Measurement and Correlation of Isobaric VaporâLiquid Equilibrium for

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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 Allyl alcohol is an important chemical intermediate and fine chemical, which is widely used in the production of agricultural chemicals, spices, medicines, and biological active compounds.1−4 Generally, some methods were applied to synthesize allyl alcohol, such as chloropropylene hydrolysis, propylene oxide isomerization, allyl aldehyde reduction, and allyl acetate hydrolysis methods. Among these methods, the allyl acetate hydrolysis method is widely used to synthesize allyl alcohol in industry. After the synthesis of allyl alcohol, an allyl alcohol aqueous solution can be obtained. Since allyl alcohol and water can form a minimum azeotrope, which cannot be separated by traditional distillation, isobutyl acetate, butyl acetate, and butyl propionate are used as suitable extractants to extract allyl alcohol from its aqueous solution. To recover the extractive agents by distillation, the isobaric vapor−liquid phase equilibrium (VLE) data are needed for the mixtures of allyl alcohol + isobutyl acetate, allyl alcohol + butyl acetate, and allyl alcohol + butyl propionate. In the previous works, McDougal et al.5 presented the isothermal VLE experimental data for the allyl alcohol + butyl acetate system at temperatures of 373.15 and 423.15 K. The isothermal VLE experimental data for the allyl alcohol + water mixture at 313.14 K and the isobaric VLE data at different pressures have been reported.6−10 To our knowledge, the isobaric VLE data for allyl alcohol + isobutyl acetate, allyl © XXXX American Chemical Society

alcohol + butyl acetate, and allyl alcohol + butyl propionate mixtures have not been found in the NIST database. In this work, the isobaric vapor−liquid phase equilibrium experimental data for the systems (allyl alcohol + isobutyl acetate/butyl acetate/butyl propionate) were determined at a pressure of 101.3 kPa. The Herington,11 van Ness,12 infinite dilution,13 and pure component consistency14 tests were adopted to verify the experimental VLE data consistency. Meanwhile, the VLE experimental data were fitted by the NRTL,15 Wilson,16 and UNIQUAC17 models and the parameters of the models were regressed. In addition, the UNIFAC18 model was employed to predict the isobaric VLE data for the three mixtures.

2. EXPERIMENTAL SECTION 2.1. Materials. Allyl alcohol, isobutyl acetate, butyl acetate, and butyl propionate were analytical reagents and purchased from the commercial sources. The mass fractions of the chemicals were confirmed by gas chromatograph (SP6890, Shandong Lunan Rui Hong Chemical Co., Ltd.). Specifications of the chemicals are summarized in Table 1. These analytical reagents were employed directly. Received: November 22, 2017 Accepted: February 22, 2018

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 isobutyl acetate butyl acetate butyl propionate

107-18-6 110-19-0 123-86-4 590-01-2

Shandong Xiya Chemical Co., Ltd. Shanghai Macklin Biochemical Co., Ltd. Chengdu Kelong Chemical Co., Ltd. J&K Scientific Ltd.

0.99 0.99 ≥0.990 0.99

369.90 389.75 399.15 418.25

369.7519 391.1519 399.1520 418.6921

GCa GCa GCa 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

a

Wilson

UNIQUAC

UNIFAC

T (K)

x1

y1

γ1

γ2

ΔTb (K)

Δy1c

ΔTb (K)

Δy1c

ΔTb (K)

Δy1c

ΔTb (K)

Δy1c

388.25 386.75 384.65 382.85 380.55 378.30 376.85 375.35 373.95 372.70 371.85 371.15 370.50 370.10 369.95

0.0216 0.0479 0.0909 0.1359 0.1994 0.2768 0.3316 0.4072 0.4858 0.5765 0.6502 0.7206 0.8054 0.9027 0.9843

0.0575 0.1216 0.2123 0.2931 0.3878 0.4810 0.5311 0.5987 0.6578 0.7126 0.7631 0.8060 0.8507 0.9186 0.9856

1.4326 1.4335 1.4118 1.3832 1.3466 1.2983 1.2575 1.2158 1.1757 1.1216 1.0976 1.0724 1.0366 1.0131 1.0023

1.0016 1.0039 1.0056 1.0040 1.0088 1.0172 1.0419 1.0557 1.0867 1.1549 1.1857 1.2445 1.4055 1.5534 1.7117

