638
Energy & Fuels 1991,5,638-642
Calculation of Molar Volume of Hydrocarbons in Coal-Derived Liquids by a Group Contribution Method? Masaaki Satou,* Hirofumi Nemoto, Susumu Yokoyama, and Yuzo Sanada Metals Research Institute, Faculty of Engineering, Hokkaido University, N-13 W-8, Kita-ku, Sapporo, 060 Japan
Received January 23,1991. Revised Manuscript Received June 17,1991 A method of calculation of molar volume of hydrocarbons in a coal-derived liquid was developed by using the contribution of atomic groups to the molar volume. Narrow-cut distillates of coal-derived liquids were separated into a set of chemically homologous fractions by HPLC, and group analyses were performed by a combination of 'H and 13C NMR and elemental analysis. Two methods are proposed in this study for the calculation of molar volume, and both need only chemical structure. The atomic groups are aliphatic methyl groups, aliphatic methylene groups, aliphatic methine groups, aromatic protonated carbons, aromatic substituted carbons, aromatic conjunction carbons, and naphthenic rings in method 1, and total carbons, aromatic rings, naphthenic rings, and aromatic conjunction carbons in method 2. The values of group contribution to molar volume by regression analysis correspond to their partial molar volumes in a hydrocarbon molecule in method 1and the incrementa per atomic group to the molar volume of normal paraffin having the same total number of carbons in method 2. By both methods 1 and 2, the calculated molar volumes and densities are in good agreement with the observed ones.
Introduction The liquid density as well as the boiling point is one of the most fundamental properties which are necessary for process design and operations of coal liquefaction and upgrading.' Coal-derived liquids have a wide distribution of molecular weight, including alkanes, aromatics, hydroaromatics, and their substituted derivatives. The data base is not always sufficient to provide dependable parameters for the estimation of densities of the liquids composing coal-derived liquids. The density estimation methods based on the correlations between the density and other properties, such as average molecular weight, boiling point, and refractive index, were proposed." In practice, these methods might be available for the density estimation of complex material such as a coal-derived liquid that could not be well-defined. It is well-known that the physical properties of a given heavy hydrocarbon molecule are closely related to its chemical structure.b Once they have been clarified, the properties can be estimated by the additivity rules. The simplest rule is that of additivity of atom properties. In this rule, one assigns partial values for the property in question to each atom in the molecule and the property is the sum of all the atom contributions. In the case of molecular weight, this rule is accurate. The next higher approximation in additivity rule is the additivity of bond properties. It is clear that this rule will give the same properties for isomeric species. Finally, the next higher approximation is to define a molecular property as composed of the contributions of various component groups. In fact, the group contribution method for the coal-derived liquids is one of the most useful methods for estimation of physical properties.- The advantage of estimation by group contribution method is that no physical constants other than chemical structure are used as inputs. Hence, group contribution method is an intuitively clear way to understand the influences of atomic groups in a compound Presented at the Symposium on Analytical Chemistry of Heavy OiWReeids, 197th National Meetina of the American Chemical Society, Dallas, TX, April 9-14, 1989.-
on ita physical property. That is, the differences in property among compounds are instantly recognized as the distinctions of their structures. To obtain the most primary information on a given compound, regardless of pure or mixture, the most common approach is to recognize it as the chemical structure. Traube introduced the concept of additivity of atomic contributions to molar volume.1° The molar volume is reduced by the density and molecular weight of compounds. Empirical relations expressing molar volumes of normal paraffins in terms of chain length were presented by Huggins" and Calingaert et al.12 Kurtz et al. developed the relation between the molar volume and the numbers of various types of atomic groups in hydrocarbons including branched alkanes, cyclic alkanes, and For the structural analysis of coal, a graphical densimetric method was established by van Krevelen.16 All these approaches have in common the concept of volumetric additivity of structural units of the molecule. Recently, Hirsch derived empirical equations from the densities of hydrocarbons in petroleum heavy ends, containing from 5 to 44 carbon atoms and ranging in molecular weight from 70 to 619.16 These equations included cor(1) Gray, J. A.; Brady, C. J.; Cunningham, J. R.; Freeman, J. R.; Wilson, G. M. Ind. Eng. Chem. Process Des. Dev. 1988,22, 410. (2) White, C. M.; Perry, M. B.; Schmidt, C. E.; Douglas, L. J. Energy Fuels 1987.1.99. (3) MazGdar, B. K. Energy Fuels 1988,2, 230. (4) Khan, M. R. Energy Fuels 1988,2,834. (5) Beneon, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. (6)Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. (7) Le, T. T.; Allen, D. T. Fuel 1985,64, 1754. (8) Allen, D. T.; Behmanesh, N.; Eatough, D. J.; White, C. M. Fuel
1988, 67, 127. (9) Hartounian, H.; Allen, D. T. Fuel 1989,68,480. (10) Traube, J. Ber. Deut. Chem. Ges. 1896,25,2722. (11) Huggine, M. L. J. Am. Chem. SOC.1941,63, 116. (12) Calingaert, G.; Beatty, H. A.; Kuder, R. C.; Thomson, G. W. Ind. Eng. Chem. 1941,33, 103. (13) Kurtz, S. S. Jr.; Lipkin, M. R. Ind. Eng. Chem. 1941, 39, 779. (14) Kurtz, S. S. Jr.; King, R. W; Stout, W. J.; Peterkin, M. E. Anal. Chem. 1968,30,1224. (15) Van Krevelen, D. W. Coal; Eleevier: New York, 1961.
