- Email: [email protected]
C5 ternary mixtures through the CA membrane
ELSEVIER
Desalination
149 (2002) 73-80
Pervaporation of methanolNTBEIC, ternary mixtures through the CA membrane Lin Zhang”, Huan-LinChen”*, Zhi-Jun Zhou”, Yin Lua, Cong-Jie Gaob “College of Materials Science and Chemical Engineering, Zhejiang University, Hangzhou 310027, Tel. +86 (571) 87952121; email: [email protected] “The Development Center of Water Treatment Technology, SOA, Hangzhou 310012 China
China
Received 3 February 2002; accepted 16 April 2002
Abstract The pervaporation separation properties for the MTBE/C,/methanol ternary system and three corresponding binary mixtures were measured with a cellulose acetate membrane. It was found that there are very high pervaporation properties for methanol/C, (the flux of methanol >430 g/m’.h). However, the flux of methanol for methanolNTBE is lower than 90 g/m’.h. The methanol concentrations in the permeate are similar for the two binary mixtures. From the result of ternary mixtures, the flux of methanol decreased from about 450 to 100 g/m’.h, with an increase of MTBE concentration in the feed from 5 to 50 wt%, and there is a strong accompany effect between methanol and MTBE. Based on Fick’s law and the accompany effect, the models of pervaporation flux and quasi-phase equilibrium of permeate components for the ternary mixture were advanced. The calculated values agreed with the experiment results. The models will be useful for separation process design of the MTBE/C,/methanol ternary mixture. Keywords:
Pervaporation;
MethanolDvlTBEK,;
Cellulose acetate membrane
1. Introduction
Organic mixtures, such as azeotropic mixtures or isomers, have traditionally been separated mainly by distillation, extraction and adsorption *Corresponding
processes; however, there are high capital investment and energy consumption for these separation technologies. Recently, much attention has been paid to the pervaporation process to separate organic mixtures because of its high separation efficiencies coupled with energy
author.
Presented at the International July 7-12, 2002
Congress
on Membranes
and Membrane
Processes
OOI I -9164/02/$- See front matter 0 2002 Elsevier Science B.V. All rights reserved PII:SOOII-9164(02)00694-X
(ICOM),
Toulouse,
France,
74
L. Zhang et al. /Desalination
saving, especially for the close boiling point and azeotropic mixtures. A great number of papers were published on pervaporation of organic mixtures, such as methanol/MTBE [l-7], ethanol/ ETBE [ 8,9], benzene/cyclohexane [ 10,111 and so on. MTBE is one component of these mixtures mainly used as an octane enhancer and a reagent in fine chemical production. It is produced by etherification of methanol with isobutylene, and the excess methanol is used in the reaction for high conversion yield. By now, the excess methanol will be separated by distillation. Cellulose acetate (CA) is an important membrane material; in 1988 a distillation-pervaporation hybrid process was proposed to separate the methanol/MTBE mixture using the CA membrane [l]. Since then some membranes on CA were studied for the methanol/ MTBE or the similar ethanol/ETBE mixtures. Cao et al. [2] studied the influence of acetylation degree of CA on pervaporation properties for the methanol/MTBE mixture. A blend membrane of CA and CAHP was made for separation of methanol from MTBE [3]. In recent years, more studies on pervaporation of methanol/MTBE mixtures were reported. Park et al. [4] prepared PVA membrane blended with PAA for pervaporation of this mixture. Nam and Lee [5] investigated the efficiency of pervaporation separation of methanol/ MTBE through a corn-posite membrane modified with sulfuric acid and four surfactants. Huang et al. [6] added anionic surfactants into the cationic chitosan solution, prepared chitosan/anionic surfactants complex membranes and tested their performance of pervaporation for the same mixture. To this day, the study on pervaporation is mainly concentrated on binary mixtures; in fact, most products to be separated are multiple mixtures in the petrochemical industry, such as methanol/MTBE/C, and cyclohexane/cyclohexanol/cyclohexanone. There is a large difference of pervaporation characteristics between ternary and binary mixtures because of the more complicated accompany effects for ternary
149 (2002) 73-80