0.04 0.11 0.10 0.03 0.05 0.10 0.00 0.03 0.06 0.11 0.16 0.22 0.25 0.13 0.04

0.0001 0.0001 0.0006 0.0009 0.0010 0.0002 0.0045 0.0012 0.0005 0.0033 0.0029 0.0043 0.0022 0.0001 0.0004

0.04 0.11 0.10 0.03 0.06 0.11 0.01 0.04 0.05 0.10 0.16 0.22 0.25 0.13 0.04

0.0001 0.0002 0.0004 0.0007 0.0006 0.0003 0.0039 0.0005 0.0010 0.0030 0.0029 0.0042 0.0025 0.0001 0.0004

0.04 0.11 0.10 0.03 0.06 0.11 0.01 0.04 0.05 0.10 0.16 0.22 0.25 0.13 0.04

0.0001 0.0002 0.0004 0.0007 0.0006 0.0003 0.0039 0.0006 0.0010 0.0030 0.0030 0.0043 0.0024 0.0000 0.0004

0.01 0.03 0.03 0.05 0.01 0.02 0.09 0.05 0.12 0.14 0.17 0.22 0.23 0.11 0.04

0.0007 0.0000 0.0012 0.0026 0.0037 0.0043 0.0007 0.0014 0.0020 0.0026 0.0033 0.0048 0.0015 0.0009 0.0006

c exp 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 − Tcal − ycal i i |. Δyi = |yi 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

a

Wilson

T (K)

x1

y1

γ1

γ2

ΔT (K)

Δy1c

395.90 393.10 390.90 388.63 386.15 384.30 382.20 380.30 378.30 376.80 375.20 373.20 372.00 370.90 370.20

0.0410 0.0825 0.1208 0.1663 0.2202 0.2670 0.3230 0.3873 0.4650 0.5389 0.6249 0.7313 0.8186 0.9118 0.9725

0.1264 0.2282 0.3076 0.3816 0.4598 0.5156 0.5756 0.6379 0.6928 0.7374 0.7900 0.8496 0.8990 0.9494 0.9832

1.3074 1.2782 1.2601 1.2200 1.2021 1.1808 1.1677 1.1500 1.1131 1.0762 1.0508 1.0357 1.0216 1.0073 1.0029

1.0017 1.0053 1.0058 1.0155 1.0244 1.0359 1.0507 1.0533 1.0927 1.1389 1.1812 1.2637 1.3097 1.4017 1.5293

0.10 0.08 0.00 0.12 0.09 0.09 0.06 0.05 0.07 0.03 0.05 0.20 0.16 0.08 0.07

0.0018 0.0001 0.0004 0.0057 0.0049 0.0055 0.0031 0.0029 0.0002 0.0038 0.0021 0.0010 0.0016 0.0009 0.0003

b

UNIQUAC

ΔT (K)

Δy1c

0.09 0.07 0.01 0.12 0.09 0.09 0.07 0.06 0.08 0.02 0.05 0.19 0.15 0.08 0.07

0.0016 0.0001 0.0003 0.0053 0.0044 0.0048 0.0024 0.0035 0.0001 0.0037 0.0021 0.0011 0.0016 0.0010 0.0002

b

UNIFAC

ΔT (K)

Δy1c

ΔT (K)

Δy1c

0.07 0.05 0.02 0.12 0.09 0.08 0.08 0.06 0.08 0.02 0.06 0.18 0.14 0.07 0.07

0.0013 0.0001 0.0006 0.0038 0.0025 0.0030 0.0007 0.0049 0.0010 0.0033 0.0021 0.0013 0.0014 0.0010 0.0002

0.01 0.01 0.08 0.17 0.12 0.10 0.07 0.07 0.10 0.00 0.04 0.19 0.14 0.06 0.07

0.0021 0.0017 0.0025 0.0019 0.0009 0.0016 0.0003 0.0055 0.0012 0.0034 0.0025 0.0020 0.0008 0.0009 0.0000

b

b

cal c exp cal 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 |.

