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Modeling the Composition of Crude Oil Fractions Using Constrained Homologous Series Steven P. Pyl,† Zhen Hou,‡ Kevin M. Van Geem,† Marie-Franc-oise Reyniers,*,† Guy B. Marin,† and Michael T. Klein‡ † ‡
Laboratory for Chemical Technology, Ghent University, Ghent, Belgium Department of Chemical Engineering, University of Delaware, Newark, Delaware, United States ABSTRACT: Composition modeling using constrained homologous series permits the derivation of the detailed composition of complex mixtures starting from a limited set of mixture bulk properties. By imposing various constraints, the number of unknowns is drastically reduced. Probability density functions are imposed on both the carbon number distribution in each homologous series of components and on the structural attribute distributions. Validation, based on detailed compositional information, shows that the use of gamma distributions to constrain the mixture composition results in an adequate approximation of the experimentally measured composition. The latter was obtained for two middle distillates and a heavy gas oil using advanced analytical techniques.
1. INTRODUCTION Despite the outstanding operational legacy and thus-derived vast knowledge base about petrochemical production and petroleum conversion processes, there is still room to improve process performance in order to reduce energy consumption, to improve selectivity, and to better protect the environment. Only process models that are based on fundamental insights in the following: (i) feed and product composition; (ii) the controlling chemical reactions; and (iii) transport phenomena possess the necessary flexibility to accommodate the needs of present-day refineries and petrochemical facilities.18 These fundamental models allow accurate process simulation over a wide range of process conditions and for a wide range of feedstock types. They permit the prediction of product yields and allow the determination of optimal process conditions, making them indispensible for state-of-the-art process design, optimization, and control. Figure 1 illustrates how the goal of these fundamental models is accomplished at a chemically detailed level: a detailed feedstock composition is transformed into a detailed product composition by a set of continuity equations that combine a reactor model and a kinetic model, i.e. a network of reactions and their associated kinetics. Figure 1 also shows that everyday application of fundamental models in an industrial environment would require frequent, yet highly detailed analyses of process feedstock, the composition of which may change on a daily or even hourly basis. Furthermore, knowledge of feedstock composition is also crucial for the development of these fundamental models and in particular for the development of the kinetic model. The latter requires modeling tools like automatic network generation and parameter optimization based on experimental data,8,9 both of which require detailed information on feedstock composition. Since crude oil fractions and the products obtained from their conversion are highly complex mixtures containing a multitude of components, detailed analysis is often a time-consuming task that calls for advanced analytical techniques, e.g. GC-MS, LC-GC, GC×GC, etc.1012 Moreover, as the complexity of these mixtures tends to increase exponentially with their average boiling point, r 2011 American Chemical Society
even the most cutting-edge analytical techniques do not provide sufficient resolution or simply can no longer be applied to unravel the detailed chemical composition of the heaviest oil fractions.13,14 The development of so-called composition modeling techniques1532 can eliminate the need for time-consuming analytical techniques. These computational methods allow modelers to derive the detailed composition of a mixture starting from a limited number of bulk mixture properties, e.g. average molar mass, distillation data, specific density, PIONA or SARA analysis, etc. Such bulk properties are widely used to characterize oil fractions and can be determined by means of relatively simple and standardized analytical procedures.33 Various composition modeling approaches have been developed. Several authors apply specific objective functions that are optimized by modifying the mole fractions of a predefined ensemble of molecules, in order to match the available bulk properties.16,25,2730 Others have combined this optimization approach with a stochastic Monte Carlo generation of the components constituting the mixture.17,18,24 In this way, not only the composition but also the identities of the mixtures components are derived from the average analytical data. Campbell and Klein19 have integrated Monte Carlo generation with a quadrature method that generates a reduced but optimal set of molecules. Other approaches start from a database containing bulk properties as well as detailed analytical data for a significantly large set of sample fractions. These methods employ a linear regression model or artificial neural network (ANN),15,21,23,31 or they determine an optimal blend of database fractions by minimizing the difference between analytical and calculated bulk properties.26,32 However, the need for such a large database mainly limits their application to composition modeling of lighter fractions such as gasoline or naphtha. Received: March 22, 2011 Accepted: August 15, 2011 Revised: August 11, 2011 Published: August 15, 2011 10850
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Figure 1. Fundamental kinetic modeling approach: from feed to product.6
The approach discussed in this work uses constrained homologous series to model the composition of complex oil fractions. The approach is validated for two kerosenes and a heavy gas oil. Not only should the calculated feedstock composition match with the available bulk properties, it should also be representative for the chemical complexity in the oil fraction to allow fundamental kinetic modeling and reliable simulation of chemical conversion of the feedstock. Comparison of the calculated composition with detailed compositional information, obtained using advanced analytical techniques, is therefore crucial.
