A New Extended Structural Parameter Set for Stochastic Molecular

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A New Extended Structural Parameter Set for Stochastic Molecular Reconstruction: Application to Asphaltenes Muzaffer Yasar, Celal Utku Deniz, and Michael T Klein Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b01006 • Publication Date (Web): 27 Jun 2017 Downloaded from http://pubs.acs.org on June 28, 2017

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A New Extended Structural Parameter Set for Stochastic Molecular Reconstruction: Application to Asphaltenes Celal Utku Deniz and Muzaffer Yasar* Chemical Engineering Department Istanbul University Avcilar, Istanbul 34820 and Michael T. Klein** Chemical and Biomolecular Engineering Department University of Delaware Newark, Delaware 19716 and Center for Refining and Petrochemicals King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia Abstract The modeling of complex hydrocarbon mixtures is a current issue. The presently available analytical techniques are insufficient alone to fully characterize the molecular details of heavy oil fractions to the level for new development of a molecular-level kinetic model. Stochastic Reconstruction (SR) methods which build a set of molecules that mimic the properties of complex mixtures by using partial analytical data help to overcome this drawback. Although the classical SR algorithm produces reasonable molecule sets for light and medium fractions, performance degrades for heavier fractions. The main reason for this is the lack of structural parameters needed to define the variations in side-chain and ring configurations. As an extension, a novel structural parameter set including specific parameters for ring and chain configurations was implemented to SR algorithm. In addition to this, in order to ensure an extensive structural connection between the generated molecules and the experimental data, 1HNMR spectrum divided into six different regions and these hydrogen types were used in an objective function. In order to validate the SR with extended parameter set, it has been applied to *

Corresponding author: [email protected] Michael T. Klein acknowledges collaborations with and support of colleagues via the Saudi Aramco Chair Program at KFUPM and Saudi Aramco.

**

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six different petroleum asphaltenes. The extended parameter set resulted in a decrease in the objective function value between 45% and 85% compared to the basic parameter set. Moreover, the extended parameter set increases the fitting ability of the SR algorithm without sacrificing the compositional space of the generated molecules. 1. Introduction Complex systems can be quite difficult to model and simulate. The main reason of such difficulty is that the events depend on a huge number of variables, which makes the solution steps more cumbersome. Complex systems are simulated using computers and depending on the complexity of the problem, the computing time to reach acceptable solutions can increase exponentially with problem size. As a result, complex systems are often modeled by using fewer significant variables without sacrificing accuracy1–3. Modeling of oil fractions, which consist of very large numbers of different molecules, is a good example of complex chemical systems. One of the most common problems in the oil refinery is the conversion processes of heavy oils and their fractions. Processes such as catalytic cracking, thermal cracking and hydrocracking aim to increase the percentage of light fractions and are highly sensitive to feedstream and operating conditions. In addition, product quality and environmental concerns restrict the contents of the fuels4–6. These restrictions force the refineries to take into account the effect of various molecular species. As a result, the accurate prediction of product properties and cost aid with operating the refinery in a more efficient manner. Development of accurate and detailed models for the refinery processes is the first step of achieving such results. The modeling of complex heavy oils and their fractions is a current issue studied by many research groups.7–11 First modeling efforts are related to lumping the molecules based on their molecular characteristics or properties such as boiling point.12–16 This approach does not include detailed information aside from features defining clusters such as boiling point and solubility, as a result of the lack of detailed information of the chemical structure. Moreover, kinetic parameters of lump kinetic models vary amongst samples, indicating that generalizing lumped models could be an issue.16 Studies done by Jacob et al.17 and Weekman18 based on the boiling temperature range principle represent pioneering work in lumped models. These models show deviations for different mixtures based on boiling point distribution only; therefore, kinetic


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models built on the lumped models are affected by these deviations. The simplest explanation for this deviation is due to two entirely different molecules that are clustered under the same group because of their similar boiling points. The prediction of reactive properties from the boiling point would not be accurate without structural information. Subsequent studies conducted on the kinetic modeling of complex mixtures dictated the necessity of the consideration of chemical structure. Jaffe19 is one of the first researchers to emphasize the "bond kinetics" concept. In their study, a successful mathematical model has been developed based on the energy released during the breaking of the carbon-carbon and hydrogenhydrogen bonds and the formation of carbon-hydrogen bonds in order to describe the hydrogenation of oil. A further kinetic model based on the structural groups was also developed by Gray.20 There also exists another individual study based on more detailed structural group, called a structure-oriented lumping (SOL), which was developed by Quann and Jaffe.8 In SOL model, mixtures were represented in terms of their analytically determined structural groups. The classic lump model groups the compounds based on their similarity in boiling point, however this similarity does not imply similar chemical structure. Similarly, this SOL model groups the compounds based on their structural groups. An independent kinetic model without lumping was developed by Peng.21 In this model, the main idea is to express the mixtures in terms of a mix of predefined model molecules that needed properties determined experimentally. The main obstacle of this method is that the molecules in a mixture can be represented with only a limited number of different molecules. Heavy oils and their fractions contain relatively higher molecular weight species, which is troublesome to determine their physical and chemical properties experimentally. The detailed modeling of complex mixtures, which consist of a large number of higher molecular weight species such as asphaltenes, has become possible due to the increasing CPU power of computers and improvements to the resolution of analytical chemistry. Detailed modeling covers various types of information about molecules such as density, boiling point distribution, H/C ratio, molecular weight and structure of atoms and bonds. This analytical data forms the basis of molecular modeling. In contrast to the models based on various clusters and pre-defined molecules discussed above, the Klein Research Group (KRG) has developed a promising


