Effect of Boiling Point and Density Prediction Methods on Stochastic

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Effect of Boiling Point and Density Prediction Methods on Stochastic Reconstruction Celal Utku Deniz, S. Hande Ozoren Yasar, Muzaffer Yasar, and Michael T Klein Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b00018 • Publication Date (Web): 21 Feb 2018 Downloaded from http://pubs.acs.org on February 23, 2018

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Effect of Boiling Point and Density Prediction Methods on Stochastic Reconstruction Celal Utku Deniza,b, S. Hande Ozoren Yasarc, Muzaffer Yasara,*, Michael T. Kleind,e a

Chemical Engineering Department Istanbul University Avcilar, Istanbul 34820

b

c

d

Chemical Engineering Department Hitit University Corum, 19030

Vocational School of Technical Science Istanbul University Avcilar, Istanbul 34820

Chemical and Biomolecular Engineering Department University of Delaware Newark, Delaware 19716 e

Center for Refining and Petrochemicals King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia Abstract Stochastic Reconstruction (SR) methods are used to generate a series of molecules that mimic the properties of complex mixtures using partial analytical data. Determining a quantitative composition using these methods is limited by the property prediction methods used. This paper addresses the use of two key measurements in the characterization of petroleum fractions, namely, density and boiling point distributions. It is known that the different methods used in estimating these two basic properties have varying error rates. Boiling point prediction performances of the various group contribution methods were tested via the molecular library established for molecules that can be found present in the petroleum fractions. It has been observed that the combined use of these methods results in close to a 50% reduction in sum of squared errors than any single method. The predictive performances of the density calculation methods were similarly tested. The best-calculated density results

*

Corresponding author: [email protected]

1 ACS Paragon Plus Environment

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were found via the Yen-Woods method with support from the linear mixing rule based on molar fractions.

1. INTRODUCTION The quality and impurity limitations of petroleum-derived fuels are subject to change, depending on the increasingly stringent environmental legislations. These limitations have led models made on the classical lump approach1–3 to fail to provide the desired precision. The main reason for this is that the molecular level information, which is required to comply with environmental constraints, can not be predicted using lumping strategy. This lack of lumping has motivated the development of molecular level models. One of the biggest challenges in the development of such models is not only the existence of a large number of molecules in petroleum feedstocks, but also the difficulties encountered in characterizing these complex mixtures. In the characterization of petroleum and fractions, the most advanced analytical techniques are used, such as high-resolution Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS)4–10. Its purpose is to identify a large number of compounds and their chemical classes. Atomic force microscopy (AFM)11,12 to be used in examination of the detailed structure of an isolated molecule. Despite the use of advanced techniques, not all of the molecular details of the petroleum and its fractions can be quantitatively measurable. The scarcity of molecular information can be overcome by using molecular reconstruction algorithms. These algorithms generate sets of molecules that mimic the properties of the fraction to be reconstructed using analytical data, model assumptions, and basic chemical information. This approach, which requires the individual generation of each molecule used in the representation of the mixture, is based on two fundamental principles. The first of these is that each molecule in petroleum fractions can be expressed using the aromatic and naphthenic ring numbers, substitution numbers, chain lengths, etc., as well as the molecule type according to these identifiers. The second principle is that the identifiers mentioned in the first principle can be expressed by probability distribution functions (PDFs). Once the structural parameters are expressed using PDFs, each is stochastically sampled and used to reconstruct a molecule. This procedure is commonly referred to as stochastic reconstruction (SR).13–16


