Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Isobaric Vapor−Liquid Equilibrium for Two Binary Systems of n‑Heptane + sec-Butyl Acetate and Methylcyclohexane + sec-Butyl Acetate under Atmosphere Lixin Liu,† Dianliang Fu,‡ Yinhai Sun,‡ Shoutao Ma,‡ and Lanyi Sun*,‡ †
College of Mechanical Engineering, Qingdao University of Technology, Qingdao, Shandong 266520, China State Key Laboratory of Heavy Oil Processing, College of Chemical Engineering, China University of Petroleum (East China), Qingdao, Shandong 266580, China
‡
ABSTRACT: Data for two systems of isobaric vapor−liquid equilibrium (VLE), n-heptane + sec-butyl acetate (SBAC) and methylcyclohexane + SBAC, were determined under atmosphere with an Ellis vapor−liquid equilibrium still. The Herington method and Wisniak test were employed to determine the thermodynamic consistency of the two systems. The experimental results of n-heptane + SBAC and methylcyclohexane + SBAC were correlated by three activity coefficient models, which are the nonrandom two-liquid, universal quasichemical, and Wilson, and the correlation results fit well with experimental data. The binary interaction parameters of these models were obtained, and the results showed that these models can give good predictions. The VLE data provide theoretical basis and data support for the further study on separation of n-heptane + SBAC and methylcyclohexane + SBAC.
1. INTRODUCTION n-Heptane is an important compound of real fuels due to its chemical kinetic properties.1 Methylcyclohexane can be used as an important organic solvent and extraction solvent with good performance.2 The difference of the boiling points between n-heptane and methylcyclohexane is 3.1 K, which cannot be separated easily with ordinary distillation method,3 so the azeotropic distillation must be considered to separate and purify this system. To explore whether sec-butyl acetate (SBAC) can form azeotrope with n-heptane or with methylcyclohexane, the isobaric vapor−liquid equilibrium (VLE) data of n-heptane + SBAC and methylcyclohexane + SBAC systems are determined. So far, no VLE data of n-heptane (1) + SBAC (2) and methylcyclohexane (1) + SBAC (2) under atmosphere have been found in NIST database. The experimental data for n-heptane (1) + SBAC (2) and methylcyclohexane (1) + SBAC (2) under atmosphere were determined with an Ellis vapor−liquid equilibrium still. The Herington4 method and Wisniak5 test were used to validate the consistency of VLE data. Experimental data for two binary mixtures were correlated using nonrandom two-liquid (NRTL),6 universal quasichemical (UNIQUAC),7 and Wilson8 activity coefficient models.
was detected. To keep them dry, all chemicals were stored in 4 Å molecular sieves. 2.2. Sample Analysis. GC was applied to analyze the liquid phase composition and vapor condensate. FID was used together with a PEG-20 M chromatographic column (30 m × 0.32 mm × 0.33 μm). High purity hydrogen was employed as carrier gas, and its flow rate was set to 20 mL/min. The temperature for the vaporizer was 405.15 K and for the detector was 405.15 K. The column temperature program was: kept the temperature at 374.084 K; after 4 min, increase to 405.15 K with 10 K per minute; then remain at 405.15 K for 2.5 min. Each sample test was performed at least two times. The test error of the two samples was within 0.005. The standard uncertainty in mole fraction of compositions was 0.005 in the two repeated tests. 2.3. Apparatus and Procedure. An Ellis equilibrium still9 was used to measure the experimental data in this work. The previous literature10 has described the still in detail, and the apparatus used in the experiment was reliable. The apparatus contained vapor-phase and liquid-phase sampling port, heating bar, equilibrium chamber, and condenser. The vapor phase and liquid phase were continuously circulating until the temperature kept unchanged for 60 min, and the equilibrium was established. Calibrated thermometer graduated in 0.01 K was used to measure the temperatures of the systems, with an uncertainty of
2. EXPERIMENTAL SECTION 2.1. Chemicals. n-Heptane, methylcyclohexane, and SBAC were used, and relevant detailed information on the three chemicals is listed in Table 1. Gas chromatography (GC, GC9790II, Zhejiang Fu Li Analytical Instrument Co., Ltd.) was used to check the purity of chemicals, and no perceptible impurity peak © XXXX American Chemical Society
Received: November 15, 2017 Accepted: April 18, 2018
A
DOI: 10.1021/acs.jced.7b00999 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
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Table 1. Description of Materials under Atmospherea
a
chemical name
CAS no.
source
initial mole fraction purity
purification method
final mole fraction purity
analysis method
n-heptane SBAC methylcyclohexane
142-82-5 105-46-4 108-87-2
McLean reagent McLean reagent McLean reagent
0.995 0.99 0.995
dehydration distillation dehydration distillation dehydration distillation
0.9991 0.9968 0.9979
GCb GCb GCb
Standard uncertainties u(P) = 0.3 kPa. bGas chromatography.
