Isobaric VaporâLiquid Equilibrium for Three Binary Systems of

Article pubs.acs.org/jced

Isobaric Vapor−Liquid Equilibrium for Three Binary Systems of Acetaldehyde + Ethanol, Ethyl Acetate, 1‑Butanol at 101.3 kPa Huanhuan Sun, Cheng Liu, Zhongfeng Geng,* Yang Lu, and Yixuan Chen Key Laboratory for Green Chemical Technology of Ministry of Education, Research and Development Center of Petrochemical Technology, Tianjin University, Tianjin 300072, PR China Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300072, PR China ABSTRACT: In this article, isobaric vapor−liquid equilibrium (VLE) data for three binary systems of acetaldehyde + ethanol, acetaldehyde + ethyl acetate, and acetaldehyde +1-butanol were determined using a modified Rose−Williams equilibrium still at 101.3 kPa. The experimental data were confirmed by the area method of Herington and point-to-point method of Van Ness. Activity coefficient models, Wilson, NRTL, and UNIQUAC were employed to correlate the experimental VLE values. Both models showed a good agreement and the binary interaction parameters were estimated.

1. INTRODUCTION 1,3-Butadiene (BD) is one of the most important basic organic materials in the chemical industry. It is a high-value added chemical intermediate which is mainly used for synthetic styrene butadiene rubber (SBR), acrylonitrile butadiene styrene (ABS), adiponitrile, nylon, and so on for a very wide range of uses.1 With the growing demand of 1,3-butadiene in domestic and overseas markets,2 the production process of 1,3-butadiene is getting more and more significant attention. Currently, there are two techniques widely used for the production of 1,3-butadiene. One is dehydrogenation of butene or butane.3 The other is extraction from the unsaturated hydrocarbon mixtures of ethylene cracking.4 But, considering the serious environmental problem associated with the use of petroleum fuels, an alternative technology for the innovation of producing 1,3-butadiene is especially crucial to develop.5,6 Along with the development of bioethanol technology, most of studies have indicated that using ethanol as the renewable and ecofriendly fuels to produce 1,3-butadiene is a more promising and potential method.7−10 And also, lots of great breakthroughs and progress have been gained from 1920s to this day.11−16 In the process of making 1,3-butadiene from ethanol, ethanol is first oxidized to acetaldehyde and then acetaldehyde reacts with ethanol to produce 1,3-butadiene.17 And the main byproducts were ethyl acetate, ethyl ether, 1-butanol, acetic acid, water, and a mixture of materials called oils.18−22 Therefore, there is a strong urge to design a reasonable and feasible process flow sheet for separating the 1,3-butadiene.23 During the design process, a distillation train is used for the recovery of ethanol and acetaldehyde. But the phase equilibrium data containing acetaldehyde are not all available in the literature. To ensure the accuracy of simulation results, a set of reliable experimental vapor−liquid equilibrium data containing acetaldehyde is needed to be measured at atmospheric pressure. © 2017 American Chemical Society

In previous works, quite a few studies related to acetaldehyde have been investigated. For example, isobaric vapor−liquid equilibrium for the binary systems of acetaldehyde + ethylene oxide,24 acetaldehyde + diethyl ether,25 acetaldehyde + ethanol,25−27 acetaldehyde + water,24−26 and acetaldehyde + ethanoic acid27,28 at atmospheric pressure have been obtained and reported by many researchers. Meanwhile, the ternary systems of acetaldehyde + diethyl ether + water25 and acetaldehyde + ethanol + ethanoic acid27 have been determined by Suška and Zhu et al. However, no literature data are available on the phase behavior of binary systems involving acetaldehyde + ethyl acetate and acetaldehyde +1-butanol. In this article, to provide basic data for industrial production, isobaric vapor−liquid phase equilibrium data containing acetaldehyde, ethanol, ethyl acetate, and 1-butanol were measured. First, isobaric vapor−liquid phase equilibrium data of acetaldehyde + ethanol at 101.3 kPa was determined by a modified Rose−Williams equilibrium still, and there were five data sources listed in the NIST Thermodynamics Research Center. So it was used to verify the reliability of the apparatus used in this work. After that, the experimental data of vapor−liquid equilibrium for acetaldehyde + ethyl acetate and acetaldehyde + 1-butanol systems were measured. Then all of the data were checked by thermodynamic consistency with the method of Herington29 and van Ness.30 Next, Wilson,31 nonrandom two-liquid (NRTL),32 and universal quasi-chemical (UNIQUAC)33 models were applied to correlate the experimental data. What’s more, the binary parameters played a significant role for many simulation processes. Received: March 3, 2017 Accepted: May 17, 2017 Published: May 31, 2017 2136

