m ELSEVIER Fluid Phase Equilibria 131 (1997) 181-188

Vapor-liquid equilibria of the ternary system methanol + acetone + methyl vinyl ketone at atmospheric pressure

Chein-Hsiun Tu a, *, Yuh-Shen Wu b, Tzu-Ling Liu a

Industrial Safety and Hygiene Department, Hung Kuang Institute of Medical and Nursing Technology, Taichung 43301, Taiwan

b Applied Chemistry Department, Providence University, Taichung 43301, Taiwan

Received 3 September 1996; accepted 25 October 1996

Abstract

Isobaric vapor-liquid equilibrium (VLE) data at atmospheric pressure for the ternary system methanol + acetone + methyl vinyl ketone have been experimentally obtained. The measurements were conducted in a two-phase recirculation still. The experimental VLE data were correlated according to the Margules, Wilson, NRTL and UNIQUAC equations. The ternary VLE data were predicted from their constituent binaries. A comparison of model performances was made using the criterion of average absolute deviations in boiling point and in vapor-phase composition. © 1997 Elsevier Science B.V.

Keywords: Experiments; Ternary data; Vapor-liquid; Methyl vinyl ketone

1. Introduction

Distillation has been used as an effective means of separation in chemical processes. Knowledge of the conditions of equilibrium between separable phases is essential for the analysis and design of industrial separation processes. However, the complexity and arduousness of the experimental determination of vapor-liquid equilibrium (VLE) data increase significantly as the number of components in the system rises. Therefore, it is of great importance to study and evaluate the methods for calculating the equilibrium characteristics of multicomponent systems by comparison with experimental results.

VLE data for the ternary system methanol + acetone + methyl vinyl ketone are not available in the literature. In this paper, we measure the isobaric VLE data for the ternary mixture methanol + acetone

* Corresponding author.

0378-3812/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0378-381 2 ( 96 ) 032 12-8

182 C.-H. Tu et al. / Fluid Phase Equilibria 131 (1997) 181-188

+ methyl vinyl ketone at atmospheric pressure, and correlate the vapor-liquid information with four methods, such as three-suffix Margules [1], Wilson [2], NRTL [3] and UNIQUAC [4]. Using the constituent binary parameters, this article compares the experimental results with those calculated from the four methods. This work is part of our research program, the purpose of which is the study of a possible manufacturing route to methyl vinyl ketone, which is obtained by alcoholysis of acetone with methanol.

2. Experimental appratus and procedure

The chemicals used were from Aldrich (USA). The purities were: methanol, 99.9%; acetone, 99.9 + %; and methyl vinyl ketone, 99%, stabilized with 0.1% acetic acid and 0.05% hydroquinone. The purity of all the chemicals was checked by gas chromatography. All chemicals were used after reduction of water with molecular sieves having a pore diameter of 0.3 nm.

The Hunsmann [5] equilibrium still (NGW/Germany) with a provision for both vapor and liquid recirculation was used for the measurements. The still has a total capacity of about 100 cm 3. The equilibrium temperature was measured with a calibrated Pt-100 resistance thermometer to an accuracy of ___ 0. I°C, and the pressure was measured with a piezo-resistive absolute-pressure transducer to an accuracy of + 0.5 kPa.

The sample for experimental runs was prepared by mixing weighed amounts of the three components. Steady-state conditions were reached after about 1-2 h, as indicated by the constant boiling temperatures of the liquid and vapor phases within the equilibrium cell. The system was allowed to maintain this equilibrium state for about 30 min, before samples were taken.

The compositions of the sampled liquid and condensed vapor phases were analyzed with a Perkin-Elmer Autosystem gas chromatograper, after calibration with gravimetrically prepared stan-

Itt dard solutions. A flame ionization detector was used together with a Porapak Q 10 feet × ~ SS packed column. The gas chromatography response peaks were integrated using a Perkin-Elmer 1020 integrator. At least two analyses were made of each liquid and each vapor composition. The accuracy of liquid and vapor mole fractions was estimated as + 0.001.