2.2. Apparatus and Procedures. To determine the isobaric VLE experimental data, a modified Rose type still was employed. The details of the equilibrium still were provided, and the validation of the experimental apparatus was verified in our previous literature.22,23 The pressure of the system was maintained at 101.3 kPa with a manometer

(supplied by Nanjing Hengyuan Automatic Gauge Co., Ltd.). The uncertainty of pressure is 1 kPa. Meanwhile, a precise mercury thermometer was used to determine the equilibrium temperature with an accuracy of ±0.1 K. To make the liquid and vapor phases contact sufficiently, the liquid and vapor phases were circulated continuously. The equilibrium state was B



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

a

Wilson

T (K)

x1

y1

γ1

γ2

ΔT (K)

Δy1c

415.92 408.95 403.50 399.80 395.30 391.50 387.25 384.80 381.85 380.55 378.90 375.60 374.15 371.95 370.85 370.20

0.0121 0.0629 0.1117 0.1521 0.2087 0.2659 0.3498 0.4065 0.4799 0.5223 0.5891 0.7142 0.7853 0.8914 0.9483 0.9818

0.0733 0.2854 0.4176 0.5021 0.5933 0.6618 0.7307 0.7706 0.8151 0.8345 0.8583 0.904 0.9275 0.9636 0.9822 0.9934

1.4496 1.3147 1.2653 1.2453 1.2278 1.2088 1.1607 1.1403 1.1260 1.1063 1.0665 1.0376 1.0184 1.0073 1.0038 1.0037

0.9971 0.9935 1.0076 1.0127 1.0235 1.0391 1.0777 1.0940 1.1155 1.1383 1.2019 1.3198 1.3997 1.5082 1.6149 1.7434

0.18 0.08 0.25 0.41 0.39 0.28 0.30 0.22 0.08 0.06 0.14 0.07 0.01 0.06 0.07 0.10

0.0079 0.0039 0.0065 0.0084 0.0071 0.0053 0.0074 0.0042 0.0011 0.0010 0.0026 0.0020 0.0020 0.0003 0.0003 0.0004

b

UNIQUAC

ΔT (K)

Δy1c

0.16 0.09 0.25 0.39 0.36 0.24 0.26 0.18 0.11 0.08 0.13 0.07 0.01 0.05 0.07 0.10

0.0078 0.0038 0.0062 0.0078 0.0064 0.0046 0.0069 0.0039 0.0011 0.0009 0.0028 0.0023 0.0022 0.0003 0.0003 0.0004

b

UNIFAC

ΔT (K)

Δy1c

ΔT (K)

Δy1c

0.12 0.13 0.24 0.34 0.27 0.13 0.15 0.09 0.19 0.15 0.08 0.10 0.00 0.05 0.07 0.10

0.0068 0.0035 0.0046 0.0052 0.0030 0.0010 0.0036 0.0010 0.0036 0.0032 0.0008 0.0008 0.0011 0.0003 0.0000 0.0003

0.12 0.39 0.18 0.11 0.02 0.10 0.09 0.12 0.07 0.00 0.24 0.03 0.08 0.03 0.07 0.10

0.0017 0.0060 0.0072 0.0090 0.0096 0.0076 0.0003 0.0002 0.0023 0.0013 0.0030 0.0024 0.0020 0.0003 0.0002 0.0001

b

b

c exp 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 − Tcal − ycal i i |. Δyi = |yi 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 sample was determined by GC three times, and the mean value was adopted.

Figure 1. T−x−y phase equilibrium for the system allyl alcohol (1) + isobutyl acetate (2) at 101.3 kPa: (■) x, T experimental data; (●) y, T experimental data; () predicted results by the UNIFAC model.

3. RESULTS AND DISCUSSION 3.1. VLE Experimental Data. The isobaric VLE data for the mixtures allyl alcohol + isobutyl acetate, allyl alcohol + butyl acetate, and allyl alcohol + butyl propionate were measured at 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 experimental data for the mixtures are presented in Figures 1−4. As shown in these figures, there is no azeotrope formed for the three binary systems, which indicates that the extractive agents can be recovered by conventional distillation. 3.2. VLE Calculation. Since the liquid phase is nonideality, the vapor−liquid phase equilibrium is expressed as follows: yP = xiγiPis i

ln(Pis/kPa) = C1i + + C6iT C7i

for

C 2i + C4iT + C5i ln T T + C 3i C 8i ≤ T ≤ C 9i

(2)

where C1i to C7i are the parameters for each component i and C8i and C9i are the limits of the temperature range, which were obtained directly from the Aspen Databank24 and are presented in Table 5. The calculated activity coefficients are listed in Tables 2−4. In addition, the relative volatility (α) for the three mixtures of allyl alcohol (1) + isobutyl acetate (2), allyl alcohol (1) + butyl acetate (2), and allyl alcohol (1) + butyl propionate (2) was calculated in terms of the following expression

