Isothermal vapor–liquid equilibria for binary mixtures of hexane, heptane, octane, nonane and cyclohexane at 333.15 K, 343.15 K and 353.15 K

Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 573–579

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Isothermal vapor–liquid equilibria for binary mixtures of hexane, heptane, octane, nonane and cyclohexane at 333.15 K, 343.15 K and 353.15 K Kun-Jung Lee a, Wei-Kuan Chen a, Jing-Wei Ko b, Liang-Sun Lee c, Chieh-Ming J. Chang a,* a

National Chung Hsing University, Department of Chemical Engineering, 250 Kuokuang Road, Taichung 402, Taiwan Process Research Department, Refining & Manufacturing Research Institute, Chiayi 600, Taiwan c Department of Chemical and Materials Engineering, National Central University, Chung-li 32001, Taiwan b

A R T I C L E I N F O

A B S T R A C T

Article history: Received 7 January 2009 Received in revised form 5 March 2009 Accepted 6 March 2009

Isothermal vapor–liquid equilibria at 333.15 K, 343.15 K and 353.15 K for four binary mixtures of hexane + heptane, heptane + octane, cyclohexane + octane and cyclohexane + nonane have been obtained at pressures ranged from 0 to 101.3 kPa. The NRTL, UNIQUAC and Wilson activity coefficient models have been employed to correlate experimental pressures and liquid mole fractions. The nonideal behavior of the vapor phase has been considered by using the Soave–Redlich–Kwong equation of state in calculating the vapor mole fraction. Liquid and vapor densities were also measured by using two vibrating tube densitometers. Phase behaviors of the P–x–y diagrams indicate that three mixtures of hexane + heptane, heptane + octane, cyclohexane + octane were close to the ideal solution. However, the cyclohexane + nonane mixture presents a large positive deviation from the ideal solution. Only the cyclohexane + octane mixture is negative in the excess Gibbs energy indicates that it is an exothermic system. ß 2009 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Vapor–liquid equilibrium Hexane Heptane Octane Nonane Cyclohexane Density Excess Gibbs energy

1. Introduction Vapor–liquid equilibrium (VLE) data are essential for engineering design of separation processes and unit operations. It is useful for an extension of a few thermodynamic models commonly applied for designing petrochemical related processes. Such information can be obtained experimentally or adopted from generalized methods to calculate properties of multi-component mixtures. Most liquid systems of industrial interest deviate from an ideal behavior. Usually, densities of vapor and liquid phases are important to give a proper size in the process design of many separation equipments. This study is aimed to obtain binary vapor–liquid equilibrium data of aromatics and straight-chain solvents, and then to obtain binary interactional parameters in liquid phase models by using a gamma–phi relationship in order to increase separation efficiencies of these distillation towers. A few commonly used liquid phase activity coefficient models have been described with detailed (Raal and Muhlbauer, 1998). The VLE data of the hexane + heptane mixture from 339.5 to

* Corresponding author. Tel.: +886 4 2285 2592; fax: +886 4 2286 0231. E-mail address: [email protected] (C.-M. J. Chang).

369.0 K and the heptane + octane mixture from 368.55 to 395.95 K have been respectively measured at 94 kPa by Wisniak et al. (1997a,b). Chen et al. (1996) successfully obtain their isobaric VLE data of the cyclohexane + octane mixture from 353.87 to 398.76 K at 101.3 kPa. In their studies, binary interaction parameters of mixtures were obtained to predict phase behavior by examining experimental data for thermodynamic consistency. Isothermal density and compressibility of the cyclohexane + nonane mixture have been measured at 298.15 K, 308.15 K, 318.15 K and 333.15 K by Alcart et al. (1980). To our knowledge, no isothermal VLE data from 0 to 101.3 kPa for the mixture of cyclohexane + nonane have been presented in literature. In this study, experimental P–x data were measured at 333.15 K and 353.15 K under pressure ranged from 0 to 101.3 kPa for four binary mixtures of hexane + heptane, heptane + octane, cyclohexane + octane and cyclohexane + nonane by using the isothermal bubble-point pressure method. These experimental data were then used to obtain vapor mole fraction (yi), activity coefficient (gi) and the system excess molar Gibbs free energies (GE). Finally, the phase equilibrium calculation was carried out by adopting the Soave– Redlich–Kwong (SRK) equation of state (Soave, 1972) for the vapor phase and the Wilson, NRTL and UNIQUAC activity coefficient models (Abrams and Prausnitz, 1975; Orye and Prausnitz, 1965; Wilson, 1964) for the liquid phase.

