Measurement and Prediction of VaporâLiquid(âLiquid) Equilibria in

Article pubs.acs.org/jced

Measurement and Prediction of Vapor−Liquid(−Liquid) Equilibria in Ternary Systems Containing Water, an Organic Component, and Cyclohexanol Mandy Klauck,* Thomas Haḧ nel, Christian Nowka, 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(−liquid) equilibria for the water + cyclohexane + cyclohexanol, water + toluene + cyclohexanol, and water + cyclohexylamine + cyclohexanol ternary systems are presented. The experimental data were determined by the dynamic method in a modified Röck and Sieg circulation still between 333.15 and 363.15 K at 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 Vapor−liquid(−liquid) equilibrium (VL(L)E) data are essential to gain insight into distillation and rectification processes. Process design and operation can be optimized through the detailed understanding of the compositions of the liquid and vapor phases as well as their pressure and temperature dependence. Reliable calculation methods are required for modeling of phase equilibria. Additionally, experimental measurements are used to verify the calculation and prediction quality of these models, especially for systems strongly deviating from ideal behavior. In order to improve the experimental database, the experimental VLE and VLLE data of the ternary systems water + cyclohexanol (CHOH) + toluene or cyclohexane (CH) or cyclohexylamine (CHA) were measured. These systems have not been considered in the literature to date, and the present results complement the liquid−liquid equilibrium (LLE) data published by Klauck et al.1 The mixtures were selected because of the variety of interactions in the mixtures, e.g., dispersion forces, dipole interactions, and hydrogen bonds, which are on the one hand interesting for theoretical considerations and on the other hand challenging for the examined prediction models. Cyclohexanol is used as extractant or solvent for the production of coatings, plastics, and intermediates. Therefore, the phase equilibria of mixtures with other solvents such as CH, toluene, and CHA in the presence of water are of particular practical interest. Furthermore, experimental data are necessary to allow comparison and evaluation of different prediction methods. In this work, the experimental results are compared to the predictions using both the UNIQUAC2 and NRTL3 activity coefficient models and the equation of state proposed by Elliott, Suresh, and Donohue (ESD EOS).4,5 The phase equilibrium data were determined by the dynamic method in a modified Röck and Sieg circulation still at reduced © 2017 American Chemical Society

pressures. The control system necessary for these measurements was developed by our group6 and has been successfully applied for several homogeneous and heterogeneous mixtures, e.g., the CHA + nonane binary system,7 the water + octane + aniline ternary system,8 and the water + toluene + aniline + CHA quaternary system.7 The compositions of liquid and vapor samples were analyzed by Karl Fischer titration and by gas chromatography.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The components CH, toluene, and CHOH were distilled over a bubble cap column at reduced pressures. CHA was used without further purification. Pretreated water was purified in a Milli-Q Academic device, which produces ultrapure water of Type 1 (DIN ISO 3696).9 The organic components were stored over sodium sulfate. The commercial sources and initial and final purities are given in Table 1. 2.2. Experimental Procedure and Analytical Methods. The measurement equipment has been described in detail by Grenner et al.6 The isothermal VLE measurements were carried out in a modified Röck and Sieg circulation still applicable for homogeneous as well as heterogeneous liquid compositions as described by Klauck et al.10 The ternary mixtures were poured into the boiling flask of the circulation still and were equilibrated at the desired temperature. When the liquid composition was heterogeneous, the liquid phases were intensively stirred in Special Issue: Memorial Issue in Honor of Ken Marsh Received: January 30, 2017 Accepted: April 28, 2017 Published: May 10, 2017 2689

DOI: 10.1021/acs.jced.7b00100 J. Chem. Eng. Data 2017, 62, 2689−2696

Journal of Chemical & Engineering Data

Article

Table 1. Substances Used in this Work

a

substance

CAS Registry number

source

initial purity manufacturer’s data (mass fraction)

purification method

final puritya (mass fraction)

water toluene cyclohexane (CH) cyclohexylamine (CHA) cyclohexanol (CHOH)

7732-18-5 108-88-3 110-82-7 108-91-8 108-93-0

water treatment equipment Acros Organics KMF Fluka Fischer Chemicals

− >0.998 >0.995 >0.995 >0.98

distillation distillation − distillation

>0.9996 >0.9999 >0.9998 >0.9995

Determined by gas chromatography.

