Measurement and Prediction of VaporâLiquid Equilibria in Ternary

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data 2018, 63, 119−126

Measurement and Prediction of Vapor−Liquid Equilibria in Ternary Systems Containing an Organic Component, Cyclohexylamine, and Cyclohexanol Mandy Klauck,* Thomas Haḧ nel, Sandra Richter, Jürgen Schmelzer, and Grit Kalies Department of Chemical Engineering, Hochschule für Technik und Wirtschaft - University of Applied Sciences, Friedrich-List-Platz 1, 01069 Dresden, Germany ABSTRACT: The isothermal vapor−liquid equilibrium data are presented for three ternary systems: octane + cyclohexylamine + cyclohexanol, cyclohexane + cyclohexylamine + cyclohexanol, and toluene + cyclohexylamine + cyclohexanol. The experimental data were determined by the dynamic method in a modified Röck and Sieg circulation still at two different temperatures and reduced pressures. The experimental results were compared with the predictions from both UNIQUAC and NRTL activity coefficient models and the equation of state proposed by Elliott, Suresh, and Donohue (ESD EOS).

1. INTRODUCTION The experimental vapor−liquid equilibrium (VLE) data were measured in the homogeneous ternary systems consisting of cyclohexylamine (CHA), cyclohexanol (CHOH), and a hydrocarbon (octane, cyclohexane (CH), or toluene) at two temperatures and reduced pressures. These data complement phase equilibrium data already published by Klauck et al.1,2 for partially heterogeneous ternary systems containing water, an organic compound (CH, toluene, or CHA), and CHOH. The ternary systems were chosen to investigate the behavior of mixtures containing amine groups and hydroxyl groups. The work contributes to the accurate prediction of phase equilibria and therefore the enhancement of distillation and rectification processes. The understanding of the compositions of liquid and vapor phases as well as their pressure and temperature dependences enables optimal process design and process operation. Cyclohexanol is used as extractant or solvent in the production of coatings, plastics, or intermediates. Therefore, the phase equilibria of mixtures with other solvents like octane, CH, toluene, or CHA can be of practical interest. Furthermore, experimental data are necessary for comparing and assessing different prediction methods. Reliable calculation methods are required for modeling phase equilibria. In this work, the experimental results are compared to the predictions using both UNIQUAC3 and NRTL4 activity coefficient models and the equation of state proposed by Elliott, Suresh, and Donohue (ESD EOS).5,6 The phase equilibrium data were determined by the dynamic method in a modified Röck and Sieg circulation still at reduced pressures. Due to the different boiling points of the organic compounds, the ternary systems were investigated at different © 2017 American Chemical Society

temperatures: octane + CHA + CHOH at 343.15 and 373.15 K, CH + CHA + CHOH at 333.15 and 353.15 K, and toluene + CHA + CHOH at 343.15 and 373.15 K. The control system necessary for this purpose was developed by our group7 and was applied successfully for several binary and morecomponent mixtures, e.g., CH + aniline,8 water + octane + phenol,9 water + toluene + aniline + CHA.10 The compositions of liquid and vapor samples were analyzed by gas chromatography.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The components octane, CH, toluene, and CHOH were distilled over a bubble cap column at reduced pressures. The hydrocarbons were stored over sodium sulfate. CHOH and CHA were dried and stored over molecular sieve 3A. The commercial source, initial and final purities are given in Table 1. 2.2. Experimental Procedure and Analytical Methods. Grenner et al.7 described the measurement equipment and the control system in detail. The modified Rö ck and Sieg circulation still used for these isothermal measurements was presented by Klauck et al.11 The ternary liquid mixtures are poured into the boiling flask of the circulation still and are equilibrated at the desired temperature. The changes in pressure during the measurement are recorded and samples of liquid and condensed vapor can be taken when the state of equilibrium, indicated by constant pressure, has been reached. Received: August 9, 2017 Accepted: November 27, 2017 Published: December 12, 2017 119

DOI: 10.1021/acs.jced.7b00721 J. Chem. Eng. Data 2018, 63, 119−126

Journal of Chemical & Engineering Data

Article

Table 1. Substances Used in This Work CAS registry number

substance octane cyclohexane (CH) toluene cyclohexylamine (CHA) cyclohexanol (CHOH) a

source

initial purity manufacturer’s data (mass fraction)

purification method

final puritya (mass fraction)

111-65-9 110-82-7 108-88-3 108-91-8

Acros Organics KMF Acros Organics Fluka

>0.995 >0.995 >0.998 >0.995

distillation distillation distillation

>0.9983 >0.9999 >0.9996 >0.9998

108-93-0

Fischer Chemicals

>0.98

distillation

>0.9995

Determined by gas chromatography.

