Prediction of Physical Properties of Hydrocarbons, Petroleum, and

Table 10. Results for MW Prediction of Coal Liquid. Fractions method. AADa. % AAEa. % max AEa. Kentucky Coal Liquid (34 Data Points)b proposed method...
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Ind. Eng. Chem. Res. 2002, 41, 1695-1702

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CORRELATIONS Prediction of Physical Properties of Hydrocarbons, Petroleum, and Coal Liquid Fractions Evagelos Retzekas, Epaminondas Voutsas,* Kostis Magoulas, and Dimitrios Tassios Thermodynamics and Transport Phenomena Laboratory, Department of Chemical Engineering, National Technical University of Athens, 9 Heroon Polytechniou Str., Zographou Campus, 157 80 Athens, Greece

A simple method that uses the molecular structure and density as input parameters for the prediction of the normal boiling point (Tb), critical temperature (Tc), and critical pressure (Pc) of pure hydrocarbons is presented. For Tb the average absolute error is 1.0% as compared to 3.3% for the Joback method and 2.9% for that of Stein and Brown. Its main advantage over the first method lies with large molecular weight compounds and that over the second with highly branched compounds. For the prediction of Tc, the average absolute error is 1% similar to that of the Joback, Riazi, and Riazi-Daubert methods which, however, require knowledge of Tb. Finally, for Pc, the proposed method gives an average absolute error of 2.7% as compared to 3.9% for the Joback method and 4.2% and 4.8% for the Tb-requiring methods of Riazi and RiaziDaubert, respectively. The proposed method gives also better results for these three properties when compared to the recently proposed and more difficult to use group interaction contribution method of Marejon and Fontevila. Using data for pure hydrocarbons, correlations have been developed for the prediction of molecular weight (MW), Tc, and Pc of petroleum and coal liquid fractions. MW prediction gives an average absolute error of 4.1% as compared to 4.6% for the Riazi-Daubert method, and both methods provide better results for coal liquids than the Starling and “single-parameter” expressions. Tc and Pc predictions with errors of 1.2% and 5.5% are similar to those of the Riazi-Daubert method, but no conclusion can be reached about the reliability of these methods because of the small number of available data. 1. Introduction Knowledge of accurate physical properties is very important in the chemical, petrochemical, and petroleum industries for the optimum design and evaluation of separation processes as well as for reservoir fluid modeling. For example, it is known that a small error in Tc may lead to a very large error in the prediction of vapor pressure through equations of state.1 The physical properties considered here are the normal boiling point and critical properties of pure hydrocarbons, which are considered in the first part of the paper, and the MW and critical properties of petroleum and coal liquid fractions considered in the second part. 2. Pure Hydrocarbons The most commonly used methods for Tb prediction are the group contribution ones of Joback2 and of SteinBrown,3 while for the prediction of critical properties, again that of Joback and those of Riazi4 and RiaziDaubert5 are the most commonly used. The recently proposed group interaction contribution (GIC) method,6 which claims improved performance over the classical group contribution methods, is also considered here. All methods are briefly described in the appendix. * Corresponding author. Tel.: +301 772 3137. Fax: +301 772 3155. E-mail: [email protected].

2.1. Proposed Method. For the prediction of the normal boiling point and the critical properties of pure hydrocarbons, the following expression, which is a combination of the group contribution approach with an empirical term that includes density, is proposed:

Q ) aFbMWc + d +

∑i NiGi

(1)

where Q stands for Tb, Tc, and Pc; F is the liquid density at 20 °C; MW is the molecular weight of the compound; a-d are constants that are the same for all hydrocarbons but different for each property; Ni is the number of times that group i appears in a compound; and Gi is the value of the group. The group assignment used at this work is the same as the one proposed by Joback.2 2.2. Results and Discussion. 2.2.1. Normal Boiling Point. Table 1 presents the database of 110 compounds used for the evaluation of the necessary parameters in eq 1, which are presented in Table 2, along with the prediction results for the database of 183 compounds used for validation. Table 1 also includes the results obtained with the methods of Joback and of Stein and Brown for comparison purposes. The overall performance, in the total of 293 compounds, of the three methods is also shown graphically in Figure 1, where the predicted Tb values are plotted against the experimental ones. Finally, Table 3 compares the performance

10.1021/ie010642a CCC: $22.00 © 2002 American Chemical Society Published on Web 02/23/2002

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Table 1. Results with the Proposed Method and Those of Joback and of Stein-Brown in Tb Predictiona homologous series

NDP

ref

alkanes alkenes alkynes alkadienes aromatics

43 22 12 11 22

8, 15, 16, 17 8, 15 8 8, 21 8, 19, 20

alkanes alkenes alkynes alkadienes aromatics

78 29 8 8 60

8, 15, 16, 22, 24, 26 8, 15, 16, 18 21 8 8, 16, 19, 21, 24

overall AAE % overall AADc (K) % max AEd

MW range

Tb(exp) range

F20°C range

% AAEb this method

Joback

Stein-Brown

Development Set: 110 Compounds 68-492 309-763 0.626-0.836 42-280 225-614 0.553-0.861 40-110 249-399 0.614-0.753 40-82 238-357 0.584-0.723 78-162 353-540 0.853-1.018

