Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Isobaric Vapor−Liquid Phase Equilibrium Measurements, Correlation, and Prediction for Separation of the Mixtures of Cyclohexanone and Alcohols Kai Zhang,§,† Dongmei Xu,§,† Yunpeng Zhou,§ Puyun Shi,§ Jun Gao,*,§ and Yinglong Wang‡ §
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
‡
S Supporting Information *
ABSTRACT: For separation of the mixtures cyclohexanone with alcohols by distillation, the isobaric vapor−liquid equilibrium data for cyclohexanone + (ethanol/n-propanol/ isopropanol) were measured at 101.3 kPa. The van Ness, pure component consistency, and Herington test were used to validate the measured data consistency. The measured data were fitted by the Wilson, NRTL, and UNIQUAC models with the optimized binary parameters. For comparison, the phase equilibrium values for the investigated mixtures were predicted by the COSMO-SAC and UNIFAC models, and the standard deviations of vapor phase composition by the two models are less than 0.0043 and 0.0055.
1. INTRODUCTION Ortho-phenyl phenol (OPP) is an important organic material, which is widely used to synthesize antiseptic, surfactant, plastic thermal stabilizer, and printing and dyeing assistant.1,2 To prepare OPP, 2-(1-cyclohexenyl)cyclohexanone (D2) and 2(cyclohexane-1-ylidene)cyclohexane-1-one (D3) are used as the intermediates,3,4 which can be obtained by the selfcondensation of cyclohexanone with a catalyst. Usually, aluminum oxide is adopted as a catalyst in the self-condensation of cyclohexanone due to its good catalytic activity and selectivity. After the self-condensation of cyclohexanone, the reaction mixture containing a certain amount of D2 and D3, aluminum oxide, and unreacted cyclohexanone is obtained. The waste of aluminum oxide with a small amount of organics is separated by filtration. To recover and reutilize the catalyst aluminum oxide, in this work, the different solvents of ethanol, n-propanol, and isopropanol were selected to dissolve the organics in the waste. After the dissolution, the catalyst of aluminum oxide was obtained by filtration, and the filtrate mainly consisted of the solvents and cyclohexanone, and a small amount of D2 and D3 was obtained. The solvents can be recovered by distillation from the filtrate.5 Designing the distillation process to separate the solvents requires the knowledge of the vapor−liquid phase equilibrium (VLE) for cyclohexanone and the solvents. Prasad et al.6 explored the systems cyclohexanone + (ethanol/n-propanol/isopropanol) at a pressure of 94.8 kPa and reported the equilibrium temperatures and liquid phase mole fractions. Weissenberger7 presented isothermal VLE values for cyclohexanone + ethanol at a temperature of © XXXX American Chemical Society
291.14 K. As for the isobaric VLE data for cyclohexanone + (ethanol/n-propanol/isopropanol) under the atmospheric pressure, these have not been reported by retrieving results from the databases of NIST and DDB. In our work, the VLE values for cyclohexanone with ethanol, n-propanol, and isopropanol were determined at pressures of 101.3 kPa. The measured data were validated by Herington, pure component consistency, and van Ness tests to check the thermodynamic consistency. The measured results were fitted by Wilson, NRTL, and UNIQUAC thermodynamic models with the optimized parameters. For comparison, the VLE values were predicted by UNIFAC and COSMO-SAC models. Meanwhile, the prediction performances of the two models were evaluated.
2. EXPETIMENTAL SECTION 2.1. Chemicals. The chemicals of cyclohexanone, ethanol, n-propanol, and isopropanol were analytical grade, which were purchased from commercial sources. The regents’ information is presented in Table 1. The mass fractions of the chemicals were tested and confirmed by GC, and no detectable impurity was observed. Thus, all the reagents were applied directly. The density (ρ) for all chemicals was determined at T = 298.15 K by an AntonPaar DMA 4500 densimeter, with the uncertainty of 0.00005 g·cm−3. The densimeter was calibrated with the dried air. The indices of refraction (nD) of the Received: January 10, 2018 Accepted: May 11, 2018
A
DOI: 10.1021/acs.jced.8b00033 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Detailed Information of the Chemicals
a
chemicals
formula
CAS number
purity (mass faction)
purification method
analysis method
cyclohexanone ethanol n-propanol isopropanol
C6H10O C2H6O C3H8O C3H8O
108-94-1 64-17-5 71-23-8 67-63-0
0.995 0.995 0.995 0.995
none none none none
GCa GCa GCa GCa
suppliers Tianjin Tianjin Tianjin Tianjin
Fuyu Fine Chemical Co., Ltd. Fuyu Fine Chemical Co., Ltd. Kermel Chemical Reagent Co., Ltd. Kermel Chemical Reagent Co., Ltd.
