Isobaric Vapor–Liquid Equilibrium for Two Binary Systems{Propane-1

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Isobaric Vapor−Liquid Equilibrium for Two Binary Systems{Propane1,2-diol + Ethane-1,2-diol and Propane-1,2-diol + Butane-1,2-diol} at p = (10.0, 20.0, and 40.0) kPa Changsheng Yang,* Xue Feng, Yankai Sun, Qian Yang, and Juan Zhi Synergetic Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin University, Tianjin 300072, China Key Laboratory for Green Chemical Technology of State Education Ministry, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China ABSTRACT: Isobaric vapor−liquid equilibrium (VLE) data for the two binary systems of {propane-1,2-diol + ethane-1,2-diol and propane-1,2diol + butane-1,2-diol} at p = (10.0, 20.0, and 40.0) kPa have been determined using a modified Rose−Williams still with continuous circulation of both vapor and liquid phases in this work. The thermodynamic consistency tests of the experimental VLE data were performed according to the methods of the Herington area test and Van Ness point test. The experimental isobaric VLE data were then correlated using the universal quasichemical (UNIQUAC), nonrandom two-liquid (NRTL), Margules, and Wilson activity coefficient models. Consequently, the calculation values showed good agreements with the experimental data measured in this study.

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INTRODUCTION Ethane-1,2-diol (EG) is considered as one of the most important organic compounds with various applications, which is extensively used in the fields of plasticizer, solvent, antifreeze production and polymer ester manufacture.1 At present, there exist several reaction routes well-known for the synthesis of EG. The conventional synthesis process for manufacturing EG is oil petroleum route which has obvious drawbacks such as the high consumption of petroleum and the negative impact on the environment. Therefore, it is necessary to develop nonpetroleum reaction routes to substitute the traditional process. In view of several promising nonpetroleum EG production processes, the C1 process based on the syngas2,3 mainly derived from coal shows great potential, as the coal resource is relatively abundant compared with the petroleum in China and many regions of the world. The C1 process based on the syngas consists of two steps: the synthesis of dimethyl oxalate (DMO) as the first step, and the second step being the conversion of DMO to EG by the process of DMO hydrogenation. In the process of DMO hydrogenation, propane-1,2-diol (PG) and butane-1,2-diol (1,2-BD) are synthesized as the byproducts due to the excessive DMO hydrogenation. However, both the propane-1,2-diol and butane-1,2-diol have a broad range of applications. For propane-1,2-diol, it has aroused much interest from researchers in many fields owing to its variety of industrial applications, such as antifreeze, emulsifier, and pharmaceutical.4 For butane-1,2-diol, it is one of four isomerides of the butanediols which is an useful chemical widely used in biotechnological processes with enormous potential.5 Thus, a good separation between EG and the byproducts will bring considerable economic benefits. © 2015 American Chemical Society

The accurate vapor−liquid equilibrium (VLE) data will make great contribution to the design of the separation process of propane-1,2-diol, ethane-1,2-diol, and butane-1,2-diol. Until now, the isobaric VLE data of the propane-1,2-diol + ethane-1,2-diol and propane-1,2-diol + butane-1,2-diol systems are relatively scarce in published papers.2,6,7 Thus, in this work, the isobaric vapor−liquid equilibrium data of propane-1,2-diol + ethane-1,2-diol and propane-1,2-diol + butane-1,2-diol systems were measured at the pressures of (10.0, 20.0, and 40.0) kPa. Furthermore, the experimental VLE data of the two systems at 10.0 kPa were compared with the previous data measured by Zhang et al.2 The results indicated the accuracy and reliability of the experimental data measured in this paper. The thermodynamic consistency of the measured VLE data of the two binary systems at three reduced pressures was checked and verified according to the methods of the Herington area test8 and Van Ness point test.9 And the isobaric VLE data were correlated by four activity coefficient models, which were the universal quasichemical (UNIQUAC)10 model, nonrandom two-liquid (NRTL)11 model, Margules12 model, and Wilson13 model, respectively. The calculation values derived from the four models showed good agreements with the experimental data.

