Ind. Eng. Chem. Res. 1994,33, 1641-1643
1641
CORRELATIONS Extension of the GCVOL Method and Application to Some Complex Compounds Ioannis N. Tsibanogiannis, Nikolaos S. Kalospiros, and Dimitrios P. Tassios' Laboratory of Thermodynamics and Transport Phenomena, Department of Chemical Engineering, National Technical University of Athens, 9, Heroon Polytechniou Street, Zographou Campus, 157 80 Athens, Greece
The group contribution method GCVOL for the estimation of liquid densities is extended to compounds such as monocarboxylic acids, tertiary alcohols, allenes, alkynes, and cycloalkanes. The method is used in the prediction of liquid densities of some complex compounds, including several used in the synthesis of vitamins A and E.
Introduction Liquid density is a very important input parameter to most process design calculations. For example, liquid densities are required for estimating storage capacities, tower heights, and compressor loads, for sizing pipelines, in calculating vapor-liquid equilibria, and, in some cases, to estimate other physical properties such as surface tension (Spencer and Adler, 1978). The development of new processes in the field of biotechnology leads to the necessity of involving new compounds in the process design calculation. Information on the physical properties of such compounds is usually incomplete or even unavailable (Baglay et al., 1988). The motivation for extending the GCVOL method is to predict the liquid densities of some of these compounds. Two main categories of methods exist for estimating liquid densities of pure compounds. The first one is based upon the law of corresponding states. Such methods have been proposed by Yen and Woods (19661, Rackett (19701, Gunn and Yamada (1971), Spencer and Danner (19721, Bhirud (1978), Hankinson and Thomson (1979), and Thomson et al. (1982). Although accurate and applicable to the entire range from the triple point to the critical point, the aforementioned methods require knowledge of critical properties (T,, P,, VJ. This disallows their application to complex compounds of medium or large molecular weight for which critical properties are unknown (and in some cases even impossible to measure experimentally, especially when the compounds are thermally unstable). On the other hand, group contribution methods (Fedors, 1974; Van Krevelen, 1990; Elbro et al., 1991) do not present the drawback mentioned above and, consequently, constitute particularly attractive candidates for the estimation of liquid densities of complex compounds. In the following, we focus attention on the GCVOL method developed by Elbro et al. (1991). The GCVOL Method The liquid density, p , of a compound is calculated from the following equation: MW
MW
P=T=Cn,6v,
where MW is the molecular weight and V the molar volume. 0888-588519412633-1641$04.50/0
The molar volume is calculated from the sum over all group volume increments, Aui, and ni is the number of appearances of the ith group in the molecular structure of the compound. The temperature dependence of the molar group volume, Aui, is calculated by the following polynomial function: Aui = A i
+ BiT + C i p ;
T in K, Aui in cm3/mol (2)
Temperature, T ,varies between the melting point (Tm) and the normal boiling point (Tb)when the model is used to predict densities of nonpolymeric compounds, and between the glass transition temperature and degradation temperature if the model is used to predict densities of amorphous polymers. Elbro et al. (1991) presented group volume temperature constants for 36 different groups.
Determination of the New Groups Six new groups (Table 1) are introduced in this work that are not considered in the original version of the GCVOL method (Elbro et al., 1991). The first three of them are of the same type proposed by Elbro et al. (1991), and the rest function as corrections to certain chemical families (cyclopentanes, cyclohexanes,allene compounds). The respective molar group volumes, Aui, follow the temperature dependence as in the GCVOL method (eq 2). The relevant constants, Ai, Bi, and Ci, shown in Table 1 are estimated by fitting liquid density data taken from DIPPR data compilation (Daubert and Danner, 1989). The compoundsused to estimate these constants are shown in Table 2, along with the resulting average percent error in the estimated liquid density, in the temperature range between the melting and the normal boiling point.