DOI: 10.1021/acs.jced.7b00231 J. Chem. Eng. Data 2017, 62, 2136−2142

Journal of Chemical & Engineering Data

Article

Purities of these materials were checked by gas chromatography (GC-7890A) equipped with a flame ionization detector (FID). All of them were used in experiments without any further purification because of no significant impurities. The boiling points (Tb) of the four pure compounds at 101.3 kPa were measured using a modified Rose−Williams equilibrium still. Both the measured and literature values are gathered in Table 2. 2.2. Apparatus and Procedures. In this work, the vapor−liquid equilibrium data were determined by a modified Rose−Williams equilibrium still (Beiyang Analytical Instrument Company) at 101.3 kPa. The experimental pressure was controlled by a vacuum pump and a U-shaped differential manometer with a precision of 0.03 kPa. The temperature was obtained with a precise mercury thermometer (Tianjin Glass Instrument Factory) with a precision of 0.02 K. The uncertainties of the pressure and temperature measurements were 0.30 kPa and 0.05 K, respectively. The detailed descriptions of the apparatus and the experimental method were given in the previous literature.35−38 In each measurement process, different ratio of light component and heavy component were prepared and added into the circulation still. Water and ethylene glycol were used as the condensed fluid to provide low temperature for total condensation. In this equilibrium process, temperature was recorded every 3 min and the equilibrium state between vapor and liquid phases was assumed when the temperature kept constant

Table 1. Materials Description chemical name

source

purity (mass %)

acetaldehyde ethyl acetate 1-butanol ethanol

Nanjingshengbicheng, China Tianjin Jiangtian, China Aladdin, China Tianjin Jiangtian, China

≥99.5 ≥99.5 ≥99.5 ≥99.7

a

purification analysis method method none none none none

GCa GCa GCa GCa

Gas chromatograph.

Table 2. CAS, Molecular Weights (M), and Experimental Boiling Points with the Literature Data of the Pure Compounds at 101.3 kPaa boiling temperature, Tb/K

a b

component

CAS

M/g·mol−1

exp.a

lit.b

lit.c


75−07−0 141−78−6 71−36−3 64−17−5

44.05 88.11 74.12 46.07

293.84 350.20 390.78 351.38

294.00 350.21 391.90 351.44

293. 6 350.261 390.875 351.44

Standard uncertainties u are u(T) = 0.05 K, and u(P) = 0.30 kPa. Taken from Aspen properties databank. cRef 34.

2. EXPERIMENTAL SECTION 2.1. Materials. The materials used in this work were all from commercial companies. Details about them are listed in Table 1.

Table 3. Isobaric Measured and Calculated VLE Data for Acetaldehyde (1) + Ethanol (2), Acetaldehyde (1) + Ethyl Acetate (2), and Acetaldehyde (1) + 1-Butanol (2) Systems at 101.3 kPaa T/K

a

x1

y1

293.84 294.85 296.92 298.17 302.95 306.24 309.44 311.52 315.21 317.96

1.0000 0.9665 0.8935 0.8491 0.7266 0.6437 0.5858 0.5561 0.4929 0.4465

1.0000 0.9987 0.9950 0.9921 0.9793 0.9656 0.9507 0.9388 0.9107 0.8825

293.84 294.94 295.83 297.12 299.42 303.41 305.91 311.12 316.53 318.43

1.0000 0.9642 0.9213 0.8757 0.7915 0.6733 0.6219 0.5147 0.4107 0.3878

1.0000 0.9967 0.9922 0.9859 0.9742 0.9514 0.9393 0.9007 0.8392 0.8178

293.84 303.46 305.63 307.76 310.13 314.49 320.12 328.09 333.60

1.0000 0.7555 0.7049 0.6566 0.6055 0.5205 0.4309 0.3272 0.2725

1.0000 0.9978 0.9966 0.9951 0.9930 0.9879 0.9779 0.9594 0.9408

α12

T/K

acetaldehyde (1) + ethanol (2) 322.98 26.63 329.44 23.72 332.17 22.32 334.66 17.80 338.35 15.54 341.49 13.64 345.16 12.24 347.97 10.49 350.19 9.31 351.38 acetaldehyde (1) + ethyl acetate (2) 322.95 11.21 324.95 10.87 329.37 9.92 332.98 9.95 335.49 9.50 337.50 9.41 340.61 8.55 345.43 7.49 349.15 7.09 350.20 acetaldehyde (1) + 1-butanol (2) 334.18 146.78 342.07 122.71 349.02 106.21 359.25 92.42 365.74 75.21 369.33 58.44 375.25 48.59 380.56 42.43 390.78