Different measurement temperatures were applied due to the different boiling points of the hydrocarbons. The compositions of the liquid and vapor samples consisting of CHA, CHOH, and octane, CH, or toluene were analyzed by gas chromatography using internal standards. The compositions of the ternary samples were determined using a Macherey Nagel Optima 5 capillary column on a HP 6890 series gas chromatograph equipped with a flame ionization detector. Tables 2, 3, 4 list the experimental results. The standard uncertainties are 0.06 kPa for pressure, 0.05 K for temperature and less than 0.01 (mole fraction) for composition.

Table 3. Isothermal VLE Data of CH (1) + CHA (2) + CHOH (3) Systema p/kPa

Table 2. Isothermal VLE Data of Octane (1) + CHA (2) + CHOH (3) Systema p/kPa

x1

x2

7.41 8.93 10.54 11.41 11.42 12.57 13.12 13.56 13.84 15.77 15.98 16.04 16.05 16.13 16.14

0.063 0.092 0.164 0.177 0.217 0.138 0.235 0.390 0.399 0.558 0.848 0.884 0.703 0.933 0.970

0.285 0.536 0.323 0.471 0.187 0.738 0.589 0.143 0.269 0.326 0.103 0.062 0.146 0.054 0.016

23.03 29.33 31.87 33.75 35.05 37.02 38.82 40.67 41.22 45.99 47.26 47.45 47.46 47.50 47.63

0.063 0.090 0.158 0.215 0.187 0.139 0.228 0.405 0.412 0.547 0.722 0.885 0.935 0.853 0.970

0.285 0.527 0.353 0.189 0.478 0.721 0.585 0.139 0.264 0.344 0.137 0.061 0.053 0.099 0.016

x3 T/K = 343.15 0.652 0.372 0.513 0.352 0.596 0.124 0.176 0.467 0.332 0.116 0.049 0.054 0.151 0.013 0.014 T/K = 373.15 0.652 0.383 0.489 0.596 0.335 0.140 0.187 0.456 0.324 0.109 0.141 0.054 0.012 0.048 0.014

y1

y2

y3

0.595 0.406 0.677 0.557 0.803 0.334 0.497 0.852 0.784 0.727 0.878 0.912 0.853 0.931 0.967

0.298 0.554 0.248 0.401 0.104 0.658 0.491 0.069 0.167 0.253 0.096 0.055 0.103 0.058 0.017

0.107 0.040 0.075 0.042 0.093 0.008 0.012 0.079 0.049 0.020 0.026 0.033 0.044 0.011 0.016

0.458 0.352 0.573 0.709 0.499 0.307 0.461 0.798 0.735 0.693 0.835 0.903 0.931 0.879 0.966

0.328 0.576 0.314 0.127 0.431 0.676 0.508 0.079 0.182 0.278 0.103 0.056 0.057 0.091 0.017

0.214 0.072 0.113 0.164 0.070 0.017 0.031 0.123 0.083 0.029 0.062 0.041 0.012 0.030 0.017

x1

x2

6.54 8.98 10.05 12.85 15.66 20.67 23.80 24.79 25.83 28.72 32.52 40.70 43.22 46.81 48.77

0.019 0.033 0.060 0.084 0.112 0.189 0.201 0.200 0.270 0.300 0.304 0.544 0.690 0.787 0.875

0.630 0.795 0.486 0.804 0.351 0.653 0.249 0.125 0.502 0.361 0.133 0.182 0.194 0.104 0.064

17.26 19.03 19.32 25.09 26.79 36.14 47.65 47.69 48.15 50.36 61.41 75.01 81.76 88.15 92.80

0.034 0.068 0.032 0.071 0.094 0.158 0.254 0.230 0.209 0.260 0.320 0.506 0.689 0.818 0.874

