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(Vapor + liquid) equilibria for the {water + poly(ethylene glycol diacetyl ether) (PEGDAE) and methanol + PEGDAE} systems
J. Chem. Thermodynamics 39 (2007) 483–487 www.elsevier.com/locate/jct
(Vapor + liquid) equilibria for the {water + poly(ethylene glycol diacetyl ether) (PEGDAE) and methanol + PEGDAE} systems Doo-hwan Cha, Joonwoo Lee, Jihoon Im, Hwayong Kim
*
School of Chemical and Biological Engineering and Institute of Chemical Processes, Seoul National University, SAN 56-1, Shilim-Dong, Gwanak-gu, Seoul 151-744, Republic of Korea Received 3 April 2006; received in revised form 18 July 2006; accepted 19 July 2006 Available online 11 August 2006
Abstract We measured binary (vapor + liquid) equilibrium data for the {water + poly(ethylene glycol diacetyl ether) (PEGDAE) and methanol + PEGDAE} systems at pressures up to 400 kPa and temperatures from 333 K to 393 K. A static apparatus was used in this study. The measured data were correlated by the Peng–Robinson equation of state using the Wong–Sandler mixing rules with NRTL as the excess Gibbs free energy model. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: (Vapor + liquid) equilibria; Poly(ethylene glycol diacetyl ether) (PEGDAE); Water; Methanol
1. Introduction Poly(oxy-methylene) (POM) is a plastic material, which has mechanical strength comparable with metals. It is used to making parts for electric appliances, cars, and other machines. In the manufacturing of POM, formaldehyde of 99.9% or higher purity is needed. Metal oxide process can be used for making formaldehyde from methanol and oxygen, but formaldehyde forms azeotrope with water, the by-product of this process. Extractive distillation is a useful technique for separating a mixture forming azeotrope. Poly(ethylene glycol dimethyl ether) (PEGDME) has been used as a solvent for this application [1]. PEGDAE can be a candidate for substituting PEGDME due to the similarity in molecular structure. Process simulation is a useful tool for evaluating PEGDAE as a solvent. But the vapor pressure of PEGDAE and phase equilibrium data for the mixtures of PEGDAE and other components (product, by-product, and remaining reactant) are essential for this process simulation. There are a few *
Corresponding author. Tel.: +82 2 880 7406; fax: +82 2 888 6695. E-mail address: [email protected] (H. Kim).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.07.019
(vapor + liquid) equilibrium data for the process (binary formaldehyde + water, formaldehyde + methanol, water + methanol), but the data for the (PEGDAE + formaldehyde), (PEGDAE + water), and (PEGDAE + methanol) systems are scarce. Therefore, we measured binary (vapor + liquid) equilibria for the (water + PEGDAE) and (methanol + PEGDAE) systems at pressures up to 400 kPa and temperatures from 333 K to 393 K. Experimental results were correlated with the Peng–Robinson equation of state with the Wong–Sandler mixing rule using the NRTL model. Formaldehyde was excluded in this study because it is available only in the form of 40% aqueous solution. 2. Experimental 2.1. Materials PEGDAE was supplied by LG Chem. Ltd. with a minimum purity of 99% (GC). The average molecular weight of PEGDAE is 300. Methanol was supplied by Aldrich with a minimum purity of 99.5% (GC). Double distilled water was made in our laboratory.
