octane number.pdf

GENERAL RESEARCH

Development of a Detailed Gasoline Composition-Based Octane Model

Prasenjeet Ghosh,* Karlton J. Hickey,† and Stephen B. Jaffe‡

Compositional Modeling Group, ExxonMobil Process Research Laboratories, Paulsboro Technical Center,Paulsboro, New Jersey 08066

We present a model that predicts the research and motor octane numbers of a wide variety of gasoline processstreams and their blends including oxygenates based on detailed composition. The octane number is correlatedto a total of 57 hydrocarbon lumps measured by gas chromatography. The model is applicable to any gasolinefuel regardless of the refining process it originates from. It is based on the analysis of 1471 gasoline fuelsfrom different naphtha process streams such as reformates, cat-naphthas, alkylates, isomerates, straight runs,and various hydroprocessed naphthas. Blends of these individual process streams are also considered in thiswork. The model predicts the octane number within a standard error of 1 number for both the research andmotor octane numbers.

1. Introduction

Octane number (ON) is one of the most important propertiesof gasoline streams and is a measure of its antiknock property.It is defined as the volume percentage ofi-octane in a blend ofn-heptane andi-octane, which produces the same knock intensityas the test fuel under standard test conditions in an ASTMinternal combustion engine. ASTM defines two different typesof ONs, the research octane number (RON) and the motor octanenumber (MON), which are evaluated using the ASTM D2699and the ASTM D2700 tests, respectively.1,2 Both methods usethe same standard test engine but differ in the operatingconditions. RON is measured in an engine running at 600 rpmand a fuel/air mixture at a temperature of 60°F, while MON ismeasured with the engine running at 900 rpm and a fuel/airmixture at a temperature of 300°F. The slower engine speedand the lower fuel/air temperature as required in the RON testare representative of the fuel performance for city driving, whilethe faster engine speeds and higher fuel/air temperature representthe fuel performance for highway driving.

Knock results from the premature combustion of the gasolinedue to compression in the engine.3 As the fuel/air mixture iscompressed in the internal combustion engine, certain moleculesin gasoline tend to self-ignite even before they reach the ignitionspark, thereby creating a resistive expansive motion in thecompression stroke of the engine and hence the knock. Depend-ing on the thermal stability of the molecule (which depends onits molecular structure) and the ensuing radicals, certainmolecules tend to combust sooner (and knock more) than others.Consequently, ON is a direct function of the molecularcomposition of the gasoline fuel, and any modeling effort shouldexplicitly acknowledge it.

Numerous studies in the past have attempted to mathemati-cally describe the ON as a function of the gasoline composition.

Lovell et al.4 were an early group to identify that aromaticsand branchedi-paraffins have higher ONs than the correspond-ing paraffins. In the middle 1950s, the American PetroleumInstitute (API) Research Project 455-7 analyzed the pure-component ONs for over 300 different hydrocarbon molecules,and several reliable correlations relating gasoline compositionto ON were developed. The work not only quantified the ONtrends with molecular structure and size, it also studied thenonlinear interactions between different molecular types towardON.7 However, the work was primarily focused on pure-component studies with a limited number of binary or ternarygasoline blends. Commercial gasoline contains many differentmolecules in the C4-C13 range, and the more recent papers inthe literature have therefore focused on predicting the octanenumber of such multicomponent mixtures. Anderson et al.8

developed a useful method for predicting the RON of differentgasolines based on the gas chromatographic (GC) analysis ofthe sample. A total of 31 molecular lumps were considered todescribe the composition of gasoline, and the contribution ofeach lump was added linearly to compute the octane numberof the fuel. Although simple in its structure, the method byAnderson et al.8 is rather restrictive in its use and is known toshow an error of around 2.8 numbers on average for catalyticallycracked naphthas.9 Part of the less than satisfactory predictionsis perhaps the assumption of linearity in octane blending becauseoctane blending is known to exhibit nonlinear interactions (bothsynergistic and antagonistic) among the various constituenthydrocarbon molecular classes (e.g., paraffins, olefins, aromatics,etc.).7 Sasano10 described a procedure similar to that of Andersonet al.8 to predict ON of the gasoline fuel from its compositionmeasured by GC. The ON of the fuel is calculated as the linearvolumetric average of the ON of each molecule in the fuel,which, in turn, is calculated using a linear correlative model.Van Leeuwen et al.11 used nonlinear regression methods,specifically projection pursuit regression and neural networks,to correlate the gasoline composition from GC to ON. However,both these techniques require much fine-tuning and experienceto develop. This is especially true for neural network based

* To whom correspondence should be addressed. E-mail:[email protected].

† E-mail: [email protected].‡ E-mail: [email protected].