0.616 0.497 0.800 0.820 0.375 0.689 0.528 0.240 0.123 0.395 0.145 0.172 0.205 0.092 0.065

x3 T/K = 333.15 0.351 0.172 0.454 0.112 0.537 0.158 0.550 0.675 0.228 0.339 0.563 0.274 0.116 0.109 0.061 T/K = 353.15 0.350 0.435 0.168 0.109 0.531 0.153 0.218 0.530 0.668 0.345 0.535 0.322 0.106 0.090 0.061

y1

y2

y3

0.278 0.337 0.602 0.516 0.844 0.762 0.930 0.957 0.854 0.915 0.969 0.969 0.963 0.977 0.991

0.682 0.653 0.337 0.480 0.125 0.234 0.049 0.018 0.135 0.075 0.014 0.023 0.032 0.014 0.007

0.040 0.010 0.061 0.004 0.031 0.004 0.021 0.025 0.011 0.010 0.017 0.008 0.005 0.009 0.002

0.356 0.524 0.272 0.432 0.742 0.670 0.813 0.909 0.935 0.868 0.950 0.956 0.953 0.973 0.989

0.588 0.408 0.713 0.560 0.196 0.321 0.176 0.057 0.021 0.112 0.022 0.031 0.041 0.018 0.008

0.056 0.068 0.015 0.008 0.062 0.009 0.011 0.034 0.044 0.020 0.028 0.013 0.006 0.009 0.003

a

The standard uncertainties u are u(T) = 0.05 K, u(p) = 0.06 kPa, u(xi) = u(yi) = 0.01.

3. APPLIED THERMODYNAMIC MODELS The VLE data in the ternary systems were predicted using the local composition activity coefficient models UNIQUAC3 and NRTL4 and the equation of state proposed by Elliott, Suresh, and Donohue (ESD).5,6 The ternary equilibrium data were predicted using binary interaction parameters without any ternary information. The binary interaction parameters were taken from our previous works1,8,12 and are listed in Tables 5, 6, and 7. The interaction parameters for the binary octane + CHOH system were determined in this work as described later. The activity coefficient models UNIQUAC3 and NRTL4 are well-known from the literature. The temperature dependence

a

The standard uncertainties u are u(T) = 0.05 K, u(p) = 0.06 kPa, u(xi) = u(yi) = 0.01. 120



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theory14−17 with two additional parameters: energy of a hydrogen bond εHB/RTcrit and volume of a hydrogen bond KAB/v*. The pure-component parameters for the substances used in this study are given in Table 9. Solvation is calculated using the Elliott combining rule,6 i.e., by geometric mean values. In its attractive term, the ESD EOS has one adjustable interaction parameter kij with an assumed linear temperature dependency:

Table 4. Isothermal VLE Data of Toluene (1) + CHA (2) + CHOH (3) Systema p/kPa

x1

x2

x3

9.66 9.81 11.07 11.66 12.70 13.00 15.00 16.29 19.14 20.77 22.94 24.65

0.122 0.054 0.061 0.178 0.153 0.214 0.271 0.329 0.457 0.553 0.691 0.809

0.331 0.574 0.769 0.107 0.620 0.346 0.440 0.127 0.163 0.210 0.219 0.093

67.23 61.78 56.88 51.70 43.53 36.78 43.88 37.08 33.69 29.67 25.67 32.20

0.802 0.661 0.639 0.557 0.315 0.204 0.297 0.146 0.058 0.074 0.082 0.170

0.104 0.256 0.181 0.142 0.158 0.371 0.418 0.634 0.775 0.563 0.351 0.108

T/K = 343.15 0.547 0.372 0.170 0.715 0.227 0.440 0.289 0.544 0.380 0.237 0.090 0.098 T/K = 373.15 0.094 0.083 0.180 0.301 0.527 0.425 0.285 0.220 0.167 0.363 0.567 0.722

y1

y2

y3

0.610 0.272 0.201 0.832 0.453 0.719 0.701 0.886 0.906 0.902 0.901 0.955

0.283 0.673 0.783 0.047 0.527 0.223 0.278 0.043 0.055 0.078 0.091 0.032

0.107 0.055 0.016 0.121 0.020 0.058 0.021 0.071 0.039 0.020 0.008 0.013

0.934 0.853 0.860 0.848 0.809 0.631 0.671 0.392 0.168 0.289 0.426 0.735

0.045 0.133 0.098 0.074 0.076 0.286 0.285 0.574 0.809 0.638 0.393 0.064

0.021 0.014 0.042 0.078 0.115 0.083 0.044 0.034 0.023 0.073 0.181 0.201

kij = kijC + kijT(T − 273.15K)