0.72 0.94 1.51 1.37 0.78

5.77 3.23 2.95 2.61 1.23

3.35 2.61 3.52 3.22 1.76

Validation Set: 183 Compounds 56-605 286-821 0.620-0.957 70-229 303-558 0.641-0.870 96-138 385-448 0.748-0.769 68-108 307-423 0.683-0.883 102-204 411-607 0.834-1.096

0.99 1.16 1.03 1.56 1.15

4.36 1.22 4.43 1.58 2.38

3.98 2.87 0.56 2.86 1.94

1.03 4.50 5.52

2.93 18.21 44.12

3.33 12.30 16.81

293 293 293

a Detailed results can be found in http://ttpl.chemeng.ntua.gr/pdf/tb.pdf. b AAE is the average absolute percent error defined as % NDP exp pred exp AAE ) (1/NDP)∑i)1 |(Tb,i - Tb,i )/Tb,i | × 100, where NDP is the number of data points. c AAD is the average absolute deviation defined NDP exp pred as AAD ) (1/NDP)∑i)1 |Tb,i - Tb,i |.

d

% max AE is the percent maximum absolute error in Tb prediction.

Table 2. Parameter Values in Eq 1 parameter/group

Tb (K)

Tc (K)

Pc (bar)

a b c d CH3 -CH2>CH>C< dCH2 dCHdC< dCd tCH tC-CH2- (ring) >CH- (ring) >C< (ring) dCH- (ring) dC< (ring)

50.4965 0.6591 0.4875 37.45 -7.73 (240)a -4.78 (495) -8.08 (25) -12.28 (16) -8.88 (29) -4.57 (40) -4.51 (11) 0.58 (4) -9.79 (7) -3.44 (17) -8.39 (40) -13.12 (7) -27.55 (2) -11.09 (101) -5.53 (47)

106.7092 0.8746 0.4016 101.26 -3.00 (168) -9.16 (232) -24.96 (16) -30.90 (12) -8.24 (15) -6.35 (17) -22.15 (4) 15.72 (1) -13.22 (2) 4.64 (4) -8.74 (73) -19.38 (10) -41.36 (3) -13.41 (140) -14.68 (72)

4651.7280 1.1815 -1.0412 5.28 -0.78 (146) -0.14 (284) 0.52 (15) 2.33 (11) 0.35 (11) -0.95 (15) -0.47 (2) not available -4.24 (2) -4.24 (2) 0.21 (72) 0.02 (7) 1.75 (1) 0.20 (77) 0.48 (42)

a In parentheses is the number of times that each group appears in the database used for the evaluation of the parameters in eq 1.

of the GIC method and the other three methods. Because of the somewhat cumbersome and timeconsuming character of the GIC method, the comparison is limited to a small number of “selected” compounds, i.e., compounds where significant errors in Tb prediction are encountered with some of the methods. The following comments summarize our observations on the obtained results for Tb: 1. For compounds that are solid at 293 K, the proposed method using hypothetical liquid densities predicted by the GCVOL method,7 presented in the appendix, gives very satisfactory results. 2. The Joback method gives poor results for alkynes and biphenyl derivatives. Figure 1 also indicates that this method becomes progressively unreliable as Tb increases beyond 600 K. 3. The Stein-Brown method gives large errors for highly branched hydrocarbons. Actually, for 48 compounds that involve three or more branches, it gives an overall average error of 5.6% against 2.1% for the Joback method and 1% for the proposed one. The SteinBrown method gives finally poor results for biphenyl

Figure 1. Comparison between the proposed, the Joback, and the Stein-Brown methods in Tb prediction.

Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002 1697 Table 3. Comparison of the Methods Used in Tb Prediction for ‘‘Selected” Compounds % AAE compound

Tb(exp)

this method

GIC

Joback

Stein-Brown

ref

n-C21H44 (GCVOL)a n-C22H46 (GCVOL) n-C23H48 (GCVOL) n-C24H50 (GCVOL) n-C25H52 (GCVOL) n-C28H58 (GCVOL) n-C29H60 (GCVOL) n-C30H62 (GCVOL) n-C32H66 (GCVOL) n-C35H72 (GCVOL) 1-eicosene (GCVOL) 2,2,4,4,6,8,8-heptamethylnonane 2,2,5,5-tetramethylhexane (GCVOL) 2,3,3-trimethylpentane 2,2,3,3-tetramethylbutane (GCVOL) 1,1,3-trimethylcyclopentane cyclodecane indene indane spiro-octane cis-bicyclopentane trans-2-phenylbutene-2 bicyclopropylidene 2,2-dimethylbiphenyl overall

629.70 641.80 653.20 664.50 675.10 704.80 714.00 722.90 740.20 763.20 614.20 513.15 410.61 387.90 379.60 378.15 475.20 455.77 451.12 447.00 319.00 447.15 374.00 529.00

0.81 0.69 0.50 0.45 0.33 0.10 0.27 0.36 0.60 1.12 0.42 0.97 1.71 0.59 2.31 3.50 2.81 1.81 2.35 0.66 1.82 2.89 1.24 3.22 1.31

1.16 1.63 2.13 2.60 3.11 4.67 5.20 5.73 6.76 8.46 0.88 1.60 0.75 0.05 0.58 1.09 9.51 2.83 1.56 16.78 8.11 3.81 1.15 4.46 3.94