Table 2. Isothermal VL(L)E Data for the Water (1) + CH (2) + CHOH (3) Systema p/kPa

x1

x2

23.22b 30.91 35.08 41.22 41.64 45.73 48.42b 54.99b 62.63b 63.37b 65.82b 66.87b 67.70b 68.39b 69.04b 69.54b

0.443 0.208 0.090 0.128 0.057 0.041 0.330 0.279 0.172 0.166 0.106 0.086 0.068 0.047 0.036 0.015

0.009 0.079 0.174 0.195 0.296 0.396 0.129 0.202 0.382 0.412 0.546 0.618 0.675 0.744 0.786 0.887

20.80 33.65 42.28 50.78b 70.12 72.04 79.14 81.21 85.88b 88.28

0.042 0.100 0.068 0.469 0.081 0.182 0.051 0.142 0.413 0.050

0.033 0.038 0.092 0.002 0.195 0.116 0.302 0.183 0.068 0.406

x3 T/K = 333.15 0.548 0.713 0.736 0.677 0.647 0.563 0.541 0.519 0.446 0.422 0.348 0.296 0.257 0.209 0.178 0.098 T/K = 353.15 0.925 0.862 0.840 0.529 0.724 0.702 0.647 0.675 0.519 0.544

y1

y2

Table 3. Isothermal VL(L)E Data for the Water (1) + Toluene (2) + CHOH (3) Systema y3

0.885 0.504 0.237 0.288 0.140 0.133 0.376 0.350 0.301 0.279 0.267 0.246 0.229 0.224 0.220 0.216

0.084 0.470 0.744 0.695 0.843 0.853 0.609 0.638 0.688 0.711 0.724 0.747 0.767 0.769 0.774 0.776

0.031 0.026 0.019 0.017 0.017 0.014 0.015 0.012 0.011 0.010 0.009 0.007 0.004 0.007 0.006 0.008

0.402 0.562 0.338 0.952 0.265 0.461 0.209 0.368 0.553 0.121

0.432 0.341 0.585 0.008 0.705 0.504 0.764 0.606 0.423 0.856

0.166 0.097 0.077 0.040 0.030 0.035 0.027 0.026 0.024 0.023

p/kPa

x1

x2

21.77 25.54 25.77 27.07b 29.88b 30.83 32.88b 35.53b 35.85b 35.87b

0.120 0.347 0.058 0.386 0.338 0.203 0.262 0.129 0.093 0.084

0.297 0.081 0.537 0.081 0.150 0.302 0.282 0.543 0.609 0.656

86.30b 93.09b 96.17b

0.326 0.204 0.127

0.209 0.400 0.571

64.30 79.70 85.76 91.02 95.62

0.075 0.060 0.366 0.259 0.175

0.340 0.552 0.086 0.194 0.351

x3 T/K = 333.15 0.583 0.572 0.405 0.533 0.512 0.495 0.456 0.328 0.298 0.260 T/K = 358.15 0.465 0.396 0.302 T/K = 363.15 0.585 0.388 0.548 0.547 0.474

y1

y2

y3

0.483 0.714 0.473 0.756 0.670 0.631 0.634 0.580 0.568 0.558

0.478 0.247 0.503 0.212 0.303 0.346 0.348 0.395 0.414 0.425

0.039 0.039 0.024 0.032 0.027 0.023 0.018 0.025 0.018 0.017

0.674 0.626 0.600

0.291 0.345 0.376

0.035 0.029 0.024

0.478 0.543 0.800 0.686 0.646

0.460 0.417 0.155 0.271 0.319

0.062 0.040 0.045 0.043 0.035

a The standard uncertainties u are u(T) = 0.05 K, u(p) = 0.06 kPa, and u(xi) = u(yi) = 0.01. bThe liquid mixture was heterogeneous. Only the organic phase was analyzed.

heterogeneous liquid compositions, the organic phase and the water-rich phase were separated after the liquid sample had been equilibrated at the measurement temperature. The organic phases were analyzed, but because the water-rich phases consisted of nearly pure water (mole fraction greater than 0.99), the composition analyses of the aqueous phases were omitted. The experimental results are provided in Tables 2 to 4. The uncertainties are 0.06 kPa for pressure, 0.05 K for temperature, and less than 0.01 (mole fraction) for composition.

