I n d . Eng. Chem. Res. 1987,26, 188-193
188
ratio from 1 to 4 generally results in an increase in aromatics production, a decrease in olefinicity of the C2 and C3 fractions, and an increase in isobutane content in the C, fraction at HZSM-5 reactor temperatures in the range of 250-300 "C. However, for HZSM-5 reactor temperatures above 300 "C, cracking reactions become prominent, resulting in a decline in selectivities to aromatics and total C5+ and a shift in the product distribution toward lower hydrocarbons. A higher temperature of the zeolite reactor also results in an increase in olefin selectivity, particularly that of ethylene in the C2 fraction, and a decrease in isobutane in the C, fraction. A comparison with earlier studies using single-stage operation suggests that further improvement in C5+ product selectivity is possible in a dual-reactor system by controlling the individual reactor temperatures within narrow limits. Acknowledgment We express our gratitude to Dr. K. Jothimurugesan for careful review of the preliminary manuscript and several valuable suggestions. The expert technical assistance of T. Olauson is gratefully acknowledged. Funding for this project was provided by DSS Contract ISU-82-00308. Registry No. CO, 630-08-0; Ni, 7440-02-0; Co, 7440-48-4.
Literature Cited Abbot, J.; Wojciechowski, B. W. Can. J . Chem. Eng. 1985,63,462. Anderson, R. B. The Fischer-Tropsch Synthesis; Academic: Orlando, FL., 1984. Anderson, J. R.; Foger, K.; Mole, T.; Rajadhyaksha, R. A.; Sanders, J. V. J . Catal. 1979,58,114. Anderson, J. R.; Mole, T.; Christov, V. J . Catal. 1980,61, 477. Argauer, R. J.; Landolt, G. R. US Patent 3 702 886, 1972. Biloen, P.; Sachtler, W. M. H. Adu. Catal. 1981,30,165. Bruce, L. A,; Hope, G. J.; Methews, J. F. Appl. Catal. 1983,8,349.
Bruce, L. A.; Hope. G. J.; Mathews, J. F. Appl. Catal. 1984,9,351. Bruce, L.; Mathews, J. F. Appl. Catal. 1982,4, 353. Caesar, P. D.; Brennan, J. A.; Garwood, W. E.; Ciric, J. J . Catal. 1979,56,274. Chang, C. D. Catal. Reu.-Sci. Eng. 1983,25,1. Chang, C. D. Catal. Reu.-Sci. Eng. 1984,26,323. Chang, C. D.; Chu, C. T.-W.; Socha, R. F. J . Catal. 1984a,86,289. Chang, C. D.; Kuo, J. C. W.; Lang, W. H.; Jacob, S.M.; Wise, J. J., Silvestri, A. J. Ind. Eng. Chem. Process Des. Deu. 1978,17,255. Chang, C. D.; Lang, W. H.; Silvestri, A. J. J . Catal. 1979,56,268. Chang, C. D.; Miale, J. N.; Socha, R. F. J . Catal. 1984b,90,84. Derouane, E. G.; Nagy, J. B.; Dejaifve, P.; van Hooff, J. H. C.; Spekman, B. P.; Vedrine, J. C.; Naccache, C. J . Catal. 1978,53, 40. Diffenbach, R. A.; Schehl, R. R.; Fauth, D. J. Presented at the Proceedings of the International Conference on Coal Science, Center for Conference Management, Pittsburgh, PA, 1983; p 240. Dry, M. E. In Catalysis-Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: Berlin, 1981; Vol. 1, Chapter IV, p 159. Dry, M. E. Hydrocarbon Process. 1982,61(8), 121. Garwood, W. E. ACS Symp. Ser. 1983,218, 383. Haag, W. 0.; Huang, T. J. US Patent 4 279830, 1981. Huang, T. J.; Haag, W. 0. ACS Symp. Ser. 1981,152,307. Kobolakis, I.; Wojciechowski, B. W. Can. J . Chem. Eng. 1985,63, 269. Plank, C. J.; Rosinski, J.; Rubin, M. K. US Patent 4 175 114, 1979. Rautavuoma, A. 0. I.; van der Baan, H. S. Appl. Catal. 1981,1,247. Shamsi, A.; Rao, V. U. S.; Gormley, R. J.; Obermyer, R. T.; Schehl, R. R.; Stencel, J. M. Ind. Eng. Chem. Prod. Res. Deu. 1984,23, 513. Storch, H.; Golumbic, N.; Anderson, R. B. The Fischer-Tropsch and Related Syntheses; Wiley: New York, 1951. Vannice, M. A. Catal. Rev.-Sci. Eng. 1976,14(2), 153. Varma, R. L.; Bakhshi, N. N.; Mathews, J. F.; Ng, S. H. Can. J . Chem. Eng. 1985,63,612. Varma, R. L.; Jothimurugesan, K.; Bakhshi, N. N.; Mathews, J. F.; Ng. S.H. Can. J . Chem. Eng. 1986,64, 141. Received for review January 24, 1986 Accepted August 7, 1986