7.97 9.50 11.09 12.64 14.26 19.19 20.86 22.53 25.85 31.05 6.43 8.22 2.71 2.35 0.95 4.00 1.20 1.80 0.61 1.08 1.26 2.63 1.43 10.22 9.16

1.67 1.72 1.65 1.58 1.40 0.62 0.28 0.10 0.90 2.42 1.30 5.16 4.27 8.58 9.18 1.06 3.02 0.05 0.37 3.61 1.28 3.91 2.15 8.97 2.72

15 15 15 15 15 15 15 15 15 15 15 17 16 15 15 15 15 8 8 18 18 8 18 21

a GCVOL in parentheses indicates that the experimental liquid density is not available or that the compound is a solid at 293 K. In such cases the liquid density or the hypothetical liquid one was obtained from the GCVOL method.

Figure 2. Comparison between the various methods used in Tc prediction.

derivatives and increased errors for compounds with Tb over 700 K, as shown in Figure 1. 4. The overall performance of the GIC method presented in Table 3 suggests no advantage in using it considering, especially, the complexity in its application. 5. Table 4 presents the results for compounds that are solid at 293 K. Wherever the GCVOL method is applicable, the proposed method coupled with GCVOL offers the best results. For the rest of the compounds, we considered extrapolated liquid density values obtained from the DIPPR8 correlations. However, the uncertainty of the extrapolated values may be significant as suggested by the case of fluorine, which gives a value of 1.376 (g/cm3) while the solid density is 1.20 (g/cm3). Thus, if the GCVOL method is not applicable, use of the Stein-Brown method is recommended.

2.2.2. Critical Temperature. Parameters in eq 1 for Tc are presented in Table 2 and were obtained using a database of 81 compounds with an overall average absolute error of 1%. The same error was obtained in the validation set that included 97 compounds. Table 5 presents a comparison, in the total of 178 compounds, of the proposed method with those of Joback, Riazi, and Riazi-Daubert, while Figure 2 demonstrates graphically the performance of the methods. A comparison, finally, of all of the methods with the GIC one in 20 “selected” compounds is presented in Table 6. The following comments summarize our observations on the obtained results: 1. All methods give similar and good overall results, but only the proposed method does not require knowledge of the Tb value.

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Table 4. Tb Prediction Results for Compounds That Are Solid at 293 K % absolute error compound

F20°C

Tb(exp)

this method

Joback

Stein-Brown

ref

n-heptadecane (GCVOL) n-octadecane (GCVOL) n-nonadecane (GCVOL) n-eicosane (GCVOL) n-C21H44 (GCVOL)a n-C22H46 (GCVOL) n-C23H48 (GCVOL) n-C24H50 (GCVOL) n-C25H52 (GCVOL) n-C28H58 (GCVOL) n-C29H60 (GCVOL) n-C30H62 (GCVOL) n-C32H66 (GCVOL) n-C34H70 (GCVOL) n-C35H72 (GCVOL) n-C37H76 (GCVOL) n-C38H78 (GCVOL) n-C43H88 (GCVOL) 1-eicosene (GCVOL) 2,2,5,5-tetramethylhexane (GCVOL) 5-methylnonane (GCVOL) 2-methyldecane (GCVOL) 4-methyldecane (GCVOL) squalane (GCVOL) 1,2,4,5-tetramethylbenzene (GCVOL) pentamethylbenzene (GCVOL) overall acenaphthene (ELD)b fluorene (ELD) anthracene (ELD) phenanthrene (ELD) camphene (ELD) diphenylmethane (ELD) 1,4-di-tert-butylbenzene (ELD) 1-methylindene (ELD) 2-methylindene (ELD) 1,2-diphenylethane (ELD) naphthalene (ELD) 1-methylnaphthalene (ELD) 2-methylnaphthalene (ELD) 1,7-dimethylnaphthalene (ELD) 2,3-dimethylnaphthalene (ELD) 2,6-dimethylnaphthalene (ELD) 2,7-dimethylnaphthalene (ELD) biphenyl (ELD) pyrene (ELD) benzo[a]pyrene fluoranthene (ELD) chrysene (ELD) octadecahydrochrysene (ELD) coronene overall

0.7763 0.7770 0.7839 0.7869 0.7900 0.7930 0.7960 0.7980 0.8000 0.8060 0.8080 0.8090 0.8120 0.8148 0.8160 0.8181 0.8191 0.8235 0.7930 0.7313 0.7293 0.7392 0.7392 0.8134 0.8739 0.8763

575.30 589.30 602.90 616.90 629.70 641.80 653.20 664.50 675.10 704.80 714.00 722.90 740.20 756.00 763.20 778.00 785.00 821.00 614.20 410.61 438.30 462.40 460.10 720.00 469.99 504.50 550.54 570.44 615.18 613.45 433.65 538.20 510.40 471.65 458.00 553.65 491.14 517.89 514.26 535.00 542.20 535.15 536.15 528.15 667.95 768.90 655.25 714.15 626.00 798.00