a The standard uncertainties u are u(T) = 0.05 K, u(p) = 0.06 kPa, and u(xi) = u(yi) = 0.01. bThe liquid mixture was heterogeneous. Only the organic phase was analyzed.

the boiling flask, mixing vessel, and liquid sample vessel to form an emulsion and prevent separation. The equilibrium pressures were recorded, and samples of liquid and condensed vapor were taken after equilibrium had been reached. Because of the different bubble points of the organic compounds, the ternary systems were investigated at different temperatures: water + CH + CHOH at 333.15 and 353.15 K; water + toluene + CHOH at 333.15, 358.15, and 363.15 K; and water + CHA + CHOH at 333.15 and 363.15 K. The compositions of the liquid and vapor samples were analyzed by gas chromatography and by volumetric Karl Fischer titration. The water content was determined with a 787 KF Titrino (Deutsche Metrohm, Filderstadt, Germany). The mole fractions of the organic compounds CH, toluene, CHA, and CHOH were determined on a Macherey Nagel Optima 5 capillary column on an HP 6890 series gas chromatograph equipped with a flame ionization detector using an internal standard. In cases of

3. THERMODYNAMIC MODELS The VLE data in the ternary systems were predicted using the UNIQUAC2 and NRTL3 activity coefficient models and the equation of state proposed by Elliott, Suresh and Donohue (ESD).4,5 The binary interaction parameters were taken from our previous works1,11,12 and are listed in Tables 5 to 7. The pure-component UNIQUAC volume (r) and surface (q) parameters and the Antoine equation parameters to calculate the vapor pressures are given in Table 8. The temperature dependence of the binary interaction parameters was assumed to be linear: Cij = CijC + CijT(T − 273.15 K) (1) R with Cij = uij − ujj for UNIQUAC and Cij = gij − gjj for NRTL. 2690



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hydrogen bond, KAB/v*. The pure-component parameters for the substances used in this study are given in Table 9. Solvation was calculated using the Elliott combining rule,5 i.e., as geometric mean values. In its attractive term, the ESD EOS has one adjustable interaction parameter kij with an assumed linear temperature dependence:

Table 4. Isothermal VLE Data for the Water (1) + CHA (2) + CHOH (3) Systema p/kPa

x1

x2

15.23 16.64 17.67 18.97 20.07 20.70 21.05 21.28 21.48

0.320 0.290 0.427 0.391 0.505 0.616 0.629 0.678 0.724

0.558 0.206 0.464 0.215 0.209 0.293 0.213 0.211 0.206

20.92 55.96 64.41 64.87 71.16 75.41 75.92 76.70 77.68

0.038 0.284 0.346 0.412 0.461 0.613 0.615 0.668 0.716

0.519 0.580 0.206 0.479 0.206 0.293 0.210 0.212 0.210

x3 T/K = 333.15 0.122 0.504 0.109 0.394 0.286 0.091 0.158 0.111 0.070 T/K = 363.15 0.443 0.136 0.448 0.109 0.333 0.094 0.175 0.120 0.074

y1

y2

y3

0.722 0.913 0.795 0.923 0.931 0.886 0.920 0.914 0.909

0.275 0.051 0.199 0.051 0.053 0.108 0.067 0.077 0.085

0.003 0.036 0.006 0.026 0.016 0.006 0.013 0.009 0.006

0.340 0.719 0.895 0.790 0.908 0.872 0.903 0.902 0.891

0.546 0.271 0.057 0.200 0.055 0.118 0.080 0.084 0.098

0.114 0.010 0.048 0.010 0.037 0.010 0.017 0.014 0.011

kij = kijC + kijT(T − 273.15K)

(2)