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Reconstruction depends on the developed molecule generation algorithm and the available analytical data. The analytical data can provide basic information such as density and viscosity or atomic information such as elemental analysis, atomic connectivity through nuclear magnetic resonance (NMR) spectroscopy, boiling-point distribution by simulated distillation (SIMDIS), fractional compositions such as saturates, aromatics, resin, asphaltenes (SARA) or paraffins, isoparaffins, olefins, naphthenes and aromatics (PIONA). The molecule generation algorithm generates the molecules based on the defined structural building diagram through sampling the PDFs of the structural identifiers.17,18 Once a molecule has been constructed, its properties such as boiling point and density are calculated by group contribution methods (GCMs) or correlations, while properties such as chemical formula, atomic connectivity and molecular weight can be directly deduced from the structure defined by its connection table. This process is repeated N times to produce N molecules. The number of molecules (N) is determined by taking into account the stochastic structure of the algorithm (reproducibility) and efficient use of time.19–21 When the molecule generation process is complete, mixing rules are applied to calculate the properties of the mixture. An objective function that compares these calculated values with analytical data is defined. This objective function is nondifferentiable due to the stochastic nature of the problem and is generally minimized via simulated annealing22–24 and genetic algorithm methods.15,18,21 Throughout the optimization process, the location and scale parameters of each structural identifier’s PDF are adjusted to form the most compatible set of molecules with analytical data. Much progress has been made in the area of stochastic reconstruction, since the Klein research group (KRG)25–27 has shown that structural identifiers can be expressed by the distribution functions. For instance, a quadrature approach was used to reduce the number of molecules formed to reconstruct the mixture.28 The use of multiple linear regression models29 and artificial neural networks30,31 were investigated, and a new set of structural identifiers was proposed.21 Recently, biomass has been reconstructed through an additionally elaborate set of PDFs in order to model the gasification process at the molecular level.32 Studies in the literature are generally focused on the stochastic reconstruction algorithms13,21,24,33, the acceleration of the optimization process13,30, and the kinetic behaviors of the generated molecules.18,19,34 However, there is a lack of studies on the effect of boiling point and density prediction methods on the molecular reconstruction procedure. The necessity for


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improvement in the calculation of reconstructed mixture density has also been pointed out in the literature.35 In this paper, a molecular reconstruction algorithm based on the "probability density function" concept has been developed in order to represent complex mixtures. Differences and benefits of this improved algorithm, which are different from the existing literature, are summarized as follows: There are several group contribution methods in the literature that have been developed for predicting the physical and chemical properties of the pure compounds. These methods present varying accuracies for different molecules. In order to evaluate these methods, the molecules used in this study were divided into groups according to their molecular weights. Therefore, molecular weights are calculated first, followed by boiling point via the suitable group contribution method. This suitable group contribution method is based on the initially calculated molecular weight. The difficulty in the prediction of density is a known issue for mixtures. The mixture densities are generally calculated by using equations of state or correlations, which offer different accuracies for different groups of molecules. The effect of the mixing rule and calculation methods over predicted mixture density is evaluated with results in this paper.

2. THEORETICAL ASPECTS 2.1. Group Contribution Methods Simulation of any chemical process is based on the physical and chemical properties of the involved components. It is not always easy or possible to obtain the desired experimental values and measurements, as they are costly and time consuming. Some physical and chemical properties of compounds can be estimated based on their chemical structure using group contribution methods. Different structural parameters and their frequencies usually have different influences on the related properties. There are several group contribution methods to predict properties pure compounds. Some of these properties are boiling point, critical temperature, critical pressure, critical volume and acentric factor. Moreover, using these methods with EOSs and correlations can be used to


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calculate the properties of a mixture such as density and the boiling point distributions within certain error percentages. The common group contribution methods are Joback, Gani and Nannoolal.36–38 These methods result in varying accuracies for different molecular weight ranges. The Joback method36 is the simplest method when compared with the others, as it has only 41 different structural groups. The Nannoolal38 and Gani37 methods have 133 and 370 structural groups, respectively. These methods are based on regression analysis of experimental data. The database used by Joback36 consists of about 400 pure compounds. Gani37 and Nannoolal38 methods were developed through the use of larger datasets; the first is based on approximately 2000 pure compounds while the latter is based on 2850 compounds. The Nannoolal method38 focuses only on the estimation of normal boiling points. Critical temperature, critical pressure, critical volume, standard enthalpy of formation, standard enthalpy of vaporization, standard Gibbs energy, normal melting point and standard enthalpy of fusion properties can be estimated by using the Gani method.37 The Joback method36 can estimate all the properties of Gani’s method37, as well as the viscosity and heat capacity. Additionally, acentric factors are calculated using the Constantinou method.39 2.2. Density Calculation Methods The density of a pure component can be calculated by using two different approaches. The first method is related to molar volume, which can be calculated by using an equation of state (EOS). The molar volume of compound is calculated first by EOS, while the molecular weight of the compound is divided by the molar volume to obtain density. The second approach uses a correlation method to calculate the pure component density. In order to compare these different approaches, densities are calculated using two different EOSs, volume translated variations of these EOSs, and a correlation method. Soave modification of Redlich – Kwong (SRK)40, Peng – Robinson (PR)41, temperature dependent volume translated Soave modification of Redlich – Kwong (SRK TVT)42, temperature dependent volume translated Peng – Robinson (PR TVT)43 EOSs and Yen – Woods44 correlation method are used to calculate the densities of pure compounds. A molecule library consisting of 150 different molecules is employed to evaluate and compare these density calculation methods. The molecular weight of these molecules varies from 67 – 422 g/mol while the boiling point


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varies from around 400 to 800 K (experimental and predicted properties of all 150 molecules presented in the Supplemental Information). These density calculation approaches usually apply to pure compounds, but estimation of the densities of liquid mixtures is more important in chemical processes. Pseudo-critical constants are used for critical constants required by the EOSs to calculate liquid mixture densities. These constants are calculated based on molar and weight fractions of the components in the mixture.

