Ind. Eng. Chem. Res. 2003, 42, 183-188
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GENERAL RESEARCH Vapor-Liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension Roland Wittig, Ju 1 rgen Lohmann,† and Ju 1 rgen Gmehling* Lehrstuhl fu¨ r Technische Chemie (FB9), Carl von Ossietzky Universita¨ t Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany
The group contribution method UNIFAC has become very popular because of its large range of applicability and its reliable predictions of vapor-liquid equilibria. With the help of new data stored in the Dortmund Data Bank (DDB), many gaps in the existing UNIFAC parameter matrix have been filled, and many new main groups have been added to the parameter table. In this paper, the parameters for 46 group combinations are provided. Additionally, a new main group for sulfones is introduced, for which the group interaction parameters for eight main groups are fitted. Introduction For the synthesis, design, and optimization of distillation processes, a reliable knowledge of the vaporliquid equilibrium behavior is necessary. Because experimental data are often not available, at least for process synthesis, group contribution methods can be used for the prediction of the required vapor-liquid equilibria. In the past several decades, the group contribution method UNIFAC1,2 has become very popular. As a result, UNIFAC has been integrated into most commercial process simulators. Because of ongoing research work, the range of applicability of UNIFAC is continuously extended, and at the same time, the reliability of the results is improved. The applicability depends on the availability of group volumes (Rk), group surface areas (Qk), and group interaction parameters (anm and amn). For that reason, the existing parameter matrix for the UNIFAC method is continually being extended with the help of VLE data stored in the Dortmund Data Bank (DDB) and systematic VLE measurements. Extensive tables with group interaction parameters for 50 main groups have been presented before.3-6 Recently, the parameters for four new main groups were published by Balslev and Abildskov.7 In this paper, new group interaction parameters for 46 group combinations are provided to fill gaps in the existing parameter table. Additionally, group interaction parameters for the newly introduced main group sulfones are presented. The Group Contribution Method UNIFAC In the UNIFAC model, the activity coefficient is calculated in terms of a combinatorial part and a residual part * Correspondence concerning this article should be addressed to Prof. Dr. J. Gmehling. E-mail: gmehling@ tech.chem.uni-oldenburg.de. Tel.: +49 441 798 3831. Fax: +49 441 798 3330. Internet: http://www.uni-oldenburg.de/tchemie. † Present address: BASF Coatings AG, Werk Mu ¨ nster, Postfach 6123, D-48163 Mu¨nster, Germany.
Table 1. New UNIFAC Group Interaction Parameters Not Previously Available n
m
anm/K
amn/K
3 ACH 4 ACCH2 4 ACCH2 6 CH3OH 6 CH3OH 6 CH3OH 7 H2O 7 H2O 8 ACOH 8 ACOH 8 ACOH 8 ACOH 9 CH2CO 10 CHO 10 CHO 11 CCOO 11 CCOO 12 HCOO 12 HCOO 13 CH2O 13 CH2O 13 CH2O 13 CH2O 14 CNH2 15 CNH 15 CNH 15 CNH 15 CNH 16 (C)3N 16 (C)3N 16 (C)3N 18 pyridine 19 CCN 21 CCl 21 CCl 21 CCl 22 CCl2 22 CCl2 23 CCl3 25 ACCl 25 ACCl 25 ACCl 32 I 33 Br 33 Br 38 ACF