mixtures. It is necessary to investigate the influence of accompany effects on pervaporation. The pervaporation performances for methanol/ MTBEK, ternary mixtures and corresponding binary mixtures through the CA membrane were measured. In addition, the methanol flux model with accompany effect was developed, and the quasi-phase equilibrium about the composing of permeation was advanced. 2. Experimental
2. I. Materials CA (39.1 wt% acetyl content) was purchased from the Shanghai Chemical Reagent Supply Station. The polyacrylonitrile (PAN) ultrafiltration membrane used as a support layer was supplied by the Development Center of Water Treatment Technology, Hangzhou. Methanol and acetone were of reagent grade. MTBE and C, were of industrial grade. All the products were used directly without further purifi-cation. Because the boiling point of C, is very low, it is difficult to experiment with pervaporation at the lab. The properties of C, and C, are similar, so C, is used instead of C, in the experiment. 2.2. Membrane preparation The casting solution of CA with a concentration of 8 g/100 mL was obtained by dissolving the polymers in acetone for 3 d at 30°C and then letting stand at room temperature. The membranes were prepared by casting polymer solutions onto a PAN ultrafiltration membrane. Pervaporation membranes were formed by slowly evaporating the solvent at about 30°C. 2.3. Pervaporation
experiment
The pervaporation experiments were conducted with equipment as reported previously [ 121. The vacuum system of the downstream side was maintained at about 150+30 Pa. The experiments were carried out in a continuous steady state. The
75
L. Zhang et al. / Desalination 149 (2002) 73-80
permeate was condensed by liquid N,. The pervaporation properties are characterized by the permeate flux, J, and the separation factor, a. The fluxes are determined by measuring the weight of liquid collected during a certain time at steadystate conditions. 3. Theory 3. I. Hypothesis
of the model
In the study, the following hypothesis can be obtained, according to the experiment conditions: 1. The current velocity of the feed is greater than 0.4 m/s in the pervaporation tank, and it can be considered turbulent current. 2. The thickness of the membrane is uniform, and the membrane is isotropic. 3. All components will transfer in the membrane at one dimension, and the mass transfer resistance can be ignored in the supporting layer (PAN ultrafiltration asymmetric membrane). 4. For the pressure of downstream side is very low. the components at the downstream side are ideal gas, and the resistance of vaporization at the downstream side can be ignored. 3.2. Flux model with the accompany effect Based on solution-diffusion theory, the transfer of pure component, i, in the membrane will accord with Fick’s law (Fig. 1). The resistance of the boundary layer can be left out, and the principal concentration substitute for the concentration at the membrane surface,
for the flow of the feed is the turbulent current. From Fick’s equation, the equation of flux for component i can be gained, as Eq (1): Jz: = 4;
(4 -
pl’)/I
(1)
where pj(=x,/SjJ and P,‘(=x,‘/S,) are partial pressures at upstream and downstream, respectively. K,(=D,Sb,) is defined as the permeability coefficient, which is a temperature function; other symbols are listed in the list of symbols. 3.3. Quasi-phase
equilibrium model
There are internal relations between the content of the feed and that of the permeation, so the equation to predicate the composition in the permeation will be attempted. It is assumed that the membrane is isotropic, and the membrane is divided into n layers. At the membrane surface, IZ = 1; that is, the first layer, component i, is absorbed and dissolved, and the concentration is X,,. The relation between X,,,,_,and X,,, which are concentrations of component i in the m layer and the m-l layer, can be estimated by following equation: Xinl = c, xim_,
(2)
where C,j is the coefficient of distribution and is determined by the feature of the membrane, component i andj. It is a constant at stationary temperature. Based on the Hildebrand equation [ 141, when the concentration of component i in membrane is X,, the enthalphy of mixing can be estimated: =
m II?
(4 -4J2Kv,,(l-xi) XJV;-V,)+ v,
(3)
Dividing by X,, taking the limit as Xj goes to zero, it is found that F, = lim $=(fi, -~
tl
I
Fig. 1. Transfer of component i in the membrane.