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detailed molecular level model founded on the idea of the Probability Density Function (PDF).22– 25

The statistical distribution approach gives reasonable results for representation of the

properties of the complex hydrocarbon mixtures. The gamma function has good flexibility, which can be expressed using two or three parameters and has important special cases. The gamma distribution can match the exponential, chi-square and normal distributions with suitable parameters. Schulz26 and Flory27 found that the molecular weight distributions of polymers were explainable by distribution functions. The gamma function was then used for fitting molecular weight and boiling point distributions by Whitson et al.28 Gamma distribution was successfully applied to 44 petroleum samples in the range of light condensates to heavy oil and they reported that the absolute average residuals were 1 g/mol for molecular weights and 3 K for boiling points. Different statistical approaches also exist in literature. For instance, Pedersen et al.29 showed that the exponential distribution is another good candidate to fitting the properties of the oil fractions in their work with 17 North Sea oil samples containing carbon numbers above 7. Molecular weight distribution of the primary coal pyrolysis products was successfully fitted with gamma distribution function by Darivakis et al.30 Nigam et al.31 extended the use of distribution functions from the molecular weights and boiling points to the structural parameters. Thus, the Stochastic Reconstruction (SR) method became available which let to Neurock25 and Trauth32 utilizing the SR method to model asphaltenes and resids respectively. The main idea behind the SR model, after determining the analytical properties of the complex mixture, is to form a great number of molecules by using suitable mathematical distributions of the structural parameters. These structural parameters include the number of aromatic and naphthenic rings, substitution numbers, side chain lengths, and other properties reflecting the features of the complex mixture. Once a reasonable number of molecules successfully represents the mixture, these representative molecules are converted into products via the reaction networks, which are generated automatically by specific rules. Although the SR method contains detailed information at the molecular level compared to other methods, the basic parameter set is limited and that restrains the adaptation potential of the


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model for heavy oil fractions. For example, the ring configuration of the molecules does not described comprehensively. In this paper, an extended parameter set has been proposed for SR method in order to increase its adaptation capability. The benefits of this study that enhance the existing literature are summarized as follows: 1. The classic parameter set does not include a parameter that defines the ring configuration. Ring compactness33 is a concept that describe the ring configurations for a given ring number. Although the effect of ring compactness is insignificant for molecules with small number of rings, the effect increases as the number of rings increases. Similarly, when the number of the naphthenic rings is increased the impact of their attachment positions becomes significantly important. Generation of molecules with a well-defined ring structure is ensured in this study by including the ring compactness and naphthenic ring neighborhood parameters. 2. Two parameters related to chains are also incorporated to SR algorithm. One is controlling the benzylic methyl fraction of the side chains attached to the aromatic rings and the other is a side chain branching parameter that eliminates the number of branches assumption of the classic parameter set. 3. Three more parameters for heteroatoms (Sulfur, Nitrogen and Oxygen) are also defined and incorporated to the SR algorithm. Forms and quantitative ratios of these heteroatoms are taken into account based on the information gathered from the literature. 4. This is the first work that uses six different hydrogen classes based on 1H NMR spectrum in the objective function. This detailed approach ensures an extensive connection between the generated molecules and the experimental data.

2. Description of The Structural Parameters Used In Molecular Reconstruction Algorithm Number of Unit Sheets. The number of polycyclic aromatic hydrocarbon (PAH) determines the architecture of asphaltenes. Some studies indicate that asphaltene molecules consists of single unit sheet.34,35 On the other hand, various studies suggested that multi-unit sheets are also possible.36,37 Single unit sheet asphaltenes are referred to as an island architecture while


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multisheet asphaltenes are named as archipelago architecture. Taking into account the different views in the literature studies, the number of unit sheet (NUS) is considered as an adjustable parameter and used in molecular reconstruction algorithm. Number of aromatic and naphthenic ring. Asphaltenes consist of various repeating structural units. Aromatic and naphthenic ring are the basic units. The number of aromatic ring (NAR) parameter controls only the number of aromatic rings; the configuration of the rings is controlled by another parameter. Similarly, the number of naphthenic ring (NNR) parameter controls the number of naphthenic rings. The placement of the naphthenic rings is also controlled by a dedicated parameter. Ring compactness. The configuration of the aromatic rings is controlled by the ring compactness (RC) parameter. The configuration of the aromatic assembly refers to a unique molecular formula. In this study, the compactness concept that introduced by Hirsch and Altgelt33 is used in order to define the ring configurations. For instance, heptacene and coronene molecules both have seven aromatic rings but coronene has a more compact structure compared to heptacene, as shown in Figure 1. The molecular formulae and the number of peripheral carbons of these two molecule are different. Ring compactness parameter is implemented to unit sheet generation algorithm (Figure 8) to take into consideration of these differences.11 However, by using three aromatic rings a phenanthrene or an anthracene molecule can be generated. The contribution of these isomers was considered to be identical and generated stochastically as a result of the two structural isomers containing identical molecular formula and comprising of the same number of peripheral carbon5.

