carbon dioxide at high pressure conditions

Fluid Phase Equilibria 267 (2008) 104–112

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Phase equilibria of the ternary system vinyl acetate/(R,S)-1-phenylethanol/carbon dioxide at high pressure conditions Alexandre Paiva, Krasimir Gerasimov, Gerd Brunner ∗ Technische Universit¨ at Hamburg-Harburg, Institut f¨ ur Thermische Verfahrenstechnik, Eissendorfer Strasse 38, D-21073 Hamburg, Germany

a r t i c l e

i n f o

Article history: Received 29 August 2007 Received in revised form 12 February 2008 Accepted 14 February 2008 Available online 17 February 2008 Keywords: Phase equilibrium Supercritical carbon dioxide Cubic equation of state Phenylethanol Vinyl acetate Group contribution method

a b s t r a c t Phase equilibrium measurements, correlations and predictions are presented for the binary systems (R,S)-1-phenylethanol/CO2 and vinyl acetate/CO2 and for the ternary system vinyl acetate/(R,S)-1phenylethanol/CO2 . Experiments for the ternary system were performed in the temperature range of 323–343 K and in the pressure range of 7–12 MPa, using a high pressure phase equilibrium apparatus with a high pressure visual variable volume cell. Phase compositions were determined by taking samples of each phase and analysing them by gas chromatography. Equilibrium data were correlated with the Peng–Robinson equation of state combined with the Mathias–Klotz–Prausnitz mixing rule. A good correlation of both phases behaviour was obtained with an average absolute deviation (AAD) of 6.80%. Predictions for the binary sub-systems and for the ternary system were performed using the Peng–Robinson and the Soave–Redlich–Kwong equation of state, with the predictive mixing rule MHV1. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The structural difference between enantiomers can be important with respect to the actions of synthetic drugs. Chiral receptor sites in the human body interact only with drug molecules having the proper absolute configuration, resulting in marked differences in the pharmacological activities of enantiomers. The most effective way for separating enantiomers is by using enzymes as reaction catalysts. Enzymes can distinguish substances on the molecular level very efficiently. They can catalyze bio-transformations, where basically only one of the enantiomers is chemically modified. In an attempt to solve the problems that enzymatic reactions sometimes pose, some progress has been made by adding organic solvents [1], working with high salt concentrations [2], and using micro-emulsions [3] or supercritical fluids [4] as reaction media. The use of supercritical fluids in this type of reactions can be advantageous for a variety of reasons. By knowing the phase behaviour of the system at hand the supercritical fluid can be used not only as the reaction medium but also as the separation medium for the extraction and fractionation of products. By changing pressure and temperature of the supercritical carbon dioxide (scCO2 ) the solubility of the compounds can be varied by changing the density. Therefore a very simple and high efficient separation is

∗ Corresponding author. Tel.: +49 40428783040; fax: +49 40428784072. E-mail address: [email protected] (G. Brunner). 0378-3812/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2008.02.010

possible using two or more separators operating at different pressure and temperature conditions. Another important advantage of using a supercritical fluid as a reaction medium is that it lowers the viscosity of the reaction medium which allows a more rapid diffusion giving faster reactions when the reactions are diffusion controlled like is the case of enzymatic reactions. Supercritical fluids like scCO2 are considered to be green solvents which bring environment advantages [5,6]. As it was said before, it is important to study not only the reactions themselves but to extend the research to what happens before and after the reaction takes place. This involves the phase equilibrium measurements of the reactants and products of the reaction. Only with this knowledge is it possible to accurately design a complete industrial process involving enzyme-catalyzed reactions. In this work, the separation of the enantiomers (R,S)-1phenylethanol by means of a biocatalytical reaction catalyzed by a lipase (Fig. 1) under scCO2 was chosen as a model reaction. scCO2 will act as the carrier of the reactants, as the solvent in the reaction and as the solvent in the extraction and separation of the reaction products. For that the phase equilibrium of the ternary system (R,S)1-phenylethanol/vinyl acetate/CO2 was studied and the experimental pTxy data were correlated using the Peng–Robinson equation of state [7] with the Mathias–Klotz–Prausnitz mixing rule [8]. Since chemical process design is often concerned with separation of fluid mixtures, reliable knowledge of the phase equilibrium behaviour as function of pTxy of multi-component mixtures is a prerequisite for the synthesis and optimization of separation pro-

