Isobaric VaporâLiquid Equilibrium for Two Binary Systems, (3-Methyl

Article pubs.acs.org/jced

Isobaric Vapor−Liquid Equilibrium for Two Binary Systems, (3-Methyl-1-butanol + 1,4-Butanediol) and (Hexylene Glycol + 1,4-Butanediol), at p = 40.0, 60.0, and 80.0 kPa Juan Zhi, Fengmin Jin, Qian Yang, Xue Feng, and Changsheng Yang* Key Laboratory for Green Chemical Technology of State Education Ministry, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China

ABSTRACT: The isobaric vapor−liquid equilibrium data for the two binary systems of (3-methyl-1-butanol + 1,4-butanediol, hexylene glycol + 1,4-butanediol) at p = 40.0, 60.0, and 80.0 kPa were obtained by a improved Rose equilibrium still. The thermodynamic consistency of the VLE (vapor−liquid equilibrium) data was checked via the methods of the Herington area test and the Van Ness point test. In addition, the nonrandom two-liquid (NRTL), Wilson, and universal quasichemical (UNIQUAC) activity coefficient models were adopted to correlate the VLE data. The calculated values of the models mentioned above showed good agreements with the measured data.

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point test of Van Ness et al.7 The activity coefficient models of the nonrandom two-liquid (NRTL),8 universal quasichemical (UNIQUAC),9 together with Wilson10 were employed to correlate the experimental data.

INTRODUCTION 1,4-Butanediol (BDO) is an essential chemical material in industry for manufacturing different substances such as tetrahydrofuran (THF), polybutylene terephthalate (PBT) resins, gamma-butyrolactone (GBL), polyurethanes, and other target compounds and pharmaceuticals.1,2 It is mainly produced by means of the multistage Reppe processes including the Reppe reaction of acetylene and formaldehyde and the hydrogenation of the reaction mixture in industry.3 Since the acetylene is costly in terms of money and nonrenewable fossil resources, a new method for synthesizing BDO has been reported by Genomatica.4 It was confirmed that the byproducts contained 3-methyl-1butanol (MB) and hexylene glycol (HG) by analyzing the raw products. So the VLE data are prerequisite in the process of separating BDO, MB, and HG in industrial production by distillation. In the process of designing the distillation column, the VLE data and the vapor−liquid equilibrium phase diagram are used to calculate the number of theoretical plates. There are no available VLE data about the two systems in the published literature. The isobaric VLE data for both systems (3-methyl-1-butanol + 1,4-butanediol) and (hexylene glycol + 1,4-butanediol) were measured at p = 40.0, 60.0, and 80.0 kPa utilizing a improved Rose−Williams still.5 The thermodynamic consistency of the VLE data was verified by the area test of Herington6 and the © XXXX American Chemical Society

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EXPERIMENTAL SECTION

Materials. MB and BDO, the mass fraction purity of which were over 0.998 and 0.990, respectively, were provided by Tianjin Guangfu Reagent Co.; HG with the mass fraction more than 0.980 was purchased from Tianjin YuanLi Co., Ltd. The chemicals’ purities were measured by gas chromatography (GC-SP2100A) with a thermal conductivity detector (TCD). It was found that the mass fraction of MB, BDO, and HG was tested to be 99.0%, 98.5%, and 98.0%, respectively. Moreover, the main impurity contained in all of the substances was water, the mass fraction of which was 0.7%, 1.0%, and 1.5%, separately. A further process was taken to purify the chemicals via a distillation column under subatmospheric pressure, and the mass fractions of the distilled chemicals listed in Table 1 were more than 99.8%, 99.7%, and 99.6%. Received: January 29, 2016 Accepted: July 21, 2016

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DOI: 10.1021/acs.jced.6b00092 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Material Description chemical namea MB HG BDO a b

source Tianjin Guangfu Reagent Co. Tianjin YuanLi Co., Ltd. Tianjin Guangfu Reagent Co.

initial mass fraction

purification method

final mass fraction

analysis method

0.998

distillation

0.998

GCb

0.980

distillation

0.996

GCb

0.990

distillation

0.997

GCb

MB: 3-methyl-1-butanol; HG: hexylene glycol; BDO: 1,4-butanediol. Gas chromatography. Figure 1. Experimental device: (1) heating rod, (2) liquid-phase sample port, (3) vapor-phase sample port, (4) condenser tube, (5) the inlet of coolant, (6) the outlet of coolant, (7) U-shaped manometer, (8) vacuum pump, (9) buffer flask, (10) regulating valve, (11) precision mercury thermometer.

