1352
Ind. Eng. Chem. Res. 1995,34, 1352-1363
Structural Group Composition and Thermodynamic Properties of Petroleum and Coal Tar Fractions Leonid P. Guilyazetdinovt Department of Technology of Petroleum and Gas Processing, Gubkin State Academy of Oil and Gas, Moscow 117917, Russia The improved G-L method was developed for determining the structural group composition of petroleum and coal tar fractions by using experimental values of refraction index, density, molecular weight, and S, N, 0, and olefinic group content. The method is useful for fractions boiling in the range 30-500 "C containing S, N, 0 and in total up to lo%, not limiting the distribution of the carbon atoms between aromatic, naphthenic, and paraffinic structures. Several correlations are proposed for prediction of the thermodynamic properties of petroleum and coal tar fractions, i.e., molar volume; surface tension; heat capacity in gas, liquid, and solid phases as a function of temperature; and also critical properties, standard heat and entropy of formation, and temperature and entropy of melting. The method and these correlations have been tested on hydrocarbons and other organic compounds with satisfactory accuracy.
Introduction High-boiling (above 250 "C) petroleum fractions consist of hybrid structure hydrocarbons containing aromatic, naphthenic, and paraffnic fragments in molecules. Characterization of the chemical nature such fractions is impossible by fractionation to homologous series of hydrocarbons. Vlugter, Waterman, and Van Westen (1932,1935) have proposed a new characterization of the composition of such fractions based on determining the distribution of carbon atoms to aromatic, naphthenic, and paraffnic structures in the average molecule. The well-known Watermans method or "direct method" assumed the average molecules of petroleum fractions to have six-membered cata-condensed aromatic and naphthenic rings. This assumption is not quite accurate as there are noncondensed branched and peri-condensed polycyclic compounds in petroleum fractions. But it gives a satisfactory approach and a good possibility for chemical simulation of petroleum fractions. On a different level it is the basis for a lot of structural group analytic methods. At first the augmentation of hydrogen content after saturating hydrogenation was used for predicting the number of rings and carbon distribution to structural fragments in the average molecule. Van Ness and Van Westen (1952) have proposed a new method for structural group analysis based on correlations between physical properties (refraction index and density) and carbon distribution to aromatic, naphthenic, and paraffinic structures. The correlations were obtained as a result of investigations of a great many petroleum fractions by direct method. The n-d-M method is widely adopted in many petrochemical laboratories worldwide. Several modifications have been proposed to improve this method, but fields of application have not been broadened and it now has the following limitations: C,, < 50%,M > 200, S < 2%, R,,& < 0.7. Additionally, this method may not be used for unsaturated petroleum fractions, for example, for cracking and coking products, and for N-, O-containing coal tar fractions. We (Guilyazetdinov, 1959, 1968) have developed a new G-L method for structural group analysis based t Deceased.
also on experimental determination of n, d, M , and S values and additional estimation of the content of olefinic hydrocarbons and N- and O-containing compounds. The accuracy of carbon distribution determination and the scope of application of the method are increased considerably. Nevertheless, high molecular components such as asphaltenes cannot be analyzed by our method. In recent years new methods have been developed by Speight (1971), Hirsch and Altgelt (19701, Camyanov et al. (1984), Posadov et al. (19841, and Ghambir et al. (1991) for structural group analysis of petroleum heavy ends using NMR spectroscopy. It should be noted that many methods had been developed but the chief aim of simulating chemical nature, i.e., predicting physical properties, thermodynamic functions, and product yields in petrochemical processes, did not obtain appreciable advances. In recent years the G-L method has improved. Several procedures have been developed for calculating thermodynamic functions of petroleum and coal tar fractions using their structural group composition. The results of these works are the object of this paper.