4. RESULTS AND DISCUSSION A detailed description of each system is given below. The results of comparisons of the experimental and predicted VL(L)E data are summarized in Table 10. The deviations are given as relative average deviations for the vapor pressure and as absolute average deviations for the vapor mole fractions. Water + Cyclohexane + Cyclohexanol. The VL(L)E in the water + CH + CHOH system were measured at 333.15 and 353.15 K. The LLE of this system were described at 298.15 and 323.15 K as Type 2 systems,1 i.e., with two partially miscible subsystems. The VL(L)E were measured at 13 homogeneous and 13 heterogeneous liquid compositions. The experimental data are given in Table 2 and are represented together with the prediction results in Figures 1 to 3. The compositions of the organic phases in heterogeneous measurements at 333.15 K confirm the binodal curve from LLE measurements at 323.15 K,1 (cf. Figure 1A). The vapor-phase compositions tend toward high amounts of water and CH, while the highboiling substance CHOH is enriched in the liquid phase. The vapor compositions measured for systems with heterogeneous liquid composition are located on a connecting line between the azeotropic points of the binary water + CH and CH + CHOH subsystems. The predictions are shown in Figure 1B. The closest agreement between experimental and predicted binodal curves was obtained using the ESD EOS, followed by the UNIQUAC model and finally the NRTL model. The VLLE predictions of five randomly selected heterogeneous

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

The ESD EOS was developed with terms for attractive and repulsive interactions and an explicit term for associating interactions. 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: the shape factor c, the characteristic size parameter b, and the interaction energy εi/kB. Association is considered as hydrogen bonding, as described by the theory of Wertheim14−17 with two additional parameters: the energy of a hydrogen bond, εHB/RTcrit, and the volume of a

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

water (1) + CH (2) water (1) + toluene (2)d water (1) + CHA (2)d water (1) + CHOH (2)e CH (1) + CHOH (2)e toluene (1) + CHOH (2)e CHA (1) + CHOH (2)e

CC12/K

CC21/K

CT12

CT21

Δp/%a

Δyb

Δxb

519.05 311.50 30.30 −37.96 237.63 480.12 −230.06

1490.82 1016.32 −13.51 285.66 −36.30 −249.96 5.58

0.9863 0.8284 −0.1823 −0.8381 0.7196 −4.3294 4.416

−5.2044 −3.6809 0.8887 1.8672 −0.9133 3.1321 −2.0812

0.99 2.74 2.06 3.23 1.46 0.53 0.79

0.0029 0.0145 0.0185 0.0179 0.0115 0.0049 0.0074

0.000002 0.000008 − 0.0211 − − −

Δp = (100/n)∑(|pcalcd − pexptl|/pexptl), where n is the number of data points. bΔz = (1/n)∑|zcalcd − zexptl|, where z represents x or y. cTaken from ref 11. dTaken from ref 12. eTaken from ref 1. a

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


CC12/K

CC21/K

CT12

CT21

α

Δp/%a

Δyb

Δxb

2723.63 1983.05 1186.17 1238.27 640.75 795.49 −951.95

2163.63 1397.47 −13.11 376.29 184.43 −58.40 1803.76

5.7069 6.0602 − −0.4896 −0.7875 −5.1667 3.2355

−7.7535 −5.3412 − −1.1300 −1.7679 2.1374 −8.5915

0.20 0.20 0.47 0.40 0.47 0.47 0.30

0.88 2.58 1.83 2.95 1.19 0.47 0.75

0.0026 0.0146 0.0187 0.0177 0.0113 0.0047 0.0074

0.000005 0.000076 − 0.0276 − − −

Δp = (100/n)∑(|pcalcd − pexptl|/pexptl), where n is the number of data points. bΔz = (1/n)∑|zcalcd − zexptl|, where z represents x or y. cTaken from ref 11. dTaken from ref 12. eTaken from ref 1. a

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Table 7. Binary Interaction Parameters (Equation 2) for the ESD EOS kC12

kT12/K−1

Δp/%a

Δyb

Δxb

0.137660 0.078281 −0.005326 0.058395 0.005137 0.002703 −0.014400

0.00077250 0.00056063 0.00084086 0.00031177 0.00003488 0.00005625 0.00010546

9.25 11.29 2.29 7.90 1.19 0.59 0.82

0.0706 0.0663 0.0141 0.0172 0.0089 0.0035 0.0089

0.000420 0.000576 − 0.0388 − − −

system c


a Δp = (100/n)∑(|pcalcd − pexptl|/pexptl), where n is the number of data points. bΔz = (1/n)∑|zcalcd − zexptl|, where z represents x or y. cTaken from ref 11. dTaken from ref 12. eTaken from ref 1.