34 CtC 34 CtC 40 CF2 27 ACNO2 30 furfural 34 CtC 12 HCOO 33 Br 12 HCOO 14 CNH2 22 CCl2 27 ACNO2 36 ACRY 19 CCN 34 CtC 18 pyridine 34 CtC 22 CCl2 33 Br 17 ACNH2 27 ACNO2 34 CtC 40 CF2 35 DMSO 17 ACNH2 18 pyridine 31 DOH 39 DMF 17 ACNH2 19 CCN 21 CCl 25 ACCl 20 COOH 30 furfural 32 I 39 DMF 30 furfural 39 DMF 33 Br 35 DMSO 39 DMF 40 CF2 33 Br 37 ClCC 39 DMF 39 DMF
154.26 -152.55 -245.39 457.88 -61.76 -119.10 233.87 777.10 -32.52 -832.97 517.27 -413.48 -63.50 -106.40 2.21 -0.13 71.48 31.00 298.13 -46.39 155.11 -156.57 -172.51 874.19 138.54 431.49 939.07 -255.22 287.43 1255.10 -182.91 -2.17 205.27 65.56 2.22 6.57 149.56 -160.28 168.80 1337.37 5143.14 309.58 6.37 -48.33 336.25 -110.65
-101.12 614.52 839.83 511.29 287.00 967.71 124.63 79.18 -234.25 -870.80 1633.50 815.12 114.55 224.66 -55.87 8.87 -111.45 80.99 -92.26 285.36 220.66 173.77 278.15 -366.51 64.30 -207.66 -213.74 10.03 -24.46 -446.86 151.38 20.18 92.07 -39.46 179.25 -55.21 -116.21 397.24 -46.80 -334.12 -374.16 33.95 37.10 322.42 -176.26 50.06
10.1021/ie020506l CCC: $25.00 © 2003 American Chemical Society Published on Web 11/21/2002
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Figure 1. Experimental and UNIFAC-predicted (s) T-x data for the systems (A) 1-octyne (1) + dibutyl ether (2) at (b) 26.66, (2) 53.33, and (9) 79.99 kPa15 and (B) 2-octyne (1) + dibutyl ether (2) at (b) 26.66, (2) 53.33, and (9) 79.99 kPa.15
Figure 2. Experimental and UNIFAC-predicted (s) P-x and T-x data for the systems (A) diethyl ether (1) + nitrobenzene (2) at (b) 289.15 K16 and (B) anisole (1) + nitrobenzene (2) at (b) 26.66, (2) 66.66, and (9) 94.93 kPa.17
The combinatorial part considers the form and the size of the molecules
(
ln γCi ) 1 - Vi + ln Vi - 5qi 1 -
)
Vi Vi + ln Fi Fi
(2)
where the parameters Vi and Fi are given as
Vi )
Fi )
ri
∑j
(3)
rjxj
qi
∑j qjxj
(4)
For the calculation of these parameters, the relative van der Waals values ri and qi of the compounds are required. They can be calculated from the relative van der Waals values Rk and Qk of the subgroups k as
ri )
∑k ν(i)k Rk
(5)
qi )
∑k ν(i)k Qk
(6)
The parameters Rk and Qk are obtained from the van
Figure 3. Experimental and UNIFAC-predicted (s) T-x data for the systems (b) ethyl acetate (1) + pyridine (2), (2) propyl acetate (1) + pyridine (2), and (9) butyl acetate (1) + pyridine (2) at 101.32 kPa.18
ln γi ) ln γCi + ln γRi
(1)
der Waals group volumes and surface areas Vwk and Awk given by Bondi8
Rk ) Vwk/15.17
(7)
Qk ) Awk/(2.5 × 109)
(8)
The normalization factors 15.17 and 2.5 × 109 are those given by Abrams and Prausnitz.9
Ind. Eng. Chem. Res., Vol. 42, No. 1, 2003 185 Table 2. UNIFAC Rk and Qk Parameters and Group Assignment for the New Main Group 55 Sulfones main group
subgroup
no.
Rk
Qk
example
group assignment
55 sulfones
CH2SuCH2 CH2SuCH
118 119
2.6869 2.4595
2.1200 1.8080
sulfolane 2,4-dimethylsulfolane
1 CH2SuCH2, 2 CH2 1 CH2SuCH, 2 CH3, 1 CH2, 1 CH
Figure 4. Structures of the subgroups CH2SuCH2 (118) and CH2SuCH (119).