GC = gas chromatography.
Table 2. Densities (ρ), Refractive Indices (nD) at T = 298.15 K, and Normal Boiling Temperature (Tb) of the Pure Components at p = 101.3 kPaa ρ (g·cm−3) chemicals
a
nD
exp.
lit.
cyclohexanone
0.9411
ethanol
0.7850
n-propanol
0.7995
isopropanol
0.7811
Tb (K)
exp. 9
lit. 9
1.4484
0.9412 0.941210 0.785211 0.785112 0.799313 0.799614 0.781316 0.780817
1.4485 1.448510 1.359511 1.359512 1.383313 1.383315 1.375016 1.375117
1.3593 1.3831 1.3750
exp.
lit.
428.6
428.8018
351.5
351.4418
370.4
370.3019
355.3
355.3919
Standard uncertainties u are u(ρ) = 0.0005 g cm−3, u(nD) = 0.0002, u(T) = 0.1 K, and u(P) = 0.1 kPa.
Table 3. Experimental VLE Data (T, x, y), Activity Coefficient (γi), Excess Gibbs Free Energies (GE), and Correlation Results for the System of Cyclohexanone (1) + Ethanol (2) at 101.3 kPaa NRTL
a
T (K)
x1
y1
351.5 352.9 354.9 357.7 361.1 364.9 369.1 373.0 379.5 384.2 392.5 401.1 412.0 418.6 423.9 428.6
0.0000 0.0754 0.1758 0.2965 0.4175 0.5119 0.5911 0.654 0.7378 0.7869 0.8539 0.9049 0.9523 0.9738 0.9888 1.0000
0.0000 0.0106 0.0232 0.0354 0.054 0.0749 0.0999 0.1247 0.1736 0.2148 0.3037 0.4152 0.6013 0.7379 0.8658 1.0000
γ1 1.6585 1.4304 1.1596 1.0966 1.0724 1.0625 1.0382 1.0191 1.0071 1.0023 0.9899 0.9893 0.9892 0.9892 1.0000
γ2 1.0000 1.0130 1.0351 1.0788 1.1229 1.1409 1.1450 1.1476 1.1500 1.1541 1.1551 1.1558 1.1587 1.1658 1.2169
−1
E
G , J mol 0.00 16.44 27.23 33.98 34.31 29.73 24.25 20.14 14.98 12.33 8.48 5.59 2.91 1.69 0.93 0.00
UNIQUAC
Wilson
ΔT (K)
Δy1
ΔT (K)
Δy1
ΔT (K)
Δy1
0.01 0.11 0.00 0.05 0.08 0.14 0.04 0.05 0.07 0.29 0.21 0.06 0.02 0.13 0.17 0.00
0.0000 0.0001 0.0013 0.0000 0.0014 0.0015 0.0004 0.0002 0.0000 0.0017 0.0014 0.0008 0.0025 0.0038 0.0048 0.0000
0.01 0.08 0.06 0.08 0.11 0.20 0.01 0.09 0.06 0.30 0.24 0.09 0.03 0.13 0.18 0.00
0.0000 0.0003 0.0012 0.0002 0.0008 0.0023 0.0014 0.0012 0.0007 0.0012 0.0013 0.0006 0.0023 0.0037 0.0049 0.0000
0.01 0.07 0.07 0.08 0.11 0.20 0.00 0.07 0.09 0.32 0.26 0.09 0.01 0.15 0.19 0.00
0.0000 0.0002 0.0014 0.0001 0.0008 0.0022 0.0013 0.0010 0.0005 0.0015 0.0016 0.0006 0.0027 0.0042 0.0052 0.0000
Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.1 kPa, and u(x) = u(y) = 0.0054.
