A Method of Estimating the Refractive Index of Hydrocarbons in Coal Derived liquids by a Group Contribution Method

Transcription

1 [Regular Paper] A Method of Estimating the Refractive Index of 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 coal derived liquids were separated into sets of chemically homologous fractions called, "compound classes", by high performance liquid chromatography (HPLC). Now, group analyses were performed by gas chromatography/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 are aromatic rings and naphthenic rings. The contributions of each component group to refractive index were determined by regression analysis with reference to the data set of pure hydrocarbons. The values obtained corresponded well, with the increments per component group, to the refractive index of normal paraffin with the same total number of carbons. Thus, the calculated refractive indices of hydrocarbon compound classes in a coal derived liquid showed good agreement with those observed. 1. Introduction Coal derived liquids, which generally consist of alkanes, aromatics, hydroaromatics and their substituted derivatives, are distributed over a wide range of molecular weights. Thus rapid and versatile method of estimating the composition of a given coal derived liquid is desirable, especially for routine analysis. As the refractive index is easy to determine with great precision in a continuous mode, a correlation between refractive index and other properties could become useful for process control of coal liquefaction and upgrading1)-3). For estimating the number of rings and the carbon percentage of an aromatic, naphthenic, or paraffinic structure from measured values of some physical properties, many methods and procedures have been proposed4)-9). The n-d-m method, using density (d), refractive index (n) and molecular weight (M) as input parameters, is one of wellknown methods8),9). Intermolecular forces have direct impact on physical and thermodynamic properties of fuel; these are mainly the van der Waals forces in the case of non-polar molecules, such as hydrocarbons. Susceptible to polarization is considered a useful * To whom correspondence should be addressed. property for understanding this force: as, it can be calculated from liquid density and refractive index by Lorentz-Lorenz equation10),11). As mentioned above, the refractive index is one of the fundamental properties, like density. A technique of estimating the refractive index becomes necessary when experimental data are not readily available: as, (1) when new compounds are involved, (2) when literature data are not at hand or (3) when the actual refractive index does not exist but it is required for establishing a particular correlation. It is well-known that the physical properties of a given heavy hydrocarbon molecule are closely related to its chemical structures12). A method, based on the contribution of each structural unit or group, assigns partial values for the property in question to each component group in the molecule, on the premise that as long as the composition rules are known, the property of the heavy molecule is the sum of all the group contributions. This is one of highly useful methods estimating the physical properties of coal derived liquids13)-16) One advantage is that the only parameter involved is the chemical structure, and another is its intuitive clarity. Few methods of predicting the refractive index of hydrocarbons by group contribution, however, have been proposed17),18)

2 It is currently impossible to identify every single component of the coal derived liquid, which is a very complex mixture. Nonetheless, the authors have proposed a program of analytical methods to reveal more and more of the chemical structures in a coal derived liquid by using high performance liquid chromatography (HPLC) and gas chromatography/mass spectrometry (GC MS), or nuclear magnetic resonance (NMR)19)-21). These analytical results have provided much information about the relationships between chemical structures and boiling points or molar volumes of hydrocarbons in a coal derived liquid, and the basis for a method of prediction of these properties22)-24). This study directs the group contribution method to the subject of the refractive index of hydrocarbons in coal derived liquids. 2. Experimental Two kinds of coals, Akabira coal and Wandoan coal, were used as sample coals. The methods of sample preparation and analyses for structural characteristics of each coal derived liquid were as previously described19),21). In brief, narrow cut distillates of a coal derived liquid were separated into chemically homologous compounds called, "compound classes", by using a HPLC equipped with an amine column, in accordance with the number of aromatic rings. There were six hydrocarbon compound classes: as, alkanes (Fr-P), monoaromatics (Fr-M), naphthalene type diaromatics (Fr-D1), biphenyl type diaromatics (Fr-D2), tri- and tetra-aromatics (Fr-T) and poly-, polar compounds (Fr-PP). GC/MS measurements19), or 13C-and 1H-NMR measurements and elemental analyses21) were carried out to find the average number of toal carbon, aromatic rings and naphthenic rings of each compound class. Refractive indices of the representative compound classes were taken at 293K using Abbe's refractometer (Atago model Type I). The measurements of their densities were made at 293K by glass pycnometer calibrated with distilled water at the same temperature. 3. Results and Discussion The changes of refractive indices with total carbon number in normal alkanes, cyclohexanes, benzenes, tetrahydro-naphthalenes and naphthalenes with a straight alkyl side chain are shown in Fig. 1. The values of these refractive indices are available in referenced literature25). It is clear from this data that the relationship between the refractive index and total carbon number are nonlinear for the respective homologous series. Consequently, this means that the refractive index Fig. 1 Changes in Refractive Index of Pure Hydrocarbon Derivatives with Total Carbon Number Fig. 2 Relationship between M/n and Total Carbon Number in Pure Hydrocarbon Derivatives cannot be calculated using a linear equation with the total carbon number as a parameter. Hoshino et 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 the group contribution method17),18) In Fig. 2 are shown the changes of M/n with total carbon number for the same homologous series as in Fig. 1. Clearly, the relationships between the value of M/n and total carbon number are linear for the homologous series, so far tested. Furthermore, each linear relationship is parallel with each other. It appears possible to derive a composite rule for the prediction of M/n of a given compound from its total carbon number. *1 The physical meaning of the value of M/n is described briefly in the Appendix.

