1992_satou et al._a method of estimating the refractive index of hydrocarbons in coal derived...

8/13/2019 1992_Satou Et Al._a Method of Estimating the Refractive Index of Hydrocarbons in Coal Derived Liquids by a Grou

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466 Seki yu Gakkai shi , 35, (6), 466-473 (1992)

[Regular Paper]

A Method of Estimating the Refractive Indexof Hydrocarbons in Coal Derived liquids

by a Group Contribution Method

Masaaki SATOU*, Hiroki YAMAGUCHI, Toshimitsu MURAI,Susumu YOKOYAMA, and Yuzo SANADA

Metals Research Institute, Faculty of Engineering, Hokkaido University,Kita-13, Nishi-8, Kita-ku, Sapporo 060

(Received April 1, 1992)

A simple method of calculating the refractive index of hydrocarbons in a coal derived liquid was

developed using contribution of component groups to the refractive index. Narrow cut distillates of coalderived liquids were separated into sets of chemically homologous fractions called, compound classes ,by high performance liquid chromatography (HPLC). Now, group analyses were performed by gaschromatography/mass spectroscopy (GC/MS) or a combination of 1H-, 13C-nuclear magnetic resonance(NMR) spectroscopies and elemental analysis. The component groups adopted in this study arearomatic rings and naphthenic rings. The contributions of each component group to refractive indexwere determined by regression analysis with reference to the data set of pure hydrocarbons. The valuesobtained corresponded well, with the increments per component group, to the refractive index of normalparaffin with the same total number of carbons. Thus, the calculated refractive indices of hydrocarboncompound classes in a coal derived liquid showed good agreement with those observed.

1. Introduction

Coal derived liquids, which generally consist ofalkanes, aromatics, hydroaromatics and their sub-stituted derivatives, are distributed over a widerange of molecular weights. Thus rapid and ver-satile method of estimating the composition of agiven coal derived liquid is desirable, especially forroutine analysis. As the refractive index is easy todetermine with great precision in a continuousmode, a correlation between refractive index andother properties could become useful for processcontrol of coal liquefaction and upgrading1)-3).For estimating the number of rings and the carbonpercentage of an aromatic, naphthenic, or paraf-finic structure from measured values of somephysical properties, many methods and procedureshave been proposed4)-9). The n-d-M method, usingdensity (d), refractive index (n) and molecularweight (M) as input parameters, is one of well-known methods8),9).

Intermolecular forces have direct impact onphysical and thermodynamic properties of fuel;these are mainly the van der Waals forces in the caseof non-polar molecules, such as hydrocarbons.Susceptible to polarization is considered a useful

property for understanding this force: as, it can becalculated from liquid density and refractive indexby Lorentz-Lorenz equation10),11).

As mentioned above, the refractive index is oneof the fundamental properties, like density. Atechnique of estimating the refractive index be-comes necessary when experimental data are notreadily available: as, (1) when new compounds areinvolved, (2) when literature data are not at hand or(3) when the actual refractive index does not existbut it is required for establishing a particularcorrelation.

It is well-known that the physical properties of agiven heavy hydrocarbon molecule are closelyrelated to its chemical structures12). A method,based on the contribution of each structural unit orgroup, assigns partial values for the property inquestion to each component group in the mole-cule, on the premise that as long as the composi-tion rules are known, the property of the heavymolecule is the sum of all the group contributions.This is one of highly useful methods estimatingthe physical properties of coal derived liquids13)-16)One advantage is that the only parameter involvedis the chemical structure, and another is its intui-tive clarity. Few methods of predicting the refrac-

tive index of hydrocarbons by group contribution,however, have been proposed17),18)

To whom correspondence should be addressed.

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It is currently impossible to identify every singlecomponent of the coal derived liquid, which is avery complex mixture. Nonetheless, the authorshave proposed a program of analytical methods toreveal more and more of the chemical structures ina coal derived liquid by using high performanceliquid chromatography (HPLC) and gas chroma-tography/mass spectrometry (GC MS), or nuclearmagnetic resonance (NMR)19)-21). These analyti-cal results have provided much information aboutthe relationships between chemical structures andboiling points or molar volumes of hydrocarbonsin a coal derived liquid, and the basis for a methodof prediction of these properties22)-24). This studydirects the group contribution method to thesubject of the refractive index of hydrocarbons incoal derived liquids.