2. COMPOSITION MODELING APPROACH The proposed composition modeling approach is depicted in Figure 2. The first step is to list all components that will be included in the composition modeling by defining a component library, i.e. a set of homologous series of components. Various constraints are imposed, relating mole fractions of groups of components to each other in order to drastically reduce the number of unknowns of this ill-defined problem. The soughtafter mixture composition is obtained by minimizing the difference between the available analytical bulk properties and those obtained from the calculated mixture composition, through adjustment of the remaining parameters. The entire approach as discussed below has been implemented into a user-friendly Visual Basic based computer program: the Composition Modeling Editor (CME). CME is part of the Kinetic Modelers Toolbox (KMT)9,34 which also comprises a tool for automatic reaction network generation, i.e. the Interactive Network GENerator (INGEN), and the Kinetic Model Editor (KME), a tool for model solving and optimization/ estimation of kinetic parameters. 2.1. Defining the Component Library. It is convenient to view the molecules in an oil fraction as the combination of a core structure and a side chain structure.2,28 A significant number of molecules in oil fractions has the same core structure but has varying aliphatic side chain length or number of side chains. Based on this observation, the components in any oil fraction can be listed in homologous series as shown in Figure 3. In each series the carbon number varies from a minimum carbon number Cmin to a maximum carbon number Cmax, by varying the (side) chain length of the series core structure. For example, if the core structure consists of one aromatic ring, then the homologous
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Figure 2. Composition modeling using constrained homologous series: general overview.
series of components based on this core structure can contain all monoaromatics ranging, for example, from toluene (C7) to n-decylbenzene (C16). If the nature of the core structure and the carbon number allows it, a third dimension can be added: varying the number of side chains for a given carbon number. In this way a distinction can be made between structural isomers, such as for example, n-propylbenzene, methylethyl-benzene, and trimethylbenzene. In CME, see Figure 4, selection of the desired core structures and input of a rough boiling point range results in an automatic generation of the complete library of components. Graph theory, in the form of a molecular structure adjacency list,9 is used to store the explicit molecular structure of each component. In this way the component library is defined, solely based on user input and a heuristics. The component library is not changed during the optimization step that follows; only the abundance of the components is modified to match the available bulk properties. Depending on the selected core structures and, if desired, the incorporation of isomers, the modeler is able to decide on the necessary level of detail. The latter basically depends on the kinetic model with which the feedstock representation should match. Once the component library is defined, the remaining goal is to determine the mole fraction of each component in order to come up with a mixture composition that matches the available bulk properties. Based on the defined component library, as shown in Figure 3, each considered component can be classified according to the homologous series it belongs to, its carbon number, and its number of side chains. Consequently, the component mole fractions yi,j,k can be defined as the product of three probabilities: (i) the series probability pSi , (ii) the carbon number probability pCN i (j), which is the probability that a component with carbon number j occurs in series i, and (iii) the number of side chains probability pSC(k), which is the probability for the structural isomer with k side chains to occur SC yi, j, k ¼ pSi 3 pCN i ðjÞ 3 p ðkÞ
ð1Þ
2.2. Imposing Constraints. Reduction of the number of unknowns is achieved by imposing probability density functions (pdf) on the carbon number distributions and number of side chains distribution. Moreover, the different series probabilities 10851
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Figure 3. Component library each column represents a homologous series, constructed from the selection of core structures and a desired boiling point range.