Table 8. Antoine Equationa Parameters for PureComponent Vapor Pressures13 and UNIQUAC Volume (r) and Surface (q) Parameters

a

substance

A

B

C

r

q

water CH toluene CHA CHOH

7.1962 5.9764 6.0758 5.8144 5.9286

1730.63 1206.47 1342.31 1229.42 1199.10

−39.724 −50.014 −53.963 −84.348 −128.150

0.9200 4.0464 3.9228 4.5137 4.3489

1.400 3.240 2.968 3.624 3.512

heterogeneous liquid composition. As at the lower temperature, the vapor composition is predicted correctly for the content of CHOH but the water and CH compositions deviate (cf. Figure 3B). Over all the data points, the predictions of the experimental data show small deviations for the UNIQUAC model (2.3% for vapor pressure, 0.037 for vapor composition) and the ESD EOS (3.2% for vapor pressure, 0.032 for vapor composition). Significantly higher deviations were obtained using the NRTL model (10% for vapor pressure, 0.049 for vapor composition). Water + Toluene + Cyclohexanol. The VL(L)E were characterized at 333.15 K with four homogeneous and six heterogeneous measurement points, at 358.15 K with three heterogeneous measurement points, and at 363.15 K with five homogeneous measurement points. The experimental data are listed in Table 3. Figure 4A shows tie lines with homogeneous and heterogeneous liquid compositions at 333.15 K and, for comparison, the experimental binodal curve at 323.15 K.1 As in the water + CH + CHOH system, Type 2 behavior was observed for this ternary system. The compositions of the organic phase for heterogeneous measurements at 333.15 K show good agreement with the binodal curve at 323.15 K.1 The vapor compositions of heterogeneous measurements have a small portion of high-boiling CHOH and are located on a connecting line between the azeotropic points of the binary water + toluene and toluene + CHOH subsystems. The predicted binodal curves, the predicted vapor compositions at VLLE, and some selected VLLE triangles are shown in Figure 4B. The experimental vapor compositions of the heterogeneous measurements are in good agreement with the predictions. The experimental results at the higher temperatures (358.15 K for heterogeneous measurements

log10(p/kPa) = A − B/(T/K + C)

measurements are presented as triangles. Furthermore, the composition of the vapor phase at VLLE is presented as a dashed line, although the curves of the NRTL and the UNIQUAC model completely overlap. The predicted vapor compositions are in good agreement with the experimental data for the CHOH content. However, the predicted content of CH is too low, and therefore the water content is too high, in the vicinity of the water + CH binary heteroazeotropic point. A spatial representation is displayed in Figure 2 to show the complex behavior of this ternary system. The binary subsystems are plotted as dotted lines. The vapor composition at VLLE is drawn as a long-dashed line and the aqueous branch of the binodal curve, shown at the right of Figure 2, is drawn as a dashed line. The plane defined by the heterogeneous organic liquid phase−vapor phase tie lines is described by all three models. The tie lines with homogeneous liquid composition are located below this plane. The experimental results at 353.15 K are presented in Figure 3A. The predicted binodal curves have been omitted, since only two measurements had a Table 9. Pure-Component Parameters for the ESD EOS substance

ref

c

(εi/kB)/K

b/(cm3/mol)

εHB/RTcrit

KAB/v*

water CH toluene CHA CHOH

18 18 18 12 1

1.0053 1.7843 1.9707 1.1089 1.7888

427.254 329.557 332.752 460.268 381.154

9.411 34.913 36.227 45.806 40.393

4.0000 − − 3.3200 4.2579

0.100 − − 0.0621 0.0022

Table 10. Deviations between Experimental and Predicted Total Pressures and Vapor Compositionsa UNIQUAC

a

NRTL

ESD EOS

system

no. of data points

Δp/%

Δy

Δp/%

Δy

Δp/%

Δy

water + CH + CHOH water + toluene + CHOH water + CHA + CHOH average

26 18 18

2.28 8.28 3.25 4.30

0.0367 0.0214 0.0061 0.0234

10.02 13.38 2.73 8.88

0.0490 0.0316 0.0052 0.0312

3.16 4.44 2.71 3.40

0.0316 0.0176 0.0068 0.0203

Δp = (100/n)∑(|pcalcd − pexptl|/pexptl) and Δy = (1/n)∑|ycalcd − yexptl|, where n is the number of data points. 2692



