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Vapour-liquid equilibrium in the carbon dioxide — p-cymene system at high pressure
Fluid PhaseEquilibria,90 (1993) 135-141 Elsevier Science Publishers B.V., Amsterdam
Vapour-liquid -
135
equilibrium in the carbon dioxide -
p-cymene system at high pressure
Zdenek Wagner and Jan PavlfEek E. Hdla Laboratory of Thermodynamics, CS-165 02 Praha 6 (Czech Republic)
Institute of Chemical Process Fundamentals,
Keywords: experiments, data, VLE high pressure, carbon dioxide, hydrocarbons. (ReceivedDecember 12,1992 ; acceptedinfinaljkrn March 8.1993)
ABSTRACT Wagner Z. and PavlRek J.: Vapour-liquid equilibrium in the carbon dioxide system at high pressure. Fluid Phase Equilibria,
p-cymene
Vapour-liquid equilibrium data in the carbon dioxide - p-cymene system were measured isothermally at 313.15 K and 323.15 K at pressures ranging from 4 MPa to 10 MPa. The experimental data were fitted to the Soave-Redlich-Kwong equation of state adopting a maximum likelihood procedure.
INTRODUCTION Carbon dioxide is a perspective solvent for supercritical fluid extraction. Due to its nontoxicity and low critical temperature it can be used for extracting natural materials, mainly in food and pharmaceutical industry. Information about equilibrium between liquid and supercritical gas presents essential data for designing extractors. We also need to know the difference between the properties of desirable compounds and those which are present in the mixture, which we are separating, but should not appear in the extract. Terpenes are contained in essential oils of many plants. Therefore it is interesting to measure the equilibrium data in systems containing terpenes or other compounds with similar structure. In this work we selected p-cymene which belongs to aromatic hydrocarbons. Its structure is very close to the structure of o-terpinene and limonene as shown below.
p-cymene
037%3B12/93/$06.00
01993
cr-terpinene
limonene
Elsevier science Publishers B.V. All rights reserved
136
2. Wagner and]. Pm&&k / Fluid Pk
Ep&&ria 90 (1993~13!%42
APPAMTUS Measurement of high-pressure vapour-liquid equilibrium was performed in a static apparatus described previously by Wagner and Wichterle (1987) which was slightly modified. Temperat~e of the eq~~bri~ cell, located in a the~ostatted bath, was measured’by the Hewlett-Packard quartz digital thermometer that was calibrated against a platinum resistance thermometer Leeds & Northrup provided with National Bureau of Standards certificate. The accuracy of temperature me~urement was within 0.002 K of the temperatures on the ITS-90. Equilibrium pressure was measured by means of bourdon type Heise pressure gauges with ranges 5 MPa and 10 MPa respectively, with declared hysteresis 0.1% of the full scale range and repeatability 0.001 MPa. The investigated system was separated by a pressure transducer manufactured by Ruska Instrument Corp. from an air reference system. The air co~terpressure is controlled automatic~y. Sampling of both phases was based upon the capillary technique developed originally by Lhot&k and Wichterle (1981). The capillaries were removably connected to a heated mixer where the sample was mixed with the carrier gas. The carrier gas with the dissolved sample flows through the chromatographic six-way sampling valve. The samples were analyzed on the Hewlett-Packard gas chromatograph using the column packed with 2% OVlOl. Response factors of a thermal conductivity detector were determined by injecting a known amount of pure components. EXPERIMENTAL Carbon dioxide (Chemical Works Litvfnov) was analyzed to have purity greater then 99.9% and p-cymene (Fluka) with certified purity 95% (free of terpenes) was used without further purification. The measured liquid density at 298.15K is di5 = 0.852419 cms3 while the value reported by Dreisbach (1955) is 0.8544 g cmm3. Vapour-liquid equilibrium data were measured isothe~~ly. The cell was first evacuated and then filled with the liquid component. The traces of dissolved air were removed by repeated charging the cell with carbon dioxide to pressure about 0.5MPa and evacuation. Afterwards the cell was charged with carbon dioxide to the desired pressure. The contents of the cell were intensively stirred until both temperat~e and pressure remained constant for 10 minutes. The sampling system wss intensively flushed with carrier gas before analysis of each phase. The liquid phase was always analyzed first because it caused smaller pressure drop (approx. 0.002 MPa) than sampling the vapour phase. It should be mentioned that sampling of the liquid phase is problematic at low pressures. Relatively high flow rate is required which results in unacceptably high pressure drop. Therefore, me~urement below 4 MPa is unreliable.
