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Ind. Eng. Chem. Res. 1997, 36, 2500-2504
Prediction of the Hydrogen Content of Petroleum Fractions Adriaan G. Goossens† Ethylene Manufacture Consultant, Bosuillaan 74, 3722 XP Bilthoven, The Netherlands
A simple and new method for the accurate prediction of the hydrogen content of petroleum fractions is presented. The new method is inferred from the concept of the molar additivity of the structural contributions of the carbon types in the average hydrocarbon molecule. It requires only basic physical properties such as the density and refractive index at 20 °C, and the 50 wt % true boiling point. The influence of heteroatoms and olefinic bonds was found to be largely implicit, except for oxygen. By its fundamental basis this new correlation features an unparalleled precision equivalent to that of the most accurate but time-consuming analytical methods. This is demonstrated by an included data set. Introduction
Model Considerations
The hydrogen content of petroleum fractions is, next to the molecular weight, the most important element in the characterization of petroleum fractions. Unfortunately, neither property is easily measurable with sufficient accuracy nor could we find in the literature satisfactory correlations making use of more easily measured analytical data. However, molecular weight must be known with an accuracy of 2% and the hydrogen content must have a relative accuracy of at least 0.5% to be useful for any chemical characterization method of petroleum fractions, starting from standard physical properties. With chemical characterization we mean a hydrocarbon’s lumping scheme that encompasses a judiciously reduced selection of true and defined mixtures of true compounds that meets the relevant physical properties of the petroleum fraction. The need for such chemical characterization methods on the basis of readily available physical data is strongly driven by the introduction of more fundamental (kinetic) models that simulate and optimize the important oil conversion processes in the petrochemical industry like steam cracking or catalytic cracking. The accurate prediction of the molecular weight of petroleum fractions as a function of the 50 wt % true boiling point (TBP) and the density was only recently discussed by Goossens (1996). Any satisfactory correlation for the hydrogen content must at least take into account the accurate average chain length or molecular weight of an oil fraction. Sofar, literature methods such as those of Winn (1957) indicate errors in the hydrogen prediction of 2% or more, usually correlating density or specific gravity and average boiling point (sometimes via the so-called UOP-K characterization factor, being itself a function of the average boiling point and the specific gravity) with the hydrogen content or the hydrogen/carbon ratio of an oil fraction. Dhulesia (1986) reports a hydrogen content correlation for fluidized catalytic cracker (FCC) feedstocks with an average deviation of 1%. We are not aware of any accepted industrial standard method for the accurate computation of the hydrogen content of oil fractions from basic physical properties. Hence we present our correlation without elaborately comparing it to other methods.
Any reasonably accurate prediction model for the hydrogen content of oil fractions must reflect somehow the underlying overall chemical constitution. For more than six decades there have been numerous attempts to arrive at suitable methods for the structural analysis of oil fractions on the basis of physical data. The feasibility to infer the apparent chemical constitution from but a few physical data requires the latter to be measured with high precision, a fact too often overlooked. We refrain here from an extensive discussion of these methods but merely refer to the publications of van Nes and van Westen (1951), Kurtz et al. (1954), and recently Guilyazetdinov (1995). Of particular interest, however, is the rather unknown work of Hrapia (1965). He introduced the socalled E-d-M method, where E stands for elemental analysis (wt % carbon, hydrogen, and heteroatoms), d for density, and M for molecular weight. His method hinges on the assumption that the molecular volume (M/d) is the result of the molar additivity of structural elements (in this case the number of paraffinic, naphthenic, aromatic and junction carbon atoms, heteroatoms, and double bonds for the average molecule), combined with expressions for the hydrogen content and the number of junction carbons (in terms of paraffinic, naphthenic, and aromatic carbons only as the variables to be solved) for the idealized system of only catacondensed six-membered rings, rendering explicit expressions for the paraffinic (CP), naphthenic (CN), and aromatic carbons (CA) of the average