Quantitative StructureâProperty Relationship Model for Hydrocarbon

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Quantitative Structure Property Relationship (QSPR) Model for Hydrocarbon Liquid Viscosity Prediction Guangqing Cai, Zhefu Liu, Linzhou Zhang, Suoqi Zhao, and Chunming Xu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b04075 • Publication Date (Web): 07 Feb 2018 Downloaded from http://pubs.acs.org on February 10, 2018

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Quantitative Structure Property Relationship (QSPR) Model for Hydrocarbon Liquid Viscosity Prediction Guangqing Cai1, Zhefu Liu1,2, Linzhou Zhang1*, Suoqi Zhao1 and Chunming Xu1 1

State Key Laboratory of Heavy Oil Processing, China University of Petroleum,

Beijing, 102249, P. R. China 2

Center for Refining and Petrochemicals, King Fahd University of Petroleum and

Minerals, Dhahran, Saudi Arabia Abstract The liquid viscosity of hydrocarbon compounds is essential in the chemical engineering process design and optimization. In this paper, we developed a Quantitative Structure Property Relationship (QSPR) model to predict the hydrocarbon viscosity at different temperature from chemical structure. We collected viscosity data at different temperatures of 261 hydrocarbon compounds (C3-C64), covering n-paraffins, iso-paraffins, olefins, alkynes, monocyclic and polycyclic cycloalkanes and aromatics. We regressed the experimental data using an improved Andrade equation at first. Hydrocarbon viscosity vs. temperature curves were characterized by only two parameters (named B and T0). The QSPR model was then built to capture the complex dependence of the Andrade equation parameters on the chemical structures. 36 key chemical features (including 15 basic groups, 20 united groups and molecular weights) were manually selected through trial-and-error process. An artificial neural network (ANN) was trained to correlate the Andrade model parameters to the selected chemical features. The average relative errors for B and T0 predictions are 2.87 % and 1.05 %, respectively. The viscosity vs. temperature profile was calculated from the predicted Andrade model parameters, reaching mean absolute error at value of 0.10 mPa·s. We also proved that the established QSPR model can describe the viscosity vs. temperature profile of different isomers, such as iso-paraffins with different branch degrees and aromatic hydrocarbons with different substituent positions. At last, we applied the QSPR model to predict gasolines and diesels viscosities based on the measured molecular composition. A good agreement was observed between predicted and experimental data (absolute mean deviation equals 0.21 mPa·s), demonstrating that it has capacity to calculate viscosity of hydrocarbon mixtures. Keywords: QSPR; Viscosity; Group Contribution; Artificial Neural Network

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1. Introduction Liquid viscosity is an important property which is widely used in chemical engineering process simulation. The measurement of liquid viscosity is expensive and time consuming. Take petroleum for example, most of the measured molecules does not commercially available to reach testable quantity. In most cases, the experimental viscosity data of targeted compounds at targeted temperature is absent. Therefore, developing a reliable model to predict viscosities under different conditions is particularly significant. Liquid viscosity is highly sensitive to the chemical structure, temperature and pressure. Building a predictive model for liquid viscosity is a great challenge for decades. A lot of efforts have been devoted in the past to develop liquid viscosity theory, trying to capture its intrinsic nature. Various mechanistic models were proposed to describe liquid viscosity variation at different temperatures and pressures. The most representative models are friction theory and expand fluid theory. Sergio et al[1] proposed a viscosity prediction model to calculate viscosities of n-alkanes from low to high pressures on the basis of friction theory and Van der Waals theory. Since then, they developed a three-single-parameter model combined friction theory with cubic equations of state, which were then applied on light oils, medium oils and heavy oils systems.[2-4] Yarranton et al[5] presented a three-parameter correlation based on expand fluid theory to calculate viscosities of hydrocarbons, heavy oils, and heavy oil mixtures. Motahhari et al[6] and Ramos-Pallares et al[7] applied the expand fluid theory to the mixtures and petroleum system using binary interaction parameters. These works have highlights in predicting the fluid viscosity variation at high temperature and high pressure and play an important role in the field of oil and gas reservoir. But it is worth noting that these mechanism models often involve excess number of parameters which were obtained by regression. The calculation process is sometimes complicated. In most of chemical engineering processes, the liquid is under medium or low pressure environment. In this circumstance, the impact of pressure on the liquid viscosity is negligible. As consequence, pure component liquid viscosity can be considered only varied with temperature. The relationship between viscosity and temperature can be described by numerical empirical equations. For instance, the Andrade[8] equation is a two-parameter model. Another viscosity equation proposed by Korsten[9] is a three-parameter model. The number of parameters depends on the desired precision and application temperature range. On this basis, the prediction of