337Ind. Eng. Chem. Res.2006,45, 337-345

10.1021/ie050811h CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 11/24/2005

approaches, where the determination of the number of layersin the network, number of nodes in each layer, the kind oftransfer functions for each node, etc., is highly user-dependent.Also, the lack of an underlying phenomenological structure andthe inherent opacity in such models make them less reliable inthe extrapolative mode. More recently, Meusinger and Morosused genetic algorithms and neural networks to quantify thepartial ON of each gasoline component in the mixture basedon the structural elements of the molecule.12,13 Other relevantwork in this area includes the work by Lugo et al.,14 Twu andCoon,15 and Albahri,16 who have all employed different varia-tions of the correlating gasoline composition to its octane.

Although the literature is replete with many relevant papers,most of the work falls into one of the two following catego-ries: first, predicting the ON of individual hydrocarbonmolecules in gasoline by correlating molecular structure descrip-tors such as topological indices, length of the backbone carbonchain, degree of branching, type of carbon atom based onspectroscopy, etc., to the pure-component ON and, second,predicting the ON of the actual gasoline fuel by correlating themolecular composition of the gasoline fuel to its ON. In thiswork, we are interested in accomplishing the second objective.In principle, any model that achieves the second objective shouldalso be able to predict (or reconcile) the ON of the individualhydrocarbon molecule because a pure component is merely thelimiting value of a mixture. However, most of these publishedmixture models do not achieve this. Part of this lack ofreconciliation in the published models originates from theirpurely empirical and statistical nature of the underlying math-ematical structure used to develop the models, making themrather restrictive for extrapolation. Further, most of the publishedmodels have focused on developing correlations that work wellwith individual or a very few naphtha process streams col-lectively like fluidized catalytically cracked (FCC) naphtha,reformates, or some light straight-run (LSR) naphtha streams.The streams were so chosen that the ONs varied in a narrowrange between 80 and 95 numbers. Although this has tradition-ally been the most important range for commercial gasolinefuels, it would be beneficial to have a model that can workwith a much extended range of ONs between 30 and 120numbers. This is especially critical in today’s refinery blendingoperations, where many different blend components (i.e.,naphthas from different processes) with widely different ONsneed to be economically blended. Finally, none of the abovework predict the octane number of gasoline fuels that containoxygenates such as methyltert-butyl ether (MTBE), ethanol(EtOH), or tert-amyl methyl ether (TAME), which are findingincreasing use in commercial gasoline.

We attempt to address some of the questions raised in theprevious paragraph. Specifically, our objectives are 2-fold: first,to develop a predictive model for ON, both RON and MONfor any gasoline fuel, dependent solely on the composition andindependent of the refining process stream and, second, to extendthe range of applicability of the model to a much broader rangeof octanes from 30 to 120 numbers. In developing such a model,we would like to ensure that, in the limiting case of a purecomponent, the model predicts the pure-component octanenumber. Further, we would also like to extend the model tofuels containing different oxygenates. The details of such amodel development are presented in the next section.

2. Development of the Octane Model

Each gasoline fuel, regardless of the process stream (e.g.,reformate, FCC, LSR, etc.), is a complex mixture of many

different hydrocarbon molecules, each contributing to the ONof the gasoline fuel. Let ON denote the measured octane numberfor the gasoline fuel while ONi represents the pure-componentoctane number for each moleculei in the fuel. Because amolecule i may not necessarily always contribute its pure-component octane number to the gasoline fuel, each molecule’scontribution toward the fuel octane number is quantified by itsblend value, denoted byBi

ON. The blend value of a moleculedepends on the overall composition of the fuel it is part of.Figure 1 schematizes the difference between ONi andBi

ON. Bydefinition, ON is a linear volumetric blend of the blendcontributions of all of the different molecules present in thegasoline fuel. Therefore

whereVi is the volume fraction of moleculei in the sample.Experimental studies in our laboratory over many years have

revealed that the blend value of a moleculei varies almostlinearly with the ON of the gasoline fuel it is part of, or blendedinto. These results have been reported previously in refs 17 and18. A typical result highlighting this observation is shown inFigure 2.18 The figure plots the variation of the blend values ofvarious n-paraffins (nC5-nC9) against the ON of the threedifferent refinery naphtha fuels in which they were volume-blended into. For each of the paraffins, the figure shows thatthe blending value ofn-paraffin increases linearly as the ON ofthe refinery naphtha fuel increases. We have observed similarresults over many other such studies. Thus, in general, we maypostulate that the blend value of moleculei may be ap-proximated as a linear function of the gasoline ON. Therefore

Equation 2 is analogous to the equation for any partial molarproperty, where the partial molar property (Bi

ON) depends onthe composition of the gasoline fuel it blends into.Bi

ON isparametrized by two parameters, a slopeai

(1) and an interceptai

(0). Although the variation of the blend value of the individualmolecules with the ON of the gasoline fuel is taken to be linear,this does not imply a linear relationship of the fuel compositionto its ON. Using the definition for ON from eq 1 in eq 2, it iseasy to see that eq 2 captures multicomponent interaction.