Figure 6. Activity coefficients at infinite dilution of (b) benzene,20-22 (2) toluene,23-26 ([) cyclohexene,23,27 (9) hexane,21,23,28,29 (O) 2,2,4-trimethylpentane,26,30 and (4) undecane30,31 in sulfolane; (s) UNIFAC predictions. Table 3. UNIFAC Group Interaction Parameters for the New Main Group 55 Sulfones
Figure 5. Experimental and UNIFAC-predicted (s) P-x data for the system benzene (1) + sulfolane (2) at (b) 303.15, (2) 313.15, (9) 323.15, and ([) 333.15 K.19
The residual part takes into account the interaction between the molecules and is calculated from the group activity coefficients in the mixture of the pure substances
ln γRi )
∑k ν(i)k (ln Γk - ln Γ(i)k )
(9)
The concentration dependence of the group activity coefficient Γk is calculated according to
[
ΘmΨkm
]
ΘmΨmk) - ∑ ∑ m m ∑n ΘnΨnm
ln Γk ) Qk 1 - ln(
(10)
where the group surface area fraction Θm and the group mole fraction Xm are given by the equations
Θm )
Xm )
QmXm
∑n QnXn ∑j
(11)
m
anm/K
amn/K
1 CH2 2 CdC 3 ACH 4 ACCH2 5 OH 6 CH3OH 7 H2O 24 CCl4
55 sulfones 55 sulfones 55 sulfones 55 sulfones 55 sulfones 55 sulfones 55 sulfones 55 sulfones
808.59 200.94 360.82 233.51 215.81 150.02 -255.63 585.19
245.21 384.45 47.05 347.13 72.19 265.75 627.39 75.04
(
Ψnm ) exp -
)
anm T
(13)
Database Used to Fit UNIFAC Parameters Because of the temperature-independent group interaction parameters used in UNIFAC, only vaporliquid equilibria (VLE) and sometimes activity coefficients at infinite dilution (γ∞) are used to fit the required group interaction parameters. For further development, the actual version of the Dortmund Data Bank (DDB) is used. Some of these data (approximately 15-20%) have been published in different volumes of the DECHEMA Chemistry Data Series.10,11 At the same time, a large number of systematic measurements have been performed to complete the database, in particular for the newly introduced main groups. The VLE data were measured with the help of a computer-operated static apparatus,12,13 and the γ∞ data were measured by gasliquid chromatography (GLC).14 Because, in contrast to modified UNIFAC, temperature-independent parameters are used, it is recommended that UNIFAC mainly be used in the temperature range covered by the database (typically 0-150 °C). Fitting Procedure To fit data, the following objective function F is used
ν(j) m xj
∑j ∑n ν(j)n xj
n
(12)
The parameter Ψnm contains the temperature-independent group interaction parameters
F(anm,amn) )
!
∑∆VLE + ∑ ∆γ∞ ) minimum
(14)
In the objective function F, the deviations between experimental and calculated data of the different types of vapor-liquid equilibria and activity coefficients at infinite dilution are summed.
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Figure 7. Current UNIFAC parameter matrix (June 2002).
For VLE data, it is necessary to distinguish between the different data types
[x, y, P, T]
[x, P, T]
[x, y, T]
∆VLE )
∆VLE )
∆VLE )
n w nk
1
1 nw
(
∑ ∑ gVLE
nwnkk)1i)1 nw
(
∑ gVLE k)1
1
n w nk
1
(
Pk
∑ ∑ gVLE
nwnkk)1i)1
γik
)
Pk - Pk,calc 2
)
γik - γik,calc
(18)
yi γif 0i Ki,calc ) ) V xi φ P
(19)
Pcalc )
(15)
2
Kik
f 0i xi γi V φi
2
(16)
)
Kik - Kik,calc 3
where the following equations are used to calculate vapor-liquid equilibria
2
(17)
∑
i
calc
The real phase behavior of the vapor phase is taken into account using the Soave-Redlich-Kwong equation of state (k12 ) 0.0). For the γ∞ data, the contribution to the objective function F is described by
∞
∆γ )
1
nw
(
∑ gγ
nwk)1
)
∞ γ∞k - γk,calc
∞
γ∞k
Ind. Eng. Chem. Res., Vol. 42, No. 1, 2003 187
2
(20)
