Ind. Eng. Chem. Res. 2006, 45, 337-345
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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 process streams and their blends including oxygenates based on detailed composition. The octane number is correlated to a total of 57 hydrocarbon lumps measured by gas chromatography. The model is applicable to any gasoline fuel regardless of the refining process it originates from. It is based on the analysis of 1471 gasoline fuels from 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 this work. The model predicts the octane number within a standard error of 1 number for both the research and motor octane numbers. 1. Introduction Octane number (ON) is one of the most important properties of gasoline streams and is a measure of its antiknock property. It is defined as the volume percentage of i-octane in a blend of n-heptane and i-octane, which produces the same knock intensity as the test fuel under standard test conditions in an ASTM internal combustion engine. ASTM defines two different types of ONs, the research octane number (RON) and the motor octane number (MON), which are evaluated using the ASTM D2699 and the ASTM D2700 tests, respectively.1,2 Both methods use the same standard test engine but differ in the operating conditions. RON is measured in an engine running at 600 rpm and a fuel/air mixture at a temperature of 60 °F, while MON is measured with the engine running at 900 rpm and a fuel/air mixture at a temperature of 300 °F. The slower engine speed and the lower fuel/air temperature as required in the RON test are representative of the fuel performance for city driving, while the faster engine speeds and higher fuel/air temperature represent the fuel performance for highway driving. Knock results from the premature combustion of the gasoline due to compression in the engine.3 As the fuel/air mixture is compressed in the internal combustion engine, certain molecules in gasoline tend to self-ignite even before they reach the ignition spark, thereby creating a resistive expansive motion in the compression stroke of the engine and hence the knock. Depending on the thermal stability of the molecule (which depends on its molecular structure) and the ensuing radicals, certain molecules tend to combust sooner (and knock more) than others. Consequently, ON is a direct function of the molecular composition of the gasoline fuel, and any modeling effort should explicitly acknowledge it. Numerous studies in the past have attempted to mathematically describe the ON as a function of the gasoline composition. * To whom correspondence should be addressed. E-mail:
[email protected]. † E-mail:
[email protected]. ‡ E-mail:
[email protected].
Lovell et al.4 were an early group to identify that aromatics and branched i-paraffins have higher ONs than the corresponding paraffins. In the middle 1950s, the American Petroleum Institute (API) Research Project 455-7 analyzed the purecomponent ONs for over 300 different hydrocarbon molecules, and several reliable correlations relating gasoline composition to ON were developed. The work not only quantified the ON trends with molecular structure and size, it also studied the nonlinear interactions between different molecular types toward ON.7 However, the work was primarily focused on purecomponent studies with a limited number of binary or ternary gasoline blends. Commercial gasoline contains many different molecules in the C4-C13 range, and the more recent papers in the literature have therefore focused on predicting the octane number of such multicomponent mixtures. Anderson et al.8 developed a useful method for predicting the RON of different gasolines based on the gas chromatographic (GC) analysis of the sample. A total of 31 molecular lumps were considered to describe the composition of gasoline, and the contribution of each lump was added linearly to compute the octane number of the fuel. Although simple in its structure, the method by Anderson et al.8 is rather restrictive in its use and is known to show an error of around 2.8 numbers on average for catalytically cracked naphthas.9 Part of the less than satisfactory predictions is perhaps the assumption of linearity in octane blending because octane blending is known to exhibit nonlinear interactions (both synergistic and antagonistic) among the various constituent hydrocarbon molecular classes (e.g., paraffins, olefins, aromatics, etc.).7 Sasano10 described a procedure similar to that of Anderson et al.8 to predict ON of the gasoline fuel from its composition measured by GC. The ON of the fuel is calculated as the linear volumetric 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 experience to develop. This is especially true for neural network based
10.1021/ie050811h CCC: $33.50 © 2006 American Chemical Society Published on Web 11/24/2005