Figure 1. The effect of RC over structural configuration.


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Naphthenic ring neighborhood. In the process of molecule generation, a naphthenic ring may be a neighbor to an aromatic or a naphthenic ring. This selection has an effect on number of aromatic peripheral carbon atoms, which is directly related to aromatic hydrogen content of the molecule.11 The naphthenic ring neighborhood (NRN) parameter is defined between 0 and 1. When it is equal to 1, all the naphthenic rings are neighbors to aromatic rings. In contrary to this, if it is equal to 0, after the first naphthenic ring has connected to an aromatic ring, the rest of the naphthenic rings are connected to naphthenic rings. For instance, 5 of the possible positions around tetralin eliminate at least 1 aromatic hydrogen while only 3 positions can have a naphthenic ring without changing the number of aromatic hydrogens as shown in Figure 2.

Figure 2. Possible ring positions and types around tetralin. Side chain/aromatic peripheral carbons. This parameter is a measure of number of side chains on aromatic (SCA) rings. In other words, SCA parameter represents the ratio of number of side chains on aromatic rings to number of total aromatic peripheral carbons. When a side chain has attached to the aromatic ring, an aromatic hydrogen decreases at the connection point. Implications of this parameter are on not only the number of aromatic hydrogens but also number of alpha/beta benzylic, methylene (Beta+) and methyl (gamma) hydrogens. Benzylic methyl. The benzylic methyl (BM) parameter is defined as a fraction of SCA parameter. The methyl functional group, which is directly connected to an aromatic ring, is considered as a special side-chain that is independent from the side-chain length (SCL) parameter. The main motivation behind this approach was the increasing flexibility of the model. Unless the occurrence of benzylic methyl group is determined by a separate parameter, it would be strictly dependent to the SCL parameter.11 The fraction of benzylic methyl hydrogens is relatively small compared to the fraction of paraffinic methylene hydrogens. This indicates that


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any change on the value of the SCL parameter has a greater influence on the ratio of benzylic methyl hydrogens rather than the ratio of paraffinic methylene hydrogens, which is important from the perspective of objective function. A descriptive example for the relation between SCA and BM parameters is shown in Figure 3.

Figure 3. Relation between SCA and BM parameters. Side chain/naphthenic peripheral carbons. Naphthenic rings can also have aliphatic side chains as well as aromatic rings. The probability of the aliphatic side chains connected to naphthenic rings is governed by side chains on naphthenic (SCN) rings parameter. Multiplication of the number of naphthenic peripheral carbons and the SCN parameter gives the number of the substitution off naphthenic carbons. This parameter has effects on number of naphthenic, methylene (Beta+) and methyl (gamma) hydrogens. Side chain length. The number of side chains, which are connected to aromatic and naphthenic rings, is controlled by using SCA and SCN parameters. These parameters only determine the number of connection points as mentioned before. The length of these chains is controlled by SCL parameter. The length of the any aliphatic chain used in molecule construction algorithm (Figure 8) is controlled by this parameter. SCL parameter primarily determines the number of methylene (Beta+) hydrogens in the molecule. Methyl branches on chains. Branch points on side chains are also taken into account in the molecule construction algorithm. These branches are considered as methyl groups while the occurrence frequency of these branch points on main chain is controlled by the methyl branches on chain (MBC) parameter. The number of main chain carbons minus 2 is defined as the maximum and 0 is accepted as minimum (no branch).


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The possible branch points are scaled between 0 and 1 by using these limit values. A representative example for MBC parameter is shown in Figure 4. This parameter mainly has an effect on methyl (gamma) hydrogens.11

Figure 4. Relation between the limits of possible branching points and MBC parameter. Sulfur. Studies in literature based on FT-IR and sulfur-33 NMR analysis shows that most of the sulfur in heavy petroleum fractions is aromatic and aliphatic.38 Moreover, the detailed XPS and XANES studies corroborate the presence of thiophene sulfur and sulfide sulfur in asphaltene samples.39,40 Based on these studies, thiophene and sulfide are presumed as sulfur-containing functional groups and the distributions of these two groups considered as 65% and 35%, respectively. The number of sulfur atoms in each unit sheet controlled by sulfur parameter (SP) while the form of the sulfur is determined by the ratios defined above. Nitrogen. According to the literature nitrogen occurs only in aromatic forms in asphaltenes and these aromatic forms of nitrogen are namely pyrrolic and pyridinic.41 Quantitative XANES studies on petroleum asphaltenes have revealed the ratios of these nitrogen forms. Pyrrolic nitrogen distribution is considered as 70% and the rest of the nitrogen atoms are accounted as pyridinic form depending on literature.40–42 The form of the nitrogen is designated by the ratios mentioned above and the number of nitrogen atoms in each unit sheet controlled by nitrogen parameter (NP). Oxygen. Although the literature presents considerable information on the forms and ratios of sulfur and nitrogen groups, there is no detailed study on quantification of oxygen forms. Several studies indicate the oxygen forms qualitatively. Main oxygen forms are considered as phenolic, carboxylic and quinonic according to literature.42,43 Because of the lack of quantitative data, oxygen forms are equally distributed among the named oxygen forms during the molecule


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construction process. Oxygen parameter (OP) only controls the number of oxygen atoms in each unit sheet.