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liquid viscosity vs. temperature profile becomes to the problem of estimating the empirical equation parameters. Joback and Reid[10] proposed a classic group contribution method which used 41 molecular groups to predict physical properties (covering the fluid viscosity ) of organic compounds. In addition, the group contribution methods presented by Lydensen[11], Klincewicz [12] and Lyman[13] are also widely used. In these methods, the structure of a molecule is represented by a series of functional groups. The property of a molecule is equal to the sum of contributions of various functional groups. Constantinou and Gani[14] developed a two-level group contribution method, containing primary and secondary groups which are used to identify and distinguish isomers. Then, Marrero et al[15] designed a three-level group contribution method which has more complex form and higher accuracy. Van Velzen[16] proposed a correlation among liquid viscosity, temperature and chemical structure according to the De Guzman-Andrade equation, characterizing chemical structures in terms of detailed molecular functional groups. However, in their work, equivalent chain length of compounds was regarded as main parameters and could not be applied to aromatic compounds. Allan et al[17] used effective carbon atoms as parameters to predict the liquid viscosity. The advantage of group contribution methods is the convenience in computation process. The disadvantage is that the group contribution methods may not be able to distinguish some isomers. Furthermore, the mathematical variability of contribution models that ever adopted may not be strong enough to explain the contribution of chemical structures to viscosity vs. temperature profile. In recent years, Quantitative Structure-Property Relationship (QSPR) methods have drawn much attention in computing the thermodynamic properties of compounds. Take octane number for example, it has been accurately predicted by a QSPR model coupled with machine learning techniques developed by Liu[18] et al. As for predicting liquid viscosities, the QSPR method developed by Suzuki[19] gave good results by multivariate linear regression and partial least-squares regression technology. The QSPR model presented by Cocchi et al[20] estimated viscosities of a series of pure organic compounds with structural formula X-CH2CH2-Y at 25 oC by multivariate linear regression. The model comprised a data set of 46 compounds with 16 molecular descriptors and the square correlation coefficient was 0.9497. Rajappan et al[21] proposed a QSPR model which consists of 403 compound data sets and received a good outcome using a random forest regression algorithm. Nevertheless, it takes up to 116 descriptors that are inconvenient to apply. The QSPR model involving in a


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database of 212 compounds developed by Kauffmann et al[22] coupled multiple linear regression with computational neural network methods to calculate liquid viscosities. Saldana et al[23-25] developed some QSPR models to predict liquid densities, viscosities, flash points, Cetane Number of pure compounds, as well as flash points of fuel mixtures. The models used functional groups and molecular descriptors to estimate these physical properties through machine learning methods respectively and obtained good results. The QSPR approach has the advantage in stronger variability and descriptiveness by using a large number of chemical descriptors in conjunction with advanced data mining algorithm. The drawback is that some chemical descriptors (such as critical parameters) are not directly available for compounds. Some chemical descriptors are indirect representations of chemical structures. An excess of chemical descriptors applied in the QSPR model may lead to over-fitting problems. The viscosity vs. temperature characteristic of liquid compounds is completely determined by their structures. The main purpose of this work is to find the primary chemical features that determines the viscosity vs. temperature profile. Those chemical features were then utilized to construct a QSPR model based on artificial neural networks (ANN). The QSPR model was expected to be able to predict viscosities of pure hydrocarbons and mixtures at different temperatures.

