Article

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX pubs.acs.org/jced

Measurement and Correlation of Isobaric Vapor−Liquid Equilibrium

for Binary Systems of Allyl Alcohol with Isobutyl Acetate, Butyl
Acetate, and Butyl Propionate at 101.3 kPa
Yangchen Gao,† Li Xu,‡ Dongmei Xu,*,‡ Puyun Shi,‡ Zhishan Zhang,‡ Jun Gao,*,‡
and Yinglong Wang§
†
College of Materials and Chemical Engineering, Hainan University, Haikou 570228, China
‡
College of Chemical and Environmental Engineering, Shandong University of Science and Technology, Qingdao 266590, China
§
College of Chemical Engineering, Qingdao University of Science and Technology, Qingdao 266042, China

ABSTRACT: For separation of the azeotrope of allyl alcohol and water, three
extractive agentsisobutyl acetate, butyl acetate, and butyl propionatewere
selected to extract allyl alcohol from the azeotrope. To recover the extractive
agents by distillation, the isobaric vapor−liquid phase equilibrium (VLE) data
for allyl alcohol + isobutyl acetate, allyl alcohol + butyl acetate, and allyl alcohol
+ butyl propionate were measured at 101.3 kPa. With the VLE data, there is no
azeotrope formed in three systems. The consistency of the measured VLE data
was validated by the Herington, infinite dilution, pure component consistency,
and van Ness tests. Moreover, the Wilson, UNIQUAC, and NRTL models were
used to fit the measured VLE data. All of the calculated results agreed with the
VLE experimental data. Meanwhile, the parameters of the Wilson, UNIQUAC,
and NRTL were regressed, which can be employed for the development and
optimization of the separation process. Furthermore, the VLE data were
predicted by the UNIFAC model for the three binary mixtures, and better
prediction values were presented.

1. INTRODUCTION alcohol + butyl acetate, and allyl alcohol + butyl propionate

mixtures have not been found in the NIST database.
Allyl alcohol is an important chemical intermediate and fine
In this work, the isobaric vapor−liquid phase equilibrium
chemical, which is widely used in the production of agricultural
experimental data for the systems (allyl alcohol + isobutyl
chemicals, spices, medicines, and biological active com-
acetate/butyl acetate/butyl propionate) were determined at a
pounds.1−4 Generally, some methods were applied to
pressure of 101.3 kPa. The Herington,11 van Ness,12 infinite
synthesize allyl alcohol, such as chloropropylene hydrolysis,
dilution,13 and pure component consistency14 tests were
propylene oxide isomerization, allyl aldehyde reduction, and adopted to verify the experimental VLE data consistency.
allyl acetate hydrolysis methods. Among these methods, the Meanwhile, the VLE experimental data were fitted by the
allyl acetate hydrolysis method is widely used to synthesize allyl NRTL,15 Wilson,16 and UNIQUAC17 models and the
alcohol in industry. After the synthesis of allyl alcohol, an allyl parameters of the models were regressed. In addition, the
alcohol aqueous solution can be obtained. Since allyl alcohol UNIFAC18 model was employed to predict the isobaric VLE
and water can form a minimum azeotrope, which cannot be data for the three mixtures.
separated by traditional distillation, isobutyl acetate, butyl
acetate, and butyl propionate are used as suitable extractants to
2. EXPERIMENTAL SECTION
extract allyl alcohol from its aqueous solution. To recover the
extractive agents by distillation, the isobaric vapor−liquid phase 2.1. Materials. Allyl alcohol, isobutyl acetate, butyl acetate,
equilibrium (VLE) data are needed for the mixtures of allyl and butyl propionate were analytical reagents and purchased
alcohol + isobutyl acetate, allyl alcohol + butyl acetate, and allyl from the commercial sources. The mass fractions of the
alcohol + butyl propionate. chemicals were confirmed by gas chromatograph (SP6890,
In the previous works, McDougal et al.5 presented the Shandong Lunan Rui Hong Chemical Co., Ltd.). Specifications
isothermal VLE experimental data for the allyl alcohol + butyl of the chemicals are summarized in Table 1. These analytical
acetate system at temperatures of 373.15 and 423.15 K. The reagents were employed directly.
isothermal VLE experimental data for the allyl alcohol + water
mixture at 313.14 K and the isobaric VLE data at different Received: November 22, 2017
pressures have been reported.6−10 To our knowledge, the Accepted: February 22, 2018
isobaric VLE data for allyl alcohol + isobutyl acetate, allyl