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EXPERIMENTAL SECTION Chemicals. EG (≥0.998, mass fraction purity) and PG (≥0.990, mass fraction purity) were purchased from Tianjin Received: November 28, 2014 Accepted: February 18, 2015 Published: March 2, 2015 1126

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Table 1. Densities (ρ), Refractive Indexes (nD), and Boiling Points (Tb)a of Pure Components Compared with Literature Values ρ(298.15 K)

compound

nD (298.15 K)

Tb (101.3 kPa)

g/cm−3 EG PG 1,2-BD a

K

exptl

lit

exptl

lit

exptl

lit

1.10982 1.03190 0.99878

1.110b 1.033b 0.99886c

1.4310 1.4320 1.4378

1.4306b 1.4314b 1.4374c

470.40 460.69 469.71

470.45b 460.75b 469.575d

Standard uncertainties of ρ and nD are 0.00001 g/cm−3 and 0.0001, respectively. bRef 14. cRef 15. dRef 16.

Guangfu Technology Development Co. Ltd., China. 1,2-BD (≥0.98, mass fraction purity) was provided by TCI (Tokyo Chemical Industry Co. Ltd., Shanghai) Development Co., Ltd. The purities of the three chemical substances were tested by gas chromatography (GC-SP2100A) analysis with a thermal conductivity detector (TCD). The impurity in EG was less than 0.002 (mass fraction), so it was used without any further purification. For obtaining a high purity, both PG and 1,2-BD were further purified in order to decrease the experimental errors. They were first dried by molecular sieves (type pore diameter 0.3 nm, Guangfu) and then given purification in a distillation column under the reduced pressure. After the processes mentioned above, the purity of PG could reach 0.997 (mass fraction). However, the purity of 1,2-BD was not improved obviously. The final purity of 1,2-BD was 0.992 (mass fraction). This fact indicated that the conventional distillation method used for the impurity removal in 1,2-BD cannot bring it a high purity. The densities (ρ), refractive indexes (nD), and the boiling points (Tb) of the three pure substances were determined in this work. The densities (ρ) were measured using an AntonPaar DMA-58 densimeter at (298.15 ± 0.01) K. The refractive indexes (nD) were measured by a ATAGO NAR-3T Abbe refractometer at (298.15 ± 0.01) K. The accuracies of the densimeter and the refractometer are 0.00001 g·m−3 and 0.0001, respectively. The boiling points were measured at 101.3 kPa with an uncertainty of 0.1 K. All of the three pure substance properties determined in this work are shown in Table 1 along with the published values.14−16 Apparatus and Procedures. The measurements of the isobaric VLE data were carried out in a modified Rose− Williams still which was made up of a condenser and a boiling chamber. This experimental device could guarantee the vapor and liquid phases full contact by continuous circulation of the two phases and reach equilibrium rapidly. The experimental apparatus is presented in Figure 1. The operating pressure in the experiments was regulated by a buffer tank and a vacuum pump. The vacuum pump ran continuously, and a needle valve linked with the vacuum pump was used to control the air amount entering into the system and change the system pressure slowly. By regulating the opening of the valve, the pressure needed in the experiments can be obtained and kept stable for a long time. We used a U-shaped differential manometer to determine the system pressure with an uncertainty of 0.13 kPa. The energy needed of the system was provided by a heating rod under the control of a thermocouple. The heating intensity was kept at a level that could enable the system to produce 30 condensate drops per minute. The equilibrium temperature was determined precisely with a mercury thermometer accurate to 0.01 K. The ethanol was chosen as the condensation liquid in the condenser whose working temperature is (263.15 to 273.15) K. It aimed at

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.

converting the vapor phase into the liquid phase quickly for avoiding the mass loss in the solution. To ensure the precision of the apparatus as much as possible, the vaseline was applied to all of the ground-glass joints for achieving good sealing. The equilibrium still had a total volumetric capacity of 140 cm3 approximately. About half of the volume was full of the solution. The solutions were prepared gravimetrically with an electronic balance accurate to 0.0001 g. In each experiment, after putting the solutions into the still, we turned on the vacuum pump, the heating equipment, and then adjusted the opening of the needle valve until the system pressure arrived at the desired value. The equilibrium was achieved with the fluctuation of the vapor temperature within 0.1 K and then both the liquid and vapor phase samples were taken out from the sampling ports by employing a microsyringe for GC analysis. The reliability of the experimental device has already been verified in our previous work.17−20 Analysis. The equilibrium of the liquid and vapor (condensed to liquid) samples were quantificationally analyzed by a BFRL SP-2100A GC that was equipped with a flame ionization detector used together with a SE-54 capillary column (30 m × 0.32 mm × 0.5 μm). We used a N2000 chromatography station to treat the GC response peaks. High purity nitrogen was used as the carrier gas whose flow velocity was maintained constant at 20 mL·min−1. The flow rates of H2 (≥0.9999, mass fraction purity) and air (≥0.9999, mass fraction purity) were both 20 mL·min−1. For the two binary systems, they had the same chromatography operation condition. The temperatures of the column, the injector, and the detector were (473.15, 513.15, and 533.15) K, respectively. The injection volume of each sample into the GC was 0.4 μL. A series of standard solutions of known compositions was prepared gravimetrically by using an analytical balance accurate to 0.0001 g for the calibration of GC. The external standard was 1127