differential manometer. An automatic control system was adopted to keep the fluctuation within 0.1 kPa. In each experiment, the condensed vapor phases and liquid were recirculated continuously to ensure full contact and achieve the equilibrium state rapidly. When the temperature of the system was kept constant at least 60 min, the system was considered at equilibrium state, and the equilibrium temperature was recorded. After that, the samples were withdrawn by syringe. The reliability of the apparatus and procedures was validated in the previous work.23−25 2.3. Analysis. All the samples were checked by GC (SP6890), which has a TCD and a capillary column (DB-624, 30 m × 0.53 m × 3 μm). The GC was validated by the samples with known compositions, and the samples were obtained with an electronic balance (AR1140), which has an uncertainty of 0.0001 g. The carrier gas was hydrogen with the purity of
chemicals were determined at 298.15 K using a 2AWJ Abbe refractometer. The measurement range was 1.3000 to 1.7000, and the value of the refractive index was obtained with the uncertainty of 0.0002.8 The boiling temperatures of the chemicals were determined by a mercury thermometer with the uncertainty of 0.1 K at 101.3 kPa. The density (ρ), index of refraction (nD) at T = 298.15 K, and boiling temperature (Tb) for all chemicals were determined at 101.3 kPa and compared with the reference values.9−19 The measured values are given in Table 2. 2.2. Apparatus and Procedures. An improved Rose still was applied for the VLE measurement. The detailed descriptions of the apparatus were provided in our previous work.20−22 A mercury thermometer was used to determine the experiment temperature, and the combined uncertainty was 0.1 K. The system pressure was maintained by a U-shaped B
DOI: 10.1021/acs.jced.8b00033 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 4. Experimental VLE Data (T, x, y), Activity Coefficient (γi), Excess Gibbs Free Energies (GE), and Correlation Results for the System of Cyclohexanone (1) + n-Propanol (2) at 101.3 kPaa NRTL
a
T (K)
x1
y1
370.4 371.1 371.9 374.1 375.7 380.9 384.4 388.1 392.1 399.7 405.1 411.4 415.4 420.3 423.9 428.6
0.0000 0.0445 0.0902 0.1868 0.2537 0.4283 0.5152 0.5944 0.6638 0.7744 0.8367 0.8931 0.9240 0.9555 0.9768 1.0000
0.0000 0.0100 0.0188 0.0392 0.0555 0.1106 0.1457 0.1875 0.2346 0.3457 0.4375 0.5605 0.6481 0.7649 0.8585 1.0000
γ1 1.3610 1.2123 1.1025 1.0730 1.0612 1.0382 1.0256 1.0008 0.9988 0.9975 0.9974 0.9963 0.9962 0.9960 1.0001
γ2 1.0000 1.0052 1.0115 1.0256 1.0372 1.0601 1.0640 1.0673 1.0690 1.0690 1.0693 1.0705 1.0705 1.0729 1.1010
−1
E
G , J mol 0.00 6.38 10.81 15.27 16.51 14.71 12.19 10.19 8.51 5.76 4.29 2.93 2.12 1.30 0.94 0.00
UNIQUAC
Wilson
ΔT (K)
Δy1
ΔT (K)
Δy1
ΔT (K)
Δy1
0.00 0.10 0.23 0.14 0.18 0.25 0.15 0.11 0.11 0.12 0.02 0.12 0.06 0.11 0.05 0.00
0.0000 0.0002 0.0006 0.0005 0.0005 0.0046 0.0041 0.0038 0.0030 0.0031 0.0004 0.0019 0.0001 0.0002 0.0062 0.0000
0.00 0.09 0.20 0.09 0.14 0.28 0.20 0.16 0.06 0.10 0.02 0.13 0.08 0.13 0.04 0.00
0.0000 0.0000 0.0006 0.0003 0.0007 0.0041 0.0033 0.0029 0.0020 0.0025 0.0001 0.0020 0.0003 0.0003 0.0057 0.0000
0.00 0.09 0.20 0.10 0.14 0.28 0.19 0.16 0.07 0.10 0.02 0.13 0.08 0.13 0.04 0.00
0.0000 0.0000 0.0006 0.0003 0.0007 0.0042 0.0034 0.0031 0.0022 0.0026 0.0002 0.0020 0.0003 0.0003 0.0058 0.0000
Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.1 kPa, and u(x) = u(y) = 0.0054.