0887-0624/91/2505-0638$02.50/00 1991 American Chemical Society
Energy & Fuels, Vol. 5, No. 5, 1991 639
Molar Volume of Hydrocarbons
rection terms which are specific to the classes of ring structures involved in the links, and so were somewhat complicated. Hoshino et al. estimated the molar volume and latent heat of vaporization of aliphatic hydrocarbons, considering the effect of the position of a functional gr0~p.l~ The prediction of various physical properties, including density, of middle distillate fuels was reported by Caswell et al.lS This method was based on average molecular structures according to liquid chromatography/ ‘H nuclear magnetic resonance (LC/’H NMR) analysis of the fuel ~amp1es.l~ Generally, prediction methods, empirical methods or group contribution methods in either case, are obtained by regression analysis, and the better accuracy we get, the more complicated they are. Therefore, we cannot readily and clearly answer such a plain question as how much the molar volume changes by the increase of aromatic rings or naphthenic rings. In the application of a group contribution method to the estimation of molar volume for a coal-derived liquid, the information of its chemical structure is necessary. As a coal-derived liquid is a mixture with very complex compounds, it is impossible to identify the whole components in it. In the preceding paper,20the authors have proposed an analytical method to clarify the chemical structures in a coal-derived liquid and seven atomic groups for estimation of ita physical properties. The purpose of this study is to develop a calculation method of molar volume or density of hydrocarbons in coal-derived liquid by using the group contribution method.
Experimental Section The sample preparation methods and structural characteristics for a coal-derived liquid discussed herein are described in the preceding article.P In brief, narrow-cut distillate of a d-derived liquid were separated into chemically homologous compounds called ’compound classes” by using a HPLC equipped with an amine column according to the number of aromatic rings. There are six hydrocarbon compound classes: alkanes (Fr-P), monoaromatics CFr-M), naphthalene type diaromatics (Fr-DO,biphenyl type diaromatics (Fr-D2),tri- and tetrmromatica (F’r-T);and poly-, polar compounds (Fr-PP). The lacand ‘HNMR measurements and elemental analyses were carried out for the characterization of these compound classes. The measurements of densities for representativecompound clasees were made at 298 K by a glass pycnometer calibrated with distilled water at the same temperature.
Results and Discussion In the use of the additive rule for the prediction of physical property of a given compound, it is thought that there are two methods. One is that partial values for the property in question are assigned to each structural factor in the molecule. And the property is the sum of all the contributions (method 1). The other method is that the difference in property between a given compound and a reference is attributed to the contributions of structural components which are absent in the reference. In hydrocarbons, for example, normal paraffins are selected as reference, and the structural contributors are aromatic rings, naphthenic rings, and so on. The property of a given (16) Hirech, E. A m l . Chem. 1970,42, 1326. (17) Hoshino, D.; Nagahama, K.; Hirata, M. J . Jpn. Pet. Inst. 1979, 22, 32. (18) Canwell,K. A.; Glaes, T. E.; Swann, M.; Dom, H. C. Anal. Chem. 1989,61,206. (10) Haw, J. F.; Glass, T. E.; Dorn, H. C. Anal. Chem. 1983,55,22. (20) Determination of Atomic Groups of Hydrocarbons in Coal Derived Liquids by High Performance Liquid Chromatographyand Nuclear Magnetic Resonance. Energy Fuels, preceding paper in this issue.
