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Vapor–liquid equilibria for the binary system of carbon dioxide and 1,3-butadiene at 303, 313 and 333 K
Fluid Phase Equilibria 153 Ž1998. 135–142
Vapor–liquid equilibria for the binary system of carbon dioxide and 1,3-butadiene at 303, 313 and 333 K K.-D. Wagner, J. Zappe, A. Reeps, N. Dahmen ) , E. Dinjus Forschungszentrum Karlsruhe, Institut fur ¨ Technische Chemie CPV, P.O.Box 3640, D-76021 Karlsruhe, Germany Received 23 February 1998; accepted 8 August 1998
Abstract In this work, the vapor–liquid equilibria for the binary system carbon dioxide—1,3-butadiene was measured at three temperatures, 303, 313 and 333 K. The measurements were carried out analytically in a recirculation apparatus. The experimental data were correlated with a modified Peng–Robinson equation of state and the Predictive Soave–Redlich–Kwong model. At 311 K, a parallel was drawn with the binary systems of n-butane, isobutane, 1-butene and carbon dioxide by means of the distribution coefficients K Ž i .. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Carbon dioxide; 1,3-Butadiene; Vapor–liquid equilibria; Peng–Robinson equation of state; Distribution coefficient
1. Introduction Carbon dioxide is not only a powerful solvent in connection with supercritical fluid extraction, but can also be combined to a variety of products at elevated pressures. In some cases, carbon dioxide is solvent and reactant at the same time. Such a solvent-free reaction is the synthesis of d-lactons from 1,3-butadiene and CO 2 w1–3x. To activate the CO 2 , organometallic catalysts have to be used. For the technical implementation of this reaction the phase equilibrium has to be known. Only binary systems with CO 2 containing other C4-hydrocarbons have been investigated so far by other authors. New data of the binary 1,3-butadiene–CO 2 system are presented in this paper within the temperature range from 303 to 333 K up to pressures of 8 MPa.
)
Corresponding author. Tel.: q49-7247-82-2596; fax: q49-7247-82-2244; e-mail: nicolaus. [email protected]
0378-3812r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 8 . 0 0 4 0 4 - X
136
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
2. Experimental The measurement of the vapor–liquid equilibria was performed using an analytical method with a modified apparatus for the determination of partition coefficients in two-phase mixtures w4,5x. It consists of a high pressure view cell Ž 200 cm3 . which allows to recirculate and to sample both phases via six-way valves. To condense 1,3-butadiene Ž Merck, purity ) 99.5%. into the autoclave at room temperature, the gas cylinder was heated up to 458C and the connecting capillary was cooled below y108C. By opening the outlet valve, the cell was filled with liquid 1,3-butadiene usually to one half. When the experimental device was at the right temperature, carbon dioxide Ž Messer Griesheim, purity 4.8. was compressed by a pneumatic pump into the cell until the desired pressure was reached. Pressure was measured at room temperature with a pressure transducer WIKA Ž type 891.23.510. outside the autoclave. Although equilibrium was reached after a few minutes by recirculating the liquid phase ŽFig. 1., it turned out to be adequate to prepare the system at one day and start the measurement without recirculation on the next. At first, the gaseous phase was sampled via the outlet valve at least three times. The escaping gas replaced a 200 grl NaCl solution in a glass gas sampling tube. While sampling the gaseous phase, equilibrium was regarded to be unchanged since the pressure drop was nearly zero. Afterwards, the liquid phase was sampled via a six-way valve in the recirculation loop at least three times, too. Sampling the liquid phase, a pressure loss of less than 0.1 MPa was observed. The sample Ž100 ml. was expanded into an evacuated glass vessel. The composition was determined by a GC, type HP 5880A, with a poropack column Ž 2 m Poropak Q. and a molecular sieve Ž2 m 13 = Mesh 60–80. in a flow switching procedure using WLD and FID detectors. Temperature was kept constant at "0.1 K, the pressure transducer showed a deviation of
Fig. 1. Approach to equilibrium in dependence of time.
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
137
less than "0.08 MPa. The reproducibility in the measured molar fractions varied within an error of "0.03 ŽFig. 1. . By selecting GC for analysis of the composition, a loss in accuracy was taken into account to be sure that no chemical reaction of the non-stabilized 1,3-butadiene occurred during the measurements. In fact, no additional substances were found.
3. Calculations The experimental data were correlated by using a modified Peng–Robinson equation of state ŽPR-EOS. ŽEq. Ž 1.. w6,7x, describing the dependence of the pressure p on molar volume Vm and temperature T. ps
RT
aŽ T .
y Vm y b
Vm Ž Vm q b . q b Ž Vm y b .
.
Ž1.
The parameters a and b are the attraction parameter and the covolume, respectively. Originally, for a mixture, these parameters are calculated from Eqs. Ž2. – Ž6.: N
aŽ T . s
N
Ý Ý x i x j ai j Ž1 y k i j .