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approaches, where the determination of the number of layers in the network, number of nodes in each layer, the kind of transfer functions for each node, etc., is highly user-dependent. Also, the lack of an underlying phenomenological structure and the inherent opacity in such models make them less reliable in the extrapolative mode. More recently, Meusinger and Moros used genetic algorithms and neural networks to quantify the partial ON of each gasoline component in the mixture based on the structural elements of the molecule.12,13 Other relevant work in this area includes the work by Lugo et al.,14 Twu and Coon,15 and Albahri,16 who have all employed different variations 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 categories: first, predicting the ON of individual hydrocarbon molecules in gasoline by correlating molecular structure descriptors such as topological indices, length of the backbone carbon chain, degree of branching, type of carbon atom based on spectroscopy, etc., to the pure-component ON and, second, predicting the ON of the actual gasoline fuel by correlating the molecular composition of the gasoline fuel to its ON. In this work, we are interested in accomplishing the second objective. In principle, any model that achieves the second objective should also be able to predict (or reconcile) the ON of the individual hydrocarbon molecule because a pure component is merely the limiting value of a mixture. However, most of these published mixture models do not achieve this. Part of this lack of reconciliation in the published models originates from their purely empirical and statistical nature of the underlying mathematical structure used to develop the models, making them rather restrictive for extrapolation. Further, most of the published models have focused on developing correlations that work well with individual or a very few naphtha process streams collectively 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 narrow range between 80 and 95 numbers. Although this has traditionally been the most important range for commercial gasoline fuels, it would be beneficial to have a model that can work with a much extended range of ONs between 30 and 120 numbers. This is especially critical in today’s refinery blending operations, where many different blend components (i.e., naphthas from different processes) with widely different ONs need to be economically blended. Finally, none of the above work predict the octane number of gasoline fuels that contain oxygenates such as methyl tert-butyl ether (MTBE), ethanol (EtOH), or tert-amyl methyl ether (TAME), which are finding increasing use in commercial gasoline. We attempt to address some of the questions raised in the previous paragraph. Specifically, our objectives are 2-fold: first, to develop a predictive model for ON, both RON and MON for any gasoline fuel, dependent solely on the composition and independent of the refining process stream and, second, to extend the range of applicability of the model to a much broader range of octanes from 30 to 120 numbers. In developing such a model, we would like to ensure that, in the limiting case of a pure component, the model predicts the pure-component octane number. Further, we would also like to extend the model to fuels containing different oxygenates. The details of such a model 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
Figure 1. Schematic showing the difference between octane numbers of the gasoline sample (ON), pure-component octane numbers (ONA and ONB), ON and the corresponding blend octane numbers (BON A and BB , respectively) for a typical binary blend. Notice that the blend numbers are obtained by extrapolating the tangent to the octane curve to the pure-component limit.
different hydrocarbon molecules, each contributing to the ON of the gasoline fuel. Let ON denote the measured octane number for the gasoline fuel while ONi represents the pure-component octane number for each molecule i in the fuel. Because a molecule i may not necessarily always contribute its purecomponent octane number to the gasoline fuel, each molecule’s contribution toward the fuel octane number is quantified by its blend value, denoted by BON i . The blend value of a molecule depends on the overall composition of the fuel it is part of. Figure 1 schematizes the difference between ONi and BON i . By definition, ON is a linear volumetric blend of the blend contributions of all of the different molecules present in the gasoline fuel. Therefore
ON )
∑i ViBON i
(1)
where Vi is the volume fraction of molecule i in the sample. Experimental studies in our laboratory over many years have revealed that the blend value of a molecule i varies almost linearly with the ON of the gasoline fuel it is part of, or blended into. These results have been reported previously in refs 17 and 18. A typical result highlighting this observation is shown in Figure 2.18 The figure plots the variation of the blend values of various n-paraffins (nC5-nC9) against the ON of the three different refinery naphtha fuels in which they were volumeblended into. For each of the paraffins, the figure shows that the blending value of n-paraffin increases linearly as the ON of the refinery naphtha fuel increases. We have observed similar results over many other such studies. Thus, in general, we may postulate that the blend value of molecule i may be approximated as a linear function of the gasoline ON. Therefore (1) ) a(0) BON i i + ai (ON)
(2)
Equation 2 is analogous to the equation for any partial molar property, where the partial molar property (BON i ) depends on is the composition of the gasoline fuel it blends into. BON i parametrized by two parameters, a slope a(1) and an intercept i a(0) i . Although the variation of the blend value of the individual molecules with the ON of the gasoline fuel is taken to be linear, this does not imply a linear relationship of the fuel composition to its ON. Using the definition for ON from eq 1 in eq 2, it is easy to see that eq 2 captures multicomponent interaction.
Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 339
Figure 2. Variation of blending ON of n-paraffins in different refinery naphtha fuels.
Although eq 2 requires two parameters, a(0) and a(1) i i , for each molecule, it is possible to eliminate one of these parameters using the special case when the gasoline fuel is a pure component. 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 this boundary condition yields (1) (0) (1) ONi ) a(0) i + ai (ONi) w ai ) (1 - ai )ONi
(3)
If we define βi ) 1 - a(1) i , eq 2 may be rewritten as
a(0) i ) βiONi
(4)
Rearranging eqs 1, 2, and 4, we get
ON )
∑i ViβiONi lumps ∑ ViβiONi )
∑i Viβi
∑ Viβi
(5)
lumps
This is the basic octane prediction model, where the summation index i runs over all of the molecules present in the gasoline fuel. However, a typical gasoline fuel contains an enormous number of different molecules, so some molecular lumping is necessary to build a practical model. Such lumping is reflected in the second part of eq 5, where we have replaced the summing variable i with “lumps” to indicate that the sum runs over all of the molecular lumps relevant for the octane model. A lump defines the compositional level of abstraction that the model uses. It could be a single molecule like n-heptane or a group of similar molecules such as C10 aromatics. Note that, in light of this lumping, the term pure-component ON for lump i may not always necessarily reflect the ON of a single molecule. For molecular lumps that correspond to single molecules, ONi is the pure-component ON of that single molecule, but for molecular lumps that correspond to a group of similar molecules, ONi is the average of the pure-component ONs of all of the different molecules in that lump. These lumps are described in more detail in section 3. βi’s are the adjustable parameters and represent whether a molecule contributes beneficially or detrimentally to the ON
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 a indicates positive interaction, curve b indicates no interaction, and curve c indicates negative interaction.
of the gasoline fuel. A contribution is considered beneficial if the blend value of the molecule/lump (BON i ) is greater than its pure-component octane number (ONi). Likewise, the contribution is detrimental if BON < ONi. For the two cases (a) βi < 1 i and ONi < ON or (b) βi > 1 and ONi > ON, the lump i contributes beneficially to the fuel ON. For the other two cases (a) βi > 1 and ONi < ON or (b) βi < 1 and ONi > ON, it contributes detrimentally to the fuel ON. βi ) 1 is the special case where the lump contributes equally to its pure-component octane number. Equation 5 forms the core of the octane model and is suitable for predicting octanes of reformates, LSR, and alkylate streams. Although nonlinear in composition, the extent of nonlinearity expressed in it is insufficient to fully capture the nonlinear interaction between paraffins and olefins and/or paraffins and naphthenes, which may be important for cat-naphtha fuels. Published studies in the literature6,7 and independent research in our laboratories reveal that hydrocarbons belonging to the same molecular class blend linearly; i.e., paraffins blend linearly with other paraffins, olefins blend linearly with other olefins, and so on. However, a blend of paraffins and olefins may exhibit significant deviation from linearity. Such nonlinear interaction in a binary blend is qualitatively described in Figure 3. Figure 3a shows a positive interaction or equivalently a positive deviation from linearity, Figure 3c shows a negative interaction, and Figure 3b shows no interaction. Paraffins and naphthenes also exhibit similar deviations from linearity. In contrast, olefins and naphthenes tend to blend linearly. The blending behavior of aromatics as a group is somewhat unclear because of the differences in the blending behavior of individual aromatic molecules and also because of the difficulty in measuring the high ONs of such blends. Also, note from Figure 3 that, for certain blends, the ON of the blend may actually be higher or lower than both the individual ON extremes defined by the purecomponent numbers. The mathematical structure of eq 5 is incapable of describing this behavior because it will always be bounded between the extremes of pure-component numbers for the two components of the binary blend, as shown in eq 6.