2. Experimental

Two kinds of coals, Akabira coal and Wandoancoal, were used as sample coals. The methods ofsample preparation and analyses for structuralcharacteristics of each coal derived liquid were aspreviously described19),21). In brief, narrow cutdistillates of a coal derived liquid were separatedinto chemically homologous compounds called, compound classes , by using a HPLC equippedwith an amine column, in accordance with thenumber of aromatic rings. There were six hydro-

carbon compound classes: as, alkanes (Fr-P),monoaromatics (Fr-M), naphthalene type diaro-matics (Fr-D1), biphenyl type diaromatics (Fr-D2),tri- and tetra-aromatics (Fr-T) and poly-, polarcompounds (Fr-PP). GC/MS measurements19),or 13C-and 1H-NMR measurements and elementalanalyses21) were carried out to find the averagenumber of toal carbon, aromatic rings and naph-thenic rings of each compound class. Refractiveindices of the representative compound classeswere taken at 293K using Abbe's refractometer(Atago model Type I). The measurements oftheir densities were made at 293K by glass pyc-nometer calibrated with distilled water at the sametemperature.

3. Results and Discussion

The changes of refractive indices with totalcarbon number in normal alkanes, cyclohexanes,benzenes, tetrahydro-naphthalenes and naphtha-lenes with a straight alkyl side chain are shown inFig. 1. The values of these refractive indices areavailable in referenced literature25). It is clearfrom this data that the relationship between therefractive index and total carbon number are non-linear for the respective homologous series. Con-sequently, this means that the refractive index

cannot be calculated using a linear equation withthe total carbon number as a parameter. Hoshinoet al. have proposed the value of M/n, that is,molecular weight (M) divided by refractive index(n)*1, for calculation of the refractive index by thegroup contribution method17),18)

In Fig. 2 are shown the changes of M/n withtotal carbon number for the same homologousseries as in Fig. 1. Clearly, the relationships be-tween the value of M/n and total carbon num-ber are linear for the homologous series, so fartested. Furthermore, each linear relationship isparallel with each other. It appears possible toderive a composite rule for the prediction of M/n ofa given compound from its total carbon number.

Fig. 1 Changes in Refractive Index of Pure Hydro-

carbon Derivatives with Total Carbon Number

Fig. 2 Relationship between M/n and Total CarbonNumber in Pure Hydrocarbon Derivatives

*1 The physical meaning of the value of M/n is describedbriefly in the Appendix.

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There are believed to be two methods to use theadditive rule for the predicting the physical prop-erties of a given compound. In one, partial valuesfor the property in question are assigned to eachstructural factor in the molecule. The property isthe sum of all the contributions (Method 1). Inthe other, the difference between the value of aproperty of a given compound and that of a refer-ence is attributed to the contributions of certainstructural features. In hydrocarbons, for exam-ple, normal paraffins are selected as reference, andthe structural contributions are attributed to aro-matic rings, naphthenic rings and so on. Theproperty of a given non-paraffin molecule is thesum of all the non-paraffin structures contributedto that of reference (Method 2). The advantage ofMethod 2 is the intuitive grasp of the influences of

component groups on a given physical property.Generally, prediction methods, empirical meth-

ods or group contribution methods, in either case,are obtained by regression analysis. Unfortunate-ly, the higher the accuracy we get, the more com-plicated they are. Therefore, we have no readyand brief answers to simple questions like, howdoes a certain physical property change from theaddition of one aromatic ring or one naphthenicring?

In Method 1, group contribution means thepartial property of an atomic group in a molecule

and thus it must be one of the principal values.As shown in Fig. 2, however, the differences in M/n among the alkyl derivatives of identical totalcarbon number are not explained immediately byMethod 1. This method is only effective to clarifyhow the value of M/n changes by the addition ofaromatic or naphthenic rings, and to take a wideview of the estimation of M/n, in accordance withthe structural distinctions between molecules. Inthe preceding paper24), the authors applied bothMethods 1 and 2 to the prediction of the molarvolume of hydrocarbon compound classes, in acoal derived liquid, obtaining good agreementbetween the calculated and observed molar vol-umes. In this study, the method of calculation forM/n is developed on the basis of Method 2 becauseof its simplicity and clearness.