exponential, chi-square, or gamma distributions, to model the boiling point and molar mass distribution of oil fractions.35,36,33 Since there is a strong correlation between the boiling point and carbon number of a molecule, especially within a homologous series of components, it is reasonable to model the carbon number distribution in each series with a pdf as well.19,20,37 The widely used gamma distribution is a flexible two-parameter distribution and is a generalization of other possible pdfs such as the exponential and the chi-square distribution. Doing so, the carbon number probability of each component within a homologous series i is a function of its carbon number (j) and is determined by the parameters defining the imposed gamma distribution, i.e. the mean value μi and standard deviation σi of the distribution, as shown in eq 2 pCN i ðj; μi , σ i Þ ¼
ðj Cmin, i Þðα 1Þ eð ðj Cmin, i Þ=θÞ ΓðαÞ 3 θα
ð2Þ
with Figure 4. CME input screen input of desired core structures and boiling point range.
can be related to each other by introducing so-called structural attribute pdfs, as will be explained in section 2.2.2. Doing so, the remaining unknowns are the parameters defining the pdfs rather than the mole fractions of all components in the constructed library. It is however often justified to impose a fixed ‘number of side chains’ distribution, since most bulk properties contain little information about the relative abundance of structural isomers. Indeed, they have the same molar mass and similar boiling point, density, etc. The imposed distribution can be based on experimental evidence. For example, Ranzi et al.3 showed that the internal distributions of structural isomers of iso-paraffins in naphtha fractions are quasi independent of the source of the oil fraction. 2.2.1. Carbon Number Distributions. Many authors have suggested to use probability density functions (pdf), such as
α ¼ ðμi Cmin, i Þ2 =σi 2 θ ¼ σ i 2 =ðμi Cmin, i Þ and Cmin,i is the minimum carbon number in homologous series i. Since the number of carbon atoms in a molecule is an integer that varies only between the minimum (Cmin,i) and maximum (Cmax,i) carbon number in each homologous series, discretization, truncation, and renormalization of the continuous distributions is necessary.6 In general, a different gamma distribution can be imposed on the carbon number distribution in each homologous series. This can however lead to a rather large number of parameters, especially when the number of homologous series is large. A reasonable approximation involves imposing the same distribution, i.e. defined by the same parameters μ and σ, in two or more related homologous series. In the discussion below, a distinction is made between three 10852
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Industrial & Engineering Chemistry Research Table 1. Overview of the Considered Component Types and Structural Attributes component types
structural attributes
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Table 2. Comparison between Experimental Bulk Properties and Those Corresponding to the Calculated Composition, for Kerosene A, Kerosene B, and a Heavy Gas Oila kerosene A
n-paraffins iso-paraffins naphthenes
naphthenic rings
aromatics
aromatic rings
exp.
naphthenic rings
carbon number distributions, i.e. one for paraffinic series, one for naphthenic series, and one for aromatic series. 2.2.2. Structural Attribute Distributions. Each core structure, categorized into a limited number of component types (n-paraffin, iso-paraffin, naphthene, or aromatic), is the combination of a small set of more basic chemical building blocks, i.e. so-called structural attributes (e.g., an aromatic ring, a naphthenic ring, etc.).1719 The structural attributes for each of the component types considered in this work are given in Table 1. Definition of these structural attributes allows the modeler to define so-called attribute pdfs, which determine the probability, patt m (n), that attribute m occurs n times in the series core structure. As a result, each series prob, ability, pSi , is the product of a component type probability, ptype l and the product of the respective attribute probabilities, patt m (n) Y type att att patt ð3Þ pSi ¼ pl 3 m ðn; μm , σ m Þ
type
Since these structural attributes are implicitly related to boiling point and molar mass, it should be possible to model the attribute pdfs with gamma distributions as well. Moreover, Trauth et al.18 and Campbell et al.19 already extended the use of gamma distributions to structural attributes with success. 2.3. Finding the Optimal Composition. Finally, the available bulk properties are used to optimize the parameters of the imposed distributions and to determine an adequate detailed mixture composition. Selection of adequate and accurate bulk properties is therefore crucial. Bulk properties commonly used to characterize unprocessed oil fractions are average molar mass, distillation data, specific density, PIONA or SARA analysis, etc. However, composition modeling of for example processed oil fractions might require other mixture characteristics that reflect the specific chemical variety in the mixture. The following objective function, i.e. the weighted squared difference between the experimental, Pexp i , and calculated bulk properties, Pcalc i , is used ! exp 2 ptype , μ, σ Picalc ðptype , μ, σÞ Pi S¼ sf MIN ð5Þ wi i
∑
Av. molar mass [g/mol]
n.a.