© XXXX American Chemical Society A DOI: 10.1021/acs.jced.7b01024

J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data Article

Table 1. Suppliers and Mass Fractions of the Chemicals

Tbb (K)
component CAS supplier mass fraction exp. lit. analysis method
allyl alcohol 107-18-6 Shandong Xiya Chemical Co., Ltd. 0.99 369.90 369.7519 GCa
isobutyl acetate 110-19-0 Shanghai Macklin Biochemical Co., Ltd. 0.99 389.75 391.1519 GCa
butyl acetate 123-86-4 Chengdu Kelong Chemical Co., Ltd. ≥0.990 399.15 399.1520 GCa
butyl propionate 590-01-2 J&K Scientific Ltd. 0.99 418.25 418.6921 GCa
a
Gas chromatograph. bThe experimental pressure for the measurement of boiling temperature is 101.3 kPa; the standard uncertainties u of P and T
are u(P) = 1 kPa and u(T) = 0.1 K.

Table 2. Isobaric Vapor−Liquid Equilibrium Data (T, x, y), Activity Coefficient γi, the Absolute Deviation between the
Experimental and Calculated Values of Temperature, ΔT, Vapor Phase Mole Fraction, Δy, for Allyl Alcohol (1) + Isobutyl
Acetate (2) at 101.3 kPaa
NRTL Wilson UNIQUAC UNIFAC
T (K) x1 y1 γ1 γ2 ΔTb (K) Δy1c ΔTb (K) Δy1c ΔTb (K) Δy1c ΔTb (K) Δy1c
388.25 0.0216 0.0575 1.4326 1.0016 0.04 0.0001 0.04 0.0001 0.04 0.0001 0.01 0.0007
386.75 0.0479 0.1216 1.4335 1.0039 0.11 0.0001 0.11 0.0002 0.11 0.0002 0.03 0.0000
384.65 0.0909 0.2123 1.4118 1.0056 0.10 0.0006 0.10 0.0004 0.10 0.0004 0.03 0.0012
382.85 0.1359 0.2931 1.3832 1.0040 0.03 0.0009 0.03 0.0007 0.03 0.0007 0.05 0.0026
380.55 0.1994 0.3878 1.3466 1.0088 0.05 0.0010 0.06 0.0006 0.06 0.0006 0.01 0.0037
378.30 0.2768 0.4810 1.2983 1.0172 0.10 0.0002 0.11 0.0003 0.11 0.0003 0.02 0.0043
376.85 0.3316 0.5311 1.2575 1.0419 0.00 0.0045 0.01 0.0039 0.01 0.0039 0.09 0.0007
375.35 0.4072 0.5987 1.2158 1.0557 0.03 0.0012 0.04 0.0005 0.04 0.0006 0.05 0.0014
373.95 0.4858 0.6578 1.1757 1.0867 0.06 0.0005 0.05 0.0010 0.05 0.0010 0.12 0.0020
372.70 0.5765 0.7126 1.1216 1.1549 0.11 0.0033 0.10 0.0030 0.10 0.0030 0.14 0.0026
371.85 0.6502 0.7631 1.0976 1.1857 0.16 0.0029 0.16 0.0029 0.16 0.0030 0.17 0.0033
371.15 0.7206 0.8060 1.0724 1.2445 0.22 0.0043 0.22 0.0042 0.22 0.0043 0.22 0.0048
370.50 0.8054 0.8507 1.0366 1.4055 0.25 0.0022 0.25 0.0025 0.25 0.0024 0.23 0.0015
370.10 0.9027 0.9186 1.0131 1.5534 0.13 0.0001 0.13 0.0001 0.13 0.0000 0.11 0.0009
369.95 0.9843 0.9856 1.0023 1.7117 0.04 0.0004 0.04 0.0004 0.04 0.0004 0.04 0.0006
a
Standard uncertainties u of T, P, x, and y are u(T) = 0.1 K, u(P) = 1 kPa, and u(x) = u(y) = 0.0059. bΔTi = |Texp
i − Tcal
i |. Δyi = |yi
c exp
− ycal
i |.