3^ 3501
--.t i 9
soot
.;” 1
Observed molar volume (ml/mol)
Figure 1. Comparison between observed and calculated molar volumes of compound classes by method 1: ( 0 )Fr-P (X) Fr-M; (A) Fr-D1; (m) Fr-D2. nonparaffinic molecule is the s u m of all the nonparaffinic structures’ contributions to that of the reference (method 2). In this paper, both methods are applied to the prediction of molar volume of hydrocarbons and compared with other methods. The Calculation of Molar Volume Based on Method 1. Based on the concept of method 1, it is reasonable to assume that the molar volume of a compound class in coal-derived liquid is represented by eq 1,where V, is the Vm = cV,ni (1) molar volume of the compound class and V , and ni denote the group increment, that is, the partial molar volume of the ith atomic group and the number of the ith atomic group per average molecule in a compound class, respectively. Molar volume is defined in eq 2, where M, and d V , = M,/d (2) are the average molecular weight and density of the compound class, respectively. In this study, the average structures of compound classes are represented by seven atomic groups as shown in the preceding paper.2O These are aliphatic methyl groups (CHJ, aliphatic methylene groups (CHJ, aliphatic methine groups (CH), aromatic protonated carbons (AH),aromatic substituted carbons (AS),aromatic conjunction carbons (AC), and naphthenic rings (NR).The values of ni, d , M, and V , of all compound classes are determined experimentally and are listed in Table I. Next, the values of V , will be evaluated by the regression analysis. In regression analysis, the values of the molar volume of well-established hydrocarbons21are included for the data because the data points of compound classes are not so many. The total number of data is 194,including 21 of compound classes. The results of regression analysis are listed in Table I1 and compared with those by Hoshino et al.” Though their study was carried out on aliphatic hydrocarbons, both results are close in values. The values of 0.994 and 13.34mL/mol were obtained as a correlation coefficient and a standard deviation of error in this method, respectively. The average absolute percent of error is 1.57%. In Figure 1, the calculated molar volumes of compound classes from eq 1and the partial molar volumes were compared with the observed molar volumes. For reference, the results of regression analysis using 21 data points of hydrocarbon compound classes (method 1 - 0and 173 of pure hydrocarbons (method 1-P) are listed in Table 11. The remarkable differences of the partial (21) Stephenson, R. M.; Malanowski,S. Handbook of the Thermodynamic of Organic Compounde; Eleevier: New York, 1987.
640 Energy & Fuels, Vol. 5, No. 5, 1991
Satou et al.
Table I. Number of Atomic Groups (q), Total Carbon Numbers (CJ, Average Molecular Weights (M"), Density, and Molar Volume (V,) in an Average Molecule of Each Fraction ni
c,
M,
0.00 0.00 0.00 0.00
NR 0.55 0.66 0.92 0.88 0.78
13.70 15.41 15.58 17.48
180 193 216 218 245
density 0.7722 0.8124 0.8312 0.8359 0.8383
Vma 233 237 260 261 292
2.28 2.81 3.10 3.31 3.36 3.03 3.78
0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.81 0.72 1.04 1.58 1.81 1.89 1.85
12.30 13.73 15.83 16.57 17.49 17.49 17.24
165 185 214 223 235 235 232
0.9246 0.9462 0.9498 0.9605 0.9644 0.9853 0.9829
178 196 225 232 244 239 236
7.83 6.51 5.92 5.41 5.33 4.81
0.17 1.49 2.08 2.59 2.67 3.19
2.00 2.00 2.00 2.00 2.00 2.00
0.01 0.33 0.65 1.25 0.94 1.57
11.74 13.76 14.20 15.60 15.60 16.64
153 180 186 204 205 218
0.9945 1.0064 1.0243 1.0273 1.0329 1.0545
154 179 181 199 198 207
6.90 6.67 6.86
5.10 5.33 5.14
0.00 0.00 0.00
1.15 1.24 1.33
15.31 16.00 14.69
198 208 189
1.0648 1.0566 1.0985
186 197 172
fraction 5P 11 P 15 P 17 P 19 P
CHS 3.00 2.43 2.85 2.65 1.46
CH2 7.65 9.52 9.87 10.53 14.99
CH 2.11 1.75 2.70 2.40 1.03
AH 000 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
5M 11 M 15 M 17 M 19 M 21 M 23 M
1.16 1.39 1.71 1.76 1.51 1.74 2.05
4.64 6.33 7.43 7.21 8.22 7.28 7.22
0.49 0.01 0.69 1.61 1.77 2.48 1.97
3.72 3.19 2.90 2.69 2.64 2.97 2.22
11 D1 15 D1 17 D1 19 D1 21 D1 23 D1
0.92 1.21 1.10 1.36 1.17 1.17
0.56 2.16 2.78 2.96 4.04 4.36
0.26 0.38 0.32 1.28 0.39 1.11
19 D2 21 D2 23 D2
0.86 1.32 0.96
2.39 2.21 1.24
0.06 0.47 0.49
a Calculated
~~~
AS
AC ~~
from eq 2.