Prediction of Cetane Number by Group Additivity and Carbon-13 Nuclear Magnetic Resonance Timothy H. DeFries* and Doren Indritz* Exxon Research and Engineering Company, Products Research Division, Linden, New Jersey 07036
Rodney V. Kastrup Exxon Research a n d Engineering Company, Corporate Analytical Science Laboratory, Annandale, New Jersey 08801
Cetane number is a measure of ignition quality, specifically ignition delay, of diesel fuel. I t is an engine measure of a kinetic phenomena. While it is typically inappropriate to use a thermodynamic measure, such as molecular structure, to predict kinetic behavior, molecular structure does correlate with cetane number. In fact, we use a group additivity approach to dissect structures and predict cetane number. For pure compounds a simple group counting scheme is used to predict the cetane numbers of normal and branched paraffins and singly substituted alkylbenzenes. T o extend the counting scheme to hydrocarbon mixtures, carbon-13 nuclear magnetic resonance (13C NMR) is used. 13C NMR is sensitive to the local environment, up to three to four carbon atoms away, of each carbon atom. Intramolecular reactions that are important for ignition kinetics imply that molecular fragments of three or four carbon atoms must be considered. We show that group concentrations derived from 13C NMR spectra are useful in predicting the cetane number of hydrocarbon mixtures. Cetane number is a specification for diesel fuel (ASTM, 1980). For more details on what cetane number is and why there is current interest in it, see the paper by Indritz (1985). This study of the effect of molecular structure on
* Authors
t o whom correspondence should be addressed. 0888-5885/87/2626-0188$01.50/0
cetane number uses carbon-13 nuclear magnetic resonance (13C NMR) as a measure of the structural groups present in pure compounds and in 93 hydrocarbon mixtures. Myers et al. (1975), Drugarin and Andru (1979), and Ohuchi et al. (1982) have correlated NMR data with octane number and cetane number: we demonstrate that this 62 1987 American Chemical Society
Ind. Eng. Chem. Res. Vol. 26, No. 2 , 1987 189 11-
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F i g u r e 2. Density of y-methylene group.
technique, when viewed in terms of group additivity, can predict the cetane numbers of pure compounds and hydrocarbon mixtures. The principle of group additivity has been accepted for many years (Benson, 1976; Benson and Buss, 1958). The principle states that many molecular properties can be considered, as a first approximation, to be made up from additive contributions of the properties of the parts of the molecule. This approximation is valid because the properties that are being predicted depend on interactions that are short range-roughly within one to three atoms away. Group additivity has been successful in predicting many molecular properties, for example, heat of formation, molar heat capacity, entropy, refractive index, ultraviolet and infrared absorption spectra, and magnetic susceptibility (Benson, 1976). Historically group additivity has been used to predict the properties of individual molecules from values assigned to each structural group in the molecule. We extend this concept to mixtures by measuring the structural group concentrations, regardless of which molecules contain the groups, using 13C NMR. The rest of the paper is organized as follows: group additivity is explored graphically for density and then for cetane number; the NMR experiment, used as the method for determining groups in complex mixtures, is described; the NMR-determined groups are first applied to pure compounds and then to hydrocarbon mixtures; and these groups are effective for estimating both density and cetane number.