Ž2.
is1 js1
ai j s ai a j
(
Ž3.
a i s a i ,c a i Ž T .
Ž4.
(
a i Ž T . s 1 q x i 1 y Ž TrTi ,c .
ž
1r2
Ž5.
/
N
bs
Ý x i bi .
Ž6.
is1
a i,c and bi are calculated from the critical data of the pure substances. a i Ž T . ŽEq. Ž5.. describes the temperature dependence of the attraction parameter a i . Instead of the original expression, the Melhem term ŽEq. Ž 7.. was used to improve the temperature behavior of a i w8x, resulting in a better description of the pure substances vapor pressure curves.
(
a i Ž T . s exp m Ž 1 y TrTi ,c . q n 1 y TrTi ,c
ž
2
/
.
Ž7.
m and n are specific constants for a substance and can be taken from tables w8x. To extend the equation of state for the calculation of mixtures, mixing rules for a and b have to be introduced. For a better description of the mixing behavior, the Margules-type mixing rule Ž Eq. Ž 8.. with the two mixing parameters k i j and k ji was implemented w9x N
aŽ T . s
N
Ý Ý x i x j a i j Ž 1 y x i k i j y x j k ji . . is1 js1
Ž8.
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
138
The parameter k i j reflects the mixing behavior in the i-rich phase, while k ji dominates the phase enriched by substance j. The covolume of the mixture is simply calculated from the arithmetic mean of the pure substance data of b ŽEq. Ž6... For the system of carbon dioxide and 1,3-butadiene, best correlation was achieved with values of k i j s 0.0577 and k ji s 0.0217. For comparison of the phase composition, predictive calculations were performed using the Predictive Soave–Redlich–Kwong model Ž PSRK. , combining the UNIFAC group contribution method with the Soave–Redlich–Kwong equation of state w10–12x. The binary critical lines also were calculated twice, using the PR-EOS and by the method of Heidemann and Khalil with numerical differentiation w13x. Both, the PSRK model calculations and the critical-curve calculations with the
Table 1 Vapor–liquid equilibrium data for the binary system of 1,3-butadiene and carbon dioxide p ŽMPa. x ŽCO 2 .
p ŽMPa. x ŽCO 2 .
p ŽMPa. x ŽCO 2 .
p ŽMPa.
y ŽCO 2 .
p ŽMPa.
y ŽCO 2 .
p ŽMPa.
y ŽCO 2 .
303 K 0.97 0.98 1.01 2.12 2.12 2.14 2.15 3.13 3.13
0.106 0.118 0.112 0.290 0.288 0.272 0.288 0.435 0.455
3.13 4.10 4.11 4.11 5.23 5.37 5.38 6.14 6.15
0.465 0.633 0.625 0.634 0.838 0.835 0.835 0.903 0.901
6.19
0.901
0.60 0.61 0.62 1.32 1.37 1.40 1.42 2.21 2.26
0.479 0.477 0.461 0.775 0.781 0.782 0.769 0.864 0.875
2.28 2.29 3.23 3.24 3.26 3.28 4.25 4.27 4.28
0.867 0.864 0.912 0.911 0.912 0.922 0.938 0.938 0.944
4.28 5.22 5.36 5.36 5.37 5.98 5.98 5.98
0.939 0.964 0.953 0.951 0.951 0.944 0.966 0.954
313 K 0.69 0.69 0.70 1.88 1.91 2.68 2.68 2.71 2.71 4.12
0.050 0.040 0.059 0.219 0.215 0.321 0.305 0.304 0.335 0.560
4.13 4.13 5.24 5.25 5.25 5.25 6.24 6.25 6.25 7.14
0.560 0.567 0.679 0.672 0.668 0.683 0.811 0.806 0.810 0.885
7.17 7.19 7.32 7.32 7.36
0.889 0.897 0.906 0.906 0.908
0.71 0.72 0.73 0.75 1.91 1.94 1.95 1.97 2.75 2.77
0.395 0.403 0.397 0.403 0.792 0.795 0.799 0.798 0.851 0.857
2.78 2.80 2.81 2.82 2.83 2.84 2.85 2.85 4.24 4.26
0.849 0.854 0.854 0.838 0.859 0.841 0.859 0.840 0.892 0.892
4.27 5.10 5.11 6.25 6.26 6.27 7.17 7.18 7.19 7.19
0.890 0.907 0.902 0.933 0.937 0.936 0.946 0.945 0.948 0.941
333 K 1.01 1.01 1.01 1.02 2.13 2.13 2.13 3.02 3.04 3.05
0.035 0.033 0.032 0.050 0.173 0.171 0.177 0.278 0.279 0.289
3.89 3.89 3.90 4.65 4.65 4.65 5.21 5.29 5.30 6.57
0.378 0.382 0.374 0.456 0.449 0.443 0.520 0.511 0.516 0.661
6.62 6.62 7.21 7.24 7.25 7.25 7.91 7.93 7.93
0.659 0.642 0.707 0.679 0.701 0.710 0.764 0.772 0.777
1.01 1.04 1.04 2.07 2.08 2.08 3.12 3.17 3.94 3.96
0.262 0.249 0.245 0.646 0.638 0.626 0.766 0.753 0.806 0.800
3.97 4.82 4.82 4.83 5.84 5.85 5.86 7.21 7.22 7.23
0.795 0.837 0.834 0.837 0.838 0.850 0.852 0.822 0.833 0.814
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
139
algorithm of Heidemann and Khalil were performed by Dohrn, Bayer, on the basis of the process simulator ASPEN PLUS.