ON1 e ON )
(
)
(
)
V1β1 V2β2 ON1 + ON2 e V1β1 + V2β2 V1β1 + V2β2 ON2 (6)
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The nonlinear interaction of Figure 3 may be quantitatively described by the following mathematical function for a binary blend:
y)
k(a) 12 V2V1
(7)
1 + k(b) 12 V2
(b) where k(a) 12 and k12 are interaction parameters. By appropriately choosing these interaction parameters, we can describe positive, negative, and no blending interactions. The structure has been borrowed from the more familiar rate expression for inhibiting and synergistic pyrolysis kinetics which tend to exhibit similar behavior. For a ternary blend where there are multiple binary interactions, i.e., between V1 and V2, between V1 and V3, and likewise between V2 and V3, eq 7 may be written as
Figure 4. Pure-component RONs for various i-octane isomers.
y)
k(a) 12 V2V1 1+
+
k(a) 13 V3V1
k(b) 12 V2 +
+
k(a) 23 V2V3
k(b) 13 V3 +
(8)
k(b) 23 V3
(b) Equation 8 has six interaction parameters: k(a) 12 and k12 for the (a) (b) 1-2 interaction, k13 and k13 for the 1-3 interaction, and k(a) 23 and k(b) 23 for the 2-3 interaction, respectively. It is easy to see from eqs 7 and 8 that if nonlinear interaction has to be modeled for every binary interaction in a typical gasoline fuel, it would lead to a large number of interaction parameters; e.g., even for a very lumped description of a typical gasoline fuel with 50 different molecular lumps, this leads to 50C2 ) 1225 binary interactions where nCr ) n!/r!(n - r)!. Consequently, the nonlinear interaction will be modeled only at the P/O/N/A level (i.e., at the level of the total paraffins, total olefins, total naphthenes, etc., and not at the individual molecule level). For the purposes of this paper, we will consider the nonlinear interaction between paraffins and naphthenes and between paraffins and olefins. Thus, a correction similar to eq 8 can now be added to eq 1 to model the nonlinear interactions in octane blending. Thus
ON )
∑ PONA
ViBON i
+
(
(a) k(a) PNVN + kPOVO
1+
k(b) PNVN +
k(b) POVO
)
∑P VjBON j
(9)
where VN and VO represent the total naphthenes and olefins in the gasoline sample. Mathematically, VN ) ∑i∈naphthenesVi and VO ) ∑i∈olefinsVi. Note that in eq 9, while the first sum runs over P, O, N, and A (i.e., paraffins, olefins, naphthenes, and aromatics) molecules, the second sum runs only over the paraffinic molecules. If the interaction term is denoted by I, eq 9 may be more succinctly rewritten as
ON )
where
Ii )
[(
(1 + Ii)ViBON ∑ i PONA
(a) k(a) PNVN + kPOVO
(b) 1 + k(b) PNVN + kPOVO 0 otherwise
)
for i ∈ P
(10)
]
Using eqs 2-4 in eq 9 and rearranging the various terms, we get
ON )
∑ ViβiONi + IP∑P ViβiONi
PONA
∑ Viβi + IP(∑P Viβi - ∑P Vi)
(11)
PONA
This is the complete octane model. Note that when I ) 0, eq 11 reduces identically to eq 5. Also, in the limiting case when the gasoline fuel is a pure component (Vi ) 1), eq 11 yields ON ) ONi, thereby returning the pure-component octane number. 3. Defining the Molecular Lumps Next we need to define the various molecular lumps that will be used in the octane model. The molecular lumps have been selected based on the following two criteria: (a) Analytical Differentiation. We have defined separate lumps where it is possible to analytically measure and differentiate the lump for most of the process streams. For instance, it is possible to analytically measure the different aromatics by carbon number for most of the naphtha process streams by different GC techniques; however, it is not always possible to differentiate between the various aromatic isomers at each carbon number with current analytical techniques. Consequently, for the aromatics, our lump definition has been restricted to total aromatics by carbon number only. (b) ON Differentiation. When