,
-s,)‘v,
(4)
From the definition of chemical potential, the free energy of pervaporation process can be obtained:
L. Zhanget al. /Desalination
76
149 (2002) 73-80
where, is the coefficient of the accompany effect $(= k,C,;-‘) . The selectivity coefficient for component i of binary mixtures in membrane is defined as
feet comes from the composition of the feed. Figs. 3 and 4 give methanol fluxes for methanol/ MTBE and methanol/C, mixtures, respectively, when the operating temperature is 298.1 SK. There is a high methanol flux for methanol/C, and a low methanol flux for the methanol/MTBE mixture; a strong accompany effect exists between methanol and MTBE. Where B, and B, are
q, = exp[(S, - S,,,)2V$‘Yxj IRT]
B, = 0.14366 - 0.03173 exp(- xi /0.03249)
(13)
Bik = {4.154-1.6723exp[(0.0075-x,)/0.0373$
(14)
AC = (S, - &,, )’ ViX;
(5)
AC = (6, - S,,,)‘V;~,x,
(6)
The percent of permeation the following equation: y; =r&x,qs
/(v,x,
(7)
can be cal-culated
+ QjXjP,f)
I(34.20178, -0.11499 (8)
4. Results and discussion 4. I. The methanol flux From experiment data, the permeability coefficients of three pure components in Eq. (1) are evaluated. -K,
= 1928.39
-115.74exp[(T-280.01)/11.5] -K,
=14.17-2.06exp[(T-300)/10.00]
-K,
=8.289
- 0.38exp[(T - 285.00)/93.20]
(9)
(10)
(11)
Fig. 2 shows the fluxes for experimental and calculated fluxes of three components; there are agreements between values of experiment and calculation. For binary mixtures, there is an accompany effect in the pervaporation process; the flux equation can be written as J, = -B,K,
(x,p,’ +)/I
(12)
where B,, is the accompany coefficient and it represents the nonideality of the feed. B,, is a function of the feed concentration, for the accompany ef-
From Figs. 3 and 4, it is found that the calculated values are in good agreement with the results of the experiments. In the ternary mixture, the accompany coefficient to component i, B,, can be derived from B, and B, and it is calculated using the following equation: B,, =B, B+,+Xk)/Xk(X,+X,) rk IJ @
(13
Fig. 5 shows the results of the calculated methanol flux for the methanol/MTBE/C, ternary mixture, as the concentration of MTBE is constant. Fig. 6 gives the comparison between calculated values and experimental fluxes of methanol for this ternary mixture under the conditions of stationary methanol concentration and temperature. 4.2. Composing of permeate Figs. 7-9 show the fitting results of the composition of permeation for methanol/MTBE, methanol/C, and MTBE/C, mixtures, respectively. The Powell optimization method is used, and the objective function is OD=$, ,I=,
%I,,
(16)
From three figures, the methanol concentrations in the permeate is similar, and C,NTBE mixture hardly be separated with the CA membrane. In
77
L. Zhang et al. /Desalination 149 (2002) 73-80
1 4ax
G-SJL! . LJ< -Je -Jc
am 3504 * 003
,
.
0.m
,
.,
0.a
.,
.,
.,
.
aai
006
a03
cm
a07
UleweigafaclandMeOHhfeed
Fig. 2. Calculated and experimental fluxes of three pure components through CA membrane mixtures.
Fig. 3. Calculated and experimental fluxes of MeOH for MeOHK, through CA membrane mixtures.
loo-l
,
O.@
Fig. 4. Calculated and experimental fluxes of MeOH for MeOH/MTBE through CA membrane.
addition, it is found that the calculated agreed with experiment results. 4.3. Analysis of the accompany
values
effect
From the results of the pervaporation experiments (Figs. 4,6,8), it is proved that there is a strong accompany effect between methanol and MTBE,
.
1
.
,
.
,
0.04 006 wm ihew$jWdcndMeOHfeixl
,
,
0.10
Fig. 5. Comparison between calculated values and experimental fluxes of methanol for the ternary mixture in the condition of invariable MTBE concentration. which impedes on the transfer of methanol in the CA membrane. The solubility parameter is an intrinsic physicochemical property of a substance, which can be used to explain the structure-activity relationship. Hansen [ 141 divided the conventional solubility parameter into three partial parameters: dispersion, b;; dipole, b; and hydrogen bonding,
L. Zhang et al. /Desalination
78
ww 00
02
01
0.3
0.4
149 (2002) 73-80
0.5
ihewfAghthadjonofMlBEhfeed
Fig. 6. Comparison between calculated values and experimental fluxes of methanol for the ternary mixture in the condition of invariable methanol concentration.
Fig. 7. Comparison of the calculated and experimental composition of permeation for the methanol/M’IBE mixture. V.”
I
ulehevalueci~
.“_. ^“.”fit$d
v&e
T,,496.15
04
/
i
OW
I
I
m
1
004
OS6
I
O.C8
&w24
00.1 0.0
0.1
0.2
0.3
04
I 5
%lrF
Fig. 8. Comparison of the calculated and experimental composition of permeation for the methanol/C, mixture.
Fig. 9. Comparison of the calculated and experimental composition of permeation for the MTESEK, mixture.