484
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487
2.2. Apparatus We used a static method to measure pTx data. This method is similar to that of Giles et al. [2]. Pressure, temperature, and liquid phase composition are measured by experiments and vapor phase composition is calculated by using the measured pTx data. While a weak point is that it needs too long time to reach equilibrium state, this method has a merit that we do not need to analyze vapor and liquid compositions. It is assumed that a feed composition is equal to the liquid composition as long as the liquid phase volume is maintained above 90% of cell volume. Figure 1 shows the schematic diagram of the experimental apparatus. This apparatus was designed to operate up to 150 °C. An oil bath, model TD-26 by JULABO, was used to maintain equilibrium temperature. An equilibrium cell was made of 316 stainless-steel, and its internal volume was approximately 100 mL. The cell had two reinforced glass windows of 20 mm thickness on both sides of the cell to observe the liquid phase level. The equilibrium temperature of the system was monitored by a 100 X platinum resistance thermometer (PRT), the model 5614 by Hart Scientific Co., with accuracy of ±0.006 °C and a 1502A digital indicator by Hart Scientific Co. The PRT was calibrated by comparison to standard platinum resistance thermometer (SPRT). The SPRT is calibrated to the international temperature scale of 1990 (ITS-90). The model Super TJE (<50 psi) pressure transducer by Sensotec Co. connected a model L20010WM1 digital indicator by Laurel was used to measure the pressure of the system. An estimated accuracy of the digital pressure gauge is 0.05%. A digital balance, MP-3000 by CHYO with minimum accuracy of ±0.02 g, was used to measure liquid sample weight.
all impurities. After evacuating, PEGDAE was charged to the cell and then water or methanol was injected. Liquid phase volume was checked through the cell window. After charging a proper amount of samples, the sample cylinders were removed from the cell and the weight of the cylinders were measured to calculate the charged composition in the cell. When equilibrium was reached at the desired temperature, the pressure was measured. Further degassing was performed to check the repeatability of the pressure. Vapor phase compositions were calculated by bubble p calculation using following thermodynamic model. 3. Results and discussion 3.1. Thermodynamic model For the correlation of the experimental data, we used the Peng–Robinson equation of state (PR EOS) [3] with the Wong–Sandler mixing rule [4]. The PR EOS is expressed as follows: p¼
RT aðT Þ ; V b V ðV þ bÞ þ bðV bÞ
ð1Þ
R2 T 2c aðT Þ; Pc RT c bðT c Þ ¼ 0:07780 ; Pc aðT Þ ¼ 0:45724
ð2Þ ð3Þ
2 aðT Þ ¼ ½1 þ jð1 T 0:5 r Þ ;
ð4Þ 2
j ¼ 0:37464 þ 1:54226x 0:26992x ;
ð5Þ
where Tc is the critical temperature, pc is the critical pressure, Tr is the reduced temperature, and x is the acentric
2.3. Experimental procedure
TABLE 1 Pure component parameters
Firstly, the samples were injected into each cylinder and the cylinders were degassed. The degassed cylinders were weighed by a digital balance separately. Then, the cylinders were equipped to the equilibrium cell and whole system containing the cell was sufficiently evacuated to remove
Chemicals
Tc/K
pc/kPa
x
PEGDAE Water Methanol
736.87 647.14a 512.64a
2469.0 22064.0a 8097.0a
0.235 0.344a 0.565a
a
Reference [7].
FIGURE 1. Schematic diagram of the experimental apparatus: 1, vacuum pump; 2, trap; 3, temperature indicator; 4, pressure indicator; 5, reservoir; 6, isothermal bath; 7, equilibrium cell; 8, cooling coil.