Density [g/cm3]
0.799 0.814 n.a.
calc.
exp.
calc.
153.81 169.80 168.02 300.39 300.39 0.809
n.a.
0.845
n-paraffins
14.31 14.31 23.46 23.46
iso-paraffins naphthenes
21.09 21.09 25.37 25.37 45.80 45.80 34.07 34.07
aromatics
18.80 18.80 17.10 17.10
22.06 22.85
Sulfur content [wt%]
n.a.
1.48
1.52
-
n.a.
-
40.11 40.26 37.83 37.89
Simulated distillation [K]
m
att pSTHC ¼ paromatic 3 patt Arom:Rings ðn ¼ 3Þ 3 pNaph:RingsonAro ðn ¼ 1Þ ð4Þ
exp.
heavy gas oil
Group-type analysis [wt%]
thiophenic rings
The former represents the probability of the component type. The latter is a function of the number of times, n, the attribute occurs in the series core structure, and is determined by the parameters defining the imposed gamma distribution, i.e. μatt m and σatt m . For example, for the homologous series having 1,2,3,4tetrahydrochrysene (THC) as core structure, the series probability is given by
calc.
kerosene B
a
IBP
386 385
434
435
510
541
5%
408 410
456
454
560
564
10%
416 425
465
458
579
576
20% 30%
438 441 450 454
474 480
471 477
593 606
589 600
40%
462 465
487
483
616
610
50%
475 475
493
490
626
620
60%
487 485
498
496
637
629
70%
498 496
505
500
648
639
80%
515 509
514
510
661
650
90%
533 527
522
518
678
667
95% FBP
543 541 577 570
527 544
529 546
689 729
681 726
n.a. = not available.
The calculated bulk properties are derived from the calculated component mole fractions using mixing rules.33 These mole fractions and therefore the calculated bulk properties are in general determined by the component type probabilities, ptype, and the pdf parameters, μ and σ, as discussed in section 2.2. The application of mixing rules to calculate mixture bulk properties also requires knowledge of physicochemical properties, such as elemental composition, normal boiling point, density, etc., of all components involved. In CME these properties are determined automatically using quantitative structure property relationships3840 and the molecular structure adjacency list mentioned above. The denominator, wi, in each term of the objective function is a weighing factor associated with each bulk property. In CME, the global optimum of the objective function in eq 5 is determined using the simulated annealing optimization routine.41
3. RESULTS AND DISCUSSION 3.1. Kerosene. The approach discussed above was used to model the composition of two different petroleum derived middle distillates or kerosenes. The available analytical bulk properties for these fractions are shown in Table 2. Based on a predefined boiling point range of 300 K600 K, and the selection of seven homologous series of components, the entire component library included in the composition modeling of both kerosenes consists of 85 components, including n-paraffins (C5C20), iso-paraffins (C5C20), mononaphthenes (C6C19), 10853
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dinaphthenes (C10C19), monoaromatics (C6C18), naphthenoaromatics (C10C18), and diaromatics (C10C16). By imposing gamma distributions on carbon number and attribute probabilities the number of remaining parameters is 16, i.e. 4 component type probabilities, 2 × 3 parameters for the carbon number distributions, as discussed in section 2.2.1, and 6 for the three relevant attribute distributions. Values for these parameters were determined by minimization of the objective function in eq 5 using the bulk properties in Table 2, and their final values are given in Table 3. Table 3. Overview of the Optimized Carbon Number and Attribute pdf Parameters for Kerosene A, Kerosene B, and the Heavy Gas Oil heavy kerosene A
kerosene B
gas oil
μ
σ
μ
σ
μ
σ
paraffins
12.1
2.23
12.7
1.31
22.1
3.40
naphthenes
11.0
1.86
12.6
1.17
22.1
3.32
aromatics
11.2
1.79
12.0
0.97
22.2
3.17
naphthenic rings on naphthenic core
1.01
0.57
2.47
0.44
1.51
0.61
aromatic rings on
1.18
0.42
1.14
0.49
1.02
1.25
1.10
0.57
2.49
0.45
0.57
0.72
-
-
-
-
0.05
2.05
Carbon number pdfs
Attribute pdfs
aromatic core naphthenic rings on aromatic core thiophenic rings on aromatic core