1876-1070/$ – see front matter ß 2009 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jtice.2009.03.002

K.-J. Lee et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 573–579

574

Nomenclature a A12, A21 b GE n N P Pc R T Tc Tr

v Vi xi yi

energy related parameter (m6/mol2) parameters of the liquid models (K) volume related parameter (m3/mol) excess molar Gibbs energies (J/mol) number of experiments number of component pressure (kPa) critical temperature (kPa) gas constant (J/mol K) temperature (K) critical temperature (K) reduced temperature molar volume (m3/mol) mole volume of pure component i (m3/mol) liquid mole fraction of component i vapor mole fraction of component i

Greek symbols difference acentric factor objective function density (g/cm3) fugacity coefficient of component i activity coefficient of component i

d v P r fi gi

Superscripts cal calculated data exp experimental data L liquid phase sat saturated state V vapor phase Subscript m mixture

2. Experimental 2.1. Chemicals De-ionized water was prepared using a milli-Q purification system and 99.99% nitrogen was obtained from Air Product Co. (Taiwan). Both are used for calibration of pressure and temperature related constants for two densitometers. All the chemicals were standard-grade reagents and purchased from a local supplier, such as, hexane (Sigma–Aldrich, 399% pure), heptane (Sigma– Aldrich, 399% pure), octane (Alfa Aesar, 398% pure), cyclohexane (Sigma–Aldrich, 399.9% pure) and nonane (Alfa Aesar, 399% pure) used without further purification. 2.2. Apparatus and procedures The apparatus used was described by Chang et al. (2005). The system employed mainly consists of a vacuum pump, a vapor– liquid equilibrium cell equipped with a side-view glass window, a data acquisition set, and two densitometers, shown in Fig. 1. Two magnetic circulation pumps (Micropump, 1805R-346) were used to speed up the achievement of the vapor–liquid equilibrium within 2 h, which is a mixed device of static and dynamic methods. The equilibrium cell possesses a specific volume of approximately

Fig. 1. Schematic flow diagram of an experimental set-up for vapor–liquid phase equilibrium measurement.

80 mL. Temperature studied at 333.15 K and 353.15 K and corresponding vapor pressure ranged from 0 to 101.3 kPa. In each experiment, the equilibrium cell was charged with 50 mL of a pure liquid or a binary mixture with a certain composition at a fixed temperature. The equilibrium cell was heated and the temperature was controlled within 0.01 K. Equilibrium was usually reached after 2 h, when the readings of temperatures, pressures and the vibration period of the liquid and vapor phases were constant and unchanged. After the equilibrium, the readings of the bubble pressure of the system and the density of two phases were recorded. Vibration periods of vapor and liquid phases were measured by two densitometers (Anton-Paar, DMA512 and DMA512P) and a digital data processor (DMA60), and densities of two phases can be obtained from individual calibration equation described by Kao et al. (2007). The temperature in the vibrating tube housing of the cell was thermally controlled by a high-precision circulator (Julabo, F10-HC) at the same temperature of the equilibrium cell. The temperature in the circulator was determined using a standard thermometer (Hart Scientific, model 1506). At a V–L equilibrium, the experimental liquid phase composition (x) was obtained by using a corresponding equation of x = ar + b from the measured density (r) at known liquid phase composition. The regression coefficients of these straight lines all attain 0.999. The correction of liquid phase composition shows Table 1 Comparison of our experimental densities with literature data at 333.15 K and mole fraction purity (x) of the liquids. Liquid

Cyclohexane n-Hexane n-Heptane n-Octane n-Nonane a

Source

Sigma–Aldrich Sigma–Aldrich Sigma–Aldrich Alfa Aesar Alfa Aesar

Reference: Alcart et al. (1980).

102x

99.9 99 99 98 99

r (g/cm3) Exp.