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487 TABLE 2 Vapor pressure data of PEGDAE T/K
p/kPa
333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15
0.86 1.25 1.82 2.45 3.19 4.02 4.96 6.19
TABLE 3 (Vapor + liquid) equilibrium measurements for the {water (1) + PEGDAE (2)} system T/K 333.15
343.15
353.15
363.15
373.15
383.15
393.15
pexp/kPa
pcal/kPa
x1,exp
y1,cal
6.80 10.78 15.23 16.95 17.40 18.13
6.79 10.10 15.11 17.33 17.87 18.26
0.229 0.398 0.609 0.700 0.800 0.900
0.934 0.963 0.984 0.989 0.990 0.991
10.63 17.98 23.58 23.60 25.96 29.65
10.15 16.55 23.24 25.74 27.25 28.77
0.229 0.398 0.609 0.700 0.800 0.900
0.933 0.967 0.984 0.988 0.990 0.991
15.92 25.25 36.00 35.43 39.21 41.60
15.92 24.12 33.05 36.32 39.28 41.53
0.229 0.398 0.609 0.700 0.800 0.900
0.931 0.963 0.980 0.985 0.989 0.993
22.62 36.72 46.43 51.07 54.79 60.74
22.54 33.77 46.22 51.20 56.29 60.97
0.229 0.398 0.609 0.700 0.800 0.900
0.925 0.959 0.978 0.984 0.989 0.994
27.78 44.79 59.51 67.82 80.00 88.57
27.68 42.20 60.21 68.49 77.92 87.32
0.229 0.398 0.609 0.700 0.800 0.900
0.909 0.951 0.977 0.984 0.991 0.996
32.12 54.21 81.32 90.97 112.79 125.81
32.00 53.33 82.28 95.58 110.34 124.43
0.229 0.398 0.609 0.700 0.800 0.900
0.889 0.948 0.979 0.986 0.992 0.997
42.75 66.22 102.76 124.76 154.91 175.60
41.85 65.84 103.13 123.70 149.58 175.45
0.229 0.398 0.609 0.700 0.800 0.900
0.874 0.936 0.974 0.985 0.993 0.998
485
factor. The critical properties and acentric factors are listed in table 1. There is no critical property data of the PEGDAE in the literature. Thus, the properties were estimated as the following: values calculated from a method of Constantinou and Gani [5] were used as initial guesses and the critical properties were obtained by fitting the vapor pressure data. For this fitting, the PR EOS was also used. The vapor pressure data of PEGDAE we measured are reported in table 2. The Wong–Sandler mixing rule is represented as PP a i j xi xj b RT ij bm ¼ ; ð6Þ P AE i 1 1 i xi biaRT CRT TABLE 4 (Vapor + liquid) equilibrium measurements for the {methanol (1) + PEGDAE (2)} system pexp/kPa
pcal/kPa
x1,exp
y1,cal
333.15
18.13 35.24 45.09 55.05 66.09 75.01
18.57 35.60 44.96 54.33 63.36 72.25
0.205 0.399 0.502 0.602 0.698 0.800
0.976 0.990 0.994 0.996 0.997 0.998
343.15
24.46 50.68 64.62 76.94 94.84 100.59
25.05 50.54 64.33 77.40 89.34 101.17
0.205 0.399 0.502 0.602 0.698 0.800
0.972 0.989 0.993 0.995 0.997 0.998
353.15
34.09 70.67 90.03 107.79 129.31 143.37
34.90 70.48 89.91 108.60 126.13 144.26
0.205 0.399 0.502 0.602 0.698 0.800
0.968 0.988 0.992 0.995 0.996 0.998
363.15
46.05 95.78 120.42 149.97 179.59 201.84
46.51 92.57 119.45 147.58 176.49 208.19
0.205 0.399 0.502 0.602 0.698 0.800
0.962 0.985 0.990 0.994 0.996 0.998
373.15
61.09 123.84 162.44 202.99 252.79 280.30
62.62 125.39 163.21 204.10 247.65 296.86
0.205 0.399 0.502 0.602 0.698 0.800
0.958 0.983 0.989 0.993 0.996 0.998
383.15
79.34 167.91 209.95 275.83 317.18 377.45
81.48 167.34 217.47 268.84 320.44 377.22
0.205 0.399 0.502 0.602 0.698 0.800
0.953 0.982 0.988 0.992 0.995 0.997
393.15
101.04 216.55 284.03 500.09
103.96 217.69 285.23 500.75
0.205 0.399 0.502 0.800
0.947 0.980 0.987 0.997
T/K
486
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487
TABLE 5 Binary parameters and average absolute deviations System
T/K
kij
g12/R
{Water (1) + PEGDAE (2)}
333.15 343.15 353.15 363.15 373.15 383.15 393.15
0.807 0.607 0.533 0.482 0.517 0.524 0.207
23539.8 1144.96 1163.37 1216.00 723.26 777.26 2853.30
740.90 115.96 237.88 267.41 212.22 5.88 354.40
0.021 0.051 0.025 0.020 0.021 0.019 0.012