(2)

Neither interaction parameters nor experimental phase equilibrium data are available in the literature for the binary octane + CHOH system. The VLE in the adjacent systems heptane + CHOH19 and nonane + CHOH20 were calculated with acceptable deviations using the modified UNIFAC (Dortmund) model.21 Thus, the binary VLE were predicted with the mod. UNIFAC (Do) model for the temperature range of 343.15 to 373.15 K. The group increments and parameters used for these calculations are given in Tables 10 and 11. Binary interaction parameters were determined for the models UNIQUAC, NRTL, and ESD EOS using this VLE data generated by the mod. UNIFAC (Do). The mod. UNIFAC (Do) predictions and the correlation results for the three models are shown in Figure 1. The UNIQUAC and NRTL correlations are nearly identical and show good agreement to the mod. UNIFAC (Do) predictions. The total pressure for octane mole fractions above 0.3 is calculated lower using the ESD EOS. In addition, the less pronounced azeotropic point seen at high octane-content is not reproduced. The calculated binary interaction parameters are given in Tables 5−7 together with the relative deviations of vapor pressure and the absolute deviations of vapor composition.

a

The standard uncertainties u are u(T) = 0.05 K, u(p) = 0.06 kPa, u(xi) = u(yi) = 0.01.

4. RESULT AND DISCUSSION In the following section, experimental and prediction results are discussed for each system. Table 12 summarizes the prediction quality, which is specified by the relative average deviation for vapor pressure and by the absolute average deviation for vapor composition. Octane + Cyclohexylamine + Cyclohexanol. The VLE for this system was determined at 343.15 and 373.15 K (cf. Table 2). Fifteen measurement points at each temperature cover the whole concentration range (see Figures 2 and 3). The binary CHA (2) + CHOH (3) subsystem shows slightly negative deviations from Raoult’s Law. The binary octane (1) + CHA (2) subsystem exhibits a homogeneous maximum pressure azeotrope (cf. Figure 2 at x2 ≈ 0.26 and Figure 3 at x2 ≈ 0.30), whereas the homogeneous maximum pressure azeotrope for octane (1) + CHOH (3) lies at x1 ≈ 0.97 (cf.

of the binary interaction parameters is assumed to be linear. It yields Cij

= CijC + CijT(T − 273.15K) (1) R with Cij = uij − ujj for UNIQUAC and Cij = gij − gjj for NRTL. The pure component vapor pressures and the UNIQUAC volume r and surface q parameters are given in Table 8. The ESD EOS5,6 was developed with terms for attractive and repulsive interaction and an explicit term for associating interaction. Hence, the ESD EOS is particularly well-suited to describe the associating and solvating constituents in the mixtures. Nonassociating components are described with three pure-component parameters: shape factor c, characteristic size parameter b, and interaction energy εi/kB. Association is considered as hydrogen bonding, as described by Wertheim’s

Table 5. Binary Interaction Parameters (Eq 1) for the UNIQUAC Model system c

octane (1) + CHA (2) CH (1) + CHA (2)d toluene (1) + CHA (2)c octane (1) + CHOH (2) CH (1) + CHOH (2)e toluene (1) + CHOH (2)e CHA (1) + CHOH (2)e

CC12/K

CC21/K

CT12

CT21

Δp/%a

Δyb

107.52 17.06 68.94 378.28 237.63 480.12 −230.06

−44.05 43.50 −43.92 −105.50 −36.30 −249.96 5.58

0.0392 0.7689 −0.2455 0.7196 −4.3294 4.4160

−0.2418 −0.6611 −0.4370 −0.9133 3.1321 −2.0812

1.13 0.94 0.30 0.6138 1.46 0.53 0.79

0.0067 0.0124 0.0111 0.0023 0.0115 0.0049 0.0074

Δp = 100/n·Σ(|pcalcd − pexptl|/pexptl), where n is the number of data points. bΔy = 1/n·Σ|ycalcd − yexptl|. cTaken from ref 12. dTaken from ref 8. Taken from ref 1.

a e

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Table 6. Binary Interaction Parameters (Eq 1) for the NRTL Model system c


