408
Ind. Eng. Chem. Res. 2003, 42, 408-412
CORRELATIONS Extension and Revision of the Group Contribution Method GCVOL for the Prediction of Pure Compound Liquid Densities E. Christian Ihmels and Ju 1 rgen Gmehling* Department of Industrial Chemistry, Carl von Ossietzky University of Oldenburg, P.O. Box 2503, D-26111 Oldenburg, Germany
The group contribution method GCVOL developed by Elbro et al. (Ind. Eng. Chem. Res. 1991, 30 (12), 2576-2582) has been extended and revised. To the already existing 36 original groups 24 new groups have been introduced utilizing the Dortmund Data Bank for Pure Component Properties (DDB-Pure). With this extension now also the densities of tertiary alcohols, alkynes, carboxylic acids, allenes, cycloalkanes, fluorides, bromides, iodides, thiols, sulfides, sulfates, amines, nitriles, and nitro compounds can be calculated between the melting point and the normal boiling point. An average mean deviation of 1.5% and 1.3% for a database of 1040 compounds has been obtained for the extended GCVOL method and the newly developed method, respectively. The applicability and reliability of this group contribution method has also been compared with the corresponding state method of Rackett (J. Chem. Eng. Data 1970, 15 (4), 514-517). Introduction Between 1991 and 1998 a data bank for purecomponent thermodynamic and transport properties was developed which is continuously updated. This project was supported by the German Federal Ministry for Research and Technology (BMBF), FIZ Chemie (Berlin), and DDBST GmbH (Oldenburg). The database is an extension of the Dortmund Data Bank (DDB) for phase equilibria and excess properties. The main objectives of the pure-component database are the determination of recommended values, the fitting of recommended correlation parameters, and the development of improved prediction methods. Besides the vapor pressure, the saturated liquid density is a very important property needed for the design of industrial plants, pipelines, pumps, etc. Most prediction methods for saturated liquid densities are based on the corresponding state principle. One of the most popular methods for the prediction of liquid densities is the very simple Rackett equation3 and the modifications by Spencer and Danner4 and by Yamada and Gunn.5 However, corresponding state methods have some crucial disadvantages. At first, they require the knowledge of the critical properties. However, there is a general lack in experimental critical temperatures, pressures, and especially critical volumes, particularly for larger molecules. For example, in the Dortmund Data Bank for Pure Component Properties (DDB-Pure),2 critical temperatures for 1247, critical pressures for 971, and critical volumes for 702 compounds are available. On the other hand, the accuracy of these quantities, especially the critical volume, is very important for the accuracy of the predicted volumes using corresponding * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: ++49-441-7983831. Fax: ++49-441-798-3330.
state methods. However, density measurements at the critical point are normally afflicted with larger errors than measurements at lower temperatures. Moreover, often these measurements are impossible because the substance in question decomposes at temperatures below the critical point. In 1997, a combination of the Rackett equation and a group contribution method for the estimation of liquid densities was published by Sastri et al.6 Nevertheless, the critical temperature and the normal boiling point are still required for this method. Another approach is the group contribution concept, which only needs the chemical structure of the desired molecule to estimate the thermophysical property, such as the liquid density. In 1991, Elbro et al.1 published the group contribution method GCVOL for the prediction of saturated liquid densities for temperatures between the melting point and the normal boiling point. The method contains 36 groups and is applicable for molecules very different in molecular weight from solvents to oligomers and even polymers. Later the GCVOL model was extended by Tsibanogiannis et al.7 by six new groups. In the thesis of Ihmels, the original GCVOL model has been extended and revised.8 The aim of the work was to allow predictions for compounds with interesting functional groups such as amines or halogenides. In the extension 24 new groups where introduced for the density prediction of tertiary alcohols, alkynes, carboxylic acids, allenes, cycloalkanes, fluorides, bromides, iodides, thiols, sulfides, sulfates, amines, nitriles, and nitro compounds. The new model now contains 60 groups. For the further development of the GCVOL method, the DDB-Pure database containing experimental liquid densities for about 6500 compounds has been employed. Furthermore, density correlation parameters for about 2000 compounds are available, which have been used as pseudo experimental data to fit the required parameters for the groups. In the first step, only the parameters of the 24 new groups were fitted
10.1021/ie020492j CCC: $25.00 © 2003 American Chemical Society Published on Web 12/24/2002
Ind. Eng. Chem. Res., Vol. 42, No. 2, 2003 409
to maintain the original parameters of Elbro et al. for the first 36 groups (the GCVOL-60 method). In the second step, the parameters of all 60 groups were fitted to the comprehensive database. In contrast to the simply extended GCVOL-60 method, the new revision has been named GCVOL-OL-60 (OLdenburger revision with 60 groups). For the development and testing of the new GCVOL group assignment, the molecular structure database CHEMDB and the powerful software package DDBSP of the DDBST GmbH have been employed.2 The graphical editor ARTIST can be used to draw molecular structures or retrieve structures from the database, which today contains more than 15 000 compounds. With ARTIST in combination with the special algorithm AUTOINKR, molecules can be automatically subdivided into structural groups for more than 70 different group contribution methods. Thus, a multitude of different thermophysical and transport properties can directly be estimated. For the prediction of normal boiling points, a new group contribution method was recently developed by Cordes and Rarey.9 They also employed the DDB-Pure database together with the DDB software package. The GCVOL Method For the calculation of liquid densities, the following simple equation has been employed by Elbro et al.1:
F)
MW ) V
MW ni∆υi
∑
(1)
where MW is the molecular weight and V the molar volume. The volume is calculated by summing up all group volume increments ∆υi, where ni is the number of groups i appearing in the compound. For determining the temperature dependence of the group volume increments, Elbro et al. employed the following polynomial function of the absolute temperature:
∆υi ) Ai + BiT + CiT 2
(2)
whereby the units are K for the temperature and cm3‚mol-1 for ∆υi. The method is applicable for compounds very different in molecular weight from solvents to oligomers and polymers. Molar volumes or densities can be predicted for temperatures between the melting and normal boiling points for nonpolymeric compounds and between the glass transition temperature and the degradation temperature for amorphous polymers. Elbro et al.1 presented parameters for 36 different groups for a variety of chemical classes, e.g., noncyclic alkanes, aromatics, alkenes, alcohols, ketones, aldehydes, ethers, esters, chlorides, and siloxanes. For the determination of the group parameters, the DIPPR database10 has been employed by Elbro et al. They used the DIPPR density correlations to calculate pseudo experimental densities in the temperature range between 200 and 500 K in 10 K steps. In 1994, the GCVOL method was extended by Tsibanogiannis et al.7 Six new groups were introduced for tertiary alcohols, alkynes, carboxylic acids, allenes, and cycloalkanes. In contrast to the other groups, the groups for allenes and cycloalkanes are correction terms. For fitting the parameters, Tsibanogiannis et al. also used
the DIPPR database. Currently, density correlations for 1685 compounds are stored in the DIPPR database. Extension and Revision of GCVOL For the extension and revision of the GCVOL model, the correlation parameters of DDB-Pure have been applied to calculate pseudo experimental data. In contrast to the DIPPR database, the parameters are based on experimental densities stored in DDB-Pure. The experimental densities are correlated with a modified Rackett equation within the experimental uncertainties. The correlation parameters for about 2000 compounds have been critically checked, e.g., by graphical representations and statistical evaluations, before they were used for the extension and revision of the GCVOL method. For further development, the correlations of some compounds were rejected because the experimental data were only available from one researcher and were dubious or when the data of different researchers showed large scattering. After the data and correlations were reviewed, the new groups were defined, depending on the database available and the importance for fitting the parameters for new functional groups, especially for the heteroatoms oxygen, nitrogen, and sulfur and for the halogenides. First, the groups proposed by Tsibanogiannis et al.7 were introduced for tertiary alcohols (group number 37), alkynes (38), and carboxylic acids (39). Instead of correction terms, a new group for allenes (40) and hydrocarbon groups for cycloalkanes (41-43) were added. However, the latter groups cannot be recommended for the small cyclopropane and cyclobutane rings. Subsequently, heteroatomic groups were introduced for fluorides (44-47), bromides (48), iodides (49), thiols (50), sulfides (51), sulfates (52), amines (53-57), nitro compounds (58 and 59), and nitriles (60). The correlations for 1040 compounds have been used for the further development and evaluation of the parameters for the 60 groups. For the original 36 groups, the correlation parameters for 670 compounds was available. From the 15 760 compounds stored in the DDB-Pure, 6375 (40%) can now be described by the 60 groups, in contrast to 3798 (24%) described by the original 36 groups. By the way, with the Rackett equation only 645 or 4% of the 15 760 molecules can be calculated, in particular because of the lack of experimental critical data. For the fits only densities in the most interesting temperature range between 200 and 500 K in 10 K steps and only compounds with one functional group other than alkyl and arene groups are used. Furthermore, only data between the melting and normal boiling points are included. Data of 680 compounds have been employed for the determination of the group parameters by a multilinear least-squares method using a GaussJordan elimination similar to the method described by Elbro et al. This method is very fast and leads to exactly one solution. Because of the very large database and in contrast to the work by Elbro et al., no weighting factors were used. For the GCVOL-60 extension, only the parameters of the 24 new groups were fitted using the original parameters of Elbro et al. for the first 36 groups. Therefore, all current users of the original GCVOL method will obtain the same results with the first 36 groups of GCVOL-60. The parameters of the remaining 24 new groups were fitted simultaneously. On the basis of the same group assignment, the parameters for all 60 groups were also fitted for the GCVOL-OL-60 method. To avoid intercorrelations, the
410
Ind. Eng. Chem. Res., Vol. 42, No. 2, 2003
Table 1. Parameters of the Extended GCVOL-60 and GCVOL-OL-60 Methods parameters of GCVOL-60
parameters of GCVOL-OL-60
103B,
105C,
no.