3. METHODS AND ALGORITHMS

3.1. Classifications of Compounds Petroleum fractions consist of a large number of molecules. Due to this, in order to develop a model to represent these mixtures the composing compounds of the mixtures need to be classified. There are two main reasons for classification. The first is related to having more analytical data about the mixtures, while secondly such classification simplifies modelling of the mixture. Representation of the hydrocarbon mixtures by individual molecules requires a systematical approach. In order to accomplish an agreement between analytical data and computer generated mixtures, each generated molecule in the mixture has to be connected to analytical data systematically. The first connection between molecular structure level variables and analytical data has been established by Trauth et al.26,45 Their studies describe a strong relationship between structural parameters and the corresponding distribution functions. The second connection between analytical data and the molecules to be generated can be established via the experimental and predicted properties of the mixture.25 Compounds in petroleum fractions can be classified as n-paraffinic, isoparaffinic, aromatic, and naphthenic. Aromatic compounds can be described by their unique properties such as aromatic ring number, naphthenic ring number, aromatic substitution degree, naphthenic substitution degree, chain lengths of these substitutions, and ring compactness factor.


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Similarly, the naphthenic compounds can be described by naphthenic ring number, naphthenic substitution degree, and chain lengths. n-Paraffinic compounds require specification with chain length number only. Characterization variables of an isoparaffinic compound are chain length, branch point, and branch lengths. Sulfur is generally found in two different forms, as thiophenic and sulfidic in petroleum fractions.46–49 Sulphur-containing molecules may be characterized by aromatic ring number, naphthenic ring number, substitutions of these rings, and chain lengths of related substitutions.

3.2. Minimum and Maximum Values of Structural Parameters The probability density function of a structural parameter can be formulated using minimum, maximum and average values of the related parameter.27 Optimization of the average value is described later in this paper. In this section the calculation methodology of the minimum and maximum values of the structural parameters is described. This simple approach is based on boiling points, especially the initial and final boiling points. The relationship between structure and boiling point can be established on the basis of group contribution methods. The lowest and highest boiling points, and even the weight fractions based on boiling points of complex mixtures, may be easily determined using analytical methods. The initial boiling point of a fraction determines the lower limits of the structural parameters while the final boiling point determines the upper limits of the parameters. The frequency of the structural parameters directly affects the boiling point. From this perspective, lower and upper limits of the boiling points restrict the number of repeated structural building blocks. For instance, n-paraffinic compounds are described by their chain lengths. This parameter controls the boiling point of molecules. If the value of chain length is systematically changed during this process, the corresponding boiling point can be calculated. Minimum and maximum chain lengths may be determined by comparison of the calculated boiling points and the initial and final boiling points. This approach is also valid for other molecular classes. Another benefit of this method is related to conditional probabilities. This feature can be summarized as the interrelations of the structural parameters in a molecule. For instance, the


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side chain length that benzene can have before crossing the upper boiling point boundary is greater than that of naphthalene. The minimum and maximum values of the structural parameters and conditional constraints are determined by systematically changing the parameters within the upper and lower bounds of the boiling points.

3.3. Generation of Virtual Molecules Generation of a virtual molecule consists of several steps. The first step is choosing the molecule class. Molecule class can be aromatic, naphthenic, n-paraffinic, or isoparaffinic. When the molecule class is chosen the next step is determining the structural parameters belonging to that class. Each structural parameter has an individual distribution function and the algorithm stochastically samples from these functions.