Table 3. Isobaric Vapor−Liquid Equilibrium Data (T, x, y), Activity Coefficient γi, the Absolute Deviation between the
Experimental and Calculated Values of Temperature, ΔT, Vapor Phase Mole Fraction, Δy, for Allyl Alcohol (1) + Butyl Acetate
(2) at 101.3 kPaa
NRTL Wilson UNIQUAC UNIFAC
T (K) x1 y1 γ1 γ2 ΔT (K)
b
Δy1c ΔT (K)
b
Δy1c ΔT (K)
b
Δy1c ΔT (K)
b
Δy1c
395.90 0.0410 0.1264 1.3074 1.0017 0.10 0.0018 0.09 0.0016 0.07 0.0013 0.01 0.0021
393.10 0.0825 0.2282 1.2782 1.0053 0.08 0.0001 0.07 0.0001 0.05 0.0001 0.01 0.0017
390.90 0.1208 0.3076 1.2601 1.0058 0.00 0.0004 0.01 0.0003 0.02 0.0006 0.08 0.0025
388.63 0.1663 0.3816 1.2200 1.0155 0.12 0.0057 0.12 0.0053 0.12 0.0038 0.17 0.0019
386.15 0.2202 0.4598 1.2021 1.0244 0.09 0.0049 0.09 0.0044 0.09 0.0025 0.12 0.0009
384.30 0.2670 0.5156 1.1808 1.0359 0.09 0.0055 0.09 0.0048 0.08 0.0030 0.10 0.0016
382.20 0.3230 0.5756 1.1677 1.0507 0.06 0.0031 0.07 0.0024 0.08 0.0007 0.07 0.0003
380.30 0.3873 0.6379 1.1500 1.0533 0.05 0.0029 0.06 0.0035 0.06 0.0049 0.07 0.0055
378.30 0.4650 0.6928 1.1131 1.0927 0.07 0.0002 0.08 0.0001 0.08 0.0010 0.10 0.0012
376.80 0.5389 0.7374 1.0762 1.1389 0.03 0.0038 0.02 0.0037 0.02 0.0033 0.00 0.0034
375.20 0.6249 0.7900 1.0508 1.1812 0.05 0.0021 0.05 0.0021 0.06 0.0021 0.04 0.0025
373.20 0.7313 0.8496 1.0357 1.2637 0.20 0.0010 0.19 0.0011 0.18 0.0013 0.19 0.0020
372.00 0.8186 0.8990 1.0216 1.3097 0.16 0.0016 0.15 0.0016 0.14 0.0014 0.14 0.0008
370.90 0.9118 0.9494 1.0073 1.4017 0.08 0.0009 0.08 0.0010 0.07 0.0010 0.06 0.0009
370.20 0.9725 0.9832 1.0029 1.5293 0.07 0.0003 0.07 0.0002 0.07 0.0002 0.07 0.0000
a
Standard uncertainties u of T, P, x, and y are u(T) = 0.1 K, u(P) = 1 kPa, u(x) = 0.0058, and u(y) = 0.0059. bΔTi = |Texp
i − Ti |. Δyi = |yi − yi |.
cal c exp cal

2.2. Apparatus and Procedures. To determine the (supplied by Nanjing Hengyuan Automatic Gauge Co., Ltd.).
isobaric VLE experimental data, a modified Rose type still The uncertainty of pressure is 1 kPa. Meanwhile, a precise
was employed. The details of the equilibrium still were mercury thermometer was used to determine the equilibrium
provided, and the validation of the experimental apparatus temperature with an accuracy of ±0.1 K. To make the liquid
was verified in our previous literature.22,23 The pressure of the and vapor phases contact sufficiently, the liquid and vapor
system was maintained at 101.3 kPa with a manometer phases were circulated continuously. The equilibrium state was
B DOI: 10.1021/acs.jced.7b01024
J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data Article

Table 4. Isobaric Vapor−Liquid Equilibrium Data (T, x, y), Activity Coefficient γi, the Absolute Deviation between the
Experimental and Calculated Values of Temperature, ΔT, Vapor Phase Mole Fraction, Δy, for Allyl Alcohol (1) + Butyl
Propionate (2) at 101.3 kPaa
NRTL Wilson UNIQUAC UNIFAC
T (K) x1 y1 γ1 γ2 ΔT (K)
b
Δy1c ΔT (K)
b
Δy1c ΔT (K)
b
Δy1c ΔT (K)
b
Δy1c
415.92 0.0121 0.0733 1.4496 0.9971 0.18 0.0079 0.16 0.0078 0.12 0.0068 0.12 0.0017
408.95 0.0629 0.2854 1.3147 0.9935 0.08 0.0039 0.09 0.0038 0.13 0.0035 0.39 0.0060
403.50 0.1117 0.4176 1.2653 1.0076 0.25 0.0065 0.25 0.0062 0.24 0.0046 0.18 0.0072
399.80 0.1521 0.5021 1.2453 1.0127 0.41 0.0084 0.39 0.0078 0.34 0.0052 0.11 0.0090
395.30 0.2087 0.5933 1.2278 1.0235 0.39 0.0071 0.36 0.0064 0.27 0.0030 0.02 0.0096
391.50 0.2659 0.6618 1.2088 1.0391 0.28 0.0053 0.24 0.0046 0.13 0.0010 0.10 0.0076
387.25 0.3498 0.7307 1.1607 1.0777 0.30 0.0074 0.26 0.0069 0.15 0.0036 0.09 0.0003
384.80 0.4065 0.7706 1.1403 1.0940 0.22 0.0042 0.18 0.0039 0.09 0.0010 0.12 0.0002
381.85 0.4799 0.8151 1.1260 1.1155 0.08 0.0011 0.11 0.0011 0.19 0.0036 0.07 0.0023
380.55 0.5223 0.8345 1.1063 1.1383 0.06 0.0010 0.08 0.0009 0.15 0.0032 0.00 0.0013
378.90 0.5891 0.8583 1.0665 1.2019 0.14 0.0026 0.13 0.0028 0.08 0.0008 0.24 0.0030
375.60 0.7142 0.904 1.0376 1.3198 0.07 0.0020 0.07 0.0023 0.10 0.0008 0.03 0.0024
374.15 0.7853 0.9275 1.0184 1.3997 0.01 0.0020 0.01 0.0022 0.00 0.0011 0.08 0.0020
371.95 0.8914 0.9636 1.0073 1.5082 0.06 0.0003 0.05 0.0003 0.05 0.0003 0.03 0.0003
370.85 0.9483 0.9822 1.0038 1.6149 0.07 0.0003 0.07 0.0003 0.07 0.0000 0.07 0.0002
370.20 0.9818 0.9934 1.0037 1.7434 0.10 0.0004 0.10 0.0004 0.10 0.0003 0.10 0.0001
a
Standard uncertainties u of T, P, x, and y are u(T) = 0.1 K, u(P) = 1 kPa, and u(x) = u(y) = 0.0060. bΔTi = |Texp
i − Tcal
i |. Δyi = |yi
c exp
− ycal
i |.