Lit.a

333.15 K

333.15 K

0.7415 0.6218 0.6499 0.6696 0.6933

0.74036 0.62221 0.64931 0.66938 0.68633

K.-J. Lee et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 573–579 Table 2 Experimental VLE data of hexane(1) + heptane(2) mixture at 333.15 K and 343.15 K. P (kPa)

x1

rV (103 g/cm3)

T = 333.15 K 27.5 33.3 37.8 42.8 48.1 52.8 57.0 62.0 66.1 71.8 77.1

0.000 0.102 0.199 0.298 0.400 0.497 0.596 0.697 0.796 0.897 1.000

1.017 1.303 1.419 1.574 1.706 1.841 1.927 2.069 2.272 2.326 2.465

T = 343.15 K 39.8 47.1 54.6 60.8 67.0 72.6 79.9 85.4 91.9 97.7 105.4

0.000 0.099 0.211 0.298 0.401 0.495 0.605 0.697 0.811 0.905 1.000

1.380 1.513 1.855 1.998 2.231 2.311 2.569 2.769 2.947 2.986 3.255

rL (g/cm3)

575

Table 4 Experimental VLE data of cyclohexane(1) + octane(2) mixture at 333.15 K and 353.15 K. P (kPa)

x1

rV (103 g/cm3)

rL (g/cm3)

0.6499 0.6463 0.6430 0.6398 0.6367 0.6339 0.6312 0.6286 0.6262 0.6239 0.6218

T = 333.15 K 10.3 14.2 18.8 22.3 26.0 30.7 34.5 38.9 43.1 48.2 53.0

0.000 0.108 0.208 0.306 0.408 0.503 0.595 0.707 0.796 0.899 1.000

0.422 0.559 0.694 0.779 0.850 1.016 1.113 1.274 1.323 1.481 1.640

0.6696 0.6738 0.6784 0.6837 0.6900 0.6965 0.7034 0.7127 0.7208 0.7309 0.7415

0.6332 0.6296 0.6259 0.6230 0.6199 0.6172 0.6142 0.6119 0.6091 0.6071 0.6051

T = 353.15 K 23.8 29.9 36.8 44.5 52.7 60.5 67.9 75.6 84.4 91.3 99.6

0.000 0.104 0.197 0.302 0.401 0.503 0.593 0.707 0.799 0.896 1.000

0.927 1.068 1.167 1.475 1.752 1.923 2.116 2.371 2.536 2.702 2.979

0.6527 0.6568 0.6611 0.6667 0.6727 0.6797 0.6865 0.6959 0.7043 0.7137 0.7246

that the deviation between the experimental and the prepared liquid composition is less than 0.001. The densitometer has a repeatability of about 5(10)5 g/cm3, the electronic balance has the minimum reading about 1(10)5 g, the variation of the temperature was found to be less than 0.01 K, the accuracy of the pressure reading was within 0.1% for the full scale, and the liquid mole fraction of each component (xi) was estimated to be deviated within 0.001. 3. Results and discussion

mole fraction. Pexp ¼ P exp

X

yi

(1)

A classical VLE relationship between the activity coefficient (gi) and fugacity coefficient (fi) was substituted into the above equation to result in Eq. (2).

Pexp ¼

 L   2 sat X g i xi Pisat fsat =RT i exp Vi P  Pi

(2)

fi

i¼1

3.1. Experimental P–x–y and density data At equilibrium under a given temperature (T), experimental pressure (Pexp) can be given by Eq. (1), while the yi is the vapor Table 3 Experimental VLE data of heptane(1) + octane(2) mixture at 333.15 K and 353.15 K. P (kPa)

x1

rV (103 g/cm3)

rL (g/cm3)

T = 333.15 K 10.3 12.4 14.4 16.0 17.8 19.7 21.5 22.9 24.4 26.0 27.6

0.000 0.116 0.198 0.297 0.399 0.503 0.599 0.696 0.799 0.898 1.000

0.398 0.424 0.496 0.558 0.615 0.656 0.692 0.733 0.785 0.836 0.862

0.6696 0.6667 0.6644 0.6619 0.6597 0.6576 0.6559 0.6539 0.6525 0.6512 0.6499

T = 353.15 K 24.1 27.5 30.4 34.1 37.4 41.4 44.0 47.1 50.4 53.9 56.9

0.000 0.105 0.203 0.299 0.395 0.503 0.604 0.695 0.797 0.897 1.000

0.751 0.852 0.978 1.129 1.255 1.357 1.458 1.559 1.660 1.761 1.862

0.6528 0.6500 0.6475 0.6452 0.6431 0.6409 0.6390 0.6374 0.6358 0.6344 0.6332

where fisat is the fugacity coefficient of pure component i in its saturated state, the saturated vapor pressure is denoted by P i sat , and V i L is the saturated liquid molar volume of pure component i. The Ponyting pressure correction was considered to be unity in this study. Then, the gi can be calculated by giving experimental bubble pressure (Pexp) and liquid mole fraction (xi). The gi was individually obtained by NRTL, UNIQUAC, or Wilson model. The fi and fisat