By varying the weighting factors gi in the objective function for the different thermodynamic properties, the results can be influenced in the desired direction. Parameters Not Previously Available New reliable vapor-liquid equilibria (VLE) data stored in the Dortmund Data Bank (DDB) allowed us to fit new group interaction parameters to remove some the gaps in the UNIFAC parameter matrix. Parameters for 46 group combinations have been added to the UNIFAC parameter table. In Table 1, the new group interaction parameters are listed. Figures 1-3 present the VLE results predicted using UNIFAC for different alkyne + dibutyl ether, ether + nitrobenzene, and ester + pyridine systems, whereby the different VLE data in each figure are predicted using the same UNIFAC group interaction parameters. As can be seen, for all systems, very good agreement between the experimental and predicted data is obtained. New Main Group and Parameters In this paper, a new main group for sulfones, which is required, for example, to describe systems with the selective solvent sulfolane, is presented. The new group interaction parameters for UNIFAC and the van der Waals properties Rk and Qk, together with the group assignment of the new main group sulfones, are given in Tables 2 and 3. Additionally, the structures of the subgroups CH2SuCH2 (118) and CH2SuCH (119) are shown in Figure 4. Figure 5 presents a comparison of the experimental and predicted VLE data for the system benzene + sulfolane in a temperature range from 303 to 333 K using the UNIFAC group interaction parameters for the new main group sulfones. For this system, a reliable description of the temperature dependence is achieved with the new group interaction parameters. Figure 6 provides an overview of the different experimental and predicted activity coefficients at infinite dilution, γ∞, of cyclic, straight, and branched aliphatics (cyclohexene, hexane, 2,2,4-trimethylpentane, and undecane) and aromatics (benzene and toluene) in sulfolane. Good agreement between the experimental data and the results predicted using UNIFAC is obtained. As can be seen, the values of the γ∞ for all systems increase with increasing chain length of the aliphatic compounds. Sulfolane alters the activity coefficients at infinite dilution of the aliphatics and aromatics so that it can be used as a selective solvent for the separation of aromatics from aliphatics in processes such as extraction and extractive distillation. Conclusion In this paper, the range of applicability of the UNIFAC model has been extended by filling 46 gaps in the UNIFAC parameter table. Furthermore, a new group for the description of sulfones has been introduced. The examples show that the new UNIFAC parameters allow for the reliable prediction of vapor-liquid equilibria. Therefore, and because of its large range of applicability, UNIFAC is a suitable model for a variety of applications of industrial interest. The UNIFAC method is also used in the group contribution equation of state (EoS) PSRK
(predictive Soave-Redlich-Kwong).32,33 This means that the extension of UNIFAC automatically also increases the range of applicability of the PSRK EoS. Because of ongoing research work, the range of applicability of UNIFAC will be further enlarged, and its reliability continually improved. Many gaps in the UNIFAC parameter matrix have already been filled with the help of the huge amount of thermodynamic phase equilibrium data continuously stored in the DDB or measured in laboratories such as ours. The main group for sulfones is just one example of a newly introduced substance class in UNIFAC. Many other main groups of industrial interest have already been introduced into the parameter matrix of UNIFAC within the UNIFAC consortium project: e.g., isocyanates, epoxides, anhydrides, carbonates, monoalkylated formamides, aromatic nitriles, cyclic amides, cyclic esters, peroxides, acetals, aromatic bromides, and monoand dialkylated anilines. The present status of the UNIFAC group interaction parameter matrix is given in Figure 7. The publication of the new group interaction parameters is in progress. The most current status of the research work is always available via the Internet at http://www.unioldenburg.de/tchemie/consortium. Acknowledgment The authors thank the members of the UNIFAC consortium for the financial support of the ongoing research work. We would also thank DDBST GmbH (Oldenburg, Germany) for providing the latest version of the Dortmund Data Bank. Nomenclature anm ) UNIFAC group interaction parameters between main groups n and m Awk ) van der Waals group surface area F ) objective