2.27 3.72 5.18 6.50 7.97 9.50 11.09 12.64 14.26 19.19 20.86 22.53 25.85 20.20 31.05 34.44 36.16 44.12 6.43 2.71 2.40 2.54 2.06 22.66 0.04 1.35 15.15 2.51 1.30 4.20 3.93 1.62 2.38 3.19 0.80 3.80 3.51 3.52 3.12 2.44 1.01 2.33 1.04 1.23 0.16 2.48 0.27 0.59 1.31 4.55 11.64 2.62

1.65 1.49 1.43 1.58 1.67 1.72 1.65 1.58 1.40 0.62 0.28 0.10 0.90 1.86 2.42 3.45 4.01 6.51 1.30 4.27 3.11 3.50 3.02 5.33 1.30 4.15 2.42 0.84 0.82 2.39 2.11 2.23 0.89 1.49 0.35 9.50 0.82 2.78 0.94 1.65 0.92 0.42 0.90 0.71 3.32 3.43 6.89 1.56 5.85 5.82 0.63 2.39

8 15 8 8 15 15 15 15 15 15 15 15 15 19 15 19 19 19 15 15 15 15 15 26 8 28

1.0819 1.3762 1.0908 1.1157 0.8688 1.0061 0.8630 0.9730 0.9770 1.0130 1.0258 1.0208 1.0018 1.0016 1.0030 1.0030 1.0030 1.0264 1.2720 c 1.1617 1.2740 0.9811 c

1.07 1.22 0.81 0.88 0.81 0.69 0.50 0.45 0.33 0.10 0.27 0.36 0.60 0.93 1.12 1.36 1.50 1.71 0.42 1.71 0.22 0.86 0.36 4.14 0.89 2.96 1.00 0.31 17.82 6.76 4.86 0.06 1.97 1.51 2.15 5.51 0.61 1.27 1.66 2.34 1.57 2.78 1.50 1.68 2.57 1.95 3.05 0.92 5.93 3.13

8 8 8 8 8 8 20 8 8 8 8 8 8 8 8 8 8 8 8 24 8 24 24 24

a

GCVOL in parentheses indicates that the hypothetical liquid density was obtained from the GCVOL method. b ELD stands for extrapolated liquid density from DIPPR correlations. c The GCVOL method was not applicable because the required groups were not available. Table 5. Overall Results for Tc of Pure Hydrocarbons method

AADa (K)

% AAEa

% max AEa

proposed method Jobackb Riazib Riazi-Daubertb

6.29 5.20 6.68 5.64

1.02 0.82 1.09 0.93

3.76 10.88 6.32 6.91

a Notations as in Table 1 but for T . b Applied to 173/178 c compounds because of the lack of reliable Tb values for the remaining ones.

2. Notice that, as shown in Figure 2, errors higher than 3% are observed in very few cases, which suggests that all methods must be considered reliable. 3. It appears that the Joback method gives increasing errors with increasing number of carbon atoms for n-alkanes above C20, and the same, but in a more

pronounced fashion, is the case for the GIC method (Table 6). The latter does not appear again to offer any advantage over the other methods. 4. Use of the GCVOL method for prediction of the hypothetical liquid density for compounds that are solid at 20° C appears to give satisfactory results with the proposed method. 5. The small errors in Tc prediction are important in the main application of critical properties, i.e., vaporpressure (Ps) and saturated volume predictions with cubic equations of state. Thus, Voulgaris et al.1 report that a given error in Tc may lead to errors in Ps larger by a factor of 20 at low Ps values while the errors in volumetric predictions are of the same magnitude as that in Tc.

Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002 1699 Table 6. Comparison of the Methods Used in Tc Prediction for ‘‘Selected” Compounds % absolute error compound

Tc(exp)

this method

GIC

Joback

Riazi

Riazi-Daubert

ref

n-C22 (GCVOL)a n-C24 (GCVOL) n-C28 (GCVOL) n-C30 (GCVOL) squalane (GCVOL) cyclooctane 3-methylcyclopentene 1-nonadecene (GCVOL) 1-eicosene (GCVOL) 1,2-diisopropylbenzene pentamethylbenzene (GCVOL) diphenylmethane 1,2,3,4-tetrahydronaphthalene trans-decahydronaphthalene cis-decahydronaphthalene indane D-limonene 2,3,3-trimethylpentane 2,3,3,4-tetramethylpentane 2,2,5,5-tetramethylhexane (GCVOL) overall

787.00 800.00 824.00 843.00 795.90 647.20 523.20 755.00 768.00 668.95 719.00 760.00 720.15 687.10 702.25 684.90 653.00 573.50 607.50 581.40

0.24 0.33 0.91 0.08 0.67 1.30 1.09 0.15 0.39 2.49 1.62 1.18 2.80 0.17 0.26 1.41 0.05 2.00 3.09 2.78 1.15

1.93 3.79 8.49 10.47 13.78 0.03 b 1.00 0.74 2.18 0.21 1.71 0.09 0.17 0.19 0.16 b 0.07 0.13 0.30 2.52

0.56 1.88 4.89 5.71 10.88 0.49 3.00 0.11 0.16 0.94 0.66 2.15 0.59 0.37 0.01 1.72 0.91 0.52 0.83 1.38 1.89

1.06 1.15 1.93 3.46 2.36 4.37 0.60 0.14 0.49 1.62 0.04 1.58 2.04 3.36 3.47 1.94 0.76 1.25 1.62 1.40 1.73

0.85 1.55 2.55 1.93 7.92 2.93 2.76 0.96 0.63 2.71 0.85 2.61 0.10 2.13 2.08 0.81 0.32 0.74 1.48 1.10 1.85

25 25 25 25 26 15 19 27 27 24 19 20 8 8 8 28 29 15 15 15

a GCVOL in parentheses indicates that the experimental liquid density is not available or that the compound is a solid at 293 K. In such cases the liquid density or the hypothetical liquid one was obtained from the GCVOL method. b Two groups are not available.