333.15 343.15 353.15 363.15 373.15 383.15 393.15 n T 1 X pcal pexp ¼ : nT i pexp
0.121 0.227 0.226 0.057 0.087 0.100 0.142
2147.61 1371.56 1323.02 2335.63 2857.89 1986.25 1936.48
61.10 170.29 196.55 3.51 26.25 155.48 227.89
0.021 0.017 0.011 0.019 0.021 0.017 0.010
{Methanol (1) + PEGDAE (2)}
DAAD
g21/R
DAAD
! ai AE1 am ¼ bm xi þ ; ð7Þ bi C i a ai þ bj RTj bi RT a ð1 k ij Þ; ¼ ð8Þ b RT ij 2 pffiffiffi pffiffiffi where C ¼ lnð 2 1Þ= 2 for the PR EOS. Because the excess Helmholtz free energy of mixing at infinite pressure is assumed equal to the excess Gibbs free energy (GE) at low pressure, the GE model is used in place of AE1 . We used the NRTL model [6] as an GE model in this study. The NRTL model is expressed as X
P GE X xi sji Gji ¼ xi Pi ; RT k xk Gki i Gij ¼ expðaij sij Þ;
ð9Þ
aij ¼ aji ;
ð10Þ
sij ¼ gij =RT ;
ð11Þ
where sij and sji are the interaction parameters and aij is the non-randomness parameter. 3.2. (Vapor + liquid) equilibrium measurements The pTx measurements were determined in a temperature range from 333.15 K to 393.15 K for the {water (1) + PEGDAE (2)} system and for the {methanol (1) + PEGDAE (2)} system. The experimental data are listed in tables 3 and 4. When the Wong–Sandler mixing rule was applied, the non-randomness parameter, a, was fixed as 0.3, and three parameters, k12, s12, s21, were fitted. The objective function for evaluating the parameters was set by: N X pexp pcal ð12Þ F ¼ ; pexp i where N is the number of experimental data points and pexp and pcal are the experimental and the calculated pressures, respectively. The average absolute deviations between the measured and calculated pressure and the value of k12, s12, s21 are listed in table 5. The maximum deviation of pressure was 0.051 for the {water (1) + PEGDAE (2)} system and 0.021 for the {methanol (1) + PEGDAE (2)}
200
p/kPa
150
100
50
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 , y1 FIGURE 2. (Vapor + liquid) equilibria of the {water (1) + PEGDAE (2)}: d, experimental data at T = 333.15 K; s, at T = 343.15 K; ., at T = 353.15 K; n, at T = 363.15 K; j, at T = 373.15 K; h, at T = 383.15 K; r, at T = 393.15 K; solid line, PR EOS with the Wong–Sandler mixing rules.
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487
487
700
600
p/kPa
500
400
300
200
100
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 , y1 FIGURE 3. (Vapor + liquid) equilibria of the {methanol (1) + PEGDAE (2)}: d, experimental data at T = 333.15 K; s, at T = 343.15 K; ., at T = 353.15 K; n, at T = 363.15 K; j, at T = 373.15 K; h, at T = 383.15 K; r, at T = 393.15 K; solid line, PR EOS with the Wong–Sandler mixing rules.
system. Figure 2 is a plot of the experimental and calculated results for the {water (1) + PEGDAE (2)} system and figure 3 is for the {methanol (1) + PEGDAE (2)} system. Both systems show nearly ideal behavior.
Acknowledgments This work was supported by the Brain Korea 21 Program of the Ministry of Education and by the National Research Laboratory (NRL) Program of Korea Institute of S&T Evaluation and Planning.
References [1] S.N. Bizzari, CEH Marketing Research Reports, The Chemical Economics Handbook, SRI International, 2000. [2] N.F. Giles, H.L. Wilson, W.V. Wilding, J. Chem. Eng. Data 41 (1996) 1223–1238. [3] D. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [4] D.S. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [5] L. Constantinou, R. Gani, AIChE J. 40 (1994) 1697–1710. [6] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [7] B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, fifth ed., McGraw-Hill, New York, 2000.