molecule. It is noteworthy to point here also to the work of Kurtz (1954), who extensively elucidates the concept of the molecular volume as the result of the additivity of structural contributions (without considering any contributions of heteroatoms). So, the E-d-M concept has basically a fundamental nature and should therefore be widely applicable. In spite of its assumptions on the catacondensed carbons and the hydrogen balance, in our work for a major oil company it was found that excellent agreement existed between the prediction of the aromatic carbon content of any oil fraction, from kerosenes to the heaviest (cracked) fractions and fuels, by the original E-d-M method and the modern analytical measurements by 13C-NMR and UV-absorption methods. In contrast to the E-d-M method, the better known n-d-M method as published (ASTM D3238-79) uses the more easily and accurately measurable refractive index (n) in stead of the cumbersome elemental analysis but
†
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Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2501
unfortunately suffers from serious restrictions in its applicability and marked deviations in predicted aromatic carbons. Importantly now, the implication of the fact that both methods aim to predict the carbon type distribution of the average molecule is that the hydrogen content of an oil fraction must have a high correlation with n, d, and M. We have therefore arrived at the idea to replace the direct hydrogen balance in the original equations of Hrapia by a molar refractivity balance (Mn/d), also inspired by the valuable work of Terres (1958), who demonstrated that n/d versus the reciprocal carbon number is quite specific for a hydrocarbon class. Combined with a suitable (regressed) expression for the molecular weight as a function of the carbon type only, one can then in principle solve the equations for explicit expressions of the carbon type as functions of n, M, and d, rendering the general form
CP,N,A ) c1 + c2Mn/d + c3M/d + c4M with c1,2,3,4 as fitting constants. After combining the above with the hydrogen balance as a function of the carbon type CP,N,A (as formulated by Hrapia (1965)) and dividing by the molecular weight one arrives at the inferred, and consequently also rather fundamental but still simple, form for the weight percent hydrogen of an oil fraction:
H ) c1 + c2n/d + c3/d + c4/M
0.3%. The hydrogen contents of the naphthas have been computed from their gas chromatographic analyses. The data base is provided as Supporting Information. The molecular weights of the oil fractions have been inferred from our molecular weight correlation with a standard deviation of only 2% (Goossens (1996)):
M ) 0.010770(TBP)[1.52869 + 0.06486 ln(TBP/(1078 - TBP))]/d (2) This renders the hydrogen correlation therefore basically and purposely dependent on the 50 wt % boiling point, the density, and the refractive index of olefin feedstocks only. Results and Discussion Using the previously discussed form of our hydrogen correlation (eq 1), we arrived at the following remarkably simple and accurate expression for olefin feedstocks:
H ) 30.346 - 65.341n/d + 82.952/d - 306/M
(3)
This fit on 61 oil fractions features a squared correlation coefficient of 0.999 with a standard deviation of 0.3% relative only in the predicted hydrogen content, which is equivalent to the standard deviation of the best analytical methods. The standard errors of the coefficients were about 3%.
(1) ranges of fit:
Equation 1 can further be expanded with the linear contributions of the weight percentages of heteroatoms and the number of olefinic bonds per kilogram. On the basis of the original equations of Hrapia, one may expect that the hydrogen prediction will not be affected by the presence of heteroatoms or double bonds, except for a small effect of oxygen. It may be noted that we actually transformed in this way the E-d-M method back into a (different) n-d-M method. On the basis of eq 1 we correlated the hydrogen content of distillate oil fractions directly versus a carefully selected data base, with hitherto unparalleled precision and range of applicability. In this way we circumvented the need for an a priori average explicit expression for the junction carbons in real mixtures, as needed in the E-d-M equations. On the other hand this proves indirectly the validity of the E-d-M approach. Data Base Considerations Partly the same data base has been used as for the derivation of our molecular weight correlation. The densities and the refractive indices have been measured with an accuracy of four decimal places. However, in contrast to the molecular weight correlation, the hydrogen correlation, as discussed, holds basically for mixtures rather than for pure compounds. The data base was selected on the quality rather than on the quantity of data. It comprises the full practical range of distillate petroleum fractions for steam cracker feedstocks with the following distribution: 6 naphthas, 4 kerosines, 2 light gas oils, 1 slack wax, 32 heavy and extra heavy gas oils,14 hydrocracked vacuum gas oils, and 2 hydrotreated vacuum gas oils (VGO), totalling 61 oil fractions. All physical properties have been determined with the best possible analytical means: simulated distillation for the 50 wt % TBP, whereas hydrogen content was measured for the majority of data points by the conventional gravimetric combustion method of Pregl & Dumas, featuring a standard deviation of about
