Isobaric VaporâLiquid Equilibrium for Two Binary Systems (Methanol

Article pubs.acs.org/jced

Isobaric Vapor−Liquid Equilibrium for Two Binary Systems (Methanol + Dibutyl Carbonate) and (n‑Butanol + Dibutyl Carbonate) at p = 40.0, 70.0, and 100.0 kPa Qian Yang,† Aijun Xu,‡ and Changsheng Yang*,† †

Key Laboratory for Green Chemical Technology of State Education Ministry, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China ‡ Henan Energy and Chemical Industry Group Fine Chemical Co., Ltd., Zhengzhou 450046 China ABSTRACT: The isobaric vapor−liquid equilibrium (VLE) data for the two binary systems of (methanol + dibutyl carbonate) and (n-butanol + dibutyl carbonate) were measured with a modified Rose equilibrium still under pressures of 40.0, 70.0, and 100.0 kPa 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. All of the experimental isobaric VLE data were well-correlated using nonrandom two-liquid (NRTL), Wilson, and Margules activity coefficient models. The results showed that the average absolute deviations of the vapor-phase mole fraction (AADy) between the calculated and the experimental values were less than 0.01 and the maximum absolute average deviations of the boiling temperature (AADT) was 0.13 K. Consequently, the calculation values showed good agreements with the experimental data measured for the two binary systems in this study.

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INTRODUCTION Dibutyl carbonate (DBC) is an important chemical intermediate and solvent, which is extensively used for the production of various organic compounds and polymeric materials.1−5 DBC is also widely applied in base material for lubricants, metal degreasing, and leather processing owing to its wonderful lubricity and high thermal oxidative stability.6 At present, there exist several reaction routes well-known for the synthesis of DBC, such as phosgenation7 and oxidative carbonylation of n-butanol. However, the two reactions have several drawbacks, including the use of highly toxic phosgene, the corrosion of metal equipment, and a large number of byproducts. Alternatively, the transesterification8 has attracted enormous interest in recent years. Especially combining transesterification with reactive distillation has some great advantages, such as it being a simple process, mild reaction conditions, low energy consumption and pollution, high conversion, and noncorrosion. In the process of synthesizing DBC, dimethyl carbonate (DMC) and n-butanol are the raw materials, and methanol is one byproduct. Methanol is broadly used as a basic organic chemical raw material and high quality fuel. n-Butanol is an indispensable raw material for chemical industry, being used in the production of plasticizers, paint, and solvents.9 In order to get highly purified products, it is essential to design distillation column precisely. Thus, the accurate vapor−liquid equilibrium (VLE) data will be useful. A survey of the published literatures shows that there are hardly any papers on the isobaric vapor−liquid equilibrium data for (methanol + dibutyl carbonate) and (n-butanol + dibutyl) carbonate up to now. In this work, the isobaric VLE data of the © XXXX American Chemical Society

(methanol + dibutyl carbonate) and (n-butanol + dibutyl carbonate) were measured at the pressures of 40.0, 70.0, and 100.0 kPa. Meanwhile, the VLE data of the two binary systems were tested and verified for thermodynamic consistency test by the Herington area test 10 and Van Ness point test.11 Furthermore, the isobaric VLE data were regressed by nonrandom two-liquid (NRTL)12 model, Wilson13 model, and Margules14 model, respectively.

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EXPERIMENTAL SECTION Chemicals. Methanol and n-butanol were purchased from Tianjin Guangfu Reagent Co. Dibutyl carbonate was synthesized by transesterification of dimethyl carbonate with n-butanol in our laboratory. The purities of the three materials were higher than Table 1. Suppliers and Mass Fractions of the Chemical Samples chemical name methanol n-butanol DBCa a

source Tianjin Guangfu Reagent Co. Tianjin Guangfu Reagent Co. synthesized in this work

mass fraction purity

analysis method

0.999

GCb

0.995

GCb

0.995

GCb

b

DBC: dibutyl carbonate. Gas chromatography.