Table 1. Parameter sets and used distribution functions. Parameter Name / Parameter

Basic +

Basic +

Basic +

Basic +

RC

BM

MBC

NRN

Basic Set

Extended

Number of Unit sheets

Γ

Γ

Γ

Γ

Γ

Γ

Number of aromatic rings

Γ

Γ

Γ

Γ

Γ

Γ

Number of naphthenic rings

Γ

Γ

Γ

Γ

Γ

Γ

Ring Compactness

U

Γ

U

U

U

Γ

Naphthenic ring neighborhood

U

U

U

U

Γ

Γ

Side chains on aromatic rings

Γ

Γ

Γ

Γ

Γ

Γ

Benzylic methyl parameter

U

U

Γ

U

U

Γ

Side chains on naphthenic rings

Γ

Γ

Γ

Γ

Γ

Γ

Side chain length

Γ

Γ

Γ

Γ

Γ

Γ

Methyl branches on chains

U

U

U

Γ

U

Γ

Sulfur

Γ

Γ

Γ

Γ

Γ

Γ

Nitrogen

Γ

Γ

Γ

Γ

Γ

Γ

Oxygen

Γ

Γ

Γ

Γ

Γ

Γ

“Γ and U represents gamma and uniform distribution, respectively.”


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Figure 5. Representation of the different hydrogen types

3. STRUCTURAL PARAMETER SET OPTIMIZATION ALGORITHM The combination of the defined structural parameters determines the accuracy of the SR model. All post-build property calculations related to the generated mixture such as density, H/C ratio, boiling point distribution are based on these parameters. In order to find the best combination of these parameters, an optimization algorithm is employed. First, a molecule reconstruction algorithm is coded in order to include all parameter sets given in Table 1, and then each parameter set is optimized by using a genetic algorithm (GA). Optimization and the stochastic molecule construction algorithms that have been used in this study are given in Figure 6 and Figure 8, respectively.


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Figure 6. Structural Parameters Optimization Algorithm Structural Parameter Set Optimization Algorithm. Optimization starts by creating a random initial population for defined parameter set and then the algorithm generates a sequence of new populations. Members of the current generation used to create the next population at each step based on their scores. The fitness function value of each member of the population represents its score. The fitness function used in this study is given by the following generalized equation.


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#஺஽

‫ = ܨ‬ඩ෍ ቆ ௜ୀଵ

‫ܦܣ‬௜

ா௫௣.

− ‫ܦܣ‬௜௉௥௘ௗ.

‫ܦܣ‬௜

ா௫௣.

ቇ

ଶ

(1)

Where AD is the number of the analytical data present. In this study AD comprises the average molecular weight, weight percentages of the C, H, S, N and O elements as well as the percentages of the six different hydrogen types shown in Figure 5. In order to obtain percentages of hydrogen types the 1H-NMR spectra are divided into regions (according to ref.44). These types and their ppm ranges are also given in Table 2. Table 2. Types and ppm ranges of hydrogens.44 Region 1 2 3 4 5 6

Range (ppm) 6.40 – 9.00 2.40 – 3.40 2.00 – 2.40 1.28 – 2.00 1.00 – 1.28 0.50 – 0.95

Proton Types Aromatic α-CH, α-CH2 α-CH3 β-CH2, CH/CH2 Naphthenic β-CH3, β+-CH2, Paraffinic CH2 γ-CH3

The scores are evaluated and then the population members that have promising fitness values are chosen as parents. The members of current population that have best scores are chosen as elites. These elite members are also transferred to the next generation. The current population is used to generate the children that create the next population. There are three types of children. The first is elite children, in which members are in the current generations directly transfer to the next generation based on the best scores. The second is crossover children, which are generated by combining the elements of a pair of parents. The last one is mutation children that are generated from a single parent by introducing random changes. GA continues to produce new generations until at least one of the stopping criteria is satisfied. Modified Stochastic Unit Sheet Generation Algorithm. Unit sheet generation algorithm (Figure 8) starts with checking if the combination of NAR and RC parameters exists in core library. If the related core was not generated before, the algorithm starts to generate random core configurations based on NAR and test whether it obeys Hückel’s rule of aromaticity simultaneously. In this point, the classical SR algorithm assumes that the contribution of each