JCT 06-83
(Vapor + liquid) equilibria for the {water + poly(ethylene glycol diacetyl ether) (PEGDAE) and methanol + PEGDAE} systems Doo-hwan Cha, Joonwoo Lee, Jihoon Im, Hwayong Kim
*
School of Chemical and Biological Engineering and Institute of Chemical Processes, Seoul National University, SAN 56-1, Shilim-Dong, Gwanak-gu, Seoul 151-744, Republic of Korea Received 3 April 2006; received in revised form 18 July 2006; accepted 19 July 2006 Available online 11 August 2006
Abstract We measured binary (vapor + liquid) equilibrium data for the {water + poly(ethylene glycol diacetyl ether) (PEGDAE) and methanol + PEGDAE} systems at pressures up to 400 kPa and temperatures from 333 K to 393 K. A static apparatus was used in this study. The measured data were correlated by the Peng–Robinson equation of state using the Wong–Sandler mixing rules with NRTL as the excess Gibbs free energy model. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: (Vapor + liquid) equilibria; Poly(ethylene glycol diacetyl ether) (PEGDAE); Water; Methanol
1. Introduction Poly(oxy-methylene) (POM) is a plastic material, which has mechanical strength comparable with metals. It is used to making parts for electric appliances, cars, and other machines. In the manufacturing of POM, formaldehyde of 99.9% or higher purity is needed. Metal oxide process can be used for making formaldehyde from methanol and oxygen, but formaldehyde forms azeotrope with water, the by-product of this process. Extractive distillation is a useful technique for separating a mixture forming azeotrope. Poly(ethylene glycol dimethyl ether) (PEGDME) has been used as a solvent for this application [1]. PEGDAE can be a candidate for substituting PEGDME due to the similarity in molecular structure. Process simulation is a useful tool for evaluating PEGDAE as a solvent. But the vapor pressure of PEGDAE and phase equilibrium data for the mixtures of PEGDAE and other components (product, by-product, and remaining reactant) are essential for this process simulation. There are a few *
Corresponding author. Tel.: +82 2 880 7406; fax: +82 2 888 6695. E-mail address: [email protected] (H. Kim).
0021-9614/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2006.07.019
(vapor + liquid) equilibrium data for the process (binary formaldehyde + water, formaldehyde + methanol, water + methanol), but the data for the (PEGDAE + formaldehyde), (PEGDAE + water), and (PEGDAE + methanol) systems are scarce. Therefore, we measured binary (vapor + liquid) equilibria for the (water + PEGDAE) and (methanol + PEGDAE) systems at pressures up to 400 kPa and temperatures from 333 K to 393 K. Experimental results were correlated with the Peng–Robinson equation of state with the Wong–Sandler mixing rule using the NRTL model. Formaldehyde was excluded in this study because it is available only in the form of 40% aqueous solution. 2. Experimental 2.1. Materials PEGDAE was supplied by LG Chem. Ltd. with a minimum purity of 99% (GC). The average molecular weight of PEGDAE is 300. Methanol was supplied by Aldrich with a minimum purity of 99.5% (GC). Double distilled water was made in our laboratory.
484
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487
2.2. Apparatus We used a static method to measure pTx data. This method is similar to that of Giles et al. [2]. Pressure, temperature, and liquid phase composition are measured by experiments and vapor phase composition is calculated by using the measured pTx data. While a weak point is that it needs too long time to reach equilibrium state, this method has a merit that we do not need to analyze vapor and liquid compositions. It is assumed that a feed composition is equal to the liquid composition as long as the liquid phase volume is maintained above 90% of cell volume. Figure 1 shows the schematic diagram of the experimental apparatus. This apparatus was designed to operate up to 150 °C. An oil bath, model TD-26 by JULABO, was used to maintain equilibrium temperature. An equilibrium cell was made of 316 stainless-steel, and its internal volume was approximately 100 mL. The cell had two reinforced glass windows of 20 mm thickness on both sides of the cell to observe the liquid phase level. The equilibrium temperature of the system was monitored by a 100 X platinum resistance thermometer (PRT), the model 5614 by Hart Scientific Co., with accuracy of ±0.006 °C and a 1502A digital indicator by Hart Scientific Co. The PRT was calibrated by comparison to standard platinum resistance thermometer (SPRT). The SPRT is calibrated to the international temperature scale of 1990 (ITS-90). The model Super TJE (<50 psi) pressure transducer by Sensotec Co. connected a model L20010WM1 digital indicator by Laurel was used to measure the pressure of the system. An estimated accuracy of the digital pressure gauge is 0.05%. A digital balance, MP-3000 by CHYO with minimum accuracy of ±0.02 g, was used to measure liquid sample weight.