CC12/K

CC21/K

CT12

CT21

α

Δp/%a

Δyb

135.08 117.11 167.80 774.26 640.75 795.49 −951.95

112.31 100.24 −69.09 297.19 184.43 −58.40 1803.76

0.1320 0.4729 −2.6760 −0.7875 −5.1667 3.2355

−0.8589 −0.5633 −1.7170 −1.7679 2.1374 −8.5915

0.47 0.47 0.47 0.47 0.47 0.47 0.30

1.03 0.95 0.31 0.18 1.19 0.47 0.75

0.0059 0.0124 0.0110 0.0007 0.0113 0.0047 0.0074

a Δp = 100/n·Σ(|pcalcd − pexptl|/pexptl), where n is the number of data points. bΔy = 1/n·Σ|ycalcd − yexptl|. cTaken from ref 12. dTaken from ref 8. eTaken from ref 1.

Table 7. Binary Interaction Parameters (Eq 2) for the ESD EOS system c


kC12

kT12/K−1

Δp/%a

Δyb

−0.003042 −0.013759 −0.019579 −0.001466 0.005137 0.002703 −0.014400

0.00010616 0.00012097 0.00004680 0.00003488 0.00005625 0.00010546

1.46 3.23 1.12 4.06 1.19 0.59 0.82

0.0154 0.0095 0.0169 0.0118 0.0089 0.0035 0.0089

a Δp = 100/n·Σ(|pcalcd − pexptl|/pexptl), where n is the number of data points. bΔy = 1/n·Σ|ycalcd − yexptl|. cTaken from ref 12. dTaken from ref 8. eTaken from ref 1.

Table 8. Antoine Equationa for Pure Component Vapor Pressures13 p* and UNIQUAC Volume r and Surface q Parameters

a

substance

A

B

C

r

q

octane CH toluene CHA CHOH

6.05632 5.97636 6.07577 5.81444 5.92860

1358.80 1206.47 1342.31 1229.42 1199.10

−63.295 −50.014 −53.963 −84.348 −128.150

5.8486 4.0464 3.9228 4.5137 4.3489

4.936 3.240 2.968 3.624 3.512

Table 10. Group Assignment and Rk and Qk Parameters for Mod. UNIFAC (Do) for the Binary Octane + CHOH System22 subgroup

Rk

Qk

CH3 CH2 secondary OH c-CH2 c-CH

0.6325 0.6325 1.0630 0.7136 0.3479

1.0608 0.7081 0.8663 0.8635 0.1071

main group “CH2” “OH” “c-CH2”

log10 (p*/kPa) = A − B/(T/K + C)

NRTL (0.039). The predicted octane content has the greatest uncertainty, which is also apparent from the predicted tie-lines in Figures 2 and 3. Cyclohexane + Cyclohexylamine + Cyclohexanol. Table 3 shows the experimental VLE data for the CH + CHA + CHOH system at 333.15 and 353.15 K. Experimental and predicted vapor−liquid tie-lines are presented in Figures 4 and 5. The measured tie-lines cover the whole concentration range. The binary subsystems do not have azeotropic points. Therefore, no peculiarities are observed, and the tie-lines are arranged according to the volatility of the components. As visible in Figures 4 and 5, the vapor phase contains high amounts of CH. The prediction of the vapor phase compositions shows smaller deviations than for the octane + CHA + CHOH system discussed before. The best predictions were obtained using UNIQUAC (vapor pressure 3.3%, vapor mole fraction 0.012), followed by ESD EOS (vapor pressure

Figure 2) and x1 ≈ 0.96 (cf. Figure 3). Ternary measurement points with a liquid phase mole fraction of less than 0.75 octane show a noticeable enrichment of octane in the vapor phase. In contrast, the tie-lines with higher contents of octane in the liquid phase are remarkably short. Our measurements at high octane mole fractions even prove a reversal of the vapor−liquid distribution ratios (K values) beyond a line connecting the homogeneous azeotropic points of the binary octane + CHA and octane + CHOH subsystems (cf. Figures 2 B and 3 B). A ternary azeotropic point was not found, since maximum pressure values are obtained in the homoazeotropic point of the binary octane + CHA subsystem. The vapor pressure was predicted with a deviation below 2.5% using UNIQUAC and ESD EOS. The prediction using NRTL deviates far more (7.6%). The deviations in the vapor mole fractions are lowest for UNIQUAC (0.021) and increase from ESD EOS (0.031) to Table 9. Pure-Component Parameters for the ESD EOS substance

ref

c

εi/kB/K

b/(cm3 mol−1)