group
A, cm3/mol
cm3/(mol K)
cm3/(mol K2)
A, cm3/mol
103B, cm3/(mol K)
105C, cm3/(mol K2)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
-CH3 -CH2- (chain) >CH- (chain) C (chain) ACH AC-CH3 AC-CH2AC-CH< AC-C CH2d -CHd >Cd -CH2OH >CHOH AC-OH CH3CO (ketone) CH2CO (ketone) CHCO (ketone) CHO (aldehyde) CH3COO (ester) CH2COO (ester) CHCOO (ester) COO (ester) ACCOO (ester) CH3O (ether) -CH2O- (ether) >CHO- (ether) CO- (ether) CH2Cl CHCl CCl CHCl2 CCl3 ACCl Si SiO COH (tertiary alcohol) -CtCH (alkyne) -COOH dCd (allene) CH2 (cyclic) CH (cyclic) C (cyclic) -CF3 -CHF2 -CH2F ACF -Br -I -SH (thiol) -CH2S- (sulfide) -CH2SO4CH2- (sulfate) -CH2-NH2 (amine) >CH-NH2 (amine) >NH (secondary amine) >N- (tertiary amine) AC-NH2 (amine) -CH2NO2 (nitro) AC-NO2 (nitro) -CN (nitrile)
18.96 12.52 6.297 1.296 10.09 23.58 18.16 8.925 7.369 20.63 6.761 -0.3971 39.46 40.92 41.2 42.18 48.56 25.17 12.09 42.82 49.73 43.28 14.23 43.06 16.66 14.41 35.07 30.12 25.29 17.4 37.62 36.45 48.74 23.51 86.71 17.41 -85.46 53.3 18.37 -24.39 24.97 -92.94 171.6 15.05 10.04 -20.84 25.7 38.71 27.01 -14.51 37.21 72.68 34.49 125.8 -64.88 -30.29 14.25 62.26 19.6 17.56
45.58 12.94 -21.92 -59.66 17.37 24.43 -8.589 -31.86 -83.6 31.43 23.97 -14.1 -110.6 -193.2 -164.2 -67.17 -170.4 -185.6 45.25 -20.5 -154.1 -168.7 11.93 -147.2 74.31 28.54 -199.7 -247.3 49.11 27.24 -179.1 54.31 65.53 9.303 -555.5 -22.18 518.5 -185.2 30.54 177.2 -48.68 531.9 -1074.7 178.2 163.9 318.3 -63.53 -96.26 22.68 224.96 -81.76 -61.92 -53.14 -809.8 456.8 187.1 8.119 -162.6 28 19.76
0 0 0 0 0 0 0 0 0 0 0 0 23.31 32.21 22.78 22.58 32.15 28.59 0 16.42 33.19 33.25 0 20.93 0 0 40.93 40.69 0 0 32.47 0 0 0 97.9 0 -80.24 39.79 0 -23.32 7.827 -65.36 168.8 -21.96 -23.92 -46.55 14.08 20.26 0 -29.11 17.62 14.46 16.8 155.6 -71.69 -34.45 0 30.75 0 0
16.43 12.04 7.299 87.8 9.929 24.71 16.84 54.39 39.37 32.69 -1.651 -10.93 36.73 14.26 46.35 30.16 53.35 33.69 -19.91 53.82 36.32 38.23 61.15 27.61 19.87 13.57 -103.2 29.91 31.47 52.97 3.07 58.25 61.39 19.86 144 41.93 -95.68 52.71 20.52 1.245 15.65 -52.95 115.8 8.659 14.57 -14.23 10.74 36.89 41.02 -23.09 44.12 78.77 36.93 126.8 -0.201 5.153 13 67.97 19.92 17.56
55.62 14.1 -26.06 -619.9 17.41 21.11 -4.642 -290.8 -272.1 -60.14 93.42 62.41 -71.25 -8.187 -167 39.19 -179.6 -84.87 278.2 -62.34 -36.46 -112.1 -248.2 -20.77 50.6 26.68 684.3 -218.5 30.12 -168.7 106.3 -85.68 -16.11 23.09 -913.9 -142.3 593.5 -177.9 23.39 -24.51 5.985 295.6 -767 218.7 123.6 276.3 28.18 -83.88 -60.69 294 -105.3 -84.73 -67.32 -808.7 63.28 -39.31 12.11 -188.2 25.38 20.3