Figure 1. Schematic showing the difference between octane numbers ofthe gasoline sample (ON), pure-component octane numbers (ONA and ONB),and the corresponding blend octane numbers (BA

ON andBBON, respectively)

for a typical binary blend. Notice that the blend numbers are obtained byextrapolating the tangent to the octane curve to the pure-component limit.

ON ) ∑i

ViBiON (1)

BiON ) ai

(0) + ai(1)(ON) (2)

338 Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006

Although eq 2 requires two parameters,ai(0) and ai

(1), foreach molecule, it is possible to eliminate one of these parametersusing the special case when the gasoline fuel is a purecomponent. For instance, if the gasoline fuel is pure toluene,then its ON is the same as the pure-component ON for toluene,which is the same as its blend value. Application of thisboundary condition yields

If we defineâi ) 1 - ai(1), eq 2 may be rewritten as

Rearranging eqs 1, 2, and 4, we get

This is the basic octane prediction model, where the summationindex i runs over all of the molecules present in the gasolinefuel. However, a typical gasoline fuel contains an enormousnumber of different molecules, so some molecular lumping isnecessary to build a practical model. Such lumping is reflectedin the second part of eq 5, where we have replaced the summingvariablei with “lumps” to indicate that the sum runs over allof the molecular lumps relevant for the octane model. A lumpdefines the compositional level of abstraction that the modeluses. It could be a single molecule liken-heptane or a group ofsimilar molecules such as C10 aromatics. Note that, in light ofthis lumping, the term pure-component ON for lumpi may notalways necessarily reflect the ON of a single molecule. Formolecular lumps that correspond to single molecules, ONi isthe pure-component ON of that single molecule, but formolecular lumps that correspond to a group of similar molecules,ONi is the average of the pure-component ONs of all of thedifferent molecules in that lump. These lumps are described inmore detail in section 3.

âi’s are the adjustable parameters and represent whether amolecule contributes beneficially or detrimentally to the ON

of the gasoline fuel. A contribution is considered beneficial ifthe blend value of the molecule/lump (Bi

ON) is greater than itspure-component octane number (ONi). Likewise, the contribu-tion is detrimental ifBi

ON < ONi. For the two cases (a)âi < 1and ONi < ON or (b) âi > 1 and ONi > ON, the lump icontributes beneficially to the fuel ON. For the other two cases(a) âi > 1 and ONi < ON or (b) âi < 1 and ONi > ON, itcontributes detrimentally to the fuel ON.âi ) 1 is the specialcase where the lump contributes equally to its pure-componentoctane number.

Equation 5 forms the core of the octane model and is suitablefor predicting octanes of reformates, LSR, and alkylate streams.Although nonlinear in composition, the extent of nonlinearityexpressed in it is insufficient to fully capture the nonlinearinteraction between paraffins and olefins and/or paraffins andnaphthenes, which may be important for cat-naphtha fuels.Published studies in the literature6,7 and independent researchin our laboratories reveal that hydrocarbons belonging to thesame molecular class blend linearly; i.e., paraffins blend linearlywith other paraffins, olefins blend linearly with other olefins,and so on. However, a blend of paraffins and olefins may exhibitsignificant deviation from linearity. Such nonlinear interactionin a binary blend is qualitatively described in Figure 3. Figure3a shows a positive interaction or equivalently a positivedeviation from linearity, Figure 3c shows a negative interaction,and Figure 3b shows no interaction. Paraffins and naphthenesalso exhibit similar deviations from linearity. In contrast, olefinsand naphthenes tend to blend linearly. The blending behaviorof aromatics as a group is somewhat unclear because of thedifferences in the blending behavior of individual aromaticmolecules and also because of the difficulty in measuring thehigh ONs of such blends. Also, note from Figure 3 that, forcertain blends, the ON of the blend may actually be higher orlower than both the individual ON extremes defined by the pure-component numbers. The mathematical structure of eq 5 isincapable of describing this behavior because it will always bebounded between the extremes of pure-component numbers forthe two components of the binary blend, as shown in eq 6.

Figure 2. Variation of blending ON ofn-paraffins in different refinerynaphtha fuels.

ONi ) ai(0) + ai

(1)(ONi) w ai(0) ) (1 - ai

(1))ONi (3)

ai(0) ) âiONi (4)

ON )

∑i

ViâiONi

∑i

Viâi

)

∑lumps

ViâiONi

∑lumps

Viâi

(5)

Figure 3. Typical nonlinear interactions between two species x1 and x2.For instance, x1 could be a paraffin while x2 could be a olefin. Curve aindicates positive interaction, curve b indicates no interaction, and curve cindicates negative interaction.