S,l. All three partial solubility parameters of CA, methanol, MTBE and C, are listed in Table 1, and the parameters of MTBE are calculated through the group contribution method [ 131. The parameter UR is defined as Eq. (17) by Hansen, which is used to evaluate the interaction between the polymer and the solute, or two solutes. The smaller the value of ‘JR is, the stronger
the interaction between two substances is. Table 2 lists the values of URbetween CA and methanol and three solutes: methanol, MTBE and C,.
From Table 2, it is found that the interaction between CA and methanol is the largest, so the
79
L. Zhang et al. / Desalination 149 (2002) 73-80
Table 1 Three partial solubility parameters (MPa”‘) of CA, methanol, MTBE and C,
than 15%, and the models can be used to predicate the pervaporation separation for this ternary mixture.
Three partial solubility parameters, MPa”’ CA Methanol MTBE C5
dd
4
6h
15.54 15.13 15.48 13.90
16.30 12.27 3.63 4.10
12.94 22.29 5.22 0
Acknowledgment The authors gratefully acknowledge the financial support of the National Science Foundation of China (No. 29836160). Symbols
Table 2 Value of URbetween CA and methanol and three solutes: methanol, MTBE and C,
CA Methanol
Methanol
MTBE
CS
10.207
14.836 19.144
18.081 23.861
selectivity of methanol through the membrane is higher than that of MTBE and C,. The value of ‘JR between methanol and MTBE is lower than that of methanol with C,, the interaction between methanol and MTBE is stronger than that of methanol with C, and methanol transport in the membrane would be restrained by MTBE in the mixture. It is in agreement with the pervaporation results.
5. Conclusions 1. The high separation efficiencies can be obtained for the methanol/C, mixture through the CA membrane. However, for the methanolA4TBE mixture, there are a low methanol flux and a high separation selectivity, and the membrane cannot be used for separation of MTBE/C, mixture. 2. For the methanol/MTBE/C, ternary mixture, the flux of methanol will decrease, with increasing MTBE concentration in the feed. There is an accompany effect between methanol and MTBE. 3. The calculated values of the flux model and the quasi-phase equilibrium agree with the experiment results. The average errors are less
*I,
-
*,
-
‘li
-
D
-
F. _‘J
-
Accompany coefficient of componentj to i in the binary mixture Accompany coefficient of componentj and k to i in the ternary mixture Distribution coefficient of component i between the conjoint layers of the membrane Diffusion coefficient of the component in the membrane, g.mm/m2.h Constant, defined by C,; and k; Flux, g/m2.h Permeability coefficient of component i in the membrane, g.mm/mzh Adsorption coefficient of the component in the membrane surface Membrane thickness, mm Partial pressure and saturation pressure of component i, respectively, kPa Proportionality constant between molar fraction and partial pressure of component i, l/KPa Molar volume of component i and total volume, respectively, cm3/mol Mass fraction of component i in the feed Mass fraction of component i in the membrane Mass fraction of component i in the permeate Separation factor Hansen’s solubility parameter, MPa’” Selection coefficient of component i in the membrane Chemical potential .I
J
-
K,
-
ki
-
1 Pi, PiJ -
s, y,VT-
2, Y,
-
a s V,
-
/J
-
80
‘PI
L. Zhang et al. /Desalination
- Volume fraction of component
i
References [II
PI
131
[41
[51
[61
[71