Received: June 23, 2016 Accepted: December 13, 2016

A

DOI: 10.1021/acs.jced.6b00517 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 2. Densities (ρ), Refractive Index (nD), and Boiling Points (Tb) of Pure Components Compared with Literature Values at 101.3 kPa ρ (g/cm−3) (298.15 K)

a

nD (298.15 K)

Tb/K (101.3 kPa)

compound

exptl

lit

exptl

lit

exptl

lit

methanol n-butanol DBC

0.78661 0.80594 0.92517

0.78656a 0.80589b 0.92511d

1.3266 1.3971 1.4115

1.3267a 1.3970b 1.4117d

337.83 390.82 477.65

337.80b 390.87c 477.67e

Reference 15. bReference 16. cReference 17. dReference 18. eReference 19. u(ρ) = 2.5 × 10−3 g·cm−3; u(nD) = 5 × 10−3; u(Tb) = 0.1 K.

Figure 1. Schematic diagram of the VLE apparatus: (1) heating rod, (2) liquid-phase sampling port, (3) vapor-phase sampling port, (4) vapor condenser pipe, (5) coolant inlet, (6) coolant outlet, (7) U-shaped differential manometer, (8) vacuum pump, (9) a buffer vessel, (10) needle valve, (11) vapor temperature thermometer.

connected to the still. Besides, a needle valve linked with the vacuum pump was employed to adjust the opening of the valve slowly to ensure the experimental pressure could keep stable for a long time. A U-shaped differential manometer whose uncertainty was estimated to be 1 kPa was used to measure the system pressure. The energy of the whole system was supplied with a heating rod under the control of a thermocouple. To keep the system temperature stable and reduce the systematic error, two layers of insulation cotton were wrapped around the still. Then the equilibrium temperature was determined precisely by using a mercury thermometer with an uncertainty of 0.1 K. In addition, the ethanol was chosen as the coolant in the condenser to convert the vapor phase into the liquid phase quickly and prevent the mass loss, and its working temperature was set to 268.15−273.15 K. In every experiment, to minimize vapor leakage from the system all ground-glass joints were daubed with Vaseline and sealed with the Teflon tapes. In each experiment, only when temperature and pressure had reached steady state about 30 min or longer were the equilibrium conditions assumed. The reliability of the experimental device has already been verified in our previous work.20−24 Analysis. All collected samples were analyzed quantificationally by a BFRL SP-2100A GC which was equipped with a TCD. The compounds were separated by using the chromatographic column (2 m × 3 mm) that was packed with Porapak QS (80100). The N2000 chromatography station was used to treat the GC response peaks. The hydrogen of high purity was used as the carrier gas at a constant flow rate of 30 mL·min−1. The two binary systems of (methanol + dibutyl carbonate, n-butanol + dibutyl carbonate) had the same chromatography operation condition. The temperatures of the column, the injector, and the detector were set to (503.15, 538.15, and 533.15) K, respectively. The injection volume of each sample was 0.2 μL. In order to convert

0.995 mass fraction, checked by gas chromatography (GCSP2100A) with a thermal conductivity detector (TCD). Therefore, the three chemical substances were used without any further purification. And the chemical specifications of the reactants used are shown in Table 1. In this work, density (ρ), refractive indexes (nD), and the boiling points (Tb) of methanol, n-butanol, and dibutyl carbonate were determined and compared with the literatures (Table 2).15−19 An Anton Paar DMA 58 densimeter and an Abbe refractometer Atago 3T were used to measure density and refractive indexes data, at 298.15 K and 101.3 kPa, respectively. The experimented uncertainties of the densimeter and the refractometer were 2.5 × 10−3 g·cm−3 and 5 × 10−3. The boiling points were measured by the following apparatus (see Figure 1) and specific procedures at atmospheric pressure. This experimental device could guarantee the vapor and liquid phases full contact by continuous circulation of the two phases and reach equilibrium rapidly. The measurements of the boiling temperatures data were carried out when temperature and pressure had reached steady state about 30 min or longer and the uncertainty was 0.1 K. Apparatus and Procedures. The VLE experiments were performed in a modified Rose-Williams still and other apparatus. The experimental apparatus are shown in Figure 1. The maximum capacity of the equilibrium still was 140 cm3 roughly, of which almost half of the volume was full of the solution. The solutions were prepared gravimetrically with a Sartorius BP210S electronic balance accurate to 1 × 10−4 g. In this work, the still was composed of a boiling chamber and condenser, which could guarantee the vapor and liquid phases intimate contact by continuous circulation of the liquid and vapor phases and reach phase equilibrium rapidly. In order to control the operating pressure of the systems, a buffer tank and a vacuum pump were B