x1

y1

α12

0.3641 0.2722 0.2358 0.2033 0.1574 0.1205 0.0783 0.0467 0.0178 0.0000

0.8240 0.7209 0.6670 0.6075 0.5049 0.4082 0.2756 0.1626 0.0612 0.0000

8.18 6.91 6.49 6.07 5.46 5.03 4.48 3.96 3.60

0.3072 0.2754 0.2236 0.1737 0.1501 0.1252 0.0926 0.0433 0.0098 0.0000

0.7560 0.7122 0.6532 0.5686 0.5071 0.4447 0.3577 0.1884 0.0467 0.0000

6.99 6.51 6.54 6.27 5.83 5.60 5.46 5.13 4.95

0.2672 0.2058 0.1634 0.1109 0.0842 0.0708 0.0495 0.0316 0.0000

0.9385 0.9006 0.8535 0.7483 0.6546 0.5923 0.4699 0.3379 0.0000

41.85 34.96 29.83 23.83 20.61 19.07 17.02 15.64

Standard uncertainties are u(T) = 0.05 K, u(p) = 0.30 kPa, and u(x1) = u(y1) = 0.002 2137



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for 0.5 h or longer. Meanwhile, the temperature as well as pressure was read. Also, the samples were taken for analysis immediately. 2.3. Analysis. The compositions of the samples were analyzed by a gas chromatography (GC-7890A, Agilent, America). The chromatographic column used was a HP-INNOWax capillary column (30m × 0.32 mm × 0.25 μm), and sharp peaks could be gotten for polar compounds. The temperature of FID detector and injector were maintained at 573.15 and 523.15 K. The oven temperature was set at temperature programming. For the acetaldehyde + ethanol and acetaldehyde + ethyl acetate systems, the oven temperature was maintained from 313.15 K initially for 3 min to 403.15 K finally for 3 min. For the acetaldehyde + 1-butanol system, the oven temperature was kept from 313.15 K initially for 3 min to 453.15 K finally for 3 min. Both the temperature rising rates were 10 K·min−1. The sampled volume in each equilibrium process was 0.2 μL. To decrease the experimental errors and acquire accurate measurement data, analysis for each sample were repeated at least four times, and the average data were taken as experimental results. In addition, a series of standard samples with different compositions had been prepared gravimetrically before. Based on the area normalization method, the correction factors of the components were obtained with an uncertainty of 0.0001 g. The uncertainties of the compositions measured were estimated to be 0.002 in mole fractions.

Figure 1. T-x-y diagram for the acetaldehyde (1) + ethanol (2) system at atmospheric pressure. (●), Ref 25; (★), Ref 26; (■), Ref 27; (▲), experimental data; (), calculated data by the Wilson equation; x1 and y1 are the mole fractions of acetaldehyde in the liquid and vapor phases, respectively.

3. RESULTS AND DISCUSSION 3.1. Experimental Vapor−Liquid Equilibrium Results. The isobaric experimental vapor−liquid equilibrium (VLE) data for acetaldehyde (1) + ethanol (2), acetaldehyde (1) + ethyl acetate (2), and acetaldehyde (1) + 1-butanol (2) systems were measured at 101.3 kPa, which are all listed in Table 3. For acetaldehyde (1) + ethanol (2) system, we compared the experimental vapor−liquid equilibrium data with the literature. The phase equilibrium diagram is presented in Figure 1, which is close to the data of Suška and Zhu et al. Table 3 also shows the values of the relative volatilities α12 for these three binary systems, which were obtained by eq 1: α12 =

Figure 2. T-x-y diagram for the acetaldehyde (1) + ethyl acetate (2) system at atmospheric pressure. (●), experimental data; (), calculated data by the Wilson equation; x1 and y1 are the mole fractions of acetaldehyde in the liquid and vapor phases, respectively.