3. Results and discussions

Altogether, 32 experimental VLE measurements for the methanol + acetone + methyl vinyl ketone ternary system were obtained at atmospheric pressure and are presented in Table 1. This table gives the boiling point temperatures, liquid and vapor compositions, activity coefficients and atmospheric pressures. The experimental temperatures, which have been corrected to 101.3 kPa, are also presented and denoted as too. The corrections have been taken as corresponding to a 1 kPa increase in pressure between 99.5 and 101.3 kPa, which gives values of 0.245°C kPa- ~ for methanol, 0.291°C kPa- l for acetone and 0.304°C kPa-1 for methyl vinyl ketone. For all mixtures, the mean values have been assumed to depend on the proportions of each constituent present. The related composition diagram for the ternary system is reproduced in Fig. 1.

The data for this ternary system were used to determine the capabilities of various equations to

C.-H. Tu et al. / Fluid Phase Equilibria 131 (1997) 181-188 183

Table 1 Vapor-liquid equilibrium data for methanol(l)+ acetone(2)+ methyl vinyl ketone(3) at atmospheric pressure

P (kPa) t (°C) too (°C) x t x2 Yl Y2 3q 3/2 3'3

99.8 56.6 57.0 0.122 0.798 0.135 0.828 1.493 1.008 1.031 99.8 58.2 58.6 0.207 0.611 0.226 0.683 1.380 1.030 1.052 99.8 58.5 58.9 0.301 0.514 0.309 0.597 1.281 1.060 1.058 99.8 58.2 58.6 0.110 0.713 0.131 0.783 1.505 1.012 1.022 99.9 59.1 59.5 0.394 0.416 0.387 0.511 1.198 I. 100 1.095

100.2 60.0 60.3 0.483 0.319 0.464 0.423 1.133 1.157 1.131 99.9 60.6 61.0 0.303 0.401 0.334 0.502 1.266 1.068 1.071

100.1 61.3 61.6 0.575 0.212 0.554 0.313 1.078 1.235 1.180 99.7 60.4 60.9 0.204 0.490 0.243 0.591 1.377 1.034 1.054 99.6 61.1 61.5 0.758 0.146 0.692 0.244 1.025 1.400 1.263

100.3 61.3 61.6 0.758 0.145 0.693 0.242 1.025 1.399 1.270 99.9 61.4 61.8 0.393 0.297 0.419 0.397 1.186 1.112 1.115 99.8 62.6 63.0 0.482 0.197 0.507 0.287 1.115 1.166 1.155 99.9 63.2 63.6 0.675 0.103 0.670 0.174 1.029 1.328 1.240

100.5 62.6 62.8 0.205 0.380 0.265 0.492 1.381 1.043 1.061 99.7 63.4 63.9 0.102 0.452 0.151 0.588 1.521 1.014 1.023 99.7 63.2 63.7 0.292 0.276 0.359 0.376 1.273 1.068 1.080 99.6 62.4 62.9 0.601 0.153 0.596 0.240 1.508 1.261 1.206 99.8 64.0 64.4 0.384 0.185 0.450 0.269 1.177 1.113 1.117 99.6 65.1 65.6 0.456 0.097 0.533 0.153 1.123 1.165 1.157 99.6 65.1 65.6 0.200 0.270 0.286 0.377 1.374 1.031 1.047