MS. Chen, R.M. Eng, J.L. Glazer and C.G Wensley, Pervaporation process for separating alcohol from ethers, U.S. Patent 4,774,365 (1988). S.G. Cao, Y.Q. Shi and GW. Chen, Influence of acetylation degree of cellulose acetate on pervaporation properties for MeOI-I/MTBE mixture, J. Membr. Sci., 165 (2000) 89-97. M. Niang, GS. Luo and P Schaetzel, Pervaporation separation of MTBE/methanol mixtures using a highperformance blended membrane, J. Appl. Polym. Sci., 64 (1997) 875-882. H.C. Park, N.E. Ramaker, M.H.V. Mulder and C.A. Smolders, Separation of MTBE/methanol mixtures by pervaporation, Sep. Sci. Technol., 30 (1995) 419-433. S.Y. Nam and Y.M. Lee, Pervaporation separation of methanol/MTBE through chitosan composite membrane modified with surfactants, J. Membr. Sci., 157 (1999) 63-71. R.Y.M. Huang, GY. Moon and R. Pal, Chitosanl anionic surfactant complex membranes for the pervaporation separation of methanol/MTBE and characterization of the polymer/surfactant system, J. Membr. Sci., 184 (2001) I-15. L. Zhang, H.L. Chen, J.W. Qian and C.J. Gao, Effect
149 (2002) 73-80 of CA/PVB blend’s compatibility on separations of pervaporation membranes, Abstr. Am. Chem. Sot., 222 (2001) 90. PI G S. Luo, M. Niang and P. Schaetzel, A high performance membrane for sorption and pervaporation separation ETBE/ethanol mixtures, Sep. Sci. Technol., 34 (1999) 391401. 191 D. Roizard, A. Jonquieres, C. Leger et al., Alcohol/ ether separation by pervaporation. High performance membrane design, Sep. Sci. Technol., 34 (1999) 369390. [lOI S. Matsui and D.R. Paul, Pervaporation separation of aromaticlaliphatic hydrocarbons by cross-linked poly(methy1 acrylate-co-acrylic acid) membranes, J. Membr. Sci., 195 (2000) 229-245. t111 Y.C. Wang, C.L. Li, J. Huang et al., Pervaporation of benzenelcyclohexane mixtures through aromatic polyamide membranes, J. Membr. Sci., 185 (2001) 193-200. t121 C.L. Zhu, M. Liu, W. Xu and WC. Ji, A study on characteristics and enhancement of pervaporation membrane separation processes, Desalination, 71 (1989) 1-18. u31 T. Matsuura, Synthetic Membranes and Membrane Separation Processes, CRC Press, Boca Raton, FL, 1994, 145. 1141 A.F.M. Barton, CRC Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed., CRC Press, Boca Raton, FL, 1991.
Desalination
149 (2002) 73-80
Pervaporation of methanolNTBEIC, ternary mixtures through the CA membrane Lin Zhang”, Huan-LinChen”*, Zhi-Jun Zhou”, Yin Lua, Cong-Jie Gaob “College of Materials Science and Chemical Engineering, Zhejiang University, Hangzhou 310027, Tel. +86 (571) 87952121; email: [email protected] “The Development Center of Water Treatment Technology, SOA, Hangzhou 310012 China
China
Received 3 February 2002; accepted 16 April 2002
Abstract The pervaporation separation properties for the MTBE/C,/methanol ternary system and three corresponding binary mixtures were measured with a cellulose acetate membrane. It was found that there are very high pervaporation properties for methanol/C, (the flux of methanol >430 g/m’.h). However, the flux of methanol for methanolNTBE is lower than 90 g/m’.h. The methanol concentrations in the permeate are similar for the two binary mixtures. From the result of ternary mixtures, the flux of methanol decreased from about 450 to 100 g/m’.h, with an increase of MTBE concentration in the feed from 5 to 50 wt%, and there is a strong accompany effect between methanol and MTBE. Based on Fick’s law and the accompany effect, the models of pervaporation flux and quasi-phase equilibrium of permeate components for the ternary mixture were advanced. The calculated values agreed with the experiment results. The models will be useful for separation process design of the MTBE/C,/methanol ternary mixture. Keywords:
Pervaporation;
MethanolDvlTBEK,;
Cellulose acetate membrane
1. Introduction
Organic mixtures, such as azeotropic mixtures or isomers, have traditionally been separated mainly by distillation, extraction and adsorption *Corresponding
processes; however, there are high capital investment and energy consumption for these separation technologies. Recently, much attention has been paid to the pervaporation process to separate organic mixtures because of its high separation efficiencies coupled with energy
author.