2. Methodology Figure 1 shows an entire process for predicting the viscosity vs. temperature profile of pure component compounds in the present work. It is composed of three main

sections,

including

data

collection/preparation,

chemical

features

generation/selection, and QSPR model construction. At the first stage, the viscosity vs. temperature data of pure hydrocarbons were gathered from API data book[26] and NIST database ( through NIST ThermoData Engine in Aspen Plus V9). After then, a multiple linear regression method was employed to obtain improved Andrade equation parameters by fitting the viscosity vs. temperature data. A dataset of molecular viscosity model parameters was created. At the second phase of this work, the chemical structure parameters of molecular structures were manually generated and evaluated through an ANN model. This process was repeated until a satisfactory error was obtained, after which a key chemical feature dataset was obtained. At the final step, the QSPR model was tuned to establish the mathematical relationship between acquired chemical feature and Andrade equation parameters. An acceptable


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error was obtained by continually training the ANN network. After all the above step, the QSPR model has capacity of predicting Andrade model parameter, from which the viscosity at different temperatures can be also calculated.

3. Data Collection The accuracy of a QSPR model of liquid fluid viscosity prediction depends on the quantity, quality, and diversity of data in the database. Building a comprehensive and reliable database is crucial to the model construction. The prime target application system of this study is petroleum fraction. Hence the application range of the model is mainly on hydrocarbons. In the present work, viscosity data of 261 pure hydrocarbons at different temperatures were collected, covering the carbon number range from C3 to C64. The chemical class and number of species is listed in Table 1. The database including 31 n-paraffins, 52 iso-paraffins, 33 monocyclic and polycyclic cycloalkanes, 76 olefins and alkynes, 69 monocyclic and polycyclic aromatic hydrocarbons. Most of these compounds are in line with the molecular structure characteristics of petroleum. The Andrade equation is capable is predicting absolute viscosity at wide temperature using 2 regressed parameters. An improved Andrade equation[27] was adopted here (shown in equation1).

= exp[( − )]

(1)

Where μ is the viscosity, T is the targeted temperature, B and T0 are two parameters of the equation. It was chosen because of the higher accuracy of this equation in calculating liquid viscosities and it has only two parameters that relatively easy to regress. The viscosity vs. temperature data of all the compounds were regressed by multiple linear regression technique (MLR) to get parameters B and T0 of the modified Andrade equation. The fitted B and T0 in the modified Andrade equation for all the compounds in the database achieved a satisfactory accuracy (the average relative error is 0.92 %). Afterwards, the major work was focused on finding the correlation between molecular structures and the modified Andrade equation parameters B and T0.

4. Generation and Selection of Chemical Features The viscosity vs. temperature profile of liquid compounds is mainly determined by molecular structures. At this stage, the primary goal is to generate and select chemical features that has significant impact on Andrade model parameters. The number of groups should be controlled at considerable low value so that the


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over-fitting problem can be lowered down. Initially, basic groups were employed to describe molecular elementary chemical characteristics, and then a series of united groups were designed to distinguish the isomers. The combination of multi-level groups is aiming to obtain structural features that adequately describe all the hydrocarbon molecules in the database. Basic groups should be able to represent all hydrocarbons, including paraffins, naphthenes and aromatics. While adding a basic group, an important criterion is that the basic group should have the simplest structures and does not allow the basic group to overlap with each other in a molecule. For example, comparing -CH2-, -CH3 and -CH2CH3, the former two groups should be added into the basic groups, and the last one should be removed since it can be represented by combining basic groups. Basic groups should also have ability to distinguish between cyclic and acyclic structures. Good performance has been obtained by using cyclic and acyclic groups to identify cyclic and acyclic structures. A collection of 15 basic groups was defined which were referred to Joback's group contribution method. They have the capacity of reflecting molecular fundamental structural features. However, it is worth noting that there are a large number of isomers in the database which have the same basic group values. Their viscosity vs. temperature properties vary from each other at different degree. The traditional group division cannot differentiate these isomers. We list two isomer series to reveal this phenomenon. Ethyltoluene from aromatic hydrocarbons (Table 2) and tetramethylpentane from isoparaffins (Table 3) are listed as examples. The two series of isomers have the same basic groups, but their viscosities, especially their low-temperature viscosities are quite different. In order to differentiate these isomers, some additional structural fragments, namely united groups, were generated to improve the model descriptive capacity. These united groups were generated by manually comparing experimental data and summarizing structural diversities. An evaluation function should be used to judge the contribution of generated structural fragment. The artificial neural network (ANN) was adopted to evaluate the generated groups and to observe whether they could distinguish among isomers. The ANN model technique can be considered as a general method of dealing with nonlinear problems. It has been applied in various fields, such as calculating the physical and thermodynamic properties of different pure compounds. The structure of selected ANN is shown in Figure 2. Figure 2 displays a schematic diagram of a three-layer neural network used in this work, including input layer, hidden layer and output layer. The basic groups were