4. Results and discussion Data were measured on three isotherms, 303, 313 and 333 K. The results are given in Table 1 and are displayed in Fig. 2. The mixture of carbon dioxide and 1,3-butadiene shows a continuous critical line connecting the critical points of pure carbon dioxide and butadiene and certainly is a type 2 phase diagram, according to the classification of van Konynenburg and Scott w14x. The corresponding liquid–liquid critical line which should exist at lower temperatures was not investigated in this study. Fig. 2 also shows data calculated from the modified PR and the PSRK equation of state. The calculated data are in adequate agreement with the experimental results, except for the critical region of the 333 K isotherm. The modified PR-EOS was introduced because of its ability to describe nearly ideal systems but also highly non-ideal systems like carbon dioxide–water w6x, which is very useful in the context with our further investigations. In the case studied here, it is also reasonable to use the PR-EOS in its original version to describe the nearly ideal system of carbon dioxide and 1,3-butadiene. This can be seen from Table 2, giving the corresponding values of k i j and k ji together with the average and maximum deviation in the resulting composition. A significant temperature dependence in the k-values could not be found within the experimental range. Also for n-butane, only slight changes in k ji are reported in literature within the temperature range studied here w15x. The binary critical line was calculated by the PR and PSRK equations. Significant deviations were only found in the maximum region of the curve, outside of the experimental range, where the PR-EOS leads to higher critical pressures. The approach of the lines towards the critical points of the
Fig. 2. Phase equilibria of 1,3-butadiene and CO 2 : experimental data at 303 K Ž`., 313 K ŽI. and 333 K Že. correlations . and PSRK-method Ž – – – .. by modified PR-EOS Ž
140
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
Table 2 Peng–Robinson parameters for binary CO 2 –C 4 H n systems k i j Ž k ji .
T Ž8C.
Absolute deviation in molar fraction Average
n-Butane Isobutane 1-Butene 1,3-Butadiene 1,3-Butadiene with modified PR-EOS
0.117 0.1240 0.086 0.0475 0.0577 Ž0.0217.
37.78 37.78 37.7 30.0–60.0 30.0–60.0
0.015 0.013
Maximum
0.044 0.048
w21x w22x w18x this work
pure substances, especially of CO 2 is better described by the PR-equation Ž CO 2 : Tc s 304.2 K, pc s 7.39 MPa; C 4 H 6 : Tc s 425.1 K, pc s 4.33 MPa.. Possibly, this is caused by the better reproduction of the vapor pressure curves by the improved a i Ž T . term ŽEq. Ž7... An increase in molecular interaction between unlike molecules is reflected by comparing the binary systems of carbon dioxide with n-butane w16x, isobutane w17x, 1-butene w18x and 1,3-butadiene. In Fig. 3, at about 311 K the distribution coefficients K Ž i . of these four systems, plotted vs. pressure using logarithmic scales, are compared. The K Ž i .-value is defined as the equilibrium ratio between the vapor and liquid molar fractions for each component i ŽEq. Ž9.. yŽi. K Ži. s . Ž9. xŽi. At the critical point of a mixture, the K-values of the components become unity. As can be seen from Table 3 w19x, the boiling points and the distribution coefficients of the hydrocarbon component
Fig. 3. Comparison of distribution coefficients of binary CO 2 –C 4 H n systems: Ž1. — — — — n-butane, 37.948C; experimental data; Ž2. 1,3-butadiene, 37.78C, calculate from PR-EOS; Ž3. – P – 1-butene, 37.78C, calculated from PR-EOS; Ž4. — – — isobutane, 37.788C, experimental data.
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
141
Table 3 Boiling point of C 4 H n hydrocarbons Boiling point Ž8C. Isobutane 1-Butene 1,3-Butadiene n-Butane
y11.7 y6.5 y4.5 y0.5
Ž K ŽC 4 H n . - 1. show the same tendency which can be explained by their symmetry and electronic molecular properties. The carbon dioxide branch Ž K ŽCO 2 . ) 1., on the other hand, is influenced by the different forces between CO 2 molecules and the C 4 compounds. Because of the smaller distances between the molecules in the liquid phase, a stronger interaction between CO 2 and C 4 H n should decrease K ŽCO 2 .. In the case of CO 2 and C 4 H n , the dispersion forces sharply dominate the electrostatic and induction forces. Especially the contributions of the quadrupolemoment of carbon dioxide can be neglected w20x. The differences in the phase behavior of the various C4 compounds will be studied in more detail in further investigations and correlations.
