Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX-XXX
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Isobaric Vapor−Liquid Equilibrium for Binary System of Tetrahydrofuran + 1,4-Butanediol and gamma-Butyrolactone at 50.0 and 70.0 kPa Feizhong Sun,† Hongmei Du,‡ Chunyu Zhang,† Siyuan Ren,† and Changsheng Yang*,† †
Key Laboratory for Green Chemical Technology of State Education Ministry, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China ‡ Shandong Provincial Key Laboratory of Chemical Energy Storage and Novel Cell Technology, School of Chemistry and Chemical Engineering, Liaocheng University, Liaocheng 252059, China S Supporting Information *
ABSTRACT: Isobaric vapor−liquid equilibrium (VLE) data for two binary systems, tetrahydrofuran (THF) + 1,4−butanediol (BDO) and THF + gammabutyrolactone (GBL), were measured at pressures of 50.0 and 70.0 kPa. The experiment data were regressed using maximum likelihood method, and binary interaction parameters were estimated for Wilson, NRTL, and UNIQUAC activity coefficient models by Aspen Plus V9.0. All of the models match well with the experimental data. All the experimental data passed the thermodynamic consistency test by Redlich−Kister area test and Van Ness test. The two binary systems both exhibit positive deviations from ideality.
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INTRODUCTION
experimental data for THF + BDO have been collected by the well-known NIST Thermodynamics Research Center. The specification of the experimental pressure is based on the saturated vapor pressure of light component. As we all know, the top distillation production is THF for the binary system of THF + BDO and THF + GBL. We used circulating cooling water in utilities system. Cooling feedwater is typically available at about 305 K. An appropriate temperature change in the heat exchanger is 20 K. Therefore, the temperature of the product at the first tray of distillation column should be about 325 K, the saturated vapor pressure of THF at 325 K is about 60 kPa. Accordingly, the experimental pressure here is determined to be 50.0 and 70.0 kPa. We concentrated our attention on the VLE data for isobaric systems of THF + GBL and THF + BDO at 50.0 and 70.0 kPa. The VLE data were measured utilizing modified Rose-Williams still. The VLE data sets were regressed using the maximum likelihood method and pairwise parameters were estimated for three activity coefficient models: Wilson, NRTL, and UNIQUAC. All models resulted in a good fit of the VLE data.
In recent years, substantial efforts have been made to study the catalytic hydrogenation of butanedioic acid or anhydride, which can mainly yield 1,4-butanediol (BDO), gamma-butyrolactone (GBL), and tetrahydrofuran (THF), or a mixture of these compounds. BDO is an important intermediate for the synthesis of organic chemicals in engineering plastics and fabrics industry. Almost half of BDO is used as an intermediate for the production of GBL and THF. THF is mainly used as a monomer to produce copolymers, such as polytetramethylene glycol and polybutylene terephthalate resin.1−3 In addition, THF and GBL which are usually made from BDO find widespread use as solvents. It is apparent to all that vapor−liquid equilibrium (VLE) data for binary or multiple components are the basis of most of the distillation processes. VLE data are necessary for the design and optimization of various purification technologies. As hydrogenation of butanedioic acid mainly produces a mixture of three compounds, we need corresponding pairwise interaction parameters for GBL + BDO, THF + GBL, and THF + BDO to design separation process. VLE data for the GBL + BDO have been reported in our previous work4 at P = 30, 50, 70 kPa, Giles N.F.5 also reported the VLE data for the BDO + GBL at 383.15 K. Ramkumar, D.H.S.6 reported VLE data for THF + GBL at 101.3 kPa. However, they did not perform consistency test by area and point test. Zhang, G.X.7 merely reported infinite dilution activity coefficients for THF in solvent BDO at the temperature range from 331.15 to 404.15 K. No isobaric © XXXX American Chemical Society
2. EXPERIMENTAL SECTION 2.1. Chemicals. THF and BDO (initial mole fraction purity are both greater than 0.9850) were supplied by Tianjin Guangfu Received: June 26, 2017 Accepted: September 27, 2017
A
DOI: 10.1021/acs.jced.7b00584 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Chemical Samples Descriptiona chemical name
CAS registry number
source
initial mole fraction
Tb (K)c
purification method
final mole fraction
analysis method
THFa GBLa BDOa
109-99-9 96-48-0 110-63-4
Tianjin Guangfu Reagent Co. Tianjin Yuanli Reagent Co. Tianjin Guangfu Reagent Co.