137 TABLE 1 Experimental data of vapour-liquid equilibrium of carbon dioxide with p-cymene YCOa
XCO~
T 0.6023 0.6908 0.7324 0.7782 0.8088 0.9455 0.9604 0.9734
p
[MPa] = 313.15K 0.9868 3.855 0.9978 5.203 0.9971 5.912 0.9959 6.700 0.9958 7.417 0.9963 8.065 0.9928 8.309 0.9927 8.418
YCO,
XCO,
T 0.5709 0.6983 0.7172 0.7475 0.7972 0.8646 0.9238 0.9649
p
[MPa] = 323.15K 0.9893 4.007 0.9938 5.227 0.9878 5.950 0.9962 6.102 0.9959 7.679 0.9959 8.793 0.9918 9.685 0.9865 9.829
The results of measurement are presented in Table 1 and the P-x,y diagram is depicted in Figure 1. DATA REDUCTION The Soave-Redlich-Kwong the form (Soave, 1972)
equation of state is traditionally written in
However, the p~~eter a is temperature dependent and therefore the classical mixing rule for a does not mix constants. This approach is inapp~priate for a mixture of components differing strongly in volatility which is a typical case of supercritical fluid extraction. Here the critical temperature of the supercritical solvent is much lower than the critical temperatures of other components. Kwak and Mansoori (1986) therefore suggested the use of true van der Waals mixing rules where temperature independent parameters are combined. Equation 1 is rewritten into the form 2=--p 1
c/(RT)
1
+ d - 2&/m 1+ bp
(2)
where c and d are temperature independent parameters which stem from the expansion of the temperature dependence of a. The constants of the mixture are evaluated from b =
TZ$lxixj(l - Icij) [(hip + bj’“)/2]’ ,
c
~CXiXj(l-lij)~,
=
i
j
6
3
Fig, 1
0.5
0.6
0.7
0.8
P-x,y diagram of the carbon dioxide 0 323.15K # 313.15K
0.9
1
p-cymene system
where A+, &j, and mij ale interaction parameters zbnd the pure components constants are obtained from the critical properties and the acentric factor using the mo~cation proposed by Graboski and Daubert (1978).
&j = 0.086644 R$/P,;,
09
cj =
#i(1+ Icd2 ,
(7)
di =
~~~~/(~~),
(81
#i =
0.42742 R'T;&,
69
Ii&” =
0.48508 + 1.55171 wi - 0.15613
w;.
(10)
The modification by Graboski and Daubert (]Eqn. 10) differs from the original version in numerical constants. Graboski and Daubert evaluated them from the temperature dependence of vapour pr,wsures of pure ~y~oc~bons. There-
139 TABLE 2 Critical properties and acentric factors of pure components Component
TC [Kf [&!a] carbon dioxide 304.10 7.375 p-cymene 650.~ 3.050
W
0.239 0.380
fore we prefer this equation to the original version of Soave. However, it will not influence the quality of fit, it only may slightly change the w&es of the interaction parameters. The critical constants and acentric factors of the pure components were taken from Ambrose and Townsend (1978) and are summarized in Table 2. All variables are determined experimentally and therefore they cannot be errorless. We could afford to neglect errors in temperature but the errors in the composition of both phases are almost the same. For this reason we adopt maximum likelihood procedure assuming that the measurement errors in all variables are additive and uncorrelated, possessing normal distribution with zero mean with known variance obtained from the analysis of the precision of measurement. The parameters are then determined by means of an iterative procedure proposed by Rod and HanEil (1980). If we derive the mixing rules from quantum mechanics, we get complex expressions which contain quantities not available experimentally. Therefore we neglect them and comprise them into interaction parameters. For equation of state such as that used here, we check the dimension of its parameters and then use the correct mixing rule as derived for the volume and intermolecular potential. We can see that the parameters b and d have the same dimension. Therefore the binary interaction parameters iE, and mij should express the same departure from the “simple” mixing rules. We can thence assume that k?. A similar result was a3 = mu. This equality was proven by c~c~atio~. obtained by Pavhcek and Richter (1993) for the carbon dioxide - cr-pinene system where only a negligible difference was observed when the authors let tE,. = mij. In this work, however, calculation lead always to the mi~mum where these parameters were equal up to the fifth decimal. The results presented in Table 3 show that the scatter of the experimental data is higher at low pressures which agrees with the observation.