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the peak areas into mole fractions of each sample, the external standard calibration curve was obtained from a set of gravimetrically prepared standard solutions. Furthermore, each experimental sample was measured repeatedly three times at least to guarantee reproducibility and accuracy of the results. In this way, the standard uncertainties of the measured vapor mole fraction were less than 0.005, while the liquid samples were less than 0.002.

Table 5. VLE Experimental Data for the Equilibrium Temperature (T), the Liquid-Phase Mole Fraction (x1), the Vapor Phase Mole Fraction (y1), and Calculated Activity Coefficient (γi) for the Methanol (1) + DBC (2) System at p = 40.0, 70.0, and 100.0 kPaa 40 kPa

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RESULTS AND DISCUSSION Pure Component Vapor Pressure. The saturated vapor pressure of the pure composition of methanol was obtained Table 3. Experimental Vapor Pressuresa of DBC (w = 0.995, Mass Fraction)

a

p/kPa

T/K

p/kPa

T/K

5 10 15 20 25 30 35 40 45 50

383.16 403.77 410.07 420.73 427.86 434.15 439.03 443.67 449.33 453.17

55 60 65 70 75 80 85 90 95 100

456.63 459.47 461.31 463.87 465.41 468.56 470.27 472.83 475.91 478.18

70 kPa

Standard uncertainties u are u(T) = 0.1 K, u(p) = 1 kPa.

according to the Antoine equation (eq 1) received from Xuemei et al.25 The saturation vapor pressures of n-butanol was calculated with Antoine equation (eq 2) taken from Yaws.26 The data for the saturated vapor pressure of DBC had not been reported up to now. The Antoine equation correlating the measured data of vapor pressure could be determined by eq 1. We measured a series of saturated vapor pressures in different ranges of temperatures which are listed in Table 3 and simulated the parameters of Antoine eq 1 with OriginPro (version 8.0).27 The Antoine parameters are presented in Table 4. A−B log(pi s /kPa) = (T /K + C) (1)

100 kPa

⎛ 760ps ⎞ i /kPa⎟ log⎜ ⎝ 101.325 ⎠ B =A+ + C log(T /K) + D(T /K) + E(T /K)2 T /K (2)

T/K

x1

y1

443.78 430.58 413.45 395.92 370.68 346.48 338.23 332.98 329.55 326.37 324.29 321.08 317.33 315.78 464.01 450.43 436.46 419.72 405.56 389.07 373.06 362.08 350.07 341.75 337.63 334.75 329.98 328.56 478.02 469.04 458.52 438.78 419.12 401.66 388.23 369.88 359.82 352.01 345.46 342.44 339.08 337.33

0.000 0.007 0.020 0.041 0.102 0.255 0.358 0.449 0.526 0.607 0.669 0.778 0.927 1.000 0.000 0.008 0.019 0.038 0.062 0.107 0.182 0.268 0.417 0.578 0.685 0.772 0.942 1.000 0.000 0.005 0.012 0.030 0.059 0.102 0.156 0.288 0.413 0.556 0.722 0.816 0.934 1.000

0.000 0.332 0.626 0.812 0.943 0.992 0.993 0.994 0.995 0.996 0.997 0.998 0.999 1.000 0.000 0.312 0.552 0.745 0.851 0.927 0.969 0.987 0.994 0.996 0.997 0.998 0.999 1.000 0.000 0.203 0.395 0.656 0.827 0.914 0.956 0.984 0.992 0.996 0.997 0.998 0.999 1.000

γ1 1.126 1.128 1.128 1.120 1.088 1.067 1.050 1.038 1.026 1.019 1.009 1.001 1.000 1.056 1.057 1.057 1.056 1.053 1.046 1.038 1.025 1.013 1.007 1.004 1.000 1.000 1.101 1.102 1.103 1.101 1.096 1.088 1.065 1.045 1.026 1.010 1.005 1.001 1.000

γ2 1.000 1.000 1.000 1.000 1.001 1.009 1.019 1.031 1.044 1.060 1.074 1.105 1.157 1.000 1.000 1.000 1.000 1.000 1.001 1.002 1.005 1.012 1.025 1.035 1.045 1.079 1.000 1.000 1.000 1.000 1.000 1.001 1.003 1.010 1.022 1.041 1.072 1.093 1.126

a

Standard uncertainties u are u(T) = 0.1 K, u(p) = 1 kPa, u(x) = 0.002, and u(y) = 0.005.