Table 7. Overall Results for Pc of Pure Hydrocarbons method

AADa (bar)

% AAEa

% max AEa

proposed method Joback Riazib Riazi-Daubertb

0.72 1.04 0.96 1.33

2.7 3.9 4.2 4.8

13.6 14.7 37.6 63.3

a Notations as in Table 1 but for P . b Applied to 136/139 c compounds because of the lack of reliable Tb values for the remaining ones.

2.2.3. Critical Pressure. Parameters of eq 1 for Pc prediction are presented in Table 2 and were determined by using a database of 71 compounds with an absolute average error of 2.9%. Validation of the method using a database of 68 compounds gave an error of 2.4%. Table 7 presents a comparison, in the total of 139 compounds, of the proposed method with those of Joback, Riazi, and Riazi-Daubert, while Figure 3 demonstrates graphically the performance of these methods. A comparison, finally, of the proposed method with the GIC in 15 “selected” compounds is presented in Table 8.

The following comments summarize our observations on the obtained results: 1. All of the methods give rather poor results, with the proposed one giving the better ones as shown in Table 7 and Figure 3. 2. The Riazi and Riazi-Daubert methods give larger overall errors because they become completely unreliable for large n-alkane Pc predictions, as shown in Table 8. 3. The GIC method does not seem to offer any advantages over the proposed and Joback methods (Table 8). 4. The larger errors in Pc prediction over that for Tc are not so important in the aforementioned application of critical properties. A given error in Pc leads to similar errors in saturated vapor-pressure and saturated volume predictions (Voulgaris et al.1). 3. Petroleum and Coal Liquid Fractions In this case what is typically known is the normal boiling point and the density. The MW is often available,

Figure 3. Comparison between the various methods used in Pc prediction.

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Table 8. Comparison of the Methods Used in Pc Prediction for ‘‘selected” compounds % absolute error compound

Tc(exp)

this method

GIC

Joback

Riazi

Riazi-Daubert

ref

n-C22 (GCVOL)a n-C24 (GCVOL) n-C28 (GCVOL) n-C30 (GCVOL) squalane (GCVOL) cyclooctane 1-nonadecene (GCVOL) 1-eicosene (GCVOL) triethylbenzene trans-decahydronaphthalene cis-decahydronaphthalene indane 2,3,3,4-tetramethylpentane 2,3,3-trimethylpentane 2,2,5,5-tetramethylhexane overall

9.91 8.71 7.44 6.36 5.90 35.60 11.90 11.40 24.40 28.37 32.42 39.50 27.20 28.20 21.90

0.4 1.9 3.7 0.9 11.5 2.9 1.8 0.8 1.1 10.0 1.1 2.2 7.1 4.1 5.1 3.6

7.4 5.8 10.3 4.7 3.5 4.8 8.0 5.5 b 12.6 1.4 b 3.9 0.5 1.9 5.4

9.0 7.4 11.9 6.4 3.3 2.6 6.6 8.5 4.3 6.7 6.7 0.1 12.3 7.6 0.3 6.2

18.6 22.0 35.9 37.6 30.9 9.7 10.4 13.4 0.6 1.5 6.9 2.3 6.3 4.3 3.1 13.6

15.6 23.8 30.5 45.8 60.5 10.2 9.2 10.5 2.5 2.4 7.7 3.1 3.5 1.6 9.6 15.8

25 25 25 25 26 15 27 27 20 8 8 8 15 15 15

a GCVOL in parentheses indicates that the experimental liquid density is not available or that the compound is a solid at 293 K. In such cases the liquid density or the hypothetical liquid one was obtained from the GCVOL method. b One group is not available.

Table 9. Parameter Values in Eq 2

Table 10. Results for MW Prediction of Coal Liquid Fractions

parameter

MW

Tc (K)

Pc (bar)

a b c

0.00024 -0.7792 2.1428

18.3908 0.3702 0.5949

5.103 × 107 2.3981 -2.2909

but its values are less reliable because of the differences in the procedure used for its experimental determination. The commonly used method for the prediction of MW, Tc, and Pc of petroleum and coal liquid fractions is the Riazi-Daubert one, while for coal liquid fractions Tsonopoulos et al.9 consider also that of Starling and the “single-parameter” one both presented in the appendix. We propose here a correlation for the prediction of these properties of the type