If density follows group additivity, then the densities of the normal paraffins will be the weighted average of the effective densities of the methylene (pCH1) and the methyl (PCHJ groups:
Density of Pure Compounds Density is a commonly measured physical property, and it will be instructive to explore some group additivity concepts for density before tackling a kinetic property like cetane number. Within a homologous series, that is, where molecular weight is increased only by the insertion of methylene groups, the density is changed according to the density of the methylene group. Figure 1 is a plot of density ( p ) as a function of molecular weight (CRC, 1981) for several homologous series with normal alkyl chains. The density appears to approach an asymptotic value at high molecular weight for all these series. This value is the inherent density of methylene groups because a t infiiite molecular weight all of the liquid would be methylene groups in alkyl chains. To show how the density ( p ) of the methylene group can be determined by using a weighted average, consider the homologous series of normal paraffins. The molecular weight (MW) of any normal paraffin is the sum of the weight of the methylenes ( WCHZ) and the weights of the methyls (WCHJ: MW =
WCH,
+
WCH3
P =
W C H ~ P C+HWCH~PCH~ ~ MW
By combining these two equations and rearranging, we find that the density is a linear function of the reciprocal of the molecular weight:
Only methylene groups are being added to form the homologous series; thus, the weight of methyls (WCH3)is constant. The equation suggests that if density follows group additivity, a plot of density against the reciprocal of molecular weight will be a straight line, and the intercept will be the density of methylene. Figure 2 is such a plot for the homologous series of Figure 1. All the series point to the same intercept at about 0.85. At the high molecular weight end, the lines are straight which affirms the assumption of group additivity for density. The plot also shows that the densities of all of the compounds within a series fall either all above or all below the methylene density (0.85). The rate a t which densities diverge from 0.85 depends on the inherent density of the other functional groups in the molecule. For example, the naphthyl group has a high density (Ws),and the methyl group has a low density (P's). Any deviation from linearity reflects the breakdown of the short-range interaction assumption. Note that there are some deviations from linearity at the low molecular weight end of each line. Thus, for example, the density of a methylene group is affected by its proximity to an aromatic ring. While Figure 2 does not show a comparison of the densities of the normal paraffins with branched paraffins, the degree of branching in a paraffin does not significantly affect the density. As we shall see, this is not the case for cetane number.
Cetane Number of Pure Compounds After exploring group additivity for density, we can apply similar ideas to cetane number. We have collected the measured cetane numbers that have been reported in the literature (Puckett and Caudle, 1948; Olson et al., 1960) for 142 pure compounds. Figure 3 shows a plot of some of these cetane numbers as a function of molecular weight in an analogous fashion to Figure 1. In Figure 3, the numbers in the plot represent the number of saturate carbon atoms in the side chains of these molecules. For example, the 5 on the benzene line represents n-pentylbenzene, while the 5 on the paraffin line represents n-
190 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 100
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pentane. For all series, it is clear that as the molecular weight increases the cetane number increases a t about 8 cetane numbers per methylene group added. At high molecular weight, the cetane number rises more gradually. This behavior is similar to the behavior of the densities of paraffins and olefins as shown in Figure 1. Graphical analysis of the pure compound data shows that cetane number follows group additivity in the same way that density does. Figure 4 is a plot of cetane number against the reciprocal of molecular weight. The lines for each series have an intercept value of 135, the inherent cetane number of the methylene group. Methylene groups which are y or farther away from all groups other than other methylene groups each contribute at the rate of 135 cetane number times their abundance. The low molecular weight end of the alkylbenzene line is curved from benzene to pentylbenzene. The naphthalene series is even more sharply curved. We believe these curvatures are real and demonstrate the cetane number depression caused by the methyl group. The curvature is similar to that seen at low molecular weights for the density in Figure 2, but the magnitude and extent of the curvature are more pronounced. This indicates that the effects of nearby structures on the cetane numbers of a group in the same molecule are larger and longer range than they are for density. If, as for density, each functional group has its own cetane number value, then it should be possible to relate the cetane numbers of pairs of molecules where the structures differ by one functional group. A homologous series can be related, especially if the data set is large. For example, when the lines for the normal paraffins and the alkylbenzenes in Figure 4 are compared, the relationship between the cetane numbers of the members of the two homologous series can be elucidated. If the cetane numbers of the groups are additive, it can be shown algebraicially that lines connecting the points for normal paraffins with N carbon atoms and the points for normal
Figure 5. Cetane number prediction of paraffins (normal and branched).