Experimental Data. The isobaric vapor−liquid equilibrium (VLE) data for the two binary systems of (methanol + DBC, nbutanol + DBC) at p = 40.0, 70.0, and 100.0 kPa are listed in Tables 5 and 6, respectively. The vapor phase could be assumed

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

a

compound

A

B

C

D

E

methanola n-butanolb DBCc

7.19736 39.6670 6.567

1574.99 −4001.7 1951.06

−34.29 −10.2950 −50.81

−3.26 × 10−10

8.67 × 10−07

range T/K 175.5−512.5 183−563 383.2−478.2

Reference 25. bReference 26. cReference 27. C



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Table 6. VLE Experimental Data for the Equilibrium Temperature (T), the Liquid-Phase Mole Fraction (x1), the Vapor Phase Mole Fraction (y1), and Calculated Activity Coefficient (γi) for the n-Butanol (1) + DBC (2) System at p = 40.0, 70.0, and 100.0 kPaa 40 kPa

70 kPa

100 kPa

T/K

x1

y1

443.78 434.24 423.24 418.54 406.73 394.82 389.47 385.20 380.89 377.62 374.26 372.17 368.79 367.03 464.01 455.48 440.98 434.52 423.65 415.56 408.62 405.48 397.48 392.45 390.72 387.82 383.48 381.07 478.02 465.66 448.22 441.31 431.96 424.38 417.84 414.82 407.17 402.65 399.95 397.35 393.77 390.78

0.000 0.034 0.086 0.113 0.202 0.334 0.413 0.489 0.576 0.655 0.743 0.806 0.926 1.000 0.000 0.028 0.089 0.126 0.203 0.282 0.364 0.408 0.546 0.654 0.702 0.773 0.913 1.000 0.000 0.042 0.125 0.169 0.244 0.322 0.402 0.445 0.572 0.665 0.726 0.793 0.896 1.000

0.000 0.278 0.523 0.602 0.765 0.878 0.913 0.942 0.961 0.978 0.985 0.991 0.997 1.000 0.000 0.234 0.525 0.628 0.761 0.841 0.889 0.910 0.953 0.972 0.981 0.987 0.995 1.000 0.000 0.292 0.594 0.685 0.784 0.858 0.902 0.918 0.955 0.970 0.978 0.985 0.993 1.000

γ1 0.832 0.844 0.851 0.874 0.907 0.925 0.942 0.959 0.972 0.984 0.991 0.999 1.000 0.874 0.884 0.891 0.906 0.921 0.936 0.944 0.965 0.979 0.984 0.991 0.999 1.000 0.849 0.867 0.877 0.894 0.912 0.930 0.938 0.962 0.976 0.984 0.991 0.998 1.000

Table 7. Results of Thermodynamic Consistency Test for the Two Systems at Three Pressures area testa

γ2 1.000 1.000 0.999 0.997 0.992 0.976 0.964 0.949 0.928 0.907 0.880 0.859 0.815

|D − J|

|Δy1|

40 70 100 40 70 100

7.839 3.614 1.697 3.913 8.687 2.073

0.003 0.003 0.003 0.005 0.005 0.004

Reference 10. bReference 11.