Presented at the International July 7-12, 2002
Congress
on Membranes
and Membrane
Processes
OOI I -9164/02/$- See front matter 0 2002 Elsevier Science B.V. All rights reserved PII:SOOII-9164(02)00694-X
(ICOM),
Toulouse,
France,
74
L. Zhang et al. /Desalination
saving, especially for the close boiling point and azeotropic mixtures. A great number of papers were published on pervaporation of organic mixtures, such as methanol/MTBE [l-7], ethanol/ ETBE [ 8,9], benzene/cyclohexane [ 10,111 and so on. MTBE is one component of these mixtures mainly used as an octane enhancer and a reagent in fine chemical production. It is produced by etherification of methanol with isobutylene, and the excess methanol is used in the reaction for high conversion yield. By now, the excess methanol will be separated by distillation. Cellulose acetate (CA) is an important membrane material; in 1988 a distillation-pervaporation hybrid process was proposed to separate the methanol/MTBE mixture using the CA membrane [l]. Since then some membranes on CA were studied for the methanol/ MTBE or the similar ethanol/ETBE mixtures. Cao et al. [2] studied the influence of acetylation degree of CA on pervaporation properties for the methanol/MTBE mixture. A blend membrane of CA and CAHP was made for separation of methanol from MTBE [3]. In recent years, more studies on pervaporation of methanol/MTBE mixtures were reported. Park et al. [4] prepared PVA membrane blended with PAA for pervaporation of this mixture. Nam and Lee [5] investigated the efficiency of pervaporation separation of methanol/ MTBE through a corn-posite membrane modified with sulfuric acid and four surfactants. Huang et al. [6] added anionic surfactants into the cationic chitosan solution, prepared chitosan/anionic surfactants complex membranes and tested their performance of pervaporation for the same mixture. To this day, the study on pervaporation is mainly concentrated on binary mixtures; in fact, most products to be separated are multiple mixtures in the petrochemical industry, such as methanol/MTBE/C, and cyclohexane/cyclohexanol/cyclohexanone. There is a large difference of pervaporation characteristics between ternary and binary mixtures because of the more complicated accompany effects for ternary
149 (2002) 73-80
mixtures. It is necessary to investigate the influence of accompany effects on pervaporation. The pervaporation performances for methanol/ MTBEK, ternary mixtures and corresponding binary mixtures through the CA membrane were measured. In addition, the methanol flux model with accompany effect was developed, and the quasi-phase equilibrium about the composing of permeation was advanced. 2. Experimental
2. I. Materials CA (39.1 wt% acetyl content) was purchased from the Shanghai Chemical Reagent Supply Station. The polyacrylonitrile (PAN) ultrafiltration membrane used as a support layer was supplied by the Development Center of Water Treatment Technology, Hangzhou. Methanol and acetone were of reagent grade. MTBE and C, were of industrial grade. All the products were used directly without further purifi-cation. Because the boiling point of C, is very low, it is difficult to experiment with pervaporation at the lab. The properties of C, and C, are similar, so C, is used instead of C, in the experiment. 2.2. Membrane preparation The casting solution of CA with a concentration of 8 g/100 mL was obtained by dissolving the polymers in acetone for 3 d at 30°C and then letting stand at room temperature. The membranes were prepared by casting polymer solutions onto a PAN ultrafiltration membrane. Pervaporation membranes were formed by slowly evaporating the solvent at about 30°C. 2.3. Pervaporation
experiment
The pervaporation experiments were conducted with equipment as reported previously [ 121. The vacuum system of the downstream side was maintained at about 150+30 Pa. The experiments were carried out in a continuous steady state. The
75
L. Zhang et al. / Desalination 149 (2002) 73-80
permeate was condensed by liquid N,. The pervaporation properties are characterized by the permeate flux, J, and the separation factor, a. The fluxes are determined by measuring the weight of liquid collected during a certain time at steadystate conditions. 3. Theory 3. I. Hypothesis
of the model
In the study, the following hypothesis can be obtained, according to the experiment conditions: 1. The current velocity of the feed is greater than 0.4 m/s in the pervaporation tank, and it can be considered turbulent current. 2. The thickness of the membrane is uniform, and the membrane is isotropic. 3. All components will transfer in the membrane at one dimension, and the mass transfer resistance can be ignored in the supporting layer (PAN ultrafiltration asymmetric membrane). 4. For the pressure of downstream side is very low. the components at the downstream side are ideal gas, and the resistance of vaporization at the downstream side can be ignored. 3.2. Flux model with the accompany effect Based on solution-diffusion theory, the transfer of pure component, i, in the membrane will accord with Fick’s law (Fig. 1). The resistance of the boundary layer can be left out, and the principal concentration substitute for the concentration at the membrane surface,
for the flow of the feed is the turbulent current. From Fick’s equation, the equation of flux for component i can be gained, as Eq (1): Jz: = 4;
(4 -
pl’)/I
(1)
where pj(=x,/SjJ and P,‘(=x,‘/S,) are partial pressures at upstream and downstream, respectively. K,(=D,Sb,) is defined as the permeability coefficient, which is a temperature function; other symbols are listed in the list of symbols. 3.3. Quasi-phase
equilibrium model
There are internal relations between the content of the feed and that of the permeation, so the equation to predicate the composition in the permeation will be attempted. It is assumed that the membrane is isotropic, and the membrane is divided into n layers. At the membrane surface, IZ = 1; that is, the first layer, component i, is absorbed and dissolved, and the concentration is X,,. The relation between X,,,,_,and X,,, which are concentrations of component i in the m layer and the m-l layer, can be estimated by following equation: Xinl = c, xim_,
(2)
where C,j is the coefficient of distribution and is determined by the feature of the membrane, component i andj. It is a constant at stationary temperature. Based on the Hildebrand equation [ 141, when the concentration of component i in membrane is X,, the enthalphy of mixing can be estimated: =
m II?