Table 11. Partial Molar Volumes of Atomic GrouDs (mL/mol) and Correlation Coefficients (R)in Regression Analysis method la method 1-Cb method 1-Pc Hoshino
VW,
VW",
VW"
VaAH
29.63 29.66 29.68 33.55
16.68 15.91 16.68 16.08
4.16 7.31 4.24 8.46
14.44 13.53 14.48 12.73d
va,
vu,
Vam
R
1.46 5.08 1.35 2.66d
3.81 5.68 3.06 6.96d
7.44 0.18 7.86
0.9945 0.9945 0.9955
Data points are 194, including 173 of pure hydrocarbons in the literature.21 *Data points are 21 of hydrocarbon compound classes in coal-derived liquid. cData points are 173 of pure hydrocarbons. dThese atomic groups are composed of an olefinic double bond.
molar volumes of atomic groups between both method is not recognized except for those of aromatic substituted carbon and naphthenic ring. Using the values obtained by method 1-P, the average percentage of deviation in the molar volume calculation of 21 hydrocarbon compound classes is 2.09%. It is suggested that the molar volume of even a mixture such as hydrocarbon compound classes can be calculated by using the partial molar volumes for pure hydrocarbons obtained by method 1-P. The Calculation of Molar Volume Based on Method 2. The change of molar volumes with the total carbon number in normal alkanes, cyclohexanes, benzenes, and naphthalenes with a straight alkyl side chain are shown in Figure 2. The values of those molar volumes are in the literaturesa From this figure, two facts can be recognized. One is that the relationship between the molar volume and total carbon number is linear for homologous series. The other is that the group contributions to the molar volume of a given hydrocarbon as against normal alkane are about -40 mL/mol per aromatic ring and -20 mL/mol per sixmembered naphthenic ring if the total carbon number is equal. Based on these considerations, the equation for molar volume calculation of hydrocarbons, is represented as (3)
where V , , Vl,,and Ni are the molar volume equivalent to normaf alkanes with the same total carbon number as a given hydrocarbon, the contribution of the ith atomic (22) Technical Data Book-Petroleum Refining, 2nd ed.; American Petroleum Institute: Washington, DC, 1970.
400 I
I
~
I
100 5
I
10 15 Number of total carbons
20
Figure 2. Relationship between molar volume and number of total carbons in normal alkanes and some alkyl aromatic derivatives: ( 0 )normal alkanes; ( X ) alkylcyclohexanes; (m) alkylbenzenes; (A)alkylnaphthalenes.
group to molar volume, and the number of atomic groups per molecule, respectively. This equation means that the molar volumes of hydrocarbons are calculated by adding the total increments of molar volume (CV',,NJ to the molar volume equivalent to normal alkane having the same total carbon number as them (V,). V are calculated by eq 4, where C, is the total carbon n u a e r of a given hyVm, = 32.72 X 2 + 16.26(Ct - 2) (4) drocarbon. This equation was obtained by regression analysis based on the correlation of the molar volumes and total carbon numbers from 5 to 18 in the normal paraffm. The value of the correlation coefficient is 0.999. The first term of this equation is the partial molar volume corre-
Energy & Fuels, Vol. 5, No. 5,1991 641
Molar Volume of Hydrocarbons
360
Table 111. Contributions of Atomic Groups to Molar Volumes (mL/mol) and Correlation Coefficients (R)in Remssion Analysis V&m
vl,,
v,,,,
R
method 20 -39.61 -19.63 4.57 0.9915 2.62 0.9889 -35.64 -22.64 method 2-Cb 4.03 0.9899 -39.87 -19.59 method 2 - F a Data points are 181, including 160 of pure hydrocarbons in the literature.*’ *Data points are 21 of hydrocarbon compound classes in coal-derived liquid. eData points are 160 of pure hydrocarbons.