analytical differentiation is possible across similar molecular lumps, we have defined separate lumps only if their ONs are widely different and their relative distributions differ across various process streams. For example, we consider separate lumps for mono-, di-, and trimethyl-i-paraffins at each carbon number as opposed to a single lump for the total i-paraffins at each carbon number. Such delumping is necessary for two reasons: first, the ONs of the branched i-paraffins vary widely with the degree of branching and, second, the relative distribution of branched isomers is very different across different naphtha streams. Figure 4 plots the pure-component ONs of all of the i-octane isomers and shows that, depending upon the particular isomer of i-octane, whether it is a mono-, di-, or trimethyl isomer, its ON could vary between 25 and 100 numbers. The relative distribution of these isomers is also different in different naphtha process streams, as shown
Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 341 Table 1. Typical Measured Isomer Distribution (wt %) for i-Octanes stream type
monomethyls
dimethyls
trimethyls
alkylates reformates
0 68.9
18.5 31.1
81.5 0
in Table 1 for alkylates and reformates. Trimethyl-i-octanes dominate C8 i-paraffins in alkylates, whereas monomethyl-ioctanes dominate C8 i-paraffins in reformates. The observations reported for i-octane are also true for other i-paraffins. Consequently, i-paraffins are modeled as three lumps at each carbon number in the model based on their degree of branching. The situation is somewhat different for aromatics or olefins. At each carbon number, the variation in the RONs for the aromatic isomers is only between 5 and 10 ONs (see Figure 6), which is not significant enough to introduce noticeable errors in the predictions across the various process streams, especially because the relative abundance of the individual isomers is small and their distribution does not change appreciably either across the process streams. The situation is similar for i-olefins, where the ON does not change significantly depending on whether the particular i-olefin is a mono-, di-, or trimethylolefin. In addition, there is great difficulty in analytical speciation of these individual isomers for most of the process streams. For streams where such detailed information might be available, e.g., aromatic isomer distribution in reformates, the fact that the isomers are always at equilibrium makes the delumping unnecessary as a single lump with an average ON of the lump (reconciled with the equilibrium isomer distribution) would be adequate. On the basis of the above two criteria, we have considered a total of 57 compositional lumps in this work to describe any naphtha stream. These include 32 lumps for n- and i-paraffins, 6 lumps for naphthenes, 7 lumps for aromatics, 9 lumps for olefins and cyclic olefins, and 3 lumps for oxygenates. The lumps range from individual molecules to a group of similar molecules at various levels of abstraction. Although the oxygenates are ON improvers, they are treated in the model similar to all of the hydrocarbon lumps. These lumps are summarized in Table 2. Once the lumps have been defined, the next step is to specify their pure-component ONs. The pure-component RONs and