Prediction of Liquid Densities Table 3 contains predictions for the liquid densities of several complex compounds. Notice that excellent agreement with the experimental data is generally obtained, with the average percent error being less than 2 % in most cases. The following comments can be made: 1. The method yields somewhat poorer predictions for the few first members of the homologous series considered in this study. See for example the absolute percent mean deviation ( % AMD) for acetic (5.4 5% ) and propionic (2.7 76 ) acids, as well as propadiene (6.7 % ). Similar behavior was 0 1994 American Chemical Society
1642 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 Table 1. GCVOL Parameters for Six New Groups new group COH C=CH COOH correction for =C= correction for cyclopentanes correction for cyclohexanes
no. 37 38 39 40 41 42
group volume temp const 1@B,cm3/(mol K) WC, cm3/(mol K2) -287.098 48.97 -28.813 18.49 -94.367 18.33 -58.082 16.86 -103.645 30.38 -105.403 25.07
A, cm3/mol 37.8699 27.8327 40.0107 14.1610 19.8947 21.9038
sample group assignment a b C
d e
f
tert-Butyl alcohol: 3 CH3,l COH. 1-Butyne: 1CH3,l CHz, 1C 4 H . Decanoic acid: 1CH3,8 CH2,l COOH. d 1,2-Butadiene: 1 CH3, 1 CH2=, 1 CH=, 1 C=, 1 correction for =C=. e Cyclopentane: 5 CH2, 1 correction for cyclopentane. fcyclohexane: 6 CHz, 1 correction for cyclohexane. Table 2. Average Percent Deviation between Calculated and Experimental Liquid Densities for the Compounds Used To Obtain the GCVOL Parameters in Table 1. Temperature Range between Melting Point and Normal Boiling Point. Data from Daubert and Danner (1989) new group
compounds used
% AMD"
COH C=CH COOH correction for allenes correction for cyclopentanes
tert-butyl alcohol methyl, ethylacetylene, 1-pentyne, 2-methyl-l-buten-3-yne, 3-methyl-1-butyne hexanoic, octanoic, nonanoic, decanoic acids 1,2-butadiene, 1,2- and 2,3-pentadienes, 3-methyl-l,%-butadiene cyclopentane, methyl-, ethyl-, n-propylcyclopentanes, and various isomeric dimethyl cyclopentanes cyclohexane, methyl-, ethyl-, n-propyl-, n-butylcyclohexanes
0.04 2.0 0.6 1.3 1.4
correction for cyclohexanes (I
0.6
Percent average mean deviation ( % AMD) is defined as %AMD = (lOO/n)~((perp - pdc)/pexpI, where n is number of data points.
Table 3. Prediction of Liquid Densities of Some Complex Compounds compound
temp range (K) 293.15-343.15 293.15-343.15
2-methyl-3-buten-2-01 3,7,11,15-tetramethyl-1hexadecen-3-01 298.15-308.15 2-methyl-2-pentanol 1-hexyne Tm-Tb 3,7-dirnethyl-6-octen-l-yn-3-01 293.15-343.15 3,7,11-trimethyl-l-dodecyn-3-ol 293.15-343.15 293.15-343.15 3,7,11,15-tetramethyl-1hexadecyn-3-01 acetic acid Trn-Tb propionic acid Tm-Tb n-butyric acid Tm-Tb n-valeric acid Trn-Tb 343.15-373.15 n-dodecanoic acid 353.15-373.15 n-tetradecanoic acid 353.15-373.15 n-hexadecanoic acid linoleic acid Trn-Tb oleic acid Tm-Tb stearic acid Tm-Tb adipic acid Tm-Tb propadiene Tm-Tb 293.15-343.15 6,10-dimethyl-4,5,9undecatrien-2-one cyclohexanol Tm-Tb cyclohexanone Tm-Tb 283.15-313.15 cyclohexene 283.15-313.15 cyclopentene 293.15-343.15 4-(2,6,6-trimethyl-1-cyclohexenl-yl)-3-buten-2-one 293.15-333.15 2,5,6-trimethyl-2cyclohexen-1-one cyclopropane Tm-Tb cyclobutane Tm-Tb cycloheptane Tm-Tb 298.84-464.95 cyclodecane 298.84-404.15 cyclodecane
%AMD rep 0.6 2 0.7 2 0.8 2.3 1.0 1.3 1.3
3 1 2 2 2
5.4 2.7 1.0 0.5 0.2 0.3 0.3 1.8 1.3 0.9 7.7 6.7 0.9
1 1 1 1 5 5 5 1 1 1 1 1 2
3.6 2.5 3.9 4.3 0.7
1 1 4 4 2
0.5
2
1.5 0.9 4.5 1.4 0.5
1 1 1
6 7
a (1)DaubertandDanner(1989);(2)Baglayetal. (1988);(3)Ortega (1985);(4) Vargaftic (1975);(5) Banipal et al. (1992);(6) McLure and Castillo (1985); (7) Meyer and Hotz (1976).