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105

Fig. 1. Scheme for the transesterification reaction of (R,S)-1-phenylethanol with vinyl acetate catalyzed by a lipase.

cesses. It is frequently necessary to estimate the phase behaviour of the system at hand. In the cases were phase equilibrium data are available, such estimations can usually be done with ease. In many other cases, where the required experimental data are not available, it is difficult to make even rough estimates on a rational basis. Where no data is available and/or the interaction parameters of the mixture are not known, it is necessary to take on a different approach. The predictive, group contribution methods like UNIFAC [9] can predict vapour–liquid equilibria of systems with high non-idealities, but they are unable to treat systems containing gaseous components. In order to achieve optimum condition for operation and separation with a minimum of experimental data the method combining an equation of state with a gE mixing rule was used. Two equations of state were tested with this method, the Soave–Redlich–Kwong and the Peng–Robinson equations. To obtain an equation of state for predicting vapour–liquid equilibria of polar and non-polar mixtures modifications are necessary. The three adjustable parameters used in the Mathias–Copeman equation [10] improve the description of the pure component vapour pressures for polar components. As previously mentioned, a predictive mixing rule is necessary for the prediction of the parameter a. Density-independent predictive mixing rules like the MHV1 [11] link the mixture parameter a with the excess Gibbs energy g0E at zero pressure. The pressure dependence of gE is small at low

pressures, which means that any group contribution method like UNIFAC can be used to calculate g0E [12]. In this work phase equilibrium measurements were made at temperatures of 323, 333 and 343 K and pressures between 7 and 12 MPa using a high pressure visual cell with variable volume. Simulation of phase equilibrium of the system and its sub-systems were carried out using the program package PE [13]. 2. Experimental section 2.1. Materials The phase behaviour of the reactants in the transesterification reaction presented in Fig. 1 is going to be studied. The (R,S)-1-phenylethanol was supplied by Fluka and has a purity of 98%. The vinyl acetate was supplied by Merck and has ¨ a purity of 99%. CO2 was supplied by KWD Kohlensaurewerk ¨ Deutschland GmbH (Bad Honningen) and has a purity of 99.95%. 2.2. Apparatus and experimental procedure The phase equilibrium measurements were made according to the analytical method using a visual high pressure variable volume cell. Samples were taken both from the liquid and vapour phases.

Fig. 2. Schematic diagram of the phase equilibrium apparatus with a variable volume high pressure visual cell: C, gas compressor; V, valve; PI, pressure indicator; TI, temperature indicator; TIC, temperature controller; P, liquid pump; T, glass trap; FM, gas flow meter; B1, water bath; B2, dry ice/acetone bath.

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Fig. 3. Measured molar fractions of CO2 at 333 K for several feed mass compositions of (R,S)-1-phenylethanol (PhEtOH) on a solvent-free basis: (䊉) 0.0 mass fraction of PhEtOH, () 0.154 mass fraction of PhEtOH, () 0.397 mass fraction of PhEtOH, () 0.753 mass fraction of PhEtOH, () 1.0 mass fraction of PhEtOH. Lines represent correlated pTxy experimental data with the Peng–Robinson EOS and the Mathias–Klotz–Prausnitz mixing rule using the program package PE.

Fig. 4. Separation factors between vinyl acetate (ViAc) and (R,S)-1-phenylethanol (PhEtOH) as a function of pressure for a feed mass composition of (R,S)-1phenylethanol on a solvent free basis of 0.753: (䊉) 323 K, () 333 K and () 343 K. Lines represented are just guide-lines.

A schematic diagram of the phase equilibrium cell used is represented in Fig. 2. Before the experimental runs the cell was heated to the desired temperature, by heating the water bath B1 using the temperature controller TC1. After the temperature was stable, air was removed

from the cell by the vacuum pump P2 with the valves V4, V5 and V6 open. When an acceptable vacuum was achieved, the valves V4–V6 were closed and a previously prepared mixture of (R,S)-1phenylethanol and vinyl acetate was loaded into the cell by the

Table 1 Vapour–liquid equilibrium data for the ternary system vinyl acetate (1)/(R,S)-1-phenylethanol (2)/CO2 (3) T (K) 323