(1)

For the saturation vapor pressure calculation of the pure component, the extended Antoine equation was adopted, which is given as follows

α12 = C

y1x 2 x1y2

(3) DOI: 10.1021/acs.jced.7b01024 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

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

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

∫0 ln(γ1/γ2) dx1 A−B D = 100 × = 100 × 1 A+B ∫0 |ln(γ1/γ2)| dx1

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, T experimental data; () predicted results by the UNIFAC model.

where xi and yi denote the mole fractions in the vapor and liquid phase. The relationships between the relative volatility and the mole fraction of allyl alcohol for the mixtures are presented in Figure 5. As shown in Figure 5, the relative values are all greater than 1, which indicates that the recovery of the selected esters is feasible by ordinary distillation. Meanwhile, the relative volatility values of allyl alcohol to butyl propionate are greater than those of allyl alcohol to butyl acetate and allyl alcohol to isobutyl acetate, which indicates that butyl propionate is easier to recover than butyl acetate and isobutyl acetate. Therefore, butyl propionate is the best solvent to extract allyl alcohol. To clarify the nonideality of the investigated mixtures, the excess Gibbs free energy GE was obtained by eq 4, which is given as follows GE = RT (x1 ln γ1 + x 2 ln γ2)

Tmax − Tmin Tmin

J = 150 ×

(5)

(6)

where A and B are the areas above and under the horizontal coordinate axis in the diagram of ln(γ1/γ2) vs x1, respectively; Tmax and Tmin are the highest and lowest boiling temperatures in the mixture. The relationship between ln(γ1/γ2) and x1 is shown in Figure 7. This test requires the |D − J| value to be less than 10. The |D − J| values for the mixtures allyl alcohol + isobutyl acetate, allyl alcohol + butyl acetate, and allyl alcohol + butyl propionate at 101.3 kPa are presented in Table 6. The results show that the measured VLE data pass the test. The van Ness test12 is defined as follows ΔP =

Δy =

(4)

where γi denotes the activity coefficients, which were calculated by the UNIQUAC model with the regressed parameters. The

N

1 N

∑ ΔPi =

1 N

∑ Δyi =

i=1 N i=1

N

Pi exp − Pi cal Pi exp

1 N

∑ 100

1 N

∑ 100|yi cal

i=1

(7)

N i=1

− yi exp |

(8)

where N represents the number of experimental data, ycal i represents the calculated composition of component i in the D



Article

Table 5. Parameters of the Extended Antoine Equationa

a

compound

C1i

C2i

C3i

C4i

C5i

C6i (×106)

C7i

C8i (K)

C9i (K)

allyl alcohol isobutyl acetate butyl acetate butyl propionate

77.8312 65.4022 115.9122 64.3202

−8057.6 −6944.3 −9253.2 −7709.8

0 0 0 0

0 0 0 0

−8.7151 −7.298 −14.99 −6.8418

1.6596 × 10−11 3.7892 10.47 6.3588 × 10−12

6.00 2.00 2.00 6.00

144.15 174.3 199.65 183.63

545.1 560.8 575.4 594.6

Taken from Aspen Property Databank.

Figure 5. α12−x1 diagram for the binary systems at 101.3 kPa: (■) allyl alcohol (1) + isobutyl acetate (2); (●) allyl alcohol (1) + butyl acetate (2); (▲) allyl alcohol (1) + butyl propionate (2); () calculated by the UNIQUAC model.