y1 /x1 (1 − y1)/(1 − x1)

(1)

From Table 3, the relative volatilities for these three binary systems are all much larger than 1, which illustrates that the three binary mixtures are more likely to be separated by ordinary distillation at atmospheric pressure. And apparently, it is much easier to separate the mixture of acetaldehyde and 1-butanol than the other two systems. In addition, the isobaric phase equilibrium diagrams for all systems measured are shown in Figures 1, 2, and 3. Azeotropic phenomenon could not be found in these three binary mixtures. 3.2. Thermodynamic Consistency Test of the Experimental Data. For the binary system at constant pressure, Herington area test method, a semiempirical method, was normally used to check the reliability of the measurement data. Therefore, the isobaric binary vapor−liquid equilibrium data for the three binary systems in this article were confirmed by Herington area test method.39 According to the Gibbs−Duhem theorem, the experimental data would pass the test, if the difference between D and J were less than 10.

Figure 3. T-x-y diagram for the acetaldehyde (1) + 1-butanol (2) system at atmospheric pressure. (●), experimental data; (), calculated data by the Wilson equation; x1 and y1 are the mole fractions of acetaldehyde in the liquid and vapor phases, respectively. 2138



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Table 4. Extended Antoine Parameters of Pure Componentsa

a

compound

C1i

C2i

C3i

C4i

C5i

C6i

C7i

C8i/K

C9i/K


46.00 59.92 99.38 66.40

−4643.10 −6227.60 −9866.40 −7122.30

0 0 0 0

0 0 0 0

−4.51 −6.41 −11.66 −7.14

2.70e-17 1.79e-17 1.08e-17 2.89e-06

6 6 6 2

149.78 189.60 183.85 159.05

466.00 523.30 563.10 514.00

Taken from Aspen properties databank.

Table 5. Results of Thermodynamic Consistency Test area test

Table 6. Correlated Binary Interaction Parameters of the Wilson, NRTL, and UNIQUAC Models

point test

systems

D−J

Δy

acetaldehyde(1) + ethanol(2) acetaldehyde(1) + ethyl acetate(2) acetaldehyde(1) + 1-butanol (2)

3.55 −2.58

0.21 0.34

0.27 0.35

0.25 0.33

passed passed

3.74

0.12

0.14

0.16

passed

a c

a

Δyb

Δyc

results

Calculated by Wilson model. Calculated by NRTL model. Calculated by UNIQUAC model. x1= 1

x1= 0 x1= 1

D = 100 ×

ln(γ1/γ2)dx1|

∫x = 0 |ln(γ1/γ2)|dx1 1

J = 150 ×

(Tmax − Tmin) Tmin

(2)

(3) aij aji bij bji cij ADTb/K AD y1b AADTc/K AAD y1c RMSDTd/K RMSDy1d

Where, the values of D can be obtained from the ln (γ1/γ2) − x1 diagram, Tmax and Tmin are the maximum and minimum temperatures of the measurement system. For every binary system, when the vapor and liquid phase reached equilibrium, the fugacities of each component must be equal. The basic thermodynamic equation is as follow: v

fi ̂ = fi ̂

l

(4)

l v Where fi ̂ is the fugacity of vapor component i; fi ̂ is the fugacity of liquid component i. According to the γ − φ method, the real behavior of the liquid phase is described by activity coefficients γi, while the real behavior of the vapor phase is described by fugacity coefficients φvi :

φi v yP = φi sPi sγixi exp(Vi l(P − Pi s)/(RT )) i

aij aji bij bji cij ADTb/K AD y1b AADTc/K AAD y1c RMSDTd/K RMSDy1d

(5)

(Psi )

In this work, the vapor pressure of pure component i at temperature T was calculated by the following extended Antoine equation: ln Pi s = C1i + C2i /(T + C3i) + C4iT + C5i ln T + C6iT7i (6)