Modified G-L Method We have proposed (1959) two new functions for hydrocarbons which are additive to their structural composition: G=
M(d - 0.8513) d
L=
M(n - 1.4752) t- 4.51 n'
+
23.6
(1) (2)
where d is the specific gravity at 20 "C (g/cm3);n is the refractive index for D lines of light a t 20 "C. The coefficients 0.8513 and 1.4752 proposed by Smittenberg and Mulder (1948) are the density and refractive index for the infinite hypothetical n-paraffin with extremely high molecular weight. As shown in Table 1, the G and L values are practically constant for a given homologous series and equal 0 for n-paraffinic hydrocarbons. Petroleum hydrocarbons, as seen from Figure 1, take places in the
0888-5885/95/2634-1352$09.QQIO 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1363 Table 1. G and L Values and Absolute Deviation of Ring Number Prediction for Homologous Series homologous series
no. of members
G
n-alkanes n-l-alkenes n-alkylcyclopentanes n-alkylcyclohexanes dicyclohexylalkanes n-cis-alkyldecalins n-trans-alkyldecalins perhydrophenanthrenes n-alkylbenzenes diphenylalkanes n-l-alkylnaphthalenes n-2-alkylnaphthalenes alkylanthracenes n-alkyltetralenes octahydrophenanthrenes mercaptans dialkyl sulfides alkylthiophenes alkylpyridines alkylquinolines phenols alcohols alcohol ethers furans Pyrans petroleum fractions coal tar fractions
12 14 10 9 4 4 4 1 10 6 5 4 4 7 4 6 4 6 5 7 3 14 10 4 2 24 14
0.0 2.9 12.1 14.5 30.2 30.5 26.7 42.3 25.2 50.4 47.1 45.4 67.6 39.8 53.8 21.8 21.4 39.5 33.4 52.2 42.7 19.6 9.7 29.5 30.9 29-58 58-65
av values
av dev of ring no.
max dev
L 0.00 0.79 1.74 2.18 4.96 4.66 4.40 6.90 5.46 11.90 12.35 12.11 20.10 8.22 10.78 2.97 2.90 6.35 5.70 12.17 7.49 1.58 -0.52 2.84 1.77 5-15 15-18
AG
AL
m a r
ARnf
0.1 0.5 0.5 0.4 0.2 0.2 0.2
0.03 0.04 0.05 0.30 0.24 0.30 0.30
fO.O1 f0.03 -0.09
0.1 0.5 0.1 0.2 0.2 0.7 1.5 1.0 1.0 0.5 0.06 1.0 0.7 0.7 0.5 0.5 1.0
0.06 0.09 0.07 0.06 0.09 0.02 0.50 0.10 0.10 0.20 0.10 0.20 0.10 0.12 0.06 0.12 0.25
-0.01 f0.02 fO.O1 fO.O1 f0.06 +0.01 fO.01 +0.04 +0.01 -0.04 -0.06 f0.13 -0.17 -0.22 f0.22 fO.08
-0.12 -0.03 -0.01 f0.06 fO.10
fO.O1 fO.19 fO.08 -0.17 0.00 f0.02 fO.08
-0.10 f0.05 $0.07 +0.08 f0.04 f0.04 fO.09 f0.09 fO.O1 f0.06
0.03 0.08 0.04
AAPD
0.04 0.12 0.30
Table 2. Recommended Values of G and L Incrementa for Different Groups groups position G L paraffinic structure olefinic structure naphthenic structure bond of two naphthenic rings aromatic structure
0.00 0.000 1.45 0.395 2.417 0.363 4.605 0.800 4.20 0.910
bond of two aromatic rings
6.33
2.475
.y bond of aromatic and naphthenic rings 6.67
1.584
-CH2-CH= -CH2-
-CH< .$-I,,
-....