5. Conclusion We have presented new experimental data for the system carbon dioxide-1,3-butadiene. The results were correlated with a modified Peng–Robinson equation of state as well as described by the Predictive Soave–Redlich–Kwong model. The calculation of intermolecular forces is to increase the understanding of phase equilibria. Since chemical reactions can be unconsidered, the accuracy of the measured data will be improved by gravimetrical determination of the composition. Later on phase equilibria of the other systems related to reactions with unsaturated hydrocarbons in compressed carbon dioxide will be determined. In the case of d-lactone synthesis, this includes the mixing behavior of the educts and products and solubilities of the organometallic catalyst.
6. List of Symbols
aŽ T . a i ,c ai , a j ai j b bi m n T Ti ,c
Temperature-dependent attraction parameter Critical attraction parameter of component i Temperature-dependent attraction parameter of components i, j Composition and temperature-dependent binary attraction parameter of components i, j Covolume Covolume of component i Temperature-dependent correlation parameter Temperature-dependent correlation parameter Absolute temperature Critical temperature of component i
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
142
p pi ,c Vm xŽ i. yŽ i . k i j , k ji K Ž i. aiŽT . xi
Absolute pressure Critical pressure of component i Molar volume Mole fraction of component i in the liquid phase Mole fraction of component i in the vapor phase Parameter for Peng–Robinson equation of state Distribution coefficient of component i Temperature-dependent term of pure component i Correlation parameter
References w1x w2x w3x w4x w5x
w6x w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x w21x w22x
Y. Inoue, Y. Sasaki, H. Hashimoto, Bull. Chem. Soc. Jpn. 51 Ž1978. 2375. P. Braunstein, D. Matt, D. Nobel, Chem. Rev. 88 Ž1988. 747–764. A. Behr, 1988, Carbon Dioxide Activation by Metal Complexes, Verlag Chemie, Weinheim, Germany. K. Brudi, N. Dahmen, H. Schmieder, J. Supercrit. Fluids 9 Ž1996. 146–151. K.-D. Wagner, K. Brudi, N. Dahmen, H. Schmieder, Influence of pressure, temperature, and salt effects on the partitioning of phenol in two-phase mixtures of water and supercritical carbon dioxide, Proceedings of the 4th Int. Symposium on Supercritical Fluids, May 11–14, Sendai, Japan, 1997, pp. 719–722. J. Zappe, Phasengleichgewichtsberechnungen und Untersuchungen zum Stoffubergang an Einzeltropfen im System ¨ CO 2 rH 2 O, Diss. Univ. Heidelberg, Wissenschaftliche Berichte des FZK 5990, 1997. D.-Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 Ž1976. 59–64. G.A. Melhem, R. Saini, B.M. Goodwin, Fluid Phase Equilibria 47 Ž1989. 189–237. R. Stryjek, J.H. Vera, Can. J. Chem. Eng. 64 Ž1986. 334–340. T. Holderbaum, J. Gmehling, Fluid Phase Equilibria 70 Ž1991. 251–265. K. Fischer, J. Gmehling, Fluid Phase Equilibria 121 Ž1996. 185–206. A. Fredenslund, J. Gmehling, P. Rasmussen, Vapour Liquid Equilibrium Using UNIFAC, Elsevier, Amsterdam, 1977. R. Stockfleth, R. Dohrn, An algorithm for calculating critical points in multicomponent mixtures which can easily be implemented in existing programs to calculate phase equilibria, accepted by Fluid Phase Equilibria. P.H. van Konynenburg, R.L. Scott, Phil. Trans. R. Soc. London 298 Ž1980. 495. A. Kordas, K. Tsoutsouras, S. Stamataki, D. Tassios, Fluid Phase Equilibria 93 Ž1994. 141–166. V.G. Niesen, J. Chem. Thermodynamics 21 Ž1989. 915–923. L.A. Weber, J. Chem. Eng. Data 34 Ž1989. 171–175. P.K. Behrens, S.I. Sandler, J. Chem. Eng. Data 26 Ž1983. 52–56. R.C. Weast ŽEd.., Handbook of Chemistry and Physics, 76th edn., CRC Press, Boca Raton, 1996. J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1964. S. Shibata, S. Sandler, J. Chem. Eng. Data 34 Ž1989. 291–298. S. Ohe, ŽEd.., Physical Science Data 42: Vapor–Liquid Equilibrium Data at High Pressure, Kodansha, Tokyo; Elsevier, Amsterdam, 1990.