(4 -4J2Kv,,(l-xi) XJV;-V,)+ v,
(3)
Dividing by X,, taking the limit as Xj goes to zero, it is found that F, = lim $=(fi, -~
tl
I
Fig. 1. Transfer of component i in the membrane.
,
-s,)‘v,
(4)
From the definition of chemical potential, the free energy of pervaporation process can be obtained:
L. Zhanget al. /Desalination
76
149 (2002) 73-80
where, is the coefficient of the accompany effect $(= k,C,;-‘) . The selectivity coefficient for component i of binary mixtures in membrane is defined as
feet comes from the composition of the feed. Figs. 3 and 4 give methanol fluxes for methanol/ MTBE and methanol/C, mixtures, respectively, when the operating temperature is 298.1 SK. There is a high methanol flux for methanol/C, and a low methanol flux for the methanol/MTBE mixture; a strong accompany effect exists between methanol and MTBE. Where B, and B, are
q, = exp[(S, - S,,,)2V$‘Yxj IRT]
B, = 0.14366 - 0.03173 exp(- xi /0.03249)
(13)
Bik = {4.154-1.6723exp[(0.0075-x,)/0.0373$
(14)
AC = (S, - &,, )’ ViX;
(5)
AC = (6, - S,,,)‘V;~,x,
(6)
The percent of permeation the following equation: y; =r&x,qs
/(v,x,
(7)
can be cal-culated
+ QjXjP,f)
I(34.20178, -0.11499 (8)
4. Results and discussion 4. I. The methanol flux From experiment data, the permeability coefficients of three pure components in Eq. (1) are evaluated. -K,
= 1928.39
-115.74exp[(T-280.01)/11.5] -K,
=14.17-2.06exp[(T-300)/10.00]
-K,
=8.289
- 0.38exp[(T - 285.00)/93.20]
(9)
(10)
(11)
Fig. 2 shows the fluxes for experimental and calculated fluxes of three components; there are agreements between values of experiment and calculation. For binary mixtures, there is an accompany effect in the pervaporation process; the flux equation can be written as J, = -B,K,
(x,p,’ +)/I
(12)
where B,, is the accompany coefficient and it represents the nonideality of the feed. B,, is a function of the feed concentration, for the accompany ef-
From Figs. 3 and 4, it is found that the calculated values are in good agreement with the results of the experiments. In the ternary mixture, the accompany coefficient to component i, B,, can be derived from B, and B, and it is calculated using the following equation: B,, =B, B+,+Xk)/Xk(X,+X,) rk IJ @
(13
Fig. 5 shows the results of the calculated methanol flux for the methanol/MTBE/C, ternary mixture, as the concentration of MTBE is constant. Fig. 6 gives the comparison between calculated values and experimental fluxes of methanol for this ternary mixture under the conditions of stationary methanol concentration and temperature. 4.2. Composing of permeate Figs. 7-9 show the fitting results of the composition of permeation for methanol/MTBE, methanol/C, and MTBE/C, mixtures, respectively. The Powell optimization method is used, and the objective function is OD=$, ,I=,
%I,,
(16)
From three figures, the methanol concentrations in the permeate is similar, and C,NTBE mixture hardly be separated with the CA membrane. In
77
L. Zhang et al. /Desalination 149 (2002) 73-80
1 4ax
G-SJL! . LJ< -Je -Jc
am 3504 * 003
,
.
0.m
,
.,
0.a
.,
.,
.,
.
aai
006
a03
cm
a07
UleweigafaclandMeOHhfeed
Fig. 2. Calculated and experimental fluxes of three pure components through CA membrane mixtures.
Fig. 3. Calculated and experimental fluxes of MeOH for MeOHK, through CA membrane mixtures.
loo-l
,
O.@
Fig. 4. Calculated and experimental fluxes of MeOH for MeOH/MTBE through CA membrane.
addition, it is found that the calculated agreed with experiment results. 4.3. Analysis of the accompany
values
effect
From the results of the pervaporation experiments (Figs. 4,6,8), it is proved that there is a strong accompany effect between methanol and MTBE,
.
1
.
,
.