0.9850 0.9800 0.9850
339.12 477.15 501.15
distillation distillation distillation
0.9980 0.9960 0.9990
GCb GCb GCb
a THF: tetrahydrofuran; GBLa: gamma−butyrolactone; BDOa: 1,4−butanediol. bGas chromatography with a FID detector. cTb (K) at 101.3 kPa. Standard uncertainties: u(purity) = 0.0007; u(T) = 0.05 K; u(P) = 0.1 kPa.
Reagent Co. China. GBL (initial mole fraction purity is greater than 0.9800) was supplied by Tianjin Yuanli Reagent Co. China. All samples were further purified by means of a glass distillation column having an inner diameter of 27 mm, the packing layer height of the column is 1.5 m. The column was equipped with external electric heating to compensate heat loss. All samples used in the measurements were checked by GC (SP2100A) with a flame ionization detector (FID). Three pure components boiling point temperatures (Tb) were measured with modified Rose-Williams still. As the temperatures directly affect the accuracy for VLE data regression, it is very important to measure pure component boiling point temperature prior to the VLE measurement in the same still. Purity and boiling point temperatures of all samples are listed in Table 1. 2.2. Apparatus and Procedure. The equilibrium apparatus used in this study was a modified Rose-Williams still. A detailed description of the apparatus was shown in our previous work.4 The still included many pieces of auxiliary equipment, vacuum pump, surge tank, a condenser, a U-shaped mercury manometer, an electrical heating rod, and a needle valve. The experimental pressures are regulated by a vacuum pump, and the surge tank which is installed in vacuum pump inlet can reduce fluctuations in pressure. The liquid samples were heated by the electrical heating rod. We adjusted the voltage of the electrical heating rod to control the speed of heating. The condenser is installed between the vacuum pump and the Rose-Williams still, which is used to prevent any vapor from entering the vacuum pump by adjusting the temperature of refrigerant supplied to the condenser. The experimental apparatus is presented in Figure 1.
Table 2. Experimental VLE Data for the System THF (1) + GBL (2) at p = 50.0 and 70.0 kPa, Liquid Mole Fraction x, Vapor Mole Fraction y, Activity Coefficient γ, and Temperature Ta T/K
x1
450.25 432.65 423.04 408.75 385.81 373.12 367.65 353.75 346.72 337.05 330.76 327.45 322.23 320.65 318.85
0.0000 0.0080 0.0131 0.0231 0.0492 0.0721 0.0944 0.2152 0.3034 0.4715 0.6281 0.7159 0.8741 0.9318 1.0000
462.65 449.49 438.31 425.65 411.47 389.25 384.25 373.25 360.21 349.39 342.25 336.86 331.06 330.78 328.15
0 0.0090 0.0180 0.0311 0.0500 0.1160 0.1432 0.2140 0.3390 0.4901 0.6153 0.7378 0.8399 0.9110 1.0000
y1 50.0 kPa 0.0000 0.4050 0.5472 0.7193 0.8820 0.9311 0.9450 0.9738 0.9820 0.9896 0.9918 0.9941 0.9980 0.9989 1.0000 70.0 kPa 0 0.3081 0.5032 0.6679 0.7951 0.9101 0.9269 0.9541 0.9771 0.9889 0.9932 0.9962 0.9980 0.9990 1.0000
γ1
2.5201 2.4980 2.4887 2.4008 2.3745 2.1268 1.4210 1.2560 1.1084 1.0307 1.0172 1.0089 1.0040 1.0000
1.7645 1.7558 1.7091 1.6809 1.3554 1.2602 1.1438 1.0521 1.0103 1.0086 1.0046 1.0038 1.0005 1.0000
γ2
α12
1.0000 1.0113 1.0473 1.0592 1.0713 1.0779 1.1163 1.1584 1.2627 1.5792 2.4846 2.8137 2.9019 3.2319
85.77 93.47 113.55 159.78 202.00 200.98 220.07 258.13 381.86 517.79 828.43 4534.34 14289.67
1.0000 1.0030 1.0059 1.0073 1.0132 1.0743 1.0969 1.1802 1.2444 1.3054 1.5153 1.6448 1.7380 1.7707
49.93 57.30 66.74 81.69 98.72 103.35 123.58 190.42 356.50 617.05 1355.16 3710.92 12321.32
a
Standard uncertainties: u(T) = 0.05 K, u(p) = 0.1 kPa, and u(x1) = u(y1) = 0.0007.