Table 5 Experimental VLE data of cyclohexane(1) + nonane(2) mixture at 333.15 K and 353.15 K. P (kPa)

x1

rV (103 g/cm3)

rL (g/cm3)

T = 333.15 K 3.7 11.8 23.1 32.5 39.8 48.7 53.0

0.000 0.103 0.312 0.519 0.718 0.899 1.000

0.168 0.321 0.688 0.985 1.228 1.511 1.600

0.6933 0.6957 0.7008 0.7090 0.7200 0.7326 0.7415

T = 353.15 K 9.5 24.1 45.1 62.0 76.7 92.2 99.1

0.000 0.104 0.308 0.498 0.701 0.901 1.000

0.425 0.829 1.333 1.933 2.242 2.768 2.964

0.6765 0.6788 0.6837 0.6914 0.7022 0.7160 0.7246

K.-J. Lee et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 573–579

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Table 6 Calculated VLE data of hexane(1) + heptane(2) mixture using NRTL, UNIQUAC and Wilson models at 333.15 K and 343.15 K.

Table 8 Calculated VLE data of cyclohexane(1) + octane(2) mixture using NRTL, UNIQUAC and Wilson model at 333.15 K and 353.15 K.

P (kPa)

P (kPa)

x1

SRK/NRTL Pcal (kPa)

y1cal

SRK/UNIQUAC

SRK/Wilson

Pcal (kPa)

Pcal (kPa)

y1cal

x1

y1cal

SRK/NRTL

SRK/UNIQUAC

SRK/Wilson

Pcal (kPa)

y1cal

Pcal (kPa)

y1cal

Pcal (kPa)

y1cal

T = 333.15 K 27.5 0.000 33.3 0.102 37.8 0.199 42.8 0.298 48.1 0.398 52.8 0.497 57.0 0.596 62.0 0.697 66.1 0.796 71.8 0.897 77.1 1.000

28.0 33.2 38.0 42.9 47.8 52.4 57.1 61.9 66.6 71.4 76.3

0.000 0.239 0.405 0.535 0.641 0.724 0.795 0.856 0.909 0.957 1.000

28.0 33.2 38.0 42.9 47.8 52.4 57.1 61.9 66.6 71.4 76.3

0.000 0.239 0.405 0.535 0.641 0.724 0.795 0.856 0.909 0.957 1.000

28.0 33.2 38.0 42.9 47.8 52.4 57.1 61.9 66.6 71.4 76.3

0.000 0.239 0.405 0.535 0.641 0.724 0.795 0.856 0.909 0.957 1.000

T = 333.15 K 10.3 0.000 14.2 0.108 18.8 0.208 22.3 0.306 26.0 0.408 30.7 0.503 34.5 0.595 38.9 0.707 43.1 0.796 48.2 0.897 53.0 1.000

10.4 14.4 18.3 22.2 26.4 30.4 34.3 39.2 43.0 47.5 51.9

0.000 0.353 0.546 0.673 0.766 0.830 0.878 0.923 0.952 0.979 1.000

10.4 14.5 18.4 22.3 26.4 30.4 34.3 39.1 43.0 47.5 51.9

0.000 0.355 0.547 0.673 0.765 0.829 0.877 0.923 0.951 0.979 1.000

10.4 14.4 18.3 22.2 26.4 30.4 34.3 39.2 43.0 47.5 51.9

0.000 0.353 0.546 0.673 0.766 0.830 0.878 0.923 0.952 0.979 1.000

T = 343.15 K 40.0 0.000 47.1 0.099 54.6 0.211 60.8 0.298 67.0 0.401 72.6 0.495 79.9 0.605 85.4 0.697 91.9 0.811 97.7 0.905 105.4 1.000