Figure 1. Elements of basic structural parameters vector. A virtual molecule can be represented by using three vectors. The first vector contains the data related to the number of basic structural parameters. As shown in Figure 1, the first and third elements of this vector determine the aromatic ring number and aromatic substitution number respectively. Similarly, the second and fourth elements determine the naphthenic ring number and naphthenic substitution numbers. If the number of aromatic substitutions is equal to n, the values of the 5th to (4 + n)th elements of the basic structural parameters vector are the chain lengths of the aromatic substitutions. In the same manner, if the number of naphthenic substitution is equal to m, the (5 + n)th to (4 + n + m)th elements of the basic structural


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parameters vector represent the chain lengths of the naphthenic substitutions. Examples of implementing this approach are shown in Figure 2.

Figure 2. Examples of basic structural parameters vector. The second vector contains the ring compactness factor described in the following subsection. This parameter affects the molecular structure when the number of aromatic rings of the molecule is equal or greater than four. In order to visualize how this parameter influences the molecular structure, a practical example is given in Figure 3.


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Figure 3. Effect of ring compactness factor (RCF). The third vector is related to isoparaffinic structure. Each element in this vector represents a carbon atom in the paraffinic chain and the values of these elements represent the branch length linked to the corresponding carbon atom. The number and lengths of branches are determined by using related distribution functions. Examples of branching vectors are shown in Figure 4. A representative molecule that includes all three of the molecule identification vectors is also shown in Figure 5.

Figure 4. Examples of branching vectors.


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Figure 5. A representative molecule containing all three identification vectors. When all desired variables are sampled, the next step is the generation of the molecular structure. The molecular structure is required for determining the structural groups and their frequencies in order to calculate the physical properties of the molecule via group contribution methods. For instance, the virtual molecule (connection table) of benzene is shown in Figure 6. The first step of the virtual molecule generation procedure is determining a central point in Cartesian coordinate system. Coordinates of six carbon atoms are then positioned around that central point to form a hexagon which is then further used to generate a ring structure. When the atom placement process ends for the ring, the bonding process begins. In this case, since it is an aromatic ring, each carbon atom needs three bonds aside from the sole carbon – hydrogen bond. The algorithm connects the atoms by using basic bonding rules. In addition, the type column in Figure 6 indicates the group that the atom belongs to; 1 specifies the atom is a member of an aromatic ring, 2 indicates the atom is a member of naphtenic/cycloparaffinic ring, while 0 indicates the atom is a member of a chain. Similarly in the atom column, 6 indicates carbon, 7 indicates nitrogen, 8 indicates oxygen, etc. When a new molecule is generated, its existence in the database is investigated. If the molecule is not found in the database, it is saved in the database and invoked from the database when it is needed again. Further details of the parameters and molecule generation algorithm are given elsewhere.21,30,31


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Figure 6. Representing benzene and its connection table. 3.3.1. Ring Compactness Factor In fused ring systems with a fixed ring number, the number of internal carbon atoms can always be formalized by a linear equation based on the ring number, however the number of peripheral carbon atoms cannot be formalized.50 The number of peripheral carbon atoms is not only related to the ring number but it is also associated with the structure formed by the rings. Unlike the isomers, structures formed through use of the same number of rings may causes change to the molecular formula. In such cases, ring compactness factor determines the structure. As shown in Figure 3 the same number of rings can form different structures. Details of the ring compactness concept is given by Hirsch and Altgelt.50

3.3.2. Branched Paraffins Isoparaffinic compound class is usually described by chain length, branch number, and branch lengths. If the branch number and the branch length parameters are defined independently of chain length, the longest chain length can be altered during the molecule generation process. Alternatively, if the branching number is considered as the maximum number of branches that a straight chain can possess, it must be defined independently for varying chain lengths. In order to simplify the algorithm, a relationship (branching ratio) is established between the number of branches and chain length. Branching ratio (BR) is obtained by normalizing branch number (BN) according to the equation (1). The BR values thus obtained vary between 0 and 1. This ratio represents the number of branches based on longest chain length. For example a value of 0 indicates the isoparaffinic compound contains only one branch point, while a value of 1 indicates the isoparaffinic compound has the maximum number of branch points corresponding to chain length minus two.


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(1)

BR and BN in equation (1) refer to the branching ratio and the branching number respectively. The subscripts Min and Max represent the possible minimum and maximum branching numbers based on the chain length. The relationship between the branching ratio and the branch number for a given chain length is shown in Figure 7.

Figure 7. Branching ratio and branching number.

The branch length ratio is quite similar to branching ratio. This ratio is determined by the mapping approach, in which the longest chain length is determined first and then all branching points are filled with the longest possible chains. This must be accomplished without exceeding the main chain length. Detailed representation of mapping is shown in Figure 8.


