may be neglected, and the anomalous sorption-permeation behavior is presumably caused by the liquid-polymer interactions and also by the tendency of ethylene glycol to form intrachain hydrogen bonding at higher concentrations of glycol, thus retarding its diffusion through the membrane. Effect of Temperature. The total and individual permeation rates (Figure 3 and 4) were found to increase considerably with temperature, while selectivities decreased (Figure 9). The solubilities of methanol and glycol also increased with temperature (Table I). Hence, it may be assumed that increased swelling of the membrane matrix at higher temperatures results in increased polymer
Figure 10. Dependence of permeation rate (total) on reciprocal temperature ( l / T ,K-l) at (a) 7.31%, (b) 15%, (c) 23%, (d) 32%, (e) 42%, (f) 62%, (g) 74%, (h) 86%, and (i) 100% methanol concentration in the feed.
segmental motions and destruction of a number of secondary valence bonds. This facilitates the transport of bulkier ethylene glycol molecules along with methanol, thus reducing the selectivities and increasing the permeation rates. Apparent Activation Energy of Pervaporation. On the assumption that Arrhenius' law is valid for pervaporation of mixtures, the apparent activation energies of pervaportion, E,, were estimated from the slopes of the plots of 6 (Figure 10) and were plotted against methanol log J , = f ( l / T ) (6)
Ind. Eng. Chem. Res., Vol. 27, No. 10, 1988 1899
I
I I
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1
HETHPM)L 001
0
L
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I2
I6
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2L
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36
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Figure 12. Desorption of methanol and ethylene glycol from cellophane at 30 O C .
content in the feed (Figure 11). The activation energy of pervaporation of ethylene glycol could not be measured due to its extremely low permeation rates, but on extrapolation, it was found to be around 38 kcal/mol. For 92.7% glycol in the feed, a value of 23.8 kcal/mol also indicated extremely difficult permeation. Thereafter, with increased methanol content in the feed, activation energies decreased significantly, suggesting that only a small quantity of methanol (15-20%) in the feed is required to initiate plasticization of the membrane. However, the rate of fall of activation energies, with increasing methanol content, was rather low above 60% methanol content. Since the apparent activation energy of pervaporation is considered to be mainly due to diffusion activation energy (Larchet et al., 1983), the above result seems to indicate that, at higher methanol concentration in the feed, separation characteristics are less dependent on the diffusion behavior of the permeants through the membrane. Diffusion of Permeants. Diffusivity at Zero Concentration. The values of Doat 30 "C, determined from the slopes of the desorption curves of methanol and ethylene glycol (Figure 121, were 0.104 X and 0.029 X cm2/s, respectively. The value of Doof the more permeating component methanol was about 3.5 times greater than that of glycol. However, these values of Do do not give an idea of the effect of one component on the diffusion of the other in binary permeation, and thus a knowledge of the integral diffusivities of the individual components in their mixtures would be more relevant in explaining the separation behavior of the present system. Integral Diffusivities at Steady State. The integral diffusivities, D, at 30 "C, of methanol and ethylene glycol were estimated from the values of equilibrium sorption from their mixtures (Figure 7 ) ,steady-state permeation rates (Figure 4), and the membrane thickness. Thus,
D = JiL/C,
(7)
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I
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,
io
I
20
,30
Lo
8
W T *I. METHANOL
$0
70
,
m
1
90
1
100
IN FKEO
Figure 13. Dependence of integral diffusivities at 30 OC of (0) methanol and ( 0 )ethylene glycol on methanol content in the feed.
The exponential concentration dependence of D of the permeants is shown in Figure 13. The integral difbivities of glycol were found to rise considerably at higher concentrations of methanol, while the rate of increase of the diffusivities of methanol, above 60% methanol content in feed, was not significant. It may therefore be inferred that pervaporation, from this stage onward, is predominantly governed by sorption behavior of permeants and polymediquid interactions in the membrane, rather than their diffusion behavior. Effect of Agitation. The pervaporation rates and selectivities remained unchanged in the range of stirrer speeds investigated (60-100 rpm). This suggests that, between 60 and 100 rpm, concentration polarization at the upstream boundary layer was negligible, and hence the pervaporation rates and selectivities of the process were not affected.
Ind. Eng. Chem. Res. 1988,27, 1900-1910
1900
Registry No, Methanol, 67-56-1;ethylene glycol, 107-21-1.
Conclusion Permeation rates and selectivities of pervaporation of methanol-ethylene glycol mixtures through a cellophane membrane were found to be functions of operating temperature and feed composition. The results indicated that the separation mechanism was governed by the sorptiondiffusion behavior of the permeants, the liquid-polymer interactions in the membrane, and the intrachain hydrogen bonding of ethylene glycol, the effect of liquid-liquid interactions being negligible. Above 60% methanol content in the feed, the effect of diffusion, however, was much less pronounced, and selective separation of methanol was attributed to the preferential sorption of methanol at the upstream side of the membrane. A more detailed analytical study of the liquid-polymer interactions is likely to elucidate further the exact mechanism of pervaporation of such binary mixtures.