all impurities. After evacuating, PEGDAE was charged to the cell and then water or methanol was injected. Liquid phase volume was checked through the cell window. After charging a proper amount of samples, the sample cylinders were removed from the cell and the weight of the cylinders were measured to calculate the charged composition in the cell. When equilibrium was reached at the desired temperature, the pressure was measured. Further degassing was performed to check the repeatability of the pressure. Vapor phase compositions were calculated by bubble p calculation using following thermodynamic model. 3. Results and discussion 3.1. Thermodynamic model For the correlation of the experimental data, we used the Peng–Robinson equation of state (PR EOS) [3] with the Wong–Sandler mixing rule [4]. The PR EOS is expressed as follows: p¼
RT aðT Þ ; V b V ðV þ bÞ þ bðV bÞ
ð1Þ
R2 T 2c aðT Þ; Pc RT c bðT c Þ ¼ 0:07780 ; Pc aðT Þ ¼ 0:45724
ð2Þ ð3Þ
2 aðT Þ ¼ ½1 þ jð1 T 0:5 r Þ ;
ð4Þ 2
j ¼ 0:37464 þ 1:54226x 0:26992x ;
ð5Þ
where Tc is the critical temperature, pc is the critical pressure, Tr is the reduced temperature, and x is the acentric
2.3. Experimental procedure
TABLE 1 Pure component parameters
Firstly, the samples were injected into each cylinder and the cylinders were degassed. The degassed cylinders were weighed by a digital balance separately. Then, the cylinders were equipped to the equilibrium cell and whole system containing the cell was sufficiently evacuated to remove
Chemicals
Tc/K
pc/kPa
x
PEGDAE Water Methanol
736.87 647.14a 512.64a
2469.0 22064.0a 8097.0a
0.235 0.344a 0.565a
a
Reference [7].
FIGURE 1. Schematic diagram of the experimental apparatus: 1, vacuum pump; 2, trap; 3, temperature indicator; 4, pressure indicator; 5, reservoir; 6, isothermal bath; 7, equilibrium cell; 8, cooling coil.
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487 TABLE 2 Vapor pressure data of PEGDAE T/K
p/kPa
333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15
0.86 1.25 1.82 2.45 3.19 4.02 4.96 6.19
TABLE 3 (Vapor + liquid) equilibrium measurements for the {water (1) + PEGDAE (2)} system T/K 333.15
343.15
353.15
363.15
373.15
383.15
393.15
pexp/kPa
pcal/kPa
x1,exp
y1,cal
6.80 10.78 15.23 16.95 17.40 18.13
6.79 10.10 15.11 17.33 17.87 18.26
0.229 0.398 0.609 0.700 0.800 0.900
0.934 0.963 0.984 0.989 0.990 0.991
10.63 17.98 23.58 23.60 25.96 29.65
10.15 16.55 23.24 25.74 27.25 28.77
0.229 0.398 0.609 0.700 0.800 0.900
0.933 0.967 0.984 0.988 0.990 0.991
15.92 25.25 36.00 35.43 39.21 41.60
15.92 24.12 33.05 36.32 39.28 41.53
0.229 0.398 0.609 0.700 0.800 0.900
0.931 0.963 0.980 0.985 0.989 0.993
22.62 36.72 46.43 51.07 54.79 60.74
22.54 33.77 46.22 51.20 56.29 60.97
0.229 0.398 0.609 0.700 0.800 0.900
0.925 0.959 0.978 0.984 0.989 0.994
27.78 44.79 59.51 67.82 80.00 88.57
27.68 42.20 60.21 68.49 77.92 87.32
0.229 0.398 0.609 0.700 0.800 0.900
0.909 0.951 0.977 0.984 0.991 0.996
32.12 54.21 81.32 90.97 112.79 125.81
32.00 53.33 82.28 95.58 110.34 124.43
