Isobaric Vapor–Liquid Equilibrium for Four Binary Systems of Ethane

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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 Changsheng Yang,* Yankai Sun, Zhenli Qin, Yang Feng, Ping Zhang, and Xue Feng Key Laboratory for Green Chemical Technology of State Education Ministry, School of Chemical Engineering and Technology, Tianjin University, Tianjin, People’s Republic of China ABSTRACT: Isobaric vapor−liquid equilibrium (VLE) data for the binary systems of {ethane-1,2-diol + butane-1,4-diol, ethane-1,2-diol + 2-(2-hydroxyethoxy)ethan-1-ol, butane-1,4diol + 2-(2-hydroxyethoxy)ethan-1-ol, and 2-(2hydroxyethoxy)ethan-1-ol + 2-[2-(2-hydroxyethoxy)ethoxy]ethanol} have been experimentally measured at 10.0 kPa, 20.0 kPa, and 40.0 kPa using a modified Rose−Williams still in this study. The experimental data of the binary systems were wellcorrelated by universal quasichemical (UNIQUAC), nonrandom two-liquid (NRTL), and Wilson activity coefficient models at the three subatmospheric pressures, and the calculated values of the three models agreed well with the experimental data. Then the VLE data of the four binary systems were checked by the Herington area test and Van Ness point test, which showed thermodynamic consistency.

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INTRODUCTION As an important organic chemical raw material, ethane-1,2-diol (EG) is mainly used in the production of polyester fibers, antifreeze, nonionic surfactants, ethanolamines, and explosives. In the fields of tobacco industry, textile industry, and cosmetic industry, EG also has a wide range of applications.1 Several papers2 have reported that petroleum is the raw material for the synthesis of EG. However, owing to the increasing consumption and soaring price of petroleum, the nonpetroleum process in production of EG is significant. The present route based on the syngas from coal has aroused more attention in many countries.3 To the route of synthesis of EG based on the syngas, the first step is synthesizing dimethyl oxalate (DMO), and then EG is synthesized by DMO hydrogenation. When EG is synthesized by DMO hydrogenation, butane1,4-diol (BDO), 2-(2-hydroxyethoxy)ethan-1-ol (DEG), and 2[2-(2-hydroxyethoxy)ethoxy]ethanol (TEG) are also obtained as byproducts. Each of byproduct has its own application. For example, BDO is widely used as a polymer feedstock among the four carbon-based diols.4 DEG is commonly used as antifreeze, lubricating, and finishing agents and aircrafts at the airports.5 For TEG, natural gas dehydration is an important operation in the gas processing and conditioning industry.6 The refined EG and byproducts are generally obtained from the crude reaction mixture by distillation. Therefore, the separation equipment is necessary for obtaining higher purities of EG7 and byproducts. Fundamental knowledge of vapor−liquid equilibrium (VLE) data is essential in the separation process design. On the other © 2014 American Chemical Society

hand, because of the high boiling point of the polybasic alcohol, the separation equipment running at low pressure is necessary to decrease energy consumption. So the VLE data about the polybasic alcohols at subatmospheric pressure are very useful in designing the separation process of EG. To our disappointment, up to now, there are few VLE data which are available in published literature about the four binary systems. Therefore, this study focused on isobaric VLE for the binary systems of EG (1) + BDO (2), EG (1) + DEG (2), BDO (1) + DEG (2), and DEG (1) + TEG (2) 10.0 kPa, 20.0 kPa, and 40.0 kPa. The VLE data of the four binary systems obtained at three subatmospheric pressures were correlated with three activity coefficient models (UNIQUAC, NRTL, and Wilson). Both Herington area test8 and Van Ness point test9 which also described by Gmehling and Onken10 were chosen to verify the thermodynamic consistency of the VLE data of the four binary systems.

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EXPERIMENTAL SECTION Experimental Materials. EG (≥ 0.998, mass fraction purity), BDO (≥ 0.990, mass fraction purity), DEG (≥ 0.990, mass fraction purity), and TEG (≥0.990, mass fraction purity) were purchased from Tianjin Guangfu Fine Chemical Research Institute, China. The purity of EG was 0.998 mass fraction by GC, and it was used without further purification. The water Received: November 25, 2013 Accepted: March 10, 2014 Published: March 19, 2014 1273

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Table 1. Densities (ρ), Refractive Index (nD), and Boiling Points of Pure Compounds Compared with Literature Data ρ/(g·cm−3) (298.15 K) compound EG BDO DEG TEG

a

exptl 1.10792 1.01304 1.11256 1.12070

nD (298.15 K)

lit.

exptl b

1.11000 1.01264b 1.11351b 1.11959b

1.4312 1.4449 1.4452 1.4457

Tb/K (101.3 kPa) lit. b

1.4306 1.4445b 1.4460b 1.4550b

exptl

lit.