Vapor–liquid equilibria for the binary system of carbon dioxide and 1,3-butadiene at 303, 313 and 333 K K.-D. Wagner, J. Zappe, A. Reeps, N. Dahmen ) , E. Dinjus Forschungszentrum Karlsruhe, Institut fur ¨ Technische Chemie CPV, P.O.Box 3640, D-76021 Karlsruhe, Germany Received 23 February 1998; accepted 8 August 1998
Abstract In this work, the vapor–liquid equilibria for the binary system carbon dioxide—1,3-butadiene was measured at three temperatures, 303, 313 and 333 K. The measurements were carried out analytically in a recirculation apparatus. The experimental data were correlated with a modified Peng–Robinson equation of state and the Predictive Soave–Redlich–Kwong model. At 311 K, a parallel was drawn with the binary systems of n-butane, isobutane, 1-butene and carbon dioxide by means of the distribution coefficients K Ž i .. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Carbon dioxide; 1,3-Butadiene; Vapor–liquid equilibria; Peng–Robinson equation of state; Distribution coefficient
1. Introduction Carbon dioxide is not only a powerful solvent in connection with supercritical fluid extraction, but can also be combined to a variety of products at elevated pressures. In some cases, carbon dioxide is solvent and reactant at the same time. Such a solvent-free reaction is the synthesis of d-lactons from 1,3-butadiene and CO 2 w1–3x. To activate the CO 2 , organometallic catalysts have to be used. For the technical implementation of this reaction the phase equilibrium has to be known. Only binary systems with CO 2 containing other C4-hydrocarbons have been investigated so far by other authors. New data of the binary 1,3-butadiene–CO 2 system are presented in this paper within the temperature range from 303 to 333 K up to pressures of 8 MPa.
)
Corresponding author. Tel.: q49-7247-82-2596; fax: q49-7247-82-2244; e-mail: nicolaus. [email protected]
0378-3812r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 8 . 0 0 4 0 4 - X
136
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
2. Experimental The measurement of the vapor–liquid equilibria was performed using an analytical method with a modified apparatus for the determination of partition coefficients in two-phase mixtures w4,5x. It consists of a high pressure view cell Ž 200 cm3 . which allows to recirculate and to sample both phases via six-way valves. To condense 1,3-butadiene Ž Merck, purity ) 99.5%. into the autoclave at room temperature, the gas cylinder was heated up to 458C and the connecting capillary was cooled below y108C. By opening the outlet valve, the cell was filled with liquid 1,3-butadiene usually to one half. When the experimental device was at the right temperature, carbon dioxide Ž Messer Griesheim, purity 4.8. was compressed by a pneumatic pump into the cell until the desired pressure was reached. Pressure was measured at room temperature with a pressure transducer WIKA Ž type 891.23.510. outside the autoclave. Although equilibrium was reached after a few minutes by recirculating the liquid phase ŽFig. 1., it turned out to be adequate to prepare the system at one day and start the measurement without recirculation on the next. At first, the gaseous phase was sampled via the outlet valve at least three times. The escaping gas replaced a 200 grl NaCl solution in a glass gas sampling tube. While sampling the gaseous phase, equilibrium was regarded to be unchanged since the pressure drop was nearly zero. Afterwards, the liquid phase was sampled via a six-way valve in the recirculation loop at least three times, too. Sampling the liquid phase, a pressure loss of less than 0.1 MPa was observed. The sample Ž100 ml. was expanded into an evacuated glass vessel. The composition was determined by a GC, type HP 5880A, with a poropack column Ž 2 m Poropak Q. and a molecular sieve Ž2 m 13 = Mesh 60–80. in a flow switching procedure using WLD and FID detectors. Temperature was kept constant at "0.1 K, the pressure transducer showed a deviation of
Fig. 1. Approach to equilibrium in dependence of time.
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
137
less than "0.08 MPa. The reproducibility in the measured molar fractions varied within an error of "0.03 ŽFig. 1. . By selecting GC for analysis of the composition, a loss in accuracy was taken into account to be sure that no chemical reaction of the non-stabilized 1,3-butadiene occurred during the measurements. In fact, no additional substances were found.
3. Calculations The experimental data were correlated by using a modified Peng–Robinson equation of state ŽPR-EOS. ŽEq. Ž 1.. w6,7x, describing the dependence of the pressure p on molar volume Vm and temperature T. ps
RT
aŽ T .
y Vm y b
Vm Ž Vm q b . q b Ž Vm y b .
.
Ž1.
The parameters a and b are the attraction parameter and the covolume, respectively. Originally, for a mixture, these parameters are calculated from Eqs. Ž2. – Ž6.: N
aŽ T . s
N
Ý Ý x i x j ai j Ž1 y k i j .
Ž2.
is1 js1
ai j s ai a j
(
Ž3.
a i s a i ,c a i Ž T .