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possible core to be identical but the atomic force microscopy (AFM) and scanning tunneling microscopy (STM) images of asphaltene molecules indicates compact structures rather than equally distributed structures. Schuler et. al.37 proposed chemical structures for asphaltene molecules based on AFM measurements and STM orbitals images. The RC values of those proposed structures having more than five rings ranging between about 0.2 and 1 with a mean value of 0.67. In this manner, we have considered the RC (Figure 1) as a controllable parameter in our algorithm. Unless the ring compactness of the randomly generated core configuration based on NAR satisfies the RC parameter, algorithm continues to generate random core configurations. When the RC condition is met, the algorithm saves the structure to the core library and advances to build molecule structure. Once the aromatic core structure is formed, naphthenic rings are attached to the core based on NNR and NRN. Decision of the placement positions of naphthenic rings differs from the classical SR algorithm. While the classical algorithm randomly places the naphthenic rings to the aromatic core, our algorithm classifies the suitable positions as aromatic or naphthenic neighborhoods and places the naphthenic rings based on NRN as shown in Figure 2. Then the algorithm attaches the five membered heteroaromatic structures (Thiophenic and Pyrrolic) to the suitable positions of the generated ring structure. When the generation of bare polycyclic core is completed, in order to determine the number of alkyl substituents the algorithm multiplies the number of peripheral aromatic and naphthenic carbon atoms by SCA and SCN, respectively. At this point, our algorithm reserves a certain amount of alkylaromatic substituents for benzylic methyl groups based on BM parameter as described in Figure 3. The length of each of these alkylaromatic and alkylnaphthenic substituents is determined by stochastically sampling from SCL distribution. Our algorithm also adds methyl branches to these chains based on MBC as defined in Figure 4, while the classical algorithm assumes no branching. Then these alkylaromatic, alkylnaphthenic and benzylic methyl substituents are attached to the related peripheral carbons of the polycyclic core. The remaining heteroatoms are incorporated to the structure based on the SP, NP, OP and predefined rules. For instance, a nitrogen atom substitutes with a random peripheral carbon atom of a six membered aromatic ring in order to form a pyridinic structure. Similarly, a sulfur atom


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substitutes with a random carbon atom of a side chain to obtain sulfide form. Phenolic and quinonic structures are generated by attaching –OH and =O functional groups to the peripheral aromatic carbon atoms while the carboxylic oxygen form generated by attaching –COOH functional group to the end of the randomly determined terminal alkyl substituents. If the NUS parameter is greater than one, the resulting asphaltene molecule includes multiple unit sheets. In such cases, the unit sheet generation algorithm is called NUS times. When all unit sheets are generated, a random terminal aliphatic chain of each unit sheet is selected as bridging chain and all unit sheet are connected to each other with these bridging chains to form archipelago type asphaltene molecules.


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Figure 7. Some of the stochastically generated asphaltene structures in this work


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Figure 8. Modified stochastic unit sheet generation algorithm Finally, the proposed parameter sets are coded in Matlab® with the parameters then optimized by using GA. The fitting performances of the different structural parameter sets are tested on the basis of analytical data (including 1H-NMR, elemental analysis and average MW by GPC) from


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our previous studies.16,45–47 The used analytical data belong to asphaltenes from Adiyaman, Batiraman, Besikli, Celikli, Garzan and Yenikoy regions of Turkey. 4. Application of The SR Algorithm with Extended Parameter Set To test the versatility of the extended parameter set, six petroleum asphaltene samples with different chemical compositions were stochastically reconstructed. The effects of the newly implemented structural parameters on fitting ability of the SR algorithm were evaluated by the means of the elemental, structural and compositional properties. The Number of Representative Molecules, Accuracy and Required CPU Time. Before comparing the performances of the structural parameter sets, the effect of the number of generations on fitness value is evaluated. The best fitness function value versus the number of generations is shown in Figure 9. It can be seen that the best fitness values tend to became stable after 60 generations and considered as constant after 100 generations for each asphaltene sample.

Figure 9. Relation between the number of generation and the best fitness value


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The standard deviation of the fitness function value and the computation time needed for each generation are highly dependent on the number of molecules used in simulations. The graphical representation of these dependencies can be seen in Figure 10.

Figure 10. Effects of number of stochastic molecules on Standard Deviation and computing time. The relationship between the number of molecules and the needed computing time for each generation is linear until the memory limitation (around 2GB per CPU core) of the used computing system. The memory limitation becomes important after 24000 molecules, which is indicated with the dash-dot lines in Figure 10 and considered as the upper limit for the number of molecules. The standard deviation of the fitness function is a nonlinear function of the number of molecules and this relationship described first by Klein Research Group.48 The upper limit for standard deviation value is chosen as 0.01 considering the reproducibility of the simulation results. The allowed upper limit for standard deviation is indicated with dash-dot orange line on standard deviation axis that corresponds to 9000 on the number of molecules axis. Considering these limitations, the feasible value of the number of molecules would be between 9000 and 24000. This interval is indicated by the green shade in Figure 10. The number of molecules is chosen as 20000 and used in all simulations.