0 0 0 88.22 0 0 0 33.01 24.92 16.28 -14.39 -14.13 14.06 0 22.13 0 28.84 0 -40.87 18.8 11.52 16.65 36.81 0 0 0 -105.6 27.32 0 26.19 -27.09 22.37 13.81 0 144 13.76 -94.79 37.37 0 16.5 0 -31.38 122.6 -28.3 -15.26 -40 0 18.3 12.12 -42.46 17.25 14.52 18.82 153.4 -13.16 0 0 32.73 0 0
four alkane groups (numbers 1-4) were fitted first using data from 69 noncyclic alkanes. Then the parameters of the other 56 groups were determined simultaneously. This means that the parameters of the GCVOL-OL-60 method of all groups are based on a larger and more reliable database. In Table 1 all groups and parameters of the extended GCVOL-60 and GCVOL-OL-60 methods are listed, including the original parameters of Elbro et al. (GCVOL-60 groups 1-36). In Table 2 a few examples for group assignments are presented. For more examples related to the first 36 groups, see work by Elbro et al.1 For a few compounds, the deviations between experimental densities taken from DDB-Pure and the predictions by GCVOL-60 and GCVOL-OL-60 are shown in
Figure 1. Besides the good agreement between the predicted and experimental values taken from DDBPure, a distinct improvement using GCVOL-OL-60 can be noticed. Higher deviations are generally observed for glycols, e.g., for triethylene glycol built with the two alcohol groups (13), three alkane groups (2), and three ether groups (26). Elbro et al. found average mean deviations of only 1% for glycol compounds, but they compared the GCVOL predictions with literature data between 298 and 328 K only. For a comprehensive comparison, the density data of all available 1040 compounds has been used. The average mean deviations (AMD) for the different substance families are given in Table 3 for the GCVOL-60 and GCVOL-OL-60 methods. The deviations were calculated in the same temperature
Ind. Eng. Chem. Res., Vol. 42, No. 2, 2003 411 Table 2. Examples for the Group Assignments by the GCVOL Methodsa compound
group assignment 1 -CH3, 1 -CH2-, 1 -CH2NO2 2 -CH3, 1 -CH2SO4CH24 -CH3, 2 >CH-, 1 >NH 1 -CH3, 1 -CH2-, 1 -COOH 2 -CH3, 1 -CH2S5 ACH, 1 AC-CH2-, 1 -CN 4 ACH, 1 AC-NH2, 1 AC-NO2 5 CH2 (cyclic), 1 CH (cyclic), 1 -SH 1 -CH3, 1 dCH2, 1 -CHd, 1 dCd 1 -CH2- 1 -COOH, 1 -I 1 -COOH, 1 -CF3 3 -CH3, 2 -CH2-, 1 -CHd, 1 >Cd, 1 COH, 1 -CtCH
nitropropane diethyl sulfate diisopropylamine propionic acid methylethyl sulfide phenylacetonitrile nitroaniline cyclohexanethiol 1,2-butadiene iodoacetic acid trifluoroacetic acid 3,7-dimethyl-6-octen-1-yn-3-ol a
For examples using the first 36 groups, see work by Elbro et
al.1
limits and intervals as those described for the parameter determination.