470.32 501.05 518.63 558.27

470.45b 501.15b 518.95c 558.15c

a c

EG: ethane-1,2-diol; BDO: butane-1,4-diol; DEG: 2-(2-hydroxyethoxy)ethan-1-ol; TEG: 2-[2-(2-hydroxyethoxy)ethoxy]ethanol. bReference 11. Reference 12.

vacuum pump to control the amount of the air into the system. In this way, the pressure of the still could be regulated to the setup of reduced pressure conditions, and we could ensure the pressure of the still stable for a long time. A U-shaped differential manometer was connected with the vacuum pump whose fluctuation was held within 0.13 kPa to measure pressure precisely. We used ethanol as coolant in the condenser. Its working temperature was 273.15 K to condense vapor phase to liquid phase quickly and return to the equilibrium chamber at the same time. A precision mercury thermometer with an uncertainty of ± 0.05 K was used to measure the equilibrium temperature. Equilibrium was achieved when the constant vapor temperature was kept more than 30 min. At last, samples of vapor (cooled to liquid) and liquid phases were taken out from the sampling ports after equilibrium was achieved. The samples were taken out by using a micro syringe and analyzed by GC. The reliability of the experimental system has been calibrated already in our previous work.14−16 Analysis. The equilibrium compositions of vapor (cooled to liquid) and liquid phases were performed using a BFRL SP2100A GC with the flame ionization detector (FID). A SE-54 capillary column (30 m × 0.32 mm × 0.5 μm) was equipped with the detector for analyzing the polybasic alcohols. The GC response peaks were treated with the N2000 chromatography station. The carrier gas was high-purity nitrogen (≥ 99.999 %, mass fraction) flowing at 20 mL·min−1. The flow rates of hydrogen (≥ 99.999 %, mass fraction) and air (≥ 99.99 %, mass fraction) were (20 and 200) mL·min−1, respectively. For the four binary systems, the operation conditions of GC were as follows: for the system of EG (1) + BDO (2), the column, injector, and detector temperatures were (413.15, 493.15 and 513.15) K; for the system of EG (1) + DEG (2), the temperatures of which were (403.15, 493.15, and 533.15) K; for the system of BDO (1) + DEG (2), the temperatures of which were (403.15, 513.15, and 533.15) K; for the system of DEG (1) + TEG (2), the temperatures of which were (423.15, 533.15, and 563.15) K. An injection volume of 0.4 μL to the GC was used for every sample. The GC was calibrated with standard solutions prepared gravimetrically by the electronic balance. For the standard solutions, different peak area ratios represented different mole fraction to establish calibration curve. Each sample was analyzed with the calibration curves at least three times to ensure the accuracy. The uncertainties of the liquid-phase mole fractions were no more than ± 0.005 and those of vapor-phase mole fractions were no more than ± 0.01, so as to make sure the results reliable.

which was contained in BDO, DEG, and TEG was 0.5 %, 0.6 %, and 0.4 % (mass fractions), respectively. These were tested by a BFRL SP-2100A gas chromatograph (GC) equipped with a thermal conductivity detector. The BDO, DEG, and TEG were dried over molecular sieves (Guangfu, type 0.3 nm) and further purified in a distillation column at subatmospheric pressure. The purity of the distilled (BDO, DEG, and TEG) was tested to be higher than (0.998, 0.996, and 0.997) (mass fractions) with GC analysis. The densities and refractive indices of the pure components were checked by an Anton Paar DMA58 densimeter with an accuracy of 10−5 g·cm−3 and a ATAGO NAR-3T Abbe refractometer at 298.15 K, respectively. The temperature was controlled with a thermostat bath to ± 0.01 K. All of the densities, refractive indices, and normal boiling points of the four pure components together with the literature values are listed in Table 1.11,12 Apparatus and Procedures. A modified Rose-Williams still (a circulation VLE still) was used to measure the vapor− liquid equilibrium data in this experiment. The apparatus of the measurement system is shown in Figure 1. This still could ensure intimate contact of the liquid and vapor phases continuously and establish phase equilibrium in a short time.

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, Ushaped differential manometer; 8, vacuum pump; 9, a buffer tank; 10, valve; 11, a precision mercury thermometer.

The total volume of the still was about 140 cm3 of which about 60 cm3 was occupied by the liquid solution. The solutions were prepared gravimetrically by an Sartorius BP210S electronic balance which had an uncertainty of ± 0.1 mg. Energy was supplied to the still by a heating rod which was controlled by an electric thermocouple. The still installed a (SHB-B95) vacuum pump supplied by Greatwall Scientific Industrial and Trade Co. and a buffer tank with a volume of 20 L to adjust the pressure of the system. The vacuum pump operated continuously, and a valve was connected with the

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RESULTS AND DISCUSSION Pure Component Vapor Pressures. The vapor pressures of EG, BDO, and DEG were calculated from the Antoine eq 1 obtained from Yaws.13 The vapor pressure of TEG was 1274

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Table 2. Antoine Coefficient of Pure Components Used in this Study Antoine coefficients A

compound a

EG BDOa DEGa TEGb a

82.4062 22.4549 6.5069 152.48

B

C

−6347.2 −4202.3 −4610.9 −16449

D

E −9

−25.433 −4.2015 4.6273 −17.67

−2.37·10 −7.45·10−10 −0.018361 6.45·10−18

range T/K −6

8.75·10 6.18·10−3 8.29·10−6 6

260.15 to 645 293.05 to 667 262.7 to 744.6 265.95 to 769.5

Reference 13. bReference 17.

calculated from the Antoine eq 2 which was taken from literature.17 The value of the A, B, C, D, and E of these two parameters are listed in Table 2.