100.1 66.2 66.6 0.093 0.341 0.156 0.481 1.553 1.010 1.022 100.3 66.7 66.9 0.248 0.162 0.358 0.241 1.314 1.053 1.066 100.1 67.5 67.8 0.310 0.082 0.437 0.129 1.242 1.084 1.088 100.2 68.1 68.4 0.096 0.258 0.173 0.387 1.548 1.012 1.014 99.8 67.2 67.6 0.208 0.169 0.321 0.253 1.377 1.042 1.054 99.9 67.5 67.9 0.109 0.260 0.191 0.385 1.540 1.017 1.021 99.7 69.5 70.0 0.213 0.070 0.358 0.113 1.371 1.045 1.049 99.7 71.4 71.9 0.143 0.064 0.283 0.107 1.502 1.021 1.024 99.7 70.3 70.8 0.101 0.156 0.201 0.251 1.573 1.015 1.019 99.7 73.8 74.3 0.078 0.062 0.187 0.111 1.668 1.019 1.004 99.8 60.4 60.8 0.109 0.589 0.142 0.698 1.508 1.017 1.030

either correlate or predict ternary behavior. The liquid-phase activity coefficients of the components in a non-ideal mixture were calculated from

4~,Pyi = y iP,°xic~;exp[ v~( P - P , ° ) / R T ] (1)

where x i and Yi are the liquid and vapor mole fractions in equilibrium, respectively, ~bi is the fugacity coefficient, P is the total pressure, ~/i is the activity coefficient, ~b~ is the pure-component fugacity coefficient at saturation, P~° is the pure-component vapor pressure, and v; is the liquid molar volume. The vapor-phase fugacity coefficients were calculated from the Soave-Redlich-Kwong (SRK) equation of state [6], where the binary interaction parameter, k~j, was set at zero. The vapor pressures of the pure components were calculated from

ln (P° /Pa) = A + B / ( T / K ) + C In(T/K) + D ( T / K ) e (2)

184 C.-H. Tu et al. / Fluid Phase Equilibria 131 (1997) 181-188

Methanol

~ . ~.~

O Vapor phase ~, °

'+

0.0 O.f 0.2 0.3 0.4 0.5 0.6 0."/ 0.8 0.9 t,O

Acetone MVK

Fig. 1. Composition chart of the ternary mixture methanol + acetone + methyl vinyl ketone at atmospheric pressure.

where A, B, C, D and E are coefficients. The liquid molar volumes were calculated from the Rackett equation as modified by Spencer and Danner [7].

Table 2 presents the parameters pertaining to this investigation. This table includes the vapor-pres- sure constants (A, B, C, D and E), critical properties, acentric factor, Rackett constant and UNIQUAC parameters for each component. The vapor-pressure constants of methanol, acetone and methyl vinyl ketone were obtained from a regression of the data sources reported by Boubl~ et al. [8] and Jakub~Eek [9]. The critical properties, acentric factors and Rackett constants of methanol and acetone were obtained form Reid et al. [10]. The critical temperature of methyl vinyl ketone was

Table 2

Physical properties for the methanol(I) + acetone(2) + methyl vinyl ketone(3) system

Parameter Methanol Acetone Methyl vinyl ketone

A 81.768 70.720 24.161

B - 6876.0 - 5685.0 - 4095.4

C - 8.7078 - 7.3510 - 0.1832

D 7.1926 X 10 -6 6.3000 X 10 -6 9.5026 X 10 -8

E 2 2 2

T c (K) 512.6 508.1 535.0

Pc (bar) 80.9 47.0 47.9

~o 0.564 0.304 0.402

ZRA 0.2334 0.2477 0.2508

r 1.4311 2.5735 3.2479

q 1.432 2.3359 2.8759

" l n ( P ° / P a ) = A + B / ( T / K ) + C I n ( T / K ) + D ( T / K ) E.

C.-H. Tu et al. / Fluid Phase Equilibria 131 (1997) 181-188 185

obtained by averaging the values estimated from two group-contribution methods [11,12]. The critical pressure and acentric factor of methyl vinyl ketone were then determined using Eq. (2). The Rackett constant of methyl vinyl ketone was estimated from the method proposed by Vetere [13]. The UNIQUAC parameters depend only on the molecular structure of the pure components and have been obtained from Fredenslund et al. [14].