achieved after the temperature of the vapor phase was stable for
at least 50 min. After that, the samples of liquid and vapor
phases were withdrawn by syringes immediately, and put into
the vials for analysis.
2.3. Analysis. The equilibrium compositions in the liquid
and vapor phases were determined by GC (SP6890, Shandong
Lunan Rui Hong Chemical Co., Ltd.) with the workstation of
N2000, which was presented by Zhejiang University. The GC
was connected with a packed column (PQ 3 mm × 2 m, Dalian
Sanjie Scientific Development Co., Ltd.) and a TCD (Lunan
Rui Hong Chem. Co., Ltd.). Hydrogen was used as the carrier
gas with a purity of 99.999%. The flow rate of the carrier gas
was 50 mL/min. The temperatures of oven, injection, and TCD
detector were 493.15, 513.15, and 513.15 K, respectively.
Before analyzing the sample compositions by GC, five known
composition mixtures were obtained by an electronic analytical
balance (SL512N, Mettler Toledo Instrument Co., Ltd.) with
an accuracy of ±0.0001 g to calibrate the analysis result. Every
Figure 1. T−x−y phase equilibrium for the system allyl alcohol (1) +
sample was determined by GC three times, and the mean value isobutyl acetate (2) at 101.3 kPa: (■) x, T experimental data; (●) y, T
was adopted. experimental data; () predicted results by the UNIFAC model.

3. RESULTS AND DISCUSSION C 2i

ln(Pis/kPa) = C1i + + C4iT + C5i ln T
3.1. VLE Experimental Data. The isobaric VLE data for T + C 3i
the mixtures allyl alcohol + isobutyl acetate, allyl alcohol + butyl
acetate, and allyl alcohol + butyl propionate were measured at + C6iT C7i for C 8i ≤ T ≤ C 9i (2)
101.3 kPa, which are expressed in mole fraction and listed in
Tables 2−4. The T−x−y and x−y diagrams of the isobaric VLE where C1i to C7i are the parameters for each component i and
experimental data for the mixtures are presented in Figures C8i and C9i are the limits of the temperature range, which were
1−4. As shown in these figures, there is no azeotrope formed obtained directly from the Aspen Databank24 and are presented
for the three binary systems, which indicates that the extractive in Table 5. The calculated activity coefficients are listed in
agents can be recovered by conventional distillation. Tables 2−4.
3.2. VLE Calculation. Since the liquid phase is nonideality, In addition, the relative volatility (α) for the three mixtures
the vapor−liquid phase equilibrium is expressed as follows: of allyl alcohol (1) + isobutyl acetate (2), allyl alcohol (1) +
butyl acetate (2), and allyl alcohol (1) + butyl propionate (2)
yP = xiγiPis (1)
i was calculated in terms of the following expression
For the saturation vapor pressure calculation of the pure y1x 2
component, the extended Antoine equation was adopted, which α12 =
is given as follows x1y2 (3)

C DOI: 10.1021/acs.jced.7b01024
J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data Article