Table 3. VLE Data and Calculated Activity Coefficients (γ) for the EG (1) + BDO (2) Systema

⎛ 760ps ⎞ B i /Pa⎟ = A + log⎜ + C log(T /K) + D(T /K) 101325 /K T ⎝ ⎠ + E(T /K)2 ln(pis /Pa) = A +

10 kPa

(1)

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

(2)

Experimental Results and Data Correlations. Isobaric (vapor + liquid) equilibrium (VLE) data for the binary system of {EG (1) + BDO (2), EG (1) + DEG (2), BDO (1) + DEG (2), DEG (1) + TEG (2)} at pressures of 10.0 kPa, 20.0 kPa, and 40.0 kPa are presented in Tables 3 to 6, respectively. At the subatmospheric pressures of (10.0, 20.0, and 40.0) kPa, the vapor phase behavior could be assumed as an ideal state. Thus, the experimental liquid-phase activity coefficient of component i was written as follows:18

γi =

20 kPa

yp i xipis

(3)

where xi is the liquid-phase mole fraction, yi represents the vapor-phase mole fraction, γi is the activity coefficient of component i, and psi represents the vapor pressure of pure solvent i (i = 1, 2) at equilibrium temperature. The UNIQUAC,19 NRTL,20,21 and Wilson22 models were used to correlate all of the VLE data. For UNIQUAC model, Z represents the lattice coordination number, and the value is 10; gij is the interaction energy between the molecules i and j; gij−gjj are the binary interaction energy parameters; the volume parameters (ri) and the van der Waals area parameters (qi) are listed in Table 7.23−25 For NRTL model, the nonrandomness parameter (aij) is set to 0.3, and gij−gjj are the binary interaction energy parameters. For Wilson model, the molar volumes vi in the Wilson equation were calculated by the equation as follows: RTci τi vi = Zci , pci

τi = 1 + (1 − T /Tci)2/7 ,

40 kPa

T/K

x1

y1

437.48 431.71 428.31 423.53 419.84 417.33 414.54 412.76 411.06 409.36 407.72 406.07 454.63 450.97 446.63 444.18 440.39 437.29 434.77 433.13 430.16 428.47 427.18 424.99 423.18 473.22 468.42 464.73 461.36 457.93 454.32 451.68 449.37 446.28 444.71 443.07 441.92

0.000 0.092 0.157 0.263 0.369 0.452 0.561 0.641 0.723 0.811 0.902 1.000 0.000 0.082 0.185 0.251 0.352 0.449 0.525 0.583 0.689 0.757 0.814 0.918 1.000 0.000 0.117 0.211 0.307 0.402 0.513 0.599 0.685 0.812 0.878 0.950 1.000

0.000 0.298 0.443 0.605 0.706 0.774 0.836 0.875 0.908 0.94 0.971 1.000 0.000 0.209 0.413 0.513 0.638 0.728 0.791 0.832 0.893 0.921 0.946 0.978 1.000 0.000 0.27 0.433 0.564 0.668 0.761 0.824 0.875 0.934 0.959 0.981 1.000

γ1 1.182 1.168 1.142 1.097 1.084 1.055 1.039 1.025 1.014 1.009 1.005 0.944 0.958 0.955 0.967 0.966 0.983 0.988 1.002 1.002 1.004 1.001 1.007 0.972 0.970 0.967 0.978 0.983 0.995 0.999 0.999 1.002 1.003 1.011

γ2 1.009 0.998 0.990 0.994 1.023 1.017 1.051 1.066 1.103 1.145 1.156 1.007 1.002 0.996 0.993 0.998 1.004 0.996 0.979 0.951 0.968 0.915 0.932 1.008 0.991 0.987 0.980 0.985 1.001 0.992 0.983 0.985 1.005 1.215

Standard uncertainties u are u(T) = ± 0.05 K, u(p) = ± 0.3 kPa, u(x) = ± 0.005, and u(y) = ± 0.01. a

T /Tci ≤ 0.75

⎡⎛ ⎞2 ⎤ ⎢⎜ γexp − γcal ⎟ ⎥ OF = ∑ ⎢⎜ γexp ⎟⎠ ⎥ ⎣⎝ ⎦

(4)

gij−gii are the binary interaction energy parameters, Tci, Pci, and Zci are the critical temperature, pressure, and compressibility factor of component i, and the values are listed in Table 7.2,14 To regress the binary parameters in the three activitycoefficient models (UNIQUAC, NRTL, and Wilson), a leastsquares method was used to minimize the objective function as follows:

(5)

where γexp and γcal are the experimental and calculated activity coefficients, respectively. The average absolute deviations (AAD) in boiling temperatures and vapor-phase mole fractions are calculated as a measure of the agreement between the experimental results and 1275

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Table 4. VLE Data and Calculated Activity Coefficients (γ) for the EG (1) + DEG (2) Systema 10 kPa

20 kPa

40 kPa

T/K

x1

y1

445.47 439.74 435.72 433.73 429.94 426.86 422.74 418.16 414.94 411.63 409.29 408.07 405.97 464.36 458.15 453.16 443.86 439.08 436.03 432.78 430.97 429.38 427.47 425.35 423.18 485.33 477.92 471.93 467.09 462.31 458.84 454.82 451.48 449.37 447.53 445.52 443.47 441.92

0.000 0.074 0.136 0.171 0.244 0.304 0.403 0.527 0.631 0.752 0.851 0.905 1.000 0.000 0.079 0.159 0.336 0.448 0.531 0.627 0.685 0.743 0.822 0.908 1.000 0.000 0.077 0.155 0.232 0.324 0.402 0.509 0.616 0.688 0.763 0.845 0.936 1.000

0.000 0.261 0.414 0.486 0.602 0.678 0.773 0.851 0.902 0.947 0.971 0.987 1.000 0.000 0.263 0.442 0.695 0.793 0.845 0.892 0.915 0.937 0.960 0.984 1.000 0.000 0.273 0.449 0.572 0.679 0.746 0.818 0.872 0.903 0.932 0.956 0.986 1.000

γ1 0.963 0.959 0.963 0.961 0.975 0.982 0.989 0.996 1.004 1.002 1.007 1.009 0.972 0.957 0.977 0.989 0.992 0.998 1.002 1.003 0.998 1.004 1.007 1.116 1.094 1.082 1.070 1.060 1.047 1.031 1.026 1.017 1.009 1.009 1.011

Table 5. VLE Data and Calculated Activity Coefficients (γ) for the BDO (1) + DEG (2) Systema

γ2 0.990 0.990 0.990 0.982 0.977 0.979 0.964 0.980 0.958 0.900 0.917 0.684

10 kPa

0.992 0.988 0.983 0.968 0.955 0.952 0.954 0.959 0.932 0.927 0.786

20 kPa

0.999 0.994 1.001 1.007 1.012 1.024 1.033 1.051 1.061 1.050 1.122 0.937

40 kPa

Standard uncertainties u are u(T) = ± 0.05 K, u(p) = ± 0.3 kPa, u(x) = ± 0.005, and u(y) = ± 0.01. a

i=1

y1 0.000 0.134 0.234 0.358 0.404 0.462 0.531 0.609 0.668 0.762 0.850 0.937 1.000 0.000 0.158 0.251 0.330 0.392 0.458 0.530 0.605 0.664 0.767 0.869 0.946 1.000 0.000 0.107 0.206 0.284 0.378 0.468 0.560 0.652 0.734 0.804 0.875 0.938 1.000

γ1 1.110 1.030 1.024 1.024 1.025 1.020 1.014 1.015 1.012 1.014 1.014 1.009 0.977 0.981 0.985 0.983 0.987 0.990 0.999 1.003 1.006 1.012 1.012 1.007 1.100 1.052 1.042 1.022 1.020 1.013 1.012 1.006 1.004 1.006 1.004 1.008

γ2 1.006 0.991 0.994 0.990 0.988 0.985 0.983 0.983 0.978 0.969 0.942 0.886 0.992 0.990 0.987 0.985 0.985 0.981 0.977 0.971 0.965 0.949 0.910 0.867 0.999 0.992 0.990 0.989 0.990 0.986 0.989 0.983 0.993 1.002 1.007 1.044

0.006), and the maximum absolute deviations |ΔT|max of temperatures were (0.18, 0.16, 0.16, and 0.17) K for the binary systems of EG (1) + BDO (2), EG (1) + DEG (2), BDO (1) + DEG (2), and DEG (1) + TEG (2), respectively. In this case, the UNIQUAC, NRTL, and Wilson models have good agreement with experimental data for the four binary systems. The experimental and calculated data in the form of T−x1−y1 diagrams at corresponding pressures are presented in Figures 2 to 5, respectively. According to the results in Tables 8 to 11, the UNIQUAC, NRTL, and Wilson models yielded similar correlation accuracy. It showed that there was no azeotropic behavior observed at the three subatmospheric pressures. All of these results suggested that the UNIQUAC, NRTL, and Wilson models showed a good correlation for all of the experimental data of the four binary systems.