NRTL

⎡ ⎤ Gji2τji Gij2τij ⎥ ln γi = xj2⎢ + 2 2 ⎢⎣ (xi + xjGji) (xj + xiGij) ⎥⎦ τij =

1.000 1.000 0.999 0.998 0.994 0.988 0.979 0.974 0.952 0.931 0.920 0.903 0.864

gij − gjj RT

,

Gij = exp(− aijτij),

aij = aji

Wilson

⎛ Aij Aji ⎞ ⎟, ln γ1 = − ln(x1 + Aijxj) + ⎜⎜ − xj + xiAji ⎟⎠ ⎝ xi + xjAij Vj ⎛ gij − gii ⎞ exp⎜− Aij = ⎟ ⎝ Vi RT ⎠

Vi =

RTci τi Zci , Pci

τi = 1 + (1 − T /Tci)2/7 ,

T ≤ 0.75 Tci

Margules

ln γi = xj2[Aij + 2xi(Aji − Aij)]

Table 9. Critical Temperature (Tc), Critical Pressure (Pc), and Critical Compressibility Factor of Component i (Zc)

1.000 1.000 0.997 0.995 0.989 0.980 0.969 0.961 0.935 0.912 0.895 0.874 0.840

a

compound

Tc/K

Pc/kPa

Zc

methanol n-butanol DBC

512.5a 562.93b 647a

8.084a 4.4124b 2.4516a

0.223a 0.259b 0.2829a

Reference19. bReference26.

experimental values of the activity coefficients of component i are also listed in Tables 5 and 6. Thermodynamic Consistency Test. In the process of measuring all of the VLE data, the thermodynamic consistency tests were checked for the two binary systems by using the Herington area test10 and Van Ness point test11 to verify the reliability of the experimental data. Just as Herington proposed, the isobaric VLE data was considered consistent if |D − J| < 10. The D was calculated by

Standard uncertainties u are u(T) = 0.1 K, u(p) = 1 kPa, u(x) = 0.002, and u(y) = 0.005.

as an ideal gas state at the experimental pressures of 40.0, 70.0, and 100.0 kPa in this experiment. Therefore, the experimental liquid-phase activity coefficients of component i were calculated from the simplified VLE equation as follows (i = 1, 2)

p/kPa

Table 8. Mathematical Forms of the Activity Coefficient Equations Used in This Work

a

γixipis = yp i

system methanol (1) + DBC (2)

n-butanol + DBC (2)

a

point testb

D=

S+ − S− × 100 S+ + S−

(4)

where the value of S+ is the area of ln(γ1 /γ2) − x1 above the x-axis and S− refers to the area of ln(γ1 /γ2) − x1 below the x-axis. The J was calculated by

(3)

in eq 3, γi is activity coefficient of component i; xi and yi are the mole fractions of component i in the liquid and vapor phases, respectively; pis refers to the saturation vapor pressure of pure component i; and p represents the system pressure. The

J = 150 × D

(Tmax − Tmin) Tmin

(5) DOI: 10.1021/acs.jced.6b00517 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 10. Parameters for the NRTL, Wilson, and Margules Equations, the Absolute Average Deviations of the Boiling Temperatures (AADT/K) and the Vapor-Phase Mole Fractions (AADy1), the Root-Mean-Square Deviations of the Boiling Temperatures (RMSDT), and Vapor-Phase Mole Fractions (RMSDy1) for Methanol (1) and DBC (2) at p = 40.0, 70.0, and 100.0 kPaab 40.0 kPa

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

AADT =

b

RMSDT =

1 N

100.0 kPa

NRTL Parameters 533.00 104.23 −79.61 104.49 0.04 0.03 0.003 0.004 0.06 0.04 0.004 0.005 Wilson Parameters 5399.4 5549.0 −4923.7 −5327.9 0.12 0.07 0.004 0.004 0.15 0.09 0.005 0.005 Margules Parameters 0.127 0.058 0.172 0.077 0.03 0.03 0.003 0.003 0.04 0.04 0.005 0.005

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

a

70.0 kPa

N

∑i = 1 |Tical − Tiexp| ∑iN= 1(Tical − Tiexp)2

AADy1 = RMSDy1 =

N

1 N

Table 11. Parameters for the NRTL, Wilson, and Margules Equations, the Absolute Average Deviations of the Boiling Temperatures (AADT/K) and the Vapor-Phase Mole Fractions (AADy1), the Root-Mean-Square Deviations of the Boiling Temperatures (RMSDT) and Vapor-Phase Mole Fractions (RMSDy1) for n-Butanol (1) and DBC (2) at p = 40.0, 70.0, and 100.0 kPaab 40.0 kPa

