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Evaluation of refractivity intercept as a method for determining fuel composition according to hydrocarbon type
Evaluation of refractivity intercept as a method for determining fuel composition according to hydrocarbon type Seetar
G. Pande and Dennis
R. Hardy*
Geo-Centers, Inc., Fort Washington, MD 20744, USA *Naval Research Laboratory, Code 6187, Washington DC 203755000, (Received I7 April 7991; revised 5 August 7991)
USA
A recently published
refractivity intercept (Ri) method for determining the composition of petroleum distillates was examined for model jet fuels. Based on five model jet fuels of diverse compound class composition, at best, the Ri method predicted the composition of only one of the five fuels within an accuracy of f26%. Limited improvement was obtained on employing Ri coefficients derived from the various model mixtures examined. Poor predictability of the Ri method is likely related to the erroneous assumption that Ri, as defined, is additive for the compositionally defined classes of interest. In addition, the methodology requires a high degree of accuracy in measuring both density and refractive index. (Keywords:
fuel; composition;
refractivity
intercept)
Fuel compositional analysis based on compound class, namely saturates, monocyclic and dicyclic aromatics, is well documented’-5. There is need however, for a simple and accurate method for differentiating the various types of fuel saturates, e.g. the linear, branched and naphthenics. Techniques such as 13C n.m.r. spectrometry1’4’5 and gas chromatography-mass spectrometry3 require either sophisticated expertise, or expensive instrumentation, or both. Nwadinigwe and Okoroji6 have recently reported that the mole fractions of paraffins, naphthenes and aromatics in olefin-free petroleum distillates of narrow boiling range can be quantitatively determined, based on refractivity intercept (Ri) as the only input parameter. Refractivity intercept, which is defined as refractive index minus one-half the density, is not a new concept. It was originally developed in the US by Kurtz and Ward’ in 1936, and since then several methods which employ its use in the compositional analysis of petroleum fractions have been reported’-“. The recently reported method6 employs the usual two parameters, density and refractive index. Predictability of the method was examined using five model jet fuels of diverse compound class composition. Its poor predictability led to an investigation of the additivity concept of Ri on which the method6 was established. Based on literature values for density and refractive index measured at 2O”C, it appears that refractivity intercepts (Ris) for the various compound classes are not additive. These results are consistent with those reported by Gooding et al.12. EXPERIMENTAL Model jet fuels
Five model jet fuels were prepared. Commercially available pure compounds were employed in preparing 001~2361/92/020231&05 Sc 1992 Butterworth-Heinemann
Ltd.
the model fuel mixtures and were used without further purification. The manufacturers’ listed purity of the samples was as follows: paraffins, 99%; naphthenes, 97-98%; aromatics, 95-99% (Table 1). The diverse composition of the model fuel mixtures ranged as follows: paraffins 25-55 wt%; naphthenes 2&60 wt%; monocyclic aromatics 1l-20 wt%; dicyclic aromatics 2-8 wt% (Table 2). Furthermore, the components and their percentages were selected such that the refractive indices of the saturates fraction and that of the saturates plus aromatics fraction would be within the range for jet fuels (Table 2). Measurements
Although refractive index and density measurements were made at 29°C by Nwadinigwe and 0koroji6, our measurements were made at 20°C for comparison with the literature values (Table I ). Density determinations Table 1 Percentage purity, refractive index and density of components employed in preparation of the model jet fuels
Component Decane Undecane Dodecane Tridecane Tetradecane Pentadecane Decalin (40% cis, 60% trans) Pentylcyclohexane Heptylcyclohexane Tetralin t-Butylbenzene l-Me naphthalene “Data
Refractive index ~ Meas. Ref.”
Density
(g ml-‘)
Purity (%)
Meas.
Ref.”
99 99 99 99 99 99 97
1.4121 1.4175 1.4219 1.4257 1.4291 1.4320 1.4738
0.730 0.740 0.748 0.757 0.763 0.770 0.881
98 99 98 99.5 95
1.4443 1.4496 1.5414 1.4924 1.6154
0.7300 0.7402 0.7487 0.7564 0.7628 0.768915 0.8805 (talc.) 0.8037 0.812415 0.9707’ 5 0.8660L6 1.0212’6
1.4119“’ 1.417315 1.4216 1.4256 1.4290 1.4319l“ 1.4741 (talc.) 1.4437 1.4520 1.5413 1.4927 1.615716
taken from Ref. 13 unless otherwise
FUEL,
1992,
0.805 0.816 0.972 0.864 1.022
stated
Vol 71, February
231
Refractivity Table 2
intercept
Composition
method:
S. G. Pande and D. R. Hardy
and specified measurements
of five model jet fuels Model jet fuels
Composition/measurement
MM1
MM2
MM3
MM4
MM5
Composition (wt%) Paraffins Naphthenes
50.2 30.0
40.0 45.0
55.0 20.0
25.0 60.0
55.0 20.0
17.5 2.3
11.3 3.8
17.5 7.5
13.0 2.0
20.0 5.0
Aromatics Monocyclic Dicyclic Refractive index Saturates Range“ (1.4318-1.4441) Saturates +aromatics Range” (1.4483-l .4642) Refractivity interceptb Ri2’ Ca1c.d Meas. Difference Ri3’
Ca1c.d Meas. Difference
’ Based on measurement b Defined as refractive ‘Refractivity intercept d Based on the known e Refractivity intercept
of 17 jet fuels index minus one-half for the fuel saturates mole fractions of the for the fuel saturates
1.4324
1.4375
1.4342
1.4429
1.4342
1.4467
I .4494
1.4539
1.4511
1.4514
1.0446 1.0429 0.0017
1.0435 1.0435 0.0000
1.0438 1.0417 0.0021
1.0422 1.0419 0.0003
1.0427
1.0492 1.0467 0.0025
1.0482 1&I64 0.0018
1.0523 1.0489 0.0034
1.0464 1.0451 0.0013
density only (paraffins and naphthenes) components and their measured plus aromatics
were based on measuring the mass of a 100 ~1 sample at 20°C ambient temperature. Accuracy of the 100 ~1 volume of the syringe was confirmed by measuring the mass of 100 ~1of dodecane, as well as that of pentadecane and determining the volume from their respective densities. The standard deviation of the density measurements generally ranged from f 0.0005 to 0.001. Refractive indices were measured using an Abbe refractometer at 20°C. The standard deviation of these measurements was generally of the order +0.00006. Methodfor deriving Ri values. The derivation of new Ri values using model mixtures is given in the Appendix. The derived Ri values are given in Table 3; for comparison, the literature value&’ ’ are also included. Calculation of mole fractions. By substituting the reported/derived Ri values for the paraffins, naphthenes and aromatics in the equations described by Nwadinigwe and Okoroji’j, the calculated mole fractions of paraffins, naphthenes and aromatics in the model mixtures l-5 were determined (Table 4).