1 AMD ) 100 n
Vexp,n - Vcalc,n | (%) Vexp,n
∑n |
(3)
The deviations for the whole database (last two lines in Table 3) in the case of the original 36 groups (670 compounds and 5880 data points) as well as for all 60
Figure 1. Deviations between the predictions with GCVOL-60 and GCVOL-OL-60 and pseudo experimental values (from correlations) taken from the Dortmund Data Bank for Pure Component Properties2 for four selected compounds.
groups (1040 compounds and 8966 data points) show improvements for GCVOL-OL-60 with 1.16 and 1.26% in comparison to 1.41 and 1.54% for GCVOL-60, respectively. In most cases the substance families are described more accurately with the GCVOL-OL-60 method than with the GCVOL-60 method. To get an impression of the scattering, the deviations for all 1040 substances compared are shown in Figures 2 and 3. The deviations show a nearly Gaussian distribution. The highest deviations obtained with GCVOL-60 are 16% for 1,3-butane-
Table 3. Average Mean Deviations for the GCVOL-60 and GCVOL-OL-60 Methods
a
substance families
group number(s)
no. of compounds (data points)
GCVOL-60 AMD, %
GCVOL-OL-60 AMD, %
alkanes cycloalkanesa alkenes alkynesa allenesa aromatics alcohols tertiary alcoholsa ketones aldehydes esters carboxylic acidsa ethers chlorides fluoridesa bromidesa iodidesa thiolsa sulfidesa sulfatesa aminesa nitro compoundsa nitrilesa siloxanes total (extension) total (GCVOL)
1-4 41, 42, 43 10, 11, 12 38 40 5-9 13-15 37 16-18 19 20-24 39 25-28 29-34 44-47 48 49 50 51 52 53-57 58, 59 60 35, 36 60 groups 36 groups
71 (716)b 29 (246)b 47 (245)b 9 (73)b 3 (6)b 38 (331)b 122 (1306) 13 (91) 38 (306) 21 (153) 255 (2422) 33 (271) 106 (753) 103 (869) 34 (220) 39 (309) 21 (177) 18 (95) 17 (138) 3 (33) 74 (667) 26 (304) 49 (428) 21 (151) 1040 (8966) 670 (5880)
1.04 2.04 1.47 0.56 0.90 1.27 2.09 1.75 1.21 1.60 1.67 2.04 2.10 1.30 1.77 1.77 1.15 1.40 1.02 0.45 1.41 1.74 1.62 2.11 1.54 1.41
0.85 2.22 1.16 0.70 1.13 1.11 1.60 2.13 0.80 1.45 1.36 1.63 1.20 0.97 1.62 1.69 1.08 1.44 1.04 0.52 1.27 1.02 1.57 1.67 1.26 1.16
New introduced structural groups. b Only compounds without further functional groups.
Table 4. Average Mean Deviations for Density Predictions of Some Multifunctional Molecules
2-cyano-3-methylpent-2-enoic acid ethyl ester (E)-3-bromo-3-phenylacrylic acid methyl ester 3-chloro-4-methylaniline 3-methoxypropionitrile 3-(hexylamino)propanenitrile 1,3,5-trichloro-2,4,6-trifluorobenzene benzenemethanethiol (benzyl mercaptan) N-ethyldiethanolamine
temp range, K
GCVOL-60 AMD, %
GCVOL-OL-60 AMD, %
300-360 303-353 303-353 290-360 300-360 350-490 294-314 302-472
2.09 2.57 0.97 4.87 0.32 1.22 0.76 1.04
0.80 0.47 0.54 4.20 0.83 0.41 0.13 0.45
412
Ind. Eng. Chem. Res., Vol. 42, No. 2, 2003
Conclusion and Outlook
Figure 2. Deviations between the predictions with GCVOL-60 and pseudo experimental values (from correlations) taken from the Dortmund Data Bank for Pure Component Properties2 for the compared 1040 substances.
Figure 3. Deviations between the predictions with GCVOL-OL60 and pseudo experimental values (from correlations) taken from the Dortmund Data Bank for Pure Component Properties2 for the compared 1040 substances.