; .C ;H ,
--CH\
-S-S-OH -0-
-N=
2 4 6 8 10 12 L Figure 1. Placing pure hydrocarbons on diagram G-L. Petroleum hydrocarbons are placed in the shaded area.
appointed area in the G-L diagram outlined by lines for aromatic and naphthenic hydrocarbons. Table 2 gives the recommended values of G and L increments for different groups. Hence, a possibility appears for the prediction of the number of aromatic and naphthenic rings. For hydrocarbons and their mixtures containing carbon atoms only in paraffinic, naphthenic, and aromatic structures,
+ +
+ +
G = 2.417mJ3, 2(4.60 - 2.42)(R, - 1) 4 . 2 0 ~ 7 ~ 8 , 2(6.33 ~ - 4.20)(Rar - 1) (6.67 - 4.20)Nmf (3) 0.910m$,,
+ 2(2.475 - 0.910)(R,
+
- 1) (1.564 - 0.910)N-f
(4)
thiophenes and thionaphthenes mercaptans and sulfides phenols furans and esters pyridines and quinolines
22.70 2.800 21.40 2.860 17.30 2.030 9.76 -0.600 12.40 1.100
where Rnf and Rar are the number of naphthenic and aromatic rings in the average molecule, mo is the number of carbon atoms in the average rings, and Nmf is the number of cata-condensed junction carbon atoms of the adjacent aromatic and naphthenic rings. The numeral values in (3) and (4) are taken from Table 2. If the total number of rings Rt = (Rnf R,) < 1, it should be assumed that mo = 6; if Rt > 1, the value of mo is calculated from
+
If (Rnr - 1) 0 or (Rar - 1) < 0, the terms containing these values in (3) and (4) are omitted and correction for cata condensation of rings is not made. The number Namf depends on the number of aromatic and naphthenic rings and can be predicted as follows:
If values of (Rar - 1) < 0 or (Rnf - 1) < 0, the terms containing them are omitted.
1354 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
Petroleum and coal tar fractions contain sulfur, nitrogen, and oxygen atoms. They can also contain “olefinic”carbon atoms in aliphatic structures. Corrections should be introduced into the G and L values, substituting S atom for two -CH2- groups, N atom for one -CH2- group, and 0 atom also for one -CH2group in corresponding structures. “Olefinic” carbon atoms are replaced by methylenic groups. After these substitutions we have
G,,, = G - 21.40Nspn- (21.40 - 2(2.42))Nsnf(22.70 - 2(4.20))Nsar- 17.5ONoH - (9.76 4.20)Noa, - (12.40 - 4.20)” - 1.45Net (7)
L,,, = L - 2.860Nspn- (2.86 - 2(0.363))Ns, (2.80 - 2(0.91))NSa,- 2.13ONoH (0.60 0.91)Noa, - (1.10 - 0.91)NN - 0.395Net (8)
+
+
2. When 16 predicted from
4, melting points do not depend practically on the cyclic part of the molecules. It may be calculated from
+
0
50 100 150 200 250 300 350 T,K Figure 2. Solid-phase heat capacity dependence on temperature for hydrocarbons: 1, n-hexane; 2, cyclohexane; 3, benzene; 4, n-decane; 5, naphthalene. Dotted lines: heat capacity in the liquid state.