M d n TBP S H
) ) ) ) ) )
84-459 0.6775-0.9292 1.3832-1.5141 59-476 °C 0-1.5 wt % (sum of heteroatoms) 12.18-15.64 wt % (H/C ) 1.66-2.21)
No significant statistical effect of sulfur could be found. It is to be observed that this correlation predicts the wt % percent hydrogen for olefin feedstocks without the need to know the content of heteroatoms. The latter should only be known to compute also the carbon content which is then equal to 100 - S - H. Note that an error of 3% in the molecular weight, 0.002 in the density, and 0.0005 in the refractive index each cause an error of 0.3% in the predicted hydrogen content. The refractive index is thus clearly the most critical parameter. It is noteworthy that if one substitutes the properties for the infinite paraffinic chain length in the above hydrogen correlation (n/d ) 1.73, d ) 0.8541, M ) infinite), the computed wt % hydrogen becomes 14.43, being quite close to the theoretical value of 14.37 wt % of the infinite CH2 chain. It should be kept in mind that the equation parameters n, d, and M are cross-correlated. So, for normal paraffins only, one would find a coefficient for 1/M of 171. For mononaphthenes, this coefficient becomes zero whereas it becomes negative with increasing absolute values with the degree of condensation of homologues, of course in conjuction with different coefficients for n/d and 1/d. Still, as for the normal paraffins, eq 3 behaves quite well (see Table 1). When fitting against n/d we investigated also the goodness of fit if n/d was replaced by other known specific refraction functions. However, this rendered no improvement of fit. In order to better verify our assumptions on the influence of heteroatoms and double bonds, we also investigated a data set of 35 FCC feeds of wide origin. As no refractive indices were measured and bearing in
2502 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 Table 1. Hydrogen Content Prediction for Some Pure Compounds, Cracked or Residual Oil Fractions, and Coal Liquidsa compound
d20/4
n20/D
O (wt %)
S (wt %)
TBP (K)
MW
wt % H
H(calcd)
% dev
n-decane (C10H22) n-eicosane (C20H42) C40H82 C120H242 methylcyclohexane C18H36-cyclohexane decaline dimethyldecaline C16H22-tetraline n-butylbenzene C30-alkylbenzene 2-methylnaphthalene n-hexadecane (C16H34) 1-hexadecene (C16H32) naphtha (visbroken) catcracked naphtha catcracked naphtha pyrolysis residueb short residue short residue short residue short residue short residue Gray cut 2 Gray cut 3 Gray cut 4 Gray cut 7 Gray cut 8 Gray cut 10 Gray cut 12 Gray cut 14 Gray cut 16 Gray cut 19
0.7301 0.7887 0.8205 0.8427 0.7737 0.8224 0.8956 0.8764 0.9891 0.8600 0.8558 1.0052 0.7734 0.7810 0.7006 0.7052 0.7408 1.1000 0.9680 0.9570 1.0140 1.0770 1.0570 0.7662 0.7657 0.8086 0.9585 0.9725 0.9942 1.0763 1.0154 1.0943 1.1920
1.4119 1.4426 1.4593 1.4711 1.4231 1.4559 1.4810 1.4736 1.5490 1.4898 1.4773 1.6030 1.4345 1.4409 1.4018 1.4039 1.4254 1.6510 1.5467 1.5382 1.5771 1.6186 1.6028 1.4290 1.4283 1.4546 1.5785 1.5759 1.5818 1.6349 1.5985 1.6461 1.7099
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.41 0.14 0.62 0.86 0.38 0.33 0.24 0.08 5.19 3.15 1.78 1.87 2.29 1.81 1.98
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.03 0.03 0.60 1.66 2.61 3.47 8.25 6.20 0.65 0.61 0.34 6.04 4.63 2.71 3.24 3.51 3.56 4.37
447 617 798 1013 374 601 469 481 598 457 727 514 560 558 367 355 377 648 890 854 898 988 973 372 394 410 493 525 573 650 572 676 794
142 282 563 1685 98 253 138 166 214 134 415 142 226 224 95 88 96 228 712 612 706 1105 1018 93 105 109 137 156 188 238 183 260 382
15.59 14.98 14.68 14.48 14.37 14.37 13.12 13.33 10.35 10.51 13.12 7.09 15.13 14.37 14.54 14.21 13.45 6.33 11.32 11.34 10.54 9.21 9.64 13.33 13.66 12.44 9.35 9.24 8.96 7.68 8.37 7.34 6.32
15.45 14.92 14.69 14.53 14.25 14.33 12.70 13.29 10.45 11.33 13.74 6.51 15.06 14.64 14.80 14.41 13.41 6.34 11.37 11.56 10.34 9.24 9.59 13.60 13.99 12.60 9.13 9.06 8.91 7.62 8.42 7.41 6.20
-0.87 -0.40 0.08 0.40 -0.82 -0.30 -3.23 -0.33 1.05 7.73 4.74 -8.09 -0.51 1.90 1.77 1.41 -0.26 0.27 0.44 1.93 -1.91 0.27 -0.49 2.02 2.41 1.35 -2.39 -1.95 -0.60 -0.70 0.63 0.88 -1.93
a
Note: see discussion in text. b Fraction boiling above 473 K.