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initially served as ANN inputs and parameters B and T0 are the ANN outputs. The number of hidden layer nodes is determined by trials-and-errors. The activation functions applied in the hidden and output layers are tansig and purelin functions, respectively. The learning algorithm that used to train ANNs is the Back Propagation (BP) algorithm, which selects the Bayesian Regularization (BR) training function. Generally, the database is divided into three subsets, containing training sets, validation sets, and test sets. The training set is used to generate the ANN model structure. The validation set is to evaluate and select models. The test set is to estimate the generalization ability of models in practical application. In evaluation section, all the data in the database were put into the ANN as training set. In other words, the training set ratio was set to be 100 %. The effectiveness of united groups was evaluated according to the ANN result errors. If a united group has significant contribution to Andrade model parameter, after adding it into ANN input, the overall training accuracy will be improved. The united groups were created and selected manually on the basis of empirical and chemical knowledge. Whenever a new united group was proposed, it would be put into the evaluation model. If the prediction error was significantly improved (especially for target isomers), then the united group would be accepted, vise versa. After repeating the above process, a series of united groups were finally obtained (see in Table 4). The model universality was also taken into account in the present work. The number of united groups must be minimized in order to lower down the over-fitting problem. In contrast to basic groups, united groups can overlap one another in a molecule. According to these guidelines, the isomers of alkanes, alkenes, cycloalkanes and aromatics in the database were selected by classification. By means of analyzing four different types of isomer structures, the crucial information of isomerization of paraffin side chain, substitutional locations of cycloalkanes and aromatic hydrocarbons and double bonds of olefins were characterized by united groups. The minimum number of groups was employed to identify and distinguish these isomers. The model’s improved effect was observed though additions and tests repeatedly. In addition, molecular weights were also added as chemical features. For one thing, the addition of molecular weights greatly improved the model’s accuracy. On the other hand, the addition of molecular weights was expected to improve the model performance while extrapolating to higher molecular weight range. It’s worth pointing out that some chemical features, such as the ratio of hydrogen to carbon and ring numbers, have also been added during trial-and-error process. However, these


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chemical features showed no significant improvement on training accuracy and were discarded during the selection process. Figures 3 and 4 show the comparison between experimental and predicted parameters B and T0 using different chemical features as inputs. When the accuracy of evaluation model is lower, it means that used chemical features are not able to accurately describe the Andrade model parameters. It can be seen from Figure 3 that the correlation coefficients for parameter B predictions are 0.9084, 0.9660 and 0.9938 while using molecular weights (a), basic groups (b), and molecular weights + basic groups + united groups (c) as inputs for the 100 % training set, respectively. As shown in Figure 3 (a), a certain tendency is observed by using only molecular weights as inputs. It is in consistent with knowledge that larger molecules will have higher viscosities. However, unsurprisingly, the training accuracy is poor since molecular weight itself cannot adequately reveal the viscosity difference. As displayed in Figure 3 (b), when the basic groups are used as inputs, the correlation coefficients have been greatly improved. Nevertheless, the overall deviation is still large since these basic groups cannot identify the isomers. While using molecular weights, basic groups and united groups together as inputs, the prediction accuracy obtained from evaluation model has been greatly enhanced. It is obvious that most features affected B parameters have been selected. Similarly, Figure 4 shows the comparison of T0 experimental with predicted values for different chemical feature sets. Their correlation coefficients varied from 0.8921 to 0.9983. The only difference is that the training results are already remarkably well when using the basic groups as inputs (Figure 4 (b)). It demonstrates that parameter T0 is easier to regress than B and less insensitive to isomer structure. Figures 3 and 4 demonstrates that the corresponding correlation coefficients increase with chemical features which have more detailed structures. The molecular weights, basic groups and united groups are sufficient to describe relationship between Andrade equation parameters and chemical structures.