was checked for any significant leaks by monitoring U-shaped mercury manometer. 2.3. Analysis. Calibration was performed using the GC to analyze purity of a set of mixture samples with known composition. The mole fraction of vapor and liquid in the still was determined by calibration curve. The GC was equipped with FID, and the column used was a SE-54 capillary column (30 m × 0.32 mm × 0.5 μm, immobilized 5% diphenyl, 95% dimethylpolysiloxane). The carrier gas was high-purity nitrogen (≥99.999%, mass fraction), and the flow rate was controlled at 30 mL·min−1. The flow rates of hydrogen (≥99.999%, mass fraction) and air (≥99.99%, mass fraction) were 30 mL·min−1 and 300 mL·min−1, respectively. For the THF + BDO and THF + GBL binary systems,8 the temperature of oven was
Figure 1. Rose-Williams still and other apparatus: (1) heating rod, (2) liquid sample connection, (3) vapor (cooled to liquid) sample connection, (4) condenser, (5) coolant inlet, (6) coolant outlet, (7) U-shaped differential manometer, (8) vacuum pump, (9) a buffer tank, (10) valve, (11) a precision mercury thermometer.
The still was cleaned by methanol prior to measurement of pure components boiling point temperatures. About 140 mL of methanol was charged to the still, heated for 1 h, and then removed from the still thoroughly. To start the VLE measurement, the system was evacuated to less than 10.0 kPa. The system B
DOI: 10.1021/acs.jced.7b00584 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 3. Experimental VLE Data for the System THF (1) + BDO (2) at p = 50.0 and 70.0 kPa, Liquid Mole Fraction x, Vapor Mole Fraction y, Activity Coefficient γ, and Temperature Ta T/K
x1
479.10 465.25 454.75 449.09 436.45 420.52 410.80 395.95 386.95 379.65 361.50 349.48 338.85 334.45 324.95 318.85
0.0000 0.0040 0.0075 0.0095 0.0144 0.0239 0.0332 0.0569 0.0806 0.1090 0.2275 0.3356 0.4731 0.5711 0.8004 1.0000
489.25 475.35 465.10 449.37 432.73 422.26 409.52 393.85 373.75 366.05 356.23 349.52 342.56 338.85 334.55 328.15
0.0000 0.0045 0.0082 0.0149 0.0242 0.0415 0.0586 0.1011 0.2261 0.2850 0.3826 0.4685 0.5924 0.6681 0.7872 1.0000
y1 50.0 kPa 0.0000 0.3890 0.5890 0.6710 0.8051 0.9053 0.9409 0.9728 0.9833 0.9891 0.9968 0.9987 0.9995 0.9997 0.9998 1.0000 70.0 kPa 0.0000 0.3753 0.5671 0.7582 0.8689 0.9187 0.9534 0.9785 0.9932 0.9954 0.9979 0.9986 0.9992 0.9996 0.9997 1.0000
γ1
2.7530 2.6434 2.6184 2.5946 2.3803 2.1698 1.8073 1.5898 1.4131 1.1018 1.0614 1.0519 1.0079 1.0001 1.0000
2.8168 2.7476 2.6282 2.4986 1.8819 1.7912 1.5026 1.1125 1.0847 1.0666 1.0631 1.0436 1.0428 1.0203 1.0000
γ2
α12
1.0000 1.0033 1.0057 1.0076 1.0114 1.0127 1.0198 1.0402 1.0831 1.1204 1.2092 1.3343 1.4560 1.5288 4.8886
159.80 192.52 216.74 291.05 409.78 496.00 666.48 794.57 934.35 1772.47 3445.40 8019.21 13604.43 31290.72
1.0000 1.0019 1.0049 1.0309 1.1299 1.1430 1.2322 1.3546 1.6179 1.9407 1.9994 2.5073 3.1551 3.2361 4.2787
134.11 161.08 213.63 280.67 284.08 370.87 500.79 834.72 1061.91 2011.67 2864.51 5172.65 11269.83 19892.61