RESULTS AND DISCUSSION Predictability of the Ri method6 was determined based on: the Ri values reported by Riazi and Daubert” for the paraffins, naphthenes and aromatics; these values were employed by Nwadinigwe and 0koroji6 in the formulation of their equations for determining the mole fraction of the compound classes; and the new Ri values derived from the model mixtures employed (Table 3). Note, the literature Ri values” are average values for the paraffins, naphthenes and aromatics in the data set employed; refractive index and density measurements of the hydrocarbons in the data set were made at 20°C.
232
FUEL,
1992,
Vol 71, February
values shown
Table 3
1.0435 0.0008 1.0507 1.0479 0.0028 __-
in Table I
Compound
class Ris: derived
versus literature
Compound
values
class Ris
Source
Paraffins
Naphthenes
Aromatics
Literature6*” Derived” MM 2,3 MM 1,3 MM 4,5
1.046
1.04
1.066
1.0394 1.0374 1.0433
1.0469 1.0515 1.0414
1.0596 1.0590 1.0592
“See Appendix. Note although Ri values are listed to four decimal places their accuracy is significant only to three decimal places
Table 4 summarizes the results obtained. Predictability of the Ri method was evaluated based on the percentage error of the calculated versus the known mole fractions for the paraffins, naphthenes and aromatics. Of the five model mixtures examined, the reported Ri values6*” predicted the compound class mole fractions of only one mixture (MM4) within an accuracy of +26%. Limited improvement was obtained for determinations based on Ris, derived from model mixtures 2 and 3, for fuels that were not employed in their derivations. Poor predictability of the method is likely to be related to two factors: 1. The assumption that Ri is additive: If this assumption were correct, based on the definition of Ri (Ref. 7) a plot of refractive index versus density for paraffins, naphthenes and aromatics should give the same slope of 0.5 for the three compound classes. The hydrocarbons used to investigate the additivity concept are listed in Table 5 together with their reported values13,‘5 for density and refractive index measured at 20°C. They comprised 44 paraffins, 24 naphthenes and 30 aromatics. Except for olefins, these hydrocarbons include many of the same compounds listed in a paper by Kurtz and Headington’, in which the original assumption of Ri being additive on
Refractivity Table 4
Compound
class determination
of model jet fuels using the Ri method:
intercept predictability
method:
S. G. Pande and 0. R. Hardy
of the literature
and derived
Ri values
Mole fraction Model mixture: determination“ MM1 Known Literature6*” Derived (MM 2331 (MM 173) (MM 4,5) MM2 Known Literature6,” Derived (MM 2,3) (MM 193) (MM 475) MM3 Known Literature6.” Derived (MM 233) (MM 133) (MM 4,5) MM4 Known Literature6.” Derived (MM 23) (MM 1,3) (MM 4,5) MM5 Known Literature6,” Derived (MM 2,3) (MM 133) (MM 435)
% Error’
Paraffins
% Errofl
Naphthenes
% Errorb
Aromatics
0.467 0.404
0.236
_
-14
0.297 0.432
+45
0.165
-30
0.399 0.463 0.726
-15 -1 +55
0.379 0.300 0.038
+27 +1 -87
0.222 0.236 0.236
-6
0.373
_
0.447
0.180
_
0.508
+36
0.363
-19
0.129
-28
0.361 0.461 1.016
-3 +24 +173
0.464 0.352 -0.203
+4 -21 - 145
0.176 0.187 0.187
-2 +4 f4
0 0
0.494
_
0.216
_
0.291
_
0.199
-60
0.504
+134
0.296
+2
0.402 0.401 0.204
-19 -19 -59
0.205 0.183 0.379
-5 -15 f76
0.228
_
0.594
0.275
+21
0.593
0.525 0.547 0.366
+131 + 141 f61
0.298 0.266 0.447
0.393 0.416 0.41b
_ 0 -50 -55 -25
f35 +43 +43
0.179
_
0.133
-26
0.177 0.187 0.187
-1 f5 f5
0.495
_
0.222
_
0.283
_
0.350
-29
0.427
f93
0.223
-21
0.376 0.422 0.579
-24 -15 +17
0.323 0.259 0.102
f46 f17 -54
0.301 0.319 0.319
+6 +13 +13
a Based on Ris as specified. Derived Ri values are significant to three decimal b Defines the error in predicting the compound classmole fraction
places and were derived from the model mixtures
slopeof regression
slope
0.60
of
0.65
regression
line -
0.70
0.75
line -
0.730
in parentheses
n
0.521
0.80
0.85
0.90
0.95
1.00
1.05
Density Fieure 1 Investieation of the conceut aromatics (A) are additive
that
a volume per cent basis was made. However, in addition to those listed by Kurtz and Headington*, we included several paraffins within carbon number range C12-CS2, cis- and trans-decalin in the naphthenes set, and tetralins and naphthalenes in the aromatics set. The results, shown in Figure I, give the slopes of
the Ris for paraffins
(x ), naphthenes
(Cl) and
the regression lines for the three compound classes as determined by Lotus 123 software. The slope of the regression line for the paraffins was 0.521 (R’=0.998) and for the naphthenes was 0.467 (R*=0.979). These slopes though not identical are fairly similar and somewhat close to 0.5. However, that of the aromatics,