40.7 47.3 54.7 60.4 66.9 72.7 79.6 85.2 92.2 98.0 103.9

0.000 0.222 0.407 0.521 0.626 0.708 0.789 0.847 0.911 0.957 1.000

40.7 47.3 54.7 60.4 66.9 72.7 79.6 85.2 92.2 98.0 103.9

0.000 0.222 0.407 0.521 0.626 0.708 0.789 0.847 0.911 0.957 1.000

40.7 47.3 54.7 60.4 66.9 72.7 79.6 85.2 92.2 98.0 103.9

0.000 0.222 0.407 0.521 0.626 0.708 0.789 0.847 0.911 0.957 1.000

T = 353.15 K 23.8 0.000 29.9 0.104 36.8 0.197 44.5 0.302 52.7 0.401 60.5 0.503 67.9 0.593 75.6 0.707 84.4 0.799 91.3 0.896 99.6 1.000

23.3 30.5 37.2 44.9 52.4 60.2 67.1 76.0 83.3 90.9 99.1

0.000 0.313 0.494 0.635 0.731 0.806 0.857 0.909 0.943 0.973 1.000

23.3 30.6 37.3 45.1 52.5 60.2 67.2 76.0 83.3 90.9 99.1

0.000 0.316 0.495 0.635 0.730 0.805 0.857 0.909 0.943 0.973 1.000

23.3 30.3 36.9 44.7 52.2 60.3 67.5 76.6 83.9 91.3 99.1

0.000 0.309 0.490 0.634 0.732 0.808 0.860 0.912 0.944 0.973 1.000

were calculated by the SRK equation of state, shown in Eq. (3). P¼

RT

vb



2

(6)

aaðTÞ vðv þ bÞ

(3)

The simple van der Waals mixing rule was used to evaluate the mixture parameters.

R2 Tc2 Pc

(4)

am ¼

RT c Pc

(5)

a ¼ 0:42748

b ¼ 0:08664

x1

N X N X x i x j ai j

(7)

i¼1 j¼1

bm ¼

N X N X xi x j bi j

(8)

i¼1 j¼1

Table 7 Calculated VLE data of heptane(1) + octane(2) mixture using NRTL, UNIQUAC and Wilson model at 333.15 K and 353.15 K. P (kPa)

aðTÞ ¼ ½1 þ ð0:48 þ 1:574v  0:176v2 Þð1  Tr0:5 Þ

SRK/NRTL

SRK/UNIQUAC

SRK/Wilson

Pcal (kPa)

y1cal

Pcal (kPa)

y1cal

Pcal (kPa)

y1cal

T = 333.15 K 10.3 0.000 12.4 0.116 14.4 0.198 16.0 0.297 17.8 0.399 19.7 0.503 21.5 0.598 22.9 0.696 24.4 0.799 26.0 0.898 27.6 1.000

10.4 12.6 14.2 16.0 17.8 19.6 21.2 22.9 24.6 26.3 28.0

0.000 0.268 0.405 0.534 0.640 0.727 0.796 0.854 0.909 0.956 1.000

10.4 12.6 14.2 16.0 17.8 19.6 21.2 22.9 24.6 26.3 28.0

0.000 0.268 0.405 0.534 0.640 0.727 0.796 0.854 0.909 0.956 1.000

10.4 12.6 14.2 16.0 17.8 19.6 21.2 22.9 24.6 26.3 28.0

0.000 0.268 0.405 0.534 0.640 0.727 0.796 0.854 0.909 0.956 1.000

T = 353.15 K 24.1 0.000 27.5 0.105 30.4 0.203 34.1 0.299 37.4 0.395 41.4 0.503 44.0 0.604 47.1 0.695 50.4 0.797 53.9 0.897 56.9 1.000