Figure 3. Relative volatilities of the THF + GBL system at 50.0 and 70.0 kPa. Comparison of model results (calculated with Wilson parameters in Table 6) to the experimental data. The chart also shows (dash lines) ± 5% deviations from the calculated relative volatilities. Black dash line, red dash line, ± 5% deviations at 50.0 and 70.0 kPa, respectively. ●, ○, experimental data at 50.0 and 70.0 kPa, respectively. Blue and green solid line, Wilson model result at 50.0 and 70.0 kPa, respectively.
a Standard uncertainties: u(T) = 0.05 K, u(p) = 0.1 kPa, and u(x1) = u(y1) = 0.0007
Figure 4. Relative volatilities of the THF + BDO system at 50.0 and 70.0 kPa. Comparison of model results (calculated with Wilson parameters in Table 6) to the experimental data. The chart also shows (dash lines) ± 10% deviations from the calculated relative volatilities. Black dash line, red dash line, ± 5% deviations at 50.0 and 70.0 kPa, respectively. ●, ○, experimental data at 50.0 and 70.0 kPa, respectively. Blue and green solid line, Wilson model result at 50.0 and 70.0 kPa, respectively.
393.15 K; the temperatures of injector and detector were 513.15 and 523.15 K, respectively. An injection volume of all the vapor and liquid sample are 0.1 μL, each sample was performed three times to test the reproducibility of result. We calculated the concentrations by calibration curve.
3. RESULTS AND DISCUSSION 3.1. Experimental Data. For two binary systems, THF (1) + GBL (2) and THF (1) + BDO (2), the VLE data were measured at 50.0 and 70.0 kPa, which are shown in Tables 2 and 3. Figure 2 shows the comparison of experiment results with the data of Ramkumar, D.H.S.6 The activity coefficients of the two binary mixtures are also listed in Tables 2, 3. From Tables 2 and 3, the activity coefficients For THF (1) + GBL (2) and THF (1) + BDO (2) are all greater than 1, which indicates
Figure 2. Isobaric VLE data of the binary system THF (1) + GBL (2): ■, experimental data at 50.0 kPa; △, experimental data at 70.0 kPa; ●, literature6 data at 101.3 kPa. C
DOI: 10.1021/acs.jced.7b00584 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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binary systems with results calculated with model parameters in Table 6. The calculated results agree well with experimental data. The maximum model deviation is 5% and 10% for THF + GBL and THF + BDO binary mixtures, respectively. 3.2. Thermodynamic Consistency Test. For the binary mixtures, testing of the thermodynamic consistency should be determined in two different methods. The first is an overall integral test which does not consider individual data points, but set of data. The second method is the checking of individual data points. For the integral test, the Redlich−Kister test11,12 which is on the basis of Gibbs−Duhem equation normally used to analyze thermodynamic consistency of VLE data. As stated by Redlich−Kister, the isobaric data set was regarded thermodynamic consistency but not necessarily correct, if the value of area test was less than 10. For the other method, point test of Van Ness13 was usually applied to remove few experimental points which have lager deviation. If the mean deviation of Δy is less than 1 and the mean deviation of Δp is less than 1, then the VLE data was regarded thermodynamically consistent. The mean deviation can be calculated by equations as follow.