3 468 There are believed to be two methods to use the additive rule for the predicting the physical properties of a given compound. In one, partial values for the property in question are assigned to each structural factor in the molecule. The property is the sum of all the contributions (Method 1). In the other, the difference between the value of a property of a given compound and that of a reference is attributed to the contributions of certain structural features. In hydrocarbons, for example, normal paraffins are selected as reference, and the structural contributions are attributed to aromatic rings, naphthenic rings and so on. The property of a given non-paraffin molecule is the sum of all the non-paraffin structures contributed to that of reference (Method 2). The advantage of Method 2 is the intuitive grasp of the influences of component groups on a given physical property. Generally, prediction methods, empirical methods or group contribution methods, in either case, are obtained by regression analysis. Unfortunately, the higher the accuracy we get, the more complicated they are. Therefore, we have no ready and brief answers to simple questions like, how does a certain physical property change from the addition of one aromatic ring or one naphthenic ring? In Method 1, group contribution means the partial 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 total carbon number are not explained immediately by Method 1. This method is only effective to clarify how the value of M/n changes by the addition of aromatic or naphthenic rings, and to take a wide view of the estimation of M/n, in accordance with the structural distinctions between molecules. In the preceding paper24), the authors applied both Methods 1 and 2 to the prediction of the molar volume of hydrocarbon compound classes, in a coal derived liquid, obtaining good agreement between the calculated and observed molar volumes. In this study, the method of calculation for M/n is developed on the basis of Method 2 because of its simplicity and clearness. The structural distinctions between various hydrocarbons and reference normal paraffins are quite clear as shown in Fig. 3, namely, the differ- carbon number. The group contributions to stant, regardless of total carbon number. They are about -10per aromatic ring and -3per sixmembered napthenic ring. Based on these considerations, the equation for calculating the M/n Fig. 3 Difference in M/n between Non-paraffinic Hydrocarbon and Normal Paraffin with Identical Total Carbon Number of hydrocarbons, is represented as follows. (1) (2) where, (M/n)p is the value of M/n equivalent to normal paraffins with the same total carbon n), and Ni is the number of component groups per molecule. Thus, the value for M/n of a given hydrocarbon is calculated by adding the toal M/n for the reference normal paraffin with the same total carbon number ((M/n)p). The values of (M/n)p are calculated by Eq. (3). ( 3) where Ct is the total carbon number of a given hydrocarbon. This equation was obtained by regression analysis based on the correlation of the values of M/n and total carbon numbers from 4 to 30 in the normal paraffins. The value of the correlation coefficient is The first term of this equation means the partial value of M/n corresponding to two terminal methyl groups and the second term is that of M/n of other methylene groups in the normal paraffin. In Eq. (2), the kinds of component groups which are absent in n- paraf f ins are to be considered, that is, aromatic rings (NAR) and naphthenic rings (NNR). The

4 measurement21) are listed with the average molecular analysis with 364 data points in the library25). The results of the regression analysis are listed in Table 1. The values of and 0.51 were obtained for the correlation coefficient and standard deviation of error, respectively. The average absolute percent of error for M/n was 0.38%. The main purpose of this paper lies in the calculation of refractive index of hydrocarbon mixture in a coal derived liquid as well as of pure hydrocarbons. The refractive indices or M/n of compound classes for coal derived liquids are calculated by four methods, including the present one and that shown in Table 2. The values of Ni obtained by GC MS measurement19) or NMR weight, mid-boiling point and density. The Fig. 4 Comparison between Observed and Calculated M/n of Hydrocarbon Compound Classes of Coal Derived Liquids by Eqs. (1)-(3) Table 2 List of Average Molecular Weight (M), Mid-boiling Point (BP), Density (d), Refractive Index (n), Total Carbon Number (Ct) and Numbers of Aromatic Rings (NAR) and Naphthenic Rings (NNR) for Each Compound Class in Coal Derived Liquids

5 470 values of M/n of hydrocarbon compound classes were calculated by using the obtained values of compared with the observed M/n values. In Fig. 4, there was good agreement between them. In Tables 3 and 4, the accuracies of refractive index calculations by various methods are summarized for pure hydrocarbons, and also for hydrocarbon compound 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.