23.3 27.2 30.7 34.1 37.3 40.9 44.2 47.2 50.4 53.8 57.0

0.000 0.230 0.390 0.513 0.613 0.707 0.782 0.841 0.899 0.953 1.000

23.3 27.2 30.7 34.1 37.3 40.9 44.2 47.2 50.4 53.8 57.0

0.000 0.230 0.390 0.513 0.613 0.707 0.782 0.841 0.899 0.953 1.000

23.3 27.2 30.7 34.1 37.3 40.9 44.2 47.2 50.4 53.8 57.0

0.000 0.230 0.390 0.513 0.613 0.707 0.782 0.841 0.899 0.953 1.000

For the measurement of the density, two pressure-dependent calibration constants of the vapor and the liquid densitometer were determined at constant temperature, using water and nitrogen as calibrated fluids for all investigated pressures, then, the density of each phase was obtained. Table 1 lists a comparison Table 9 Calculated VLE data of cyclohexane(1) + nonane(2) mixture using NRTL, UNIQUAC and Wilson model at 333.15 K and 353.15 K. P (kPa)

x1

SRK/NRTL

SRK/UNIQUAC

SRK/Wilson

Pcal (kPa)

y1cal

Pcal (kPa)

y1cal

Pcal (kPa)

y1cal

T = 333.15 K 3.7 0.000 11.8 0.103 23.1 0.312 32.5 0.519 39.8 0.718 48.7 0.899 53.0 1.000

3.4 11.5 23.4 32.3 40.0 47.4 51.9

0.000 0.725 0.889 0.937 0.966 0.987 1.000

3.4 11.4 23.4 32.3 40.0 47.4 51.9

0.000 0.723 0.889 0.937 0.966 0.987 1.000

3.4 11.5 23.4 32.3 40.0 47.4 51.9

0.000 0.725 0.889 0.937 0.966 0.987 1.000

T = 353.15 K 9.5 0.000 24.1 0.104 45.1 0.308 62.0 0.499 76.7 0.701 92.2 0.901 99.1 1.000

8.5 23.3 45.8 61.9 76.4 91.1 99.0

0.000 0.667 0.861 0.918 0.953 0.984 1.000

8.5 23.3 45.8 61.9 76.5 91.1 99.0

0.000 0.667 0.861 0.918 0.953 0.984 1.000

8.5 23.3 45.8 61.9 76.5 91.1 99.0

0.000 0.667 0.860 0.918 0.953 0.984 1.000

K.-J. Lee et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 573–579

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Fig. 2. P–x–y diagram of hexane(1) + heptane(2) mixture at 333.15 K and 343.15 K.

Fig. 4. P–x–y diagram of cyclohexane(1) + octane(2) mixture at 333.15 K and 353.15 K.

of our experimental densities of the liquids at mole fraction purity (x  98%) with literature data at 333.15 K. The deviations between these densities are very small. Tables 2–5 present experimental data of the liquid mole fraction of one component and the density of each phase for four binary systems at 333.15 K and 353.15 K, respectively. Tables 6–9 lists calculated data including the system bubble pressure and the vapor mole fraction for four binary systems at 333.15 K and 353.15 K, respectively. In this study, 11 experiments have been done at each temperature for the V–L equilibrium. Only 7 experiments were carried out at each temperature for the cyclohexane + nonane system since the nonane is very expensive. Fig. 2 shows P–x–y diagrams of the hexane + heptane binary mixture at 333.15 K and 343.15 K. Figs. 3–5 display P–x–y diagrams of the hexane + octane, cyclohexane + octane and cyclohexane + nonane mixtures at 333.15 K

and 353.15 K by using the NRTL, UNIQUAC and Wilson models, respectively. These three models fit experimental data well for all four binary systems. No azeotrope was found for these four binary systems. Fig. 6 displays the calculated activity coefficient (gi) using the NRTL model at 333.15 K (a) and 353.15 K (b), respectively. Activity coefficients (gi) approaching to the unity indicate three symmetric systems of the hexane + heptane, heptane + octane and cyclohexane + octane mixtures are close to an ideal solution. However, the asymmetric system of the cyclohexane + nonane mixture was largely deviated from the ideal solution, shown in Fig. 6. Usually, the order of magnitude of the Gibbs excess energy in a binary regular mixing solution is mainly determined by that of the excess enthalpy because of the excess entropy is small. Fig. 7 displays the calculated excess Gibbs energy (GE) using the NRTL

Fig. 3. P–x–y diagram of heptane(1) + octane(2) mixture at 333.15 K and 353.15 K.

Fig. 5. P–x–y diagram of cyclohexane(1) + nonane(2) mixture at 333.15 K and 353.15 K.

578

K.-J. Lee et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 573–579

Fig. 6. Calculated activity coefficients for four binary mixtures at (a) 333.15 K and (b) 353.15 K using the NRTL model.