5. QSPR Model Development Since the evaluation model put all the data into the ANN model training set, it can only reflect the group's descriptive ability. But the obtained model will have overfitting problem due to the absence of validation and testing sets. In other words, although the accuracy seems to be considerable, it cannot be directly applied to predict viscosity of molecules that is not included in the training datasets. In this section, a generalized QSPR model was constructed by using the selected chemical


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features. The database was divided into training sets, validation sets and test sets to retrain the model. The database of 261 monomer hydrocarbons was divided into a training set, a validation set and a test set, each accounting for 80 %, 10 % and 10 % of the total number of samples. To ensure that the validation set and test set cover different hydrocarbon

structures,

a

certain

percentage

of

n-paraffins,

iso-paraffins,

cycloalkanes, alkenes, and aromatics were included in the validation set and test set. The QSPR model used the ANN as correlation method as well. The layers and amounts of hidden layers in the ANN model were constantly adjusted to search optimal combination of parameters. Through repeating attempts, the optimal result is a single hidden layer neural network with 12 hidden layer nodes. Two three-layer neural networks (using molecular weights, basic groups and united groups as inputs) with structures 36-12-1 and 36-12-1 were developed to predict parameters B and T0, respectively. Table 5 lists the optimal parameters for ANN. Through the above steps, the QSPR model of estimating viscosities of pure hydrocarbons was obtained by combining group contribution method and artificial neural network. Liquid viscosities of hydrocarbons at any temperatures can be calculated by the modified Andrade equation using predicted parameters B and T0. Figure 5 shows the parity plots of experimental and predicted Andrade model parameters B (a) and T0 (b) for developed ANN model. For training set, validation set and test set of parameter B, the correlation coefficients are 0.9938, 0.9991 and 0.9871 respectively. The average relative errors are 2.86 %, 1.09 % and 4.08 %. For training set, validation set and test set of parameter T0, the correlation coefficients are 0.9988, 0.9997 and 0.9935. The average relative errors are 0.93 %, 0.51 % and 2.50 %. From the above results, we can conclude that the predictive performance of ANN model is reliable. The details of predicted results and errors for each compound in the database are shown in Supporting Information. In order to demonstrate the predictive performance of QSPR model, we show more details of the model predictions. The current QSPR model was expected to be able to extrapolate to larger molecules. Therefore, it should correctly reflect the parameter varying trend with carbon number for homologous series. Several classes of

homologues

were

selected

from

datasets,

which

were

n-alkanes,

2-methylisoparaffins, 1-alkenes, cyclohexane and benzene. Figure 6 compares the predicted and experimental values of B and T0 for these series. As can be observed from the figure, the predicted Andrade model parameters B and T0 are gradually


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increasing, and in accordance with experimental values. What is worth mentioning is that there exist mutations between molecules without side chains (head of homologous) and a series with side chains for cyclohexane and benzene homologues. This phenomenon has already been mentioned in the previous literature

[9]

, and the

QSPR model correctly predict these mutations. The QSPR model is designed to estimate liquid viscosities of hydrocarbons at different temperatures. Hence, comparing only the Andrade model parameters is not enough. Figure 7 shows comparisons between predicted and experimental values of viscosity data at different temperatures calculated from the predicted Andrade model parameters for five homologues series. In the shown carbon number range, the predicted values match well with experimental values. It should be note that the predictive performance of viscosities is relative low at the higher temperature range. However, the absolute liquid viscosities in this range is quite small (less than 0.5 mPa·s). Considering the pactical in chemical engineering process simulation, the errors at high temperature are acceptable. The results indicate the QSPR model can accurately estimate viscosities of pure compounds at different temperatures. To demonstrate the ability of QSPR model of distiguishing the isomers, the comparisons of

predicted

and

expermental

viscosity

vs.

temperature

properties

for

tetramethylpentane and ethyltoluene isomers are presented (their experimental data are mentioned in Table 2 and 3). As can be observed from Figure 8, the viscosity vs. temperature curves of these isomers were correctly predicted.