ON1 e ON ) ( V1â1

V1â1 + V2â2)ON1 + ( V2â2

V1â1 + V2â2)ON2 e

ON2 (6)

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006339

The nonlinear interaction of Figure 3 may be quantitativelydescribed by the following mathematical function for a binaryblend:

wherek12(a) andk12

(b) are interaction parameters. By appropriatelychoosing these interaction parameters, we can describe positive,negative, and no blending interactions. The structure has beenborrowed from the more familiar rate expression for inhibitingand synergistic pyrolysis kinetics which tend to exhibit similarbehavior. For a ternary blend where there are multiple binaryinteractions, i.e., betweenV1 and V2, betweenV1 and V3, andlikewise betweenV2 andV3, eq 7 may be written as

Equation 8 has six interaction parameters:k12(a) andk12

(b) for the1-2 interaction,k13

(a) and k13(b) for the 1-3 interaction, andk23

(a)

andk23(b) for the 2-3 interaction, respectively. It is easy to see

from eqs 7 and 8 that if nonlinear interaction has to be modeledfor every binary interaction in a typical gasoline fuel, it wouldlead to a large number of interaction parameters; e.g., even fora very lumped description of a typical gasoline fuel with 50different molecular lumps, this leads to50C2 ) 1225 binaryinteractions wherenCr ) n!/r!(n - r)!. Consequently, thenonlinear interaction will be modeled only at the P/O/N/A level(i.e., at the level of the total paraffins, total olefins, totalnaphthenes, etc., and not at the individual molecule level).

For the purposes of this paper, we will consider the nonlinearinteraction between paraffins and naphthenes and betweenparaffins and olefins. Thus, a correction similar to eq 8 can nowbe added to eq 1 to model the nonlinear interactions in octaneblending. Thus

whereVN andVO represent thetotal naphthenes and olefins inthe gasoline sample. Mathematically,VN ) ∑i∈naphthenesVi andVO ) ∑i∈olefinsVi. Note that in eq 9, while the first sum runs overP, O, N, and A (i.e., paraffins, olefins, naphthenes, andaromatics) molecules, the second sum runs only over theparaffinic molecules. If the interaction term is denoted by I, eq9 may be more succinctly rewritten as

where

Using eqs 2-4 in eq 9 and rearranging the various terms, weget

This is the complete octane model. Note that whenI ) 0, eq11 reduces identically to eq 5. Also, in the limiting case whenthe gasoline fuel is a pure component (Vi ) 1), eq 11 yieldsON ) ONi, thereby returning the pure-component octanenumber.

3. Defining the Molecular Lumps

Next we need to define the various molecular lumps that willbe used in the octane model. The molecular lumps have beenselected based on the following two criteria:

(a) Analytical Differentiation. We have defined separatelumps where it is possible to analytically measure and dif-ferentiate the lump for most of the process streams. For instance,it is possible to analytically measure the different aromatics bycarbon number for most of the naphtha process streams bydifferent GC techniques; however, it is not always possible todifferentiate between the various aromatic isomers at eachcarbon number with current analytical techniques. Consequently,for the aromatics, our lump definition has been restricted tototal aromatics by carbon number only.

(b) ON Differentiation. When analytical differentiation ispossible across similar molecular lumps, we have definedseparate lumpsonly if their ONs are widely different and theirrelative distributionsdiffer across various process streams. Forexample, we consider separate lumps for mono-, di-, andtrimethyl-i-paraffins at each carbon number as opposed to asingle lump for the totali-paraffins at each carbon number. Suchdelumping is necessary for two reasons: first, the ONs of thebranchedi-paraffins vary widely with the degree of branchingand, second, the relative distribution of branched isomers is verydifferent across different naphtha streams. Figure 4 plots thepure-component ONs of all of thei-octane isomers and showsthat, depending upon the particular isomer ofi-octane, whetherit is a mono-, di-, or trimethyl isomer, its ON could vary between25 and 100 numbers. The relative distribution of these isomersis also different in different naphtha process streams, as shown

y )k12

(a)V2V1

1 + k12(b)V2

(7)

y )k12

(a)V2V1 + k13(a)V3V1 + k23

(a)V2V3

1 + k12(b)V2 + k13

(b)V3 + k23(b)V3

(8)

ON ) ∑PONA

ViBiON + ( kPN

(a)VN + kPO(a)VO

1 + kPN(b)VN + kPO

(b)VO)∑P

VjBjON (9)

ON ) ∑PONA

(1 + Ii)ViBiON (10)

Ii ) [( kPN(a)VN + kPO

(a)VO

1 + kPN(b)VN + kPO

(b)VO) for i ∈ P

0 otherwise]

Figure 4. Pure-component RONs for variousi-octane isomers.