N

∑ |Uiexp − Uical|

x1 0.000 0.092 0.178 0.284 0.325 0.378 0.446 0.527 0.589 0.694 0.796 0.906 1.000 0.000 0.118 0.192 0.258 0.313 0.373 0.441 0.514 0.575 0.689 0.810 0.915 1.000 0.000 0.067 0.140 0.201 0.283 0.364 0.456 0.552 0.649 0.736 0.827 0.915 1.000

a Standard uncertainties u are u(T) = ± 0.05 K, u(p) = ± 0.3 kPa, u(x) = ± 0.005, and u(y) = ± 0.01.

the calculated values. The AAD is defined in the following form: 1 AAD = N

T/K 445.07 444.24 443.55 442.68 442.34 441.90 441.40 440.81 440.34 439.62 438.92 438.15 437.48 464.36 463.09 462.35 461.65 461.14 460.52 459.86 459.08 458.48 457.44 456.32 455.38 454.63 485.33 484.17 483.06 482.15 481.08 480.05 478.92 477.84 476.77 475.84 474.87 474.04 473.22

(6)

where U indicates a variable quantity, for instance, the temperature and vapor-phase mole fraction. The superscript “exp” and “cal” represent experimental and calculated, separately. N stands for the number of experimental data points. The binary interaction energy parameters of UNIQUAC, NRTL, and Wilson models, the absolute average deviations of the boiling temperatures (AADT), and vapor-phase mole fractions (AADy1) at each experimental pressure are shown in Tables 8 to 11, respectively. The maximum absolute deviations |Δy1|max of vapor-phase components correlated by UNIQUAC, NRTL, and Wilson models were (0.006, 0.006, 0.009, and 1276

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Table 6. VLE Data and Calculated Activity Coefficients (γ) for the DEG (1) + TEG (2) Systema 10 kPa

20 kPa

40 kPa

T/K

x1

y1

480.39 474.78 470.05 466.82 463.47 460.57 458.34 455.58 452.58 449.75 448.14 446.97 445.47 500.97 492.27 487.72 483.37 480.35 477.65 474.67 472.23 469.72 467.88 466.28 464.36 524.64 515.35 510.24 505.77 501.93 499.73 497.46 494.43 492.71 490.98 489.12 486.95 485.33

0.000 0.097 0.187 0.259 0.342 0.421 0.485 0.572 0.676 0.787 0.858 0.913 1.000 0.000 0.128 0.219 0.314 0.387 0.462 0.558 0.642 0.740 0.822 0.894 1.000 0.000 0.130 0.222 0.316 0.407 0.465 0.529 0.624 0.684 0.751 0.832 0.921 1.000

0.000 0.269 0.451 0.560 0.661 0.735 0.787 0.842 0.892 0.932 0.955 0.973 1.000 0.000 0.341 0.493 0.617 0.696 0.756 0.821 0.866 0.908 0.939 0.964 1.000 0.000 0.328 0.482 0.602 0.694 0.740 0.788 0.848 0.875 0.908 0.940 0.972 1.000

γ1

Table 8. Parameters for the UNIQUAC, NRTL, and Wilson Equations and AADT and AADy1a for {EG (1) + BDO (2)} at p = (10.0, 20.0, and 40.0) kPa

γ2

0.969 0.985 0.986 0.989 0.989 0.995 0.998 0.999 0.996 0.995 0.996 0.990 1.079 1.045 1.043 1.050 1.042 1.032 1.025 1.014 1.005 1.001 0.992 1.071 1.056 1.047 1.044 1.037 1.036 1.033 1.023 1.018 1.006 1.004 0.999

10.0 kPa

0.997 0.988 0.983 0.978 0.966 0.963 0.952 0.951 0.973 1.051 1.118 1.151

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

1.002 1.003 1.004 1.003 0.990 0.998 0.993 1.004 1.043 1.086 1.142

a

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

Standard uncertainties u are u(T) = ± 0.05 K, u(p) = ± 0.3 kPa, u(x) = ± 0.005, and u(y) = ± 0.01.

Table 7. Molecule Volume Parameters r, Area Parameters q for the UNIQUAC Model, and Critical Properties (Tc, Pc, Zc)

a

q

r

Tc/K

Pc/kPa

Zc

2.248a 3.328c 3.568c 4.888e

2.4088a 3.7576c 4.0013c 5.5942e

645b 667d 744.6d 769.5d

7.53b 4.88d 4.606d 3.32d

0.262b 0.261d 0.232d 0.2462d

Reference 23. Reference 25.

e

b

Reference 2.

c

Reference 24.

d

26.365 0.014 0.14 0.003 −220.206 −23.028 0.15 0.003 34.973 115.006 0.16 0.003

exp N cal exp AADT = (1/N)∑Ni=1|Tcal i − Ti | and AADy1 = (1/N)∑i=1|yi − yi |.