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Figure 1. Vapor−liquid(−liquid) equilibria in the water (1) + CH (2) + CHOH (3) ternary system at 333.15 K. (A) Experimental results: circle symbols with black tie lines, homogeneous liquid (●) and vapor (○) compositions; square symbols with black tie lines, heterogeneous liquid (organic phase) (■) and vapor (□) compositions; blue solid curve with blue ◆, experimental binodal curve at 323.15 K;1 red ☆, binary heteroazotropic point (from interpolation of experimental data19); red ★, binary heteroazotropic point (from interpolation of experimental data20). (B) Prediction results: green, NRTL; black, UNIQUAC; red, ESD EOS; solid lines, binodal curves at 333.15 K, dashed lines, corresponding vapor compositions (VLLE); triangles, VLLE predictions of selected data points.

and 363.15 K for homogeneous measurements) are presented in Figure 5A, and the predicted vapor−liquid tie lines are shown in Figure 5B. All of the predicted measurement points show higher average deviations of the vapor pressure compared with the water + CH + CHOH system. The deviations of the total pressure are 4.4% for ESD EOS, 8.3% for UNIQUAC, and 13.4% for NRTL. Conversely, the vapor composition predictions have lower deviations: 0.018 for ESD EOS, 0.021 for UNIQUAC, and 0.032 for NRTL. Water + Cyclohexylamine + Cyclohexanol. The LLE of this Type 1 system have been previously determined at 298.15 and 323.15 K.1 The VLE were measured at 333.15 and 363.15 K. The experimental data are presented in Table 4 and in Figures 6 and 7. Nine homogeneous liquid compositions were measured at each temperature. The determined vapor compositions point to the azeotropic compositions of the binary water + CHA and water + CHOH systems. The experimental data at 333.15 K are presented in Figure 6A and the predicted vapor−liquid tie lines in Figure 6B. Additionally, the predicted binodal curves and the vapor compositions at VLLE are shown. Furthermore, the measured binodal curve at 323.15 K1 is drawn to demonstrate the reasonability of the predictions. All of the measured data points lie in the experimentally homogeneous region. Since the calculated heterogeneous region is larger than the experimental heterogeneous region for all three models, three data points are calculated to be heterogeneous with the UNIQUAC and NRTL models at 333.15 K. The measurement results at 363.15 K are presented in Figure 7. The small deviation between the experimental and predicted tie lines confirms the good agreement of the predicted VLE. This result is also confirmed by the numerical values of the deviations: the vapor pressure deviates by 2.7% for NRTL and ESD EOS and by 3.3% for UNIQUAC, and the deviations of the vapor composition are between 0.005 and 0.007. Summary of the Prediction Results. The lowest deviations for vapor pressure and vapor composition were obtained with the ESD EOS for all of the considered systems. The average deviations for the three measured systems are 3.4% for pressure and 0.020 for vapor composition. Slightly higher average deviations were obtained with the UNIQUAC model

Figure 2. Vapor−liquid(−liquid) equilibria in the water (1) + CH (2) + CHOH (3) ternary system at 333.15 K (three-dimensional, with pressure). Experimental results: circle symbols with solid black tie lines, homogeneous liquid (●) and vapor (○) compositions; square symbols with solid black tie lines, heterogeneous liquid (organic phase) (■) and vapor (□) compositions. Lines are calculation results: green, NRTL; black, UNIQUAC; red, ESD EOS; continuous lines, organic branches of the binodal curves; dashed lines, aqueous branches of the binodal curves; long-dashed lines, vapor compositions at VLLE; dotted lines, binary subsystems.

(4.3% for pressure and 0.023 for composition). Significantly greater average deviations were obtained using the NRTL model (8.9% for pressure and 0.031 for composition). The prediction quality was system-dependent. For the water + CHA + CHOH ternary system, by far the best prediction results were obtained for the investigated models. 2693



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Figure 3. Vapor−liquid equilibria in the water (1) + CH (2) + CHOH (3) ternary system at 353.15 K. (A) Experimental results: circle symbols with black tie lines, homogeneous liquid (●) and vapor (○) compositions; square symbols with black tie lines, heterogeneous liquid (organic phase) (■) and vapor (□) compositions. (B) Predicted vapor−liquid tie lines: green, NRTL; black, UNIQUAC; red, ESD EOS.