The structural distinctions between varioushydrocarbons and reference normal paraffins arequite clear as shown in Fig. 3, namely, the differ-ences i n the val ue of Mn( (Mn)) versus total

carbon number. The group contributions to (Mn) of a given hydrocarbon are almost con-

stant, regardless of total carbon number. Theyare about -10per aromatic ring and -3per six-membered napthenic ring. Based on these con-siderations, the equation for calculating the M/n

of hydrocarbons, is represented as follows.

Mn= M n)p+ (M n) (1)

(Mn)= (Mn) i N (2)

where, (M/n)p is the value of M/n equivalent to

normal paraffins with the same total carbonnumber as a given hydrocarbon, (Mn)i i s the

cont ri but i on of the i - th component group to (M

n), and Ni is the number of component groups permolecule. Thus, the value for M/n of a givenhydrocarbon is calculated by adding the toali ncrements of Mn( (M n)i N = (M n)) to the

M/n for the reference normal paraffin with thesame total carbon number ((M/n)p).

The values of (M/n)p are calculated by Eq. (3).

(Mn)p =12. 35 2+9.51 (Ct-2) ( 3)

where Ct is the total carbon number of a givenhydrocarbon. This equation was obtained byregression analysis based on the correlation of thevalues of M/n and total carbon numbers from 4 to30 in the normal paraffins. The value of thecorrelation coefficient is 0.999. The first term ofthis equation means the partial value of M/ncorresponding to two terminal methyl groups andthe second term is that of M/n of other methylenegroups in the normal paraffin. In Eq. (2), thekinds of component groups which are absent in n-paraf f ns are to be considered, that is, aromaticrings (NAR) and naphthenic rings (NNR). The

Fig. 3 Difference in M/n between Non-paraffinicHydrocarbon and Normal Paraffin with

Identical Total Carbon Number

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val ues of (Mn)i have been eval uated by regressi on

analysis with 364 data points in the library25).The results of the regression analysis are listed in

Table 1. The values of 0.995 and 0.51 were ob-tained for the correlation coefficient and standard

deviation of error, respectively. The average ab-solute percent of error for M/n was 0.38%.

The main purpose of this paper lies in thecalculation of refractive index of hydrocarbon mix-ture in a coal derived liquid as well as of purehydrocarbons. The refractive indices or M/n ofcompound classes for coal derived liquids arecalculated by four methods, including the presentone and that shown in Table 2. The values of Niobtained by GC MS measurement19) or NMR

measurement21) are listed with the average molecularweight, mid-boiling point and density. The

Table 1 Contri but i ons of Component Groups, (Mn)i ,

to (M n)i n Regressi on Anal ysis

Table 2 List of Average Molecular Weight (M), Mid-boiling Point (BP), Density (d), Refractive Index (n), TotalCarbon Number (Ct) and Numbers of Aromatic Rings (NAR) and Naphthenic Rings (NNR) for EachCompound Class in Coal Derived Liquids

Fig. 4 Comparison between Observed and CalculatedM/n of Hydrocarbon Compound Classes ofCoal Derived Liquids by Eqs. (1)-(3)



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values of M/n of hydrocarbon compound classeswere calculated by using the obtained values ofcontr i buti ons t o (M n), l i sted i n Tabl e 1, and

compared with the observed M/n values. InFig. 4, there was good agreement between them.

In Tables 3 and 4, the accuracies of refractive indexcalculations by various methods are summarizedfor pure hydrocarbons, and also for hydrocarboncompound classes in coal derived liquids. The

group contribution method by Hoshino et al.18) is

Table 3 Refractive Index Calculation of Pure Hydrocarbons

Table 4 Refractive Index Calculation of Hydrocarbon Compound Classes in Coal Derived Liquids

a) APE denotes the absolute percent of error.