10.0 kPa

a

EG BDO DEG TEG

UNIQUAC Parameters 95.742 8.033 296.853 8.032 0.04 0.09 0.003 0.004 NRTL Parameters 397.112 −225.432 392.738 −30.995 0.11 0.09 0.005 0.004 Wilson Parameters 728.97 61.265 326.807 39.823 0.06 0.10 0.003 0.004

40.0 kPa

Table 9. Parameters for the UNIQUAC, NRTL, and Wilson Equations and AADT and AADy1a for {EG (1) + DEG (2)} at p = (10.0, 20.0, and 40.0) kPa

0.997 1.002 1.004 1.005 1.004 1.013 1.009 1.000 1.035 1.024 1.053 1.125

compound

20.0 kPa

20.0 kPa

UNIQUAC Parameters 54.5775 58.473 −1.3217 5.314 0.10 0.09 0.006 0.005 NRTL Parameters −226.5514 −223.6 −32.6411 −27.985 0.09 0.10 0.006 0.005 Wilson Parameters −21.8089 −7.152 −15.1093 −4.793 0.11 0.12 0.005 0.005

40.0 kPa 237.7476 128.6491 0.04 0.002 347.687 225.888 0.16 0.001 465.806 327.926 0.10 0.003

exp N cal exp AADT = (1/N)∑Ni=1|Tcal i − Ti | and AADy1 = (1/N)∑i=1|yi − yi |.

the Wilson model to perform the thermodynamic consistency test. Thermodynamic Consistency Test. There were experimental errors caused from deviation of the activity coefficients which were derived from the Gibbs−Duhem equation.26 So the reliability of the binary VLE data should be tested, and we chose the Wilson model to perform the consistency test. The experimental VLE data for the binary systems at three pressures were tested for thermodynamic consistency using the Herington area test and the point test of Van Ness et al. For the Herington area test:

Reference 13.

Then we have compared the correlation values of the UNIQUAC, NRTL, and Wilson activity-coefficient models. The UNIQUAC, NRTL, and Wilson models yielded similar correlation accuracies, while the Wilson model showed slightly better results to correlate the four binary systems. So we chose

D=

S+ − S− S+ + S−

(7)

where S+ is the area of ln(γ1/γ2)−x1 above the x-axis, and S‑ is the area of ln(γ1/γ2)−x1 below the x-axis. 1277

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Table 10. Parameters for the UNIQUAC, NRTL, and Wilson Equations and AADT and AADy1a for {BDO (1) + DEG (2)} at p = (10.0, 20.0, and 40.0) kPa 10.0 kPa g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 a

20.0 kPa

UNIQUAC Parameters 6.476 −31.147 6.476 −31.079 0.02 0.09 0.009 0.007 NRTL Parameters 8.071 −111.949 8.071 −112.048 0.07 0.10 0.009 0.006 Wilson Parameters 14.141 −50.365 15.525 −55.573 0.07 0.16 0.009 0.004

40.0 kPa 16.088 17.809 0.10 0.004 8.071 8.071 0.08 0.006 16.088 17.809 0.08 0.006

Figure 2. VLE data for the system {EG (1) + BDO (2)} at 10.0 kPa, 20.0 kPa, and 40.0 kPa. ■, experimental data for T−x; □, experimental data for T−y. , calculated data by the UNIQUAC equation; ···, calculated data by the NRTL equation; ---, calculated data by the Wilson equation; x1 and y1 are the mole fractions of EG in the liquid and vapor phases, respectively.

exp N cal exp AADT = (1/N)∑Ni=1|Tcal i − Ti | and AADy1 = (1/N)∑i=1|yi − yi |.

Table 11. Parameters for the UNIQUAC, NRTL, and Wilson Equations and AADT and AADy1a for {DEG (1) + TEG (2)} at p = (10.0, 20.0, and 40.0) kPa 10.0 kPa g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 g12−g22/J·mol−1 g21−g11/J·mol−1 AADT/K AADy1 a

20.0 kPa

UNIQUAC Parameters 5.747 124.372 −7.801 19.78 0.06 0.07 0.006 0.004 NRTL Parameters −105.863 198.411 −105.949 197.555 0.07 0.11 0.005 0.005 Wilson Parameters 68.505 401.891 118.266 381.678 0.08 0.08 0.006 0.004

40.0 kPa 128.651 33.35 0.09 0.004 327.795 132.014 0.12 0.003 501.488 326.123 0.07 0.003

exp N cal exp AADT = (1/N)∑Ni=1|Tcal i − Ti | and AADy1 = (1/N)∑i=1|yi − yi |.

J = 150·

(Tmax − Tmin) Tmin

Figure 3. VLE data for the system {EG (1) + DEG (2)} at 10.0 kPa, 20.0 kPa, and 40.0 kPa. ■, experimental data for T−x; □, experimental data for T−y. , calculated data by the UNIQUAC equation; ···, calculated data by the NRTL equation; ---, calculated data by the Wilson equation; x1 and y1 are the mole fractions of EG in the liquid and vapor phases, respectively.