MONs for most of the lumps have been chosen from the values reported in the API-45 project.5,6 For lumps that correspond to individual molecules, e.g., n-butane, n-pentane, etc., the purecomponent values are taken as is from ref 6, while for lumps that correspond to a group of similar molecules such as monomethyl-i-octanes, an average value is chosen based on the ONs of all of the different monomethyl-i-octane isomers. Two important trends emerge from this dataset: first, ON decreases with the carbon number and, second, ON increases with the degree of branching at the same carbon number. Such trends are shown for the paraffins and aromatics in Figures 5 and 6, respectively, where the pure-component ONs are plotted against the number of carbon atoms in the hydrocarbon molecule. These trends have been used to estimate the pure-component ONs of the lumps that are not reported in ref 6. The final set of purecomponent RONs and MONs for the various molecular lumps in the model is shown in Table 2. 4. Experimental Program An extensive database of 1471 gasoline fuels was collected from many naphtha process streams found in the petroleum refinery. These include 143 alkylates, 165 cat-naphtha (FCC) gasolines, 440 reformates, 366 hydroprocessed naphtha streams, 117 SCANfining [Selective CAtalytic Naphtha Refining, a proprietary ExxonMobil Technology] products, 40 LSR naphthas, 13 isomerates, and 187 finished blends of these different process streams. Fuels with oxygenates contained TAME, MTBE, and EtOH in the range of 2-10 vol % oxygenates. Each of these 1471 fuels was analyzed for its detailed composition using a multitude of different GC techniques. RON and MON were also measured on these fuels. Because the composition was measured through multiple GC columns, each measuring certain carbon number ranges of the composition, a thorough data-reconciliation procedure was employed to reconcile the analysis by the different analytical measurements. For example, fuel samples with both the overall PIONA analysis and the specific GC analysis (which yield detailed information in a particular carbon number range) were checked to ensure that the two analyses were consistent. Likewise, the compositional information based on GC and PIONA was reconciled with the boiling point curve wherever available. Further, many repeats
Table 2. Various Lumps Considered in the Present Octane Model along with Their Pure-Component RONs and MONs
Paraffins n-butane isobutane n-pentane i-pentane n-hexane C6 monomethyls 2,2-dimethylbutane 2,3-dimethylbutane n-heptane C7 monomethyls C7 dimethyls 2,2,3-trimethylbutane n-octane C8 monomethyls C8 dimethyls C8 trimethyls n-nonane C9 monomethyls C9 dimethyls C9 trimethyls n-decane C10 monomethyls C10 dimethyls C10 trimethyls
RON
MON
94 102 62 92 24.8 76 91.8 105.8 0 52 93.76 112.8 -15 25 69 105 -20 15 50 100 -30 10 40 95
89.6 97.6 62.6 90.3 26 73.9 93.4 94.3 0 52 90 101.32 -20 32.3 74.5 98.8 -20 22.3 60 93 -30 10 40 87
RON
MON
Paraffins (cont’d.) n-undecane C11 monomethyl C11 dimethyls C11 trimethyls n-dodecane C12 monomethyl C12 dimethyls C12 trimethyls
-35 5 35 90 -40 5 30 85
-35 5 35 82 -40 5 30 80
Naphthenes cyclopentane cyclohexane m-cyclopentane C7 naphthenes C8 naphthenes C9 naphthenes
100 82.5 91.3 82.0 55 35
84.9 77.2 80 77 50 30
Aromatics benzene toluene C8 aromatics C9 aromatics C10 aromatics C11 aromatics
102.7 118 112 110 109 105
105 103.5 105 101 98 94
RON
MON
Aromatics (cont’d.) C12 aromatics
102
90
Olefins/Cyclic Olefins n-butenes n-pentenes i-pentenes cyclopentene n-hexenes i-hexenes total C6 cyclic olefins total C7d total C8d
98.7 90 103 93.3 90 100 95 90 90
82.1 77.2 82 69.7 80 83 80 78 77
Oxygenates MTBE TAME EtOH
115.2 115 108
97.2 98 92.9
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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 run on the RON and MON measurements of each fuel to ensure high fidelity in the dataset. 5. Results 5.1. Parameter Estimation: Constrained Least-Squares Formulation. A constrained least-squares minimization problem was solved using the Levenberg-Marquadt algorithm in order to regress the parameters of the model. The adjustable parameters β were allowed to vary between a lower bound of 0 and
an upper bound of 10. Although, in principle, β may be