Table 2. Parameters in Extended Antoine Equation for the Chemicals component
C1
C2
C3
C4
C5
C6
C7
T/K range
n-heptane SBAC methylcyclohexane
80.921 45.693 85.776
−6996.4 −6097.9 −7080.8
0 0 0
0 0 0
−9.8802 −4.2398 −10.695
7.21 × 10−6 2.15 × 10−18 8.14 × 10−6
2 6 2
182.57−540.2 174.15−561 146.58−572.1
Table 3. Isobaric VLE Data for the System n-Heptane (1) + SBAC (2), Activity Coefficient γ, and Relative Volatilities α at 101.3 kPaa
0.05 K. The testo-511 digital vacuum gauge was used to measure the pressure, which had an uncertainty of 0.3 kPa.
3. RESULTS AND DISCUSSION 3.1. VLE Model. Eq 1 is the vapor−liquid equilibrium relationship:11 s s yi φivP = xiγφ P exp(vil(P − Pis)/RT ) i i i
(1)
where yi and xi represent the mole fraction of n-heptane or methylcyclohexane in vapor phase and liquid phase, respectively; φvi and φsi are the fugacity coefficients of n-heptane or methylcyclohexane in the vapor mixture and in the saturate state, respectively; P, R, and T represent the total pressure, the universal gas constant, and the temperature, respectively. vli is the liquid molar volume of pure n-heptane or methylcyclohexane. The saturated vapor pressure psi is calculated using the extended Antoine equation. In eq 2, the coefficients C1−C7 and T range were obtained from Aspen Plus, as shown in Table 2. The Poynting factor exp [Vli (p − psi )/RT] was basically equal to unity under atmosphere, so eq 1 can be simplified as eq 3. ln(pis ) = C1, i +
C2, i T + C3, i
+ C4, iT + C5, i ln T + C6, iT C7,i (2)
yp = i
xiγipis
y1
γ1
γ2
α12
371.58 371.64 372.21 372.94 373.44 374.18 374.9 375.71 376.61 377.5 378.42 379.34 380.01 380.73 381.46 382.02 382.59 383.08 383.98 384.59 385.15
1.0000 0.9750 0.8740 0.7630 0.6960 0.6180 0.5420 0.4686 0.3840 0.3277 0.2739 0.2237 0.1884 0.1494 0.1051 0.0776 0.0561 0.0426 0.0181 0.0071 0.0000
1.0000 0.9796 0.8961 0.8006 0.7486 0.6903 0.6303 0.5753 0.4936 0.4355 0.3807 0.3268 0.2904 0.2434 0.1891 0.1501 0.1152 0.0892 0.0407 0.0165 0.0000
1.00178 1.00525 1.00704 1.01735 1.03408 1.05449 1.08772 1.10991 1.11892 1.14019 1.16761 1.20905 1.25273 1.35600 1.43394 1.50065 1.51003 1.57551 1.60029
1.23949 1.23005 1.22512 1.18466 1.13383 1.10286 1.06382 1.06333 1.05576 1.04176 1.02911 1.01611 1.01081 1.00672 1.00627 1.00580 1.00556 1.00484 1.00001
1.23132 1.24265 1.24680 1.30038 1.37759 1.44074 1.53654 1.56392 1.58327 1.63012 1.68476 1.76304 1.83205 1.98645 2.09779 2.19239 2.20319 2.29381 2.33663
Standard uncertainties u are u(T) = 0.05 K, u(P) = 0.3 kPa, and u(x1) = u(y1) = 0.005.