Figure 7. Relationship between activity coefficients (ln(γ1/γ2)) and mole fractions in liquid phase (x1): (■) experimental data for allyl alcohol (1) + isobutyl acetate (2); (●) experimental data for allyl 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 allyl alcohol (1) + isobutyl acetate (2) allyl alcohol (1) + butyl acetate (2) allyl alcohol (1) + butyl propionate (2)

|D − J| < 10 FHerington

D

J

3.5308

8.0495

4.5187

0.25

19.069

11.8613

7.2077

0.25

27.5279

19.6067

7.9213

0.25

Table 7. van Ness Test for Thermodynamic Consistency Check

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 acetate (2); (- · -), allyl alcohol (1) + butyl propionate (2).

system

ΔP < 1

Δy < 1

Fvan Ness

allyl alcohol (1) + isobutyl acetate (2) allyl alcohol (1) + butyl acetate (2) allyl alcohol (1) + butyl propionate (2)

0.0277 0.0263 0.0601

0.1490 0.2287 0.3757

0.25 0.25 0.25

I1 = 100

vapor phase by the NRTL model, and yexp stands for the i experimental composition of component i in the vapor phase. The values of ΔP and Δy are listed in Table 7 and are less than 1, which means that the measured VLE data passed this test. To check the consistency of data by the infinite dilution test,13 the infinite dilution test criterion is that I1 and I2 should be smaller than 30. I1 and I2 are defined as follows

I2 = 100

GE /(x1x 2RT ) − ln(γ1/γ2) ln(γ1/γ2)

x1= 0

(9)

GE /(x1x 2RT ) − ln(γ1/γ2) ln(γ1/γ2)

x2 = 0

(10)

where GE /RT = x1x 2[c1 + c 2(x1 − x 2) + c3(x1 − x 2)2 ] E

(11)



Article

Table 8. Parameters of Infinite Dilution Test system

c1

c2

c3

d1

d2

d3

d4


0.3465 0.0843 0.2127

−0.5362 −0.3076 −0.3945

−0.6663 −0.2170 −0.3842

−0.0388 −0.0930 −0.1116

0.5029 0.3259 0.3760

0.2156 0.0305 0.0735

0.0287 −0.0442 0.0686

If QVLE is close to 1, the VLE data are thermodynamically consistent. The quality factors for the above four consistency tests are presented in Table 11. As shown in Table 11, the values of the overall quality factor, QVLE, for the three systems are equal to 1, which indicates that the experimental data pass this test.

ln(γ1/γ2) = d1 + d 2(x 2 − x1) + d3(6x1x 2 − 1) + d4(x 2 − x1)(1 − 8x1x 2)

(12)

The values of c1−c3 in eq 11 and d1−d4 in eq 12 were optimized on the basis of the nonlinear least-squares method using MATLAB. The calculated results are presented in Table 8. The I1 and I2 values of the three systems are presented in 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 infinite dilution test.

Table 11. Overall Quality Factor for VLE Results system allyl alcohol (1) + isobutyl acetate (2) allyl alcohol (1) + butyl acetate (2) allyl alcohol (1) + butyl propionate (2)

Table 9. Infinite Dilution Test for Thermodynamic Consistency Check system

I1 < 30

I2 < 30

FInf. Dil.


21.91 10.61 14.06

8.89 8.67 10.12

0.25 0.25 0.25

0

ΔP2 =

P1

where Pbubble is the bubble point pressure of the mixture and P10 and P20 are the vapor pressures of the pure components. If the VLE data is an isobaric set, the ΔP10 and ΔP20 values can be replaced by the mean deviations in calculated dew or bubble pressure.14 The results of ΔP10 and ΔP20 are presented in Table 10. All of the ΔP10 and ΔP20 values are smaller than 1, which indicates that the VLE data are consistent. Table 10. Pure Component Consistency Test for Thermodynamic Consistency Check ΔP20 (×105)

FPure


2.1780 2.0790 1.8810

3.7283 4.4433 2.2590

1 1 1

Combining the above four consistency tests, an overall VLE data quality factor, QVLE, is established.25−27 The QVLE is defined as follows: Q VLE =

FPure(FHerington + FVan Ness + FInf. Dil.) 0.25 × 3

1

0.25

0.25

0.25

1

1

0.25

0.25

0.25

1

1

(16)

where N represents the experimental data number, exp and cal represent the measured data and calculated results, and T and P are the equilibrium temperature and pressure. xi and yi represent the compositions in the liquid and vapor phase; σ is the standard deviation. The absolute deviations of the vapor phase composition and temperature are listed in Tables 2−4, which are less than 0.0084 and 0.41 K. Furthermore, the comparisons between the measured VLE data and calculated values for the mixtures are presented in Figures 1−4. The results indicate that the Wilson, UNIQUAC, and NRTL models can correlate the isobaric VLE data. The regressed parameters of the three thermodynamic models for all of the systems along with the root-mean-square deviation (RMSD) and average absolute deviation (AAD) of the temperature (T) and mole fraction of the vapor phase (y1) are presented in Table 12. The RMSD and AAD are expressed in the following:

(14)

ΔP10 (×105)

1

2 ⎛ x exp − x cal ⎞2 ⎛ y exp − y cal ⎞ ⎤ i i i i ⎟⎥ ⎟⎟ + ⎜⎜ + ⎜⎜ ⎟⎥ σ σ ⎝ ⎠ x y ⎝ ⎠⎦

Pbubble(x1 → 0) − P2 0

system

0.25

⎡⎛ exp ⎛ pexp − pcal ⎞2 cal ⎞2 ⎢⎜ Ti − Ti ⎟ i i ⎟ Q = ∑ ⎢⎜ ⎟ + ⎜⎜ ⎟ σT σp ⎠ ⎝ ⎠ i = 1 ⎣⎝

(13)

p2 0

FPure QVLE ≤ 1

0.25

N

Pbubble(x1 → 1) − P10 0

Fvan Ness FInf. Dil.

0.25

3.4. VLE Data Correlation and Prediction. In this work, the NRTL,15 UNIQUAC,16 and Wilson17 models were adopted to fit the measured VLE data. The maximum likelihood objective function was adopted to obtain the model interaction parameters, which was carried out by Aspen Plus. The objective function is described as follows

The pure component consistency test14 was applied to verify the “end-points” consistency for the measured data. In this test, ΔP10 and ΔP20 should be less than 1. Considering the requirements about the Gibbs−Duhem formula, this test enforces the consistency between the pure component vapor pressures and the VLE curve “end-points”.25−27 ΔP10 and ΔP20 are expressed as follows ΔP10 =

FHerington

(15) F

⎛N ⎞0.5 RMSD(T ) = ⎜⎜∑ (Tical − Ti exp)2 /N )⎟⎟ ⎝ i=1 ⎠

(17)

⎛N ⎞0.5 cal exp 2 RMSD(y) = ⎜⎜∑ (yi − yi ) /N ⎟⎟ ⎝ i=1 ⎠

(18)



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 aij

model

aji

bij (K)

RMSD α

bji (K)

NRTL Wilson UNIQUAC UNIFAC

11.044 4.715 −4.899

−4.802 −12.309 4.452

allyl alcohol (1) + isobutyl acetate (2) −3710.699 1636.540 0.3 −1691.292 4278.053 1830.185 −1751.445


−6.105 −4.154 5.436

4.154 6.103 −7.695

allyl alcohol (1) + butyl acetate (2) 2336.044 −1448.256 0.3 1458.128 −2348.197 −1929.566 2668.019


−4.068 −1.875 3.463

2.213 3.814 −4.874

allyl alcohol (1) + butyl propionate (2) 1556.826 −662.824 0.3 564.790 −1492.110 −1166.492 1548.050

N

∑ |Ti cal − Ti exp|/N

AAD(Ti ) =

N

AAD(yi ) =

∑ |yi

cal

− yi

exp

|/N (20)

i=1

As shown in Table 12, the RMSD(T) and RMSD(y1) values are less than 0.21 K and 0.0047. Meanwhile, AAD(T) is less than 0.17 K and AAD(y1) is less than 0.0038. For comparison, the VLE data for the three mixtures were predicted by the UNIFAC model. The group type and number of the involved compounds used in the UNIFAC model are presented in Table 13. The volume parameter (Rk) and area

a

Table 13. Group Type and Group Number for Each Component compound allyl alcohol

isobutyl acetate

butyl acetate

butyl propionate

group type

group number

CH2CH OH CH2 CH3 CH2 CH CH3COO CH3 CH2 CH3COO CH3 CH2 CH2COO

1 1 1 2 1 1 1 1 3 1 2 3 1

T (K)

y1

T (K)