Table 5. Experimental VLE Data (T, x, y), Activity Coefficient (γi), Excess Gibbs Free Energies (GE), and Correlation Results for the System of Cyclohexanone (1) + Isopropanol (2) at 101.3 kPaa NRTL
a
T (K)
x1
y1
γ1
355.3 358.0 360.8 364.0 367.8 371.9 375.0 381.1 387.8 394.0 401.1 407.5 413.7 416.3 423.0 428.6
0.0000 0.1253 0.2332 0.3458 0.4585 0.5515 0.6124 0.7052 0.7859 0.8409 0.8895 0.9243 0.9515 0.9615 0.9840 1.0000
0.0000 0.0187 0.0341 0.0530 0.0735 0.0998 0.1209 0.1714 0.2392 0.3119 0.4102 0.5150 0.6320 0.6867 0.8426 1.0000
1.4295 1.2573 1.1642 1.0563 1.0267 1.0015 0.9982 0.9974 0.9949 0.9943 0.9936 0.9928 0.9922 0.9916 1.0000
UNIQUAC
Wilson
γ2
GE, J mol−1
ΔT (K)
Δy1
ΔT (K)
Δy1
ΔT (K)
Δy1
1.0000 1.0032 1.0127 1.0301 1.0589 1.0729 1.0869 1.0963 1.1133 1.1166 1.1169 1.1176 1.1184 1.1189 1.1380
0.00 11.76 18.13 22.03 24.17 21.61 19.91 15.06 11.40 8.23 5.48 3.68 2.33 1.85 0.88 0.00
0.11 0.00 0.06 0.09 0.06 0.23 0.28 0.45 0.39 0.26 0.19 0.11 0.11 0.09 0.21 0.01
0.0000 0.0022 0.0020 0.0026 0.0012 0.0012 0.0028 0.0007 0.0002 0.0000 0.0002 0.0021 0.0071 0.0078 0.0128 0.0000
0.11 0.00 0.07 0.10 0.07 0.24 0.29 0.45 0.39 0.26 0.19 0.11 0.11 0.09 0.21 0.01
0.0000 0.0022 0.0021 0.0027 0.0010 0.0010 0.0027 0.0006 0.0003 0.0000 0.0003 0.0021 0.0071 0.0078 0.0127 0.0000
0.11 0.00 0.07 0.09 0.06 0.23 0.28 0.45 0.39 0.26 0.20 0.12 0.10 0.09 0.21 0.01
0.0000 0.0022 0.0021 0.0026 0.0011 0.0011 0.0028 0.0007 0.0002 0.0000 0.0002 0.0020 0.0070 0.0078 0.0128 0.0000
Standard uncertainties u are u(T) = 0.1 K, u(P) = 0.1 kPa, u(x) = u(y) = 0.0054.
99.99%. The flow rate was 20 mL·min−1. The column inlet pressure was 0.15 MPa. The GC operating temperatures are presented as follows: injector, 433.15 K, detector, 433.15 K, and oven, 403.15 K, respectively. All the samples were checked three times. The mean data were adopted as the analysis results.