Figure 4. x−y phase equilibrium for the systems at 101.3 kPa: (■)
Figure 2. T−x−y phase equilibrium for the system allyl alcohol (1) +
experimental data for allyl alcohol (1) + isobutyl acetate (2); (●)
butyl acetate (2) at 101.3 kPa: (■) x, T experimental data; (●) y, T
experimental data for allyl alcohol (1) + butyl acetate (2); (▲)
experimental data; (○) literature data by McDougal et al.;5 ()
experimental data for allyl alcohol (1) + butyl propionate (2); ()
predicted results by the UNIFAC model.
predicted results by the UNIFAC model.

calculated results of the excess Gibbs free energy for the three
systems are shown in Figure 6. The excess Gibbs free energy
values are positive with the entire range of composition. The
largest value of the excess Gibbs free energy is shown when the
compositions of allyl alcohol and esters are equal. Furthermore,
the values of GE follow the order allyl alcohol + isobutyl acetate
> allyl alcohol + butyl propionate > allyl alcohol + butyl acetate.
3.3. Consistency Test. To check the measured VLE data,
the Herington,11 van Ness,12 infinite dilution,13 and pure
component consistency14 tests were used to examine the
experimental data thermodynamic consistency, which were
carried out by the method provided by Kang et al.14
The Herington area test11 method is expressed as follows
1
A−B ∫0 ln(γ1/γ2) dx1
D = 100 × = 100 × 1
A+B ∫0 |ln(γ1/γ2)| dx1 (5)
Figure 3. T−x−y phase equilibrium for the system allyl alcohol (1) +
butyl propionate (2) at 101.3 kPa: (■) x, T experimental data; (●) y,
Tmax − Tmin
T experimental data; () predicted results by the UNIFAC model. J = 150 ×
Tmin (6)
where xi and yi denote the mole fractions in the vapor and where A and B are the areas above and under the horizontal
liquid phase. The relationships between the relative volatility coordinate axis in the diagram of ln(γ1/γ2) vs x1, respectively;
and the mole fraction of allyl alcohol for the mixtures are Tmax and Tmin are the highest and lowest boiling temperatures
presented in Figure 5. As shown in Figure 5, the relative values in the mixture. The relationship between ln(γ1/γ2) and x1 is
are all greater than 1, which indicates that the recovery of the shown in Figure 7. This test requires the |D − J| value to be less
selected esters is feasible by ordinary distillation. Meanwhile, than 10. The |D − J| values for the mixtures allyl alcohol +
the relative volatility values of allyl alcohol to butyl propionate isobutyl acetate, allyl alcohol + butyl acetate, and allyl alcohol +
are greater than those of allyl alcohol to butyl acetate and allyl butyl propionate at 101.3 kPa are presented in Table 6. The
alcohol to isobutyl acetate, which indicates that butyl results show that the measured VLE data pass the test.
propionate is easier to recover than butyl acetate and isobutyl The van Ness test12 is defined as follows
acetate. Therefore, butyl propionate is the best solvent to N N
extract allyl alcohol. 1 1 Pi exp − Pi cal
ΔP = ∑ ΔPi = ∑ 100
To clarify the nonideality of the investigated mixtures, the N i=1
N i=1
Pi exp (7)
excess Gibbs free energy GE was obtained by eq 4, which is
given as follows N N
1 1
Δy = ∑ Δyi = ∑ 100|yi cal − yi exp |
GE = RT (x1 ln γ1 + x 2 ln γ2) (4) N i=1
N i=1 (8)
where γi denotes the activity coefficients, which were calculated where N represents the number of experimental data, ycal i
by the UNIQUAC model with the regressed parameters. The represents the calculated composition of component i in the
D DOI: 10.1021/acs.jced.7b01024
J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data Article

Table 5. Parameters of the Extended Antoine Equationa

compound C1i C2i C3i C4i C5i C6i (×106) C7i C8i (K) C9i (K)
allyl alcohol 77.8312 −8057.6 0 0 −8.7151 1.6596 × 10−11 6.00 144.15 545.1
isobutyl acetate 65.4022 −6944.3 0 0 −7.298 3.7892 2.00 174.3 560.8
butyl acetate 115.9122 −9253.2 0 0 −14.99 10.47 2.00 199.65 575.4
butyl propionate 64.3202 −7709.8 0 0 −6.8418 6.3588 × 10−12 6.00 183.63 594.6
a
Taken from Aspen Property Databank.