For ≤ T ≤ P is in kPa, T is in K. The extended Antoine parameters were obtained from Aspen, which are presented in Table 4. The measurement pressure in this work was 101.3 kPa, therefore, the value of exp (Vli (P − Psi )/(RT)) is nearly equal to 1. And the vapor phase mixture is approximately considered as an ideal gas. The thermodynamic equation for these three systems can be simplified as the following relation: Ci8

s

Pi xiγi = Pyi

Ci9,

NRTLa

UNIQUACa

acetaldehyde (1) + ethanol (2) 9.52 −6.35 −8.13 11.36 −3131.16 1758.41 2759.82 −3406.94 0.3 0.16 0.24 0.0002 −0.0003 0.28 0.32 0.0021 0.0027 0.32 0.37 0.0029 0.0035 acetaldehyde (1) + ethyl acetate (2) 1.56 −2.15 −6.24 2.98 −196.55 493.33 1426.67 −756.92 0.3 0.09 0.17 −0.0027 −0.0032 0.24 0.28 0.0034 0.0035 0.30 0.36 0.0055 0.0057 acetaldehyde (1) + 1-butanol (2) 0.72 −8.59 −23.57 18.54 105.93 2574.90 6802.33 −5774.00 0.3 0.07 0.03 0.0003 −0.0011 0.14 0.14 0.0012 0.0014 0.16 0.18 0.0019 0.0024

aij aji bij bji cij ADTb/K AD y1b AADTc/K AAD y1c RMSDTd/K RMSDy1d

b

|∫

Wilsona

parameters

3.68 −6.97 −999.42 2056.64 0.23 −0.0005 0.32 0.0025 0.37 0.0034 1.85 −1.09 −772.71 481.12 0.11 −0.0029 0.24 0.0033 0.31 0.0055 4.36 −10.16 −1248.57 3058.04 0.10 −0.0006 0.23 0.0016 0.28 0.0023

Wilson: ln Λ ij = a ij + b ij /T; NRTL: τ ij = a ij + b ij /T; UNIQUAC: ln τij = aij + bij/T b AD(y) = (∑in= 1 (yi cal − yi exp ))/n a

n

AD(T ) = (∑i = 1 (Ti cal − Ti exp))/n

c

n

AAD(y) = (∑i = 1 |yi cal − yi exp |)/n;

n

AAD(T ) = (∑i = 1 |Ti cal − Ti exp|)/n d

RMSD(y) =

RMSD(T ) =

(7)

n

(∑i = 1 (yi cal − yi exp )2 )/n ; n

(∑i = 1 (Ti cal − Ti exp)2 )/n

component i in the liquid mixture; Psi is the vapor pressure of pure component at temperature T. The test results of thermodynamic consistency by Herington area test method for the three binary systems are listed in Table 5.

Where yi is the mole fraction of the component i in the vapor phase; xi is the mole fraction of the component i in the liquid phase; P is the total pressure; γi is the activity coefficient of 2139



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Figure 4. Absolute deviations between the calculated values (y1 and T) and the experimental data with the liquid phase composition (x1) for the binary system of acetaldehyde (1) + ethanol (2). (a): (■), calculated temperature by Wilson model; (●), calculated temperature by NRTL model; (▲), calculated temperature by UNIQUAC model; (b): (■), calculated vapor phase composition by Wilson model; (●), calculated vapor phase composition by NRTL model; (▲), calculated vapor phase composition by UNIQUAC model.

Figure 5. Absolute deviations between the calculated values (y1 and T) and the experimental data with the liquid phase composition (x1) for the binary system of acetaldehyde (1) + ethyl acetate (2). (a): (■), calculated temperature by Wilson model; (●), calculated temperature by NRTL model; (▲), calculated temperature by UNIQUAC model; (b): (■), calculated vapor phase composition by Wilson model; (●), calculated vapor phase composition by NRTL model; (▲), calculated vapor phase composition by UNIQUAC model.

In addition, point-to-point method of Van Ness were carried to check the isobaric binary vapor−liquid equilibrium data for the three binary systems.30 In this method, the experimental data would pass the test, if Δy was less than or equal to 1.40,41

were determined by the following objective function F (maximum likelihood method): ⎧ m ⎡ cal 2 ⎛ y cal − y exp ⎞2 ⎪ ⎢⎛ xi − xi exp ⎞ i ⎟ ⎟⎟ + ⎜⎜ i F = ∑ ⎨∑ ⎢⎜⎜ ⎟ σ σ ⎪ ⎝ ⎠ x , i y , i ⎝ ⎠ k=1 i=1 ⎣ ⎩ n

n

Δy = (∑ 100|yi cal − yi exp |)/n i=1

(8)