Fig. 7. Calculated excess Gibbs energies for four binary mixtures at (a) 333.15 K and (b) 353.15 K using the NRTL model.

model at 333.15 K (a) and 353.15 K (b), respectively. The cyclohexane + octane mixture exhibiting a negative GE value indicates it is an exothermic system. Other three mixtures of the hexane + heptane, heptane + octane and cyclohexane + nonane presenting positive GE values indicate that they belong to endothermic systems.

function (P).

3.2. Modelling The experimental results were then used to obtain the binary parameters by using the Soave–Redlich–Kwong equation of state (SRK-EOS) combined with various activity coefficient models of NRTL, UNIQUAC and Wilson. The expressions of the activity coefficients models for the NRTL (Santiago et al., 2007), UNIQUAC (Simoni et al., 2008) and Wilson (Huang and Lee, 1996) are listed in the literature. The optimal interaction parameters for each binary system were obtained by minimizing the following objective

#   n " cal exp  100 X Pk  Pk  P¼   2n k¼1  Pkexp 

(9)

The regression results are shown in Table 10. The root mean square deviations of dP were defined as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn cal exp k ðPk  Pk Þ dP ¼ n

(10)

The deviation between experimental and calculated equilibrium bubble pressures is reasonably small, and it is indicated that these three activity coefficient models are suitable to represent the binary experimental data. The calculated P–x–y diagrams of four binary systems are shown in Figs. 2–5, respectively. As expected, nevertheless, there is little difference among three liquid activity

K.-J. Lee et al. / Journal of the Taiwan Institute of Chemical Engineers 40 (2009) 573–579

579

Table 10 Optimal binary interaction parameters in NRTL, UNIQUAC and Wilson correlations for four binary mixtures. T (K)

NRTL A12

Hexane(1) + heptane(2) 333.15 45.95 343.15 29.19

UNIQUAC A21 64.95 8.724

dP

A12

Wilson A21

dP

A12

A21

dP

0.366 0.529

51.15 27.22

60.49 34.23

0.366 0.529

78.27 38.24

60.49 17.86

0.366 0.529

34.58 86.86

10.36 57.60

0.221 0.309

Heptane(1) + octane(2) 333.15 35.46 353.15 42.85

11.09 73.14

0.221 0.310

21.44 52.93

27.97 64.17

0.221 0.310

Cyclohexane(1) + octane(2) 333.15 16.41 353.15 128.8

14.32 122.0

0.452 0.564

51.93 23.59

51.92 23.59

0.453 0.595

120.6 145.8

Cyclohexane(1) + nonane(2) 333.15 61.93 353.15 182.1

136.6 33.85

0.673 0.678

107.3 81.20

0.677 0.683

295.1 238.8

193.6 157.8

151.2 320.7

89.73 16.76

0.452 0.463

0.671 0.668

NRTL: A12 = (g12  g22)/R; A21 = (g21  g11)/R; a = 0.3. UNIQUAC: A12 = (U12  U22)/R; A21 = (U21  U11)/R. Wilson: A12 = (l12  l22)/R; A21 = (l21  l11)/R. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn cal exp k Pk  Pk dP ¼ . n

coefficient models for the four binary systems studied. Figs. 6 and 7 individually show the calculated activity coefficient (gi) and excess Gibbs energy (GE) using the NRTL model. 4. Conclusions Vapor–liquid equilibria of four binary mixtures of hexane, heptane, octane, nonane and cyclohexane have successfully been obtained at 333.15 K, 343.15 K and 353.15 K in this study. Experimental data of phase densities, liquid mole fractions and system pressures were determined using the bubble-point method coupled with two vibration densitometers. Three activity coefficient models have been employed to correlate the experimental data and the results are satisfactory. The calculated activity coefficient and excess Gibbs energy values reveal that the hexane + heptane, heptane + octane and cyclohexane + octane systems were close to the ideal solution. However, the cyclohexane + octane system shows a high deviation from the ideal solution. The associated binary interaction parameters between each component for four mixtures were finally obtained from the optimal correlation of our experimental data. Acknowledgements The authors would like to thank the National Science Council of the Republic of China, Taiwan for financially supporting this research (NSC 97-2622-E005-011-CC1). This work is also supported in part by the ministry of Education, Taiwan, ROC under the ATU plan and China Petroleum Company and National Chung Hsing University project (EEA9715003).

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