FUEL, 1992, Vol 71, February
233
Refractivity Table 5
intercept
Literature
method:
S. G. Pande and 0. R. Hardy
values for refractive
index and density
measured
at 20°C”
_~ Hydrocarbon Parajins n-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3_Dimethylbutane n-Heptane 2-Methylhexane 3-Methylhexane 3-Ethylpcntane 2,2-Dimethylpentane 2,3_Dimethylpentane 2,4_Dimethylpentane 3,3-Dimethylpentane n-Octane 2,2-Dimethylhexane 3-Methylheptane 4-Methylheptane 2,4_Dimethylhexane 2,2,3_Trimethylpentane 2,2,4_Trimethylpentane 4-Methyloctane 2,6_Dimethylheptane 2-Methylnonane 4-Prop;lheptaneb 3,6-Dimethyloctane” 2,2,6-Trimethylheptaneb 4-Methyldecane 3,3-Dimethylnonane* 2,2,4,6_Tetramethylheptane* Dodecane 4-Methylundecaneb 5-Propylnonaneb 3,6-Diethyloctaneb 2,6-Dimethyl-3_isopropylheptane* 4,5-Diethyloctaneb 5-Methyldodecane” 2,10-Dimethylundecane* 4-Ethvlundecaneb Tetrahecane 2,7-Dimethyl-4,5-diethyloctaneb 4-Propylundecane* 5-Propyldodecaneb 9-Octyleicosane (C28H58) Dotriacontane (Dicetyl: C32H66) Naphthenes Cyclopentane Cyclohexane Methylcyclohexane l,l-Dimkthylcyclohexane cis-1.2-Dimethvlcvclohexane _ _ trans-1,2-Dimethylcyclohexane n-Propylcyclohexane
Refractive index
Densitv (g ml- i
1.375 1 1.3715 1.3765 1.3688 1.3750 1.3878
1.3749 1.3712
1.3915 1.4061 1.4011 1.4099 1.4150 1.4145 1.4078 1.4177 1.4212 1.4127 1.4216 1.4231 1.4228 1.4316 1.432 1.4279 1.4244 1.4271 1.4270 I .4290 I .4328 1.4309 1.4333 1.4515 1.4550
0.6603 0.6532 0.6645 0.6485 0.6616 0.6837 0.6787 0.6872 0.6982 0.6739 0.695 1 0.6727 0.6936 0.7025 0.6953 0.7058 0.7046 0.7004 0.7161 0.6919 0.7199 0.7089 0.7281 0.7364 0.730 0.7238 0.7422 0.7469 0.7326 0.7487 0.7514 0.7559 0.7675 0.7654 0.7632 0.7576 0.7633 0.7628 0.7628 0.7767 0.7666 0.7746 0.8075 0.8125
I .4065 1.4266 I.423 1 1.4290 1.4360 1.4270 1.4370
0.7457 0.7785 0.7694 0.7809 0.7963 0.7760 0.7936
1.4133 1.4286 1.4243 1.4297 1.4369 1.4274 1.4356
1.3848 1.3885 1.3934 1.3822 1.3919 1.3815 1.3909
1.3974 1.3935 1.3985
1.3979 1.3953
1.4030
’ Data taken from Ref. 13 unless otherwise *Taken from Ref. 15
Regression
) line-
1.3771 1.3687 1.3755 1.3871 1.3845
1.3889 I .3946 1.3820 1.3930 1.3813 I .3922 1.3968 1.3931
1.3986 1.3979 I .3957 1.4039 1.3913 1.4059 1.4002 I .4102 I .4145 1.4112
1.4079 1.4175 1.4200
1.4125 1.4209 1.4223
1.4247 1.4307 1.4296 1.4285 1.4255 I .4285 1.4282 1.4282 1.4355
1.4302 1.4344 1.4515 1.4541
is significantly higher. These results clearly demonstrate that the assumption of the additivity of Ris, particularly for mixtures of saturates and aromatics, is erroneous. These results are also consistent with those reported by Gooding et al.“. Furthermore, the erroneous assumption that Ri is additive may be related to the hydrocarbon data set employed. 2. The high degree of accuracy required in the refractive index and density measurements. The small difference between the reported 6*11 Ris for the paraffins and the naphthenes being 0.006 (Table 3) attests to this, for this numerical difference is part of the computation6 in determining the molar fractions of the compound classes. Thus, for density measurements, an accuracy of at least
FUEL,
1992,
iso-Propylcyclohexane 1,2-Methylethylcyclohexaneb 1,2,4-Trimethylcyclohexane n-Butylcyclohexane 1,2-Methyl-n-propylcyclohexane’ c&1,2,4,5Tetramethylcyclohexaneb trans-1,2,4,5Tetramethylcyclohexaneb 1,2-Methyl-n-propylcyclohexaneb 1,4-Methyl-n-propylcyclohexaneb iso-Amylcyclohexane tert-Amylcyclohexane* 1,2,3,5,6-Pentamethylcyclohexaneb I ,2-Methyl-n-butylcyclohexaneb 1,4-Methyl-n-butylcyclohexane* cis-Decalin trans-Decalin Cyclopentylcyclopentane* Aromatics Ethylbenzene o-Xylene m-Xylene p-Xylene 1.3-Methylethylbenzene 1,4_Methylethylbenzene 1,3,5_Trimethylbcnzene (mesitylene) 1,2,4_Trimethylbenzene (pseudocumene) 1,2,3_Trimethylbenzene Propylbenzene iso-Propylbenzene (cumene) Butylbenzene 1,2-Methylisopropylbnzene (o-Cymene) I ,2,3,4_Tetramethylbenzene 1,2,4_Triethylbenzene l-Methylnaphthalene I-Butylnaphthalene* 2-tert-Butylnaphthalene* 1,4_Diethylnaphthalene*
1,7_Dimethylnaphthalene iso-Amylbenzene* 2-Methyl-6-p-tolylheptaneb fl-Isopropylnaphthalene 1,2,3,4_Tetraethylbenzene 2-Ethyltoluene Tetralin Butyl tetralin* Propyl tetralinb I ,I-Dimethyl tetralin l-Ethyl tetralin
Refractive index
Density (g ml-‘)
Regression line
1.4410 1.4400 1.4266 1.4408 1.4442
0.8023 0.805 0.7720 0.7992 0.810 0.8122
1.4397 1.4409 I.4255 1.4382‘_ 1.4433 1.4443
1.4423
0.8100
1.4433
1.4445 1.4393 1.4420 1.4510 1.4500 1.4467 1.4441 1.4810 1.4695 I .4638
0.810 0.798 0.8023 0.821 0.8200 0.813 0.807 0.8965 0.8699 0.8612
I .4433