The experimental VLE data of the ternary system were fitted with the three-suffix Margules, Wilson, NRTL and UNIQUAC equations by a bubble temperature calculation procedure [15]. Estimation of the energy parameters of all the models studied was based on minimization of the objective function F in terms of predicted and experimental Yi values. The function F for a ternary system can be stated as

F = E E -- (3) k i = 1 "~? k

where N is the number of data points, and the superscripts 'e' and 'c' indicate experimental and calculated values, respectively. The fitted binary parameters together with the mean and maximum values of the absolute deviations in boiling point, 6 , and in vapor-phase mole fraction, 6y, for the correlation are shown in Table 3. The four methods used gave almost the same accuracy in the correlation of the ternary system. However, the Wilson equation yields the best overall results.

Table 3

Correlation result of the ternary system methanol ( 1 ) + acetone(2)+ methyl vinyl ketone(3) for various methods

Parameter ~ Margules b Wilson N R T L U N I Q U A C

A 12 0 .47102 307.68 136.61 - 43 .506

A13 0 .64882 572.72 - 193.73 - 169.70

A21 0.54409 - 109.72 50.510 190.42

A23 - 0 .10435 20.548 - 211.72 - 138.88

A31 0.30111 -- 314.60 475.12 434.39

A 32 - - 0.06002 - 0 .85626 281.87 187.73

0/12 0 .26808

%3 0 .31889

0/23 0 .30238 Mean 6 t (°C) 0.13 0.09 0.10 0.12

Max. 6 t (°C) 0.25 0.26 0.35 0.39

Mean 6,q 0 .0024 0 .0008 0 .0009 0 .0009

Max. 6,. l 0.0059 0 .0027 0 .0022 0 .0019

Mean 6,, 2 0.0025 0 .0009 0.0015 0 .0019

Max. 8,. 2 0.0059 0 .0026 0 .0039 0.0045

Wilson parameter: Aij = (Aq - Aii)/R. N R T L parameter: Aii= (gij - g i j ) /R. U N I Q U A C parameter : Aii= (Uij - ~;)/R. b Three-suffix Margules equation:

l n y i = (1 - xi) [ a i + 2 x i ( B i - a i ) ] where

-- ~ xjAij B i = j ~ ' xjAji A i - (l----ffi) ( l~- xi) j = l =

186 C-H. Tu et aL / Fluid Phase Equilibria 131 (1997) 181-188

Table 4 Average absolute deviations for the prediction of the methanol(l)+ acetone(2)+ methyl vinyl ketone(3) ternary from constituent binaries

6 Margules Wilson NRTL UNIQUAC

Mean 8, (°C) 0.64 0.25 O. 15 O. 15 Max. 6 t (°C) 1.09 0.61 0.46 0.46 Mean 6y I 0.0049 0.0028 0.0022 0.0024 Max. 8,. 1 0.0129 0.0078 0.0052 0.0059 Mean 6y 2 0.0058 0.0036 0.0026 0.0026 Max. ~y2 0.0117 0.0067 0.0052 0.0059

In a previous paper [16], VLE measurements for the constituent binaries of methanol, acetone and methyl vinyl ketone were reported. The VLE information of these three binaries was used to determine the parameters for the Margules, Wilson, NRTL and UNIQUAC methods. In this study, the ternary data were used to examine the capabilities of the four methods to predict ternary behavior from their constituent binary parameters. The results from all these methods are summarized in Table 4. Of these predictive methods, the NRTL equation best predicted the temary data, followed by the UNIQUAC, Wilson and three-suffix Margules equations. Surprisingly, the three-suffix Margules equation yielded the poorest results among all the methods, despite the fact that the three-suffix Margules equation was able to correlate the ternary behavior very well.

4. Conclusion

The experimental VLE data on a ternary system formed by methanol, acetone and methyl vinyl ketone are determined at atmospheric pressure. Analysis of experimental data for the temary system using the three-suffix Margules, Wilson, NRTL and UNIQUAC equations shows that all four equations are generally satisfactory for the system. In this context, the Wilson equation yields the best overall results.