ON )

∑PONA

ViâiONi + IP∑P

ViâiONi

∑PONA

Viâi + IP(∑P

Viâi - ∑P

Vi)

(11)


in Table 1 for alkylates and reformates. Trimethyl-i-octanesdominate C8 i-paraffins in alkylates, whereas monomethyl-i-octanes dominate C8 i-paraffins in reformates. The observationsreported fori-octane are also true for otheri-paraffins. Conse-quently,i-paraffins are modeled as three lumps at each carbonnumber in the model based on their degree of branching. Thesituation is somewhat different for aromatics or olefins. At eachcarbon number, the variation in the RONs for the aromaticisomers is only between 5 and 10 ONs (see Figure 6), which isnot significant enough to introduce noticeable errors in thepredictions across the various process streams, especiallybecause the relative abundance of the individual isomers is smalland their distribution does not change appreciably either acrossthe process streams. The situation is similar fori-olefins, wherethe ON does not change significantly depending on whetherthe particulari-olefin is a mono-, di-, or trimethylolefin. Inaddition, there is great difficulty in analytical speciation of theseindividual isomers for most of the process streams. For streamswhere such detailed information might be available, e.g.,aromatic isomer distribution in reformates, the fact that theisomers are always at equilibrium makes the delumping un-necessary as a single lump with an average ON of the lump(reconciled with the equilibrium isomer distribution) would beadequate.

On the basis of the above two criteria, we have considered atotal of 57 compositional lumps in this work to describe anynaphtha stream. These include 32 lumps forn- andi-paraffins,6 lumps for naphthenes, 7 lumps for aromatics, 9 lumps forolefins and cyclic olefins, and 3 lumps for oxygenates. Thelumps range from individual molecules to a group of similarmolecules at various levels of abstraction. Although the oxygen-ates are ON improvers, they are treated in the model similar toall of the hydrocarbon lumps. These lumps are summarized inTable 2.

Once the lumps have been defined, the next step is to specifytheir pure-component ONs. The pure-component RONs and

MONs for most of the lumps have been chosen from the valuesreported in the API-45 project.5,6 For lumps that correspond toindividual molecules, e.g.,n-butane,n-pentane, etc., the pure-component values are taken as is from ref 6, while for lumpsthat correspond to a group of similar molecules such asmonomethyl-i-octanes, an average value is chosen based on theONs of all of the different monomethyl-i-octane isomers. Twoimportant trends emerge from this dataset: first, ON decreaseswith the carbon number and, second, ON increases with thedegree of branching at the same carbon number. Such trendsare shown for the paraffins and aromatics in Figures 5 and 6,respectively, where the pure-component ONs are plotted againstthe number of carbon atoms in the hydrocarbon molecule. Thesetrends have been used to estimate the pure-component ONs ofthe lumps that are not reported in ref 6. The final set of pure-component RONs and MONs for the various molecular lumpsin the model is shown in Table 2.

4. Experimental Program

An extensive database of 1471 gasoline fuels was collectedfrom many naphtha process streams found in the petroleumrefinery. These include 143 alkylates, 165 cat-naphtha (FCC)gasolines, 440 reformates, 366 hydroprocessed naphtha streams,117 SCANfining [Selective CAtalytic Naphtha Refining, aproprietary ExxonMobil Technology] products, 40 LSR naph-thas, 13 isomerates, and 187 finished blends of these differentprocess streams. Fuels with oxygenates contained TAME,MTBE, and EtOH in the range of 2-10 vol % oxygenates. Eachof these 1471 fuels was analyzed for its detailed compositionusing a multitude of different GC techniques. RON and MONwere also measured on these fuels. Because the compositionwas measured through multiple GC columns, each measuringcertain carbon number ranges of the composition, a thoroughdata-reconciliation procedure was employed to reconcile theanalysis by the different analytical measurements. For example,fuel samples with both the overall PIONA analysis and thespecific GC analysis (which yield detailed information in aparticular carbon number range) were checked to ensure thatthe two analyses were consistent. Likewise, the compositionalinformation based on GC and PIONA was reconciled with theboiling point curve wherever available. Further, many repeats

Table 1. Typical Measured Isomer Distribution (wt %) fori-Octanes

stream type monomethyls dimethyls trimethyls

alkylates 0 18.5 81.5reformates 68.9 31.1 0

Table 2. Various Lumps Considered in the Present Octane Model along with Their Pure-Component RONs and MONs