Figure 4. Vapor−liquid(−liquid) equilibria in the water (1) + toluene (2) + CHOH (3) ternary system at 333.15 K. (A) Experimental results: circle symbols with black tie lines, homogeneous liquid (●) and vapor (○) compositions; square symbols with black tie lines, heterogeneous liquid (organic phase) (■) and vapor (□) compositions; blue solid curve with blue ◆, experimental binodal curve at 323.15 K;1 red ☆, binary heteroazotropic point (from interpolation of experimental data19); red ★, binary heteroazotropic point (from interpolation of experimental data21). (B) Prediction results: green, NRTL; black, UNIQUAC; red, ESD EOS; solid lines, binodal curves at 333.15 K; dashed lines, corresponding vapor compositions (VLLE); triangles, VLLE predictions of selected data points.

Figure 5. Vapor−liquid equilibria in the water (1) + toluene (2) + CHOH (3) ternary system at 358.15 and 363.15 K. (A) Experimental results: square symbols with black tie lines, heterogeneous liquid (organic phase) (■) and vapor (□) compositions at 358.15 K; circle symbols with black tie lines, homogeneous liquid (●) and vapor (○) compositions at 363.15 K. (B) Predicted vapor−liquid tie lines: green, NRTL; black, UNIQUAC; red, ESD EOS. 2694



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Figure 6. Vapor−liquid equilibria in the water (1) + CHA (2) + CHOH (3) ternary system at 333.15 K. (A) Experimental results: circle symbols with black tie lines, homogeneous liquid (●) and vapor (○) compositions; blue solid curve with blue ◆ symbols, experimental binodal curve at 323.15 K.1 (B) Prediction results: green, NRTL; black, UNIQUAC; red, ESD EOS; continuous lines, predicted vapor−liquid tie lines and binodal curves; dashed lines, corresponding vapor compositions (VLLE).

ORCID

Mandy Klauck: 0000-0001-8922-8295 Funding

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

The authors declare no competing financial interest.

■ Figure 7. Vapor−liquid equilibria in the water (1) + CHA (2) + CHOH (3) ternary system at 363.15 K. Experimental results: circle symbols with dotted tie-lines, homogeneous liquid (●) and vapor (○) compositions. Solid lines are predicted vapor−liquid tie lines: green, NRTL model; black, UNIQUAC model; red, ESD EOS.

5. CONCLUSION The isothermal VL(L)E data of the water + CHOH + organic component (CH, toluene, or CHA) ternary systems were determined by the dynamic method in a modified Röck and Sieg circulation still at different temperatures and reduced pressures. The VL(L)E were predicted with the UNIQUAC model, the NRTL model, and the ESD EOS using binary interaction parameters. Comparisons of the predicted and experimental data yielded the following results: The lowest deviations for vapor pressure and vapor composition were obtained with the ESD EOS, followed by the UNIQUAC model and, with significantly greater deviations, the NRTL model. The same order of prediction quality of the thermodynamic models was ascertained for LLE prediction.1

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LIST OF SYMBOLS

A, B, C parameters of the Antoine equation 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 measure of bonding volume (ESD EOS) n number of data points p pressure q UNIQUAC surface parameter R gas constant r UNIQUAC volume parameter T temperature u interaction energy (UNIQUAC) u measurement uncertainty b molar characteristic size parameter (ESD EOS) x liquid mole fraction y vapor mole fraction Δ deviation ε potential energy well depth (ESD EOS) v* molecular characteristic size parameter (ESD EOS) Subscripts

calcd calculated crit critical exptl experimental HB hydrogen bond i, j components

AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 351 462 2373. Fax: +49 351 462 2151. E-mail: [email protected]. 2695



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(20) Landauer, O.; Mateescu, C.; Iulian, O.; Geana, D. Experimental determination of liquid-vapor equilibrium curves and correlation by different activity models for the cyclohexane-chlorocyclohexane and cyclohexane-water systems. Rev. Roum. Chim. 1988, 33, 237−251. (21) Omoto, T.; Ezaki, M. Determination of vapor liquid equilibriums by dynamic distillation method. Kagaku Kogaku 1966, 30, 709−711.

C constant temperature part T temperature-dependent part

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REFERENCES

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