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Figure 11. Parameter sets and fitness function values for asphaltene samples. The Effect of the Parameter Set on Fitness Value. The optimization processes were carried out on different asphaltene samples by using various sets of structural parameters. These structural parameters and applied distribution functions are given in Table 1. The best fitness values, after 100 generations, can be seen in Figure 11. The fitness value of the basic parameter set is taken as reference and one parameter added at a time in order to evaluate the effect of the new structural parameters on fitness function value. As shown in Figure 11, controlling RC along with the basic parameter set has only a slightly positive or not very negative effect on the fitness value. Likewise controlling the MBC in addition the basic parameters has a very small positive or negative impact on fitness function values. On the contrary, to these two parameters, the fitness function value is noticeably affected by the BMF and the NRN parameters. If expressed in numbers, controlling the NRN parameter provides a reduction of up to 80 % in the value of the fitness function. Similarly, the controlling of the BMF parameter provides a reduction of up to 50 % in the fitness function value.


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Table 3. Comparison between experimental46 and calculated properties of selected asphaltene samples by using basic and extended parameter sets

exp.

carbon hydrogen sulfur nitrogen oxygen Aromatic α-CH, α-CH2 α-CH3 β-CH2, CH/CH2 Naphthenic β-CH3, β+-CH2, Paraffinic CH2 γ-CH3

Adiyaman sim. sim. exp. (Basic PS) (Extended PS) Average Molecular Weight 861 855 989 Elemental Analysis 83.12 83.02 83.87 8.02 7.97 7.90 3.73 3.84 3.87 3.10 3.18 3.16 2.00 1.96 1.20 1 H-NMR 10.30 10.13 8.58 11.62 10.27 7.10 6.60 6.46 4.73

g/mol

858

wt % wt % wt % wt % wt %

83.52 7.51 3.80 3.17 2.00

% % %

9.97 10.17 6.45

%

30.61

28.42

31.50

%

25.63

25.22

%

17.17

Objective Function Value

Besikli sim. sim. (Basic PS) (Extended PS) 974

981

83.42 8.31 3.94 3.09 1.22

83,30 8,67 3,78 3,06 1,16

8.94 10.01 4.53

8,81 7,35 4,78

35.28

25.94

34,71

24.64

27.44

29.30

27,26

17.84

16.99

16.87

21.29

17,09

18.55

8.51

56.45

12.17

The extended parameter set includes RC, BMF, NRN and MBC parameters along with the basic parameter set. Composite effect of the controlling of all four additional parameters on fitness function is also shown in Figure 11. The Extended parameter set resulted in a decrease of the fitness value between 45% and 85% compared to the smallest parameter set. A comparison table that including the measured and fitted properties for selected asphaltene samples is given in Table 3. The results from both of the parameter sets (Basic and Extended) and their objective function values are also given.


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Figure 12. Parity plots for average MWs and elemental compositions based on used parameter set.

Elemental Composition of the Generated Molecule Sets. Once a stochastic molecule is generated, its properties can be calculated by using correlations or group contribution methods. In a similar way, the elemental composition and the molecular weight of the molecule can be calculated. Parity plots for the average molecular weight and the elemental analysis (including carbon, hydrogen, sulfur, nitrogen and oxygen) of the asphaltene samples, based on basic and


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Energy & Fuels

extended parameter sets, are given in Figure 12a−f where the 5% error lines are indicated. As shown in Figure 12a, the average molecular weights of asphaltenes were well predicted with both parameter sets. In terms of the elemental analysis of the asphaltenes, the carbon contents (Figure 12b) are all well predicted. The hydrogen contents (Figure 12c) are overestimated for all asphaltene samples with both parameter sets. We have no explanation for this, but this situation was also reported by other authors.49 As illustrated in Figure 12d the sulfur has the largest variability (2.1−8.8%) among the elements. The predicted sulfur contents are reasonably close to the experimental values. It is important to note the extended parameter set provided a better fit compared to the basic parameter set. The nitrogen and the oxygen are the elements that have the smallest presence and variability compared to the other elements (1.6−3.1% for nitrogen and 1.2−2.2% for oxygen). The nitrogen and the oxygen contents of the samples are also well predicted as shown in Figure 12e and 12f, respectively. It should be noted that the nitrogen and the oxygen contents are very low. In order to construct a well-balanced objective function, all terms in it are defined as unweighted relative errors between experimental and predicted values. Hence, the relatively small variables are also efficiently fitted.


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Figure 13. Parity plots for hydrogen types based on used parameter set.