(R,S)-1-Phenylethanol mass fraction in feed

p (MPa)

x1

x2

x3

y1

y2

y3

0.154

7.0 9.0 7.0 9.0 9.0 10.0 9.0 10.0 12.0

0.3128 0.1149 0.3087 0.1260 0.1536 0.1999 0.1937 0.1221 0.1109

0.0818 0.0340 0.1166 0.0773 0.3753 0.3193 0.4141 0.4299 0.4188

0.6054 0.8510 0.5747 0.7967 0.4711 0.4808 0.3922 0.4480 0.4703

0.0051 0.0046 0.0040 0.0037 0.0011 0.0066 0.0005 0.0011 0.0048

0.0004 0.0008 0.0003 0.0009 0.0008 0.0066 0.0006 0.0018 0.0096

0.9945 0.9946 0.9956 0.9954 0.9982 0.9868 0.9989 0.9972 0.9856

7.0 9.0 10.0 7.0 9.0 10.0 7.0 9.0 10.0 12.0 7.0 9.0 10.0 12.0

0.2842 0.1690 0.1459 0.2318 0.2753 0.1568 0.2979 0.1587 0.1702 0.1449 0.2250 0.1632 0.1641 0.1672

0.0615 0.1074 0.0614 0.2404 0.1597 0.1124 0.4575 0.4498 0.3606 0.4130 0.5498 0.4951 0.4150 0.3533

0.6543 0.7235 0.7927 0.5278 0.5650 0.7308 0.2447 0.3914 0.4692 0.4421 0.2252 0.3417 0.4209 0.4795

0.0020 0.0014 0.0040 0.0010 0.0037 0.0034 0.0022 0.0007 0.0019 0.0043 0.0009 0.0003 0.0008 0.0015

0.0002 0.0003 0.0013 0.0002 0.0007 0.0015 0.0003 0.0003 0.0014 0.0053 0.0001 0.0002 0.0014 0.0037

0.9978 0.9983 0.9947 0.9988 0.9956 0.9951 0.9975 0.9989 0.9967 0.9904 0.9990 0.9994 0.9977 0.9948

7.0 9.0 10.0 7.0 9.0 10.0 12.0 7.0 9.0 10.0 12.0 9.0 10.0 12.0

0.4827 0.2824 0.1874 0.3455 0.2778 0.2143 0.0875 0.2098 0.1967 0.1669 0.1868 0.2102 0.1700 0.1858

0.1317 0.1375 0.0747 0.1562 0.1968 0.2575 0.1448 0.4217 0.4076 0.4091 0.4183 0.4668 0.4607 0.3930

0.3856 0.5801 0.7379 0.4983 0.5254 0.5282 0.7677 0.3686 0.3957 0.4240 0.3949 0.3230 0.3693 0.4212

0.0040 0.0024 0.0043 0.0027 0.0038 0.0100 0.0062 0.0013 0.0011 0.0008 0.0016 0.0011 0.0007 0.0012

0.0003 0.0003 0.0005 0.0002 0.0005 0.0015 0.0051 0.0004 0.0002 0.0004 0.0029 0.0008 0.0007 0.0025

0.9958 0.9974 0.9952 0.9971 0.9957 0.9885 0.9887 0.9983 0.9987 0.9988 0.9955 0.9981 0.9986 0.9963

0.397 0.753 0.898

333

0.154

0.397

0.753

0.898

343

0.154

0.397

0.753

0.898

p is the total pressure and x and y represents the molar fraction of each component in the liquid and vapour phase, respectively.

A. Paiva et al. / Fluid Phase Equilibria 267 (2008) 104–112

valve V3. Temperature and pressure inside the cell were measured in the temperature indicator TI1 and in the pressure indicator PI1. CO2 was compressed with the C1 compressor and then inserted into the cell through the valve V1 to the desired pressure. Before each sample was taken the system inside the cell was stirred for 1 h and then let to rest for 30 min. Vacuum was then applied to the sampling line. Samples from the gas phase were taken through the valve V4 and samples for the liquid phase were taken through the valve V6. Valve V5 was used in case of the existence of a second liquid phase. The samples were taken to the glass trap T1 under vacuum and cooled in B2 with a mixture of dry ice and acetone. In this trap the liquid was separated from the CO2 . The CO2 amount in the sample was measured by the flow meter FM1. During the sampling the pressure inside the cell was maintained constant by moving the piston and decreasing the volume. The piston moves by pumping water to the piston’s back using an automatic water pump P1, so by increasing the pressure of water the piston moves forward and by decreasing the pressure of water the piston moves backwards. The water pressure was controlled with the help of the pressure indicator PI2. Each experiment consists in taking around six samples of each phase. The reproducibility of the method was checked by randomly selecting a pair of pressure and temperature conditions and repeating the experimental trial. Reproducibility varied by less than 3% of the mean value. The liquid composition of each sample was measured by a HP5890 GC with a J&W SCIENTIFIC (30 m length, 0.25 mm internal diameter, 0.1 ␮m film) column. A solution of hexadecane in n-hexane (0.18 g/l) was used as the standard. The retention time for the (R,S)-1-phenylethanol was 5.4 min and for the hexadecane (standard) was 9.2 min.