mind that generally there is a linear relationship between the refractive index and the density of specific hydrocarbon classes, we fitted the hydrogen content against 1/d and 1/M only and further against the presence of oxygen, nitrogen, sulfur and double bonds. This revealed indeed no significant effects of sulfur, nitrogen, or double bonds. However, some influence of the presence of oxygen could not be neglected. As the refractive index itself would also be affected by the presence of oxygen, we assessed the remaining effect of oxygen in eq 3 to be 0.4O (with O in wt %). So, for more general use, eq 3 should be extended with +0.4O as an additional term:
H ) 30.346 - 65.341n/d + 82.952/d - 306/M + 0.4O (4) Figure 1 depicts the predicted hydrogen content versus observed values, also including some less accurately measured data for short (vacuum) residues from primary crude oil distillation. These short residues stem from five different crude oils. The refractive index of the short residues was estimated (see Appendix 1). These fractions are of particular interest to test our correlation because of their high content of heteroatoms, being mainly sulfur (see Table 1). Table 1 compares the predictions of the proposed hydrogen content correlation to the theoretical values of some selected pure compounds and also to the measured values of some cracked and residual oil fractions and coal liquids. This comparison is purposely made to support the following discussion. The correlation behaves excellently for paraffins and mononaphthenes. For more condensed structures (pure compounds) there seems to be more deviation. Now we have to realize that the theoretical basis of our hydrogen correlation (the E-d-M method) requires an expression for the junction carbons in ring structures. For purely
Figure 1.
six-membered catacondensed structures, such an expression is straightforward. However, in the real world there is an abundance of five-membered ring structures, next to polyphenylic and pericondensed structures, featuring different expressions. There are thermodynamic reasons that certain structures are more favored than others. By fitting our hydrogen correlation against real hydrocarbon mixtures, the true average effect of
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2503
junction carbons is implicitly taken into account. One must therefore indeed expect some deviation for pure condensed compounds which do not reflect the average composition of real mixtures with their inherent compensating effects. Earlier van Nes and van Westen (1951) signaled such compensating effects in the development of the n-d-M method. So, Table 1 should not be construed as an indication that our hydrogen correlation tends to falter for more condensed (aromatic) oil fractions. On the contrary, it is encouraging to observe that even for cracked fractions (the visbroken naphtha contains some 35 wt % olefins and diolefins) the deviations in predicted hydrogen are still relatively small and seem random rather than systematic. As a matter of fact, particularly for the highly polyaromatic steam cracker residue, there is a strong indication that our correlation can be extrapolated far beyond its original range of fit, confirming its fundamental basis. This is also illustrated by the data in Table 1 for the short residues. To further demonstrate the potential of our hydrogen correlation, we also included in Table 1 some reported data form Tables 1 and 2 of Gray et al. (1983) on coal liquids. These fractions are particularly interesting for their high contents of nitrogen and oxygen. As the refractive index of these fractions was not reported, we estimated this through eq 5. This rendered a smooth linear apparent refractive index-density correlation for this class of hydrocarbons. It is noteworthy that Gray did not attempt or succeed in presenting a suitable hydrogen correlation for coal liquids himself, whereas the application of our correlation at least strongly suggests the feasibility of this. The percent deviations for the short residues and coal liquids must be judged against the standard errors of their hydrogen content measurements through microcombustion mass spectrometric methods (about 1%) and the uncertainty of the estimated refractive indices (0.002), allowing no better standard deviation than some 2%. If there are any remaining explicit effects of heteroatoms and olefinic bonds, not accounted for in our