1.4959 1.5055 1.4972 1.4958 1.4966 1.4959 1.4994
0.8670 0.8802 0.8642 0.8611 0.8645 0.8614 0.8652
1.4948 1.5044 1.4927 1.4904 1.4929 1.4907
1.5048
0.8758
1.5012
1.5139
1.5006
0.8944 0.8620 0.8618 0.8601 0.8766
1.5148 1.491’ 1.49;; 1.4897 I .5018
1.5203 1.5024 1.6170 1.5790 1.5768 I.603 1.6083 1.4835 1.4813 1.5848 1.5125 1.5046 1.5413 1.5258 1.5308 1.5292 1.5318
0.9052 0.8738 1.0202 0.9659 0.9687 0.993 1.0115 0.8550 0.8488 0.9753 0.8875 0.8807 0.9702 0.9312 0.9395 0.950 0.9285
1.5227 1.4997 1.6066 1.5670 1.5690 1.586n 1.6od; 1.4860 1.4815 1.5739 1.5097 1.5048 1.5701 1.5416 1.5477 1.5554 1.5397
1.4445
1.4920 1.4915
1.4898
1.4377 1.4397 1.4484 1.4479 1.4447 1.4419 1.48?& 1.47;; 1.4672
1.4934
stated
0.730 (R’=0.933),
234
Hydrocarbon
Vol 71, February
four significant figures would be required; and for refractive index measurements, at least five significant figures. Both these factors of the non-additivity of the compound classes and the high accuracy being required in the measurements of refractive index and density may well account for the differences between the calculated and measured Ri2 and Ri3 values for the various model mixtures (Table 2). Furthermore, for the same model mixture, the consistently relatively larger differences between the calculated and measured Ri3 values versus the corresponding Ri2 values also appear to support the non-additivity of the Ris of mixtures containing saturates and aromatics.
Refractivity
CONCIJJSIONS
14
The non-additivity of refractivity intercepts particularly for mixtures of saturates and aromatics is likely to be a significant contributor to the poor predictability of the Ri method for predicting the molar fractions of paraffins, naphthenes and aromatics. Another contributing factor is the high degree of accuracy required in measuring the refractive index and density. These results focus yet again on the need for an accurate method for predicting the composition of fuels according to their paraffinic, naphthenic and aromatic content.
15
REFERENCES Cookson, D. J. and Smith, B. E. Energy & Fuels 1990, 4, 152; and references therein Trussell, F. C., Yonko, T., Beardsley, J. D. ef al. Anal. Chem. 1985, 57, 191 R Glavincevski, B. and Gardner, L. SAE Paper 852079, Society of Automotive Engineers Inc., Warrendale, 1985; and references therein Gillet, S., Rubini, P., Delpuech, J. etal. Fuel 1981,60,221,226 Dickinson, E. M. Fuel 1980, 59, 290 Nwadinigwe, C. A. and Okoroji, K. A. Fuel 1990, 69, 340 Kurtz, S. S. and Ward, A. L. J. Franklin Insr. 1936, 222, 563 Kurtz, S. S. and Headington, C. E. Ind. Eng. Chem., Anal. Edn 1937,9,21 Kurtz, S. S., Mills, 1. W., Martin, C. C. er al. Anal. Chem. 1947, 19, 175 ASTM D 2159-83. ‘Annual Book of ASTM Standards’, Vol. 05.02, American Society for Testing and Materials, Philadelphia, 1988 Riazi, M. R. and Daubert, T. E. Ind. Eng. Chem. Proc. Des. Deu. 1980, 19, 289 Gooding, R. M., Adams, N. G. and Rail, H. T. Ind. Eng. Chem. Anal. Edn 1946, 18,2 Weast, R. C. (Ed.) ‘CRC Handbook of Chemistry and Physics’, 68th Edn, CRC Press Inc., Boca Raton, 1987-1988
16
intercept
method:
S. G. Pande
and 0. R. Hardy
Dean, J. A. (Ed.) ‘Lange’s Handbook of Chemistry’, 13th Edn, McGraw Hill Book Co., New York, 1985 DOSS,M. P. ‘Physical Constants of the Principal Hydrocarbons’, 4th Edn, Texas Company, New York City, 1943 Egloff, G. ‘Physical Constants of Hydrocarbons’, Vols III and IV, American Chemical Society Monograph Series, Rheinhold Pub. Co., New York, 1947
APPENDIX Derivation
of new Ri values using model mixtures
The three sets of Ri values for paraffins, naphthenes and aromatics (Table 3) were derived using the model mixtures specified i.e. MM2 and 3; MM1 and 4; and MM4 and 5. The values obtained are based on the concept that Ris for the compositionally defined classes of interest are additive. Thus, for a two-component system, i.e. the saturate fraction, which contains paraffins and naphthenes only: (Ri-p x Mp2) + (Ri-n x Mn2) = Ri2 where Ri-p, Ri-n and Ri2 are the Ris for the paraffins, naphthenes and their mixture, respectively; and Mp2 and Mn2 are the mole fractions of the paraffins and naphthenes, respectively. By solving for Ri-p and Ri-n using the saturate fractions of two model mixtures and for which Mp2, and Mn2 are known and Ri2 is determined, Ri-p and Ri-n can be obtained. The Ri for the aromatics (Ri-a) is then subsequently calculated from either of the two model mixtures initially employed, using the following equation: (Ri-p x Mp3) + (Ri-n x Mn3)+ (Ri-a x Ma3) = Ri3 where Mp3, Mn3 and Ma3 are the mole fractions of the paraffins, naphthenes and aromatics, respectively; and Ri3 is the Ri of the model mixture.