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superior to that by the others for pure hydro-carbons. Unfortunately, their method cannot beapplied to the calculation of refractive index ofcompound classes in coal derived liquids becausethe components of such liquids cannot be sepa-

rated into the atomic groups defined in Hoshino'smethod. White et al. advanced the exponentialequation for calculating the refractive index of coalderived liquids, using the average molecularweight, mid-boiling point and atomic ratio ofhydrogen to carbon as parameters1). Recently,Mazumdar has proposed a much simpler linearequation than that of White et al., and used themolecular weight of a hypothetical unit of a sub-stance per carbon atom, i.e. molecular weightdivided by total carbon number, as a parameter2).Mazumdar's method is superior to that of White

et al. for aromatic hydrocarbons and compoundclasses, as shown in Tables 3 and 4. His method,however, is not as accurate as ours, especially foralkanes and cyclohexanes. Riazi's method26) usesthe mid-boiling point and specific gravity as

parameters, and the calculated refractive indicesare in good agreement with those observed, exceptfor the decahydronaphthalenes, naphthalenes andthe naphthalene type diaromatic hydrocarboncompound classes.

The method introduced in this paper enables thedetermination, by calculation, of the refractive

indices of various types of hydrocarbons, that is,alkanes, aromatics, hydroaromatics and their alkylderivatives, regardless whether they be puresubstances or mixtures, over a wide range of totalcarbon number from 4 to 30, and within less than2% of the average absolute percent of error.

4. Conclusion

A simple method of calculating the refractiveindex of hydrocarbons in a coal derived liquid wasdeveloped using the group contribution method.The contributions of component groups to M/n,that is, molecular weight (M) divided by refractiveindex (n), were calculated by regression analysisusing the values of pure hydrocarbons found in thelibrary; the calculated contributions correspondedwell with the increments per component group toM/n over reference values for normal paraf f ns ofthe same total carbon number. These values areapplicable to the prediction of the refractive indexof liquid hydrocarbon mixtures such as coalderived liquids as well as pure hydrocarbons.

Appendix

In this study, the value of M/n was used as aphysical quantity instead of the refractive index ofa given compound. Molar refraction defined by

the Lorentz-Lorenz equation10) is well-known as a

physical value concerned with the refractive index.Van Krevelen used this value for the prediction ofrefractance of a coal by a contribution method27).The value of M/n was first used for calculation of

the refractive index of hydrocarbons by Hoshinoet al.17). However, they did not discuss this valuein any detail.

Then, what is the physical meaning of theunusual value of M/n? In this appendix, we de-scribe the physical meaning of the value of M/nbriefly. As a light wave is a type of electromag-netic wave, strictly speaking, it can be described interms of electromagnetics or quantum physics.Nevertheless, the fact is, a light wave is also aclassical transverse wave. Therefore, we willdiscuss the nature of light waves on the basis of

classical mechanics here.Let us consider a medium vibrating as a harmonic

oscillator28). Then its energy per unit volume,that is the energy density, is presented as follows,

E= 1/ 2)A2 2 (A-1)

where E, A, and are the energy densi ty, ampl i -

tude, angular frequency of an oscillator and thedensity of the medium, respectively. If a wavemotion propagates at a given velocity, a certain

amount of energy passes through the unit crosssection perpendicular to the direction of wave

propagation per unit time. This energy is calledthe wave intensity, and is expressed as follows,

I =E = 1/ 2)A2 2 A-2)

where I and are the wave i ntensi ty and the veloci -

ty of wave motion, respectively. Here, there existsthe relationship:

p= 1 2)A (A-3)

p corresponds to the pressure amplitude in acompressional wave. Then, Eq. (A-2) can be re-arranged as:

I =p2

/ ( A-4)

In electromagnetics, electric power is defined as:

P=V2

/ R (A-5)



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where, P, V and R are the electric power, voltageand resistance, respectively. Comparing Eqs. (A-4) and (A-5), i t i s f ound that I , p and corr espond

to P, V and R, respecti vel y. That i s, pl ays a

role of resistance in Eq. (A-5).As Eq. (A-1) is defined per unit volume, it is

consi dered t hat i s t he resi stance of medi a per

unit volume. Consequently, a hypothetical re-sistance of media per unit molar number, that is

per molar volume, is defined as follows;

VM= M =M A-6)

where, VM and M are the molar volume andmolecular weight, respectively. Then, from theright side of Eq. (A-6) is derived Eq. (A-7) using therefractive index.

M =M C/ n=Wn C (A- 7)

C is the velocity of light in vacuum. Therefore,the value of M/n used in this study reflects thehypothetical resistance of media per unit molarnumber in the propagation of light waves.