RON MON RON MON RON MON

Paraffins Paraffins (cont’d.) Aromatics (cont’d.)n-butane 94 89.6 n-undecane -35 -35 C12 aromatics 102 90isobutane 102 97.6 C11 monomethyl 5 5n-pentane 62 62.6 C11 dimethyls 35 35 Olefins/Cyclic Olefinsi-pentane 92 90.3 C11 trimethyls 90 82 n-butenes 98.7 82.1n-hexane 24.8 26 n-dodecane -40 -40 n-pentenes 90 77.2C6 monomethyls 76 73.9 C12 monomethyl 5 5 i-pentenes 103 822,2-dimethylbutane 91.8 93.4 C12 dimethyls 30 30 cyclopentene 93.3 69.72,3-dimethylbutane 105.8 94.3 C12 trimethyls 85 80 n-hexenes 90 80n-heptane 0 0 i-hexenes 100 83C7 monomethyls 52 52 Naphthenes total C6 cyclic olefins 95 80C7 dimethyls 93.76 90 cyclopentane 100 84.9 total C7d 90 782,2,3-trimethylbutane 112.8 101.32 cyclohexane 82.5 77.2 total C8d 90 77n-octane -15 -20 m-cyclopentane 91.3 80C8 monomethyls 25 32.3 C7 naphthenes 82.0 77 OxygenatesC8 dimethyls 69 74.5 C8 naphthenes 55 50 MTBE 115.2 97.2C8 trimethyls 105 98.8 C9 naphthenes 35 30 TAME 115 98n-nonane -20 -20 EtOH 108 92.9C9 monomethyls 15 22.3 AromaticsC9 dimethyls 50 60 benzene 102.7 105C9 trimethyls 100 93 toluene 118 103.5n-decane -30 -30 C8 aromatics 112 105C10 monomethyls 10 10 C9 aromatics 110 101C10 dimethyls 40 40 C10 aromatics 109 98C10 trimethyls 95 87 C11 aromatics 105 94


were run on the RON and MON measurements of each fuel toensure high fidelity in the dataset.

5. Results

5.1. Parameter Estimation: Constrained Least-SquaresFormulation. A constrained least-squares minimization problemwas solved using the Levenberg-Marquadt algorithm in orderto regress the parameters of the model. The adjustable param-etersâ were allowed to vary between a lower bound of 0 and

an upper bound of 10. Although, in principle,â may be<0,the restriction ofâ g 0 was necessary to avoid singularity ineq 11. Softer constraints in the form of inequality constraintswere also employed to ensure thatâ did not vary arbitrarilywith the carbon number within the same molecular class butrather maintained the directional trend with the carbon numberand branching as shown previously in Figures 5 and 6.

The experimental dataset was partitioned into atraining set(90% of the samples) and atestingset (10% of the samples),and many such partitions (total partitions considered) 200)

Figure 5. Variation of pure-component RONs for various paraffins (adapted from ref 5).

Figure 6. Variation of pure-component RONs for various aromatics (adapted from ref 5).


were considered to ensure the robustness of the parameterestimates. Many different initial guesses were assumed and theparameters reoptimized to ensure that the optimization problemwas not trapped in an inferior local solution. Sensitivity analysisin the form of a local perturbation of the parameters was alsoperformed to see whether the parameters returned to the sameoptimal or not.

Although the final set of parameter values (â) for all of theindividual molecular lumps used in this model cannot bedisclosed in the publication for proprietary reasons, the averagevalues of these parameters, grouped by P, I, O, N, and A classes,are reported in Table 3. Also included in the table (last row)are the four interaction parameters used in the model. The resultsbased on these average parameter values are satisfactory, thoughwe may point out that the use of individualâ values for thedifferent molecular lumps enhances model predictions. Theresults presented below are based on the individualâ parameters.

5.2. Prediction Statistics.The results of the model are shownin Figures 7 and 8 for both RON and MON across the 1471gasoline fuels. The plots summarize not only the overallperformance of the model but also the performance across theindividual process streams. The overall standard errors (SEs)

defined asxΣ(meas- pred)2/n for RON and MON are 1.01and 1.05 numbers, respectively, on all of these process streams

and blends. The individual SE and the standard deviation aresummarized in Table 4. The FCC gasoline fuels are predictedwith the highest accuracy (SE) 0.67), while the predictionson the straight-run fuels have the highest error (SE) 1.45)relative to other process streams. The higher relative error isdue to the higher measurement error in the ONs of straight-runnaphtha fuels, which have octanes in the range of 40-70numbers where the octane test itself is less than satisfactory.The process blends, many of which have 2-10 vol % oxygen-ates, are also predicted quantitatively, suggesting that the modelstructure is sufficient to capture the effect of oxygenates on thegasoline fuel. The prediction results on all of the process streams

Figure 7. Model predictions for RONs for various process streams and blends.N ) number of samples. SE) standard error.