FUEL, 1992, Vol 71, February
235
G. Pande and Dennis
R. Hardy*
Geo-Centers, Inc., Fort Washington, MD 20744, USA *Naval Research Laboratory, Code 6187, Washington DC 203755000, (Received I7 April 7991; revised 5 August 7991)
USA
A recently published
refractivity intercept (Ri) method for determining the composition of petroleum distillates was examined for model jet fuels. Based on five model jet fuels of diverse compound class composition, at best, the Ri method predicted the composition of only one of the five fuels within an accuracy of f26%. Limited improvement was obtained on employing Ri coefficients derived from the various model mixtures examined. Poor predictability of the Ri method is likely related to the erroneous assumption that Ri, as defined, is additive for the compositionally defined classes of interest. In addition, the methodology requires a high degree of accuracy in measuring both density and refractive index. (Keywords:
fuel; composition;
refractivity
intercept)
Fuel compositional analysis based on compound class, namely saturates, monocyclic and dicyclic aromatics, is well documented’-5. There is need however, for a simple and accurate method for differentiating the various types of fuel saturates, e.g. the linear, branched and naphthenics. Techniques such as 13C n.m.r. spectrometry1’4’5 and gas chromatography-mass spectrometry3 require either sophisticated expertise, or expensive instrumentation, or both. Nwadinigwe and Okoroji6 have recently reported that the mole fractions of paraffins, naphthenes and aromatics in olefin-free petroleum distillates of narrow boiling range can be quantitatively determined, based on refractivity intercept (Ri) as the only input parameter. Refractivity intercept, which is defined as refractive index minus one-half the density, is not a new concept. It was originally developed in the US by Kurtz and Ward’ in 1936, and since then several methods which employ its use in the compositional analysis of petroleum fractions have been reported’-“. The recently reported method6 employs the usual two parameters, density and refractive index. Predictability of the method was examined using five model jet fuels of diverse compound class composition. Its poor predictability led to an investigation of the additivity concept of Ri on which the method6 was established. Based on literature values for density and refractive index measured at 2O”C, it appears that refractivity intercepts (Ris) for the various compound classes are not additive. These results are consistent with those reported by Gooding et al.12. EXPERIMENTAL Model jet fuels
Five model jet fuels were prepared. Commercially available pure compounds were employed in preparing 001~2361/92/020231&05 Sc 1992 Butterworth-Heinemann
Ltd.
the model fuel mixtures and were used without further purification. The manufacturers’ listed purity of the samples was as follows: paraffins, 99%; naphthenes, 97-98%; aromatics, 95-99% (Table 1). The diverse composition of the model fuel mixtures ranged as follows: paraffins 25-55 wt%; naphthenes 2&60 wt%; monocyclic aromatics 1l-20 wt%; dicyclic aromatics 2-8 wt% (Table 2). Furthermore, the components and their percentages were selected such that the refractive indices of the saturates fraction and that of the saturates plus aromatics fraction would be within the range for jet fuels (Table 2). Measurements
Although refractive index and density measurements were made at 29°C by Nwadinigwe and 0koroji6, our measurements were made at 20°C for comparison with the literature values (Table I ). Density determinations Table 1 Percentage purity, refractive index and density of components employed in preparation of the model jet fuels
Component Decane Undecane Dodecane Tridecane Tetradecane Pentadecane Decalin (40% cis, 60% trans) Pentylcyclohexane Heptylcyclohexane Tetralin t-Butylbenzene l-Me naphthalene “Data
Refractive index ~ Meas. Ref.”
Density
(g ml-‘)
Purity (%)
Meas.
Ref.”
99 99 99 99 99 99 97
1.4121 1.4175 1.4219 1.4257 1.4291 1.4320 1.4738
0.730 0.740 0.748 0.757 0.763 0.770 0.881
98 99 98 99.5 95
1.4443 1.4496 1.5414 1.4924 1.6154
0.7300 0.7402 0.7487 0.7564 0.7628 0.768915 0.8805 (talc.) 0.8037 0.812415 0.9707’ 5 0.8660L6 1.0212’6
1.4119“’ 1.417315 1.4216 1.4256 1.4290 1.4319l“ 1.4741 (talc.) 1.4437 1.4520 1.5413 1.4927 1.615716
taken from Ref. 13 unless otherwise
FUEL,
1992,
0.805 0.816 0.972 0.864 1.022
stated
Vol 71, February
231
Refractivity Table 2
intercept
Composition
method:
S. G. Pande and D. R. Hardy
and specified measurements
of five model jet fuels Model jet fuels
Composition/measurement
MM1
MM2
MM3
MM4
MM5
Composition (wt%) Paraffins Naphthenes
50.2 30.0
40.0 45.0
55.0 20.0
25.0 60.0
55.0 20.0
17.5 2.3
11.3 3.8
17.5 7.5
13.0 2.0
20.0 5.0
Aromatics Monocyclic Dicyclic Refractive index Saturates Range“ (1.4318-1.4441) Saturates +aromatics Range” (1.4483-l .4642) Refractivity interceptb Ri2’ Ca1c.d Meas. Difference Ri3’
Ca1c.d Meas. Difference
’ Based on measurement b Defined as refractive ‘Refractivity intercept d Based on the known e Refractivity intercept
of 17 jet fuels index minus one-half for the fuel saturates mole fractions of the for the fuel saturates
1.4324
1.4375
1.4342
1.4429
1.4342
1.4467
I .4494
1.4539
1.4511
1.4514
1.0446 1.0429 0.0017
1.0435 1.0435 0.0000
1.0438 1.0417 0.0021
1.0422 1.0419 0.0003
1.0427
1.0492 1.0467 0.0025
1.0482 1&I64 0.0018
1.0523 1.0489 0.0034
1.0464 1.0451 0.0013
density only (paraffins and naphthenes) components and their measured plus aromatics
were based on measuring the mass of a 100 ~1 sample at 20°C ambient temperature. Accuracy of the 100 ~1 volume of the syringe was confirmed by measuring the mass of 100 ~1of dodecane, as well as that of pentadecane and determining the volume from their respective densities. The standard deviation of the density measurements generally ranged from f 0.0005 to 0.001. Refractive indices were measured using an Abbe refractometer at 20°C. The standard deviation of these measurements was generally of the order +0.00006. Methodfor deriving Ri values. The derivation of new Ri values using model mixtures is given in the Appendix. The derived Ri values are given in Table 3; for comparison, the literature value&’ ’ are also included. Calculation of mole fractions. By substituting the reported/derived Ri values for the paraffins, naphthenes and aromatics in the equations described by Nwadinigwe and Okoroji’j, the calculated mole fractions of paraffins, naphthenes and aromatics in the model mixtures l-5 were determined (Table 4).