Fig. 5. Separation factors between vinyl acetate (ViAc) and (R,S)-1-phenylethanol (PhEtOH) at 333 K and 9.0 MPa for several feed mass compositions of 1phenylethanol on a solvent free basis: () 0.154 mass fraction of PhEtOH, () 0.397 mass fraction of PhEtOH, () 0.753 mass fraction of PhEtOH and () 0.898 mass fraction of PhEtOH. Lines represented are just guide-lines.

the higher solubility of vinyl acetate in CO2 in comparison with (R,S)-1-phenylethanol. The higher selectivity of CO2 towards vinyl acetate instead of (R,S)-1-phenylethanol can be better seen by analysis of the separation factor ˛, that evaluates the capability of a solvent to separate two compounds at the determined conditions of temperature, pressure and feed composition. This parameter is calculated from the compositions of the vapour and liquid phase of vinyl acetate and (R,S)-1-phenylethanol:

3. Results and discussion ˛= Isothermal vapour–liquid phase equilibria were measured at 323, 333 and 343 K for the ternary system vinyl acetate/(R,S)1-phenylethanol/CO2 , in the pressure range of 7–12 MPa. Four different feed compositions were studied: 0.154, 0.397, 0.753, 0.898 mass fraction (R,S)-1-phenylethanol in vinyl acetate. All the compositions take into account the purity of the components. Due to the residual nature of each impurity it is assumed that they have a negligible effect on the phase equilibrium measurements. The overall absolute deviation for each experimental point of 3% already includes the effect of the purity of each component used. The experimental molar compositions of the liquid and vapour phases are given in Table 1. The experimental data reported is the average of six values. The pseudo-binary system liquid mixture/CO2 for the ternary system at 333 K is represented in Fig. 3 where the carbon dioxide mole fraction is plotted as a function of pressure at several feed composition for comparison. The comparison with the data from Overmeyer for the binary systems vinyl acetate/CO2 and (R,S)-1phenylethanol/CO2 is also shown [14]. In Fig. 3, correlation of the experimental pTxy data using the Peng–Robinson equation of state with the Mathias–Klotz–Prausnitz mixing rule is also presented. The correlation results will be discussed further on. As can be observed the solubility of the liquid mixture in CO2 increases with pressure as well as the solubility of CO2 in the liquid phase. The increase of (R,S)-1-phenylethanol in the feed composition causes an increase of the two phase region, which means that the solubility of the liquid mixture in CO2 decreases as the mixture becomes richer in (R,S)-1-phenylethanol. This is due to

107

yViAc /xViAc yPhEtOH /xPhEtOH

(1)

where y represents the vapour mole fraction and x represents the liquid mole fraction of each compound. ViAc stands for vinyl acetate as PhEtOH stands for (R,S)-1-phenylethanol. In Fig. 4 the separation factor ˛ as a function of pressure and temperature for a liquid mixture with a 0.753 feed mass composition (solvent free basis) of (R,S)-1-phenylethanolv is represented. As can be observed CO2 is highly selective towards vinyl acetate with separation factors between 8 and 11 at 7 MPa. The selectivity of CO2 towards vinyl acetate decreases with increasing pressure and increases with increasing temperature. The pressure effect can be explained by a decrease of the amount of the most volatile compound of the mixture that is vinyl acetate, in the vapour phase. This is due to the increase of the solvent capacity of supercritical CO2 with pressure. The effect of the temperature can be explained by the increasing vapour pressure of the liquid mixture components. Because vinyl acetate is more volatile than (R,S)1-phenylethanol it is expected that the relative change of the vapour pressure will be higher in vinyl acetate than in (R,S)-1phenylethanol, resulting in an enrichment of the more volatile compound in the vapour phase, hence an increase of the separation Table 2 Pure component physical properties [15–17] Compound