Ž4.
(
a i Ž T . s 1 q x i 1 y Ž TrTi ,c .
ž
1r2
Ž5.
/
N
bs
Ý x i bi .
Ž6.
is1
a i,c and bi are calculated from the critical data of the pure substances. a i Ž T . ŽEq. Ž5.. describes the temperature dependence of the attraction parameter a i . Instead of the original expression, the Melhem term ŽEq. Ž 7.. was used to improve the temperature behavior of a i w8x, resulting in a better description of the pure substances vapor pressure curves.
(
a i Ž T . s exp m Ž 1 y TrTi ,c . q n 1 y TrTi ,c
ž
2
/
.
Ž7.
m and n are specific constants for a substance and can be taken from tables w8x. To extend the equation of state for the calculation of mixtures, mixing rules for a and b have to be introduced. For a better description of the mixing behavior, the Margules-type mixing rule Ž Eq. Ž 8.. with the two mixing parameters k i j and k ji was implemented w9x N
aŽ T . s
N
Ý Ý x i x j a i j Ž 1 y x i k i j y x j k ji . . is1 js1
Ž8.
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
138
The parameter k i j reflects the mixing behavior in the i-rich phase, while k ji dominates the phase enriched by substance j. The covolume of the mixture is simply calculated from the arithmetic mean of the pure substance data of b ŽEq. Ž6... For the system of carbon dioxide and 1,3-butadiene, best correlation was achieved with values of k i j s 0.0577 and k ji s 0.0217. For comparison of the phase composition, predictive calculations were performed using the Predictive Soave–Redlich–Kwong model Ž PSRK. , combining the UNIFAC group contribution method with the Soave–Redlich–Kwong equation of state w10–12x. The binary critical lines also were calculated twice, using the PR-EOS and by the method of Heidemann and Khalil with numerical differentiation w13x. Both, the PSRK model calculations and the critical-curve calculations with the
Table 1 Vapor–liquid equilibrium data for the binary system of 1,3-butadiene and carbon dioxide p ŽMPa. x ŽCO 2 .
p ŽMPa. x ŽCO 2 .
p ŽMPa. x ŽCO 2 .
p ŽMPa.
y ŽCO 2 .
p ŽMPa.
y ŽCO 2 .
p ŽMPa.
y ŽCO 2 .
303 K 0.97 0.98 1.01 2.12 2.12 2.14 2.15 3.13 3.13
0.106 0.118 0.112 0.290 0.288 0.272 0.288 0.435 0.455
3.13 4.10 4.11 4.11 5.23 5.37 5.38 6.14 6.15
0.465 0.633 0.625 0.634 0.838 0.835 0.835 0.903 0.901
6.19
0.901
0.60 0.61 0.62 1.32 1.37 1.40 1.42 2.21 2.26
0.479 0.477 0.461 0.775 0.781 0.782 0.769 0.864 0.875
2.28 2.29 3.23 3.24 3.26 3.28 4.25 4.27 4.28
0.867 0.864 0.912 0.911 0.912 0.922 0.938 0.938 0.944
4.28 5.22 5.36 5.36 5.37 5.98 5.98 5.98
0.939 0.964 0.953 0.951 0.951 0.944 0.966 0.954
313 K 0.69 0.69 0.70 1.88 1.91 2.68 2.68 2.71 2.71 4.12
0.050 0.040 0.059 0.219 0.215 0.321 0.305 0.304 0.335 0.560
4.13 4.13 5.24 5.25 5.25 5.25 6.24 6.25 6.25 7.14
0.560 0.567 0.679 0.672 0.668 0.683 0.811 0.806 0.810 0.885
7.17 7.19 7.32 7.32 7.36
0.889 0.897 0.906 0.906 0.908
0.71 0.72 0.73 0.75 1.91 1.94 1.95 1.97 2.75 2.77
0.395 0.403 0.397 0.403 0.792 0.795 0.799 0.798 0.851 0.857
2.78 2.80 2.81 2.82 2.83 2.84 2.85 2.85 4.24 4.26
0.849 0.854 0.854 0.838 0.859 0.841 0.859 0.840 0.892 0.892
4.27 5.10 5.11 6.25 6.26 6.27 7.17 7.18 7.19 7.19
0.890 0.907 0.902 0.933 0.937 0.936 0.946 0.945 0.948 0.941
333 K 1.01 1.01 1.01 1.02 2.13 2.13 2.13 3.02 3.04 3.05
0.035 0.033 0.032 0.050 0.173 0.171 0.177 0.278 0.279 0.289
3.89 3.89 3.90 4.65 4.65 4.65 5.21 5.29 5.30 6.57
0.378 0.382 0.374 0.456 0.449 0.443 0.520 0.511 0.516 0.661
6.62 6.62 7.21 7.24 7.25 7.25 7.91 7.93 7.93
0.659 0.642 0.707 0.679 0.701 0.710 0.764 0.772 0.777
1.01 1.04 1.04 2.07 2.08 2.08 3.12 3.17 3.94 3.96
0.262 0.249 0.245 0.646 0.638 0.626 0.766 0.753 0.806 0.800
3.97 4.82 4.82 4.83 5.84 5.85 5.86 7.21 7.22 7.23
0.795 0.837 0.834 0.837 0.838 0.850 0.852 0.822 0.833 0.814
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
139
algorithm of Heidemann and Khalil were performed by Dohrn, Bayer, on the basis of the process simulator ASPEN PLUS.