The densities, refractive indexes, and boiling points of the pure substances mentioned above were also determined in this work. The densities were determined at (298.15 ± 0.01) K via an Anton Paar DMA58 densimeter. The refractive indexes were checked at (298.15 ± 0.01) K with an ATAGO NAR-3T Abbe refractometer. The uncertainties of the densimeter and the refractometer were 5 × 10−3 g·cm−3 and 1 × 10−4, separately. The boiling points were obtained under the atmosphere of 101.3 kPa whose uncertainty is 2 K. The properties of the three pure chemicals obtained in this study as well as the values inquired from the literature are shown in Table 2.11−14 Apparatus and Procedures. A changed Rose−Williams still was adopted to determine the isobaric VLE data. The whole device is shown in Figure 1. A vacuum pump purchased from the Greatwall Scientific Industrial and Trade Co. together with a buffer flask was contacted to the modified still to regulate the vacuum degree of this system. The pressure was revealed via a U-shaped differential manometer whose accuracy was 0.13 kPa. For the sake of letting the read of the U-shaped differential manometer maintain at a fixed value, a needle valve linked with the pump was used to adjust the volume of air entering into the device. The coolant in the circulating coolant pump and the condenser tube was ethanol. Its refrigerating temperature ranges from 273.15 to 283.15 K to make vapor phase condensate into liquid phase. The equilibrium temperature was shown by a high precision mercury thermometer, whose accuracy was 0.1 K and uncertainties were 2 K. A heating rod was used to provide energy for the system, and the heating intensity was maintained at the point that the condenser could produce a droplet every 3 s by adjusting the heater voltage. Equilibrium was achieved at the time that the temperature was kept constant under the same pressure about 30 min or even longer. As soon as the equilibrium was achieved, a micro syringe was taken to extract vapor phase (cooled into liquid) and liquid phase samples from their respective sampling ports, and then injected the samples directly into gas chromatography (GC). The feasibility of the whole experimental apparatus has been verified in our published work already.15−19 Analysis. The components of liquid and vapor samples were analyzed via a BFRL SP-2100A gas chromatography equipped

with a thermal conductivity detector (TCD), and the chromatographic column (2 m × 3 mm) of the GC was packed with Porapak QS (80−100). The N2000 chromatography station was installed on the computer to integrate the GC response peaks. High-purity hydrogen served as the carrier gas with the flow velocity maintained at 20 mL·min−1. For both binary systems of (MB + BDO) and (HG + BDO), the column, injector, and detector temperatures of the GC were remained at 503.15, 538.15, and 533.15 K, respectively. The external standard method was adopted to obtain quantitative results for the vapor−liquid equilibrium. For purpose of obtaining the external standard curve, a series of standard solutions of known mass fraction were gravimetrically premade using a Sartorius BP210S electronic balance whose uncertainty is 1 × 10−4 g. At least three analyses were executed of every standard solution, and the injection volume of it was 0.2 μL. The final values were obtained by the average of the closest three analysis results. The uncertainties in terms of the mole fraction were within 0.005.

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RESULTS AND DISCUSSION Pure Component Vapor Pressure. As for 3-methyl-1butanol, the calculation of the saturated vapor pressure was used by Antoine eq 1 derived from literature.20 For hexylene glycol, the saturated vapor pressure was calculated by Antoine eq 2.12 As for the 1,4-butanediol, its pressure was estimated with the Antoine eq 3.21 The related Antoine equation parameters are listed in Table 3.22 B ln(pis /kPa) = A − (C + T /K) (1) ⎛ 760ps ⎞ B i /kPa⎟ = A − log⎜ (C + (T − 273.15)/K) ⎝ 101.325 ⎠

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Table 2. Literature Values, Densities (ρ), Refractive Indices (nD), and Boiling Points (Tb) at p = 101.3 kPa of Pure Components ρ (g·cm−3) (298.15 K)

a

nD (298.15 K)

Tb/K (101.3 kPa)

compound

exptl

lit.

exptl

lit.

exptl

lit.