ACKNOWLEDGMENT The authors would like to acknowledge the partial support of the Grant Agency of the Czechoslovak Academy of Sciences. The work has been carried out under grant No. 47218.
TABLE 3 Results of fitting the vapour-liquid equilibriuim data to the Soave-Redlich-Kwong of state a = experimental - calculated “CO*
YCO,
T ]K]
P [MPa]
Axcoa
AYCO,
AT
AP
[K]
[MPa]
0.5208 0.6893 0.7667 0.8413 0.9004 0.9504 0.9690
0.9995 0.9994 0.9993 0.9992 0.9989 0.9983 0.9977
313.149 313.150 313.152 313.154 313.158 313.155 313.166
3.8578 5.2031 5.9102 6.6959 7.4099 8.0615 8.2993
0.08151 0.00150 -0.03425 -0.06315 -0.09158 -0.00489 -0.00860
-0.01271 -0.00161 -0.00222 -0.00325 -0.00308 -0.00197 -0.00486
0.000 -0.000 -0.002 -0.004 -0.008 -0.005 -0.016
-0.0028 -0.0001 0.0018 0.0041 0.0071 0.0035 0.0097
0.4538 0.5870 0.6611 0.6762 0.8139 0.8928 0.9505 0.9657
0.9992 0.9990 0.9989 0.9989 0.9982 0.9970 0.9933 0.9901
323.150 323.148 323.149 323.147 323,151 323.154 323.160 323.138
4.0101 5.2325 5.9535 6.1066 7.6784 8.7899 9.6785 9.8792
0.11708 0.11127 0.05613 0.07133 -0.01671 -0.02822 -0.02670 -0.00080
-0.00987 -0.00523 -0.01109 -0.00265 -0.00231 -0.00110 -0.00148 -0.00359
0.000 0.002 0.000 0.003 -0.001 -0.004 -0.010 0.012
-0.0031 -0.0055 -0.0035 -0.0046 0.0006 0.0031 0.0065 -0.0502
Parameters: Ers = m12 = -0.18960,
11s= -0.14340
LIST OF SYMBOLS
Latin letters
a,4 c,d k,l,m P
R
T 2 Y z
parameters of the Soave-Redlich-Kwong interaction parameters pressure universal gas constant temperature liquid mole fraction vapour mole fraction compressib~ty factor
equation of state
Greek letters
443 W
parameters defined by equations 10 and 9, respectively acentric factor
equation
Z. WagnermrdI. PadiEekf Fluid Phase &pdibria 90 (2993) 13.5-M
141
s?dwr+ts c
i,j
critical property related to the i-th or j-th component, respectively
REFERENCES Ambrose D. and Townsend R., 1978. Vapour-liquid critical properties. Nationaf Physical Laboratory, T~dington. Dreisbach R. R., 1955. Physical properties of chemical compounds. Advan. Chem. Ser. No. 15, American Chemical Society, Washington. Graboski M. S. and Daubert T. E., 1978. A modified Soaveequation of state for phase equilibrium calculations. I. Hydrocarbon systems. Ind. Eng. Chem., Proc. Des. Dev., 17: 443-448. Kwak T. Y. and Mansoori G. A., 1986. Van der Waals mixing rules for cubic equations of state. Appli~tion for supercritical fluid extraction modeling. Chem. Eng. Sci., 41: 1303-1309. Lhot&.kV. and Wichterle I., 1981. Vapour-liquid equilibrium in the ethaue - n-butane systems at high pressures. Fluid Phase Equil., 6: 229-235. PavliEek J. and Richter M., 1993, High pressure vapour-liquid equilibrium in the carbon dioxide - a-pinene system. Submitted to Fluid Phase Equil. Rod V. and Han&l V., 1980. Iterative estimation of model parameters when me~urements of all variables are subject to errors. Comput. Chem. Eng., 4: 33-38. Soave G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203. Wagner Z. and Wichterle I., 1987. High-pressure vapour-liquid equilibrium in systems containing carbon dioxide, l-hexene, and n-hexane. Fluid Phase Equil., 33: 109-123.