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chosen to obtain quantitative analysis results by using the external standard curve to convert the peak areas into mole fractions of each sample. At least three measurements were done of each sample to ensure the accuracy and reproducibility of the quantitative analysis results, and the final value was the average of the most close three results. The uncertainties of the vapor and liquid mole fractions were within 0.005 and 0.002, respectively.

Table 3. VLE Experimental Data and Calculated Activity Coefficient (γ) for the PG (1) + 1,2-BD (2) system at p = (10.0, 20.0, and 40.0) kPaa T

RESULTS AND DISCUSSION Experimental Data. The isobaric vapor−liquid equilibrium (VLE) data for the two binary systems of {propane-1,2-diol + Table 2. VLE Experimental Data and Calculated Activity Coefficient (γ) for the PG (1) + EG (2) system at p = (10.0, 20.0, and 40.0) kPaa x1

y1

γ1

1.000 0.939 0.859 0.768 0.662 0.596 0.452 0.339 0.280 0.156 0.075 0.000 1.000 0.976 0.854 0.732 0.577 0.476 0.349 0.223 0.151 0.079 0.000 1.000 0.928 0.796 0.699 0.629 0.561 0.468 0.417 0.308 0.205 0.091 0.051 0.000

1.000 0.945 0.883 0.810 0.728 0.667 0.543 0.434 0.364 0.227 0.120 0.000 1.000 0.978 0.884 0.785 0.648 0.551 0.436 0.299 0.212 0.115 0.000 1.000 0.933 0.825 0.747 0.693 0.632 0.543 0.497 0.392 0.284 0.145 0.084 0.000

1.000 0.998 1.004 1.009 1.026 1.024 1.056 1.088 1.079 1.145 1.207

γ2 20 kPa

K 10 kPa

20 kPa

40 kPa

398.25 398.46 398.79 399.27 399.86 400.31 401.23 402.02 402.57 403.82 404.83 406.10 414.88 415.05 415.62 416.19 417.08 417.82 418.87 420.12 421.01 422.02 423.29 433.22 433.64 434.27 434.77 435.14 435.54 436.19 436.59 437.53 438.61 440.14 440.91 442.17

1.000 0.995 1.005 1.018 1.030 1.031 1.068 1.092 1.105 1.102 1.000 0.990 0.998 1.011 1.028 1.037 1.043 1.057 1.092 1.144 1.248 1.256

y1

γ1

1.000 0.942 0.832 0.757 0.667 0.570 0.436 0.291 0.179 0.107 0.020 0.000 1.000 0.969 0.846 0.751 0.625 0.564 0.469 0.344 0.282 0.157 0.032 0.000 1.000 0.953 0.848 0.695 0.660 0.560 0.404 0.339 0.235 0.112 0.011 0.000

1.000 0.954 0.859 0.798 0.721 0.637 0.511 0.373 0.254 0.164 0.031 0.000 1.000 0.974 0.873 0.792 0.683 0.628 0.541 0.419 0.354 0.213 0.048 0.000 1.000 0.962 0.869 0.737 0.706 0.615 0.467 0.404 0.297 0.159 0.020 0.000

1.000 1.000 0.993 0.998 1.005 1.019 1.038 1.095 1.167 1.218 1.162

γ2

K 10 kPa

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T

x1

1.259 1.142 1.104 1.057 1.061 1.031 1.023 1.031 1.013 1.007 1.003

40 kPa

1.077 1.063 1.064 1.064 1.032 1.023 1.016 1.011 1.002 1.271

398.26 398.55 399.14 399.51 399.92 400.37 401.06 401.89 402.78 403.58 404.96 405.41 414.88 415.01 415.62 416.09 416.82 417.17 417.78 418.67 419.16 420.31 421.73 422.15 433.22 433.53 434.14 434.97 435.17 435.79 436.82 437.27 438.12 439.42 440.68 440.83

1.000 1.000 1.002 1.005 1.012 1.017 1.029 1.049 1.061 1.097 1.148 1.000 0.998 0.991 0.996 0.998 1.002 1.017 1.032 1.062 1.140 1.397

1.076 1.109 1.080 1.069 1.055 1.051 1.033 1.020 1.014 1.008 1.000 1.117 1.072 1.065 1.046 1.041 1.029 1.017 1.013 1.004 1.000 1.000 1.050 1.095 1.063 1.058 1.047 1.031 1.023 1.011 0.995 0.996 1.000

a Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.13 kPa, u(x) = 0.002, and u(y) = 0.005.