RESULTS AND DISCUSSION Predictability of the Ri method6 was determined based on: the Ri values reported by Riazi and Daubert” for the paraffins, naphthenes and aromatics; these values were employed by Nwadinigwe and 0koroji6 in the formulation of their equations for determining the mole fraction of the compound classes; and the new Ri values derived from the model mixtures employed (Table 3). Note, the literature Ri values” are average values for the paraffins, naphthenes and aromatics in the data set employed; refractive index and density measurements of the hydrocarbons in the data set were made at 20°C.
232
FUEL,
1992,
Vol 71, February
values shown
Table 3
1.0435 0.0008 1.0507 1.0479 0.0028 __-
in Table I
Compound
class Ris: derived
versus literature
Compound
values
class Ris
Source
Paraffins
Naphthenes
Aromatics
Literature6*” Derived” MM 2,3 MM 1,3 MM 4,5
1.046
1.04
1.066
1.0394 1.0374 1.0433
1.0469 1.0515 1.0414
1.0596 1.0590 1.0592
“See Appendix. Note although Ri values are listed to four decimal places their accuracy is significant only to three decimal places
Table 4 summarizes the results obtained. Predictability of the Ri method was evaluated based on the percentage error of the calculated versus the known mole fractions for the paraffins, naphthenes and aromatics. Of the five model mixtures examined, the reported Ri values6*” predicted the compound class mole fractions of only one mixture (MM4) within an accuracy of +26%. Limited improvement was obtained for determinations based on Ris, derived from model mixtures 2 and 3, for fuels that were not employed in their derivations. Poor predictability of the method is likely to be related to two factors: 1. The assumption that Ri is additive: If this assumption were correct, based on the definition of Ri (Ref. 7) a plot of refractive index versus density for paraffins, naphthenes and aromatics should give the same slope of 0.5 for the three compound classes. The hydrocarbons used to investigate the additivity concept are listed in Table 5 together with their reported values13,‘5 for density and refractive index measured at 20°C. They comprised 44 paraffins, 24 naphthenes and 30 aromatics. Except for olefins, these hydrocarbons include many of the same compounds listed in a paper by Kurtz and Headington’, in which the original assumption of Ri being additive on
Refractivity Table 4
Compound
class determination
of model jet fuels using the Ri method:
intercept predictability
method:
S. G. Pande and 0. R. Hardy
of the literature
and derived
Ri values
Mole fraction Model mixture: determination“ MM1 Known Literature6*” Derived (MM 2331 (MM 173) (MM 4,5) MM2 Known Literature6,” Derived (MM 2,3) (MM 193) (MM 475) MM3 Known Literature6.” Derived (MM 233) (MM 133) (MM 4,5) MM4 Known Literature6.” Derived (MM 23) (MM 1,3) (MM 4,5) MM5 Known Literature6,” Derived (MM 2,3) (MM 133) (MM 435)
% Error’
Paraffins
% Errofl
Naphthenes
% Errorb
Aromatics
0.467 0.404
0.236
_
-14
0.297 0.432
+45
0.165
-30
0.399 0.463 0.726
-15 -1 +55
0.379 0.300 0.038
+27 +1 -87
0.222 0.236 0.236
-6
0.373
_
0.447
0.180
_
0.508
+36
0.363
-19
0.129
-28
0.361 0.461 1.016
-3 +24 +173
0.464 0.352 -0.203
+4 -21 - 145
0.176 0.187 0.187
-2 +4 f4
0 0
0.494
_
0.216
_
0.291
_
0.199
-60
0.504
+134
0.296
+2
0.402 0.401 0.204
-19 -19 -59
0.205 0.183 0.379
-5 -15 f76
0.228
_
0.594
0.275
+21
0.593
0.525 0.547 0.366
+131 + 141 f61
0.298 0.266 0.447
0.393 0.416 0.41b
_ 0 -50 -55 -25
f35 +43 +43
0.179
_
0.133
-26
0.177 0.187 0.187
-1 f5 f5
0.495
_
0.222
_
0.283
_
0.350
-29
0.427
f93
0.223
-21
0.376 0.422 0.579
-24 -15 +17
0.323 0.259 0.102
f46 f17 -54
0.301 0.319 0.319
+6 +13 +13
a Based on Ris as specified. Derived Ri values are significant to three decimal b Defines the error in predicting the compound classmole fraction
places and were derived from the model mixtures
slopeof regression
slope
0.60
of
0.65
regression
line -
0.70
0.75
line -
0.730
in parentheses
n
0.521
0.80
0.85
0.90
0.95
1.00
1.05
Density Fieure 1 Investieation of the conceut aromatics (A) are additive
that
a volume per cent basis was made. However, in addition to those listed by Kurtz and Headington*, we included several paraffins within carbon number range C12-CS2, cis- and trans-decalin in the naphthenes set, and tetralins and naphthalenes in the aromatics set. The results, shown in Figure I, give the slopes of
the Ris for paraffins
(x ), naphthenes
(Cl) and
the regression lines for the three compound classes as determined by Lotus 123 software. The slope of the regression line for the paraffins was 0.521 (R’=0.998) and for the naphthenes was 0.467 (R*=0.979). These slopes though not identical are fairly similar and somewhat close to 0.5. However, that of the aromatics,