Figure 2 shows that the temperature dependence of the solid-phase heat capacity for hydrocarbons is exponential. The exponent is less than unity. The relation may be written as
C, = AP,'
(67)
where coefficient A is a constant value for a given compound or fraction. It may be calculated from
A = 0.0086P 0.07Nn,
+ 0.196Npn+ 0.30Net + 0.245Nn, + + o.2o3NW1+ 0.058(Nar2+ Namf)O.3ONoH + 0.05NN + 0.25Ns (68)
The average deviation of 3.4% and maximum one of 6.3% are obtained for a 52 data set (14 hydrocarbons). As shown in Figure 2, there are jumps of heat capacity about 10-40 J/(mol-K)at the melting point. Melting Point. Temperature of melting is needed for thermodynamic calculation of equilibria in a solidliquid system for petroleum and coal tar fractions. However, there are no methods for its prediction. Melting point T, is very sensitive to the chemical nature of organic compounds and depends intricately on the structure, dimensions, and polarity of molecules. The use of computer procedure and structural group composition allows calculation of this value in a branching algorithm. In this case we consider only narrow fractions both in the sense of boiling range and in the sense of chemical composition. They might be paraffinic, naphthenic, monocyclic, or polycyclic aromatic fractions with a boiling interval of 10-20 "C, which could be named as quasi petroleum components or coal tar ones. If (Npn+Net Uvs) > 6 and Rd R, = 0, the melting point of n-paraffinic, olefinic hydrocarbons, and aliphatic sulfur compounds is near
+
Tm = 410.3 -
+
2240 Npn
+ Net
+
5333
+
(ivDn+ N ~ ~ > ~ 4.7uVet
+ lO.2Ns
(69)
The average deviation of T m values from (69) for n-alkanes is not more than f8 K (3.5%). For low molecular alkyl sulfides and mercaptans it increases to 18 K (6%),but above c8 the deviation of T , is decreased with increasing molecular weight.
2520 T m = 4 1 0 . 3 -Nc
+
3464
Nc2
(71)
Deviations of the T m values were obtained to be not more 4.0 K for 3-phenylhexane, n-octadecylbenzene, and Net) < 4, it is n-tetradecylnaphthalene. If ( N p n necessary to take into account the number of aromatic and naphthenic rings in a molecule and also the presence of the heteroatoms:
+
Tm=
+ 38Nar2- 2IN, - [120 - 10(Npn+ Net)]x (1- NO)- 44Nsar + 49Nsnf+ 36NoH - l o ~ o a-r 278
48"
(72)
If Npn= 0 or No > 1,the fourth term of this equation is omitted. In the presence of oxygen atoms the importance of side chains decreases considerably. The melting point depends only on the place of side chains in this case. For example, the melting point of cresols, ethylphenols, and xylenols varies in the range 10-70 "C independently of number and length of side chains. Maximum deviations were obtained for phenols and n-ethylcyclohexane(up to 16 K). The average deviation for other tested compounds was equal f 9 K (6.1%). Entropy of Melting. The entropy of melting in contrast to the boiling one depends strongly on the structure of molecules and composition of fractions. The prediction difficulty of this value consists in the presence of isomorphic phase transitions preceding the melting. Bondi (1968)proposed to sum up heats of all these phase transitions referring to the melting. Using this conception, we have obtained a correlation for the calculation of the melting entropy:
ASm = R(1.344 - 1.59Wc3 - 3.144Nc4 0.048Net - 0.432Nar - 0.808Nnf 2.48Ns 0.14NOH 0.33NN) R{(Nc - 2Ns - NN - No) x r1.233 - O.o%N,, o.055Nar2- 0.088Nc3 0.015Nc,1} (73)
+
+ +
+
If (Nc3 + 2Nc4) > 2, it is assumed that N c = ~ Nc4 = 1. Equation (73) was tested on 32 hydrocarbons and other compounds. The average deviation was equal to 3.9%, and was not above 10%(for n-propylnaphthalene).