1.265 1.140 1.096 1.065 1.063 1.064 1.054 1.038 1.023 1.012 1.011 1.002

the liquid phase (xi), the activity coefficient (γi) of each component, and the equilibrium temperature (T). Pure Component Vapor Pressure. For propane-1,2-diol and ethane-1,2-diol, the saturation vapor pressures of the pure components were calculated with Antoine eq 1 taken from Yaws.14 For 1,2-butanediol, the pure component vapor pressure was calculated with Antoine eq 2 obtained from literature.21 ⎛ 760ps ⎞ i /kPa⎟ log⎜ ⎝ 101.325 ⎠ B =A+ + C log(T /K) + D(T /K) + E(T /K)2 T /K

a

Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.13 kPa, u(x) = 0.002, and u(y) = 0.005.

ethane-1,2-diol, propane-1,2-diol + butane-1,2-diol} at p = (10.0, 20.0, and 40.0) kPa are presented in Tables 2 and 3, separately. The VLE data listed consist of the equilibrium mole fraction of the vapor phase (yi), the equilibrium mole fraction of

(1)

ln(pis /kPa) = A + 1128

B + C ln(T /K) + D(T /K)E T /K

(2)

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Table 4. Antoine Coefficient of Pure Components Used in This Study Compound a

EG PGa 1,2-BDb a

Range of T

Antoine coefficients A

B

82.4062 90.2930 96.3722

C

−6347.2 −6696.8 −11548

D

E −09

−25.433 −28.109 −10.925

K −06

−2.37 × 10 −1.33 × 10−10 4.26 × 10−18

8.75 × 10 9.37 × 10−06 6

260.15 to 645 213.15 to 626 220 to 680

Ref 14. bRef 21.

Table 7. Mathematical Forms of the Activity Coefficient Equations Used in This Work Wilson

⎛ Aij Aji ⎞ ⎟ ln γ1 = − ln(x1 + Aijxj) + ⎜⎜ − + + x x A x xiAji ⎟⎠ ⎝ i j ij j Vj ⎛ gij − gii ⎞ Aij = exp⎜− ⎟ ⎝ Vi RT ⎠

RTci τi Zci Pci

Vi =

τi = 1 + (1 − T /Tci)2/7

T /Tci ≤ 0.75

NRTL

⎡ ⎤ Gji2τji Gij2τij ⎥ ln γi = xj2⎢ + 2 2 ⎢⎣ (xi + xjGji) (xj + xiGij) ⎥⎦ Gij = exp(− aijτij) aij = aji RT UNIQUAC ⎛ϕ⎞ ⎛ r ⎞ ⎛Z⎞ ⎛θ ⎞ ln γi = ln⎜⎜ i ⎟⎟ + ⎜ ⎟qi ln⎜⎜ i ⎟⎟ + ϕj⎜⎜li − i l j⎟⎟ − qi(θi + θτ j ji) ⎝ 2 ⎠ ⎝ϕ⎠ rj ⎠ ⎝ ⎝ xi ⎠ i

Table 5. Experimental Vapor Pressuresa of 1,2-Butanediol at w = 0.992 Mass Fraction T

P

T

P

K

kPa

K

kPa

392.06 397.24 402.31 406.54 412.23 417.66 422.48 427.21 a

5.62 7.21 8.86 10.62 13.56 16.89 20.34 24.45

432.29 437.41 442.77 447.52 452.13 457.24 462.57 466.64

⎛ τji τij ⎞ ⎟⎟ + θjqi⎜⎜ − θ + θτ θ + θτ ⎝ i j ji j i ij ⎠ li =

29.56 35.54 41.92 50.54 58.86 69.36 81.92 92.78

PG(1) + EG(2) PG(1) + 1,2- BD(2) a

area testa

point testb

kPa

D−J

|Δy1|

10 20 40 10 20 40

3.739 8.237 7.759 6.327 1.604 4.900

+ + + + + +

0.004 0.005 0.004 0.005 0.001 0.004

θi =

qixi qixi + qjxj

φi =

rx i i rx i i + rjxj

Margules

ln γi = xj2[Aij + 2xi(Aji − Aij)]