Tc (K)

Pc (MPa)

ω

Vinyl acetate (R,S)-1-Phenylethanol CO2

518.71 668.00 304.10

3.958 3.990 7.380

0.351 0.706 0.225

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A. Paiva et al. / Fluid Phase Equilibria 267 (2008) 104–112

Fig. 6. Correlation of the pTxy experimental data for the system (R,S)-1-phenylethanol/vinyl acetate/CO2 with the Peng–Robinson EOS and the Mathias–Klotz–Prausnitz mixing rule using the program package PE at 333 K. Points represent experimental data.

factor of vinyl acetate to (R,S)-1-phenylethanol with the temperature. The increase of the amount of (R,S)-1-phenylethanol in the feed composition results in an increase of the separation factor as can be seen in Fig. 5. This means that in a separation process, as the mixture gets richer in vinyl acetate, the separation of these two compounds becomes more difficult. 3.1. Models and parameters 3.1.1. Correlations The experimental pTxy data were correlated using the Peng–Robinson equation of state (PR-EOS) [7] with the Mathias– Klotz–Prausnitz mixing rule (MKP-MR) [8]. Pure component critical properties and acentric factor presented in Table 2 were used to determine the parameters ai and bi used in the correlation of the experimental data. While for CO2 critical properties are already known from experimental data [15], in the case of vinyl acetate and (R,S)-1-phenylethanol critical

properties had to be estimated by the Joback group contribution method [16] using the simulation software ASPEN PLUS® [17]. The ternary system was fitted with the PR-EOS and MKP-MR by finding the best set of interaction parameters that minimized the deviations between the calculated and experimentally determined liquid and vapour phase compositions, as well as the distribution factors of all components of the mixture. The objective function used to calculate the deviation between the experimental and the correlated data is

  n  1  exp 2 deviation =  (z − z EOS ) n

i

i

(2)

i=1

with z = x, y and n = number of data. Because the binary interaction parameters are temperaturedependent, different values for the binary interaction parameter were obtained for different temperatures. The optimum set of

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Table 3 Optimized interaction parameters of the ternary system vinyl acetate (1)/(R,S)-1-phenylethanol (2)/CO2 (3) with the Peng–Robinson EOS and the Mathias–Klotz–Prausnitz mixing rule 323 K

333 K

343 K

1–2

1–3

2–3

1–2

1–3

2–3

1–2

1–3

2–3

kij lij ij

−0.0255 0.0007 −0.0286

−0.0204 0.0685 0.0000

0.0268 −0.0638 0.0643

−0.0306 0.0879 0.0172

0.0001 0.0166 0.0000

0.0173 −0.0714 0.0538

−0.0673 0.1064 0.0668

−0.0704 −0.0478 0.0328

−0.0745 −0.1386 0.1899

AADa



a

Liquid phase: 8.58%; gas phase: 0.27%

AAD =

1 n

n 

exp

(zi

Liquid phase: 6.5%; gas phase: 0.87%

Liquid phase: 10.92%; gas phase: 1.06%

2

− ziEOS ) .

i=1

values obtained for the ternary system vinyl acetate/(R,S)-1phenylethanol/CO2 at 323, 333 and 343 K, as well as the absolute average deviation (AAD) between the experimental and the correlated data for the liquid and vapour phases are presented in Table 3. Experimental and correlated phase boundary lines for the ternary system at 333 K are presented in Fig. 6 and 9 MPa in Fig. 7. Once again the increase of the two-phase region with increasing temperature and decreasing pressure can be observed both in the experimental data as in the calculated data. The PR–MKP was able to correlate accurately the VLE data at all three temperatures with a total AAD of 6.80%.