Table 4. Result of the Thermodynamic Consistency Test point testa system
p/kPa
area test
Δy1
Δp %
result
THF (1) + GBL (2)
50.0 70.0 50.0 70.0
−3.44 2.79 0.17 6.51
0.45 0.03 0.11 0.37
0.88 0.21 0.78 0.93
passed passed passed passed
THF (1) + BDO (2)
a
Δy =
1 N
N
∑i = 1 100|yiexp − yical |, Δp =
1 N
N
∑i = 1 100
piexp − pical
.
piexp
Table 5. Parameters of Extended Antoine Equation parameters
THF
GBL
BDO
A B C D E range T/K
34.87 −2752.3 −9.5958 1.9889 × 10−10 3.5465 × 10−6 164 to 540
10.8996 −2866.1 −0.38645 −2.6501 × 10−3 1.2711 × 10−6 229 to 739
22.4549 −4202.3 −4.2015 −7.45 × 10−10 6.18 × 10−7 293 to 667
that the two binary systems both exhibit positive deviations from ideality. Tables 2 and 3 also show the relative volatilities9,10 α12 for two binary systems, which can be calculated by eq 1: α12 =
Δy =
y1 /x1
Δp =
(1 − y1)/(1 − x1)
(1)
n
1 n
∑ 100|yiexp − yical |
1 n
∑ 100
(2)
i=1
piexp − pical
n
piexp
i=1
(3)
Where n is the number of property values, exp is measured data, cal is estimated data with the NRTL equation, i indicates data for data point. The results of the Redlich−Kister area test and Van Ness test for the experimental systems are summarized in Table 4, Vapor phase mole fraction and residual of pressure prove the dependability for the measured VLE data sets. As it is shown in
The relative volatilities of two binary systems are all much larger than 50, which mean they can be easily separated by ordinary distillation. As can be seen in above tables, the relative volatility increases with decreasing of pressure for two binary systems, the process of separate THF (1) + BDO (2) mixture seems to be easier than THF (1) + GBL (2) mixture. Figures 3 and 4 compare experimental relative volatilities for two
Table 6. Wilsona, NRTL,b and UNIQUACc Parameters and Mean Relative Deviation for the Two Binary Systems at 50.0 and 70.0 kPa Wilsona parameters
50.0 kPa
aij aji bij bji cij=cji AADTd/K AADyd RMSDT/Ke RMSDye aij aji bij bji cij=cji AAD T/Kd AADyd RMSD T/Ke RMSDye a e
NRTLb 70.0 kPa
−3.79 4.97 −313.52 −1586.75
2.33 3.20 −2455.57 −896.34
0.62 0.0041 0.90 0.0061
0.36 0.0026 0.48 0.0038
0.40 3.13 −2007.75 −854.61
−1.97 3.09 −959.89 −857.41
0.41 0.0019 0.65 0.0038
0.87 0.0053 0.98 0.0086
50.0 kPa THF (1) + GBL (2) −6.36 10.86 1888.01 −2682.97 0.3 0.44 0.0039 0.68 0.0062 THF (1) + BDO (2) −9.83 21.49 3185.50 −5655.92 0.3 1.00 0.0048 1.18 0.0086
UNIQUACc 70.0 kPa
50.0 kPa
70.0 kPa
−6.62 11.68 1984.83 −2962.84 0.3 0.08 0.0006 0.12 0.0009
4.02 −7.05 −1122.57 1248.94
2.55 −3.25 −613.66 279.26
0.32 0.0044 0.41 0.0079
0.11 0.0008 0.16 0.0013
−10.06 18.71 3400.91 −4682.12 0.3 0.71 0.0027 1.05 0.0038
2.59 −6.01 −580.13 1235.63
0.38 −2.34 −316.46 999.17
0.26 0.0024 0.39 0.0036
1.86 0.0062 2.35 0.0103
Wilson: ln Λij = aij + bij/T. bNRTL: τij = aij + bij/T. cUNIQUAC: ln τij = aij + bij/T. dAADy =
RMSDT/K =
n
∑i = 1 (Tical − Tiexp)2 /n RMSDy =
1 n
n
∑i = 1 |yiexp − yical |. AADT =
1 n
n
∑i = 1 |Tiexp − Tical|.