0.229 0.398 0.609 0.700 0.800 0.900
0.889 0.948 0.979 0.986 0.992 0.997
42.75 66.22 102.76 124.76 154.91 175.60
41.85 65.84 103.13 123.70 149.58 175.45
0.229 0.398 0.609 0.700 0.800 0.900
0.874 0.936 0.974 0.985 0.993 0.998
485
factor. The critical properties and acentric factors are listed in table 1. There is no critical property data of the PEGDAE in the literature. Thus, the properties were estimated as the following: values calculated from a method of Constantinou and Gani [5] were used as initial guesses and the critical properties were obtained by fitting the vapor pressure data. For this fitting, the PR EOS was also used. The vapor pressure data of PEGDAE we measured are reported in table 2. The Wong–Sandler mixing rule is represented as PP a i j xi xj b RT ij bm ¼ ; ð6Þ P AE i 1 1 i xi biaRT CRT TABLE 4 (Vapor + liquid) equilibrium measurements for the {methanol (1) + PEGDAE (2)} system pexp/kPa
pcal/kPa
x1,exp
y1,cal
333.15
18.13 35.24 45.09 55.05 66.09 75.01
18.57 35.60 44.96 54.33 63.36 72.25
0.205 0.399 0.502 0.602 0.698 0.800
0.976 0.990 0.994 0.996 0.997 0.998
343.15
24.46 50.68 64.62 76.94 94.84 100.59
25.05 50.54 64.33 77.40 89.34 101.17
0.205 0.399 0.502 0.602 0.698 0.800
0.972 0.989 0.993 0.995 0.997 0.998
353.15
34.09 70.67 90.03 107.79 129.31 143.37
34.90 70.48 89.91 108.60 126.13 144.26
0.205 0.399 0.502 0.602 0.698 0.800
0.968 0.988 0.992 0.995 0.996 0.998
363.15
46.05 95.78 120.42 149.97 179.59 201.84
46.51 92.57 119.45 147.58 176.49 208.19
0.205 0.399 0.502 0.602 0.698 0.800
0.962 0.985 0.990 0.994 0.996 0.998
373.15
61.09 123.84 162.44 202.99 252.79 280.30
62.62 125.39 163.21 204.10 247.65 296.86
0.205 0.399 0.502 0.602 0.698 0.800
0.958 0.983 0.989 0.993 0.996 0.998
383.15
79.34 167.91 209.95 275.83 317.18 377.45
81.48 167.34 217.47 268.84 320.44 377.22
0.205 0.399 0.502 0.602 0.698 0.800
0.953 0.982 0.988 0.992 0.995 0.997
393.15
101.04 216.55 284.03 500.09
103.96 217.69 285.23 500.75
0.205 0.399 0.502 0.800
0.947 0.980 0.987 0.997
T/K
486
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487
TABLE 5 Binary parameters and average absolute deviations System
T/K
kij
g12/R
{Water (1) + PEGDAE (2)}
333.15 343.15 353.15 363.15 373.15 383.15 393.15
0.807 0.607 0.533 0.482 0.517 0.524 0.207
23539.8 1144.96 1163.37 1216.00 723.26 777.26 2853.30
740.90 115.96 237.88 267.41 212.22 5.88 354.40
0.021 0.051 0.025 0.020 0.021 0.019 0.012
333.15 343.15 353.15 363.15 373.15 383.15 393.15 n T 1 X pcal pexp ¼ : nT i pexp
0.121 0.227 0.226 0.057 0.087 0.100 0.142
2147.61 1371.56 1323.02 2335.63 2857.89 1986.25 1936.48
61.10 170.29 196.55 3.51 26.25 155.48 227.89
0.021 0.017 0.011 0.019 0.021 0.017 0.010
{Methanol (1) + PEGDAE (2)}
DAAD
g21/R
DAAD
! ai AE1 am ¼ bm xi þ ; ð7Þ bi C i a ai þ bj RTj bi RT a ð1 k ij Þ; ¼ ð8Þ b RT ij 2 pffiffiffi pffiffiffi where C ¼ lnð 2 1Þ= 2 for the PR EOS. Because the excess Helmholtz free energy of mixing at infinite pressure is assumed equal to the excess Gibbs free energy (GE) at low pressure, the GE model is used in place of AE1 . We used the NRTL model [6] as an GE model in this study. The NRTL model is expressed as X