266.51 119.02 0.03 0.004 0.04 0.005

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

5625.4 −5219.1 0.07 0.003 0.09 0.003

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

0.102 0.143 0.04 0.004 0.05 0.005

N

∑i = 1 |yical − yiexp |

a

∑iN= 1(yical − yiexp )2

AADT =

1 N

b

RMSDT =

N

70.0 kPa

100.0 kPa

NRTL Parameters −170.99 −50.07 −534.77 −490.59 0.06 0.11 0.004 0.004 0.09 0.15 0.005 0.005 Wilson Parameters 140.65 310.91 221.27 140.80 0.07 0.07 0.005 0.005 0.09 0.10 0.006 0.005 Margules Parameters −0.184 −0.124 −0.250 −0.194 0.06 0.09 0.004 0.004 0.05 0.11 0.006 0.005

N

∑i = 1 |Tical − Tiexp| ∑iN= 1(Tical − Tiexp)2 N

AADy1 = RMSDy1 =

1 N

−156.56 −532.46 0.13 0.002 0.16 0.002 174.04 217.75 0.04 0.004 0.05 0.005 −0.151 −0.242 0.03 0.004 0.04 0.005

N

∑i = 1 |yical − yiexp | ∑iN= 1(yical − yiexp )2 N

where Tmax and Tmin refer to the maximum and minimum temperatures of the systems, respectively. For the Van Ness point test, a four-parameter Legendre polynomial was used to evaluate the excess Gibbs free energy k

GE = x1(1 − x1) ∑ ak Lk (x1) (6) RT Here, k is 4 and a nonlinear optimization method was chosen to minimize the following objective function g=

F=

∑ (y1cal

+ y2cal − 1)

(7)

where y1 cal and y2 cal represent the calculated values of vaporphase mole fractions of component 1 and 2, respectively. Gmehling and Onken28 believed the isobaric VLE data were thermodynamically consistent if the average deflection of the vapor mole fractions was no more than about 0.01. The results of the thermodynamic consistency tests of the (methanol + DBC, nbutanol + DBC) are presented in Table 7. It showed that all of the experimental data passed both the area test of Herington10 and the point test of Van Ness11 and turned out to be reliable. Data Correlation. All of the experimental VLE data were regressed by the NRTL,12 Wilson,13 and Margules14 activity coefficient models. The equation forms of three models are listed in Table 8. For NRTL model, the nonrandomness parameter (aij) is set to 0.3 and gij − gjj are the binary interaction energy parameters. As to Wilson model, gij − gii are the binary interaction energy parameters; Tci, Pci, Zci are the critical temperature, pressure, and compressibility factor of component i and the

Figure 2. Experimental and calculated T−x1−y1 diagram for the system Methanol (1) + DBC (2) at 40.0 kPa. (■), experimental data for T−x1; (□), experimental data for T−y1. (), calculated data by the NRTL equation for T−x−y; (---), calculated data by the Wilson equation. (···), calculated data by the Margules equation.

values are listed in Table 9.19,26 Aij and Aji represent the Margules parameters. E



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Figure 5. Experimental and calculated T−x1−y1 diagram for the system n-Butanol (1) + DBC (2) at 40.0 kPa. (■), experimental data for T−x1; (□), experimental data for T−y1. (), calculated data by the NRTL equation for T−x−y; (---), calculated data by the Wilson equation. (···), calculated data by the Margules equation.


Figure 6. Experimental and calculated T−x1−y1 diagram for the system n-Butanol (1) + DBC (2) at 70.0 kPa. (■), experimental data for T−x1; (□), experimental data for T−y1. (), calculated data by the NRTL equation for T−x−y; (---), calculated data by the Wilson equation. (···), calculated data by the Margules equation.