In the equation of state the parameter a for the mixture is calculated by an expression for the mixture excess Gibbs energy by means of the MHV1 mixing rule [11]:

 1 aRT zi ˛i + = q1 b



i

g0E RT

+



zi ln

i

b



(4)

bi

with q1 = −0.53 for the Peng–Robinson EOS and g0E is calculated from the UNIFAC model. To calculate the parameter b a linear mixing rule is used: b=



zi bi

(5)

i

3.1.2. Predictions The vapour–liquid phase equilibrium of the system vinyl acetate/(R,S)-1-phenylethanol/CO2 was predicted using the PR-EOS and the Soave–Redlich–Kwong EOS (SRK-EOS). For these predictions, the Mathias–Copeman equation (MC) [10] was used for the calculation of the temperature-dependent pure component parameter a:





a(Tr ) = 1 + c1 1 −



Tr



+ c2 1 −

2 Tr



+ c3 1 −

Pure component parameters of vinyl acetate and (R,S)-1phenylethanol used for the prediction methods were estimated by adjusting both the PR–MC-EOS and the SRK–MC-EOS to the vapour pressure curve of each pure compound. The vapour pressures were obtained from the database of the simulation software ASPEN PLUS® [17]. The pure component parameters are presented in Table 4. Before the phase equilibria of any multi-component system can be predicted, an understanding of its binary sub-systems is necessary. Therefore predictions were made using the two equations referred above for the binary systems vinyl acetate/CO2 and (R,S)-1-phenylethanol/CO2 , and for the ternary system vinyl

3 2 Tr

(3)

Table 4 Estimated pure component physical properties with the Peng–Robinson EOS using the Mathias–Copeman correlation Compound

EOS

Tc (K)

Pc (MPa)

c1

c2

c3

Vinyl acetate

PR–MC SRK–MC

527.71 521.30

43.84 42.77

0.865 1.051

−0.284 −0.121

1.071 −4.246

(R,S)1Phenylethanol

PR–MC SRK–MC

669.62 662.21

39.25 42.33

1.467 2.156

−0.984 −4.000

0.697 5.016

PR–MC SRK–MC

304.10 304.10

73.80 73.80

0.727 0.586

−0.604 −0.220

2.936 0.000

CO2

Table 5 UNIFAC structure used in the calculation of the UNIFAC parameters for the ternary system vinyl acetate/(R,S)-1-phenylethanol/CO2

(vinyl acetate) Group CH2 CH CH3 COO

a

Number of groups 1 1

r: carbon atom that is part of a ring.

((R,S)-1-phenylethanol) Group a

rCH rCCHa OH CH3

CO2 (carbon dioxide)

Number of groups

Group

5 1 1 1

CO2

Number of groups 1

110

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Fig. 7. Correlation of the pTxy experimental data for the system (R,S)-1phenylethanol/vinyl acetate/CO2 with the Peng–Robinson EOS and the Mathias–Klotz–Prausnitz mixing rule using the program package PE at 9 MPa. Points represent experimental data.

acetate/(R,S)-1-phenylethanol/CO2 . All VLE predictions were done using the program package PE. For the calculation of the g0E parameter using the UNIFAC method it was necessary to define the UNIFAC structure, which means defining the groups that constitute each molecule of each compound. The UNIFAC structure for each component is represented in Table 5. The comparison between the predictive methods SRK–MC-EOS with the MHV1 mixing rule (SRK–MC-MHV1), PR–MC-EOS with

the MHV1 mixing rule (PR–MC-MHV1) and the correlation with the PR–MKP for the two binary systems can be seen in Fig. 8, where the phase boundary at 333 K is presented. While both predictive methods were able to accurately represent the phase behaviour of the binary system vinyl acetate/CO2 in both the liquid and the vapour phase, this is not the case for the binary system (R,S)-1-phenylethanol/CO2 . For the binary system vinyl acetate/CO2 using the PR–MC-MHV1 method an overall deviation (AAD) of 2.62% is achieved while the SRK–MC-MHV1 method can predict the phase equilibria behaviour for that binary system with an AAD for the experimental data of 3.15%. As for the binary system (R,S)-1-phenylethanol/CO2 , the results are not as expected. Using the PR–MC-MHV1 method some predictions are possible but with an AAD of 23.8% and with an incorrect prediction of the mixture critical point. Although the overall prediction is incorrect, this method is able to predict with some accuracy the composition of the vapour phase of this system with an AAD for the experimental vapour equilibrium data of 1.53% below the mixture critical pressure using the PR–MC-MHV1 method. The SRK–MC-MHV1 is not able to give any prediction for the binary system (R,S)-1-phenylethanol/CO2 . For this reason, some difficulties are expected in the prediction of the ternary system vinyl acetate/(R,S)-1-phenylethanol/ CO2 . In fact, the SRK–MC-MHV1 cannot give any prediction for the ternary system. This can be explained by the high deviation to the experimental values of this method for the binary system (R,S)-1phenylethanol/CO2 . The comparison between the predictive method PR–MC-MHV1 and the correlation with the PR–MKP for the ternary system at 333 K and 9 MPa is presented in Fig. 9. This method is able to predict accurately the vapour phase composition of the ternary system vinyl acetate/(R,S)-1phenylethanol/CO2 with an AAD to the experimental vapour equilibrium data of 1.0%, but gives a poor prediction of the liquid phase composition which has an AAD to the experimental liquid equilibrium data of 17.31%. The AAD between the data predicted by the PR–MC-MHV1 method and the experimental equilibrium data is 12.26%. The phase boundary for this system in the liquid phase is only accurate for the vinyl acetate/CO2 binary tie-line. This was expected regarding the correct prediction with PR–MC-MHV1 of the binary system vinyl acetate/CO2 . Once again, the bad predictions given by this method in the liquid phase are explained by the high deviation observed in the liquid phase of the binary system (R,S)-1-phenylethanol/CO2 .