Figure 5. α12−x1 diagram for the binary systems at 101.3 kPa: (■) Figure 7. Relationship between activity coefficients (ln(γ1/γ2)) and
allyl alcohol (1) + isobutyl acetate (2); (●) allyl alcohol (1) + butyl mole fractions in liquid phase (x1): (■) experimental data for allyl
acetate (2); (▲) allyl alcohol (1) + butyl propionate (2); () alcohol (1) + isobutyl acetate (2); (●) experimental data for allyl
calculated by the UNIQUAC model. alcohol (1) + butyl acetate (2); (▲) experimental data for allyl alcohol
(1) + butyl propionate (2); () calculated by the UNIQUAC model.

Table 6. Herington Test for Thermodynamic Consistency

Check
system D J |D − J| < 10 FHerington
allyl alcohol (1) + 3.5308 8.0495 4.5187 0.25
isobutyl acetate (2)
allyl alcohol (1) + 19.069 11.8613 7.2077 0.25
butyl acetate (2)
allyl alcohol (1) + 27.5279 19.6067 7.9213 0.25
butyl propionate (2)

Table 7. van Ness Test for Thermodynamic Consistency

Check
system ΔP < 1 Δy < 1 Fvan Ness
allyl alcohol (1) + isobutyl acetate (2) 0.0277 0.1490 0.25
allyl alcohol (1) + butyl acetate (2) 0.0263 0.2287 0.25
allyl alcohol (1) + butyl propionate (2) 0.0601 0.3757 0.25
Figure 6. Plot of estimated values of the excess Gibbs energy at 101.3
kPa from the UNIQUAC model versus mole fraction: () allyl
alcohol (1) + isobutyl acetate (2); (- - -) allyl alcohol (1) + butyl GE /(x1x 2RT ) − ln(γ1/γ2)
I1 = 100
acetate (2); (- · -), allyl alcohol (1) + butyl propionate (2). ln(γ1/γ2)
x1= 0 (9)

vapor phase by the NRTL model, and yexp i stands for the GE /(x1x 2RT ) − ln(γ1/γ2)
experimental composition of component i in the vapor phase. I2 = 100
ln(γ1/γ2)
The values of ΔP and Δy are listed in Table 7 and are less than x2 = 0 (10)
1, which means that the measured VLE data passed this test.
To check the consistency of data by the infinite dilution where
test,13 the infinite dilution test criterion is that I1 and I2 should
be smaller than 30. I1 and I2 are defined as follows GE /RT = x1x 2[c1 + c 2(x1 − x 2) + c3(x1 − x 2)2 ] (11)

E DOI: 10.1021/acs.jced.7b01024
J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data Article

Table 8. Parameters of Infinite Dilution Test

system c1 c2 c3 d1 d2 d3 d4
allyl alcohol (1) + isobutyl acetate (2) 0.3465 −0.5362 −0.6663 −0.0388 0.5029 0.2156 0.0287
allyl alcohol (1) + butyl acetate (2) 0.0843 −0.3076 −0.2170 −0.0930 0.3259 0.0305 −0.0442
allyl alcohol (1) + butyl propionate (2) 0.2127 −0.3945 −0.3842 −0.1116 0.3760 0.0735 0.0686