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Figure 8. Longest chain length and mapping. As shown in Figure 8, maximum chain lengths of all possible branches are determined by fixing the longest chain length. It can be seen that a BR value of 0 results in branch length of 1, while the branch length of BR values greater than zero is determined by the branch pointlength map. Detailed chromatographic studies in the literature show that the isoparaffinic compounds with branches longer than methyl are not present in petroleum in any applicable amounts.51,52 Considering this information during the simulations, the branch length is limited to methyl by fixing the BR parameter to zero.

3.4. Structural Parameter Optimization Algorithm Average values of the structural parameters determine the fitting performance of the model. All calculated properties of generated mixture such as density, H/C ratio, and boiling point distribution are based on these parameters. In order to find the most appropriate values of these parameters, an optimization algorithm is employed. First, the proposed model is coded in Matlab© then the parameters are optimized by using genetic algorithm. The optimization algorithm that has been used in this study is shown in the flowchart as depicted in Figure 9.


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Figure 9. Structural parameters optimization algorithm. Optimization begins via generating a random initial population for average structural parameters between lower and upper limits. The algorithm then generates a sequence of new populations. Members of the current generation are used to generate the next population at each step. The objective function used in this study is given by the equation (2).

(2)

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MW, H/C and SimDis represent the average molecular weight; hydrogen to carbon atomic ratio and simulated distillation. Fraction number in simulated distillation is expressed as i in


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equation (2). Experimental and predicted values of these parameters are subscripted by Exp. and Pred. The objective function values (OFVs) are calculated, while members with promising OFV are then selected as parents. Members of the current population with low OFV are chosen as elites. These elite members are transferred directly to the next generation. Chosen members of the current population are used to generate the next population. There are three types of members in the next generation; elite members, crossover children, and mutation children. Elite members of the current generation are directly transferred to the next generation based on their OFVs. Crossover children are generated by combining the elements of a pair of parents. Mutation children are generated from a single parent by introducing random changes. The genetic algorithm continues to produce new generations until one of the stopping criteria is met. In this study, population size and crossover fraction are selected as 500 and 0.8, while the OFV and number of generation limits are selected as 10-4 and 100 respectively. In addition, the multi-core central processing unit (CPU) support is utilized and no time limit employed in the optimization process.

3.5. Complex Mixture Generation Algorithm Molecule generation algorithm is developed to generate individual molecules based on the molecular class. In order to generate a complex mixture this algorithm should be employed systematically. Paraffinic, isoparaffinic, naphthenic and aromatic (PINA) distribution is the major element of the complex mixture generation process. The algorithm starts with randomly choosing the molecular class of the first molecule. The molecule is then generated by sampling each structural parameter distribution of the selected molecular class. The algorithm compares the number of generated molecules with the targeted molecule number during molecule generation procedure. If the number of generated molecules is equal to the number of desired molecules, the algorithm outputs the generated complex mixture. If the number of molecules produced is less than the target number, the algorithm determines the deviations by comparing the generated molecular class distribution with the experimental ones. The class which shows the maximum deviation is then chosen to be the molecular class of the following molecule to be generated. This algorithm iterates until a desired molecule number is reached.


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The basics of this algorithm is shown in Figure 10. When the mixture generation step has completed, its calculated properties which include boiling point distribution, density, molecular weight and H/C ratio are compared with the experimental data. The parameters of distribution functions are optimized by using the genetic algorithm described in Figure 9.

Figure 10. Generation of complex mixtures.

4. RESULTS AND DISCUSSION 4.1. Boiling Point Prediction for Pure Compounds Evaluation of group contribution methods was conducted via prediction of the normal boiling points of pure compounds. The predicted boiling points are compared with the experimental ones from the aforementioned molecule library. For each group contribution method, boiling point prediction shows a slight deviation from experimental boiling point (Figure 11). The coefficient of determination of these group contribution methods is approximately 0.99 for the molecule library. The intercepts of the lines are fixed to 0 and slopes are calculated between


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0.97 and 1.03. Gani and Nannoolal methods were found to predict lower boiling points on average, while the Joback method predicted higher values when compared to experimental values. Residual sum of squares (RSS) for each method is also shown in Figure 11. RSSs of Joback, Gani and Nannoolal methods are calculated as 220733, 59872 and 64731 respectively. The boiling point prediction performance of the Gani method is found to be high when compared to Joback and Nannoolal methods for the utilized molecule library.