Fig. 8. Measured, correlated and predicted VLE data for the binary systems: (a) (R,S)-1-phenylethanol/CO2 and (b) vinyl acetate/CO2 at 333 K. (䊉) Experimental VLE data. (—) Correlated VLE data with the Peng–Robinson EOS and the Mathias–Klotz–Prausnitz mixing rule. (- - -) Predicted VLE data with the Peng–Robinson–Mathias–Copeman EOS and the MHV1 mixing rule. (· · ·) Predicted VLE data with the Soave–Redlich–Kwong–Mathias–Copeman EOS and the MHV1 mixing rule.

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111

Fig. 9. Comparison between (a) predicted VLE data with the Peng–Robinson–Mathias–Copeman EOS and the MHV1 mixing rule and (b) correlated VLE data with the Peng–Robinson EOS and the Mathias–Klotz–Prausnitz mixing rule; using the program package PE at 333 K and 9 MPa. Points represent experimental data.

4. Conclusions Vapour–liquid equilibria were determined for the ternary system vinyl acetate/(R,S)-1-phenylethanol/CO2 at 323, 333 and 343 K in a range of pressures 7–12 MPa. The measurements were made by an analytical method using a high pressure visual variable volume cell. The experimental pTxy data were correlated using the Peng–Robinson equation of state and the Mathias–Klotz–Prausnitz mixing rule, with an AAD of 6.80% for all temperatures. This EOS with the referred mixing rule accurately represents both liquid and vapour phases of the ternary system. The phase equilibria of the ternary system and of the binary subsystems were predicted using two group contribution methods. The Peng–Robinson–Mathias–Copeman EOS with the MHV1 predictive mixing rule and the Soave–Redlich–Kwong–Mathias–Copeman EOS with the MHV1 predictive mixing rule. While both methods were able to predict the binary system vinyl acetate/CO2 with an AAD of 2.62% for the PR–MC-EOS and with an AAD of 3.15% for the SRK–MC-EOS, the same was not observed for the binary system (R,S)-1-phenylethanol/CO2 ,

where both methods used gave poor predictions for the system at hand. For that reason is to be expected that the prediction for the ternary system will not be completely accurate. In fact, the method using the SRK–MC-EOS was not even able to predict the phase equilibria, while the method using the PR–MC-EOS gave good predictions for the vapour phase with an AAD of 1.0% but not for the liquid phase. List of symbols a equation of state parameter for attractive force b equation of state parameter for repulsive force Mathias–Copeman equation parameters c1,2,3 gE excess Gibbs energy of equation of state g0E excess Gibbs energy from gE model k binary interaction parameter l binary interaction parameter n number of components p pressure Pc critical pressure q1 MHV1 mixing rule constant

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R T Tc Tr v x y zi

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gas constant temperature critical temperature reduced temperature partial molar volume liquid fraction vapour fraction fraction of component i in mixture

Subscripts i, j components i, j ij binary mixture of components i and j Greek letters ˛ separation factor  binary interaction parameter ω acentric factor Acknowledgements The authors wish to thank the Marie-Curie Foundation under the project “Supergreenchem Network”, EC Contract No. MRTN-2003504005 for financial support.

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