Table 8. Critical Constants (Tc, Pc, Zc), Molecule Volume Parameters r, and Area Parameters q for the UNIQUAC Model

Table 6. Results of Thermodynamic Consistency Test for the Two Systems at Three Pressures p

Z (ri − qi) − (ri − 1) 2

⎛ gji − gii ⎞ τji = exp⎜− ⎟ ⎝ RT ⎠

Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.13 kPa.

system

gij − gjj

τij =

Figure 2. Experimental saturation pressures of butane-1,2-diol (w = 0.992, mass fraction) compared with the literature values calculated by the Antoine eq 2. Figure: ●, experimental values; , literature values.

+ + + + + +

a

compound

q

r

Tc

Pc

K

kPa

PG EG 1,2-BD

2.784a 2.248c 3.324a

3.0824a 2.4088c 3.7568a

626b 645b 680d

6.1b 7.53b 5.21d

Zc 0.280b 0.268b 0.279a

Ref 21. bRef 14. cRef 24. dRef 25.

pressures of 1,2-butanediol (w = 0.992, mass fraction) were determined in this work in order to make a comparison with the values calculated with Antoine eq 2, as shown in Figure 2. The experimental vapor pressures of 1,2-butanediol are listed in Table 5. The average deviation between the experimental saturation pressures and literature values calculated by the Antoine eq 2 was Δp = 0.013, so the experimental saturation pressures fitted well with the literature values. Therefore, Antoine eq 2 was capable of accurately calculating the pressure of 1,2-BD. Δp is defined as follows:

Ref 8 and 23. bRef 9.

where A, B, C, D, and E are Antoine constants and T stands for the system temperature in Kelvin. The values of Antoine constants14,21 for all of the components are listed in Table 4. To verify the reliability of the Antoine eq 2 from Aspen Physical Property System pure-component data bank, the vapor 1129

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Table 9. Parameters for the UNIQUAC, NRTL, Wilson, and Margules Equations, AADT/K, AADy1, RMSDT/K and RMSDy1 for {PG (1) + EG (2)} at p = (10.0, 20.0, and 40.0) kPa 10.0 kPa

20.0 kPa

UNIQUAC Parameters 35.479 36.850 249.606 250.302 0.07 0.04 0.002 0.005 0.09 0.05 0.003 0.006 NRTL Parameters 106.938 111.485 518.451 520.148 0.08 0.06 0.002 0.004 0.01 0.07 0.003 0.005 Wilson Parameters 505.062 399.916 289.867 524.030 0.06 0.03 0.002 0.004 0.07 0.04 0.003 0.005 Margules Parameters 0.2384 0.2153 0.1328 0.1394 0.05 0.03 0.004 0.005 0.06 0.04 0.005 0.006

g12 − g22/J·mol−1 g21 − g11/J·mol−1 AADT/K AADy1 RMSDT/K RMSDy1 g12 − g22/J·mol−1 g21 − g11/J·mol−1 AADT/K AADy1 RMSDT/K RMSDy1 g12 − g11/J·mol−1 g21 − g22/J·mol−1 AADT/K AADy1 RMSDT/K RMSDy1 A12 A21 AADT/K AADy1 RMSDT/K RMSDy1

Table 10. Parameters for the UNIQUAC, NRTL, Wilson, and Margules Equations, AADT/K, AADy1, RMSDT/K, and RMSDy1 for {PG (1) + 1,2-BD (2)} at p = (10.0, 20.0, and 40.0) kPa

40.0 kPa

10.0 kPa

86.4096 264.852 0.17 0.004 0.20 0.005

g12 − g22/J·mol−1 g21 − g11/J·mol−1 AADT/K AADy1 RMSDT/K RMSDy1

237.8216 538.281 0.18 0.005 0.22 0.006

g12 − g22/J·mol−1 g21 − g11/J·mol−1 AADT/K AADy1 RMSDT/K RMSDy1

504.051 296.727 0.15 0.004 0.18 0.005

g12 − g11/J·mol−1 g21 − g22/J·mol−1 AADT/K AADy1 RMSDT/K RMSDy1

0.3313 0.1001 0.05 0.005 0.06 0.007

A12 A21 AADT/K AADy1 RMSDT/K RMSDy1

exp N cal exp AADT = (1/N)Σi N= 1|Tcal i − Ti |, AADy1 = (1/N)Σi = 1|yi − yi |, N cal exp 2 N cal 1/2 RMSDT = ((Σi = 1(Ti − Ti ) )/N) , RMSDy1 = ((Σi = 1(yi − 2 1/2 yexp i ) )/N) .