Vapour-liquid -
135
equilibrium in the carbon dioxide -
p-cymene system at high pressure
Zdenek Wagner and Jan PavlfEek E. Hdla Laboratory of Thermodynamics, CS-165 02 Praha 6 (Czech Republic)
Institute of Chemical Process Fundamentals,
Keywords: experiments, data, VLE high pressure, carbon dioxide, hydrocarbons. (ReceivedDecember 12,1992 ; acceptedinfinaljkrn March 8.1993)
ABSTRACT Wagner Z. and PavlRek J.: Vapour-liquid equilibrium in the carbon dioxide system at high pressure. Fluid Phase Equilibria,
p-cymene
Vapour-liquid equilibrium data in the carbon dioxide - p-cymene system were measured isothermally at 313.15 K and 323.15 K at pressures ranging from 4 MPa to 10 MPa. The experimental data were fitted to the Soave-Redlich-Kwong equation of state adopting a maximum likelihood procedure.
INTRODUCTION Carbon dioxide is a perspective solvent for supercritical fluid extraction. Due to its nontoxicity and low critical temperature it can be used for extracting natural materials, mainly in food and pharmaceutical industry. Information about equilibrium between liquid and supercritical gas presents essential data for designing extractors. We also need to know the difference between the properties of desirable compounds and those which are present in the mixture, which we are separating, but should not appear in the extract. Terpenes are contained in essential oils of many plants. Therefore it is interesting to measure the equilibrium data in systems containing terpenes or other compounds with similar structure. In this work we selected p-cymene which belongs to aromatic hydrocarbons. Its structure is very close to the structure of o-terpinene and limonene as shown below.
p-cymene
037%3B12/93/$06.00
01993
cr-terpinene
limonene
Elsevier science Publishers B.V. All rights reserved
136
2. Wagner and]. Pm&&k / Fluid Pk
Ep&&ria 90 (1993~13!%42
APPAMTUS Measurement of high-pressure vapour-liquid equilibrium was performed in a static apparatus described previously by Wagner and Wichterle (1987) which was slightly modified. Temperat~e of the eq~~bri~ cell, located in a the~ostatted bath, was measured’by the Hewlett-Packard quartz digital thermometer that was calibrated against a platinum resistance thermometer Leeds & Northrup provided with National Bureau of Standards certificate. The accuracy of temperature me~urement was within 0.002 K of the temperatures on the ITS-90. Equilibrium pressure was measured by means of bourdon type Heise pressure gauges with ranges 5 MPa and 10 MPa respectively, with declared hysteresis 0.1% of the full scale range and repeatability 0.001 MPa. The investigated system was separated by a pressure transducer manufactured by Ruska Instrument Corp. from an air reference system. The air co~terpressure is controlled automatic~y. Sampling of both phases was based upon the capillary technique developed originally by Lhot&k and Wichterle (1981). The capillaries were removably connected to a heated mixer where the sample was mixed with the carrier gas. The carrier gas with the dissolved sample flows through the chromatographic six-way sampling valve. The samples were analyzed on the Hewlett-Packard gas chromatograph using the column packed with 2% OVlOl. Response factors of a thermal conductivity detector were determined by injecting a known amount of pure components. EXPERIMENTAL Carbon dioxide (Chemical Works Litvfnov) was analyzed to have purity greater then 99.9% and p-cymene (Fluka) with certified purity 95% (free of terpenes) was used without further purification. The measured liquid density at 298.15K is di5 = 0.852419 cms3 while the value reported by Dreisbach (1955) is 0.8544 g cmm3. Vapour-liquid equilibrium data were measured isothe~~ly. The cell was first evacuated and then filled with the liquid component. The traces of dissolved air were removed by repeated charging the cell with carbon dioxide to pressure about 0.5MPa and evacuation. Afterwards the cell was charged with carbon dioxide to the desired pressure. The contents of the cell were intensively stirred until both temperat~e and pressure remained constant for 10 minutes. The sampling system wss intensively flushed with carrier gas before analysis of each phase. The liquid phase was always analyzed first because it caused smaller pressure drop (approx. 0.002 MPa) than sampling the vapour phase. It should be mentioned that sampling of the liquid phase is problematic at low pressures. Relatively high flow rate is required which results in unacceptably high pressure drop. Therefore, me~urement below 4 MPa is unreliable.