ln(γ1/γ2) = d1 + d 2(x 2 − x1) + d3(6x1x 2 − 1) If QVLE is close to 1, the VLE data are thermodynamically
consistent. The quality factors for the above four consistency
+ d4(x 2 − x1)(1 − 8x1x 2) (12) tests are presented in Table 11. As shown in Table 11, the
values of the overall quality factor, QVLE, for the three systems
The values of c1−c3 in eq 11 and d1−d4 in eq 12 were are equal to 1, which indicates that the experimental data pass
optimized on the basis of the nonlinear least-squares method this test.
using MATLAB. The calculated results are presented in Table
8. The I1 and I2 values of the three systems are presented in
Table 11. Overall Quality Factor for VLE Results
Table 9. All of the values of I1 and I2 are smaller than 30, which
indicates that the measured data for the mixtures passed this system FHerington Fvan Ness FInf. Dil. FPure QVLE ≤ 1
infinite dilution test. allyl alcohol (1) + 0.25 0.25 0.25 1 1
isobutyl acetate (2)
Table 9. Infinite Dilution Test for Thermodynamic allyl alcohol (1) + 0.25 0.25 0.25 1 1
butyl acetate (2)
Consistency Check
allyl alcohol (1) + 0.25 0.25 0.25 1 1
system I1 < 30 I2 < 30 FInf. Dil. butyl propionate (2)
allyl alcohol (1) + isobutyl acetate (2) 21.91 8.89 0.25
allyl alcohol (1) + butyl acetate (2) 10.61 8.67 0.25
allyl alcohol (1) + butyl propionate (2) 14.06 10.12 0.25 3.4. VLE Data Correlation and Prediction. In this work,
the NRTL,15 UNIQUAC,16 and Wilson17 models were adopted
The pure component consistency test14 was applied to verify to fit the measured VLE data. The maximum likelihood
the “end-points” consistency for the measured data. In this test, objective function was adopted to obtain the model interaction
ΔP10 and ΔP20 should be less than 1. Considering the parameters, which was carried out by Aspen Plus. The objective
requirements about the Gibbs−Duhem formula, this test function is described as follows
enforces the consistency between the pure component vapor N ⎡⎛ exp cal ⎞2 ⎛ pexp − pcal ⎞2
pressures and the VLE curve “end-points”.25−27 ΔP10 and ΔP20 ⎢⎜ Ti − Ti ⎟
⎟ + ⎜⎜
i i ⎟
Q = ∑ ⎢⎜ ⎟
are expressed as follows i = 1 ⎣⎝ σT ⎠ ⎝ σp ⎠
Pbubble(x1 → 1) − P10
⎛ x exp − x cal ⎞2 ⎛ y exp − y cal ⎞ ⎤
2
ΔP10 =
⎟⎥
0
P1 (13) + ⎜⎜ i i
⎟⎟ + ⎜⎜ i i
⎟⎥
⎝ σx ⎠ ⎝ σy ⎠⎦ (16)
0 Pbubble(x1 → 0) − P2 0
ΔP2 = where N represents the experimental data number, exp and cal
p2 0 (14) represent the measured data and calculated results, and T and P
where Pbubble is the bubble point pressure of the mixture and P10 are the equilibrium temperature and pressure. xi and yi
and P20 are the vapor pressures of the pure components. If the represent the compositions in the liquid and vapor phase; σ
VLE data is an isobaric set, the ΔP10 and ΔP20 values can be is the standard deviation. The absolute deviations of the vapor
replaced by the mean deviations in calculated dew or bubble phase composition and temperature are listed in Tables 2−4,
pressure.14 The results of ΔP10 and ΔP20 are presented in Table which are less than 0.0084 and 0.41 K. Furthermore, the
10. All of the ΔP10 and ΔP20 values are smaller than 1, which comparisons between the measured VLE data and calculated
indicates that the VLE data are consistent. values for the mixtures are presented in Figures 1−4. The
results indicate that the Wilson, UNIQUAC, and NRTL
Table 10. Pure Component Consistency Test for models can correlate the isobaric VLE data.
Thermodynamic Consistency Check The regressed parameters of the three thermodynamic
models for all of the systems along with the root-mean-square
system ΔP10 (×105) ΔP20 (×105) FPure deviation (RMSD) and average absolute deviation (AAD) of
allyl alcohol (1) + isobutyl acetate (2) 2.1780 3.7283 1 the temperature (T) and mole fraction of the vapor phase (y1)
allyl alcohol (1) + butyl acetate (2) 2.0790 4.4433 1 are presented in Table 12. The RMSD and AAD are expressed
allyl alcohol (1) + butyl propionate (2) 1.8810 2.2590 1 in the following:
⎛N ⎞0.5
Combining the above four consistency tests, an overall VLE RMSD(T ) = ⎜⎜∑ (Tical − Ti exp)2 /N )⎟⎟
data quality factor, QVLE, is established.25−27 The QVLE is ⎝ i=1 ⎠ (17)
defined as follows:
⎛N ⎞0.5
FPure(FHerington + FVan Ness + FInf. Dil.) RMSD(y) = ⎜⎜∑ (yi − yi ) /N ⎟⎟
cal exp 2
Q VLE =
0.25 × 3 (15) ⎝ i=1 ⎠ (18)

F DOI: 10.1021/acs.jced.7b01024
J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data Article

Table 12. Binary Interaction Parameters of the Activity Coefficient Models, the Root-Mean-Square Deviation (RMSD), and the
Average Absolute Deviations (AAD) of the Equilibrium Temperature (T) and the Vapor Phase Mole Fractions (y1) for the
Systems
binary interaction parameters RMSD AAD
model aij aji bij (K) bji (K) α T (K) y1 T (K) y1
allyl alcohol (1) + isobutyl acetate (2)
NRTL 11.044 −4.802 −3710.699 1636.540 0.3 0.12 0.0021 0.10 0.0015
Wilson 4.715 −12.309 −1691.292 4278.053 0.12 0.0020 0.10 0.0014
UNIQUAC −4.899 4.452 1830.185 −1751.445 0.12 0.0020 0.10 0.0014
UNIFAC 0.11 0.0035 0.09 0.0021
allyl alcohol (1) + butyl acetate (2)
NRTL −6.105 4.154 2336.044 −1448.256 0.3 0.10 0.0030 0.08 0.0023
Wilson −4.154 6.103 1458.128 −2348.197 0.09 0.0028 0.08 0.0022
UNIQUAC 5.436 −7.695 −1929.566 2668.019 0.09 0.0023 0.08 0.0018
UNIFAC 0.10 0.0032 0.08 0.0018
allyl alcohol (1) + butyl propionate (2)
NRTL −4.068 2.213 1556.826 −662.824 0.3 0.21 0.0047 0.17 0.0038
Wilson −1.875 3.814 564.790 −1492.110 0.19 0.0045 0.16 0.0036
UNIQUAC 3.463 −4.874 −1166.492 1548.050 0.16 0.0031 0.13 0.0024
UNIFAC 0.14 0.0047 0.11 0.0033