FUEL, 1992, Vol 71, February
233
Refractivity Table 5
intercept
Literature
method:
S. G. Pande and 0. R. Hardy
values for refractive
index and density
measured
at 20°C”
_~ Hydrocarbon Parajins n-Hexane 2-Methylpentane 3-Methylpentane 2,2-Dimethylbutane 2,3_Dimethylbutane n-Heptane 2-Methylhexane 3-Methylhexane 3-Ethylpcntane 2,2-Dimethylpentane 2,3_Dimethylpentane 2,4_Dimethylpentane 3,3-Dimethylpentane n-Octane 2,2-Dimethylhexane 3-Methylheptane 4-Methylheptane 2,4_Dimethylhexane 2,2,3_Trimethylpentane 2,2,4_Trimethylpentane 4-Methyloctane 2,6_Dimethylheptane 2-Methylnonane 4-Prop;lheptaneb 3,6-Dimethyloctane” 2,2,6-Trimethylheptaneb 4-Methyldecane 3,3-Dimethylnonane* 2,2,4,6_Tetramethylheptane* Dodecane 4-Methylundecaneb 5-Propylnonaneb 3,6-Diethyloctaneb 2,6-Dimethyl-3_isopropylheptane* 4,5-Diethyloctaneb 5-Methyldodecane” 2,10-Dimethylundecane* 4-Ethvlundecaneb Tetrahecane 2,7-Dimethyl-4,5-diethyloctaneb 4-Propylundecane* 5-Propyldodecaneb 9-Octyleicosane (C28H58) Dotriacontane (Dicetyl: C32H66) Naphthenes Cyclopentane Cyclohexane Methylcyclohexane l,l-Dimkthylcyclohexane cis-1.2-Dimethvlcvclohexane _ _ trans-1,2-Dimethylcyclohexane n-Propylcyclohexane
Refractive index
Densitv (g ml- i
1.375 1 1.3715 1.3765 1.3688 1.3750 1.3878
1.3749 1.3712
1.3915 1.4061 1.4011 1.4099 1.4150 1.4145 1.4078 1.4177 1.4212 1.4127 1.4216 1.4231 1.4228 1.4316 1.432 1.4279 1.4244 1.4271 1.4270 I .4290 I .4328 1.4309 1.4333 1.4515 1.4550
0.6603 0.6532 0.6645 0.6485 0.6616 0.6837 0.6787 0.6872 0.6982 0.6739 0.695 1 0.6727 0.6936 0.7025 0.6953 0.7058 0.7046 0.7004 0.7161 0.6919 0.7199 0.7089 0.7281 0.7364 0.730 0.7238 0.7422 0.7469 0.7326 0.7487 0.7514 0.7559 0.7675 0.7654 0.7632 0.7576 0.7633 0.7628 0.7628 0.7767 0.7666 0.7746 0.8075 0.8125
I .4065 1.4266 I.423 1 1.4290 1.4360 1.4270 1.4370
0.7457 0.7785 0.7694 0.7809 0.7963 0.7760 0.7936
1.4133 1.4286 1.4243 1.4297 1.4369 1.4274 1.4356
1.3848 1.3885 1.3934 1.3822 1.3919 1.3815 1.3909
1.3974 1.3935 1.3985
1.3979 1.3953
1.4030
’ Data taken from Ref. 13 unless otherwise *Taken from Ref. 15
Regression
) line-
1.3771 1.3687 1.3755 1.3871 1.3845
1.3889 I .3946 1.3820 1.3930 1.3813 I .3922 1.3968 1.3931
1.3986 1.3979 I .3957 1.4039 1.3913 1.4059 1.4002 I .4102 I .4145 1.4112
1.4079 1.4175 1.4200
1.4125 1.4209 1.4223
1.4247 1.4307 1.4296 1.4285 1.4255 I .4285 1.4282 1.4282 1.4355
1.4302 1.4344 1.4515 1.4541
is significantly higher. These results clearly demonstrate that the assumption of the additivity of Ris, particularly for mixtures of saturates and aromatics, is erroneous. These results are also consistent with those reported by Gooding et al.“. Furthermore, the erroneous assumption that Ri is additive may be related to the hydrocarbon data set employed. 2. The high degree of accuracy required in the refractive index and density measurements. The small difference between the reported 6*11 Ris for the paraffins and the naphthenes being 0.006 (Table 3) attests to this, for this numerical difference is part of the computation6 in determining the molar fractions of the compound classes. Thus, for density measurements, an accuracy of at least
FUEL,
1992,
iso-Propylcyclohexane 1,2-Methylethylcyclohexaneb 1,2,4-Trimethylcyclohexane n-Butylcyclohexane 1,2-Methyl-n-propylcyclohexane’ c&1,2,4,5Tetramethylcyclohexaneb trans-1,2,4,5Tetramethylcyclohexaneb 1,2-Methyl-n-propylcyclohexaneb 1,4-Methyl-n-propylcyclohexaneb iso-Amylcyclohexane tert-Amylcyclohexane* 1,2,3,5,6-Pentamethylcyclohexaneb I ,2-Methyl-n-butylcyclohexaneb 1,4-Methyl-n-butylcyclohexane* cis-Decalin trans-Decalin Cyclopentylcyclopentane* Aromatics Ethylbenzene o-Xylene m-Xylene p-Xylene 1.3-Methylethylbenzene 1,4_Methylethylbenzene 1,3,5_Trimethylbcnzene (mesitylene) 1,2,4_Trimethylbenzene (pseudocumene) 1,2,3_Trimethylbenzene Propylbenzene iso-Propylbenzene (cumene) Butylbenzene 1,2-Methylisopropylbnzene (o-Cymene) I ,2,3,4_Tetramethylbenzene 1,2,4_Triethylbenzene l-Methylnaphthalene I-Butylnaphthalene* 2-tert-Butylnaphthalene* 1,4_Diethylnaphthalene*
1,7_Dimethylnaphthalene iso-Amylbenzene* 2-Methyl-6-p-tolylheptaneb fl-Isopropylnaphthalene 1,2,3,4_Tetraethylbenzene 2-Ethyltoluene Tetralin Butyl tetralin* Propyl tetralinb I ,I-Dimethyl tetralin l-Ethyl tetralin
Refractive index
Density (g ml-‘)
Regression line
1.4410 1.4400 1.4266 1.4408 1.4442
0.8023 0.805 0.7720 0.7992 0.810 0.8122
1.4397 1.4409 I.4255 1.4382‘_ 1.4433 1.4443
1.4423
0.8100
1.4433
1.4445 1.4393 1.4420 1.4510 1.4500 1.4467 1.4441 1.4810 1.4695 I .4638
0.810 0.798 0.8023 0.821 0.8200 0.813 0.807 0.8965 0.8699 0.8612
I .4433
1.4959 1.5055 1.4972 1.4958 1.4966 1.4959 1.4994