sponding to two terminal methyl groups and the second term is the volume of other methylene groups of the corresponding normal paraffin. In eq 3, it is considered that the kinds of atomic groups, which are absent in normal paraffins, are three, that is, aromatic rings (NAR),naphthenic rings (NNR),and aromatic conjunction carbons (NAc).Though the categories of atomic groups are somewhat different between methods 1 and 2, Ni for method 2 are easily obtained because the compound classes were separated according to the number of aromatic rings by using a HPLC equipped with an amine column. For example, in naphthalene type diaromatics (Fr-Dl), Nm and NAcare 2 and 2, respectively. Ct and NNRwere already calculated as mentioned in the preceding paper,20and the values of V& are evaluated by regression analysis. As the data of normal paraffins are deducted from those in method 1, the total number of data is 181 in this method. The results of regression analysis are listed in Table 111. The values of 0.991 and 11.23 mL/mol were obtained for the correlation coefficient and the standard deviation of error in this method, respectively. The average absolute percent of error is 1.23%. In Figure 3, the calculated molar volumes of compound classes by eq 3 and the contributions to molar volume are compared with the observed ones. The results of regression analysis using 21 data points of hydrocarbon compound classes (method 2-C) and 160 data of pure hydrocarbons (method 2-P) are listed in Table 111. Both results are close in values. Using the values obtained by method 2-P, the average absolute percent of error in the molar volume calculation of 21 hydrocarbon compound classes is 1.97%. In this way, it is considered that the result of regression analysis using pure hydrocarbon data points, that is, method 2-P as well as method 1-P, could give enough accuracy to the molar volume estimation of hydrocarbon compound classes in a coal-derived liquid, which is a very complex mixture. Furthermore, using the values by method 2 4 , the average absolute percent of error in the molar volume calculation of 160 pure hydrocarbons is 2.39%, and these values could be available for the molar volume calculation of pure hydrocarbons. Comparison of Calculation Methods for Molar Volume and Density. By use of the obtained values of partial molar volumes (method 1) or group contributions to molar volume (method 2), the molar volumes of well-
a
u 100
]’,,”
100
,
I
I
1
160
200
260
300
350
Observed malar volume (ml/mol)
Figure 3. Comparison between observed and calculated molar volumes of compound classes by method 2. Symbols are the m e as in Figure 1.
established hydrocarbons with one straight alkyl chain are calculated, compared with those obtained from the literature22and by other methodslc17 for the molar volume calculation. The results are listed in Table IV. In this table, the molar volumes were exactly calculated by the methods proposed by Kurtz et al.“ and Hirsch.lB In van Krevelen’s method,ls it is assumed that the molar free space due to end groups in Traube’s methodlo is negligible. Consequently, his method produces poor estimation, especially in case of normal alkanes, although it is somewhat easier to use. The van Krevelen’s method produces an average absolute error of 18.53 mL/mol. On the contrary, Hoshino’s method17 uses a molar volume data base of aliphatic hydrocarbons, and molar volumes of some aromatic hydrocarbons are calculated with less accuracy than those of aliphatic hydrocarbons, the average absolute error ia 6.14 mL/moI. Though methods 1 and 2 in this study are somewhat inferior to the methods by Krutz et al. and Hirsch, it is considered that they have enough accuracy for even pure hydrocarbons. The final purpose of this paper is the molar volume calculation of hydrocarbon mixture in a coal-derived liquid as well as pure hydrocarbons. The molar volume and density of compound classes for coal-derived liquid before narrow-cut distillation are calculated by four methods, including methods 1 and 2 in this study. The values of ni, d , M,, and V, of each compound class are listed in Table V. The results are shown in Figure 4 and 5. It is impossible to apply two methods by Krutz et al. and Hirsch to the molar volume calculation for a coal-derived liquid, because of the nondetermination of some atomic groups used in their methods. By method 2 and by Krevelen’s method, the molar volume and density of Fr-T cannot be calculated due to lack of information about the ring structure in Fr-T. In the calculation of density from Figure 5, generally, Hoshino’s method is inclined to overestimate the number of aromatic hydrocarbons. On the contrary, Krevelen’s method7overestimates Fr-P and D1. By both methods 1 and 2, the calculated values are
Table IV. Molar Volume Calculation of Hydrocarbons with One Straight Alkyl Chain average absolute error, mL/mol comwund class no. of data Points method 1 method 2 Hoshino Krevelen Kurtz normal alkanes 27 2.67 0.77 1.51 28.84 0.79 cycloalkanes 25 18.21 2.14 1.00 7.32 1.13 decahydronaphthalenes 4 2.56 2.56 6.53 6.88 2.56 benzenes 25 19.26 1.24 1.74 1.73 10.72 tetrahydronaphthalenee 11 0.99 1.21 0.62 7.70 8.59 naphthalenes 12 1.32 2.23 1.83 1.80 10.01 biphenyls 4 1.44 0.54 9.61 2.47 10.99 1.18 all compound claeees 108 2.09 1.21 6.14 18.53
Hirsch 0.73 0.99 4.08 0.95 0.59 1.36 1.03
642 Energy & Fuels, Vol. 5, No. 5, 1991
Satou et al.