to test consistency of isobaric VLE data. The Herington method was adopted to examine the VLE data by area test. The Wisniak test was used to examine the VLE data by point-topoint test. The Herington method is expressed as follows: 1
D=
∫0 ln(γ1/γ2)dx1 1
× 100
∫0 |ln(γ1/γ2)|dx1
y1 /x1 (1 − y1)/(1 − x1)
x1
a
(3)
3.2. VLE Data. The measured isobaric VLE data (temperature T, liquid phase mole fraction x, vapor phase mole fraction y), the calculated activity coefficients, and the relative volatilities for n-heptane (1) + SBAC (2) and methylcyclohexane (1) + SBAC (2) under atmosphere are listed in Tables 3 and 4, respectively. The relative volatility12,13 α12 is calculated by the liquid mole fraction x1 and the vapor mole fraction y1, which are shown in eq 4. α12 =
T/K
(4)
J = 150 ×
The experimental relative volatilities of n-heptane (1) + SBAC (2) binary system and the experimental relative volatilities of methylcyclohexane (1) + SBAC (2) binary system are compared with results calculated using model parameters, plotted in Figures 1 and 2, respectively. The maximum model deviation is 5% for both binary systems, which demonstrates that the measured VLE data are in agreement with calculated results. 3.3. Thermodynamic Consistency Tests of Binary Systems. The Herington method and Wisniak test were employed
Tmax − Tmin Tmin
(5)
(6)
The consistency criteria of the Herington method is that the difference between D and J is no more than 10. Tmax is the maximum boiling temperature, and Tmin is the minimum boiling temperature in the system. The results of the Herington test for n-heptane (1) + SBAC (2) and methylcyclohexane (1) + SBAC (2) under atmosphere are −2.562 and 9.083 and are shown in Table 5. The plots of ln(γ1/γ2) to x of the two systems are shown in Figures 3 and 4, also indicating the isobaric VLE data pass the area test. B
DOI: 10.1021/acs.jced.7b00999 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 4. Isobaric VLE Data for the System Methylcyclohexane (1) + SBAC (2), Activity Coefficient γ, and Relative Volatilities α at 101.3 kPaa T/K
x1
y1
γ1
γ2
α12
374.08 374.24 374.54 374.57 374.65 374.86 375.08 375.41 375.78 376.33 376.89 377.51 378.07 378.64 379.37 379.97 380.62 381.55 385.15
1.0000 0.8832 0.7692 0.7095 0.6738 0.6390 0.5864 0.5401 0.5120 0.4731 0.4426 0.3969 0.3588 0.3320 0.2928 0.2613 0.2193 0.1658 0.0000
1.0000 0.8923 0.7903 0.7400 0.7107 0.6805 0.6411 0.6034 0.5830 0.5510 0.5255 0.4873 0.4557 0.4294 0.3885 0.3541 0.3084 0.2457 0.0000
0.99962 1.00804 1.02260 1.03174 1.03574 1.05667 1.06997 1.07938 1.08735 1.09142 1.10963 1.13007 1.13298 1.13945 1.14518 1.16774 1.20044
1.28751 1.25610 1.23597 1.22175 1.21067 1.17907 1.15922 1.13504 1.11220 1.09117 1.06880 1.04844 1.03610 1.02526 1.01758 1.01014 1.00186
1.09502 1.13042 1.16529 1.18899 1.20346 1.25953 1.29541 1.33258 1.36682 1.39509 1.44436 1.49601 1.51414 1.53429 1.54984 1.58776 1.63951
Figure 2. Relative volatilities of methylcyclohexane (1) + SBAC (2) under atmosphere. ■, experimental data; -, NRTL, UNIQUAC, and Wilson model; ---, ±5% deviations from the calculated relative volatilities.
Table 5. Results of Thermodynamic Consistency Tests
a
Standard uncertainties u are u(T) = 0.05 K, u(P) = 0.3 kPa, and u(x1) = u(y1) = 0.005.
E = 100
1
1
∫0 Lk dx1 − ∫0 Wk dx1 ∫0 Lk dx1 + ∫0 Wk dx1
Lk =
Wk =
(7)
∑ TioxiΔsio ∑ xiΔsio − T RT ⎛ ⎜∑ xi ln γi − ∑ xiΔsio ⎝
(8)
∑ xi ln
yi ⎞ ⎟ xi ⎠
Wisniak test
results
n-heptane (1) + SBAC (2) methylcyclohexane (1) + SBAC (2)
−2.562 9.083
−0.703 −4.481
passed passed
that the coefficient E is smaller than 3. The values of E for the two systems are −0.703 and −4.481, also shown in Table 5, indicating the reliable quality of the obtained data. 3.4. Data Regression. All the VLE data of n-heptane (1) + SBAC (2) and methylcyclohexane (1) + SBAC (2) under atmosphere were correlated using NRTL,6 UNIQUAC,7 and Wilson8 activity coefficient models. Aspen Plus was employed to calculate the binary interaction parameters of the models in the regression calculation.14 Eq 10 is the objective function in the regression calculation.
The Wisniak method is defined in eqs 7−9. 1
Herington test
Figure 3. Diagram of ln (γ1/γ2) to x1 for n-heptane (1) + SBAC (2) system.
Figure 1. Relative volatilities of n-heptane (1) + SBAC (2) under atmosphere. ■, experimental data; -, NRTL, UNIQUAC, and Wilson model; ---, ±5% deviations from the calculated relative volatilities.