Structural Composition of the Generated Molecule Sets. The number and types of the unique structural groups of generated molecules gives useful information that can be connected to its 1H NMR spectrum. In other words, the structural functional groups can be used not only to calculate the various physical and chemical properties but also the identification of hydrogen types in molecules.11 Hence, the amounts of six hydrogen types given in Table 2 can be calculated for the generated stochastic molecules. The various types and percentages of hydrogens in generated


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molecules are predicted and parity plots are given in Figure 13a-f. The aromatic hydrogen contents of the various asphaltene samples are well predicted by both parameter sets. As shown in Figure 13a, the advanced parameter set exhibits a slightly better fit for all samples, compared to basic parameter set. For alpha positioned -CH plus -CH2 hydrogens basic parameter set shows a poor fit while extended parameter set gives well-predicted results. The α-CH, α-CH2 hydrogens (Figure 13b) are overestimated for all asphaltene samples with basic parameter set. The fitting success of the extended parameter set for this type of hydrogens was due to the BMF parameter. The predicted BMF value of the Adiyaman, Batiraman, Besikli, Celikli, Garzan and Yenikoy asphaltenes were 0.70, 0.89, 0.66, 0.80, 0.76 and 0.49 respectively. The number of benzylic -CH and -CH2 hydrogens are effectively limited with this parameter and the overestimating is prevented. The predicted benzylic CH3 hydrogen contents of the asphaltenes are reasonably close to the measured values for basic and extended parameter sets. As shown in Figure 13b and 13c, the results achieved by using extended parameter set are almost on the diagonal line while the results obtained by basic parameter set are close to upper and lower error lines or out of these lines. The β-CH2 plus naphthenic hydrogens is well predicted for all samples using extended parameters (Figure 13d) while the basic parameter set is tending to underestimate this type of hydrogens. This superiority of the extended parameter set over basic parameter set is well explained by the effectiveness of the NRN parameter within the extended parameter set. The predicted NRN value of the Adiyaman, Batiraman, Besikli, Celikli, Garzan and Yenikoy asphaltenes were 0.50, 0.62, 0.34, 0.43, 0.52 and 0.40 respectively. The sum of β–CH3, β+–CH2 and paraffinic –CH2 hydrogens has been fitted successfully (Figure 13e) to experimental data by both parameter sets. As shown in Figure 13f, the extended parameter set was flexible enough to fit the all observed data for the γ and further positioned –CH3 hydrogens while the basic parameter set had trouble in fitting some of the data. It is important to note by using extended parameter set the number of unitsheet (NUS) values of the Adiyaman, Batiraman, Besikli, Celikli, Garzan and Yenikoy asphaltenes were 1.03, 1.56, 1.18, 1.18, 1.02 and 1.07 respectively. NUS values calculated with the basic structural parameter set were 1.19, 1.64, 1.08, 1.15, 1.04 and 1.15 in the same order. Architecture of the samples fit to the island type. Predominant molecular architecture for ashaltenes is also specified as island by Yen-Mullins.50 Moreover, Schuler et al.37 unraveled the architecture of the asphaltenes by using


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AFM and STM techniques. According to their study, island architecture is dominant for asphaltenes. Some of the asphaltene structures that have been generated in this study are given in Figure 7. Representative molecules for island architecture are shown in Figure 7a and Figure 7c. Archipelago structures are also presented in Figure 7b and Figure 7d.

Figure 14. Simulated DBE-CN plots of Adiyaman asphaltene based on basic (a) and extended (b) parameter sets. Compositional Spaces of the Generated Molecules. Asphaltenes are defined practically as nheptane-insoluble and toluene-soluble fraction of a fossil fuel source such as petroleum, tar sands and coal. The solubility definition of asphaltenes comprises a broad array of compounds of different structures. In order to determine the solubility class of a stochastically generated molecule, its solubility parameter needs to be calculated. The solubility parameter can be calculated by using the melting point and the enthalpy of fusion of the compound. These two properties can be predicted by using the structure of the molecule and a group contribution method. There are several group contribution methods in literature that represents different Average Relative Error (ARE%) values based on method and the predicted property. The Marrero and Gani51 method predicts the melting points and the enthalpy of fusion with an accuracy of 7.5 and 15.6 (ARE%) respectively, while the Joback52 method can only reach 14.6 (ARE%) for the melting point and 45.6 (ARE%) for the enthalpy of fusion. The


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Energy & Fuels

accuracy of the group contribution methods is unacceptable for both of the properties, therefore the solubility parameters calculated based on these predicted properties are considered as unreliable. Another approach for the solubility classification of a generated molecule is the use of the Solvent – Resid phase diagram.53 The solubility class of the generated molecule can be determined by using its molecular weight and hydrogen percent. However, the Solvent – Resid phase diagram was plotted by using the molecular weights measured with vapor pressure osmometer (VPO), so it is unable to use when the molecular weight is measured with another method. The recent studies are focused on the double bond equivalent (DBE) and carbon number (CN) concepts to define the compositional spaces for the heavy ends in fossil fuels.54–58 According to this approach, the asphaltenes and the maltenes can be separated with a boundary on the DBE – CN plot.58 In this study, the classification of the generated molecules is performed based on their DBE and CN values. The simulated DBE – CN plots are given in Figure 14. The black and orange lines on Figure 14a and 14b are represents the boundary between the asphaltene and the maltene compositional spaces57 and the theoretical upper limit59 for DBE/CN respectively. A larger part of the generated molecules by using the extended parameter set (Figure 14b) appears in asphaltene compositional space compared to molecules generated by using the basic parameter set (Figure 14a). A noticeable fraction of the generated molecules appears in maltene compositional space when the basic parameter used.