MB HG BDO

0.80728 0.91567 1.01283

0.8071a 0.9157b 1.01264d

1.4054 1.4267 1.4446

1.4052a 1.4263b 1.4445d

403.85 470.38 501.08

403.70a 470.45c 501.15d

Reference 11. bReference 12. cReference 13. dReference 14. u(p) = 0.13 KPa; u(T) = 0.01 K; u(ρ) = 5 × 10−3 g·cm−3; u(nD) = 1 × 10−4; u(Tb) = 2 K. B



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Table 3. Antoine Parameters Involved in This Study Antoine coefficients compound a

MB HGb BDOc a

b

A

B

C

D

E

range T/K

14.6977 7.8876 22.4549

3026.43 1890.38 −4202.3

−104.10 180.46 −4.2015

−7.45 × 10−10

6.18 × 10−7

293−667

c

Reference 20. Reference 12. Reference 21.

Table 4. Experimental VLE Data for 3-Methyl-1-butanol (1) + 1,4-Butanediol (2) at p = 40.0, 60.0, and 80.0 kPaa 40 kPa

60 kPa

80 kPa

T/K

x1

y1

473.44 453.48 438.77 428.38 420.25 415.30 412.50 408.61 403.96 402.70 399.07 397.19 379.01 485.11 466.76 452.91 442.41 434.05 428.73 425.74 421.58 416.57 415.21 411.28 409.23 389.52 493.78 477.27 463.64 453.16 444.51 439.09 435.97 431.59 426.30 424.85 420.68 418.48 397.48

0.000 0.050 0.103 0.154 0.208 0.250 0.276 0.319 0.378 0.396 0.454 0.488 1.000 0.000 0.051 0.102 0.154 0.207 0.249 0.276 0.319 0.378 0.396 0.455 0.489 1.000 0.000 0.050 0.103 0.154 0.208 0.250 0.276 0.319 0.378 0.396 0.454 0.488 1.000

0.000 0.548 0.767 0.854 0.905 0.930 0.942 0.956 0.970 0.974 0.983 0.986 1.000 0.000 0.497 0.718 0.833 0.894 0.921 0.934 0.949 0.964 0.967 0.976 0.982 1.000 0.000 0.456 0.681 0.802 0.869 0.900 0.916 0.934 0.952 0.957 0.968 0.972 1.000

γ1 1.049 1.043 1.038 1.035 1.030 1.033 1.028 1.027 1.027 1.024 1.021 1.000 1.019 1.025 1.031 1.032 1.028 1.025 1.020 1.018 1.017 1.012 1.012 1.000 1.005 0.991 1.005 1.005 1.000 1.003 1.000 1.001 1.002 1.001 1.000 1.000

Table 5. Experimental VLE Data for Hexylene Glycol (1) + 1,4-Butanediol (2) at p = 40.0, 60.0, and 80.0 kPaa

γ2 1.000 1.002 0.992 1.031 1.033 1.013 0.993 0.966 0.908 0.863 0.751 0.727

40 kPa

1.000 1.012 1.014 0.972 0.936 0.928 0.918 0.911 0.887 0.893 0.868 0.767

60 kPa

1.000 1.000 1.016 0.999 0.997 1.005 0.998 1.005 1.011 0.996 0.990 1.022

80 kPa

a

T/K

x1

y1

473.44 469.53 466.85 463.75 460.18 456.69 455.05 453.54 452.04 450.31 448.27 445.69 442.09 485.11 481.98 479.39 476.40 473.02 469.47 467.83 466.29 464.74 462.87 460.29 457.71 453.84 493.78 491.32 489.19 486.69 483.57 480.07 478.39 476.75 475.14 473.12 470.07 467.14 462.67

0.000 0.055 0.105 0.169 0.251 0.350 0.401 0.452 0.507 0.578 0.685 0.803 1.000 0.000 0.057 0.107 0.171 0.253 0.352 0.403 0.454 0.509 0.580 0.687 0.805 1.000 0.000 0.058 0.108 0.172 0.254 0.353 0.404 0.455 0.510 0.581 0.688 0.806 1.000

0.000 0.177 0.293 0.411 0.529 0.639 0.687 0.726 0.763 0.806 0.863 0.917 1.000 0.000 0.155 0.267 0.385 0.505 0.617 0.665 0.708 0.750 0.798 0.860 0.917 1.000 0.000 0.132 0.233 0.347 0.470 0.592 0.647 0.695 0.742 0.795 0.863 0.922 1.000