Table 2 also allows comparison of the analytically determined bulk properties with those calculated from the generated mixture composition. It is clear that there is a good agreement between them, indicating that the selected component library is an adequate representation of the constituents of both fractions. If the calculated composition is to be used successfully as input for fundamental process models, it should compare well with the detailed quantitative composition obtained with comprehensive 2D gas chromatography (GC×GC). The latter is an advanced analytical technique that allows to subject the entire sample to two independent separation mechanisms, resulting in a much enhanced resolution compared to conventional 1D gas chromatography. The GC×GC used to characterize the kerosene discussed here is equipped with both a time-of-flight mass spectrometer (TOF-MS) and a flame ionization detector (FID), enabling both qualitative and quantitative analysis of complex mixtures as discussed by Van Geem et al.42 Figure 5 shows that there is a good agreement between the experimental and calculated carbon number distributions for each of the four main hydrocarbon types in kerosene A. Both the carbon range and shape of the slightly skewed distributions are predicted well from the available bulk properties. Since similar results are obtained for the more narrow boiling kerosene B, as shown in Figure 6, it is clearly possible to model the composition of these distinctly different middle distillates, see Table 2 and Table 3, with the same component library. In Table 4 experimental and calculated group-type compositions are presented. The calculated data in this table are directly related to the imposed attribute distributions. The difference between, for example, mono- and diaromatics is determined by the pdf imposed on the number of aromatic rings distribution. The agreement with the experimental data is quite good for both
Figure 5. Experimental (() and calculated (lines) carbon number distributions [wt%] for kerosene A: (a) n-paraffins, (b) iso-paraffins, (c) naphthenes, (d) aromatics. 10854
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Figure 6. Experimental (() and calculated (lines) carbon number distributions [wt%] for kerosene B: (a) n-paraffins, (b) iso-paraffins, (c) naphthenes, (d) aromatics.
Table 4. Experimental and Calculated Group-Type Compositions [wt%] for Kerosene A, Kerosene B, and the Heavy Gas Oil kerosene A exp.
calc.
kerosene B exp.
calc.
Table 5. Absolute Deviations [wt%] between Experimental and Calculated Component Mass Fractions for Kerosene A, Kerosene B, and Heavy Gas Oil kerosene A
kerosene B
heavy gas oil
25% percentile
0.00
0.00
0.01
50% percentile
0.09
0.05
0.06
heavy gas oil exp.
calc.
Paraffins
35.4
35.4
48.8
48.8
40.1
40.3
75% percentile
0.26
0.34
0.23
Naphthenes
45.8
45.8
34.1
34.1
37.8
37.9
AADa
0.24
0.24
0.19
mononaphthenes
34.7
34.0
23.8
22.7
13.3
30.8
dinaphthenes
11.1
11.8
10.3
11.4
9.90
5.56
trinaphthenes
-
-
-
-
6.87
1.20
tetranaphthenes Aromatics
18.8
18.8
17.1
17.1
7.82 20.6
0.28 20.3
monoaromatics
17.1
16.4
16.6
16.9
8.93
13.2
diaromatics
1.69
2.39
0.47
0.10
8.06
3.38
triaromatics
-
-
-
-
2.39
1.96
tetra-aromatics
-
-
-
-
1.18
1.75
Thiophenes
-
-
-
-
1.48
1.52
benzothiophenes
-
-
-
-
0.86
0.96
dibenzothiophenes
-
-
-
-
0.62
0.56
kerosenes. In Table 5 the absolute deviations between the experimental and calculated component mass fractions are given for both kerosenes, indicating, for example, that for 75% of all components in kerosene A the absolute deviation does not exceed 0.26 wt %. 3.2. Heavy Gas Oil. To model the composition of a heavy gas oil, a component library consisting of 16 homologous series of components was constructed. Based on a predefined boiling point range of 400 K750 K, the entire component library consists of
exp Average Absolute Deviation, AAD = (1/n)∑ni=1|xcalc i xi |; with n being the number of components in the oil fraction. a
395 components, including n-paraffins (C9C40), iso-paraffins (C9C40), mono- (C8C39), di- (C10C39), tri- (C14C39), and tetranaphthenes (C18C38), mono- (C8C39), di(C10C36), tri- (C15C33), and tetra-aromatics (C19C28), naphthenomonoaromatics (C10C38), dinaphthenomonoaromatics (C15C37), naphthenodiaromatics (C15C35), naphthenotriaromatics (C19C30), benzothiophenes (C8C33), dibenzothiophenes (C12C30). By imposing constraints on carbon number and attribute distributions, the number of unknown parameters was reduced to 18: 4 component type probabilities, 2 × 3 parameters for the carbon number distributions, as discussed in section 2.2.1, and 8 for the four relevant attribute distributions. The available bulk properties as well as the calculated bulk properties for this gas oil are given in Table 2. The optimized values of the distribution parameters are given in Table 3. To validate the composition modeling approach, the calculated composition was compared with a detailed quantitative composition. The employed analytical method consists of two major steps. First, the entire sample is separated into saturates 10855