4. Results and discussion Data were measured on three isotherms, 303, 313 and 333 K. The results are given in Table 1 and are displayed in Fig. 2. The mixture of carbon dioxide and 1,3-butadiene shows a continuous critical line connecting the critical points of pure carbon dioxide and butadiene and certainly is a type 2 phase diagram, according to the classification of van Konynenburg and Scott w14x. The corresponding liquid–liquid critical line which should exist at lower temperatures was not investigated in this study. Fig. 2 also shows data calculated from the modified PR and the PSRK equation of state. The calculated data are in adequate agreement with the experimental results, except for the critical region of the 333 K isotherm. The modified PR-EOS was introduced because of its ability to describe nearly ideal systems but also highly non-ideal systems like carbon dioxide–water w6x, which is very useful in the context with our further investigations. In the case studied here, it is also reasonable to use the PR-EOS in its original version to describe the nearly ideal system of carbon dioxide and 1,3-butadiene. This can be seen from Table 2, giving the corresponding values of k i j and k ji together with the average and maximum deviation in the resulting composition. A significant temperature dependence in the k-values could not be found within the experimental range. Also for n-butane, only slight changes in k ji are reported in literature within the temperature range studied here w15x. The binary critical line was calculated by the PR and PSRK equations. Significant deviations were only found in the maximum region of the curve, outside of the experimental range, where the PR-EOS leads to higher critical pressures. The approach of the lines towards the critical points of the
Fig. 2. Phase equilibria of 1,3-butadiene and CO 2 : experimental data at 303 K Ž`., 313 K ŽI. and 333 K Že. correlations . and PSRK-method Ž – – – .. by modified PR-EOS Ž
140
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
Table 2 Peng–Robinson parameters for binary CO 2 –C 4 H n systems k i j Ž k ji .
T Ž8C.
Absolute deviation in molar fraction Average
n-Butane Isobutane 1-Butene 1,3-Butadiene 1,3-Butadiene with modified PR-EOS
0.117 0.1240 0.086 0.0475 0.0577 Ž0.0217.
37.78 37.78 37.7 30.0–60.0 30.0–60.0
0.015 0.013
Maximum
0.044 0.048
w21x w22x w18x this work
pure substances, especially of CO 2 is better described by the PR-equation Ž CO 2 : Tc s 304.2 K, pc s 7.39 MPa; C 4 H 6 : Tc s 425.1 K, pc s 4.33 MPa.. Possibly, this is caused by the better reproduction of the vapor pressure curves by the improved a i Ž T . term ŽEq. Ž7... An increase in molecular interaction between unlike molecules is reflected by comparing the binary systems of carbon dioxide with n-butane w16x, isobutane w17x, 1-butene w18x and 1,3-butadiene. In Fig. 3, at about 311 K the distribution coefficients K Ž i . of these four systems, plotted vs. pressure using logarithmic scales, are compared. The K Ž i .-value is defined as the equilibrium ratio between the vapor and liquid molar fractions for each component i ŽEq. Ž9.. yŽi. K Ži. s . Ž9. xŽi. At the critical point of a mixture, the K-values of the components become unity. As can be seen from Table 3 w19x, the boiling points and the distribution coefficients of the hydrocarbon component
Fig. 3. Comparison of distribution coefficients of binary CO 2 –C 4 H n systems: Ž1. — — — — n-butane, 37.948C; experimental data; Ž2. 1,3-butadiene, 37.78C, calculate from PR-EOS; Ž3. – P – 1-butene, 37.78C, calculated from PR-EOS; Ž4. — – — isobutane, 37.788C, experimental data.
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
141
Table 3 Boiling point of C 4 H n hydrocarbons Boiling point Ž8C. Isobutane 1-Butene 1,3-Butadiene n-Butane
y11.7 y6.5 y4.5 y0.5
Ž K ŽC 4 H n . - 1. show the same tendency which can be explained by their symmetry and electronic molecular properties. The carbon dioxide branch Ž K ŽCO 2 . ) 1., on the other hand, is influenced by the different forces between CO 2 molecules and the C 4 compounds. Because of the smaller distances between the molecules in the liquid phase, a stronger interaction between CO 2 and C 4 H n should decrease K ŽCO 2 .. In the case of CO 2 and C 4 H n , the dispersion forces sharply dominate the electrostatic and induction forces. Especially the contributions of the quadrupolemoment of carbon dioxide can be neglected w20x. The differences in the phase behavior of the various C4 compounds will be studied in more detail in further investigations and correlations.