Table 3. Parameter Values

molecular class molecular lumps â(RON) â(MON)

n-paraffins nC4-nC12 2.0559 0.3092i-paraffins C4-C12mono-, di-, and trimethyl-i-paraffins 2.0204 0.4278naphthenes C5-C9 naphthenes 1.6870 0.2821aromatics benzene-C12aromatics 3.3984 0.4773olefins/cyclic olefins C4-C12 linear, branched, and cyclic olefins 8.9390 10.0000oxygenates MTBE, EtOH, TAME 3.9743 2.0727interaction parameters kPN

(a), kPN(b), kPO

(a), kPO(b) 0.2, 2.4, 0.4, 3.6 0.2, 2.4, 0.4, 3.6

Table 4. Model Performance across Various Process Streams

RON MON

SE st dev SE st dev

total 1.0194 1.0296 1.0572 1.0263alkylates 0.8822 0.9122 0.6935 0.6505cat-naphthas 0.6732 0.6065 0.5468 0.5846reformates 0.8869 0.9115 0.9132 0.9889hydroprocessed naphtha

products1.2359 1.2352 1.1718 1.1094

SCANfining products 1.2188 1.2278 1.1926 1.1033LSR naphtha 1.4531 1.3800 1.3921 1.2598isomerates 0.7683 0.6734 0.7522 0.2977process blends 0.9095 0.9104 1.3255 1.2048


and their blends are within the measurement error; therefore, itis unlikely that the average error can be further reduced for amodel that spans such a diverse set of naphtha fuels.

An important requirement of any regression model is that itspredictions are unbiased with respect to its inputs. To ensurethis, the frequency distribution of the model errors is plotted inFigure 9. The abscissa in the figure represents the error level inthe model predictions, while the ordinate represents the numberof fuels predicted at these various error levels. Approximately75% of the samples are predicted within(1.0 ON, 93% ()75+ 18) are predicted within(2.0 ON, and 99% of the samplesare predicted within(3.0 ON. The frequency distribution ofFigure 9 closely resembles a normal distribution, suggestingthat the model is independent of any inherent bias. Further, theplot of the prediction error against each of the compositionallumps also revealed no directional trend of the composition withthe model error.

5.3. Independent Model Validation and Prediction Im-provement via Data Reconciliation.To test thepurepredictivecapabilities of the model, an independent dataset comprising

many commercial gasoline fuels from seven different refineriesworldwide was collected. The gasoline fuels collected wereblends of various refinery process streams such as alkylates,reformates, FCC-naphtha, and so on. The individual processstreams are therefore the “blend components” of the finalgasoline blend. On each individual blend component, thecomposition was measured using a combination of GCs alongwith RON and MON. In addition, some bulk properties suchas gravity and the boiling point curve were also measured. Onthe final gasoline blends, only RON and MON were measured.

On the basis of the measured composition of the blendcomponents and using the blend recipe (i.e., the volumetric ratiosof how the components were blended), the composition of thefinal gasoline blend was calculated and RON and MON werepredicted using eq 11. A comparison of the model predictionsagainst the measured RON for these fuels is shown in the firstcolumn of Table 5. The results are segmented based on theperformance in each individual refinery. The table shows that,on average, the model predicts all of the data with a SE of(0.9number, which is within the experimental error of the different

Figure 8. Model predictions for MONs for various process streams and blends.N ) number of samples. SE) standard error.

Figure 9. Error distribution for RON across the various samples.

Table 5. Comparison of Model Predictions with and without DataReconciliation of the Measured Composition

SE (Standard Error)

model predictions(using the measuredcomposition “as is”)

model predictions(using autotunedcompositions)

refinery 1 0.9105 0.8444refinery 2 0.5457 0.4482refinery 3 0.7016 0.7069refinery 4 1.0197 1.0085refinery 5 1.1686 1.1682refinery 6 0.7850 0.7833refinery 7 1.2074 0.8436


measurements, thus providing credence to the robustness andreliability of the model. Similar results are obtained for MONas well.

However, a part of the error in the model predictionsoriginates from the error in measuring the composition itselfand the elimination of which might improve the model predic-tions. We will use a data-reconciliation formulation, which wecall autotuning, to eliminate this error contribution. Autotuning,described in eq 12, attempts to make minimal changes in themeasured composition subject to the constraints that targetmeasured properties are matched exactly or very closelyapproximated within anε tolerance, whereε is a very smallnumber,g0.