Through Calculations The proposed correlations as shown above allow prediction of several physical and thermodynamic prop-
1360 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 Table 3. Calculation of Structural Group Composition and Physical Propertiesa fr fr
450-500°C
eth 1 perhydrooctahydroof 200-450 "C anthracene pitch ncycro: cis- phenan- n-butyl- l-meth l phenan- thiom- Manhyshlac catal oil oil nomen nonane hexane decalin threne benzene naphtharene tetralin threne phene pyridine cresol crude cracking (coal tar) (coal tar) Experimental Data 151 128.3 0.7180 1.4054
132 112.2 0.7879 1.4330
196 138.3 0.8967 1.4810
263 192.3 0.9430 1.5033
183 134.2 0.8601 1.4898
245 142.2 1.0130 1.6111
208 132.2 0.9694 1.5415
14.57 30.60 2.207 4.876 0.00 0.040 6.00 4.937 108.15 96.08 122.53
42.30 6.901 0.00 4.659 169.89
24.97 47.32 5.393 12.290 0.984 1.00 4.982 6.00 119.96 132.98
39.71 8.199 0.604 4.992 120.99
0.997 0.009 0.988 0.68 74.11 25.21 7.999 0.054
3.035
0.990 0.990
294 186.3 1.0260 1.5661
84 84.1 1.0648 1.5289
115 202 79.1 108.1 0.9835 1.0336 1.5102 1.5438
399 345.1 0.9102 1.5126
340 254.1 0.9890 1.5770
342 182.7 1.1075 1.6762
360 174.5 1.1564 1.6963
26.03 5.624 1.00 5.953 72.18
45.54 10.108 0.699 4.900 305.18
55.98 14.706 0.946 4.806 230.51
61.79 17.522 1.00 4.719 172.28
65.12 17.734 0.966 4.69 165.43
1.005 2.222 1.005 1.553 0.669 76.74 29.95 12.90 23.26 57.15 7.993 25.41 6.124 4.946 0.010 1.106 3.278
2.482 2.348 0.134 58.80 3.36 37.84 19.19 7.903 2.696 0.645
2.782 2.782
2.90 2.80 0.099 96.39 3.37 1.24 13.77 8.849 3.604 0.464
1.338 0.859 14.30
0.268 7.058 0.204 1.164 0.209
Intermediate Data 0.00 0.00 0.00
55.32 11.415 0.461 4.623 171.08
26.14 5.463 0.937 5.908 73.73
25.17 5.491 1.00 5.990 96.00
Structural Group Composition
100.0 9.004
5.929 9.004
2.017
2.000
1.000
2.133 0.085 2.048 4.11 95.89 10.20 0.349 7.686 2.096 0.037 1.000
3.035 59.47 99.97 0.03 14.15
40.53 9.928 5.940
10.07 4.070
2.037 2.004 0.033 90.18 1.48 8.34 11.07 7.911 2.008 0.164
2.016 1.218 0.798 60.36 39.55 0.09 10.07 4.048 0.436 3.984
0.004
3.988
0.066 0.923
1.596 0.009
1.000
1.000
1.00
1.000
3.211 1.480 1.731 48.04 51.96
1.048 1.024 0.982 1.024 0.066 94.51 100.00 5.49
14.24 3.881 0.960 5.939 1.462 2.002
6.139 6.009 3.706 4.961 0.096 0.048 0.337
1.000
1.000 1.000 1.000
1.000 1.487 0.110 0.110
1.000 1.000
91.53 8.47 14.34 9.384 3.564
0.828 0.194 1.000 0.030
0.198 0.104 1.000 0.068
0.072 0.049 0.193
0.162 0.067 0.189
Molar Volume at 373 K (9= 1.043) 196.5 0.11
154.9 0.34
169.2 1.08
219.8 1.29
167.6 -0.69
149.5 -1.34
147.1 -1.16
593.8 -0.8 2.280 0.00 540.2 Abc, % -1.42 0 0.436 Am, % -1.71
606.2 -2.8 3.124 4.49 440.2 -2.17 0.289 2.12
703.9 1.7 3.160 0.60 496.0 5.78 0.275 1.78
783.5
659.6 -0.8 2.865 0.01 487.9 -1.83 0.385 -1.76
773.4 1.4 3.441 -3.57 455.8 2.40 0.357 -0.25
728.2 8.2 3.531 -0.43
193.2 0.35
85.9 -
101.4
111.9 408.9 0.50 -0.21
278.0 -0.63
176.6 0.8
164.2 -0.46
620.5 0.5 5.637
877.7
861.1
884.8
900.2
1.414
2.030
3.302
-
-
3.627
253.6 -0.06 0.235 -2.25
711.6 5.8 4.909 0.01 305.6 -1.42 0.466 -0.11
1283.4
861.9
552.8
520.8
0.966
0.672
0.457
-
-
0.416
198.3 36.96 0.67 1.167 26.65 -0.41
253.8 34.69 -0.66 1.067 27.66 -1.91
930.4 36.26
646.4 40.06
397.9 48.34
-
-
425.1 44.11
1.331 29.81 4.23
1.319 32.79 4.03
1.244 36.82 1.81
1.251 40.51 2.39
-
Critical Properties
-
2.605
-
699.3
0.339
-
831.8 -17.5 2.916
440.7 610.7 0.26 0.306 0.83
0.02 0.379
-