separate the solvents from the filtrate by distillation. Also, the T−x experimental data for the systems at a pressure of 94.8 kPa reported by Prasad et al.6 are presented in Figures 1−3 and compared with the measured VLE data in this work. As seen from Figures 1−3, there are certain deviations between the measured VLE data and those reported by Prasad6 due to pressure difference. The relationship of VLE can be expressed as follows:26
3. RESULTS AND DISCUSSION 3.1. Experimental Data. The VLE experimental results for cyclohexanone + ethanol, cyclohexanone + n-propanol, and cyclohexanone + isopropanol were determined at 101.3 kPa. The results are presented in Tables 3−5 and are shown in Figures 1−6, respectively. Meanwhile, the x−y diagram for the binary mixtures is plotted in Figure 4. As shown in Figures 1−3, no intersection point can be observed between the dew point and bubble point curves, which means no azeotropic behavior existed in the three investigated systems. So, it is convenient to
⎛ V L(P − P s) ⎞ i ⎟ φî v Pyi = γixiPi sφi s exp⎜ i RT ⎝ ⎠
(1)
where T is the equilibrium temperature; γi represents the activity coefficient in liquid phase; φi denotes the fugacity coefficient in vapor phase; φis denotes the fugacity coefficient in saturated vapor phase; xi and yi are the liquid and vapor mole fractions; ViL is the liquid molar volume; R is universal gas C
DOI: 10.1021/acs.jced.8b00033 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 1. VLE phase diagram for cyclohexanone (1) + ethanol (2) at 101.3 kPa: ●, experimental liquid phase, and ○, experimental vapor phase; ―, correlated by the NRTL model; ---, correlated by the UNIQUAC model; -·-, correlated by the Wilson model; ···, predicted by the UNIFAC model; -·-·-·-, predicted by the COSMO-SAC model. □, literature data (94.8 kPa) by Prasad et al.6
Figure 3. VLE phase diagram for cyclohexanone (1) + isopropanol (2) at 101.3 kPa: ●, experimental liquid phase, and ○, experimental vapor phase; ―, correlated by the NRTL model; ---, correlated by the UNIQUAC model; -·-, correlated by the Wilson model; ···, predicted by the UNIFAC model; -·-·-·-, predicted by the COSMO-SAC model. □, literature data (94.8 kPa) by Prasad et al.6
Figure 2. VLE phase diagram for cyclohexanone (1) + n-propanol (2) at 101.3 kPa: ●, experimental liquid phase, and ○, experimental vapor phase; ―, correlated by the NRTL model; ---, correlated by the UNIQUAC model; -·-, correlated by the Wilson model; ···, predicted by the UNIFAC model; -·-·-·-, predicted by the COSMO-SAC model. □, literature data (94.8 kPa) by Prasad et al.6
Figure 4. x−y diagram for the binary systems at 101.3 kPa: ■-■, cyclohexanone (1) + ethanol (2); ●-●, cyclohexanone (1) + npropanol (2); ▲-▲, cyclohexanone (1) + isopropanol (2).
and the Poynting factor are close to 1,29,30 and eq 1 is simplified as follows: Pyi = γixiPi s
constant; P stands for the total pressure; Psi stands for the saturated pressure at equilibrium temperature, and the extended Antoine equation is used to calculate Psi , which is presented as follows:27
(3)
(2)
The values of the activity coefficients for the three systems calculated by eq 3 are listed in Tables 3−5. In addition, the relative volatilities (α) of the three systems cyclohexanone + ethanol, cyclohexanone + n-propanol, and cyclohexanone + isopropanol were obtained as follows: y xB αAB = A xAyB (4)
The constants of the extended Antoine equation for all components were obtained from the physical properties databank, Aspen plus V7.2,28 and are presented in Table 6. In this work, the vapor phase is ideal, since the pressure of the VLE equilibrium experiments was 101.3 kPa. Therefore, φ̂ vi , φsi ,
where the subscript A presents the volatile components of ethanol, n-propanol, and isopropanol in the investigated systems, and the subscript B presents the nonvolatile component of cyclohexanone. The relationships between relative volatility and mole fractions of ethanol, n-propanol,
ln(pi s , kPa) = C1i + + C6iT C7i
C 2i + C4iT + C5i ln T T + C 3i
C 8i ≤ T ≤ C 9i
D
DOI: 10.1021/acs.jced.8b00033 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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and isopropanol to cyclohexanone, which indicate that ethanol is a suitable solvent for the recovery of the catalyst aluminum oxide. 3.2. Consistency Test. The consistency of the experiment data was checked by the Herington test, van Ness test and pure component consistency test. In the Herington test,31,32 the value of |D − J| should be less than 10. D and J are expressed as follows: 1
D = 100 ×
J = 150 ×
∫0 ln(γ1/γ2) dx1 1
∫0 |ln(γ1/γ2)| dx1
(5)
Tmax − Tmin Tmin
(6)
where Tmax and Tmin are the highest and lowest boiling temperatures, respectively. The values of |D − J| for the three mixtures are listed in Table 7, and all the values of |D − J| are less than 10. Therefore, the experimental VLE data for the three investigated systems are thermodynamic consistency.