N Table 14. Volume Parameter (Rk) and Area Parameter (Qk)

AAD(Ti ) = ∑ |Ti cal − Ti exp|/N of the Groupsa
i=1 (19)
main group Rk Qk
N
cal exp CH2CH 1.3454 1.1760
AAD(yi ) = ∑ |yi − yi |/N CH3COO 1.9031 1.728
i=1 (20)
CH2COO 1.6764 1.420
As shown in Table 12, the RMSD(T) and RMSD(y1) values CH3 0.9011 0.8480
are less than 0.21 K and 0.0047. Meanwhile, AAD(T) is less CH2 0.6744 0.5400
than 0.17 K and AAD(y1) is less than 0.0038. CH 0.4469 0.2280
For comparison, the VLE data for the three mixtures were OH 1.0000 1.200
predicted by the UNIFAC model. The group type and number a
Reference 28.
of the involved compounds used in the UNIFAC model are
presented in Table 13. The volume parameter (Rk) and area

Table 13. Group Type and Group Number for Each 4. CONCLUSIONS
Component
In this work, the isobaric VLE data for the mixtures allyl alcohol
compound group type group number + isobutyl acetate, allyl alcohol + butyl acetate, and allyl alcohol
allyl alcohol CH2CH 1 + butyl propionate were measured at 101.3 kPa. The
OH 1 nonideality of the three systems follows the order of allyl
CH2 1 alcohol + isobutyl acetate > allyl alcohol + butyl propionate >
isobutyl acetate CH3 2 allyl alcohol + butyl acetate. Besides, no azeotropic point
CH2 1 formed in the three binary mixtures. The consistency of the
CH 1 measured VLE data was validated using the Herington, van
CH3COO 1 Ness, infinite dilution, and pure component consistency tests.
butyl acetate CH3 1 Meanwhile, the Wilson, UNIQUAC, and NRTL models were
CH2 3 adopted to fit the experimental data for the mixtures, and the
CH3COO 1 model parameters were also regressed. The correlated values
butyl propionate CH3 2 show an agreement with the experimental data. Meanwhile, the
CH2 3 UNIFAC model was applied to present the VLE values, and
CH2COO 1 good predicted results were achieved.

parameter (Qk) are given in Table 14.28 The temperature

■ AUTHOR INFORMATION
Corresponding Authors
absolute deviation and the vapor phase composition absolute
*E-mail: xudongmei.cn@163.com. Phone: +86 532 86057798.
deviation are listed in Tables 2−4, and the RMSD(T),
*E-mail: gao@sdust.edu.cn. Phone: +86 532 86057103.
RMSD(yi), AAD(T), and AAD(yi) for the three systems are
presented in Table 12. In the meantime, the predicted values by ORCID
the UNIFAC model are plotted in Figures 1−4. As shown in Dongmei Xu: 0000-0002-5770-0513
Figures 1−4, better predictions were obtained by the UNIFAC Jun Gao: 0000-0003-1145-9565
model for the three binary mixtures. Yinglong Wang: 0000-0002-3043-0891
G DOI: 10.1021/acs.jced.7b01024
J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data Article

Funding (19) James, G. S. Lange’s Chemistry Handbook, 16th version;

Financial support from the National Natural Science McGraw-Hill: New York, 2005.
Foundation of China (Grant 21776145) is acknowledged. (20) Wu, Y. Y.; Zhu, J. W.; Chen, K.; Wu, B.; Shen, Y. L. Vapor liquid
equilibria for the binary mixtures of 2,3-butanediol with n-butanol, n-
Notes butyl acetate, and ethyl acetate at 101.3 kPa. Fluid Phase Equilib. 2007,
The authors declare no competing financial interest. 262, 169−173.

■
(21) Lladosa, E.; Montòn, J. B.; Burguet, M. C.; Muñoz, R. Isobaric
vapor-liquid equilibria for binary and ternary mixtures of dipropyl
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H DOI: 10.1021/acs.jced.7b01024
J. Chem. Eng. Data XXXX, XXX, XXX−XXX