Δp =

20.0 kPa

UNIQUAC Parameters 103.385 24.125 103.675 125.375 0.27 0.06 0.005 0.004 0.31 0.07 0.008 0.004 NRTL Parameters 80.196 200.000 508.002 199.203 0.21 0.04 0.006 0.001 0.26 0.05 0.007 0.002 Wilson Parameters 533.346 253.3156 67.161 208.741 0.23 0.05 0.006 0.002 0.28 0.07 0.008 0.003 Margules Parameters 0.3488 0.1453 0.0136 0.0851 0.03 0.01 0.005 0.001 0.03 0.01 0.007 0.001

40.0 kPa 8.726 118.349 0.12 0.005 0.13 0.005 68.373 261.463 0.09 0.005 0.11 0.007 275.423 102.902 0.10 0.006 0.12 0.007 0.1518 0.0334 0.02 0.002 0.02 0.003

exp N cal exp AADT = (1/N)Σi N= 1|Tcal i − Ti |, AADy1 = ((1/N))Σi = 1|yi − yi |, N cal exp 2 N cal 1/2 RMSD T = ((Σi = 1(Ti − Ti ) )/N) , RMSD y1 = ((Σi = 1(yi − 2 1/2 yexp i ) )/N) .

∑N |(pexp − pcal )/pexp | N

(3)

where N is the number of the experimental data points. pexp and pcal represent the experimental and calculated saturation pressures, respectively. Thermodynamic Consistency Test. The thermodynamic consistency tests of the experimental VLE data were treated for the two binary systems by the methods of the Herington area test and Van Ness point test so as to check the reliability of the experimental data. According to the method of the Herington area test, the isobaric VLE data was considered consistent if |D − J| < 10. D=

S+ − S− ·100 S+ + S−

(4)

Figure 3. VLE data for the system {PG (1) + EG (2)} at 10.0 kPa: △, experimental data for T−x; ▲, experimental data for T−y; ○, literature data for T−x; ●, literature data for T−y; , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the Wilson equation; ---, calculated data by the NRTL equation; -·-·-, calculated data by the Margules equation. x1 and y1 are the mole fractions of PG in the liquid and vapor phases, respectively.

where S+ and S− are obtained from the ln (γ1/γ2) − x1 plot. S+ is the area of the plot above the x axis. S− is the area of the plot below the x axis J = 150·

(Tmax − Tmin) Tmin

(5)

For the Van Ness point test, Gmehling and Onken21 suggested the isobaric VLE data were thermodynamically

where Tmax and Tmin represent the maximum and minimum temperatures of the system, respectively. 1130

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Figure 4. VLE data for the system {PG (1) + EG (2)} at 20.0 kPa: △, experimental data for T−x; ▲, experimental data for T−y; , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the Wilson equation; ---, calculated data by the NRTL equation; -·-·-, calculated data by the Margules equation; x1 and y1 are the mole fractions of PG in the liquid and vapor phases, respectively.

Figure 6. VLE data for the system {PG (1) + 1,2-BD (2)} at 10.0 kPa: △, experimental data for T−x; ▲, experimental data for T−y; ○, literature data for T−x; ●, literature data for T−y; , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the Wilson equation; ---, calculated data by the NRTL equation; -·-·-, calculated data by the Margules equation. x1 and y1 are the mole fractions of PG in the liquid and vapor phases, respectively.

Figure 5. VLE data for the system {PG (1) + EG (2)} at 40.0 kPa: △, experimental data for T−x; ▲, experimental data for T−y; , calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the Wilson equation; ---, calculated data by the NRTL equation; -·-·-, calculated data by the Margules equation. x1 and y1 are the mole fractions of PG in the liquid and vapor phases, respectively.