εHB/RTcrit

KAB/v*

octane CH toluene CHA CHOH

18 18 18 12 1

2.4842 1.7843 1.9707 1.1089 1.7888

285.211 329.557 332.752 460.268 381.154

54.157 34.913 36.227 45.806 40.393

3.3200 4.2579

0.0621 0.0022

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Table 11. Mod. UNIFAC (Do) Parameters for the Binary Octane + CHOH System main groups

group interaction parameters

1

2

ref

a12/K

b12

c12/K−1

a21/K

b21

c21/K−1

CH2 CH2 OH

OH c-CH2 c-CH2

22 23 23

2777.0 −117.1 3121.0

−4.6740 0.5481 −13.6900

0.001551 −0.000980 0.014460

1606.0 170.9 2601.0

−4.7460 −0.8062 −1.2500

0.0009181 0.001291 −0.006309

Figure 1. VLE in the binary octane (1) + CHOH (2) system. Mod. UNIFAC (Do) prediction of ■ liquid and □ vapor composition at 343.15 K; Mod. UNIFAC (Do) prediction of ● liquid and ○ vapor composition at 373.15 K; continuous lines are calculation results: green NRTL model, black UNIQUAC model, red ESD EOS.

3.6%, vapor mole fraction 0.012) and, with significantly higher deviations, NRTL (vapor pressure 12.2%, vapor mole fraction 0.018). Toluene + Cyclohexylamine + Cyclohexanol. The experimental data at 343.15 and 373.15 K are listed in Table 4 and shown in Figures 6 and 7 for the ternary toluene + CHA + CHOH system. Since the binary subsystems again do not have azeotropic points, the pathway of the vapor−liquid tielines is very similar to the CH + CHA + CHOH system. The predicted toluene content in the vapor phase is too low, therefore the predicted tie-lines in Figures 6 and 7 are too short. In detail, the following prediction results were obtained: UNIQUAC (vapor pressure 3.0%, vapor mole fraction 0.017), ESD EOS (vapor pressure 3.1%, vapor mole fraction 0.017) and NRTL (vapor pressure 4.8%, vapor mole fraction 0.021). Comparing all systems, the smallest deviations between experimental results and predictions were obtained using the

Figure 2. Vapor−liquid equilibrium in the ternary octane (1) + CHA (2) + CHOH (3) system at 343.15 K. (A) Gibbs diagram for the whole concentration range. (B) Part of the Gibbs diagram: magnification of the octane-rich region. ●·····○, experimental liquid vapor tie-lines; filled blue star, homoazeotropic point in the binary octane + CHA subsystem, UNIQUAC calculation; open blue star, homoazeotropic point in the binary octane + CHOH subsystem, mod. UNIFAC (Do) calculation; dashed blue line, line connecting binary azeotropic points; continuous lines are prediction results: green NRTL model, black UNIQUAC model, red ESD EOS.

UNIQUAC model with average deviations for vapor pressure of 2.9% and vapor mole fraction of 0.016. A nearly equivalent result was achieved using ESD EOS (vapor pressure 3.1% and vapor mole fraction 0.020). Significantly worse predictions were obtained using the NRTL model (vapor pressure 8.23% and vapor composition 0.026). The good prediction of vapor

Table 12. Deviations of Experimental and Predicted Total Pressures and Vapor Compositionsa UNIQUAC

a

NRTL

ESD EOS

system

no. of data points

Δp/%

Δy

Δp/%

Δy

Δp/%

Δy

octane + CHA + CHOH CH + CHA + CHOH toluene + CHA + CHOH average

30 30 24

2.44 3.28 2.99 2.90

0.0207 0.0114 0.0168 0.0163

7.63 12.2 4.84 8.23

0.0386 0.0184 0.0207 0.0259

2.45 3.57 3.14 3.05

0.0312 0.0120 0.0173 0.0201

Δp = 100/n·Σ(|pcalcd − pexptl|/pexptl) and Δy = 1/n·Σ|ycalcd − yexptl|, where n is the number of data points. 123



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Figure 5. Vapor−liquid equilibrium in the ternary CH (1) + CHA (2) + CHOH (3) system at 353.15 K: ●·····○, experimental liquid vapor tie-lines; continuous lines are prediction results: green NRTL model, black UNIQUAC model, red ESD EOS.