137 TABLE 1 Experimental data of vapour-liquid equilibrium of carbon dioxide with p-cymene YCOa
XCO~
T 0.6023 0.6908 0.7324 0.7782 0.8088 0.9455 0.9604 0.9734
p
[MPa] = 313.15K 0.9868 3.855 0.9978 5.203 0.9971 5.912 0.9959 6.700 0.9958 7.417 0.9963 8.065 0.9928 8.309 0.9927 8.418
YCO,
XCO,
T 0.5709 0.6983 0.7172 0.7475 0.7972 0.8646 0.9238 0.9649
p
[MPa] = 323.15K 0.9893 4.007 0.9938 5.227 0.9878 5.950 0.9962 6.102 0.9959 7.679 0.9959 8.793 0.9918 9.685 0.9865 9.829
The results of measurement are presented in Table 1 and the P-x,y diagram is depicted in Figure 1. DATA REDUCTION The Soave-Redlich-Kwong the form (Soave, 1972)
equation of state is traditionally written in
However, the p~~eter a is temperature dependent and therefore the classical mixing rule for a does not mix constants. This approach is inapp~priate for a mixture of components differing strongly in volatility which is a typical case of supercritical fluid extraction. Here the critical temperature of the supercritical solvent is much lower than the critical temperatures of other components. Kwak and Mansoori (1986) therefore suggested the use of true van der Waals mixing rules where temperature independent parameters are combined. Equation 1 is rewritten into the form 2=--p 1
c/(RT)
1
+ d - 2&/m 1+ bp
(2)
where c and d are temperature independent parameters which stem from the expansion of the temperature dependence of a. The constants of the mixture are evaluated from b =
TZ$lxixj(l - Icij) [(hip + bj’“)/2]’ ,
c
~CXiXj(l-lij)~,
=
i
j
6
3
Fig, 1
0.5
0.6
0.7
0.8
P-x,y diagram of the carbon dioxide 0 323.15K # 313.15K
0.9
1
p-cymene system
where A+, &j, and mij ale interaction parameters zbnd the pure components constants are obtained from the critical properties and the acentric factor using the mo~cation proposed by Graboski and Daubert (1978).
&j = 0.086644 R$/P,;,
09
cj =
#i(1+ Icd2 ,
(7)
di =
~~~~/(~~),
(81
#i =
0.42742 R'T;&,
69
Ii&” =
0.48508 + 1.55171 wi - 0.15613
w;.
(10)
The modification by Graboski and Daubert (]Eqn. 10) differs from the original version in numerical constants. Graboski and Daubert evaluated them from the temperature dependence of vapour pr,wsures of pure ~y~oc~bons. There-
139 TABLE 2 Critical properties and acentric factors of pure components Component
TC [Kf [&!a] carbon dioxide 304.10 7.375 p-cymene 650.~ 3.050
W
0.239 0.380
fore we prefer this equation to the original version of Soave. However, it will not influence the quality of fit, it only may slightly change the w&es of the interaction parameters. The critical constants and acentric factors of the pure components were taken from Ambrose and Townsend (1978) and are summarized in Table 2. All variables are determined experimentally and therefore they cannot be errorless. We could afford to neglect errors in temperature but the errors in the composition of both phases are almost the same. For this reason we adopt maximum likelihood procedure assuming that the measurement errors in all variables are additive and uncorrelated, possessing normal distribution with zero mean with known variance obtained from the analysis of the precision of measurement. The parameters are then determined by means of an iterative procedure proposed by Rod and HanEil (1980). If we derive the mixing rules from quantum mechanics, we get complex expressions which contain quantities not available experimentally. Therefore we neglect them and comprise them into interaction parameters. For equation of state such as that used here, we check the dimension of its parameters and then use the correct mixing rule as derived for the volume and intermolecular potential. We can see that the parameters b and d have the same dimension. Therefore the binary interaction parameters iE, and mij should express the same departure from the “simple” mixing rules. We can thence assume that k?. A similar result was a3 = mu. This equality was proven by c~c~atio~. obtained by Pavhcek and Richter (1993) for the carbon dioxide - cr-pinene system where only a negligible difference was observed when the authors let tE,. = mij. In this work, however, calculation lead always to the mi~mum where these parameters were equal up to the fifth decimal. The results presented in Table 3 show that the scatter of the experimental data is higher at low pressures which agrees with the observation.