Figure 7. VLE data for the system {PG (1) + 1,2-BD (2)} at 20.0 kPa: △, experimental data for T−x; ▲, experimental data for T−y; calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the Wilson equation; ---, calculated data by the NRTL equation; -·-·-, calculated data by the Margules equation. x1 and y1 are the mole fractions of PG in the liquid and vapor phases, respectively.

consistent, if the average deviation of the vapor mole fractions was less than or equal to 0.01. A four-parameter Legendre polynomial was used to express the excess Gibbs free energy

vapor mole fractions were less than 10 and 0.01, respectively. Therefore, the experimental data were consistent and reliable. Data Correlation. At experimental pressures of (10.0, 20.0, and 40.0) kPa, the vapor phase could be assumed as an ideal phase. Therefore, the VLE equation can be simplified as follows:

k

g=

GE = x1(1 − x1) ∑ ak Lk (x1) RT

and a nonlinear optimization method was chosen to minimize the following objective function: F=

∑ (y1cal

+ y2cal − 1)

γ1x1pis = yp i

(6)

(i = 1, 2)

(7)

where xi and yi are the mole fractions of component i in the liquid and vapor phases, respectively; p stands for the system pressure; and pis represents the saturation vapor pressure of pure component i. In this way, the experimental values of the activity coefficients of component i of the liquid phase can be calculated and also listed in Tables 2 and 3.

where y1cal and y2cal represent the calculated values of vaporphase mole fractions of component 1 and 2, respectively. The results of the thermodynamic consistency tests of the two systems are presented in Table 6. As it could be seen directly, all of the |D − J| values and the average deviations in 1131

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where U is a variable quantity, which stands for the equilibrium temperature and vapor-phase mole fraction in this work; N is the number of experimental data points. The values of the binary interaction energy parameters, AADT, AADy1, RMSDT, and RMSDy1 for each system at three pressures are presented in Tables 9 and 10. The experimental VLE data as symbols together with the calculated values as lines are plotted as T−x1−y1 diagrams for the systems of {propane-1,2-diol + ethane-1,2-diol} and {propane-1,2-diol + butane-1,2-diol} at p = (10.0, 20.0, and 40.0) kPa in Figures 3 to 8. Besides, the published data2 for the two systems at 10.0 kPa are also plotted in Figures 3 and 6. A comparison was made between the experimental data and the published values. On the whole, the data measured in this work agreed well with the literature data. The quality of the fit was good. For the two binary systems of {propane-1,2-diol + ethane1,2-diol} and {propane-1,2-diol + butane-1,2-diol}, the maximum absolute deviations of the temperatures |ΔT|max between the correlated values derived from the four activity coefficient models and experimental values were (0.22, 0.13, and 0.45) K and (0.50, 0.12, and 0.21) K at p = (10.0, 20.0, and 40.0) kPa, respectively. The maximum absolute deviations of the vapor-phase mole fraction|Δy1|max between the correlated values derived from the four activity coefficient models and the experimental values were (0.007, 0.009, and 0.009) and (0.009, 0.006, and 0.011), respectively. As it can be seen from the results in Tables 9 and 10, the deviations of the regression are reasonably small. Therefore, the UNIQUAC, NRTL, Margules, and Wilson models were able to correlate the experimental data determined in this study accurately and the four models had similar accuracies.

Figure 8. VLE data for the system {PG (1) + 1,2-BD (2)} at 40.0 kPa: △, experimental data for T−x; ▲, experimental data for T−y; calculated data by the UNIQUAC equation for T−x−y; ···, calculated data by the Wilson equation; ---, calculated data by the NRTL equation; -·-·-, calculated data by the Margules equation. x1 and y1 are the mole fractions of PG in the liquid and vapor phases, respectively.

All of the experimental VLE data were correlated by using the UNIQUAC, NRTL, Margules, and Wilson activity coefficient models. The equation forms are listed in Table 7. For UNIQUAC model, Z stands for the lattice coordination number whose value is 10; gij represents the interaction energy between the molecules i and j; the van der Waals area parameters (qi) and the volume parameters (ri) are presented in Table 8; gij − gjj are the binary interaction parameters. As to NRTL model, the nonrandomness parameter (aij) is fixed to 0.3; and gij − gjj are the binary interaction energy parameters. Aij and Aji stand for the Margules parameters. For Wilson model, gij − gii are the binary interaction energy parameters; the values of the critical temperature (T ci ), pressure (P ci ), and compressibility factor of component i are also presented in Table 8. The values of the binary interaction energy parameters of the four models studied in this work were obtained by minimizing the following objective function: ⎡⎛ ⎞2 ⎤ ⎢⎜ γexp − γcal ⎟ ⎥ OF = ∑ ⎢⎜ γexp ⎟⎠ ⎥ ⎣⎝ ⎦