581.2 1.8 5.655 -0.68 218.9 -0.01 0.208 4.20
-
-
-
-
-
-
-
-
Surface Tension 383.1 22.77 A~293,% 1.27 4 1.297 ~ 3 7 3 15.24 A~373,% -1.14
Pch ~293
320.4 25.64 -0.12 1.336 17.28 2.46
365.5 31.53 -1.93 1.383 23.37 -2.80
485.5 32.13
-
1.418 24.96
-
365.3 30.04 2.74 1.308 21.77 3.50
349.0 38.22 0.31 1.322 30.04 -1.88
331.4 34.86 -3.91 1.341 26.55 -0.45
433.5 32.49
-
1.381 28.10
-
-, not available; blank spaces, 0. erties of hydrocarbons and some heteroorganic compounds on the basis of their structural formulas. Our purpose is t o use them for petroleum and coal tar fractions on the basis of their structural group composition. Therefore, the deviations of errors are added up in calculating structural group composition. It was necessary to make through thermodynamic calculations beginning from the structural group analysis and the prediction of the intermediate parameters. The numerical examples of through calculation of structural group composition for several representative hydrocarbons, S-,N-, and 0-containing compounds, and petroleum and coal tar fractions are given in Table 3. The technical fractions had the following initial supplementary data: fraction 450-500 "C of Manhyshlac crude ( P = 48.7%, S = 0.2%); fraction of catalytic cracking products (P = 16.4%)S = 2.64%;E = 0.52%); anthracenic oil from coal tar ( E = 9.7%, Ph = 4.9%)S = 0.52%,0 = 2.12%);pitch oil from coal tar (Ph = 6.7%, S = 1.25%,N = 1.3%,0 = 2.35%).
188.0 32.13 2.51 1.260 21.32 2.90
-
-
a
Table 3 shows the calculation sequence, significant intermediate data, and results. It should be noted that the modified G-L method gives several new structural parameters, i.e., the numbers of carbon, sulfur, nitrogen, and oxygen atoms belonging to different structural groups: aliphatic chains, aromatic and naphthenic rings, and heterocycles. These numbers are balanced with the molecular weight of the average molecule and the elemental composition of samples. The summary absolute deviation of the carbon atom distribution varies from 0.04 t o 12.6. These values are considerably less than an erroneous attribution of one carbon atom t o some group. The influence of heteroatoms on the accuracy of structural calculations is very greately. The ordinary error of the structural group composition calculation for coal tar fractions by the G-L method exceeded the number of aromatic rings over the total value of rings and obtained a negative value of the carbon content in paraffinic structures. In the modified method as shown
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1361 Table 4. Thermodynamic Calculations ~~
nomen
n-nonane
ethylcyclohexane
36.86 46.50 0.79 15.28 -10.0
35.02 40.36 0.27 19.21 22.4
-229.3 -0.10
-171.1 -0.84
505.4 -0.13
382.4 -0.12
13.24 747.78 275.83 212.75 -0.01 401.53 0.04 485.19 0.05
-42.32 758.80 296.23 158.66 0.081 343.69 -0.79 420.25 -0.65
250.24 -0.48 298.68 2.59
183.88 -0.33 183.88 0.67
227.3 3.51 12.45 4.41
173.2 10.47 6.36 2.71
cis-decalin
n-butylbenzene
1-methylnaphthalene
Heat of Vaporization 41.20 39.95 45.94 50.10 49.90 60.08 2.27 0.67 2.01 33.42 28.69 41.37 4.6 2.5 Standard Enthalpy of Formation -172.8 -12.7 116.5 2.11 -9.31 -0.14 Standard Entropy of Formation 379.3 434.1 381.4 0.34 -1.29 0.37 Heat Capacity in Ideal Gas State -86.09 -11.82 -20.06 946.61 705.43 696.30 372.76 278.182 289.37 164.34 174.72 168.79 -2.15 -0.79 -1.40 393.88 345.36 325.56 1.37 -0.60 -0.44 487.76 414.79 386.87 -0.36 1.38 -0.28 Heat Capacity in Liquid Phase 22.55 205.76a -1.83 -0.03 252.64 221.3Ba -0.69 -0.27 Entropy of Melting 234.0 97.9 253.3 1.65 -10.44 4.37 6.98 5.67 7.83 9.93 -0.58