References

1) White, C. M., Perry, M. B., Schmidt, C. E., Douglas, L. J.,Energy & Fuels, 1, 99 (1987).2) Mazumdar, B. K., Energy & Fuels, 2, 230 (1988).3) Khan, M. R., Energy & Fuels, 2, 834 (1988).4) Kurtz Jr., S. S., Headington, C. E., Ind. Eng. Chem., 9, 21

(1937).5) Hersh, R. E., Fenske, M. R., Booser, E. R., Koch, E. F., J.

Inst. Pet., 36, 624 (1950).6) Riazi, M. R., Daubert, T. E., Ind. Eng. Chem., Process Des.

Dev., 25, 1009 (1986).

7) Nwadingwe, C. A., Okoroji, K. A., Fuel, 69, 340 (1990).8) Van Nes, K., Van Westen, H. A., Aspects of the

Consititution of Mineral Oils , Elsevier Publishing,New York (1951).

9) Waterman, H. I., Boelhouwer, C., Cornelissen, J., Cor-relation Between Physical Constants and ChemicalStructure , Elsevier Publishing, New York (1958).

10) Moore, W. J., Basic Physical Chemistry , Prentice-Hall, Inc., New Jersey (1983).

11) White, C. M., Schmidt, C. E., Fuel, 66, 1030 (1987).12) Benson, S. W., Thermochemical Kinetics , 2nd ed.,

John Wiley & Sons, New York (1976).13) Reid, R. C., Prausnitz, J. M., Sherwood, T. K., The

Properties of Gases and Liquids , 3rd ed., McGraw-HillBook Co., New York (1977).

14) Le, T. T., Allen, D. T., Fuel, 64, 1754 (1985).15) Allen, D. T., Behmanesh, N., Eatough, D. J., White, C.

M., Fuel, 67, 127 (1988).16) Hartounian, H., Allen, D. T., Fuel, 68, 480 (1989).17) Hoshino, D., Nagahama, K., Hirata, M., Sekiyu Gakkai-

shi, 22, (4), 218 (1979).18) Hoshino, D., Nagahama, K., Hirata, M., Sekiyu Gakkai-shi, 24, (3), 197 (1981).

19) Uchino, H., Yokoyama, S., Satou, M., Sanada, Y., Fuel,64, 842 (1985).

20) Yokoyama, S. , Uchino, H., Tanabe, K., Satou, M.,Sanada, Y., Fuel, 66, 1330 (1987).

21) Satou, M., Nemoto, H., Yokoyama, S., Sanada, Y., Energy& Fuels, 5, 632 (1991).

22) Satou, M., Yokoyama, S., Sanada, Y., Fuel, 68, 1048(1989).

23) Satou, M., Yokoyama, S., Sanada, Y., Fuel, 71, 565 (1992).24) Satou, M., Nemoto, H., Yokoyama, S., Sanada, Y., Energy

& Fuels, 5, 638 (1991).25) Technical Data Book-Petroleum Refining , 2nd ed.,

American Petroleum Institute, Washington D.C. (1970).26) Riazi, M. R., Daubert, T. E., Hydrocarbon Processing, 59,

(3), 115 (1980).27) Van Krevelen, D. W., Coal , Elsevier Publishing, New

York (1961), p. 343.28) Tada, M. ed., Shinko Buturigaku Gaisetu Jokan ,

Gakujutu Tosho Shuppan, Tokyo (1974), p. 254., , ,

(1974) , p. 254.



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473

, , , ,

, 060 13 8

10) ,

,

4)9)

23) , 24)

,

(Fi gs. 1, 2) , 25)

Mn ( / )

,

(Fi gs. 2, 3) , M n

, Mn ,

1 -10, 1

- 3 ( Fi g. 3)

, Eqs. (1)

(3) , Tabl e 1

Tabl e 2 19) , 21)

0. 4

0. 8 (Tabl es 3, 4)

Keywords

Calculation equation, Refractive index, Group contribution method, Hydrocarbon, Coal derived liquid

Sekiyu Gakkaishi, Vol. 35, No. 6, 1992

1992_satou et al._a method of estimating the refractive index of hydrocarbons in coal derived...

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