In eq 12,wmeasuredis the vector of raw measured compositionfrom the GC,w the autotuned composition reconciled to anumber of different measured properties, andPj the varioustarget measured properties. Because the formulation of eq 12results in a highly underdetermined set of equations, the choiceof the number and type of property constraints is important toobtain a better autotuned composition. The following propertyconstraints were used in this work: (a) RON, (b) MON, (c)gravity at 60 °F, (d) total paraffin/i-paraffin ratio, (e) totalolefins, and (f) boiling point curve. The results based on theautotuned compositions of the blend components are shown inthe second column of Table 5. Remarkably, using an autotunedcomposition consistently improves the ON predictions for thegasoline blends across all of the seven refineries. On average,the SE improved from(0.9 numbers to(0.8 numbers. Thisimprovement may seem marginal, but even a 0.1 numberimprovement in the prediction error below a(1 number has asignificant economic consequence.

6. Conclusions

We have developed a composition-based predictive modelfor both RON and MON that can be universally applied acrossa wide variety of gasoline fuels derived from different naphthaprocess streams and blends. Each gasoline fuel is composition-ally represented by 57 different molecular lumps and by acombination of different GCs and correlated to the ON. Themodel structure permits a wide range of composition extrapola-tion from pure components to real gasoline blends. Its predic-tions are within a SE of(1 number for both RON and MONacross the multitude of gasoline fuels. The model is applicablefor a broad range of ONs from 30 to 120. Further improvements

in the model predictions are demonstrated using a data-reconciliation algorithm used in tandem with the predictivemodel.

Acknowledgment

We express our appreciation to N. L. Avery, D. I. Hoel, M.R. Apelian, K. D. Rose, R. J. Quann, and C. R. Kennedy fortheir many helpful discussions and suggestions.

Literature Cited

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(2) Knock characteristics of motor fuels by the motor method.AmericanSociety for Testing and Materials Test Method D2700; American Societyfor Testing and Materials: West Conshohocken, PA, 1989.

(3) Cornelius, W.; Caplan, J. D. Some Effects of Fuel Structure,Tetraethyl Lead and Engine Deposits on Precombustion Reactions in a FiringEngine.SAE Quart. Trans.1952, 6 (3), 488.

(4) Lovell, W. G.; Campbell, J. M.; Boyd, T. A. Detonation Charac-teristics of Some Aliphatic Olefin Hydrocarbons.Ind. Eng. Chem. 1931,23, 555.

(5) Knocking characteristics of pure hydrocarbon. Special TechnicalPublication No. 225; American Society for Testing and Materials: WestConshohocken, PA, 1958.

(6) API Technical Data Book on Petroleum Refining; API: Washington,DC, 1986.

(7) Scott, E. J. Y. Knock Characteristics of Hydrocarbon Mixtures.Proc.API DiV. Refin.1958, 38, 90.

(8) Anderson, P. C.; Sharkey, J. M.; Walsh, R. P. Calculation of ResearchOctane Number of Motor Gasolines from Chromatographic Data and a NewApproach to Motor Gasoline Quality Control.J. Inst. Pet.1972, 59, 83.

(9) Huskey, D.; Zhrmann, U. Determinacion de Octanaje RON medianteCromatografia de Gases en Columnas Capilares.Informe Tecnico InteVep;INTEVEP: Caracas, Venezuela, 1988.

(10) Sasano, Y. Measuring method of research octane number of gasolineby gas chromatograph and its apparatus. JP Patent 09-318613, 1997.

(11) Van Leeuwen, J. A.; Jonker, R. J.; Gill, R. Octane number predictionbased on gas chromatographic analysis with non-linear regression tech-niques.Chem. Intell. Lab. Syst.1994, 24, 325.

(12) Meusinger, R.; Moros, R. Determination of quantitative structure-octane rating relationships of hydrocarbons by genetic algorithms.Chem.Intell. Lab. Syst.1999, 46, 67.

(13) Meusinger, R.; Moros, R. Determination of octane numbers ofgasoline compounds from their chemical structure by13C NMR spectroscopyand neural networks.Fuel 2001, 80, 613.

(14) Lugo, H. J.; Ragone, G.; Zambrano, J. Correlations between OctaneNumbers and Catalytic Cracking Naphtha Composition.Ind. Eng. Chem.Res.1999, 38, 2171.

(15) Twu, C. H.; Coon, J. E. Estimate octane numbers using an enhancedmethod.Hydrocarbon Process.1997, 76, 65.

(16) Albahri, T. A. Structural Group Contribution Method for Predictingthe Octane Number of Pure Hydrocarbon Liquids.Ind. Eng. Chem. Res.2003, 42, 657.

(17) Jaffe, S. B. Control of Gasoline Manufacture. U.S. Patent 4,251,-870, 1981.

(18) Heck, R. H. Contribution of Normal Paraffins to the Octane Pool.Energy Fuels1989, 3, 109.

ReceiVed for reView July 11, 2005ReVised manuscript receiVed October 10, 2005

AcceptedOctober 14, 2005

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octane number.pdf

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