y1

0.12 0.12 0.12 0.11

0.0021 0.0020 0.0020 0.0035

0.10 0.10 0.10 0.09

0.0015 0.0014 0.0014 0.0021

0.10 0.09 0.09 0.10

0.0030 0.0028 0.0023 0.0032

0.08 0.08 0.08 0.08

0.0023 0.0022 0.0018 0.0018

0.21 0.19 0.16 0.14

0.0047 0.0045 0.0031 0.0047

0.17 0.16 0.13 0.11

0.0038 0.0036 0.0024 0.0033

Table 14. Volume Parameter (Rk) and Area Parameter (Qk) of the Groupsa

(19)

i=1

AAD

main group

Rk

Qk

CH2CH CH3COO CH2COO CH3 CH2 CH OH

1.3454 1.9031 1.6764 0.9011 0.6744 0.4469 1.0000

1.1760 1.728 1.420 0.8480 0.5400 0.2280 1.200

Reference 28.

4. CONCLUSIONS In this work, the isobaric VLE data for the mixtures allyl alcohol + isobutyl acetate, allyl alcohol + butyl acetate, and allyl alcohol + butyl propionate were measured at 101.3 kPa. The nonideality of the three systems follows the order of allyl alcohol + isobutyl acetate > allyl alcohol + butyl propionate > allyl alcohol + butyl acetate. Besides, no azeotropic point formed in the three binary mixtures. The consistency of the measured VLE data was validated using the Herington, van Ness, infinite dilution, and pure component consistency tests. Meanwhile, the Wilson, UNIQUAC, and NRTL models were adopted to fit the experimental data for the mixtures, and the model parameters were also regressed. The correlated values show an agreement with the experimental data. Meanwhile, the UNIFAC model was applied to present the VLE values, and good predicted results were achieved.

■

parameter (Qk) are given in Table 14.28 The temperature absolute deviation and the vapor phase composition absolute deviation are listed in Tables 2−4, and the RMSD(T), RMSD(yi), AAD(T), and AAD(yi) for the three systems are presented in Table 12. In the meantime, the predicted values by the UNIFAC model are plotted in Figures 1−4. As shown in Figures 1−4, better predictions were obtained by the UNIFAC model for the three binary mixtures.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +86 532 86057798. *E-mail: [email protected]. Phone: +86 532 86057103. ORCID

Dongmei Xu: 0000-0002-5770-0513 Jun Gao: 0000-0003-1145-9565 Yinglong Wang: 0000-0002-3043-0891 G



Article

Funding

(19) James, G. S. Lange’s Chemistry Handbook, 16th version; McGraw-Hill: New York, 2005. (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, nbutyl acetate, and ethyl acetate at 101.3 kPa. Fluid Phase Equilib. 2007, 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 ether, 1-propyl alcohol, and butyl propionate. J. Chem. Eng. Data 2006, 51, 2233−2238. (22) Zhu, Z.; Ma, Y.; Gao, J. Isobaric vapor-liquid equilibria for binary systems of acetic acid + benzene. J. Chem. Eng. Data 2010, 55, 3387−3390. (23) Gao, J.; Zhao, L.; Zhang, L.; Xu, D.; Zhang, Z. Isobaric vaporliquid equilibrium for binary systems of 2,2,3,3-tetrafluoro-1-propanol + 2,2,3,3,4,4,5,5- octafluoro-1-pentanol at 53.3, 66.7, 80.0 kPa. J. Chem. Eng. Data 2016, 61, 3371−3376. (24) Aspen Plus software, version 7.3; Aspen Technology, Inc.: Burlington, MA, 2001. (25) Martins, V. D.; Granato, M. A.; Rodrigues, A. E. Isobaric vapor− liquid equilibrium for binary systems of 2,2,4-trimethylpentane with oxylene, m-xylene, p-xylene, and ethylbenzene at 250 kPa. J. Chem. Eng. Data 2014, 59, 1499−1506. (26) Gao, J.; Zhang, K.; Xu, D.; Zhang, L.; Chen, N.; Li, C. Isobaric vapor−liquid equilibrium for binary systems of cyclohexanone + benzene, cyclohexanone + toluene, and cyclohexanone + p-xylene at 101.3 kPa. J. Chem. Eng. Data 2017, 62, 1948−1954. (27) Shi, P.; Gao, Y.; Wu, J.; Xu, D.; Gao, J.; Ma, X.; Wang, Y. Separation of azeotrope (2,2,3,3-tetrafluoro-1-propanol + water): isobaric vapour-liquid phase equilibrium measurements and azeotropic distillation. J. Chem. Thermodyn. 2017, 115, 19−26. (28) Magnussen, T.; Rasmussen, P.; Fredenslund, A. UNIFAC parameter table for prediction of liquid-liquid equilibria. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 331−339.