6 superior to that by the others for pure hydrocarbons. Unfortunately, their method cannot be applied to the calculation of refractive index of compound classes in coal derived liquids because the components of such liquids cannot be separated into the atomic groups defined in Hoshino's method. White et al. advanced the exponential equation for calculating the refractive index of coal derived liquids, using the average molecular weight, mid-boiling point and atomic ratio of hydrogen to carbon as parameters1). Recently, Mazumdar has proposed a much simpler linear equation than that of White et al., and used the molecular weight of a hypothetical unit of a substance per carbon atom, i.e. molecular weight divided by total carbon number, as a parameter2). Mazumdar's method is superior to that of White et al. for aromatic hydrocarbons and compound classes, as shown in Tables 3 and 4. His method, however, is not as accurate as ours, especially for alkanes and cyclohexanes. Riazi's method26) uses the mid-boiling point and specific gravity as parameters, and the calculated refractive indices are in good agreement with those observed, except for the decahydronaphthalenes, naphthalenes and the naphthalene type diaromatic hydrocarbon compound classes. The method introduced in this paper enables the determination, by calculation, of the refractive indices of various types of hydrocarbons, that is, alkanes, aromatics, hydroaromatics and their alkyl derivatives, regardless whether they be pure substances or mixtures, over a wide range of total carbon number from 4 to 30, and within less than 2% of the average absolute percent of error. 4. Conclusion A simple method of calculating the refractive index of hydrocarbons in a coal derived liquid was developed using the group contribution method. The contributions of component groups to M/n, that is, molecular weight (M) divided by refractive index (n), were calculated by regression analysis using the values of pure hydrocarbons found in the library; the calculated contributions corresponded well with the increments per component group to M/n over reference values for normal paraf f ins of the same total carbon number. These values are applicable to the prediction of the refractive index of liquid hydrocarbon mixtures such as coal derived liquids as well as pure hydrocarbons. Appendix the Lorentz-Lorenz equation10) is well-known as a physical value concerned with the refractive index. Van Krevelen used this value for the prediction of refractance of a coal by a contribution method27). The value of M/n was first used for calculation of the refractive index of hydrocarbons by Hoshino et al.17). However, they did not discuss this value in any detail. Then, what is the physical meaning of the unusual value of M/n? In this appendix, we describe the physical meaning of the value of M/n briefly. As a light wave is a type of electromagnetic wave, strictly speaking, it can be described in terms of electromagnetics or quantum physics. Nevertheless, the fact is, a light wave is also a classical transverse wave. Therefore, we will discuss 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, tude, angular frequency of an oscillator and the density of the medium, respectively. If a wave motion propagates at a given velocity, a certain amount of energy passes through the unit cross section perpendicular to the direction of wave propagation per unit time. This energy is called the wave intensity, and is expressed as follows, đ (A-2) ty of wave motion, respectively. Here, there exists the relationship: (A-3) p corresponds to the pressure amplitude in a compressional wave. Then, Eq. (A-2) can be rearranged as: ( A-4) In electromagnetics, electric power is defined as: In this study, the value of M/n was used as a physical quantity instead of the refractive index of a given compound. Molar refraction defined by (A-5)

7 where, P, V and R are the electric power, voltage and resistance, respectively. Comparing Eqs. (A- role of resistance in Eq. (A-5). As Eq. (A-1) is defined per unit volume, it is unit volume. Consequently, a hypothetical resistance of media per unit molar number, that is per molar volume, is defined as follows; where, VM and M are the molar volume and molecular weight, respectively. Then, from the right side of Eq. (A-6) is derived Eq. (A-7) using the refractive index. C is the velocity of light in vacuum. Therefore, the value of M/n used in this study reflects the hypothetical resistance of media per unit molar number 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., "Correlation Between Physical Constants and Chemical Structure", 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-Hill Book 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 Gakkaishi, 22, (4), 218 (1979). 18) Hoshino, D., Nagahama, K., Hirata, M., Sekiyu Gakkaishi, 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 ) Tada, M. ed., "Shinko Buturigaku Gaisetu Jokan", Gakujutu Tosho Shuppan, Tokyo (1974), p. 254.

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