Figure 5. α−xA diagram for the binary systems at 101.3 kPa: ■-■, ethanol (A) + cyclohexanone (B); ●-●, n-propanol (A) + cyclohexanone (B); ▲-▲, isopropanol (A) + cyclohexanone (B).
Table 7. Thermodynamic Consistency Tests of the VLE Data for the Three Systems
system cyclohexanone + ethanol cyclohexanone + n-propanol cyclohexanone + isopropanol
|D − J| < 10
ΔP < 1 Δy < 1
n-propanol
isopropanol
78.5162 −7944.40 0.0 0.0 −9.2862 4.9957 2.00 242.00 653.00
66.3962 −7122.30 0.0 0.0 −7.1424 2.8853 2.00 159.05 591.75
77.7562 −8307.20 0.0 0.0 −8.5767 7.5091 × 10−12 6.00 146.95 536.80
103.8122 −9040.00 0.0 0.0 −12.6760 5.5380 2.00 185.26 616.20
ΔP20 < 1
0.33
0.00004
0.00002
8.19
0.02
0.17
0.00003
0.00002
4.41
0.05
0.25
0.00030
0.00002
N
N
ethanol
ΔP10 < 1
0.04
N
Δy =
cyclohexanone
pure component consistency test
6.89
1 1 ∑ ΔPi = ∑ 100|Pi cal − Pi exp| N i=1 N i=1
ΔP =
Table 6. Extended Antoine Constants for the Pure Componenta
a
van Ness test
The van Ness test33,34is applicable to check the reliability of each experiment point. In this test, ΔP and Δy should be less than 1. ΔP and Δy are defined as follows::
Figure 6. Plot of the calculated values of excess Gibbs free energy at 101.3 kPa by the NRTL model against the composition of cyclohexanone: ―, cyclohexanone (1) + ethanol (2); ---, cyclohexanone (1) + n-propanol (2); -·-, cyclohexanone (1) + isopropanol (2).
C1i C2i C3i C4i C5i C6i (×10−6) C7i C8i (K) C9i (K)
Herington test
(7)
N
1 1 ∑ Δy = ∑ 100|yi cal − yi exp | N i=1 i N i=1
(8)
where N stands for the number of the VLE data; Piexp and yiexp represent the experimental pressures and mole fraction in vapor phase; Pical and yical represent the calculated values by the NRTL activity coefficient model. The van Ness test results are listed in Table 7. As shown in Table 7, the measured VLE data are thermodynamically consistent. The pure component consistency test35,36 can validate the “end-points” thermodynamic consistency of the measured data. This test requires ΔP10 and ΔP20 be less than 1, which are defined as
The constants were taken from Aspen property databank.
and isopropanol for the three binary systems are shown in Figure 5. As shown in Figure 5, the relative volatility values of ethanol to cyclohexanone are greater than those of n-propanol
ΔP10 = E
Pbubble(x1 → 1) − P10 P10
(9) DOI: 10.1021/acs.jced.8b00033 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 8. Binary Interaction Parameters, Root-Mean-Square Deviation (RMSD), and Average Absolute Deviations (AAD) for the NRTL, UNIQUAC, and Wilson Activity Coefficient Models RMSDs
binary interaction parameters aij
model
aji
NRTL UNIQUAC Wilson
−0.104 0.399 0.562
−1.622 −0.012 0.716
NRTL UNIQUAC Wilson
1.366 0.023 1.863
−3.603 0.545 −0.285
NRTL UNIQUAC Wilson
−0.317 −0.312 0.891
−0.962 0.682 0.401
bij (K)
bji (K)
p2
0
(10)
P10
where Pbubble stands for the bubble point pressure and and P20 stand for saturation pressures. The values of ΔP10 and ΔP20 are presented in Table 7. As shown in Table 7, all the results of ΔP10 and ΔP20 are less than 1, which indicate that the three investigated systems passed this test. 3.3. Data Correlation. The experimental data of the three mixtures were fitted by the NRTL,37 UNIQUAC,38 and Wilson39 models, which was carried out using Aspen chemical process software. For the NRTL model, the nonrandomness parameter (αij) was fixed at 0.3, as recommended by Renon and Prausnitz.37 The interaction parameters for the thermodynamic models were obtained based on the maximum likelihood principle.40 The objective function is presented as follows:
T (K)
y1