function Fi ) auxiliary property for component i (surface fraction/ mole fraction) gi ) weighting factor i, j ) components n, m ) main groups P ) pressure (kPa) qi ) relative van der Waals surface area of component i Qk ) relative van der Waals surface area of subgroup k ri ) relative van der Waals volume of component i Rk ) relative van der Waals volume of subgroup k T ) absolute temperature (K) VLE ) vapor-liquid equilibrium Vi ) auxiliary property for component i (volume fraction/ mole fraction) Vwk ) van der Waals group volume xi ) mole fraction of component i in the liquid phase yi ) mole fraction of component i in the vapor phase Xm ) mole fraction of group m in the liquid phase γ∞ ) activity coefficient at infinite dilution γi ) activity coefficient of component i Γk ) group activity coefficient of group k in the mixture Γ(i) k ) group activity coefficient of group k in pure substance i Θm ) surface fraction of group m in the liquid phase ν(i) k ) number of structural groups of type k in molecule i Ψnm ) UNIFAC parameter (eqs 13)
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(2) Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. VaporLiquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. (3) Gmehling, J.; Rasmussen, P.;Fredenslund, Aa. VaporLiquid Equilibria by UNIFAC Group Contribution. Revision and Extension. 2. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 118. (4) Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension. 3. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 676. (5) Tiegs, D.; Gmehling, J.; Rasmussen, P.; Fredenslund, Aa. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 4. Revision and Extension. Ind. Eng. Chem. Res. 1987, 26, 159. (6) Hansen, H. K.; Rasmussen, P.;Fredenslund, Aa.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and Extension. Ind. Eng. Chem. Res. 1991, 30, 2352. (7) Balslev, K.; Abildskov, J. UNIFAC Parameters for Four New Groups. Ind. Eng. Chem. Res. 2002, 41, 2047. (8) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968. (9) Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly and Completely Miscible Systems. AIChE J. 1975, 21, 116. (10) Gmehling, J.; Onken, U.; Arlt, W.; Grenzheuser, P.; Kolbe, B.; Weidlich, U.; Rarey, J. R. Vapor-Liquid Equilibrium Data Collection I; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, Germany, 1977-2001 (24 Parts). (11) Gmehling, J.; Tiegs, D.; Medina, A.; Soares, M.; Bastos, J.; Alessi, P.; Kikic, I.; Menke, J.; Schiller, M. Activity Coefficients at Infinite Dilution; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, Germany, 1986-1994 (4 Parts). (12) Rarey, J.; Gmehling, J. Computer-Operated Differential Static Apparatus for the Measurement of Vapor-Liquid Equilibrium Data. Fluid Phase Equilib. 1993, 83, 279. (13) Rarey, J.; Horstmann, S.; Gmehling, J. Vapor-Liquid Equilibria and Vapor Pressure Data for the System Ethyl tertButyl Ether + Ethanol and Ethyl tert-Butyl Ether + Water. J. Chem. Eng. Data 1999, 44, 532. (14) Weidlich, U.; Gmehling, J. Measurement of γ∞ using GLC. Part I. Results for the stationary phases 1-octacosane, 1-docosanol, 10-nonadecanone, and 1-eicosene. J. Chem. Eng. Data 1987, 32, 138. (15) Kirss, H.; Siimer, E.; Kudryavtseva, L. S. Isobaric vaporliquid equilibria in the mixtures of 1-heptyne + butanal, 1-octyne + 3-octyne, + ethybenzene and + dibutyl ether, 2-octyne + 1-octene. Thermochim. Acta 1993, 228, 283. (16) Raoult, F. M. U ¨ ber die Dampfdru¨cke aetherischer Lo¨sungen. Z. Phys. Chem. Stoechiom. Verwandtschaftsl. 1888, 2, 353. (17) Viswanathan, S.; Rao, M. A.; Prasad, D. H. L.; Rao, M. V. Isobaric Vapour-Liquid Equilibria in the Binary Systems Formed by Anisole with Benzonitrile and Nitrobenzene. Phys. Chem. Liq. 1995, 30 (4), 227. (18) Correa, A.; Blanco, A.; Tojo, J.; Correa, J. M.; Arce, A. Vapour-Liquid Equilibria of Pyridine + Acetate Mixtures at 101.325 kPa. Collect. Czech. Chem. Commun. 1991, 56, 2773.
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Received for review July 9, 2002 Revised manuscript received October 9, 2002 Accepted October 17, 2002 IE020506L