hydrogen correlation, they must indeed be rather small. This supports our belief that the new hydrogen correlation may be applied with confidence for any oil fraction. Finally it is worthwhile to refer to the work of Dhulesia (1986), comparing his own hydrogen correlation, being a curve fit between wt % hydrogen and refractive index, specific gravity, molecular weight, sulfur content (only!), and viscosity (as an additional parameter) derived from a data bank of 33 fluidized catalytic cracker feeds, to other known methods. The explicit effect of sulfur in Dhulesia’s correlation is within the total standard deviation. Still, the average absolute deviation as reported by Dhulesia for his correlation, being two to three times better than other methods, is three times more than that observed with our correlation for our data base! Significance The accurate prediction of the hydrogen content of petroleum fractions as a function of easily and commonly determined physical properties is of crucial importance for any structural analysis or chemical characterization of oil fractions. Particularly, the (revised) E-d-M method has become more easily applicable now for the characterization of oil fractions in terms of carbon type. This new method may also be useful to cross-check any measured hydrogen content of oil fractions. The development of the proposed novel correlation proved to be essential in the successful development
of the characterization of distillate feedstocks for olefin plants in conjunction with the fundamental kinetic pyrolysis simulation models which nowadays are routinely being used. A similar use of this highly accurate hydrogen correlation is foreseen in various other oil conversion processes and to improve hydrogen balance computations for refinery models. Conclusion A new method to accurately predict the hydrogen content of petroleum fractions from basic physical properties is presented. The correlation method was inferred from the fairly well proven assumption of the molar additivity of structural contributions of carbon types for the average molecule and accounts implicitly for the effects of olefinic bonds and heteroatoms, except for oxygen. The only information necessary is the density and the refractive index at 20 °C, the 50 wt % TBP as derived from simulated distillation, and the (estimated) content of any oxygen. This information is easily obtainable with adequate precision. In addition, the measurement of the content of heteroatoms allows the accurate computation of the carbon content as well. The observed standard deviation in predicted wt % hydrogen for the full practical range of oil fractions for olefin manufacture is 0.3% only, being equivalent to that of the best analytical methods. The extrapolability of the method to the full range of oil fractions without yielding excessive errors is demonstrated. However, additional good-quality physical data for such fractions that include also the measured refractive index should become available in order to better confirm the ultimate accuracy of this new method or any need for further refinement. The standard deviation is at least doubled if the refractive index, if not available, is estimated from suitable density correlations for specific classes of oil fractions. Compared to published methods, this new correlation features an improved precision of three to ten times. Nomenclature CP,N,A ) average paraffinic, naphthenic, or aromatic carbon number c1,2,3,4 ) fitting constants in eq 1 d ) liquid density at 20/4 °C H ) wt % hydrogen M ) molecular weight (kg/kmol) n ) liquid refractive index at 20 °C (sodium D-line) O ) wt % of oxygen atoms S ) sum of weight percents of sulfur and other heteroatoms s ) slope of the refractive index-density correlation TBP ) 50 wt % true boiling point (simulated distillation)
Appendix 1: Estimation of the Refractive Index Existing data on oil fractions often do not contain measured refractive indices. In that case one would like to estimate this basic property through other simple physical properties. However, considering the required accuracy, no such correlation exists for the full range of oil fractions. This can better be understood if one transforms eq 4 for the explicit assessment of the refractive index:
n ) 1.2695 + (0.4644 + 0.006O - 0.0153H 4.68/M)d (5) So, an a priori estimate of H with a 2% relative accuracy (which is implicitly the case if one tries to correlate with the usual parameters such as boiling