Q ) aFbTbc

(2)

where Q stands for MW, Tc, and Pc. It must be noted that the parameters a, b, and c of eq 2, presented in Table 9, were obtained using data for pure compounds only: 112 for MW, 60 for Tc, and 53 for Pc selected to cover parafinic, aromatic, and naphthenic compounds in a wide range of MW and density. Molecular weight prediction results for four different types of coal liquids, which include 92 data points,9-11 and two sets of petroleum fractions, which include 26 data points,12,13 are summarized in Tables 10 and 11, respectively, for the proposed, the Riazi-Daubert, the Starling, and the single-parameter methods. The proposed method and that of Riazi-Daubert yield the best results, with overall errors for both coal liquid and petroleum fractions of 4.1% and 4.6%, respectively, with the proposed method having a slight advantage in coal liquid fractions. The poorer results obtained with the two methods developed for coal liquids, those of Starling and the single-parameter, when compared with that of the Riazi-Daubert one are in agreement with the findings of Tsonopoulos et al.9 They both show a consistent underprediction of the MW values with errors of 9.4% and 7.5%, respectively. They were probably developed using MW data determined by benzene freezing point depression, which tend to be lower than those determined with osmometry9 and used here. The results for Tc prediction appear satisfactory for both the proposed method (1.2% absolute average error) and that of Riazi-Daubert (1.4% absolute average

method

AADa

% AAEa

% max AEa

Kentucky Coal Liquid (34 Data Points)b proposed method 7.6 3.8 Riazi-Daubert 8.1 4.2 Starling 16.4 8.4 single parameter 13.3 6.6

7.5 9.6 13.8 13.2

Wyoming Coal Liquid (34 Data Points)c proposed method 8.2 4.4 Riazi-Daubert 9.9 5.4 Starling 19.8 10.5 single parameter 15.8 8.3

8.7 10.3 14.7 12.2

Illinois Coal Liquid (18 Data Points)c proposed method 6.0 3.2 Riazi-Daubert 10.1 5.2 Starling 21.0 10.5 single parameter 17.1 8.5

7.9 9.5 13.4 11.6

EDS Coal Liquid (6 Data Points)d proposed method 8.6 4.9 Riazi-Daubert 7.2 4.0 Starling 9.7 5.3 single parameter 7.2 4.1

9.7 6.1 10.3 6.2

Total Number of Coal Liquids (92 Data Points) proposed method 7.6 4.0 9.7 Riazi-Daubert 9.1 4.8 10.3 Starling 18.1 9.4 14.7 single parameter 14.5 7.5 13.2 a Notations as in Table 1 but for MW. b Data from ref 10. c Data from ref 11. d Data from ref 9.

Table 11. Results for MW Prediction of Petroleum Fractions method

AADa

% AAEa

% max AEa

SCN Petroleum Fractions (17 Data Points)b proposed method 9.9 3.9 10.1 Riazi-Daubert 9.6 4.0 9.6 Chinese Petroleum Fractions (9 Data Points) c proposed method 9.7 5.5 17.7 Riazi-Daubert 8.9 4.9 17.8 Total Number of Petroleum Fractions (26 Data Points) proposed method 9.8 4.4 17.7 Riazi-Daubert 9.3 4.3 17.8 a Notations as in Table 3 but for MW. b Data from ref 12. c Data from ref 13.

error), but the small number of data points,14 only five, does not allow for any real conclusions. The errors in Pc prediction are, as expected, larger (5.5% absolute average error for the proposed method and 6.1% for the Riazi-Daubert method), but the very small number of

Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002 1701

data points,14 only three, does not allow again for any real conclusions. 4. Conclusions In the first part of this paper, a simple method, which uses the molecular structure and density as input parameters, for the prediction of Tb, Tc, and Pc of pure hydrocarbons is presented. Furthermore, a comparison with the commonly used methods for prediction of physical properties of pure hydrocarbons is performed. For Tb the average absolute error is 1.0% as compared to 3.3% for the Joback method and 2.9% for that of Stein and Brown. The main advantage of the proposed method over that of Joback lies with alkynes, biphenyl derivatives, and large MW compounds and the main advantage over that of Stein-Brown with highly branched hydrocarbons. The proposed method gives also better results when compared to the recently proposed and more difficult to use GIC method. For compounds that are solid at 293 K, use of the GCVOL method for the prediction of the hypothetical liquid density combined with the proposed method gives the best results. When the parameters required for the GCVOL method are not available, the Stein-Brown method is recommended. It is apparent that the use of density in combination with the group contribution concept provides improved results over the use of the group contribution concept alone. For Tc the proposed method gives an average absolute error of 1% similar to that of the Joback, Riazi, and Riazi-Daubert methods, which, however, require knowledge of Tb. For Pc it gives an average absolute error of 2.7% as compared to 3.9% for the Joback method and 4.2% and 4.8% for the Tb-requiring methods of Riazi and Riazi-Daubert, respectively. The last two methods give, however, poor results for large n-alkanes. Finally, the proposed method gives again better results than the GIC one for both Tc and Pc. In the second part of this paper using data for pure hydrocarbons, correlations have been developed for the prediction of MW, Tc, and Pc of petroleum and coal liquid fractions. MW prediction gives an average absolute error of 4.1% as compared to 4.6% for the Riazi-Daubert method, while both methods provide improved results for coal liquid fractions over the Starling and singleparameter expressions. Tc and Pc predictions with 1.2% and 5.5% errors, respectively, are similar to those of the Riazi and Riazi-Daubert methods, although no clear conclusions can be derived for these properties because of the very limited database available. Appendix: Brief Presentation of the Methods Considered in This Paper Joback Method.2 One of the very first successful group contribution methods to estimate physical properties of pure fluids was developed by Lydersen.2 Joback evaluated Lydersen’s scheme, added several functional groups, and determined the values of the group contributions. His proposed correlations are