observed with methylacetylene (4.6%) and cyclopentane (4.2% ) in the categories of Table 2 containing triple bonds and cyclopentanes, respectively. 2. Caution is needed when using the carboxylic group to predict liquid densities of dicarboxylic acids, as shown
n i i h o u t r i n g Correction
0
6 0 150 200 250 300 350 400 450 (K) Figure 1. Predicted liquid densities for cyclic products with and without the respective ring correction. Upper curves corresponds to cyclohexanone; lower set of curves corresponds to n-propylcyclopentanone. Experimental data are taken from Daubert and Danner (1989). 100
with the results for the adipic acid (HOOC(CH2)&OOH). However, better accuracy is expected as the molecular weight of the dicarboxylic acid increases. 3. The ring corrections for cyclopentane and cyclohexane can be satisfactorily applied to the prediction of the density of cyclic derivatives containing rings of the same carbon number (e.g., cycloalkenes,cycloalcohols, and cycloketones) as shown with the typical results in Figure 1. Better liquid density predictions can be obtained by introducing new groups for napthenic ketones, alcohols, etc. These groups were not estimated here due to lack of experimental data for more than one compound and in order to keep the method as simple as possible. Furthermore, the ring correction for cyclopentanes can be used for density prediction of cyclopropanes and cyclobutanes, and the one for cyclohexanes may be used for density prediction of cycloheptanes. As also implied by the results of Elbro et al. (1991))any cyclic compound with carbon number larger than 10 can be treated as astandard linear hydrocarbon. For example, cyclodecane can be treated as a structure containing 10
Ind. Eng. Chem. Res., Vol. 33, No. 6,1994 1643
Literature Cited
U
c '-
0
C
0 .-+.-0 - I
\
>
a, U &&&A *cH*
3.7-dimethyl-6-octen1 -yn-3-ol 6,10-d1methyl-4,5,9-undecatr1en-2-one
Oeeeo 3,7,1 1 , 1 5 - t e t r a m e t h y l - l -hexadecen-3-01
-
290
310
3
330
350 1
T (K) Figure 2. Percent deviation in the prediction of liquid density of three complex compounds used in the synthesis of vitamins A and E as a function of temperature. Experimental data are taken from Baglay et al. (1988).
-CHz- groups corresponding to a linear hydrocarbon (see also Table 3). 4. Finally, the groups shown in Table 1 are used to predict liquid densities of several complex compounds used in the synthesis of vitamins A and E (Baglay et al., 1988). Some of these compounds contain more than one of the groups presented in this work, and thus, prediction of their density constitutes a rather severe test for the extension of the GCVOL method proposed here. Indeed, very good agreement with the experimental data is obtained. Typical examples are shown in Figure 2 for three of these compounds.
Conclusions An extension of the GCVOL method to compounds such as monocarboxylicacids, alkynes, tertiary alcohols,allenes, and cycloalkaneshas been presented. The estimated group volume constants for the corresponding groups are applied to the prediction of liquid densities of several medium to high molecular weight complex compounds, with emphasis on compounds used in the synthesis of vitamins A and E. Very good agreement is obtained between predicted and experimental results.
Baglay, A. K.; Gurariy, L. L.; Kuleshov, G. G. Physical Properties of Compounds Used in Vitamin Synthesis. J. Chem. Eng. Data 1988, 33, 512. Banipal, T. S.; Garg, S. K.; Ahluwalia, J. C. Densities of some higher alkan-1-oic acids at temperatures from 343.15 K to 373.15 K and at pressures up to 9 MPa. J. Chem. Thermodyn. 1992,24,729. Bhirud, V. S. Saturated Liquid Densities of Normal Fluids. AZChE J. 1978,24, 1127 Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties ojPure Compounds: Data Compilation; Hemisphere: New York, 1989. 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. Znd. Eng. Chem. Res. 1991,30,2576. Fedors, R. F. A Method for Estimating Both the Solubility Parameter and Molar Volumes of Liquids. Polyrn. Eng. Sci. 1974, 14, 147. Gunn, R. D.; Yamada, T. A Corresponding States Correlation of Saturated Liquid Volumes. AIChE J. 1971,17, 1341. Hankinson, R. W.; Thomson, C . H. A New Correlation for Saturated Densities of Liquids and Their Mixtures. AZChE J. 1979,25,653. McLure, I. A.; Castillo, J. M. B. Density of Cyclodecane from 25 to 192 "C. J. Chem. Eng. Data 1985, 30, 253. Meyer, G. S; Hotz, C. A. Cohesive Energies in Polar Organic Liquids. 3. Cyclic Ketones. J. Chem. Eng. Data 1976,21, 274. Ortega, J. Densities and Thermal Expansivities of Hexanol Isomers at Moderate Temperatures. J. Chern. Eng. Data 1985,30, 5. Rackett, H. G. Equation of State For Saturated Liquids. J. Chem. Eng. Data 1970, 15, 514. Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 1972,17, 236. Spencer, C. F.; Adler, S. B. A Critical Review of Equations for Predicting Saturated Liquid Density. J. Chem. Eng. Data 1978, 23, 82. Thomson, G. H.; Brobst, K. R.; Hankinson, R. W. An Improved Correlation for Densities of Compressed Liquids and Liquid Mixtures. AZChE J. 1982,28, 671. Van Krevelen, D. W. Properties of Polymers, 3rd ed.; Elsevier Scientific: Amsterdam, 1990; Chapter 4, pp 71-107. Vargaftic, N. B. Tables on the Thermophysical Properties ojLiquids and Gases, 2nd ed.; J. Wiley: New York, 1975. Yen, L. C.; Woods, S. S. A Generalized Equation for Computer Calculation of Liquid Density. AZChE J. 1966, 12, 95.
Received f o r review March 1, 1994 Accepted March 7, 1994 @
Abstract published in Advance ACS Abstracts, April 1,1994.