alkylbenzenes with N carbon atoms in the side chain will all have the same intercept on the plot of cetane number vs. reciprocal of molecular weight. The dashed lines in Figure 4 show that group additivity works between paraffins and alkylbenzenes; all the points have a common intercept of 20. The ability of group additivity to predict cetane number can be further demonstrated by considering the cetane numbers of both normal and branched paraffins. The branchiness of a molecule greatly affects the cetane number, in contrast to the case of density. It is known that branching lowers the cetane number, but to our knowledge this is the first effort to quantify the effect of branchiness. By use of a simple counting scheme, such as the following, the cetane numbers of many pure compounds can be easily estimated. For the paraffins, we chose to count the number of carbon atoms in six different categories. The categories are methyl, methyne, quaternary, methylene y or farther, methylene 0,and methylene a to a carbon atom which is not a methylene. The three methylene categories enable the model to account for proximity effects, the finding that the neighboring groups affect the cetane number contribution of the group under evaluation; however, for simplicity we do not make similar distinctions for methyls, methynes, and quaternaries. The cetane numbers of 34 paraffin compounds were regressed against the fraction of the carbon atoms in each of these categories, subject to the constraint that the y-methylene group has an effective cetane number of 135 as determined by the graphical analysis of the pure compound data. The regression equation is CN = CCN,F, where F, = N , / C N , CN is the measured cetane number of the pure compound, CN, is the effective cetane number of the ith group determined by the regression, F, is the fraction of the molecule’s carbon atoms in the ith category, and N , is the number of carbon atoms in the ith category. In this case, i ranges from 1 to 6. This is the statistical analogue of making a plot of the cetane number against the reciprocal of molecular weight. The results of the regression are shown in Figure 5. The normal paraffin data are shown by the long curved line of points in the upper left corner of the plot. The other points on the plot represent the branched paraffins and demonstrate the large cetane number debit caused by branching. The fitted values (dots) are quite good estimates of the measured (squares) cetane numbers for both normal and branched paraffins. Analysis of the residuals of the fit
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 191 Table I. Cetane Number Group Additivity Values for Normal and Branched Paraffins and Singly Substituted Alkylbenzenes group description cetane no. 10 22 87 135
methyl a-methylene &methylene y-methylene
CH3 CH, a to one or two CH,, CH, or C CH, 0 to one or two CH,, CH, or C CH2 y or farther from one or two, CH,, CH, or C
84 -20 0
methyne quaternary phenyl
CH C C or CH
shows that the error increases with molecular weight. This is an indication that the model does not explain all of the variability in the data. The inadequacy of the model probably results from the elimination of proximity effects for functional groups other than methylenes. The fact that the model does so well indicates that cetane number can be predicted using group additivity. The estimates of the cetane number values of the six paraffin groups are listed in Table I. To extend the group additivity cetane number prediction of pure compounds to alkylbenzenes, the group value of the carbons in the phenyl group must be estimated. The cetane number value of the phenyl carbons can be calculated by using the cetane numbers of an n-alkylbenzene and the group additivity values calculated for branched and normal paraffins. For example, the cetane number of n-tetradecylbenzene has been reported as 72.0. If the cetane number value of each of the carbons in phenyl is P, then according to group additivity and the paraffin group values in Table I, 72.0 = (6P + 1 X 10 + 2 X 22 2 X 87 + 9 X 135)/20
+
The average value of the phenyl carbons to the nearest integer is then P = 0. The estimates of the cetane number group additivity values for the six paraffin groups and the phenyl carbon group, shown in Table I, for the first time allow the estimation of cetane number of any paraffin or singly substituted alkyl benzene, normal or branched. Note that the cetane numbers of cycloparaffins, such as cyclohexane, cannot be predicted with these values. A sample calculation is instructive. Suppose we want to estimate the cetane number of 4-phenyldodecane. We first count the number of carbon atoms in each category. There are six phenyl, two methyl, four a-methylene, two @-methylene, three y-methylene, and one methyne carbon atoms. The corresponding group concentrations can be calculated by dividing by 18 (the number of carbon atoms in the whole molecule): 