P GE X xi sji Gji ¼ xi Pi ; RT k xk Gki i Gij ¼ expðaij sij Þ;
ð9Þ
aij ¼ aji ;
ð10Þ
sij ¼ gij =RT ;
ð11Þ
where sij and sji are the interaction parameters and aij is the non-randomness parameter. 3.2. (Vapor + liquid) equilibrium measurements The pTx measurements were determined in a temperature range from 333.15 K to 393.15 K for the {water (1) + PEGDAE (2)} system and for the {methanol (1) + PEGDAE (2)} system. The experimental data are listed in tables 3 and 4. When the Wong–Sandler mixing rule was applied, the non-randomness parameter, a, was fixed as 0.3, and three parameters, k12, s12, s21, were fitted. The objective function for evaluating the parameters was set by: N X pexp pcal ð12Þ F ¼ ; pexp i where N is the number of experimental data points and pexp and pcal are the experimental and the calculated pressures, respectively. The average absolute deviations between the measured and calculated pressure and the value of k12, s12, s21 are listed in table 5. The maximum deviation of pressure was 0.051 for the {water (1) + PEGDAE (2)} system and 0.021 for the {methanol (1) + PEGDAE (2)}
200
p/kPa
150
100
50
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 , y1 FIGURE 2. (Vapor + liquid) equilibria of the {water (1) + PEGDAE (2)}: d, experimental data at T = 333.15 K; s, at T = 343.15 K; ., at T = 353.15 K; n, at T = 363.15 K; j, at T = 373.15 K; h, at T = 383.15 K; r, at T = 393.15 K; solid line, PR EOS with the Wong–Sandler mixing rules.
D.-h. Cha et al. / J. Chem. Thermodynamics 39 (2007) 483–487
487
700
600
p/kPa
500
400
300
200
100
0 0.0
0.2
0.4
0.6
0.8
1.0
x1 , y1 FIGURE 3. (Vapor + liquid) equilibria of the {methanol (1) + PEGDAE (2)}: d, experimental data at T = 333.15 K; s, at T = 343.15 K; ., at T = 353.15 K; n, at T = 363.15 K; j, at T = 373.15 K; h, at T = 383.15 K; r, at T = 393.15 K; solid line, PR EOS with the Wong–Sandler mixing rules.
system. Figure 2 is a plot of the experimental and calculated results for the {water (1) + PEGDAE (2)} system and figure 3 is for the {methanol (1) + PEGDAE (2)} system. Both systems show nearly ideal behavior.
Acknowledgments This work was supported by the Brain Korea 21 Program of the Ministry of Education and by the National Research Laboratory (NRL) Program of Korea Institute of S&T Evaluation and Planning.
References [1] S.N. Bizzari, CEH Marketing Research Reports, The Chemical Economics Handbook, SRI International, 2000. [2] N.F. Giles, H.L. Wilson, W.V. Wilding, J. Chem. Eng. Data 41 (1996) 1223–1238. [3] D. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [4] D.S. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [5] L. Constantinou, R. Gani, AIChE J. 40 (1994) 1697–1710. [6] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [7] B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, fifth ed., McGraw-Hill, New York, 2000.
JCT 06-83