6. Application on Viscosity Prediction on Gasoline and Diesel Mixtures For purpose of verifying the validity of the proposed QSPR model, we made application on the gasoline and diesel complex systems. The viscosity and measured molecular composition data of gasoline and diesel viscosity data were collected from literature.[28, 29] The molecular composition of gasoline and diesels were measured by one-dimensional and comprehensive two-dimensional gas chromatography methods. The Andrade model parameters of each measured molecules were directly predicted through the proposed QSPR model. The details of molecular composition and predicted Andrade equation parameters can be found in Supporting Information. The overall viscosity of a hydrocarbon mixture should be calculated by combining the pure component viscosity data and mixing rule. The researchers developed various mixing rules to calculate viscosities of mixtures[30], which required viscosities of pure compounds and mole fractions, weight fractions, or volume


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fractions of components as input variables. Kendall and Monroe[31] proposed a mixing rule that is widely used to estimate the viscosity of a mixture from mole fractions and viscosities of pure component compounds as shown in equation (2). = [∑ ( )

]

(2)

Where χi is the mole fraction, µi is the viscosity of pure compound, and µ is the viscosity of mixture. The mixing rule was applied to calculate overall viscosities of corresponding gasoline and diesel fractions. The results are in good agreement with experimental values. As shown in Figure 9, the predicted viscosities are consistent with experimental values for gasoline, light diesel, middle diesel and heavy diesel. The predicted viscosity shows same trend as experimental values with an average absolute error of 0.21 mPa·s. It is demonstrated that the QSPR model is applicative to the mixtures such as gasolines and diesels. It should be noted that the method may have some limitations in predicting viscosities of petroleum fractions heavier than diesels. According to Korsten’s study [9]

, when the distillates become heavier, the high freezing point compounds in the

mixture would have an excessive impact on the overall viscosity. Therefore, the impact of freezing point need to be considered for heavier fractions than diesels. This issue will be further addressed in future work.

7. Conclusion In this paper, 36 chemical features that affect liquid viscosities of hydrocarbon compounds have been selected, including molecular weights, basic groups and united groups. The ANN was used to construct a QSPR model of hydrocarbon liquid viscosity prediction based on structural characteristics. The model first predicted the Andrade model parameters B and T0 through chemical features of hydrocarbon molecules with mean relative errors of 2.87 % and 1.05 %, respectively, after which it estimated liquid viscosities at any temperatures. For monomeric hydrocarbon compounds, the predicted values agreed well with experimental values with a mean absolute error of 0.10 mPa·s. In order to verify the reliability and accuracy of QSPR model for calculating viscosities of mixtures, the experimental and predicted viscosities for four groups of gasoline and diesel oils were compared and a satisfactory result was obtained. The mean absolute error was 0.21 mPa·s. It indicated that the QSPR model can accurately predict liquid viscosities of pure hydrocarbons


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and their mixtures. Associated Content The supporting information is available free of charge on the ACS publication website. A Demo Executable file (.exe) is also available for who are interested in using the proposed QSPR model, which can be found at Github (https://github.com/LinzhouZhang/ViscosityPredictor). A complete list of database (261 compounds with carbon number ranging from 3 to 64). A complete molecular composition, calculated group information and predicted Andrade model parameters of gasolines and diesels. All the data are provided in Excel format (.xlsx). Author Information Corresponding Authors *Email: [email protected] (L. Zhang); Notes The authors declare no competing financial interest. Acknowledgments This work was supported by National Natural Science Foundation of China (21506254) and Science Foundation of China University of Petroleum, Beijing (2462014YJRC020). The authors acknowledge the collaborations and support of Prof. Quan Shi at China University of Petroleum. References (1) Quiñones-Cisneros, S.E., C.K. Zéberg-Mikkelsen, and E.H. Stenby, The friction theory ( f-theory ) for viscosity modeling. Fluid Phase Equilibria, 2000. 169(2): p. 249-276. (2) Quiñones-Cisneros, S.E., C.K. Zéberg-Mikkelsen, and E.H. Stenby, One parameter friction theory models for viscosity. Fluid Phase Equilibria, 2001. 178(1): p. 1-16. (3) Quiñones-Cisneros, S.E., C.K. Zéberg-Mikkelsen, and E.H. Stenby, The friction theory for viscosity modeling: extension to crude oil systems. Chemical Engineering Science, 2001. 56(24): p. 7007-7015. (4) Quiñones-Cisneros, S.E., et al., Viscosity Modeling and Prediction of Reservoir Fluids: From Natural Gas to Heavy Oils. International Journal of Thermophysics, 2004. 25(5): p. 1353-1366. (5) Yarranton, H.W. and M.A. Satyro, Expanded Fluid-Based Viscosity Correlation for Hydrocarbons. Industrial & Engineering Chemistry Research, 2009. 48(7): p. 1– 11. (6) Motahhari, H., M.A. Satyro, and H.W. Yarranton, Predicting the Viscosity of Asymmetric Hydrocarbon Mixtures with the Expanded Fluid Viscosity Correlation.