0.8670 0.8802 0.8642 0.8611 0.8645 0.8614 0.8652
1.4948 1.5044 1.4927 1.4904 1.4929 1.4907
1.5048
0.8758
1.5012
1.5139
1.5006
0.8944 0.8620 0.8618 0.8601 0.8766
1.5148 1.491’ 1.49;; 1.4897 I .5018
1.5203 1.5024 1.6170 1.5790 1.5768 I.603 1.6083 1.4835 1.4813 1.5848 1.5125 1.5046 1.5413 1.5258 1.5308 1.5292 1.5318
0.9052 0.8738 1.0202 0.9659 0.9687 0.993 1.0115 0.8550 0.8488 0.9753 0.8875 0.8807 0.9702 0.9312 0.9395 0.950 0.9285
1.5227 1.4997 1.6066 1.5670 1.5690 1.586n 1.6od; 1.4860 1.4815 1.5739 1.5097 1.5048 1.5701 1.5416 1.5477 1.5554 1.5397
1.4445
1.4920 1.4915
1.4898
1.4377 1.4397 1.4484 1.4479 1.4447 1.4419 1.48?& 1.47;; 1.4672
1.4934
stated
0.730 (R’=0.933),
234
Hydrocarbon
Vol 71, February
four significant figures would be required; and for refractive index measurements, at least five significant figures. Both these factors of the non-additivity of the compound classes and the high accuracy being required in the measurements of refractive index and density may well account for the differences between the calculated and measured Ri2 and Ri3 values for the various model mixtures (Table 2). Furthermore, for the same model mixture, the consistently relatively larger differences between the calculated and measured Ri3 values versus the corresponding Ri2 values also appear to support the non-additivity of the Ris of mixtures containing saturates and aromatics.
Refractivity
CONCIJJSIONS
14
The non-additivity of refractivity intercepts particularly for mixtures of saturates and aromatics is likely to be a significant contributor to the poor predictability of the Ri method for predicting the molar fractions of paraffins, naphthenes and aromatics. Another contributing factor is the high degree of accuracy required in measuring the refractive index and density. These results focus yet again on the need for an accurate method for predicting the composition of fuels according to their paraffinic, naphthenic and aromatic content.
15
REFERENCES Cookson, D. J. and Smith, B. E. Energy & Fuels 1990, 4, 152; and references therein Trussell, F. C., Yonko, T., Beardsley, J. D. ef al. Anal. Chem. 1985, 57, 191 R Glavincevski, B. and Gardner, L. SAE Paper 852079, Society of Automotive Engineers Inc., Warrendale, 1985; and references therein Gillet, S., Rubini, P., Delpuech, J. etal. Fuel 1981,60,221,226 Dickinson, E. M. Fuel 1980, 59, 290 Nwadinigwe, C. A. and Okoroji, K. A. Fuel 1990, 69, 340 Kurtz, S. S. and Ward, A. L. J. Franklin Insr. 1936, 222, 563 Kurtz, S. S. and Headington, C. E. Ind. Eng. Chem., Anal. Edn 1937,9,21 Kurtz, S. S., Mills, 1. W., Martin, C. C. er al. Anal. Chem. 1947, 19, 175 ASTM D 2159-83. ‘Annual Book of ASTM Standards’, Vol. 05.02, American Society for Testing and Materials, Philadelphia, 1988 Riazi, M. R. and Daubert, T. E. Ind. Eng. Chem. Proc. Des. Deu. 1980, 19, 289 Gooding, R. M., Adams, N. G. and Rail, H. T. Ind. Eng. Chem. Anal. Edn 1946, 18,2 Weast, R. C. (Ed.) ‘CRC Handbook of Chemistry and Physics’, 68th Edn, CRC Press Inc., Boca Raton, 1987-1988
16
intercept
method:
S. G. Pande
and 0. R. Hardy
Dean, J. A. (Ed.) ‘Lange’s Handbook of Chemistry’, 13th Edn, McGraw Hill Book Co., New York, 1985 DOSS,M. P. ‘Physical Constants of the Principal Hydrocarbons’, 4th Edn, Texas Company, New York City, 1943 Egloff, G. ‘Physical Constants of Hydrocarbons’, Vols III and IV, American Chemical Society Monograph Series, Rheinhold Pub. Co., New York, 1947
APPENDIX Derivation
of new Ri values using model mixtures
The three sets of Ri values for paraffins, naphthenes and aromatics (Table 3) were derived using the model mixtures specified i.e. MM2 and 3; MM1 and 4; and MM4 and 5. The values obtained are based on the concept that Ris for the compositionally defined classes of interest are additive. Thus, for a two-component system, i.e. the saturate fraction, which contains paraffins and naphthenes only: (Ri-p x Mp2) + (Ri-n x Mn2) = Ri2 where Ri-p, Ri-n and Ri2 are the Ris for the paraffins, naphthenes and their mixture, respectively; and Mp2 and Mn2 are the mole fractions of the paraffins and naphthenes, respectively. By solving for Ri-p and Ri-n using the saturate fractions of two model mixtures and for which Mp2, and Mn2 are known and Ri2 is determined, Ri-p and Ri-n can be obtained. The Ri for the aromatics (Ri-a) is then subsequently calculated from either of the two model mixtures initially employed, using the following equation: (Ri-p x Mp3) + (Ri-n x Mn3)+ (Ri-a x Ma3) = Ri3 where Mp3, Mn3 and Ma3 are the mole fractions of the paraffins, naphthenes and aromatics, respectively; and Ri3 is the Ri of the model mixture.
FUEL, 1992, Vol 71, February
235