0.16 0.15 0.15
0.0045 0.0044 0.0044
0.13 0.11 0.12
0.0033 0.0032 0.0031
0.08 0.08 0.08
0.0024 0.0019 0.0020
0.07 0.06 0.06
0.0017 0.0012 0.0013
0.19 0.19 0.19
0.0036 0.0037 0.0036
0.16 0.14 0.14
0.0025 0.0025 0.0025
(15)
N
AAD =
∑ |Xi cal − Xi exp|/N
(16)
i=1
where X stands for temperature and vapor phase composition. The correlated parameters and the values of RMSD and AAD for the NRTL, UNIQUAC, and Wilson models for all mixtures are presented in Table 8. As seen from Table 8, the RMSD (y1) and RMSD (T) calculated by the three models are less than 0.0045 and 0.19 K. And the AAD (y1) and AAD (T) calculated are less than 0.0033 and 0.16 K. From the calculation results, the three activity coefficient models are suitable to fit the VLE data for the investigated mixtures. 3.4. Data Prediction. For comparison, the UNIFAC41 and COSMO-SAC models42,43 were adopted to produce the VLE data for the three systems. The category and group number for each component are presented in Table 9, and the values of group parameters are given in Table 10. The acquired interaction parameters were obtained from the literature44 and are presented in Table 11. The COSMO-SAC model42,43 was used extensively to predict the phase equilibrium data,45,46 where the description of this model is presented in the Supporting Information.
⎡⎛ exp ⎛ pexp − pcal ⎞2 cal ⎞2 ⎢⎜ Ti − Ti ⎟ i i ⎟ OF = ∑ ⎢⎜ ⎟ + ⎜⎜ ⎟ σ σ ⎠ T p ⎝ ⎠ i = 1 ⎣⎝
(11)
The objective function is to minimize the differences of experimental (exp) and calculated (cal) values of T, P, xi, and yi. σ denotes standard deviation, and N denotes the experimental data number. The interaction parameters of the three models are expressed as NRTL:
τij = aij + bij /T
y1
⎛N ⎞0.5 cal exp ⎜ RMSD = ⎜∑ (Xi − Xi )/N ⎟⎟ ⎝ i=1 ⎠
N
2 ⎛ x exp − x cal ⎞2 ⎛ y exp − y cal ⎞ ⎤ i i i i ⎟⎥ ⎟⎟ + ⎜⎜ + ⎜⎜ ⎟⎥ σ σ ⎝ ⎠ x y ⎝ ⎠⎦
T (K)
propanol, and cyclohexanone + isopropanol are presented in Tables 3−5. Also, the results are illustrated graphically in Figures 1−3, respectively. For comparison with the T−x data for the systems at pressure of 94.8 kPa measured by Prasad et al.,6 the NRTL model with the regressed interaction parameters at 101.3 kPa was used to calculate the VLE data for the three mixtures at 94.8 kPa. The results are shown in Figures S1−S3 in the Supporting Information. The deviations RMSD and AAD of temperature and vapor phase composition for the models were presented as follows:
Pbubble(x1 → 0) − P2 0
ΔP2 0 =
α
cyclohexanone (1) + ethanol (2) −254.146 1175.710 0.3 −21.373 −210.319 −680.576 −76.148 cyclohexanone (1) + n-propanol (2) −875.153 1965.595 0.3 221.820 −553.295 −1205.308 358.684 cyclohexanone (1) + isopropanol (2) 117.857 454.662 0.3 0.797 −177.442 −410.846 −167.055
AADs
(12)
UNIQUAC: τij = exp(aij + bij /T )
Table 9. Group Category and Number for Each Component
(13)
component
Wilson:
ln Aij = aij + bij /T
cyclohexanone ethanol n-propanol isopropanol
(14)
The correlation results by the three thermodynamics models for the systems of cyclohexanone + ethanol, cyclohexanone + nF
group category and number −CH2, 4 −CH3,1 −CH3, 1 −CH3, 2
−CH2CO, 1 −CH2,1 −CH2, 2 −CH, 1
−OH,1 −OH, 1 −OH, 1
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excess Gibbs free energy. Based on the calculated GE values, the system of cyclohexanone + ethanol showed higher nonideality than the other two systems. The determined VLE data and the regressed parameters of the thermodynamic models for the mixtures cyclohexanone + (ethanol/n-propanol/isopropanol) could be helpful for the separation of cyclohexanone and alcohols by distillation.