■

The isobaric vapor−liquid equilibrium data of two binary systems of {propane-1,2-diol + ethane-1,2-diol} and {propane1,2-diol + butane-1,2-diol} were determined at p = (10.0, 20.0, and 40.0) kPa in a modified Rose−Williams still. The saturation vapor pressures of 1,2-BD were determined at the temperatures T = (392.06 to 466.64) K. The experimental vapor pressures indicated that the Antoine eq 2 from Aspen data bank was able to calculate the saturation vapor pressures of 1,2-BD at certain temperatures accurately. All of the experimental data passed the thermodynamic consistency tests by means of the Herington area test and Van Ness point test. The UNIQUAC, Wilson, Margules, and NRTL activity coefficient equations were used to correlate the experimental VLE data. For the two binary systems, the absolute average deviations of the boiling temperature AADT were below (0.27, 0.15, and 0.18) K, and the absolute average deviations of the vapor-phase mole fraction AADy1 were below (0.006, 0.005, and 0.006) at p = (10.0, 20.0, and 40.0) kPa, respectively. In addition, the rootmean-square deviations (RMSD) of the regression were also reasonably small (less than 0.008 in vapor-phase mole fraction and 0.31 K in boiling temperature). The results indicated that the four models were capable of correlating the measured systems accurately. The experimental binary data measured in this work will be a valuable reference to the chemical engineering systems including ethane-1,2-diol, propane-1,2diol, and butane-1,2-diol in the future.

(8)

where γexp and γcal are the experimental and calculated activity coefficients, respectively. The average absolute deviations (AAD) and the root-meansquare deviations (RMSD) of the equilibrium temperatures and vapor-phase mole fractions of the two binary systems at three reduced pressures were both calculated to measure the agreement between the experimental and calculated values. The AAD and RMSD are given as follows: AAD =

1 N

N

∑ |Uiexp − Uical| i=1

(9)

N

RMSD =

∑i = 1 (Uiexp − Uical)2 N

CONCLUSION

(10) 1132

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of Methanol, Diethylamine, and N,N-Diethylethanolamine at p = (60.0 and 101.3) kPa. J. Chem. Eng. Data 2013, 58, 482−487. (19) Yang, C. S.; Zhang, P.; Qin, Z. L.; Feng, Y.; Zeng, H.; Sun, F. Z. Isobaric Vapor−Liquid Equilibrium for the Binary Systems (Diethylamine + Ethanol), (Ethanol + N,N-Diethylethanolamine), and (Diethylamine + N,N-Diethylethanolamine) at p = (80.0 and 40.0) kPa. J. Chem. Eng. Data 2014, 59, 750−756. (20) Yang, C. S.; Sun, Y. K.; Qin, Z. L.; Feng, Y.; Zhang, P.; Feng, X. Isobaric Vapor−Liquid Equilibrium for Four Binary Systems of Ethane-1,2-diol, Butane-1,4-diol, 2-(2-Hydroxyethoxy)ethan-1-ol, and 2-[2-(2-Hydroxyethoxy)ethoxy]ethanol at 10.0 kPa, 20.0 kPa, and 40.0 kPa. J. Chem. Eng. Data 2014, 59, 1273−1280. (21) Aspen Plus, version 7.0; Aspen Technology, Inc.: Burlington, MA, 2011. (22) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; Chemistry Data Series; DECHEMA: Frankfurt, Germany, 1977. (23) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345−348. (24) Kamihama, N.; Matsuda, H.; Kurihara, K.; Tochigi, K.; Oba, S. Isobaric Vapor−Liquid Equilibria for Ethanol + Water + Ethylene Glycol and Its Constituent Three Binary Systems. J. Chem. Eng. Data 2012, 57, 339−344. (25) Steele, W. V.; Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A. Vapor Pressure of Acetophenone, (±)-1,2-butanediol, (±)-1,3Butanediol, Diethylene Glycol Monopropyl Ether, 1,3-Dimethyladamantane, 2-Ethoxyethyl Acetate, Ethyl Octyl Sulfide, and Pentyl Acetate. J. Chem. Eng. Data 1996, 41, 1255−1268.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: 022-2740-3389. Telephone: 022-2789-0907. Notes

The authors declare no competing financial interest.

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