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Ind. Eng. Chem. Res. 1996, 35, 2484-2486
Correlation of the Acentric Factor for Hydrocarbons Liming Liu and Shaozhou Chen* Petroleum Processing Research Center, East China University of Science and Technology, Shanghai 200237, China
Correlations are developed to estimate the acentric factor for hydrocarbons. The correlations are expressed as functions of the Antoine constants and liquid density. A general correlation for hydrocarbons and four correlations for paraffins, naphthenes, aromatics, and olefins are developed. Introduction The acentric factor (Pitzer, 1955) is widely used in calculating the thermodynamic and transport properties of pure substances as well as mixtures. The acentric factor, ω, is defined as
ω ) -log(Pvp)r|Tr)0.7 - 1.00
(1)
The acentric factor of a pure substance is assumed to represent the acentricity or nonsphericity of a molecule. For a monatomic molecule the value of ω is close to zero (0.001 for argon), while for a long-chain molecule the value of ω is considerably larger (0.907 for n-eicosane). It also increases with polarity (0.099 for ethane contrasts with 0.644 for ethanol). Therefore, the acentric factor is often employed to measure the geometry and polarity of a molecule. For most molecules the acentric factors are between 0 and 1. Several methods for estimating ω have been presented. The correlations Edmister (1958), Lee and Kesler (1975), Nath et al. (1976), and Chen et al. (1993) require known Tc, Pc, and Tb. Watanasiri (1985) uses the easily measurable SG, MW, and Tb, and Lin and Chao (1984) use d20, MW, Tb, and Tc to calculate ω. Han and Peng (1993) uses a group-contribution method to estimate ω. Table 1 shows that the correlations containing both Pc and Tc as input parameters are much more accurate than those otherwise. This is not surprising since the inherent relation is shown in eq 1. However, when Pc and Tc are unknown and the estimated values have to be used, the deviations of those correlations increase significantly (see Table 1). In fact, both the deviations of Tc and Pc contribute to the deviaiton of ω calculated, and the deviation of ω is more sensitive to Tc deviation than to Pc deviation (see Figures 1 and 2). In this work, we developed a correlation of the acentric factor for hydrocarbons. We also developed four separate correlations for paraffins, naphthenes, aromatics, and olefins to obtain further prediction accuracy. In these correlations, we use the Antoine constants, A, B, and C, which are widely available in the literature and easily measurable, and the liquid density d20 as input parameters to correlate ω. Since the estimations of Pc and Tc are avoided, these correlations can be directly used for substances whose Tc and Pc are not available. Correlation Development Antoine proposed a simple correlation of vapor pressure which has been widely used to calculate the vapor pressure of substances:
ln Pvp ) A -
B T+C
(2)
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Table 1. AAD % of Several Correlations Calculated from Literature Tc and Pc Values and from Estimated Tc and Pc Valuesa paraffins naphthenes aromatics olefins overall
no. of points
I
II
III
Ib
IIb
IIIb
62 40 26 43 171
2.79 5.49 2.60 7.76 4.64
1.73 3.59 1.41 5.51 3.06
1.73 3.39 1.22 5.30 2.94
9.22 30.53 12.45 19.32 17.24
9.61 29.97 12.01 18.87 17.07
9.74 30.17 11.97 19.02 17.19
a I ) Edmister (1958); II ) Lee-Kesler (1975); III ) Chen et al. (1993). b Tc and Pc are calculated from Kesler-Lee (1976).
Figure 1. Sensitivity of ω deviation to Tc deviation: (O) Edmister (1958); (×) Lee-Kesler (1975); (4) Chen et al. (1993). x axis: % Tc deviation. y axis: % AAD in ω estimation.
Figure 2. Sensitivity of ω deviation to Pc deviation: (O) Edmister (1958); (×) Lee-Kesler (1975); (4) Chen et al. (1993). x axis: % Pc deviation. y axis: % AAD in ω estimation.
in which A, B, and C are characteristic of the substance and are widely available in the literature. Considering that the correlations containing Tc and Pc give satisfactory accuracy while the correlations without Pc and Tc are often rather rough, we assume that this is because, in the definition, the acentric factor is highly involved in Tc and Pc. Thus, in order to develop a more accurate correlation, a possible approach is to introduce parameters which can represent the properties of compounds at high temperature and high pressure (near Tc and Pc). However, the values of this type of parameters are scarce in the literature or difficult to measure. The Antoine constants seem to be an alternative. Although they do not represent high-temperature and high-pressure properties nor are they applicable in such a situation, they somehow reflect the tendency of the vapor pressure toward this situation. The database used in this correlation consists of 171 © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 7, 1996 2485 Table 2. Comparison of the Proposed Correlations with Several Other Correlations AAD % of correlations proposed correlations no. of points
separate
general
Edmistera
Lee-Keslera
Chena
Watanasiri
62 40 26 43 171
1.49 4.61 7.10 6.12 4.23
3.35 8.11 9.90 15.00 7.71
9.22 30.53 12.45 19.32 17.24
9.61 29.97 12.01 18.87 17.07
9.74 30.17 11.97 19.02 17.19
11.61 17.33 11.96 22.10 15.64
paraffins naphthenes aromatics olefins overall a
Tc and Pc are calculated from Kesler-Lee (1976).