Tb ) 198 +

∑∆b

(A1)

∑∆T - (∑∆T)2]-1

Tc ) Tb[0.584 + 0.965

Pc ) (0.113 + 0.0032na -

∑∆p)

-2

Tb, ∑∆T is the sum of group contributions concerning Tc, ∑∆p is the sum of group contributions concerning Pc, and na is the total number of atoms of the compound. Stein-Brown Method.3 Based on the method of Joback, Stein and Brown extended the group contribution method for Tb by considering a greater number of groups. They also proposed two corrections for a temperature-dependent bias. The main advantage of the method is the extended database used for the development of the method. Stein and Brown proposed the following relations:

Tb ) 198.2 +

∑i nigi

(A4)

where ∑inigi represents the sum of the group contributions for Tb prediction. The corrections are

Tb(corr.) ) Tb - 94.84 + 0.5577Tb - 0.0007705Tb2 for Tb e 700 (A5) Tb(corr.) ) Tb + 282.7 - 0.5209Tb for Tb > 700 (A6) Group Interaction Contribution (GIC) Method.6 A step beyond the simple group contribution methods is the GIC method that also takes into account the interaction between the simple groups. The equations of this method are the same as those proposed by Joback. In addition, an alternative nonlinear equation for estimating the normal boiling point is proposed, which claims significant improvement in accuracy. The authors propose the following equations:

Tb ) MW-0.404

∑ + 156

Tc ) Tb[0.5851 - 0.92865

∑ - ∑2]-1

Pc ) (0.1285 - 0.0059na -

∑)-2

(A7) (A8) (A9)

where ∑ is the sum of group interactions for each property and na is the total number of atoms of the compound. Riazi Method.4 This is a generalized method for predicting critical constants of both polar and nonpolar compounds. The equation used requires molecular weight, normal boiling point, and liquid density as input parameters. The equation used is

Θ ) exp(a + bMW + cTb + dF + eTbF)MWfTbg+hMWFi (A10) where Θ is the critical property, MW is the molecular weight of the compound, Tb is the normal boiling point, F is the liquid density at 20 °C, and a-i are constants that are the same for all of the compounds but different for each property. Riazi-Daubert Method.5,9 This is a simple method for predicting critical constants of nonpolar compounds. The equation proposed by the authors is

(A2)

Θ ) aTbbFc

(A3)

where Θ is the critical property or MW, Tb is the normal boiling point, and F is the specific gravity at 15 °C. For converting density values from 15 to 20 °C, we used an

where ∑∆b is the sum of group contributions concerning

(A11)

1702

Ind. Eng. Chem. Res., Vol. 41, No. 6, 2002

equation proposed by Tsonopoulos et al.9 for coal liquids according to which

F15°C ) 1.003F20°C

(A12)

In eq A11, a-c are constants that are the same for all of the compounds but different for each property. Starling Method.9 This method is a modification of the Kesler and Lee expression for the prediction of the molecular weight of petroleum fractions to make it applicable to coal liquids:

MW ) -1242.7 + 9316.25S + (7.753212 5.362614S)Tb + (1 - 0.753344S - 0.0173543S2) (1.42072 - 405.3994/Tb)(5.5556 × 106/Tb) + (1 - 0,88972S + 0.118591S2)(1.66192 46.75250/Tb)(1.714678 × 1011/Tb3) (A13) where MW is the molecular weight, S is the specific gravity at 68/68 °F (20 °C), and Tb is the experimental boiling point in degrees Kelvin. Single-Parameter Method.9 For coal liquids of unknown specific gravity, the molecular weight can be predicted with the following equation:

MW ) 3.91434 + 3.32452(Tb/1000) 2.17723(Tb/1000)2 + 0.776121(Tb/1000)3 (A14) GCVOL Method.7 This is a method for the prediction of liquid densities of pure solvents, oligomers, and polymers. The liquid density of a compound is calculated from the following equation:

F)

MW ) V

MW ni∆vi

∑

(A15)

In the above equation, MW is the molecular weight and V the molar volume. The molar volume is calculated from the sum over all group volume increments, ∆vi, and ni is the number of times the i group appears in the molecular structure of the compound. The temperature dependence of the molar group volume, ∆vi, is calculated by the following polynomial function: ∆vi ) Ai + BiT + CiT2, with T in degrees Kelvin and ∆vi in cubic centimeters per mole. Literature Cited (1) Voulgaris, M.; Stamatakis, S.; Magoulas, K.; Tassios, D. Prediction of Physical Properties for Non-Polar Compounds, Petroleum and Coal Liquid Fractions. Fluid Phase Equilib. 1991, 64, 73. (2) Reid, R. C.; Prausnitz, P. E. Properties of Gases and Liquids; McGraw Hill: New York, 1988. (3) Stein, S. E.; Brown, R. L. Estimation of Normal Boiling Point from Group Contributions. J. Chem. Inf. Comput. Sci. 1994, 34, 581. (4) Riazi, M. R.; Sahhaf, T. A.; Shammari, M. A. A Generalized Method for Estimation of Critical Constants. Fluid Phase Equilib. 1998, 147, 1. (5) Riazi, M. R.; Daubert, T. E. Simplify Property Predictions. Hydrocarbon Process. 1980, 3, 115. (6) Marejon, J. M.; Fontdevila, P. E. Estimation of Pure Compound Properties Using Group-Interaction Contributions. AIChE J. 1999, 45, 615.