γ1 1.299 1.223 1.175 1.141 1.107 1.097 1.082 1.066 1.047 1.014 1.006 1.000 1.138 1.125 1.108 1.087 1.063 1.053 1.044 1.035 1.025 1.013 1.002 1.000 0.977 0.982 0.985 0.986 0.989 0.991 0.992 0.991 0.990 0.996 0.994 1.000

γ2 1.000 1.002 1.003 1.009 1.023 1.033 1.035 1.051 1.071 1.097 1.126 1.210 1.000 0.997 0.999 1.002 1.009 1.023 1.031 1.039 1.048 1.061 1.087 1.142 1.000 0.999 1.000 0.997 0.998 0.999 0.995 0.995 0.991 0.990 0.991 1.010

a

Standard uncertainties u are u(T) = 2 K, u(p) = 0.13 kPa, u(x) = 0.002, and u(y) = 0.005.

Standard uncertainties u are u(T) = 2 K, u(p) = 0.13 kPa, u(x) = 0.002, and u(y) = 0.005.

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

glycol + 1,4-butanediol) measured at p = 40.0, 60.0, and 80.0 kPa together with the activity coefficients of each constituent are displayed in Tables 4 and 5, respectively. It indicated that there was no azeotrope in the systems. Thermodynamic Consistency Test. The thermodynamic consistency of the VLE data was tested by way of the Herington area test by Ness et al.6,7 together with the point test of Van Ness23 modified by Fredenslund et al.24

(3)

Experimental Data. The isobaric VLE data for both binary systems of (3-methyl-1-butanol + 1,4-butanediol) and (hexylene C



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Table 6. Calculated Values of the Thermodynamic Consistency Test area testa

a

point testb |Δy1|

system

p/kPa

D−J

MB(1) + BDO(2)

40 60 80 40 60 80

−8.284 −8.910 0.298 7.786 6.940 6.008

HG(1) + BDO(2)

Table 9. Interaction Energy Parameters for Every Model and the Calculated Values of AADT/K, AADy1, RMSDT/K, and RMSDy1 for 3-Methyl-1-butanol (1) + 1,4-Butanediol (2) at p = 40.0, 60.0, and 80.0 kPaa

+ + + + + +

0.002 0.004 0.002 0.002 0.002 0.001

40.0 kPa

+ + + + + +

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

Reference 6. bReference 7.

Table 7. Mathematical Formulas of NRTL, UNIQUAC, and Wilson Equations Used in This Study


NRTL 2 ⎡ ⎤ G Gij2τij τ ji ji ⎥ ln γi = xj2⎢ + 2 2 ⎢⎣ (xi + xjGji) (xj + xiGij) ⎥⎦

τij =

gij − gjj RT

Gij = exp(− aijτij),

,

aij = aji


UNIQUAC ⎛ ⎛θ ⎞ r ⎞ ⎛Z⎞ ln γi = ln + ⎜ ⎟qi ln⎜⎜ i ⎟⎟ + φj⎜⎜li − i l j⎟⎟ − qi(θi + θτ j ji) ⎝2⎠ xi rj ⎠ ⎝ φi ⎠ ⎝

φi

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

Z (ri − qi) − (ri − 1), 2

θi =

qixi qixi + qjxj

,

φi =

rx i i , rx i i + rjxj

RTci τi Zci , τi = 1 + (1 − T /Tci)2/7 , Pci

k

GE = x1(1 − x1) ∑ ak Lk (x1) (6) RT the following objective function was minimized through a nonlinear regression method:

T /Tci ≤ 0.75

F=

q

r

Tc/K

Pc/MPa

Zc

MB HG BDO

3.478a 3.896a 3.328c

4.2729a 4.5742a 3.7576c

579.45b 621.00b 667.00b

3.88b 4.01b 4.88b

0.263b 0.309b 0.261b

In terms of the rule of Herington area test, the experimental VLE data were considered as thermodynamically consistent under the condition that |D − J| < 10.