5. Conclusion We have presented new experimental data for the system carbon dioxide-1,3-butadiene. The results were correlated with a modified Peng–Robinson equation of state as well as described by the Predictive Soave–Redlich–Kwong model. The calculation of intermolecular forces is to increase the understanding of phase equilibria. Since chemical reactions can be unconsidered, the accuracy of the measured data will be improved by gravimetrical determination of the composition. Later on phase equilibria of the other systems related to reactions with unsaturated hydrocarbons in compressed carbon dioxide will be determined. In the case of d-lactone synthesis, this includes the mixing behavior of the educts and products and solubilities of the organometallic catalyst.
6. List of Symbols
aŽ T . a i ,c ai , a j ai j b bi m n T Ti ,c
Temperature-dependent attraction parameter Critical attraction parameter of component i Temperature-dependent attraction parameter of components i, j Composition and temperature-dependent binary attraction parameter of components i, j Covolume Covolume of component i Temperature-dependent correlation parameter Temperature-dependent correlation parameter Absolute temperature Critical temperature of component i
K.-D. Wagner et al.r Fluid Phase Equilibria 153 (1998) 135–142
142
p pi ,c Vm xŽ i. yŽ i . k i j , k ji K Ž i. aiŽT . xi
Absolute pressure Critical pressure of component i Molar volume Mole fraction of component i in the liquid phase Mole fraction of component i in the vapor phase Parameter for Peng–Robinson equation of state Distribution coefficient of component i Temperature-dependent term of pure component i Correlation parameter
References w1x w2x w3x w4x w5x
w6x w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x w21x w22x
Y. Inoue, Y. Sasaki, H. Hashimoto, Bull. Chem. Soc. Jpn. 51 Ž1978. 2375. P. Braunstein, D. Matt, D. Nobel, Chem. Rev. 88 Ž1988. 747–764. A. Behr, 1988, Carbon Dioxide Activation by Metal Complexes, Verlag Chemie, Weinheim, Germany. K. Brudi, N. Dahmen, H. Schmieder, J. Supercrit. Fluids 9 Ž1996. 146–151. K.-D. Wagner, K. Brudi, N. Dahmen, H. Schmieder, Influence of pressure, temperature, and salt effects on the partitioning of phenol in two-phase mixtures of water and supercritical carbon dioxide, Proceedings of the 4th Int. Symposium on Supercritical Fluids, May 11–14, Sendai, Japan, 1997, pp. 719–722. J. Zappe, Phasengleichgewichtsberechnungen und Untersuchungen zum Stoffubergang an Einzeltropfen im System ¨ CO 2 rH 2 O, Diss. Univ. Heidelberg, Wissenschaftliche Berichte des FZK 5990, 1997. D.-Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 Ž1976. 59–64. G.A. Melhem, R. Saini, B.M. Goodwin, Fluid Phase Equilibria 47 Ž1989. 189–237. R. Stryjek, J.H. Vera, Can. J. Chem. Eng. 64 Ž1986. 334–340. T. Holderbaum, J. Gmehling, Fluid Phase Equilibria 70 Ž1991. 251–265. K. Fischer, J. Gmehling, Fluid Phase Equilibria 121 Ž1996. 185–206. A. Fredenslund, J. Gmehling, P. Rasmussen, Vapour Liquid Equilibrium Using UNIFAC, Elsevier, Amsterdam, 1977. R. Stockfleth, R. Dohrn, An algorithm for calculating critical points in multicomponent mixtures which can easily be implemented in existing programs to calculate phase equilibria, accepted by Fluid Phase Equilibria. P.H. van Konynenburg, R.L. Scott, Phil. Trans. R. Soc. London 298 Ž1980. 495. A. Kordas, K. Tsoutsouras, S. Stamataki, D. Tassios, Fluid Phase Equilibria 93 Ž1994. 141–166. V.G. Niesen, J. Chem. Thermodynamics 21 Ž1989. 915–923. L.A. Weber, J. Chem. Eng. Data 34 Ž1989. 171–175. P.K. Behrens, S.I. Sandler, J. Chem. Eng. Data 26 Ž1983. 52–56. R.C. Weast ŽEd.., Handbook of Chemistry and Physics, 76th edn., CRC Press, Boca Raton, 1996. J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York, 1964. S. Shibata, S. Sandler, J. Chem. Eng. Data 34 Ž1989. 291–298. S. Ohe, ŽEd.., Physical Science Data 42: Vapor–Liquid Equilibrium Data at High Pressure, Kodansha, Tokyo; Elsevier, Amsterdam, 1990.