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Figure 7. Experimental (() and calculated (lines) carbon number distributions [wt%] for a heavy gas oil: (a) n-paraffins, (b) iso-paraffins, (c) naphthenes, (d) mono- and diaromatics (e), tri+ aromatics, (f) benzo- and dibenzothiophenes.
and aromatics by High Performance Liquid Chromatography (HPLC).10 Second, each fraction is analyzed in detail using GC-MS, as described by ASTM procedures D2786 and D3239, respectively. The detailed composition obtained by these analyses again allowed to compare of the experimental with the calculated carbon number distributions, as shown in Figure 7 for several classes of components, showing a satisfactory agreement. Table 4 presents the experimental and calculated group-type composition. In contrast to the kerosenes discussed above, this heavy gas oil contains a small amount of sulfur components, i.e. benzo- and dibenzothiophenes. Figure 7 and Table 4 show that also the amounts of thiophenes calculated from the available bulk properties, which include the elemental amount of sulfur, compare well with the experimental amounts. Comparing the mass fractions of the aromatics shows that the calculated aromatic rings distribution is steeper than the experimentally observed distribution, resulting in a overestimated amount of monoaromatics at the expense of the amount of diaromatics. The same conclusion holds for the naphthenes, where the calculated rings distribution is also steeper than the measured distribution. In Table 5 the performance of the composition modeling is quantified based
on the absolute deviations between the experimental and calculated component mass fractions, indicating that for 75% of all components in the HGO the absolute deviation does not exceed 0.23 wt %.
4. CONCLUSIONS The concepts of homologous series of components and of structural attributes allow modeling of the composition of oil fractions, starting from a limited number of bulk properties. The proposed methodology consists of imposing constraints on carbon number and structural attribute distributions. In this way an ill-defined problem is converted into a defined one, the parameters being those of the imposed distributions. Validation based on detailed information obtained using advanced analytical techniques shows that the use of gamma distributions results in an adequate approximation of the measured composition. This approach, implemented into a user-friendly Composition Modeling Editor (CME), allows the modeler to decide on the necessary level of detail of the feedstock representation. The latter basically depends on the kinetic model with which it should match. 10856
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The authors acknowledge the financial support from the Long Term Structural Methusalem Funding by the Flemish Government - grant number BOF09/01M00409. K.V.G. holds a Postdoctoral Fellowship of the Fund for Scientific Research, Flanders, Belgium. ’ NOTATION AAD average absolute deviation [wt%] GC×GC comprehensive 2D gas chromatography HPLC high performance liquid chromatography μ statistical distribution mean value p probability P bulk property PIONA n-paraffins, iso-paraffins, olefins, naphthenes, and aromatic σ statistical distribution standard deviation SARA saturates, aromatics, resins, and asphalthenes w weighing factor x component mass fraction [wt%] y component mole fraction [mol %] Subscripts
i homologous series index j carbon number index k number of side chains index l component type index m structural attribute index n structural attribute frequency Superscripts
att structural attribute calc calculated CN carbon number exp experimental S homologous series SC side chain type component type
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