ACKNOWLEDGMENT The authors would like to acknowledge the partial support of the Grant Agency of the Czechoslovak Academy of Sciences. The work has been carried out under grant No. 47218.
TABLE 3 Results of fitting the vapour-liquid equilibriuim data to the Soave-Redlich-Kwong of state a = experimental - calculated “CO*
YCO,
T ]K]
P [MPa]
Axcoa
AYCO,
AT
AP
[K]
[MPa]
0.5208 0.6893 0.7667 0.8413 0.9004 0.9504 0.9690
0.9995 0.9994 0.9993 0.9992 0.9989 0.9983 0.9977
313.149 313.150 313.152 313.154 313.158 313.155 313.166
3.8578 5.2031 5.9102 6.6959 7.4099 8.0615 8.2993
0.08151 0.00150 -0.03425 -0.06315 -0.09158 -0.00489 -0.00860
-0.01271 -0.00161 -0.00222 -0.00325 -0.00308 -0.00197 -0.00486
0.000 -0.000 -0.002 -0.004 -0.008 -0.005 -0.016
-0.0028 -0.0001 0.0018 0.0041 0.0071 0.0035 0.0097
0.4538 0.5870 0.6611 0.6762 0.8139 0.8928 0.9505 0.9657
0.9992 0.9990 0.9989 0.9989 0.9982 0.9970 0.9933 0.9901
323.150 323.148 323.149 323.147 323,151 323.154 323.160 323.138
4.0101 5.2325 5.9535 6.1066 7.6784 8.7899 9.6785 9.8792
0.11708 0.11127 0.05613 0.07133 -0.01671 -0.02822 -0.02670 -0.00080
-0.00987 -0.00523 -0.01109 -0.00265 -0.00231 -0.00110 -0.00148 -0.00359
0.000 0.002 0.000 0.003 -0.001 -0.004 -0.010 0.012
-0.0031 -0.0055 -0.0035 -0.0046 0.0006 0.0031 0.0065 -0.0502
Parameters: Ers = m12 = -0.18960,
11s= -0.14340
LIST OF SYMBOLS
Latin letters
a,4 c,d k,l,m P
R
T 2 Y z
parameters of the Soave-Redlich-Kwong interaction parameters pressure universal gas constant temperature liquid mole fraction vapour mole fraction compressib~ty factor
equation of state
Greek letters
443 W
parameters defined by equations 10 and 9, respectively acentric factor
equation
Z. WagnermrdI. PadiEekf Fluid Phase &pdibria 90 (2993) 13.5-M
141
s?dwr+ts c
i,j
critical property related to the i-th or j-th component, respectively
REFERENCES Ambrose D. and Townsend R., 1978. Vapour-liquid critical properties. Nationaf Physical Laboratory, T~dington. Dreisbach R. R., 1955. Physical properties of chemical compounds. Advan. Chem. Ser. No. 15, American Chemical Society, Washington. Graboski M. S. and Daubert T. E., 1978. A modified Soaveequation of state for phase equilibrium calculations. I. Hydrocarbon systems. Ind. Eng. Chem., Proc. Des. Dev., 17: 443-448. Kwak T. Y. and Mansoori G. A., 1986. Van der Waals mixing rules for cubic equations of state. Appli~tion for supercritical fluid extraction modeling. Chem. Eng. Sci., 41: 1303-1309. Lhot&.kV. and Wichterle I., 1981. Vapour-liquid equilibrium in the ethaue - n-butane systems at high pressures. Fluid Phase Equil., 6: 229-235. PavliEek J. and Richter M., 1993, High pressure vapour-liquid equilibrium in the carbon dioxide - a-pinene system. Submitted to Fluid Phase Equil. Rod V. and Han&l V., 1980. Iterative estimation of model parameters when me~urements of all variables are subject to errors. Comput. Chem. Eng., 4: 33-38. Soave G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203. Wagner Z. and Wichterle I., 1987. High-pressure vapour-liquid equilibrium in systems containing carbon dioxide, l-hexene, and n-hexane. Fluid Phase Equil., 33: 109-123.