Table V. Number of Atomic ~ O U (ni), ~ STotal Carbon Numbers (C&,Average Molecular Weights (M”), Density, and Molar Volume ( V J in an Averaue Molecule of Each ComDound Class before Narrow-Cut Distillation ~~
~~
~
~~
*i
comDound classa
CH,
CH,
CH
AH
AS
AC
NR
C,
M,
P M D1
2.02 1.25 0.80 0.73 1.09
12.76 4.97 2.43 2.13 1.86
1.22 0.23 0.03 0.10 0.17
0.00 2.89 6.25 7.02 7.86
0.00 3.11 1.75 4.98 1.79
0.00 0.00 2.00 0.00 5.18
0.60 1.05 0.49 1.18 0.43
16.01 12.45 13.26 14.96 17.96
225 166 173 193 231
D2
T
density 0.8239 0.9580 0.9829 1.0740 1.1337
Vmb 273 173 176 180 204
OContents of compound classes are 17.29,23.97,18.06,6.43 and 10.89 w t 70 for P,M,D1,D2,and T,respectively. bCalculated from eq 2.
1
I I I Zoo 260 SO0 360 Observed molar volume (mllmol)
100
160
Figure 4. Comparison between observed and calculated molar volumes of compound classes before narrow-cut distillation by four methods: (D) method 1; (A)method 2; (0)Hoehino’smethd, (X) Krevelen’s method.
3
I
1 I 0.7
0.8
I 1.0
I
1.1 Obsemed density (g/mI) 0.9
1.2
Figure 5. Comparison between observed and calculated densities of compound classes before narrow-cut distillation by four methods. Symbols are the same as in Figure 4.
in good agreement with the observed ones. Between the two methods in this study, method 2 is matched with method 1,according to the statistical data. The advantage of method 2 is not only that that fewer kinds of atomic groups are considered than in method 1, but also that method 2 is an intuitively clear way to understand the influences of atomic groups on the molar
volume. In method 1,group contributions mean the partial molar volume and so must be one of the principal values of physical properties. However, as shown in Figure 2, the differences of molar volume between the alkyl derivatives having same total carbon number are not explained immediately by method 1. That is, it could be possible to clarify how the molar volume changes by the increase of aromatic or naphthenic rings and to take a wide view of molar volume estimation according to the structural distinctions of molecules by this method. Consequently, by both methods in this study, the molar volumes of various types of hydrocarbons, that is, alkanes, aromatics, hydroaromatics, and alkyl derivatives of them, could be calculated over a wide range of total carbon number from 6 to 20 and within less than 5 % of the average absolute percent of error. Conclusion A method of calculation of molar volume or density of hydrocarbons in a coal-derived liquid was developed using a group contribution method. Structural parameters of hydrocarbons were obtained as follows. Narrow-cut distillates of coal-derived liquids were separated into some chemically homologous fractions by HPLC, and structural analyses were performed by a combination of ‘H and lac NMR and elemental analysis. For the calculation of molar volume, two methods are proposed in this study. The values of group contribution to molar volume by the regression analysis correspond to the partial molar volume in a hydrocarbon molecule in method 1 and the incrementa per atomic group to the molar volume of normal paraffin having the same total number of carbons in method 2. By both methods 1and 2, the calculated molar volume and density are in good agreement with observed values. The obtained group contributions are characteristic values for atomic groups comprising hydrocarbons and are useful in predicting the molar volume and density of hydrocarbon mixture in a coal-derived liquid as well as pure hydrocarbons. Acknowledgment. We are very grateful to the New Japan, for the Energy Development Organization (NEDO), supply of coal-derived liquid for this study.