compounds, including 62 paraffins, 40 naphthenes, 26 aromatics, and 43 olefins. The acentric factor data are those compiled by Daubert and Danner (1985) and Reid et al. (1987). The Antoine constants’ values are from Boublik et al. (1984) and API Research Project 44 (1971). Correlations
General correlation ln(ω + 1.0) ) 0.425 983 × 10-4(B/273.15)3 48.6468/A2 + 0.396 627 × 10-2C + 0.107 632(-C/d20)1/2 + 0.061 172 0 Separate correlations a. for paraffins ln(ω + 1.0) ) 0.137 976 × 10-4(B/273.15)3 45.8873/A2 - exp(200.595 90 - B/A) - exp(-C 145.2569) + 0.0571 505(-C/d20)1/2 + 0.300 461 b. for naphthenes ln(ω + 1.0) ) -15 212.0/A + 64438.4/A2 0.140 713 × 10-2 exp(A) + 0.106 496 × 10-5C3 + exp(-C - 147.7853) - 0.697 822 × 10-6(C/d20)3 exp(52.7281 + C/d20) + 906.247 c. for aromatics ln(ω + 1.0) ) 0.190 349 × 10-4 exp(A) 11.2746/C + 0.093 732 2(-C/d20)1/2 - 0.941 545 d. for olefins ln(ω + 1.0) ) 0.290 312 × 10-3(B/273.15)3 + 654.966/A - 3006.79/A2 + exp(108.272 47 + C/d203) -0.305 771 × 10-3C2 + exp(-C 130.2832) - 17.6929/(C/d20) + 0.181 353 × 10-3(C/d20)2 - 36.160 17 Discussion Comparisons of the proposed correlations with several commonly used correlations are given in Table 2. The same database was used in all of the calculations. The proposed correlations, although still giving no better results than those containing literature values of Tc and Pc as input parameters, provide improved prediction
accuracy over all previous correlations which do not use literature values of Tc and Pc as input parameters. We have also noted that correlatin ω + 1.0 rather than ω itself gives slight better results. In case the Antoine constants are not available, the proposed correlations are still applicable. One can easily measure the vapor pressure of a substance at three different temperatures and fit these data into the Antoine equation to calculate the Antoine constants. We also expect that, by developing similar correlations, this conception can be applied to mixtures, especially undefined mixtures such as coal and petroleum fractions. Nomenclature ω ) Pitzer’s acentric factor A, B, C ) Antoine constants in eq 2 AAD % ) ∑(|calc - expl|/expl)/no. of points × 100% d20 ) liquid density at 20 °C, g/cm3 MW ) molecular weight Pc ) critical pressure, atm Pvp ) vapor pressure, atm (Pvp)r ) reduced vapor pressure, Pvp/Pc SG ) specific gravity at 60/60 °F Tb ) normal boiling point, K Tc ) critical temperature, K Tr ) reduced temperature, T/Tc
Literature Cited Antoine, C. Comput. Rend. 1888, 107, 681, 836. API Research Project 44. Selected Values of Properties of Hydrocarbons and Related Compounds; Thermodynamics Research Center, Texas A&M University, 1971. Boublik, T.; Fried, V.; Hala, E. The Vapor Pressure of Pure Substance, 2nd ed.; Elsevier: New York, 1984. Chen, D. H.; Dinivahi, M. V.; Jeng, C. Y. New Acentric Factor Correlation Based on the Antoine Equation. Ind. Eng. Chem. Res. 1993, 32, 241. Daubert, T. E.; Danner, R. P. Data Compilation: Tables of Properties of Pure Compounds; American Institute of Chemical Engineers: New York, 1985. Edmister, W. C. Applied Hydrocarbon Thermodynamics. Part 4: Compressibility Factors and Equations of State. Pet. Refin. 1958, 37, 173. Han, B.; Peng, D. Y. A Group-Contribution Correlation for Predicting the Acentric Factors of Organic Compounds. Can. J. Chem. Eng. 1993, 71, 332. Hoshino, D.; Nagahama, K.; Hirata, M. Prediction of Acentric Factor of Alkanes by the Group Contribution Method. J. Chem. Eng. Jpn. 1982, 15 (2), 153. Kesler, M. G.; Lee, B. I. Improve Prediction of Enthalpy of Fractions. Hydrocarbon Process. 1976, 55 (3), 153. Kesler, M. G.; Lee, B. I.; Sandler, S. I. A Third Parameter for Use in Generalized Thermodynamic Correlations. Ind. Eng. Chem. Fundam. 1979, 18 (1), 49. Lee, B. I.; Kesler, M. G. A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States. AIChE J. 1975, 21 (3), 510.
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Lin, H. M.; Chao, K. C. Correlation of Critical Properties and Acentric Factor of Hydrocarbons and Derivatives. AIChE J. 1984, 30 (6), 981. Nath, J.; Das, S. S.; Yadava, M. L. On the Choice of Acentric Factor. Ind. Eng. Chem. Fundam. 1976, 15 (3), 223. Pitzer, K. S.; Lippmann, D. M.; Curl, R. F.; Huggins, C. M.; Peterson, D. E. The Volumetric and Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of Vaporization. J. Am. Chem. Soc. 1955, 77, 3433. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Riazi, M. R.; Daubert, T. E. Simplify Properly Predictions. Hydrocarbon Process. 1980, 59 (3), 115.
Watanasiri, S.; Owens, V. H.; Starling, K. E. Correlations for Estimating Critical Constants. Acentric Factor and Dipole Moment for Undefined Coal-Fluid Fractions. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 294.
Received for review August 29, 1995 Revised manuscript received December 20, 1995 Accepted March 27, 1996X IE9505423 X Abstract published in Advance ACS Abstracts, May 1, 1996.