thiophene
pyridine
m-cresol
30.38 32.59
33.38 37.46
41.78 53.72
11.19
19.06
32.84
107.0 -75.0
138.9 -0.81
-124.1 4.50
284.2 1.76
284.7 0.48
359.2 0.49
-5.96 298.52 126.38 72.22 -1.47 141.08 -0.07 166.18 0.45
-18.34 369.95 154.45 78.75 0.11 164.94 -0.05 197.16 -0.10
0.63 464.74 181.51 123.72 -1.14 237.01 -0.95 283.86 -0.96
148.07 -0.44
225.30 0.87
230.0 -0.35 4.33 0.79
314.4 10.43 4.83 7.16
234.0 -0.43 8.26
For naphthalene a t 373.15 and 423.15 K.
in Table 3, these shortcomings are abolished. This was possible owing to introducing correctives on the oxygen content in etheric groups and heterocycles as a considerable part of oxygen in coal tar molecules is placed in such ones. The sequence and values of intermediate and final data would be helpful for beginning users of this method. The examples of through thermodynamic calculations are given in Table 4. The same compounds and fractions were used as above to obtain total deviations connected with structural group composition determination and intermediate data prediction. It is seen from Table 4 that deviations in determination of molar volume and critical properties are about twice as great as those that were predicted from theoretical formulas. The deviations of surface tension and heat of vaporization include in addition the deviations of critical temperature prediction. However, their total deviations are not more than 8% (at 573 K). Only near the critical point are they increased sufficiently. Near the boiling point the deviations of surface tension and heat vaporization do not increase above 3% and 5%, respectively. The standard enthalpy of formation is the property most sensitive t o change of structural parameters. It is difficult to develop a good correlation for its prediction even for pure hydrocarbons. As shown in Table 4, we have obtained enough satisfactory results also in this part. Deviations of enthalpy are not more than those predicted from theoretical formulas and vary in the range of &3%. Only for values near zero and for heterocyclic compounds do they increase to lo%, not exceeding in the absolute 2 kJ/mol. The standard entropy of formation has the predicted deviation of less than 1.5%.
In conclusion it should be noted that the G-L method does not give values ofNc3 and Nc4 distribution of sulfur and oxygen atoms among structures. Neglecting the content of isoparaffhic chains, i.e., replacing tertiary and quaternary carbon atoms by methylenic groups, in the calculation process give deviations in predicting critical volume and entropy of formation (up to 8%), heat of formation and entropy of melting (up to 45%), and melting point (up t o 50 K). Therefore, it the necessity has arisen to determine the values of Nc3 and Nc4, as well as Ns, and No, in addition to G-L parameters using spectral methods, i.e., IR spectrometry. In this connection the deviations are not large in predicting the molar volume, surface tension, critical temperature, critical pressure, heat of vaporization, and heat capacity in all phases. They are no more than 5%. Such precision is sufficient for many engineering calculations. When the content of paraffins in fractions is not large (