0.33,0.11,0.22,0.11,0.17, and 0.06. The linear combination of these group concentrations with the cetane number group additivity values in Table I gives the predicted cetane number of 42.8. The measured value for 4-phenyldodecane is 42.0 (Puckett and Caudle, 1948). It is important to note that, with the exception of 135 for the y-methylene group, the group additivity values are not inherent to the structural groups. They are a function of the carbon counting scheme used. Thus, group additivity values should only be used within the counting scheme from which they were derived, to estimate the cetane number of unknowns. An improvement in the group additivity model for cetane number would result from the use of a larger number of carbon group categories and their corresponding cetane number group additivity values. The use of group additivity for cetane number requires that each carbon atom be categorized according to not only its functionality but
also the the functionality of all carbon atoms a and /3 from it. This may not seem like a great distance; however, up to 17 carbon atoms could be involved, and each carbon atom could have perhaps 8 different kinds of functionalities. This means that there are about 1015 different chemical environments for carbon atoms. Since it is clearly impractical to determine the cetane number contributions for all possible carbons, an analytical technique is needed which is quantitative and is sensitive to the chemical environment of the different carbon atoms that are most important to cetane number. NMR Spectral Peak Interpretation Thus, there is evidence, based on pure compound studies, that cetane numbers follow carbon group additivity. To extend this technique to mixtures, the fraction of carbon atoms in each functional group category is needed. To avoid separation and identification of every component of a mixture, 13C NMR spectroscopy can be used to categorize and measure the functional group concentrations. Although, 'H NMR has operational advantages over 13C NMR, 13C NMR was chosen for this study because it provides direct information about the carbon skeletal structure. If a molecular group does not have a hydrogen, for example, a quaternary carbon or a substituted aromatic carbon, the group will not be detected with IH NMR, but it will with 13C NMR. The NMR experiment is an absorption spectroscopy experiment; it measures the energy (resonance frequency) required to cause a transition between nuclear spin states in a magnetic field. The energy difference between these spin states is a function of the strong field of the magnet as well as smaller local fields arising from the chemical envrionment at the observed nucleus. These local fields cause a shift in the I3C NMR resonance frequency; this so-called chemical shift is therefore a measure of the chemical environment surrounding the carbon atom. The absorbances measured in an NMR spectrum are quantitative, that is, peak areas in the spectra are proportional to the relative abundances of the different carbon atom types in the sample. The NMR spectra in this study were obtained on a JEOL FX-9OQ spectrometer at 22.5 MHz. Samples were prepared by making a 50 vol % solution with CDC1, to which 25-30 mg/mL of Cr"' (acac), was added as a relaxation reagent. Gated decoupling was used te suppress any nuclear Overhauser effect. A pulse delay of 1.5 s was used to get quantitative spectra. All of the sharp and broad features of each spectrum were zone integrated. The one set of zones used for the integrations was chosen to correspond to the regions between valleys which were common to all of the spectra. The structural interpretation of major NMR spectral features is in the literature (Levy, 1980; Lindeman and Adams, 1971). With the aid of this information, Figure 6 shows an NMR spectrum of a hydrocarbon mixture with nine major spectral features labeled. This structural identification of the peak locations is the same for pure compounds or complex mixtures. Figure 6 shows that the major peaks that are present in a typical hydrocarbon mixture are those that are also important to cetane number: (1)aromatic carbon bonded to an ethyl or longer chain, (2) aromatic carbon bonded to a methyl, (3) aromatic carbon bonded to a hydrogen, (4) methyl on a long chain, ( 5 ) methylene a to a methyl on a long chain, (6) methylene /3 to a methyl on a long chain, (7) methylene y or farther from anything other than a methylene, (8) methyl carbon on an aromatic ring, and (9) methyl carbon on a naphthenic ring or at a branch point. The aliphatic
192 Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987