2504 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
temperature, density, and molecular weight) renders an uncertainty of 0.004 already in the refractive index. As a matter of fact, one can successfully correlate the hydrogen content of specific hydrocarbon classes against 1/d and 1/M only (as there is a linear relationship between the refractive index and the density), be it at the expense of a reduced precision of at least three times. However, the error is only doubled if one correlates the refractive index against the density for specific hydrocarbon classes. The following empiric correlations with a standard deviation in the refractive index of 0.001 should then be used:
with:
H ) wt % hydrogen S ) wt % sulfur and other heteroatoms CH ) C/H weight ratio HC ) H/C atom ratio It is important that density and refractive index, if measured under other than the chosen reference conditions at 20 °C, are corrected using the following formulas (van Nes and van Westen (1951)):
naphthas: n ) 1.0280 + 0.53d
(6)
d20 ) dt + 10-4(t - 20)(336/M + 5.35)
straight run or hydrodesulfurized gas oils: n ) 0.9734 + 0.59d
(7)
n20 - nt ) s(d20 - dt)
deeply hydrogenated fractions: n ) 0.9713 + 0.59d
(8)
with:
and more tentatively:
short residues: n ) 0.9345 + (0.63 + 0.006O)d
(9)
t ) measurement temperature in °C s ) slope of the refractive indexdensity correlation ) 0.59 for gas oils
FCC feeds: n ) 0.9365 + (0.63 + 0.006O)d (10)
In case the specific gravity (SG at 60/60 °F ) 15.6/ 15.6 °C) is given:
coal liquids: n ) 0.9448 + (0.63 + 0.006O)d (11)
d20/4 ) SG - (4.4 × 10-4)(336/M + 5.35) - c
steam cracker residue: n ) 0.881 + 0.70d
(12)
It is to be noted that the slope (s) of the refractive index-density correlation increases with the overall aromatic (condensed) nature of an oil fraction. This slope is well established for the gas oil range ()0.59). Relative to this value one can then compute the general slope as
s ) 0.81 + 0.006O - 0.0153H - 4.68/M
(13)
The slopes of eqs 6-12 are in good agreement with eq 13. We emphasize however that the variation of the refractive index for a given density is a measure for the varying aromaticity and thus the hydrogen content of an oil fraction. It is therefore recommended to always measure the refractive index of oil samples on a routine basis. Dark samples may be diluted with a suitable light diluent. According Kurtz (1954), the mixture refractive index is calculated on a molar or volumetric basis. However, to avoid volume dilitation effects, the diluent should be of a similar chemical nature to that of the sample. Even for solid opaque samples such as the ethylene cracker residue, refractive indices can be measured through so-called laser ellipsometry (reflectometry). Appendix 2. Conversions The wt % H can be converted into other common definitions through
H ) (100 - S)HC/(11.916 + HC) CH ) 11.916/HC
with c as the correction for the reference water temperature:
c ) 0.0006 for naphthas c ) 0.0008 for gas oils Supporting Information Available: Data base of full practical range of distillate petroleum fractions (1 page). Ordering information is available on any current masthead page. Literature Cited Dhulesia, H. New Correlations Predict FCC Feed Characterizing Parameters. Oil Gas J. 1986, Jan. 13, 51-54. Goossens, A. G. Prediction of Molecular Weight of Petroleum Fractions. Ind. Eng. Chem. Res. 1996, 35 (3), 985-988. Gray, J. A.; et al. Thermophysical Properties of Coal Liquids. Ind. Eng. Chem. Process Des. Dev. 1983, 22 (3), 410-424. Guilyazetdinov, L. P. Structural Group Composition and Thermodynamic Properties of Petroleum and Coal Tar Fractions. Ind. Eng. Chem. Res. 1995, 34, 1352-1363. Hrapia, H. Structural Group Analysis of Petroleum Tar. Erdoel Kohle, Erdgas, Petrochem. 1965, 18 (8), 629-632. Kurtz, S. S. Physical Properties and Chemical Structure. In The Chemistry of Petroleum Hydrocarbons; Brooks, B. T., et al., Eds.; Reinhold: New York, 1954; Vol. 1, Chapter 11. Terres, E. Brennst.-Chem. 1958, 39 (7/8), 97-128. van Nes, K.; van Westen, H. A. Aspects of the Constitution of Mineral Oils; Elsevier: New York, 1951. Winn, F. W. Physical Properties by Nomogram. Pet. Refin. 1957, 36 (2), 157-159.
Received for review December 5, 1996 Revised manuscript received March 19, 1997 Accepted March 24, 1997X IE960772X
CH ) (100 - S - H)/H HC ) 11.916H/(100 - S - H)
X Abstract published in Advance ACS Abstracts, May 1, 1997.