1
system
⎡⎛ exp 2 ⎛ pexp − pest ⎞2 Ti − Tiest ⎞ i ⎟ ⎢ Q=∑ ⎜ ⎟ + ⎜⎜ i ⎟ ⎢⎝ σ σ ⎠ ⎝ ⎠ T p i=1 ⎣ N
(9)
2 ⎛ xiexp − xiest ⎞2 ⎛ yiexp − yiest ⎞ ⎤ ⎥ ⎜ ⎟ +⎜ ⎟ +⎜ ⎟⎥ σ σ ⎝ ⎠ ⎝ ⎠⎦ x y
Toi
where is the boiling point of component i, k represents each experimental point, and Δsoi represents the molar entropy of vaporization of component i. The criteria of the Wisniak test is C
(10)
DOI: 10.1021/acs.jced.7b00999 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 5. T−x−y diagram for the system of n-heptane (1) + SBAC (2) under atmosphere. ■, experimental x1; △, experimental y1; ---, calculated x1 with NRTL, UNIQUAC, and Wilson model; -, calculated y1 with NRTL, UNIQUAC, and Wilson model.
Figure 4. Diagram of ln (γ1/γ2) to x1 for methylcyclohexane (1) + SBAC (2) system.
where σ represents the standard deviation of the indicated data; T, xi, and yi represent the temperature of equilibrium, the liquid mole fraction of n-heptane or methylcyclohexane, and vapor mole fraction of n-heptane or methylcyclohexane, respectively. N represents the number of experimental points, superscripts exp and est are the abbreviations of experiment and estimate, respectively, and Q represents the objective function in data regression. The correlation parameters for the three models were obtained, and RMSD of temperature and vapor-phase mole fraction were calculated, which are all shown in Table 6. It can be seen that RMSD of temperature is less than 0.27, and RMSD of vapor-phase mole fraction is less than 0.008. The correlated results agree well with measured isobaric VLE data for the three activity coefficient models, and Wilson is the best fitted model for the system of n-heptane (1) + SBAC (2), while NRTL is the best fitted model for the system methylcyclohexane (1) + SBAC (2) under atmosphere with reasonable deviations. The T−x−y diagrams for n-heptane (1) + SBAC (2) and methylcyclohexane (1) + SBAC (2) together with their correlated curves with NRTL,6 UNIQUAC,7 and Wilson8 models are shown in Figures 5 and 6, respectively.
Figure 6. T−x−y diagram for the system of methylcyclohexane (1) + SBAC (2) under atmosphere. ■, experimental x1; △, experimental y1; ---, calculated x1 with NRTL, UNIQUAC, and Wilson model; -, calculated y1 with NRTL, UNIQUAC, and Wilson model.
data can pass the test. NRTL,6 UNIQUAC,7 and Wilson8 models were employed to correlate the experimental VLE data. The binary interaction parameters of these models were obtained, and the calculated results showed good agreement with the experimental data. The experiments show that neither of the two systems forms an azeotrope, but the VLE data and the regressed binary interaction parameters for n-heptane (1) + SBAC (2) and
4. CONCLUSION New isobaric VLE data for n-heptane (1) + SBAC (2) and methylcyclohexane (1) + SBAC (2) were measured under atmosphere with an Ellis vapor−liquid equilibrium still. Thermodynamic consistency of experimental data was validated by the Herington method and Wisniak test, and the results showed that the VLE
Table 6. Binary Interaction Parameters and RMSD of the Binary Systems correlation parametersa system n-heptane (1) + SBAC (2)
methylcyclohexane (1) + SBAC (2)
models f
NRTL UNIQUAC Wilson NRTL UNIQUAC Wilson
aijb
ajic
bij
−16.0314 5.2215 −16.0554 4.5840 −3.3490 15.8936
27.7865 −8.3999 8.4520 −20.9058 9.7067 −0.4610
5794.76 −1814.23 5708.57 −1861.57 1423.52 −6224.61
RMSD bji
σTd
σy1e
−10000 2935.41 −3044.51 8191.29 −3890.27 237.53
0.2613 0.2366 0.2018 0.1666 0.1691 0.1690
0.0065 0.0071 0.0064 0.0023 0.0024 0.0024
a
a and b are the parameters of the NRTL,6 UNIQUAC,7 or Wilson8 model. bSubscripts ij represents the pair interaction. cSubscripts ji represents the 15 exp 2 est exp 2 1/2 e 1/2 f pair interaction. dσT = (∑ (Test i − Ti ) /n) . σy1 = (∑ (y1,i − y1,i ) /n) . The value of αij was fixed at 0.3 according to the literature. D
DOI: 10.1021/acs.jced.7b00999 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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methylcyclohexane (1) + SBAC (2) are of great significance and will be an extension of the VLE database.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Lanyi Sun: 0000-0002-3158-6388 Funding
This work was supported by the National Natural Science Foundation of China (Grants 21676299 and 21476261) and the Fundamental Research Funds for the Central Universities (Grant 17CX06025). Notes
The authors declare no competing financial interest.
■
REFERENCES
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DOI: 10.1021/acs.jced.7b00999 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