n
∑i = 1 (y ical − y iexp)2 /n . D
DOI: 10.1021/acs.jced.7b00584 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 5. Experimental and calculated T−x−y diagram of the binary system THF (1) + GBL (2) at 50.0 kPa. ●, experimental data; solid line, calculated using the Wilson equation; dash line, calculated using the NRTL equation; dot line, calculated using the UNIQUAC equation.
Figure 7. Experimental and calculated T−x−y diagram of the binary system THF (1) + BDO (2) at 50.0 kPa. ●, experimental data; solid line, calculated using the Wilson equation; dash line, calculated using the NRTL equation; dot line, calculated using the UNIQUAC equation.
Figure 6. Experimental and calculated T−x−y diagram of the binary system THF (1) + GBL (2) at 70.0 kPa. ●, experimental data; solid line, calculated using the Wilson equation; dash line, calculated using the NRTL equation; dot line, calculated using the UNIQUAC equation.
Figure 8. Experimental and calculated T−x−y diagram of the binary system THF (1) + BDO (2) at 70.0 kPa. ●, experimental data; solid line, calculated using the Wilson equation; dash line, calculated using the NRTL equation; dot line, calculated using the UNIQUAC equation.
Table 4, all the results of area test and point test satisfy the consistent criteria, hence, the measured data can be considered as thermodynamically consistent. 3.3. Correlation of the Binary Vapor Liquid Equilibrium. Under negative pressure, the vapor phase is usually treated as ideal gas, so the fugacity coefficient of vapor phase can be assumed to be 1; therefore the relationship of VLE can be simplified as
The two binary systems THF (1) + GBL (2) and THF (1) + BDO (2) were fitted with Wilson,15 NRTL,16 and UNIQUAC17 models to calculate pairwise parameter by Aspen plus V9.0. The Wilson, NRTL, and UNIQUAC models contain two pairs of adjustable parameters. As recommended by Renon and Prausnitz,14 the nonrandomness parameter (αij) in the NRTL model was set at 0.3. For binary VLE measurements, all four measured variables (pressure, temperature, vapor, and liquid compositions) are considered to contain error. The parameters sought are those that minimize the objective function to phase equilibrium constraints for each component. The objective function is
yP = Pisγixi i
(4)
where xi is the liquid phase mole fraction of component i, γi is the liquid phase activity coefficient of component i, yi is the vapor phase mole fraction of component i, P is the equilibrium pressure, Pis is the vapor pressure of pure component i, which can be obtained by extended Antoine equation ln(pis /kPa) = A +
B + C ln(T /K) + D(T /K)E T /K
⎡⎛
2 ⎛ T exp − T cal ⎞2 ⎛ x exp − x cal ⎞2 Piexp − Pical ⎞ i i ⎟⎟ ⎟⎟ + ⎜⎜ i ⎟⎟ + ⎜⎜ i σP σT σx ⎠ ⎝ ⎠ ⎝ ⎠ i = 1 ⎣⎝ n
F=
∑ ⎢⎢⎜⎜
⎛ y exp − y cal ⎞2 ⎤ i ⎟ ⎥ + ⎜⎜ i ⎟⎥ σy ⎝ ⎠⎦
(5)
The value of parameters (A, B, C, D, E) procured from Chemical Properties Handbook14 are presented in Table 5, respectively. E