Table 10. UNIFAC Group Volume (Rk) and Surface Area (Qk)a main group −CH2
−CH2CO −OH a
sub group
Rk
Qk
−CH3 −CH2 −CH −CH2CO −OH
0.9011 0.6744 0.4469 1.4457 1.0000
0.8480 0.5400 0.2280 1.1800 1.2000
■
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.8b00033. Description of the COSMO-SAC model and validation of the VLE data with Prasad’s work (PDF)
Table 11. UNIFAC Interaction Parametersa
a
n
m
αnm (K)
αmn (K)
−CH2CO −CH2CO −OH
−CH2 −OH −CH2
26.76 164.5 156.4
476.4 84.00 986.5
■
The interaction parameters were taken from ref 44.
G = RT (x1 ln γ1 + x 2 ln γ2)
AUTHOR INFORMATION
Corresponding Author
*(J.G.) E-mail:
[email protected]. Telephone: +86 532 86057798.
The predicted results by the two models are plotted in Figures 1−3, which agreed with the experimental data. The values of RMSD (T) and RMSD (y1) calculated by the UNIFAC model for the system of cyclohexanone + ethanol are 0.16 K and 0.0055, for the system of cyclohexanone + npropanol are 0.15 K and 0.0039, and for the system of cyclohexanone + isopropanol are 0.22 K and 0.0054, respectively. The values of RMSD (y1) calculated by the COSMO-SAC model for the systems of cyclohexanone + ethanol, cyclohexanone + n-propanol, and cyclohexanone + isopropanol are 0.0042, 0.0039, and 0.0043, respectively. Therefore, the UNIFAC and COSMO-SAC model could predict well for the three investigated systems. To evaluate the nonideality of the three systems, the excess Gibbs free energy (GE) was obtained as follows: E
ASSOCIATED CONTENT
S Supporting Information *
The group parameters were taken from Aspen property databank.
ORCID
Dongmei Xu: 0000-0002-5770-0513 Jun Gao: 0000-0003-1145-9565 Yinglong Wang: 0000-0002-3043-0891 Author Contributions †
Kai Zhang and Dongmei Xu contributed equally.
Funding
The financial support by the National Natural Science Foundation of China (21776145) is gratefully acknowledged. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS The authors thank Dr. Yixin Ma and Mr. Xiaolong Ma (Shandong University of Science and Technology) for their help in supporting the experiment.
(17)
where γi was obtained by the NRTL model. The values of GE for the investigated mixtures are listed in Tables 3−5 and are shown in Figure 6, respectively. As shown in Figure 6, the GE values of each system are greater than zero in the whole composition range and are in an order of cyclohexanone (1) + ethanol (2) > cyclohexanone (1) + isopropanol (2) > cyclohexanone (1) + n-propanol (2), for values of the activity coefficients of ethanol are larger than that of propanol. So the system cyclohexanone (1) + ethanol (2) shows higher nonideality than the other two systems.
■
REFERENCES
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4. CONCLUSIONS In this work, to separate the mixtures of cyclohexanone with alcohols by distillation, the isobaric VLE data for the mixtures cyclohexanone + (ethanol/n-propanol/isopropanol) were determined at a pressure of 101.3 kPa. The measured VLE data for the mixtures were validated by thermodynamic consistency tests. Meanwhile, no azeotropic behavior exists in the investigated mixtures. The measured values were fitted by three activity coefficients models. The values of RMSD (y1) and RMSD (T) are less than 0.0045 and 0.19 K. The parameters of the three thermodynamics models were also optimized. In addition, the UNIFAC and the COSMO-SAC models gave good predictions for the three systems. The values of RMSD (y1) predicted by the UNIFAC and COSMO-SAC models are less than 0.0055 and 0.0043, respectively. The nonideality of the three systems was evaluated by the calculated values of G
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