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Figure 15. Simulated DBE-CN plots on the bare stochastic molecule cores based on basic (a) and extended (b) parameter sets. In order to evaluate the compositional space of the generated molecule cores, DBE – CN plots are also given in Figure 15. Therefore, the side chains are subtracted from the structure of all generated molecules and the DBE – CN plots are simulated for the bare molecule cores. As shown in Figure 15a and 15b, all bare cores take place in asphaltene compositional space, no matter the used parameter set. However, the lowest DBE value for the molecules generated by using the basic parameter set is around 15, while the minimum DBE is near 20 for extended parameter set. Nevertheless, the position of the contour in Figure 15b is closer to the upper limit line of the DBE/CN compared to Figure 15a. This is explained with the RC parameter, increasing the structural compactness increases the DBE/CN ratio of the molecule, thus a higher DBE value can be reached by using the same CN. The predicted values of the RC parameters for the Adiyaman, Batiraman, Besikli, Celikli, Garzan and Yenikoy asphaltenes were 0.82, 0.59, 0.81, 0.81, 0.60 and 0.64 respectively. The more compact cores can have longer side chains without shifting to maltene space. This is also indicated in Figure 15, where for the same carbon number (CN=40), the more compact cores (RC=0.82 in Figure 15b) can have longer side chains (C-8 to C-30), while the less compact cores (RC≈0.5 in Figure 15a) have shorter side chains (C-5 to C-27).


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5. CONCLUSIONS

Adiyaman, Batiraman, Besikli, Celikli, Garzan and Yenikoy Asphaltenes obtained from six Turkish crude oils were reconstructed by using the SR algorithm with the extended parameter set in order to evaluate the performance of the proposed parameter set. The extended parameter set enables the control over the ring compactness, benzylic methyl fraction, naphthenic ring neighborhood and branches on side chains. The SR algorithm provided better results in terms of the fitting elemental compositions and structural configuration when used with extended parameter set for six different asphaltenes. The stochastic molecules generated by the extended parameter set successfully simulated the properties of the asphaltenes, despite the variability of the attributes of the different crude oils. The compositional space of the generated molecules was also simulated and it is validated that the generated molecules were in asphaltene space. According to these findings, the extended parameter set increases the fitting ability of the SR algorithm without sacrificing the compositional space of the generated molecules. In order to reflect the detailed structural composition of the samples to the stochastic molecules, 1

H NMR spectra of samples are divided into six regions and each term added to the objective

function. The set of molecules was generated and the hydrogen types in different regions were calculated. The comparison between calculated and analytical data show that the 1H NMR data were well mimicked. This fact reveals that the extended parameter set adapts well to a strictly defined objective function with respect to 1H NMR data. In conclusion, the extended parameter set is able to produce a better representation of asphaltenes by using its available analytical properties, compared to the basic parameter set. The mimicked molecule sets then allow performing additional simulations (for instance in this study DBE/CN graphs are simulated). The stochastically reconstructed molecule sets can therefore not only be used to reach to the molecular information that it is analytically unavailable but also provide a better starting point for molecule based kinetic models.


Energy & Fuels

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It is recommended that further studies should focus on algorithms that including conditional probabilities related to DBE concept, allowing the side chains to attach to the molecule cores based on their DBE number. This may ensures a better placement for the contours on DBE/CN plots. It is also recommended that the training of an artificial neural network (ANN) or a support vector machine (SVM) by using inputs and outputs of the GA driven SR algorithm may help to drastically decrease the time needed for the parameter optimization step.

ABBREVIATIONS AD = Analytical Data ANN = Artificial Neural Network ARE = Average Relative Error BM = Benzylic Methyl CN = Carbon Number CPU = Central Processing Unit DBE = Double Bond Equivalent FTIR = Fourier Transform Infrared (Spectroscopy) GA = Genetic Algorithm GB = Gigabyte GPC = Gel Permeation Chromatography KRG = Klein Research Group MBC = Methyl Branches on Side Chains MW = Molecular Weight NAR = Number of Aromatic Ring NMR = Nuclear Magnetic Resonance NNR = Number of Naphthenic Ring NP = Nitrogen Parameter NRN = Naphthenic Ring Neighborhood NUS = Number of Unit Sheets


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Energy & Fuels

OP = Oxygen Parameter PAH = Polycyclic Aromatic Hydrocarbon PDF = Probability Density Function PS = Parameter Set RC = Ring Compactness SCA = Side Chains on Aromatic Rings SCL = Side Chain Length SCN = Side Chains on Naphthenic Rings SOL = Structure Oriented Lumping SP = Sulfur Parameter SR = Stochastic Reconstruction SVM = Support Vector Machine VPO = Vapor Pressure Osmometer XANES = X-ray Absorption Near-Edge Structure XPS = X-ray Photoelectron Spectroscopy

ACKNOWLEDGMENTS This work was supported in part by the Research Fund of University of Istanbul, Project Number: 41216. Celal Utku Deniz would like to thank The Scientific and Technological Research Council of Turkey (TÜBĐTAK) for research grant 2214A/2014.

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A New Extended Structural Parameter Set for Stochastic Molecular

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