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Industrial & Engineering Chemistry Research, 2011. 50(22): p. 12831-12843. (7) Pallares, F.R., et al., Predicting the Viscosity of Hydrocarbon Mixtures and Diluted Heavy Oils Using the Expanded Fluid Model. Energy & Fuels, 2016. 30(5): p. 151022145837006. (8) Reid, R.C., B.E. Poling, and J.M. Prausnitz, The Properties of Gases and Liquids, Vol. 5. 1987. (9) Korsten, H., Viscosity of liquid hydrocarbons and their mixtures. Aiche Journal, 2010. 47(2): p. 453-462. (10) JOBACK, K.G. and R.C. REID, ESTIMATION OF PURE-COMPONENT PROPERTIES FROM GROUP-CONTRIBUTIONS.Chemical Engineering Communications, 1987. 57(1-6): p. 233-243. (11) Simon, R.H.M., Estimation of critical properties of organic compounds by the method of group contributions. A. L. Lyderren. Engineering Experiment Station Report 3.College of Engineering, University of Wisconsin, Madison, Wisconsin (1955). 22 pages. Aiche Journal, 1956. 2(3): p. 12S-12S. (12) Klincewicz, K.M. and R.C. Reid, Estimation of critical properties with group contribution methods. Aiche Journal, 1984. 30(1): p. 137-142. (13) Lyman, W.J., W.F. Reehl, and D.H. Rosenblatt, Handbook of chemical property estimation methods : environmental behavior of organic compounds / Warren J. Lyman, William F. Reehl, David H. Rosenblatt. 1990. (14) Constantinou, L. and R. Gani, New group contribution method for estimating properties of pure compounds. Aiche Journal, 1994. 40(40): p. 1697-1710. (15) Marrero, J. and R. Gani, Group-contribution based estimation of pure component properties. Fluid Phase Equilibria, 2001. s 183–184(01): p. 183-208. (16) Velzen, D.V., R.L. Cardozo, and H. Langenkamp, A Liquid Viscosity-Temperature-Chemical Constitution Relation for Organic Compounds. Ind.eng.chem.fundamen, 1972. 11(1). (17) Allan, J.M. and A.S. Teja, Correlation and prediction of the viscosity of defined and undefined hydrocarbon liquids. Canadian Journal of Chemical Engineering, 2010. 69(4): p. 986-991. (18) Liu, Z., et al., Multiobjective Feature Selection Approach to Quantitative Structure Property Relationship Models for Predicting the Octane Number of Compounds Found in Gasoline. Energy & Fuels, 2017. 31(6). (19) Suzuki, T., K. Ohtaguchi, and K. Koide, Computer-assisted Approach to Develop a New Prediction Method of Liquid Viscosity of Organic Compounds. 1996. (20) Cocchi, M., et al., ChemInform Abstract: Development of Quantitative Structure—Property Relationships Using Calculated Descriptors for the Prediction of the Physicochemical Properties (nD, ϱ, bp, ε, η) of a Series of Organic Solvents. Cheminform, 2010. 31(9): p. no-no. (21) Rajappan, R., et al., Quantitative Structure−Property Relationship (QSPR) Prediction of Liquid Viscosities of Pure Organic Compounds Employing Random Forest Regression. Industrial & Engineering Chemistry Research, 2009. 48(21): p. 9708-9712. (22) Kauffman, G.W. and P.C. Jurs, ChemInform Abstract: Prediction of Surface