Financial support from the National Natural Science Foundation of China (Grant 21776145) is acknowledged. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Oblinger, E.; Montgomery, J. A new stereoselective method for the preparation of allylic alcohols. J. Am. Chem. Soc. 1997, 119, 9065− 9066. (2) Bandini, M.; Tragni, M. π-Activated alcohols: an emerging class of alkylating agents for catalytic Friedel−Crafts reactions. Org. Biomol. Chem. 2009, 7, 1501−1507. (3) Wu, Y. K.; Liu, H. J.; Zhu, J. L. An efficient procedure for the 1,3transposition of allylic alcohols based on lithium naphthalenide induced reductive elimination of epoxy mesylates. Synlett 2008, 2008, 621−623. (4) Wang, X. L.; Li, X. D.; Xue, J. J.; Zhao, Y. L.; Zhang, Y. M. A novel and efficient procedure for the preparation of allylic alcohols from α, β-unsaturated carboxylic esters using LiAlH4/BnCl. Tetrahedron Lett. 2009, 50, 413−415. (5) McDougal, R. J.; Jasperson, L. V.; Wilson, G. M. Vapor−liquid equilibrium for several compounds relevant to the biofuels industry modeled with the wilson equation. J. Chem. Eng. Data 2014, 59, 1069− 1085. (6) Grabner, R. W.; Clump, C. W. Liquid-Vapor equilibrium and heats of vaporization of allyl alcohol-water mixtures. J. Chem. Eng. Data 1965, 10, 13−16. (7) Zhang, L.; Gao, Y.; Xu, D.; Zhang, Z.; Gao, J.; Pratik, D. Isobaric vapor−liquid equilibrium for binary systems of allyl alcohol with water, methanol, and ethanol at 101.3 kPa. J. Chem. Eng. Data 2016, 61, 2071−2077. (8) Aucejo, A.; Loras, S.; Monton, J. B. Isobaric vapor-liquid equilibria of prop-2-en-1-ol (allyl alcohol) + water system at 30, 60, and 100 kPa. ELDATA: Int. Electron. J. Phys.-Chem. Data 1996, 2, 1−4. (9) Harper, B. G.; Moore, J. C. Vapor-liquid equilibrium new still and method for determining vapor-liquid equilibrium. Ind. Eng. Chem. 1957, 49, 411−414. (10) Lesteva, T. M.; Khrapkova, E. I. Duhen - margules equation used to check isothermic data on liquid-vapor equilibrium in binary and ternary system. Zh. Fiz. Khim. 1972, 46, 612−616. (11) Herington, E. F. G. Tests for the consistency of experimental isobaric vapour-liquid equilibrium data. J. Inst. Petrol. 1951, 37, 457− 470. (12) van Ness, H. C.; Byer, S.; Gibbs, M. R. E. Vapour-Liquid equilibrium: Part I. An appraisal of data reduction methods. AIChE J. 1973, 19, 238−244. (13) Kojima, K.; Moon, H. M.; Ochi, K. Thermodynamic Consistency Test of Vapour-Liquid Equilibrium Data: - Methanol ∼ water, benzene ∼ cyclohexane and ethyl methyl ketone ∼ water. Fluid Phase Equilib. 1990, 56, 269−284. (14) Kang, J. W.; Diky, V.; Chirico, R. D.; Magee, J. W.; Muzny, C. D.; Abdulagatov, I.; Kazakov, A. F.; Frenkel, M. Quality assessment algorithm for vapour− liquid equilibrium data. J. Chem. Eng. Data 2010, 55, 3631−3640. (15) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (16) Wilson, G. M. Vapour-Liquid equilibrium. XI. a new expression for the excess free energy of mixing. J. Am. Chem. Soc. 1964, 86, 127− 130. (17) Abrams, D. S.; Prausnitz, J. M. Statistical thermodynamics of liquid mixtures: a new ptxpression for the excess gibbs energy of partly or completely miscible Systems. AIChE J. 1975, 21, 116−128. (18) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Groupcontribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J. 1975, 21, 1086−1099 11. H


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