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hump (Figure 6) contains immobile saturated carbon atoms, e.g., methylene groups in naphthenic rings. Since these descriptions of the major NMR peaks are more numerous and detailed (they include the impact of surrounding atoms) than the simple counting scheme we used above for the pure compounds, we can expect that the NMR measurement of group concentrations will provide a better estimate of cetane number. The four carbon types (four, five, six, and seven) that are the tracers for long aliphatic chains have the same descriptors as the four carbon groups that were used in the pure compound counting schemed to describe the structures of normal alkyl chains. Thus, 13C NMR (but not IH NMR) has spectral features that provide information to describe long, medium, and short length chain effects on cetane number. Thus, 13C NMR has all of the features that are necessary to predict the cetane numbers of fuels. Liquids are treated as mass weighted mixtures of pure compounds, and each peak in the NMR spectrum can be interpreted in terms of the molecular structure. The NMR chemical shift of a given carbon atom is influenced by its chemical environment, extending to a distance of about three carbon atoms. As discussed earlier, the application of group additivity to the cetane numbers of pure compounds revealed that cetane number group additivity values are influenced by neighboring carbon atoms which extended to about three carbon atoms. In addition, the construction of a generalized kinetic model of oxidation and ignition would require the use of hydrocarbon fragments that include about three or four carbon atoms. This size fragment is necessary so that important reactions, such as various intramolecular reactions (e.g., p-scission (Stein, 1982)),may be included in the model. Since NMR is sensitive to the chemical structure of a fairly large piece of the molecule, NMR picks up the information that is important for intramolecular reactions.
NMR Spectra of Pure Compounds Before the results of NMR experiments are used on complex mixtures of molecules, it is important to see how well NMR can be used to predict the cetane numbers of pure compounds. The NMR technique was tested on the 34 paraffin compounds for which cetane numbers are known (Puckett and Caudle, 1948; Olson et al., 1960). The NMR chemical shifts for each molecule were either obtained from the literature (Lindeman and Adams, 1971) or calculated by using the Hercules program (Cheng and Ellingsen, 1983). The peak areas for each paraffin were categorized ac-
110
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NMR spectra with cetane number of
cording to the regions which are observed in NMR spectra of complex mixtures. The cetane numbers were regressed against the fraction of carbon atoms in each region. This simple correlation had a very good fit. The coefficient for the aliphatic peak at 30 ppm, which represents the methylenes y or farther from any other molecular feature, was 130, which is very close to the value of 135 derived earlier from graphical techniques.
Hydrocarbon Mixtures The examination of the 13C NMR spectra of several hydrocarbon mixtures over a wide range of cetane numbers reveals the changes in relative peak areas, which are a reflection of the different relative abundances of carbon atom groups. We have measured the cetane number of 93 different hydrocarbon mixtures from various sources and determined their 13C NMR spectra. One of the great advantages of NMR is that for different hydrocarbon mixtures, the locations (chemical shift) of the peaks are constant; however, the relative areas reflect changes in the different relative abundances of carbon atom groups. Thus, the same categories as for the pure paraffin regression above were used. Figure 7 shows a comparison of the 13C NMR spectra of five different hydrocarbon mixtures ranging in cetane number from 13 to 57. The spectra have been plotted so that all spectra have the same total areas. As a result, peak height is an approximate measure of the relative carbon atom abundance. The two major features which are apparent are the decrease of aromatic carbons and the increase of saturate carbons with increasing cetane number. Thus, upon first examination, these 13C NMR spectra make a kind of gray scale for the cetane number. A closer look at the spectra shows that all saturate peaks are not increasing and decreasing together. In the 57 cetane number liquid, 4 peaks dominate the saturate region; these are produced by relatively long saturate chains, which are good for cetane number. In the 13 cetane number liquid, while the 4 peaks are still present, they are relatively smaller, and consequently the 3 other saturate peaks are also important. These other peaks are produced by carbon atoms in very short chains at branch points or on aromatic or naphthenic rings-structures which have low cetane number. A method more quantitative than a gray scale is desirable for predicting cetane number. Therefore, the cetane numbers of these 93 streams were regressed against the
Ind. Eng. Chem. Res. Vol. 26, No. 2, 1987 193 eo
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Figure 8. 13C NMR prediction of cetane number.