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Tension, Viscosity, and Thermal Conductivity for Common Organic Solvents Using Quantitative Structure—Property Relationships. Cheminform, 2001. 32(22): p. no-no. (23) Saldana D A, Starck L, Mougin P, et al. Prediction of Density and Viscosity of Biofuel Compounds Using Machine Learning Methods[J]. Energy & Fuels, 2012, 26(4):2416-2426. (24) Saldana D A, Creton B, Mougin P, et al. Rational Formulation of Alternative Fuels using QSPR Methods: Application to Jet Fuels[J]. Oil & Gas Science & Technology, 2013, 68(4):651-662. (25) Saldana D A, Starck L, Mougin P, et al. Prediction of Flash Points for Fuel Mixtures Using Machine Learning and a Novel Equation[J]. Energy & Fuels, 2013, 27(7):3811-3820. (26) Institute, A.P. and P.S. University, Technical data book, petroleum refining. 1976. (27) Murata, A., K. Tochigi, and H. Yamamoto, Prediction of the Liquid Viscosities of Pure Components and Mixtures Using Neural Network and ASOG Group Contribution Methods. Molecular Simulation, 2004. 30(7): p. 451-457. (28) Kanti, M., et al., Viscosity of liquid hydrocarbons, mixtures and petroleum cuts, as a function of pressure and temperature. J.phys.chem, 1989. 93(9): p. 3860-3864. (29) Aquing, M., et al., Composition Analysis and Viscosity Prediction of Complex Fuel Mixtures Using a Molecular-Based Approach. Energy & Fuels, 2012. 26(26): p. 2220-2230. (30) Centeno, G., et al., Testing various mixing rules for calculation of viscosity of petroleum blends. Fuel, 2011. 90(12): p. 3561-3570. (31) Kendall, J. and K.P. Monroe, THE VISCOSITY OF LIQUIDS. II. THE VISCOSITY-COMPOSITION CURVE FOR IDEAL LIQUID MIXTURES.1. Journal of the American Chemical Society, 2002. 39(9).


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Tables Table 1. Numbers of compounds in different chemical class in the viscosity database. chemical class

NO. of compounds

n-paraffins

31

iso-paraffins

52

cycloalkanes

33

olefins/alkynes

76

aromatics

69


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Table 2. Comparison of parameters B, T0 and viscosities in the same temperatures among isomers of Ethyltoluene Chemical Isomer Name

B Formula

T

0

Viscosity

Viscosity

Viscosity

µ/mPa·s

µ/mPa·s

µ/mPa·s

(220 K)

(240 K)

(260 K)

O-ETHYLTOLUENE

CH

1421.83

290.33

4.78

2.72

1.75

M-ETHYLTOLUENE

CH

1307.60

283.60

3.74

2.31

1.49

P-ETHYLTOLUENE

CH

1150.21

270.41

2.71

1.67

1.15

9 9 9

12 12 12


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Energy & Fuels

Table 3. Comparison of parameters B, T0 and viscosities in the same temperatures among isomers of Tetramethylpentane Chemcal Isomer Name

T

B

0

Formula

Viscosity

Viscosity

Viscosity

µ/mPa·s

µ/mPa·s

µ/mPa·s

(211 K)

(230 K)

(258 K)

2,2,3,4-TETRAMETHYLPENTANE

CH

1342.54

281.45

4.85

2.91

1.45


CH

1583.66

281.43

6.51

3.54

1.65


CH

284.35

5.13

3.03

1.57

9

9

9

20

20

20

1352.4 8


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Table 4. Basic Groups and United Groups after Selection. Category Basic Group

Group Information −CH

Comments Basic groups to characterize the molecular structure.

3

−CH − 2

>CH− >C< =CH

2

=CH− =C< =C= ≡CH ≡C−

−CH −(cyclic) 2

>CH−(cyclic) >CCHB-12 Andrade Equation

>C

Quantitative StructureâProperty Relationship Model for Hydrocarbon

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