In order to regress the three model parameters, the leastsquares method was used to minimize the following objective function ⎡⎛ ⎞2 ⎤ ⎢⎜ γexp − γcal ⎟ ⎥ OF = ∑ ⎢⎜ γexp ⎟⎠ ⎥ ⎣⎝ ⎦

agreement between the experimental and calculated values. The AAD and RMSD are defined as follows AAD =

(8)

for this equation, γexp and γcal are the experimental and calculated activity coefficients, respectively. The average absolute deviations (AAD) and the root-meansquare deviations (RMSD) of the vapor-phase mole fractions and equilibrium temperatures of the two binary systems at three reduced pressures were both calculated so as to measure the

1 N

N

∑ |Uiexp − Uical|

(9)

i=1 N

RMSD =

Uiexp

∑i = 1 (Uiexp − Uical)2 N

(10)

Uical

where is the experimental variable quantity and stands for the calculated variable quantity in this work; N is the number of experimental data points. F



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the experimental data were successfully correlated by the NRTL, Wilson, and Margules activity coefficient models at the three pressures. For the two binary systems, the AADT were below (0.12, 0.11, and 0.13) K and the AADy1 were below (0.005, 0.005, and 0.004) at p = 40.0, 70.0, and 100.0 kPa, respectively. In addition, the RMSDy1 were less than (0.006, 0.005, and 0.005) and the RMSDT were less than (0.15, 0.15, and 0.16). Therefore, it turned out that the experimental binary data measured will be of great important academic value and practical significance. For example, the experimental data not only provide an important theoretical basis for further research but also are beneficial to designing distillation column precisely. Besides, the experimental binary data measured are also helpful for industrial simulation for the process of separation and purification in synthesizing dibutyl carbonate.

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AUTHOR INFORMATION

Corresponding Author

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

Figure 7. Experimental and calculated T−x1−y1 diagram for the system n-Butanol (1) + DBC (2) at 100.0 kPa. (■), experimental data for T−x1; (□), experimental data for T−y1. (), calculated data by the NRTL equation for T-x-y; (---), calculated data by the Wilson equation. (···), calculated data by the Margules equation.

ORCID

Changsheng Yang: 0000-0002-3226-8517 Notes

The authors declare no competing financial interest.

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Consequently, all of the experimental VLE data were correlated with the NRTL,12 Wilson,13 and Margules14 activity coefficient models. In Tables 10 and 11, the absolute average deviations of the boiling temperatures (AADT), vapor-phase mole fractions (AADy1), the root-mean-square deviations of the boiling temperatures (RMSDT), and vapor-phase mole fractions (RMSDy1) were presented at the pressures of (40.0, 70.0, and 100.0) kPa, respectively. For the system of (methanol + DBC) at p = 40.0, 70.0, and 100.0 kPa, the maximum absolute deviations of the temperatures |ΔT|max correlated with NRTL,12 Wilson,13 and Margules14 models were (0.11, 0.30, and 0.08), (0.09, 0.19, and 0.07), and (0.08, 0.17, and 0.11), respectively; the maximum absolute deviations of the vapor-phase mole fraction |Δy1|max were (0.008, 0.009, and 0.010), (0.008, 0.008, and 0.009), and (0.009, 0.006, and 0.010), respectively. For the system of (nbutanol + DBC) at p = 40.0, 70.0, and 100.0 kPa, the maximum absolute deviations of the temperatures |ΔT|max correlated with NRTL, Wilson, and Margules models were (0.18, 0.21, and 0.09), (0.32, 0.25, and 0.22), and (0.26, 0.11, and 0.09), respectively; the maximum absolute deviations of the vaporphase mole fraction |Δy1|max were (0.009, 0.009, and 0.008), (0.009, 0.009, and 0.010), and (0.004, 0.009, and 0.010), respectively. Simultaneously, the comparison of the experimental and calculated data for the two binary systems with the form of T−x1−y1 diagrams are plotted in Figures 2 to 7. Thus, it turned out that the NRTL, Wilson, and Margules models had a good correlation for all of the experimental data of the two studied systems.

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CONCLUSION The isobaric experimental VLE of the binary systems for the two binary systems of (methanol + DBC, n-butanol + DBC) have been measured by using a improved Rose-Williams equilibrium still at p = 40.0, 70.0, and 100.0 kPa in this work. All of the experimental data were found to have passed the thermodynamic consistency tests by means of the Herington integral and pointto-point test methods. For the two binary systems of (methanol + DBC) and (n-butanol + DBC), it have been proved that all of G



Article

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