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+ Methyl Chloride; and 1,4-Butanediol + γ-Butyrolactone. J. Chem. Eng. Data 2006, 51, 1954−1962. (6) Ramkumar, D. H. S.; Odak, S. V.; Kudchadker, A. P. Mixture Properties of the Water + γ-Butyrolactone + Tetrahydrofuran System. 3. Isobaric Vapor-Liquid Equilibrium of Water + γ-Butyrolactone and Tetrahydrofuran + γ-Butyrolactone at 1.013 bar. J. Chem. Eng. Data 1989, 34, 466−467. (7) Zhang, G. X.; Lin, H. M.; Bian, B. G.; Shi, J. Determination of Infinite Dilution Activity Coefficients for Tetrahydrofuran and Other Substances in Solvent 1,4-butanediol. Huaxue Gongcheng 1996, 24, 54− 58 17.. (8) Regenhardt, S. A.; Meyer, C. I.; Garetto, T. F.; Marchi, A. J. Selective gas phase hydrogenation of maleic anhydride over Nisupported catalysts: Effect of support on the catalytic performance. Appl. Catal., A 2012, 449, 81−87. (9) Mathias, P. M. Guidelines for the Analysis of Vapor−Liquid Equilibrium Data. J. Chem. Eng. Data 2017, 62, 2231−2233. (10) Mathias, P. M. Effect of VLE Uncertainties on the Design of Separation Sequences by Distillation − Study of the Benzene− Chloroform−Acetone System. Fluid Phase Equilib. 2016, 408, 265−272. (11) Wisniak, J. A new test for the thermodynamic consistency of vapor-liquid equilibrium. Ind. Eng. Chem. Res. 1993, 32, 1531−1533. (12) Redlich, O.; Kister, A. T. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 1948, 40, 345−348. (13) Van Ness, H. C.; Byer, S. M.; Gibbs, R. E. Vapor-liquid equilibrium: part I. An appraisal of data reduction methods. AIChE J. 1973, 19, 238−244. (14) Yaws, C. L. Chemical Properties Handbook, 1st ed.; McGraw-Hill Yaws Co.: New York, 1999. (15) Wilson, G. M. Vapor-Liquid Equilibrium. XI. A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127− 130. (16) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (17) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A new Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J. 1975, 21, 116−128.
where n is the number of property values; P, T, x, y, are pressure, temperature, mole fraction of light composition in liquid, and vapor phase, respectively; exp denotes the measured value of the variables; cal denotes the calculated value of the variables; σ is the standard deviation of indicated data. The correlated pairwise interaction parameters of the three models and average absolute deviations (AAD) are shown in Table 6, together with the root-mean-square-deviations (RMSD) of the data correlation. The comparisons between experimental and correlated results of the two systems are plotted in Figures 5, 6, 7, and 8. All Tables and Figures show that the correlated values agree well with those of experimental.
4. CONCLUSION New isobaric VLE data for binary mixtures THF (1) + GBL (2) and THF (1) + BDO (2) have been measured at 50.0 and 70.0 kPa. No azeotropic behavior was found at experimental pressures. All the measured data passed the thermodynamic consistency test. The VLE data sets were regressed using the maximum likelihood method and pairwise parameters were estimated for the Wilson, NRTL, and UNIQUAC models. All models resulted in a good fit of the VLE data. The two binary systems both exhibit positive deviations from ideality.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00584. Experimental vapor pressure and relevant literature data (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]; Fax: +86-22-27403389; Telephone: +86-22-27890907. ORCID
Changsheng Yang: 0000-0002-3226-8517 Notes
The authors declare no competing financial interest. Funding
The authors thank the financial support from the National Natural Science Foundation of China (21601079) and the Shandong Provincial Natural Science Foundation (ZR2016EMQ06).
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REFERENCES
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DOI: 10.1021/acs.jced.7b00584 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