Literature Cited Baker, T. H.; Fisher, G. T.; Roth, J. A. “Vapour-Liquid Equilibrium and Refractive Indices of the Methanol-Ethylene Glycol System”. J . Chem. Eng. Data 1964,9, 11-12. Binning, C. R.; Lee, R. J.; Jennings, J. R.; Martin, E. C. “Separation of Liquid Mixtures by Permeation”. Znd. Eng. Chem. 1961,53, 45-50. Brun, J. P.; Larchet, C.; Melet, R.; Bulvestre, G. “Modelling of the Pervaporation of Binary Mixtures Through Moderately Swelling, Non-Reacting Membranes”. J. Membrane Sci. 1985,23,257-283. Fels, M.; Huang, R. Y. M. “Theoretical Interpretation of the Effect of Mixture Composition on Separation of Liquids in Polymers”. J . Macromol. Sci. Phys. 1971,B5(1), 89-110. Greenlaw, F. W.; Shelden, R. A,; Thompson, E. V. “Dependence of Diffusive Permeation Rates on Upstream and Downstream Pressures 11. Two Component Permeant”. J. Membrane Sci. 1977, 2,333-348. Itoh, T.; Toya, H.; Ishihara, K.; Shinohara, I. “Design of Polymer Membrane with Permselectivity for Water-Ethanol Mixutre. I1 Preparation of Crosslinked Poly(methy1Acrylate) Membrane an Diethylene Triamine and its Permselectivity”. J . Appl. Polym. Sci. 1985,30, 179-188. Larchet, C.; Brun, J. P.; Guillou, M. “Separation of Benzene-nHeptane Mixture by Pervaporation with Elastomeric Membrane. Performance of Membranes”. J. Membrane Sci. 1983,15,81-96. Mark, H. F., Gaylord, N. G., Bikales, N. M., Eds. “Cellulose”. In Encyclopedia of Polymer Science and Technology; Interscience: New York, 1965;Vol. 111. Rautenbach, R.; Albrecht, R. “Separation of Organic Binary Mixtures by Pervaporation”. J. Membrane Sci. 1980, 7, 203-223. Rogers, C. E.; Fels, M.; Li, N. N. “Separation by Permeation through Polymeric Membranes”. In Recent Developments in Separation Science; Li, N. N., Ed.; CRC: Cleveland, OH, 1976;Vol. 11. Suzuki, F.; Onozato K. “Pervaporation of CH30H-H20 Mixture by Poly(methy1 L-glutamate) Membrane and Synergetic Effect of their Mixture on Diffusion Rate”. J. App. Polym. Sci. 1983,28, 1949-1956. Suzuki, F.; Onozato, K.; Takahashi, N. “Pervaporation of Athermal Mixture of Benzene-Toluene by Poly(ethy1ene terephthalate) Membrane and Synergetic Effect on Concentration Dependence of Diffusion Rate”. J . Appl. Polym. Sci. 1982,27, 2179-2188. Suzuki, F.; Onozato, K.; Yaegashi, H.; Masuko, T. “Pervaporation of Organic Solvents by Poly[bis( 2,2,2-trifluoroethoxy)phosphazene] Membrane”. J . Appl. Polym. Sci. 1987,34,2197-2204.
Acknowledgment We acknowledge the assistance extended to us by the Advanced Cryogencis Centre of Research, Calcutta, for kindly providing us with liquid nitrogen. We are also grateful to M/S. Kesoram Rayon Ltd., India, for supplying the cellophane films for our studies. Nomenclature
J, = total permeation rate, kg/(h m2) Ji = individual permeation rate, g/(cm2 s) J, = permeation ratio T = absolute temperature, K E, = apparent activation energy, kcal/mol Do= diffusivity at zero concentration, cm2/s D = integral diffusivity, cm2/s C, = g sorbed/cm3 dry membrane L = thickness of membrane, cm W , = weight of dry membrane, mg W , = weight of solvent saturated membrane, mg W , = weight of membrane after time t, mg Subscripts
Received for reuiew December 2, 1987 Revised manuscript receiued May 17,1988 Accepted June 4,1988
M = methanol G = ethylene glycol
Simulation and Optimization of Three-phase Distillation Processes Jeffrey P. Kingsley and Angelo Lucia* Department of Chemical Engineering, Clarkson University, Potsdam, New York 13676
The relationship between two-phase and three-phase solutions to heterogeneous distillation simulation and optimization problems is studied. Simulation results illustrate that bifurcation points can occur in the two-phase solutions and that, in regions of steady-state two-phase solution multiplicity, not all two-phase solutions can be used to compute a three-phase solution. Numerical difficulties are attributed to marked differences in the separation performed by the two- and three-phase solutions and to ill-conditioning when a second liquid phase is present in small amount. The optimization study shows that multiple local optima with different numbers of three-phase trays can occur. These local optima need not be spurious and indicate that some global optimization method is required to guarantee the correct solution is located. Accordingly, the tunneling algorithm for global optimization is used to solve a three-phase distillation optimization problem. Results show that tunneling can be used to successfully find the global solution. In this manuscript, we are primarily concerned with building an understanding of the various solutions to heterogeneous distillation processes. In particular, we are
* Author to whom correspondence should be addressed. 0888-5885/88/2627-1900$01.50/0
interested in the relationships between homogeneous (two-phase) and heterogeneous (three-phase) solutions to the same problem and in the associated implications of these relationships. Recently there have been a number of simulation papers 0 1988 American Chemical Society