fraction of total spectral area in each of the 18 regions of the spectrum, subject to the constraint that the sum of all spectral regions for each spectrum must sum to unity. The fit was quite good as is shown in Figure 8. It has an r2 of 0.98. The standard deviation of the fit was 2.0 cetane numbers. ASTM D-613 cites a reproducibility of about 0.8 cetane number (ASTM, 1980). The regression coefficients for the aromatic peaks are negative, which means that the cetane number decreases as the number of these groups increases, as would be expected. The regression coefficient for the peak at 20 ppm (which represents methyl groups that are directly attached to rings or branch points) is also negative. The decrease of the cetane number with increasing abundance of these methyl groups is consistent with the idea of the methyl retardation factor for oxidation reactions, introduced by Hinshelwood in 1948. The regression coefficient of the 30 ppm peak (methylenes y or farther) for the mixtures is 137, very close to the value obtained for the regression of the pure compounds. The choice of the particular integration regions was found to not be critical. That is, as long as the group additivity principle was applied to the spectra using any reasonable integration regions, the cetane number could be fitted fairly well. This implies that some sets of integration regions are better than others. The set used to generate Figure 8 may not be the best set possible. The same sort of regression of the areas under the various peaks can be used to predict mixture physical properties that follow group additivity. A regression for density against 13C NMR chemical shifts for these same
93 hydrocarbon mixtures has an 1.2 of 0.97 with a root mean square error of 0.009. For refractive index, the r2 is 0.98 with a root mean square error of 0.0057. Thus, I3C NMR is a useful tool for elucidating the chemical structures in hydrocarbon mixtures that impact on various physical properties and even a kinetic property. Summary We have shown that the concept of group additivity which has been historically used for predicting thermodynamic properties can be extended to predict a kinetically related property-cetane number. In addition, we used I3C NMR to extend this prediction method from single pure compounds to hydrocarbon mixtures. Thus, we are able to measure the detailed molecular structure in mixtures which affect physical properties and performance properties without having to perform detailed separations of the mixtures. Literature Cited ASTM Annual Book of ASTM Standards; ASTM: Philadelphia, PA, 1980; Part 47, D-613 and D-975. Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976. Benson, S. W.; Buss, J. H. J . Chem. Phys. 1958, 29(3), 546-572. Cheng, H. N.; Ellingsen, S. J. J. Chem. I n f . Comput. Sci. 1983, 23, 197-203. Chemical Rubber Company Handbook; CRC: Cleveland, OH, 1981. Drugarin, C.; Andru, D. An. Uniu. Timisoara, Stiinte Fiz.-Chim. 1979, 17(1), 65-70. Hinshelwood, C. N. J. Chem. SOC.1948, 531-538. Indritz, D. Prep.-Am. Chem. SOC.,Diu. Pet. Chem., 1985, 30(2), 282-286. Levy, G. C.; Lichter, R. L.; Nelson, G. L. Carbon-13Nuclear Magnetic Resonance Spectroscopy; Wiley: New York, 1980. Lindeman, L. P.; Adams, J. Q. Anal. Chem. 1971, 43, 1245-1252. Myers, M. E., Jr.; Stollsteimer, J.; Wims, A. M. Anal. Chem. 1975, 47(13), 2301-2304. Ohuchi, H.; Ohi, A.; Aoyama, H. J . Jpn. Pet. Inst. 1982, 25(4), 205-212. Olson, D. R.; Meckel, N. T.; Quillian, R. D., Jr. SAE Paper 263A, Nov 2-4, 1960. Puckett, A. D.; Caudle, B. H. Information Circular 7474, July 1948; US Bureau of Mines. Stein, S. E., National Bureau of Standards, Gaithersburg, MD, personal communication, 1982.
Receiued for reuieu; November 1, 1985 Accepted August 7 , 1986