Inspection of various predictions for the ternary equilibrium of the system methanol + acetone + methyl vinyl ketone based on the information of the constituent binaries shows that although all four methods used (Margules, Wilson, NRTL and UNIQUAC) may be deemed satisfactory, the NRTL method exhibits rather smaller deviations from the experimental results than the others. The predictive capability of the three-suffix Margules equation proves limited for this ternary system, despite the fact that it was able to correlate the ternary behavior very well.

5. List of symbols

A12, A21

mi j , A j i A , B , C , D , E F

parameters of the liquid activity coefficient model parameters used in three-suffix Margules equation constants of the pure-component vapor-pressure equation objective function

C-H. Tu et al . / Fluid Phase Equilibria 131 (1997) 181-188 187

gij' gjj k i j

MVK N P e i ° R r , q

t

tco

T

uij, u i x i

Yi ZRA

5.1. Greek letters

Ol i j

hi j , hii

4,, oo

5.2. Subscripts

1,2 ,3 , i, j CO

t

Y

5.3. Superscripts

NRTL parameters (cal tool -1) binary interaction parameter of the SRK equation of state methyl vinyl ketone number of experimental points system pressure vapor pressure of pure component i universal gas constant molecular parameters for the UNIQUAC equation boiling temperature (°C) boiling temperature corrected to 101.3 kPa (°C) temperature (K) UNIQUAC parameters (cal mol - l ) saturated molar volume of pure component i mole fraction of component i in the liquid phase mole fraction of component i in the vapor phase Rackett equation parameter

NRTL parameter liquid-phase activity coefficient for component i average absolute deviation Wilson parameters (cal mol -~) fugacity coefficient of component i acentric factor

components corrected value to 101.3 kPa temperature vapor-phase mole fraction

c calculated value e experimental value s saturated state o pure component

Acknowledgements

The authors wish to extend their deep gratitude for the support by the National Science Council of the Republic of China under grant NSC 84-2214-E126-001.

188 C.-H. Tu et a l . / Fluid Phase Equilibria 131 (1997) 181-188

References

[1] J.M. Prausnitz, R.N. Lichtenthaler and E. Gomes de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd edn., Prentice-Hall, Englewood Cliffs, N J, 1986.

[2] G.M. Wilson, J. Am. Chem. Soc., 86 (1964) 127-130. [3] H. Renon and J.M. Prausnitz, AIChE J., 14 (1968) 135-144. [4] D.S. Abrams and J.M. Prausnitz, AIChE J., 21 (1975) 116-128. [5] W. Hunsmann, Chem.-Ing.-Tech., 39 (1967) 1142-1145. [6] G. Soave, Chem. Eng. Sci., 27 (1972) 1197-1203. [7] C.F. Spencer and R.P. Danner, J. Chem. Eng. Data, 17(2) (1972) 236-241. [8] T. Boublik, V. Fried and E. Hala, The Vapor Pressure of Pure Substances, 2nd edn., Elsevier Science, New York, 1984. [9] J. Jakubicek, Collect. Czech. Chem. Commun., 26 (1961) 300-305.

[10] R.C. Reid, J.M. Prausnitz and B.E. Poling, The Properties of Gases and Liquids, 4th edn., McGraw-Hill, New York, 1987.

[11] C.H. Tu, Chem. Eng. Sci., 50(22)(1995) 3515-3520. [12] R.F. Fedors, Chem. Eng. Commun., 16 (1982) 149-151. [13] A. Vetere, Chem. Eng. J,, 49 (1992) 27-33. [ 14] A. Fredenslund, J. Gmehling and P. Rasmusen, Vapor-Liquid Equilibria Using UNIFAC, Elsevier, Amsterdam, 1977. [15] J.M. Smith and H.C. Van Ness, Introduction to Chemical Engineering Thermodynamics, 4th edn., McGraw-Hill, New

York, 1987. [16] C.H. Tu, Y.S. Wu and T.L. Liu, Fluid Phase Equilibria, in press.