,
0.04 006 wm ihew$jWdcndMeOHfeixl
,
,
0.10
Fig. 5. Comparison between calculated values and experimental fluxes of methanol for the ternary mixture in the condition of invariable MTBE concentration. which impedes on the transfer of methanol in the CA membrane. The solubility parameter is an intrinsic physicochemical property of a substance, which can be used to explain the structure-activity relationship. Hansen [ 141 divided the conventional solubility parameter into three partial parameters: dispersion, b;; dipole, b; and hydrogen bonding,
L. Zhang et al. /Desalination
78
ww 00
02
01
0.3
0.4
149 (2002) 73-80
0.5
ihewfAghthadjonofMlBEhfeed
Fig. 6. Comparison between calculated values and experimental fluxes of methanol for the ternary mixture in the condition of invariable methanol concentration.
Fig. 7. Comparison of the calculated and experimental composition of permeation for the methanol/M’IBE mixture. V.”
I
ulehevalueci~
.“_. ^“.”fit$d
v&e
T,,496.15
04
/
i
OW
I
I
m
1
004
OS6
I
O.C8
&w24
00.1 0.0
0.1
0.2
0.3
04
I 5
%lrF
Fig. 8. Comparison of the calculated and experimental composition of permeation for the methanol/C, mixture.
Fig. 9. Comparison of the calculated and experimental composition of permeation for the MTESEK, mixture.
S,l. All three partial solubility parameters of CA, methanol, MTBE and C, are listed in Table 1, and the parameters of MTBE are calculated through the group contribution method [ 131. The parameter UR is defined as Eq. (17) by Hansen, which is used to evaluate the interaction between the polymer and the solute, or two solutes. The smaller the value of ‘JR is, the stronger
the interaction between two substances is. Table 2 lists the values of URbetween CA and methanol and three solutes: methanol, MTBE and C,.
From Table 2, it is found that the interaction between CA and methanol is the largest, so the
79
L. Zhang et al. / Desalination 149 (2002) 73-80
Table 1 Three partial solubility parameters (MPa”‘) of CA, methanol, MTBE and C,
than 15%, and the models can be used to predicate the pervaporation separation for this ternary mixture.
Three partial solubility parameters, MPa”’ CA Methanol MTBE C5
dd
4
6h
15.54 15.13 15.48 13.90
16.30 12.27 3.63 4.10
12.94 22.29 5.22 0
Acknowledgment The authors gratefully acknowledge the financial support of the National Science Foundation of China (No. 29836160). Symbols
Table 2 Value of URbetween CA and methanol and three solutes: methanol, MTBE and C,
CA Methanol
Methanol
MTBE
CS
10.207
14.836 19.144
18.081 23.861
selectivity of methanol through the membrane is higher than that of MTBE and C,. The value of ‘JR between methanol and MTBE is lower than that of methanol with C,, the interaction between methanol and MTBE is stronger than that of methanol with C, and methanol transport in the membrane would be restrained by MTBE in the mixture. It is in agreement with the pervaporation results.
5. Conclusions 1. The high separation efficiencies can be obtained for the methanol/C, mixture through the CA membrane. However, for the methanolA4TBE mixture, there are a low methanol flux and a high separation selectivity, and the membrane cannot be used for separation of MTBE/C, mixture. 2. For the methanol/MTBE/C, ternary mixture, the flux of methanol will decrease, with increasing MTBE concentration in the feed. There is an accompany effect between methanol and MTBE. 3. The calculated values of the flux model and the quasi-phase equilibrium agree with the experiment results. The average errors are less
*I,
-
*,
-
‘li
-
D
-
F. _‘J
-
Accompany coefficient of componentj to i in the binary mixture Accompany coefficient of componentj and k to i in the ternary mixture Distribution coefficient of component i between the conjoint layers of the membrane Diffusion coefficient of the component in the membrane, g.mm/m2.h Constant, defined by C,; and k; Flux, g/m2.h Permeability coefficient of component i in the membrane, g.mm/mzh Adsorption coefficient of the component in the membrane surface Membrane thickness, mm Partial pressure and saturation pressure of component i, respectively, kPa Proportionality constant between molar fraction and partial pressure of component i, l/KPa Molar volume of component i and total volume, respectively, cm3/mol Mass fraction of component i in the feed Mass fraction of component i in the membrane Mass fraction of component i in the permeate Separation factor Hansen’s solubility parameter, MPa’” Selection coefficient of component i in the membrane Chemical potential .I
J
-
K,
-
ki
-
1 Pi, PiJ -
s, y,VT-
2, Y,
-
a s V,
-
/J
-
80
‘PI
L. Zhang et al. /Desalination
- Volume fraction of component
i
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