Figure 3. Vapor−liquid equilibrium in the ternary octane (1) + CHA (2) + CHOH (3) system at 373.15 K. (A) Gibbs diagram for the whole concentration range. (B) Part of the Gibbs diagram: magnification of the octane-rich region. ●·····○, experimental liquid vapor tie-lines; filled blue star, homoazeotropic point in the binary octane + CHA subsystem, UNIQUAC calculation; open blue star, homoazeotropic point in the binary octane + CHOH subsystem; dashed blue line, line connecting binary azeotropic points; continuous lines are prediction results: green NRTL model, black UNIQUAC model, red ESD EOS.

Figure 6. Vapor−liquid equilibrium in the ternary toluene (1) + CHA (2) + CHOH (3) system at 343.15 K: ●·····○, experimental liquid vapor tie-lines; continuous lines are prediction results: green NRTL model, black UNIQUAC model, red ESD EOS.

Figure 4. Vapor−liquid equilibrium in the ternary CH (1) + CHA (2) + CHOH (3) system at 333.15 K: ●·····○, experimental liquid vapor tie-lines; continuous lines are prediction results: green NRTL model, black UNIQUAC model, red ESD EOS.

Figure 7. Vapor−liquid equilibrium in the ternary toluene (1) + CHA (2) + CHOH (3) system at 373.15 K: ●·····○, experimental liquid vapor tie-lines; continuous lines are prediction results: green color NRTL model, black color UNIQUAC model, red color ESD EOS.

pressures in the ternary octane + CHA + CHOH system with the UNIQUAC model and ESD EOS confirms the applicability of mod. UNIFAC (Do) for the binary octane + CHOH subsystem. Similar trends for the three evaluated models were obtained in our previous study2 of ternary systems consisting of water, CHOH, and an organic compound (CH, toluene, or CHA). In this former study, slightly better results were delivered using ESD EOS than using UNIQUAC. The NRTL model delivered repeatedly poorest predictions.

5. CONCLUSION The isothermal VLE data of the homogeneous ternary systems consisting of organic component (octane, CH, or toluene) + CHA + CHOH were determined by the dynamic method in a modified Röck and Sieg circulation still at different temperatures and reduces pressures. The VLE were predicted using 124



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Superscripts

the activity coefficient models UNIQUAC and NRTL and the equation of state ESD by means of binary interaction parameters. The comparison of predictions and experimental data yields the following result: Lowest deviations for vapor pressure and vapor composition were obtained with the UNIQUAC model, closely followed by the ESD EOS and with significantly greater deviations the NRTL model. A similar ranking of the prediction quality of the thermodynamic models was found for predictions of partially heterogeneous ternary systems consisting of water + organic component (CH, toluene, or CHA) + CHOH for LLE1 and VL(L)E.2

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C constant temperature part T temperature-dependent part

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 351 462 2373; Fax: +49 351 462 2151; E-mail: [email protected]. ORCID

Mandy Klauck: 0000-0001-8922-8295 Funding

The financial support for this project by Deutsche Forschungsgemeinschaft (DFG, KL-2907/2-1) and by Bundesministerium für Bildung und Forschung (BMBF, 03FH041PX4) is gratefully acknowledged. Notes

The authors declare no competing financial interest.

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ABBREVIATIONS

List of Symbols

A, B, C parameters of the Antoine equation anm, bnm, cnm group interaction parameter between group n and m (mod. UNIFAC Do) b characteristic size parameter (ESD EOS) c shape factor for the repulsive term (ESD EOS) C binary interaction parameter (UNIQUAC and NRTL) g interaction energy (NRTL) k binary interaction parameter (ESD EOS) kB Boltzmann constant KAB/v* measure of bonding volume (ESD EOS) n number of data points p pressure Qk relative van der Waals surface area of subgroup k (mod. UNIFAC Do) q UNIQUAC surface parameter R gas constant Rk relative van der Waals volume of subgroup k (mod. UNIFAC Do) r UNIQUAC volume parameter T temperature u interaction energy (UNIQUAC) u measurement uncertainties x liquid mole fraction y vapor mole fraction Δ deviation ε potential energy well depth (ESD EOS) Subscripts

calcd crit exptl HB i,j

REFERENCES

calculated critical experimental hydrogen bond components 125



Article

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