(8)

where Tmax and Tmin are the maximum and minimum temperatures of the systems. For the Van Ness point test, we used a four-parameter Legendre polynomial for excess Gibbs free energy:

For the Herington area test, if |D − J| < 10, the experiment data could be considered thermodynamic consistency. As could be seen in Table 12, |D − J|max for the four binary systems were 4.610, 5.682, 8.116, and 7.001, respectively. For the Van Ness point test, Gmehling and Onken suggested that the data were internally consistent when the average error in vapor mole fractions Δy were less than or equal to 0.01. The results of Van Ness point test are also presented in Table 12. For the four binary systems, the maximum absolute deviation |Δy1|max of vapor-phase components were 0.005, 0.004, 0.008, and 0.006. The values of the consistency test turned out that the binary system data passed the Herington area test and the Van Ness point test. It showed that the data of the experiment were reliable.

k

g=

GE = x1(1 − x1)∑ ak Lk (x1) RT

(9)

The value of K is 4. A nonlinear optimization method was used to minimize the following objective function: F=

∑ (y1cal

+ y2cal − 1)

(10)

where y1cal represents the calculated value of vapor-phase mole fraction of component 1 and y2cal represents the calculated value of vapor-phase mole fraction of component 2. 1278

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Table 12. Results of Thermodynamic Consistency Test for the Four Systems at Different Pressures

EG (1) + BDO (2)

EG (1) + DEG (2)

BDO (1) + DEG (2)

DEG (1) + TEG (2)

a

Figure 4. VLE data for the system {BDO (1) + DEG (2)} at 10.0 kPa, 20.0 kPa, and 40.0 kPa. ■, experimental data for T−x; □, experimental data for T−y. , calculated data by the UNIQUAC equation; ···, calculated data by the NRTL equation; ---, calculated data by the Wilson equation; x1 and y1 are the mole fractions of BDO in the liquid and vapor phases, respectively.

point testb |Δy1|

P/kPa area testa D−J

system

10.0 20.0 40.0 10.0 20.0 40.0 10.0 20.0 40.0 10.0 20.0 40.0

3.197 5.682 4.970 4.610 2.041 3.140 8.116 4.818 6.438 −7.001 −0.477 5.469

+ + + + + + + + + + + +

0.003 0.002 0.005 0.004 0.004 0.003 0.008 0.004 0.006 0.006 0.004 0.001

+ + + + + + + + + + + +

References 5 and 6. bReference 7.

model was slightly more suitable than the UNIQUAC and NRTL models for correlating the measured isobaric VLE data at the three pressures. All of the experimental data of the binary systems were found to be thermodynamically consistent by the area test of Herington and the point test of Van Ness et al. We could use the experimental data for further research of the separation process of EG containing of BDO, DEG, and TEG.

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AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. Fax: 02227403389. Telephone: 022-27890907. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Jou, F. Y.; Schmidt, K. A. G.; Mather, A. E. Vapor-Liquid Equilibrium in the System Ethane + Ethylene Glycol. Fluid Phase Equilib. 2006, 240, 220−223. (2) Zhang, L. H.; Wu, W. H.; Sun, Y. L.; Li, L. Q.; Jiang, B.; Li, X. G.; Yang, N. Isobaric Vapor−Liquid Equilibria for the Binary Mixtures Composed of Ethylene Glycol, 1,2-Propylene Glycol, 1,2-Butanediol, and 1,3-Butanediol at 10.00 kPa. J. Chem. Eng. Data 2013, 58, 1308− 1315. (3) William, J. B.; Charleston, W. V. Ethylene Glycol by Catalytic Hydrogenation. U.S. Patent 4,628,128, 1986. (4) Li, Q. S.; Tian, Y. M.; Wang, S. Densities and Excess Molar Volumes for Binary Mixtures of 1,4-Butanediol + 1,2-Propanediol, + 1,3-Propanediol, and + Ethane-1,2-diol from (293.15 to 328.15) K. J. Chem. Eng. Data 2008, 53, 271−274. (5) Turan-Ertas, T.; Gurol, M. D. Oxidation of Diethylene Glycol with Ozone and Modified Fenton Processes. Chemosphere 2002, 47, 293−301. (6) Twu, C. H.; Tassone, V.; Sim, W. D. Advanced Equation of State Method for Modeling TEG-Water for Glycol Gas Dehydration. Fluid Phase Equilib. 2005, 228−229, 213−221. (7) Monroy-Loperena, R.; Alvarez-Ramirez, J. On the Steady-State Multiplicities for an Ethylene Glycol Reactive Distillation Column. Ind. Eng. Chem. Res. 1999, 38, 451−455. (8) Herington, E. F. G. Tests for the Consistency of Experimental Isobaric Vapour-Liquid Equilibrium Data. J. Inst. Petrol 1951, 37, 457− 470. (9) 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.