⎫ ⎛ T cal − T exp ⎞2 ⎛ P cal − P exp ⎞2 ⎤⎪ ⎥ i i i i ⎟⎟ + ⎜⎜ ⎟⎟ ⎬ + ⎜⎜ σT , i σP , i ⎝ ⎠ ⎝ ⎠ ⎥⎦⎪ ⎭

Where n is the total number of experimental data; exp are measured values; cal are the calculated results which were obtained from the Wilson, NRTL, and UNIQUAC models. The test results of thermodynamic consistency by van Ness test method for the three binary systems are also listed in Table 5. From Table 5, all the experimental vapor−liquid equilibrium data passed the thermodynamic consistency. So the measured data in this work were reliable. 3.3. Correlation of Vapor−Liquid Equilibrium Data. In this work, acetaldehyde, ethanol, ethyl acetate, and 1-butanol are all polar compounds. Considering the nonidealities of the liquid phase, the Wilson,31 NRTL,32 and UNIQUAC33 thermodynamic models based on local composition theory were applied to regress all the isobaric vapor−liquid equilibrium measured data. The binary interaction parameters of models

(9)

Where n is the total number of experimental data; m is the number of components; x and y are mole fractions in the liquid phase and vapor phase; T and P represent equilibrium temperature and pressure for every equilibrium system. Cal and exp are the calculated results and experimental data; σ is the standard deviation. The regression results of each model’s binary interaction parameters for acetaldehyde (1) + ethanol (2), acetaldehyde (1) + ethyl acetate (2), and acetaldehyde (1) + 1-butanol (2) systems, the average deviations (AD), average absolute deviations (AAD), and room-mean-squared deviations (RMSD) of the vapor phase mole fraction and temperature 2140



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NRTL models all showed a good agreement with the experimental data.

4. CONCLUSIONS The isobaric vapor−liquid equilibrium data for the three binary systems of acetaldehyde + ethanol, acetaldehyde + ethyl acetate, and acetaldehyde +1-butanol were determined at 101.3 kPa. The data of the acetaldehyde + ethanol system were in good agreement with the literature. All the experimental data passed the thermodynamic consistency test. Azeotropic behavior was not found in these three binary systems. The experimental data were successfully correlated by the Wilson, NRTL, and UNIQUAC thermodynamics models. And the Wilson model presented a much better result for these three systems. Furthermore, the experimental VLE data and the binary parameters obtained can be used in any design process containing these materials directly and will be of great value in the future.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Fax: +86-22-27406119; Telephone: +86-22-27406119. ORCID

Zhongfeng Geng: 0000-0002-8376-2574 Notes

The authors declare no competing financial interest.

■

REFERENCES

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Figure 6. Absolute deviations between the calculated values (y1 and T) and the experimental data with the liquid phase composition (x1) for the binary systems of acetaldehyde (1) + 1-butanol (2). (a): (■), calculated temperature by Wilson model; (●), calculated temperature by NRTL model; (▲), calculated temperature by UNIQUAC model; (b): (■), calculated vapor phase composition by Wilson model; (●), calculated vapor phase composition by NRTL model; (▲), calculated vapor phase composition by UNIQUAC model.

between the calculated values and experimental data are all listed in Table 6. The T-x-y phase diagrams fitted by Wilson activity coefficient models are plotted in Figures 1−3. For these materials used in this work, the sequence of the boiling points is 1-butanol > ethanol > ethyl acetate > acetaldehyde. Generally, there were some differences in deviations among the three correlation models. And the deviation plots can be found in details in Figures 4, 5, and 6. The calculated results correlated by Wilson, NRTL, and UNIQUAC models compared to the experimental data, the AD, AAD, RMSD values of the temperature and vapor compositions for these three systems are all below 0.37 K and 0.0057. And no significant differences for these three activity coefficient models were found. The RMSD results and phase diagrams illustrated that the measured VLE data in this work were successfully regressed by these three models. For the acetaldehyde (1) + ethanol (2) system, the RMSD of the temperature and vapor compositions correlated by Wilson are 0.32 K and 0.0029, which gives a better result than the other models. For the acetaldehyde (1) + ethyl acetate (2) system, the RMSD of the temperature and vapor compositions correlated by Wilson are 0.30 K and 0.0055, and also the Wilson model was the optimal model. For the acetaldehyde (1) + 1-butanol (2) system, Wilson and 2141



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