diol at 482 K (GCVOL-OL-60: 1.5%), whereas with GCVOL-OL-60, a maximum deviation of 10.7% for the multifunctional compound monoethanolamine at 431 K (GCVOL-OL: 15%) was obtained. The high deviation for monoethanolamine is mainly caused by the proximity effect, caused by the use of just two functional groups (groups 13 and 53) next to each other. Although amides were not considered for the development, maximum deviations of about 10% are obtained for amides (such as dimethylformamide or methylformamide) if the aldehyde group (group 19) and the secondary amine (group 55) or the tertiary amine (group 56) group are used to build an amide group. For an estimation of the uncertainty of the GCVOL methods, the usual scattering of experimental saturated liquid densities from different researchers should be considered. Deviations of 1% are not unusual even for measurements at room temperature of common substances (e.g., acetone, butanol, or octane). In most cases, the deviations are not a function of the publication year. The GCVOL method can be very reliably applied for molecules with more than one functional group. In Table 4 the average mean deviations for various compounds with different functional groups are given. With some exceptions, the deviations are moderate. For the Rackett equation, an average mean deviation of 6.7% for 551 compounds (7861 data points) with the highest deviation of 188% for methylhydrazine is obtained. These rather large deviations are mainly a result of uncertainties of the experimental critical temperatures, critical pressures, and especially critical densities. On the other hand, the advantage of corresponding state models is their applicability for calculating densities between the normal boiling point and the critical point.
The group contribution method GCVOL of Elbro et al.1 has been extended and revised. With this extension also liquid densities of tertiary alcohols, alkynes, carboxylic acids, allenes, cycloalkanes, fluorides, bromides, iodides, thiols, sulfides, sulfates, amines, nitriles, and nitro compounds can be predicted between the melting point and the normal boiling point. For the predictions, an average mean deviation of 1.5% with the extended GCVOL-60 or 1.3% for the GCVOL-OL-60 method has been obtained for a database of 1040 compounds. Also, reliable density predictions for compounds with more than one functional group are possible. The GCVOL methods can also be used to predict liquid densities required for the estimation of other thermophysical properties, as shown by Retzekas et al.11 for the prediction of normal boiling points, critical temperatures, and pressures. Moreover, the range of applicability is much larger and the reliability of this group contribution method is much better than those of a corresponding state method like the Rackett equation. Because of the simplicity, the reliability, and the large range of applicability of the GCVOL methods, further developments are appropriate. Of special importance are aromatic hydrocarbons from petroleum or liquid coal fractions. Therefore, an extension for polycyclic (condensed) aromatic hydrocarbons is in progress. Literature Cited (1) Elbro, H. S.; Fredenslund, A.; Rasmussen, P. Group Contribution Method for the Prediction of Liquid Densities as a Function of Temperature for Solvents, Oligomers, and Polymers. Ind. Eng. Chem. Res. 1991, 30 (12), 2576-2582. (2) Dortmund Data Bank for Pure Component Properties (DDBPure) and DDB software package, DDBST GmbH (www.ddbst.de), Oldenburg, Germany, 2002. (3) Rackett, H. G. Equation of State for Saturated Liquids. J. Chem. Eng. Data 1970, 15 (4), 514-517. (4) Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972, 17 (2), 236-241. (5) Yamada, T.; Gunn, R. D. Saturated Liquid Molar Volumes. The Rackett Equation. J. Chem. Eng. Data 1973, 18 (2), 234-236. (6) Sastri, S. R. S.; Mohanty, S.; Rao, K. K. Prediction of Saturated Liquid Volumes of Organic Compounds. Fluid Phase Equilib. 1997, 132, 33-46. (7) Tsibanogiannis, I. N.; Kalospiros, N. S.; Tassios, D. P. Extension of the GCVOL Method and Application to Some Complex Compounds. Ind. Eng. Chem. Res. 1994, 33 (6), 1641-1643. (8) Ihmels, E. C. Experimentelle Bestimmung, Korrelation und Vorhersage von Dichten und Dampfdru¨cken. Ph.D. Dissertation, University of Oldenburg, Oldenburg, Germany, 2002 (www.shaker.de). (9) Cordes, W.; Rarey, J. A New Method for the Estimation of the Normal Boiling Point of Non-Electrolyte Organic Compounds. Fluid Phase Equilib. 2002, 201, 409-433. (10) Design Institute for Physical Properties (DIPPR) Project No. 801 (Evaluated Process Design Data), Version 2000, http:// dippr.byu.edu, Provo, UT, 2001. (11) Retzekas, E.; Voutsas, E.; Magoulas, K.; Tassios, D. Prediction of Physical Properties of Hydrocarbons, Petroleum, and Coal Liquid Fractions. Ind. Eng. Chem. Res. 2002, 41 (6), 16951702.
Received for review July 1, 2002 Revised manuscript received November 13, 2002 Accepted November 15, 2002 IE020492J