Figure 11. Boiling point prediction performances of the methods. As seen in Figure 11, each method has significant deviations for some of the compounds. In order to minimize these deviations, boiling points are associated with molecular weights. The plots of experimental and predicted boiling points versus molecular weights are shown in Figure 12. From Figure 12, using Joback method, high deviation for compounds with molecular weights (>200 g/mol) is observed. With Gani method the boiling point predictions are slightly less than the experimental boiling point of compounds with molecular weight greater than 250 g/mol.


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Figure 12. Boiling point deviations based on molecular weight and prediction method. The compounds in the library are separated according to their molecular weights and then each compound’s boiling point in all fractions is predicted by the GCMs. This procedure involves determining the best GCM based on the molecular weight range. The corresponding mean absolute percentage errors (MAPEs) for the predicted values of each molecular weight fraction are shown in Table 1.

Table 1. Error Comparison of Group Contribution Methods for Different MW Ranges MW (g/mol) 50 - 100 100 - 150 150 - 200 200 - 250 250 - 300 300 - 450

Joback 2.7 1.9 2.2 3.3 6.5 15.3

MAPE Gani 4.5 2.7 1.6 3.5 5.2 5.9

Nannoolal 4.0 2.2 2.8 2.3 2.0 2.6


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Based on minimum error criteria, the Joback method is chosen for MW in the range of 50 – 150 g/mol, the Gani method for 150 – 200 g/mol range and Nannoolal method for greater than 200 g/mol. The plot of predicted boiling point values by combined GCM versus experimental boiling point is shown in Figure 13. The coefficient of determination was found to be greater than 0.99, with RSS of 29292. This indicates the combined GCM approach gives a better fit compared to using any GCM alone.

Figure 13. Performance of the combined GCM.

4.2. Density Calculation of Pure Compounds SRK, PR, SRK TVT, PR TVT EOSs and Yen – Woods methods were used to calculate densities of the pure compounds in the molecule library. The required critical thermodynamic parameters are calculated by using Gani and Joback methods and the corresponding acentric factors are calculated using Constantinou method. MAPEs of these methods are shown in Figure 14. When the critical thermodynamic parameters are estimated using Joback method,


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the MAPEs of the calculated densities are higher than those calculated via the Gani method for all density calculation methods used in this study.

Figure 14. Error evaluation of calculated densities by various methods. The MAPEs of the calculated densities with EOSs are higher than the values reported in literature. For instance, Ahlers and Gmehling43 reported error values of density calculations using SRK, PR and PR-TVT EOSs for pure compounds as 13.09%, 6.66% and 2.47% respectively. Similarly Ji and Lempe42 reported 1.80% for SRK-TVT EOS. These lower error values are obtained using experimental values of the critical thermodynamic parameters of the compounds. In this study, the critical thermodynamic properties are calculated using GCMs and therefore each critical property is determined with a certain margin of error. These prediction errors adversely affect the density, which is calculated through the use of these parameters. As shown in Figure 14, the Yen – Woods correlation is the least sensitive method to errors in the prediction of the critical thermodynamic properties compared to other methods.

4.3. Application to Complex Mixtures Densities of mixtures are calculated by using five different methods. Pseudo-critical parameters which are used in these methods are determined by employing molar and weight basis mixing rules. In order to evaluate the density calculation methods, density is excluded from the objective function and calculated separately by using aforementioned methods. The


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experimental data used in this study were adopted from the literature35 and belong to six different samples.

Table 2. Mixture Density Determination Errors for Different Methods Method SRK SRK-TVT PR PR-TVT Yen Woods