(4)

γixipis = yp i

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. (Tmax − Tmin) Tmin

∑ (y1cal

+ y2cal − 1)

(7)

where y1cal and y2cal stand for the calculated values of vapor-phase mole fractions of components 1 and 2, respectively. When it comes to the Van Ness point-to-point test, the VLE data were turned out to be internally consistent only in case that the mean deviation of vapor mole fraction is no more than 0.01, suggested by Gmehling and Onken.25 The calculated results of the thermodynamic consistency tests of the VLE data are demonstrated in Table 6. As it could be seen from the results, all of the VLE data measured in this work pass the thermodynamic consistency check. Data Correlations. Under the conditions of p = 40.0, 60.0, and 80.0 kPa, the vapor phase of the two systems was assumed to behave almost the same as ideal gas. Neglecting the nonideality of vapor, the VLE equation is

Reference 25. bReference 21. cReference 26.

J = 150 ×

16.767 63.138 0.04 0.002 0.05 0.003

g=

compound

S+ − S− × 100 S+ + S−

−54.365 1.173 0.05 0.002 0.06 0.003

where Tmax is the maximum temperature, besides Tmin is the minimum value. As for the Van Ness point test, the excess Gibbs energy can be expressed with a four-parameter Legendre polynomial:

Table 8. Critical Constants (Tc, Pc, Zc) and Values of r and q Involved by the UNIQUAC Model

D=

11.000 0.954 0.03 0.002 0.05 0.003

exp N cal exp AADT = (1/N)∑Ni=1|Tcal i − Ti |, AADy1 = (1/N)∑i=1|yi − yi |, N cal exp N cal 1/2 RMSDT = {∑i=1(Ti − Ti )/N} , and RMSDy1 = {∑i=1(yi − 1/2 yexp i )/N} .

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

a

80.0 kPa

a

⎛ gji − gii ⎞ τji = exp⎜− ⎟ ⎝ RT ⎠

Vi =

60.0 kPa

NRTL Parameters 99.262 7.202 99.293 117.779 0.03 0.04 0.002 0.004 0.04 0.05 0.003 0.005 UNIQUAC Parameters 8.715 1.072 −4.904 −20.055 0.05 0.04 0.004 0.006 0.07 0.04 0.004 0.006 Wilson Parameters −4.552 86.110 239.880 104.333 0.04 0.04 0.002 0.004 0.04 0.05 0.003 0.004

(i = 1, 2)

(8)

where xi and yi stand for the mole fractions of composition i in the liquid phase and vapor phase, respectively; p stands for the experimental pressure of the system, and pis refers to the saturate vapor pressure of pure composition i at the equilibrium temperature.

(5) D



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Table 10. Interaction Energy Parameters for Every Model and the Calculated Values of AADT/K, AADy1, RMSDT/K, and RMSDy1 for Hexylene Glycol (1) + 1,4-Butanediol (2) at p = 40.0, 60.0, and 80.0 kPaa 40.0 kPa 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

60.0 kPa

NRTL Parameters 490.582 507.679 487.682 78.532 0.07 0.02 0.003 0.001 0.113 0.03 0.004 0.001 UNIQUAC Parameters 246.149 129.088 28.562 41.2186 0.10 0.06 0.004 0.001 0.117 0.07 0.005 0.001 Wilson Parameters 67.497 −411.004 1113.18 1135.63 0.19 0.07 0.005 0.001 0.24 0.08 0.006 0.002

80.0 kPa −48.478 −48.517 0.04 0.001 0.06 0.002 0.119 −25.734 0.05 0.008 0.06 0.008

Figure 3. VLE data for 3-methyl-1-butanol (1) + 1,4-butanediol (2) under the pressure of 60.0 kPa. ■ and ● refers to the measured data for T−x and T−y, respectively. ---, ···, and -·-·- stands for the calculated data by NRTL, UNIQUAC, and Wilson equations for T−x−y, respectively.

237.898 100.194 0.05 0.001 0.06 0.001

exp N cal exp AADT = (1/N)∑Ni=1|Tcal i − Ti |, AADy1 = (1/N)∑i=1|yi − yi |, N cal exp N cal 1/2 RMSDT = {∑i=1(Ti − Ti )/N} , and RMSDy1 = {∑i=1(yi − 1/2 yexp i )/N} . a


presented in Table 8.21,25,26 In addition, gij − gjj stand for the binary interaction coefficients in the activity coefficient models mentioned above. The following objective function was applied to the regression of the model parameters via the least-square method:


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

The activity coefficients of constituent i displayed in Tables 4 and 5 were calculated by eq 8. The VLE data were correlated utilizing the activity coefficient models including the UNIQUAC and NRTL as well as Wilson. The corresponding equations are demonstrated in Table 7. As to the NRTL model, the value of nonrandomness coefficient (aij) is fixed as 0.3. As to the UNIQUAC model, Z, the value of which is set as 10, represents the lattice coordination number. The van der Waals area parameters (qi), the volume parameters (ri), the values of the critical temperature (Tci), and critical pressure (Pci) together with compressibility factor (Zci) of component i are

(9)

where γexp and γcal are the symbols of the experimental and calculated activity coefficients, respectively. The average absolute deviations (AAD) together with the root-mean-square deviations (RMSD) of the equilibrium temperature and vapor-phase mole fraction were counted to assess the consistency between the measured data and calculated value. The equations of AAD and RMSD are given as follows: 1 AAD = N E

N

∑ |Uiexp − Uical| i=1

(10) DOI: 10.1021/acs.jced.6b00092 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Figure 7. VLE data for hexylene glycol (1) + 1,4-butanediol (2) under the pressure of 80.0 kPa. ■ and ● refers to the measured data for T−x and T−y, respectively. ---, ···, and -·-·- stands for the calculated data by NRTL, UNIQUAC, and Wilson equations for T−x−y, respectively.

Figure 5. VLE data for hexylene glycol (1) + 1,4-butanediol (2) under the pressure of 40.0 kPa. ■ and ● refers to the measured data for T−x and T−y, respectively. ---, ···, and -·-·- stands for the calculated data by NRTL, UNIQUAC, and Wilson equations for T−x−y, respectively.

The measured and calculated values for the systems of (3-methyl-1-butanol + 1,4-butanediol) and (hexylene glycol + 1,4-butanediol) are plotted in the form of T−x1−y1 charts at different pressures shown in Figures 2 to 7, separately. The results suggested that the UNIQUAC, NRTL, and Wilson models are all well agreed with the data.

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CONCLUSION In this study, isobaric VLE data for both of the binary systems (3-methyl-1-butanol + 1,4-butanediol) and (hexylene glycol + 1,4-butanediol) have been obtained utilizing an improved Rose− Williams still under the conditions of p = 40.0, 60.0, and 80.0 kPa. The Herington area test together with the Van Ness point test was adopted to test out the thermodynamic consistency of the experimental data. The results shown that all of the data passed the test. In addition, the activity coefficient models of NRTL, UNIQUAC, and Wilson were employed to correlate the obtained data. The absolute average deviation of the boiling temperature and the mole fraction of vapor phase for these two different systems were no more than AADT = 0.19, 0.07, and 0.05 K and AADy1 = 0.005, 0.006, and 0.008 under the condition of p = 40.0, 60.0, and 80.0 kPa, separately. Moreover, the root-mean-square deviations of the regression were also pretty small with the root-mean-square deviation of vapor-phase mole fraction RMSDy1 no more than 0.008 and the root-mean-square deviation of boiling temperature RMSDT no more than 0.24 K. The values suggest that all of the three activity coefficient models agreed well with the VLE data. So the VLE data measured in this paper are of good reliability, and they can be used for designing unit processes and further research.

Figure 6. VLE data for hexylene glycol (1) + 1,4-butanediol (2) under the pressure of 60.0 kPa. ■ and ● refers to the measured data for T−x and T−y, respectively. ---, ···, and -·-·- stands for the calculated data by NRTL, UNIQUAC, and Wilson equations for T−x−y, respectively. N

RMSD =

∑i = 1 (Uiexp − Uical)2 N

(11)

where U is regarded as a variable parameter standing for both of the equilibrium temperature and the vapor-phase mole fraction in this study; N refers to the number of the counted data points in each system. The values of the binary interaction energy parameters, AADT, AADy1, RMSDT, and RMSDy1 for each system under three different pressures are shown in Tables 9 and 10, respectively. For both of the binary systems (3-methyl-1-butanol + 1,4-butanediol and hexylene glycol + 1,4-butanediol), the maximum absolute deviation of the temperature |ΔT|max and the vapor phase mole fraction |Δy1|max between the correlated values deduced from the activity coefficient models and the experimental values were (0.17, 0.09, and 0.17 K), (0.40, 0.15, and 0.15 K), (0.008, 0.009, and 0.010), and (0.010, 0.003, and 0.005) under the pressure of 40.0, 60.0, and 80.0 kPa, respectively.

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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

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