Figure 5. VLE data for the system {DEG (1) + TEG (2)} at 10.0 kPa, 20.0 kPa, and 40.0 kPa. ■, experimental data for T−x; □, experimental data for T−y. , calculated data by the UNIQUAC equation; ···, calculated data by the NRTL equation; ---, calculated data by the Wilson equation; x1 and y1 are the mole fractions of DEG in the liquid and vapor phases, respectively.

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CONCLUSIONS The isobaric VLE data of the binary systems EG (1) + BDO (2), EG (1) + DEG (2), BDO (1) + DEG (2), and DEG (1) + TEG (2) at 10.0 kPa, 20.0 kPa, and 40.0 kPa were measured in this work. No azeotrope was formed in the four binary systems. The UNIQUAC, NRTL, and Wilson activity coefficient models were used to correlate the experimental data. The absolute average deviation of temperature and the vapor phase components for the four systems were below AADT = (0.18, 0.16, 0.16 and 0.17) K and AADy1 = (0.006, 0.006, 0.009, and 0.006), which showed that all of the models were suitable for the four measured systems. The Wilson activity coefficient 1279

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(10) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, 1977. (11) Sastry, N. V.; Patel, M. C. Densities, Excess Molar Volumes, Viscosities, Speeds of Sound, Excess Isentropic Compressibilities, and Relative Permittivities for Alkyl (Methyl, Ethyl, Butyl, and Isoamyl) Acetates + Glycols at Different Temperatures. J. Chem. Eng. Data 2003, 48, 1019−1027. (12) Anil, N. D. Densities and Volumetric Properties of Binary Mixtures of Formamide with 1-Butanol, 2-Butanol, 1,3-Butanediol and 1,4-Butanediol at Temperatures between 293.15 and 318.15 K. J. Solution Chem. 2007, 36, 497−516. (13) Yaws, C. L. Chemical Properties Handbook, 1st ed.; McGraw-Hill Co.: New York, 1999. (14) Yang, C. S.; Qin, Z. L.; Xu, Y. L.; Zeng, H.; Sun, F. Z.; Zhang, P.; Feng, Y. Isobaric Vapor-Liquid Equilibrium for the Binary Systems of Methanol, Diethylamine, and N,N-Diethylethanolamine at P = (60.0 and 101.3) kPa. J. Chem. Eng. Data 2013, 58, 482−487. (15) Yang, C. S.; Feng, Y.; Cheng, B.; Zhang, P.; Qin, Z. L.; Zeng, H.; Sun, F. Z. Vapor-Liquid Equilibria for Three Binary Systems of NMethylethanolamine, N-Methyldiethanoliamine, and Ethylene Glycol at P = (40.0, 30.0, and 20.0) kPa. J. Chem. Eng. Data 2013, 58, 2272− 2279. (16) Yang, C. S.; Zeng, H.; Yin, X.; Ma, S. Y.; Sun, F. Z.; Li, Y. F.; Li, J. Measurement of (Vapor + Liquid) Equilibrium for the Systems {Methanol + Dimethylcarbonate} and {Methanol + Dimethylcarbonate + Tetramethylammonium Bicarbonate} at P = (34.43, 67.74) kPa. J. Chem. Thermodyn. 2012, 53, 158−166. (17) Breil, M. P.; Kontogeorgis, G. M. Thermodynamics of Triethylene Glycol and Tetraethylene Glycol Containing Systems Described by the Cubic-Plus-Association Equation of State. Ind. Eng. Chem. Res. 2009, 48, 5472−5480. (18) Mohsen-Nia, M.; Memarzadeh, M. R. Isobaric (Vapour + Liquid) Equilibria for the (1-Propanol + 1-Butanol) Binary Mixture at (53.3 and 91.3) kPa. J. Chem. Thermodyn. 2010, 42, 1311−1315. (19) 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. (20) Renon, H.; Prausnitz, J. M. Estimation of Parameters for the NRTL Equation for Excess Gibbs Energies of Strongly Nonideal Liquid Mixtures. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 413−419. (21) Gow, A. S. Calculation of Vapor-Liquid Equilibria from InfiniteDilution Excess Enthalpy Data Using the Wilson or NRTL Equation. Ind. Eng. Chem. Res. 1993, 32, 3150−3161. (22) 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. (23) 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. (24) Gmehling, J.; Onken, U.; Weidlich, U. Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series; DECHEMA: Frankfurt/Main, 1982. (25) Mostafazadeh, A. K.; Rahimpour, M. R.; Shariati, A. VaporLiquid Equilibria of Water + Triethylene Glycol (TEG) and Water + TEG + Toluene at 85 kPa. J. Chem. Eng. Data 2009, 54, 876−881. (26) Jackson, P. L.; Wilsak, R. A. Thermodynamic Consistency Tests Based on the Gibbs-Duhem Equation Applied to Isothermal, Binary Vapor-Liquid Equilibrium Data: Data Evaluation and Model Testing. Fluid Phase Equilib. 1995, 103, 155−197.

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