Mixing Rule Molar Weight Molar Weight Molar Weight Molar Weight Molar Weight

NGC1 1.48% -7.04% 3.19% -5.48% 14.42% 4.67% 15.12% 5.32% -0.46% -8.63%

NGC2 6.10% -1.84% 7.45% -1.34% 19.55% 10.49% 20.17% 11.00% 3.33% -7.16%

Errors MD1 -4.74% -6.85% 1.13% -1.24% 6.94% 4.56% 7.81% 5.40% 3.71% 1.27%

MD2 -3.67% -8.69% 0.98% -2.71% 7.99% 2.36% 8.90% 3.35% 3.12% 0.64%

HGO -12.77% -16.76% -3.28% -6.89% -2.44% -6.92% -1.14% -5.60% 5.17% 1.84%

VGO -24.03% -26.89% -10.96% -14.50% -15.17% -18.38% -13.44% -16.74% 0.25% -3.31%

MAE 8.80% 11.35% 4.50% 5.36% 11.09% 7.90% 11.10% 7.90% 2.67% 3.81%

As shown in Table 2, densities calculated on a weight basis are lower than those of calculated molar basis for different samples and different methods. Weight-based SRK and SRK-TVT methods led to lower values than experimental values for all samples. Both of the SRK methods exhibit smaller error values for lighter fractions when compared to heavier fractions in the majority of cases. SRK methods are more suitable for lighter fractions and less suitable for heavier fractions. As compared the EOS methods, the Yen – Woods method presents more stable error values for different fractions. Mean absolute errors (MAEs) are also calculated and given in Table 2. Yen – Woods method is chosen as a default density calculation method for further calculations as a result of its low MAE value and relatively large range of application.

Table 3. Experimental and Calculated Properties of NGC Samples

Density P Wt. frac. I Wt. frac. N Wt. frac. A Wt. frac.

Exp. 0.7110 0.175 0.325 0.347 0.152

NGC1 Calc. 0.7111 0.175 0.325 0.347 0.152

Ref.35 0.7244 0.177 0.326 0.346 0.151

Exp. 0.7380 0.143 0.149 0.356 0.351

NGC2 Calc. 0.7400 0.142 0.148 0.355 0.350

Ref.35 0.7672 0.150 0.150 0.352 0.347


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Sulphur Wt. %

0.028

0.028

0.022

0.120

0.120

0.120

Experimental and calculated values of the properties for two different natural gas condensate (NGC) samples are shown in Table 3. This table also includes calculated values from another study.35 It will be cited throughout the paper as "reference study" since the previous work has been extensively addressed. Calculated properties including densities are in agreement with experimental values. The calculated properties from reference study are also in concordance with the experimental values. The major difference is in calculated density values, as values in this study are closer to measured values when compared to the reference study.

Figure 15. Boiling point distributions for NGC1 (a) and NGC2 (b) samples.

Figure 15 shows the calculated, experimental and reference study boiling point distributions for NGC samples. The calculated curve exhibits a good match with the experimental data and the reference study. Table 4. Experimental and Calculated Properties of MD Samples

Density P Wt. frac. I Wt. frac. N Wt. frac. A Wt. frac.

Exp. 0.7987 0.143 0.211 0.458 0.188

MD1 Calc. 0.7987 0.143 0.211 0.458 0.188

35

Ref. 0.8174 0.143 0.211 0.458 0.188

Exp. 0.7980 0.235 0.254 0.341 0.171

MD2 Calc. 0.7990 0.235 0.254 0.341 0.171

Ref.35 0.8249 0.238 0.252 0.338 0.172

Experimental, calculated and reference values of analytical properties for two different middle distillate (MD) samples are shown in Table 4. Calculated and reference values shown in Table 4 are reasonably close to experimental values. Densities calculated in this study are closer to


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experimental values when compared to the reference study. Calculated PINA distributions are also in agreement with experimental values to a greater extent than the reference study.

Figure 16. Boiling point distributions for MD1 (a) and MD2 (b) samples.

Figure 16 shows the calculated, experimental and reference boiling point distributions for MD samples. The calculated and reference curves for MD samples exhibits good fit with the experimental data. There was no significant improvement on boiling point distributions for NGC and MD samples. The main improvement is observed in heavier fractions such as Heavy Gas Oil (HGO) and Vacuum Gas Oil (VGO). As shown in Figure 17(a) the reference model tends to predict the boiling point distribution lower than experimental values while the proposed model presents a better fit. The reason behind this better agreement is can be explained by the new proposed combined GCM approach and the ring compactness factor included in the model.

Figure 17. Boiling point distributions for HGO (a) and VGO (b) samples.


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Different structures can be obtained through using the same aromatic ring number. Moreover, these structures are not structural isomers as shown in Figure 3. The diversity of the generated molecules in the complex mixture is increased by using the ring compactness factor. This diversity creates possibility for better fit through increased model flexibility. Table 5. Experimental and Calculated Properties of HGO and VGO Samples

Ma Density H/C P Wt. frac. I Wt. frac. N Wt. frac. A Wt. frac. Sulphur Wt. %

Exp. 300.4 0.8621 0.156 0.245 0.378 0.221 0.148

HGO Calc. 300.4 0.8621 0.155 0.243 0.374 0.218 0.146

35

Ref. 300.4 0.8465 0.156 0.246 0.378 0.220 0.148

Exp. 0.9030 1.995 0.061 0.241 0.478 0.220 -

VGO Calc. 0.9030 1.988 0.061 0.241 0.478 0.220 -

Ref.35 0.8420 1.963 0.054 0.250 0.478 0.219 -

Calculated and reference properties for HGO and VGO samples are shown in Table 5 with corresponding experimental data. Calculated properties in this study and the reference study are in a good agreement with the experimental data.