(7) Elbro, H. S.; Fredenslund, A.; Rasmussen, P. GroupContribution Method for the Prediction of Liquid Densities as a Function of Temperature for Solvents, Oligomers, and Polymers. Ind. Eng. Chem. Res. 1991, 30, 2576. (8) Daubert, T. E.; Danner, R. P. Physical and Thermodynamic Properties of Pure Chemicals: Data Compilation; Hemisphere: New York, 1994. (9) Tsonopoulos, C.; Heidman, J. L.; Hwang, S. Thermodynamic and Transport Properties of Coal Liquid; Wiley: New York, 1986. (10) Lin, H. M.; Kim, H.; Guo, T.; Chao, K. Equilibrium Vaporization of a Coal Liquid from a Kentucky No. 9 Coal. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1049. (11) Lin, H. M.; Leet, W. A.; Kim, H.; Chao, K. Measurement and Prediction of Vapor-Liquid Equilibrium for an H-Coal and an SRC Coal Liquid With and Without Hydrogen. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1225. (12) Riazi, M. R.; Sahhaf, T. A. Physical Properties of Heavy Petroleum Fractions and Crude Oils. Fluid Phase Equilib. 1996, 117, 217. (13) Fang, W.; Yu, Q.; Zong, H.; Lin, R. Calorimetric Determination of the Vapor Heat Capacity of Petroleum Cuts. Fuel 1998, 77, 895. (14) Gray, J. A.; Holder, G. D.; Brady, C. J.; Cunningham, J. R.; Freeman, J. R.; Wilson, G. M. Thermophysical Properties of Coal Liquids. 3. Vapor Pressure and Heat of Vaporization of Narrow Boiling Coal Liquid Fractions. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 97. (15) National Institute of Standards and Technology (NIST) Thermochemistry Database. Available online at http:/ www.nist.gov. (16) Howard, F. L.; Mears, T. W.; Fookson, A.; Brooks, D. B. National Advisory Committee For Aeronautics (NACA); Technical Note No. 1247; NACA: Washington, DC, 1947. (17) Sigma-Aldrich Company Database. Available online at http:/www.sigma-aldrich.com. (18) Kolesov, V. P.; Pimenova, S. M.; Lukyoanova, V. A.; Kuznetova, T. S.; Kozina, M. P. The Thermochemistry of Some Polycyclic Compounds. J. Chem. Thermodyn. 1998, 30, 1455. (19) Lin, C. T.; Young, F. K.; Brule, M. R.; Lee, L. L.; Starling, K. E. Databank For Synthetic FuelssPart 2. Hydrocarbon Process. 1980, 8, 117. (20) Steele, W. V.; Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A. Vapor Pressure, Heat Capacity and Density Along the Saturation Line. J. Chem. Eng. Data 1997, 42, 1008. (21) Weast, R. C. CRC Handbook of Chemistry and Physics; The Chemical Rubber Co.: Cleveland, OH, 1970-1971. (22) Syracuse Research Corporation Databases. Available online at http:/www.syrres.com. (23) Cholakov, G. S.; Wakeham, W. A.; Stateva, R. P. Estimation of Normal Boiling Points of Hydrocarbons from Descriptors of Molecular Structure. Fluid Phase Equilib. 1999, 163, 21. (24) Lin, C. T.; Young, F. K.; Brule, M. R.; Lee, L. L.; Starling, K. E. Databank for Synthetic FuelssPart 3. Hydrocarbon Process. 1980, 11, 225. (25) Nikitin, E. D.; Pavlov, P. A.; Popov, A. P. Vapour-Liquid Critical Temperatures and Pressures of Normal Alkanes with 19 to 36 Carbon Atoms, Naphthalene and m-Terphenyl Determined by the Pulse-Heating Technique. Fluid Phase Equilib. 1997, 141, 155. (26) Von Niederhausern, D. M.; Wilson, G. M.; Giles, N. F. Critical Point and Vapor Pressure Measurements at High Temperatures by Means of a New Apparatus with Ultralow Residence Times. J. Chem. Eng. Data 2000, 45, 157. (27) Nikitin, E. D.; Pavlov, P. A.; Popov, A. P. Critical Temperatures and Pressures of Linear Alk-1-enes with 13 to 20 Carbon Atoms Using the Pulse-Heating Technique. Fluid Phase Equilib. 1999, 166, 237. (28) Tsonopoulos, C.; Ambrose, D. Vapor-Liquid Critical Properties of Elements and CompoundssAromatic Hydrocarbons. J. Chem. Eng. Data 1995, 40, 547. (29) Tsonopoulos, C.; Ambrose, D. Vapor-Liquid Critical Properties of Elements and CompoundssUnsaturated Aliphatic Hydrocarbons. J. Chem. Eng. Data 1996, 41, 645.

Received for review July 27, 2001 Revised manuscript received November 14, 2001 Accepted November 15, 2001 IE010642A