5. CONCLUSION The boiling point prediction performances of Joback, Gani and Nannoolal group contribution methods were evaluated. The Gani method was found to have lower prediction error compared to others for the utilized molecule library. The RSS value of 59872 belonging to the Gani method is lower than the Joback and Nannoolal methods RSS of 220733 and 64731, respectively. There are significant deviations for some compounds in each method. To reduce these deviations, different GCMs were used in a combined method. The boiling points were associated with the molecular weights of the compounds and the most appropriate GCMs were determined for different molecular weight ranges. A significant improvement was observed with this approach in predicting the boiling points of molecules in the molecular library. The RSS values calculated from predicted boiling points with combined GCM was found to be 29292. This value is approximately half of that found via the Gani method, which is considered the best available method.


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The densities of molecules in the molecular library were calculated through SRK, PR, SRK TVT, PR TVT EOSs and Yen - Woods methods. The required critical parameters were estimated via Gani and Joback GCMs. In addition, linear mixing rules were applied to find the mixture densities. The critical thermodynamic properties predicted by the Gani method have been found to be more successful in calculating the densities of the molecules in the molecule library in comparison to the Joback method. The MAPEs of the calculated densities for SRK, PR, SRK-TVT, PR-TVT and Yen-Woods methods were found to be 24%, 16%, 12%, 15%, and 5.7% when the critical parameters were predicted through Joback method. When the Gani method is used, MAPEs were found as 19%, 10.5%, 10%, 9% and 5.2% in the same order. For the density calculations of the mixtures, a linear mixing rule based on the molar fraction resulted in lower errors in the SRK, SRK TVT and Yen - Woods methods, while a linear mixing rule based on the weight fraction resulted in lower errors in the PR and PR TVT methods. Mixture densities calculated by the mole fraction basis linear mixing rule for SRK, SRK TVT and Yen-Woods methods were approximately 5% closer to the experimental results. Furthermore, the Yen-Woods method has been found to have the lowest MAPE value in the calculation of the densities of both pure compounds and stochastically reconstructed complex mixtures. The implementation of the ring compactness factor and the combined GCM approach based complex mixture generation algorithm had a positive influence on calculated densities. For six different samples, calculated mixture densities were closer to experimental values without making significant sacrifices on the other properties. Furthermore, the boiling point distribution of HGO sample was better fit by virtue of these improvements. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. ORCID Celal Utku Deniz: 0000-0003-0948-9626 Muzaffer Yasar: 0000-0001-5877-8008 Michael T. Klein: 0000-0001-5444-1512 Notes The authors declare no competing financial interest. 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


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Research Council of Turkey (TÜBĐTAK) for research grant 2214A/2014. Michael T. Klein acknowledges collaborations with and support of colleagues via the Saudi Aramco Chair Program at KFUPM and Saudi Aramco. NOMENCLATURE AFM = Atomic Force Microscopy BN= Branching Number BR = Branching Ratio CPU = Central Processing Unit EOS = Equation of State FT-ICR-MS = Fourier Transform Ion Cyclotron Resonance Mass Spectrometry GCM = Group Contribution Method HGO = Heavy Gas Oil KRG = Klein Research Group MAE = Mean Absolute Error MAPE = Mean Absolute Percentage Error MD = Middle Distillate MW = Molecular Weight NGC = Natural Gas Condensate NMR = Nuclear Magnetic Resonance OFV = Objective Function Value PDF = Probability Density Function PINA = Paraffins, Isoparaffins, Naphthenes and Aromatics PIONA = Paraffins, Isoparaffins, Olefins, Naphthenes and Aromatics PR = Peng – Robinson RCF = Ring Compactness Factor RSS = Residual Sum of Squares SARA = Saturates, Aromatics, Resin, Asphaltenes SIMDIS = Simulated Distillation SR = Stochastic Reconstruction SRK = Soave modification of Redlich – Kwong TVT = Temperature dependent Volume Translated VGO =Vacuum Gas Oil REFERENCES (1)

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