Determination of Parachor of Various Compounds ... - ACS Publications

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Determination of Parachor of Various Compounds Using an Artificial Neural NetworkGroup Contribution Method Farhad Gharagheizi,† Ali Eslamimanesh,‡ Amir H. Mohammadi,*,‡,§ and Dominique Richon‡ †

Saman Energy Giti Co., Postal Code 3331619636, Tehran, Iran nergetique et Procedes, 35 Rue Saint Honore, 77305 Fontainebleau, France MINES ParisTech, CEP/TEP—Centre E § Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa ‡

bS Supporting Information ABSTRACT: In this communication, an Artificial Neural NetworkGroup Contribution algorithm is applied to represent/predict the parachor of pure chemical compounds. To propose a reliable and predictive tool, 227 pure chemical compounds are investigated. Using the developed method, we obtain satisfactory results that are quantified by the following statistical parameters: absolute average deviations of the represented/predicted parachor values from existing experimental ones, %AAD = 1.2%; and squared correlation coefficient, R2 = 0.997.

1. INTRODUCTION Effects of different physical forces on fluid phase equilibria have generated many discussions in the past century.1 Surface tension is among these forces, which exists at the interface of fluid phases.13 Surface forces affect the onset of formation of new phases and is significant in multiphase flow, especially in hydrocarbon reservoirs during production and in pipelines during transportation.2 The molecular tension at the interface is quantitatively expressed as interfacial tension (IFT), which refers to the force exerted at the interface per unit length.2 One of the applications of this parameter is to determine the capillary pressure, which is used to investigate the effects of surface forces on fluid distribution within a reservoir. Furthermore, the relative permeability of the fluids, which is a significant factor that is used to describe the fluid flow and phase behavior (in a dynamic way) in the hydrocarbon reservoirs, is related to the interfacial tension.2 Of particular interest are the effects of the values of interfacial tensions of the gas condensates on the condensate recovery in the case of retrograde condensation in gas condensate reservoirs.2 Regarding the aforementioned significance of interfacial tension concept, so far, several calculation/estimation methods have been proposed for this purpose. In 1923, Macleod4 presented an empirical equation to correlate the experimental values of interfacial tension based on the difference between the density of a liquid and vapor of compounds in equilibrium with each other at a given temperature and a constant characteristic of the liquid phase. Later, Sugden5,6 reported the constant characteristic of the Macleod’s correlation4 to be a function of molecular weight and another parameter (called the “parachor” of a compound) as follows: ðIFTÞ1=4 ¼

PðFL FV Þ M

r 2011 American Chemical Society

ð1Þ

where P denotes the parachor property, F is the density (in kg/m3), M is the molecular weight, and the subscripts L and V refer to the liquid and vapor phases, respectively. Macleod4 stated that the parachor is a number that represents the molar volume of a compound when its temperature is such that its surface tension is unity.1 In other words, the parachor parameter addresses the molar volume of a substance, ignoring the effects of temperature. Therefore, there are unique values of this property for each chemical compound.2 Bayliss7 calculated the parachor values by fitting the experimental parachor data of n-paraffins, using the least-squares method. A correlation based on molecular weight has been presented by Schechter and Guo8 and Baker and Swerdloff9 for evaluation of the parachor of n-paraffins. However, the parachor property can be related to the critical properties of compounds, including critical temperature and molar volume, as follows:10 P ¼ 0:324Tc 1=4 vc 7=8

ð2Þ

where T is the temperature (in K), v is the molar volume (in m3/ kmol), and the subscript c denotes the critical value. A similar correlation was reported by Fanchi,10 who fitted the experimental parachor values of 21 compounds (mostly n-alkanes), using a six-parameter correlation. He indicated that the absolute deviations of the calculated parachor values were ∼1.5% for these investigated compounds. Another approach has been presented by Quayle,11 who reported group contributions for the calculation of parachor properties. However, the reported group contributions are incomplete and many functional groups are not represented.3 Received: December 9, 2010 Accepted: March 9, 2011 Revised: February 26, 2011 Published: March 21, 2011 5815

dx.doi.org/10.1021/ie102464t | Ind. Eng. Chem. Res. 2011, 50, 5815–5823

Industrial & Engineering Chemistry Research

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Table 1. Functional Groups Used To Develop This Methodb

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dx.doi.org/10.1021/ie102464t |Ind. Eng. Chem. Res. 2011, 50, 5815–5823


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Table 1. Continued

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Table 1. Continued

a The superscript represents the formal oxidation number. b In the chemical formulas and functional groups: R represents any group linked through carbon; X represents any electronegative atom (O, N, S, P, Se, halogens); Al and Ar represent the aliphatic and aromatic groups, respectively; the symbol = represents a double bond; the symbol # represents a triple bond; the symbol grouping -- represents an aromatic bond (such as that in benzene) or delocalized bonds (such as the NO bond in a nitro group); and the symbol grouping 3 3 represents aromatic single bonds (such as the CN bond in pyrrole).

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Industrial & Engineering Chemistry Research In a previous work,12 the quantitative structureproperty relationship (QSPR) molecular-based method has been applied to evaluate the parachor values of pure compounds. The obtained results show an absolute average deviation of 2.8% for the represented/predicted parachor values of 227 pure compounds. In order to improve the accuracy of the results, we propose a different approach in this work, based on the Artificial Neural NetworkGroup Contribution (ANN-GC) method, to represent/predict the parachor of the same group of pure chemical compounds.

2. EXPERIMENTAL DATASET AND METHODS 2.1. Experimental Dataset. The same database as that used for the previous work (i.e., the DIPPR 801 database,13 which is one of the best sources of physical property data for pure compounds) has been applied. It contains the parachor values of 227 chemical species from various chemical families.

Figure 1. The schematic structure of the Feed Forward Artificial Neural Network (FFANN) used in this study.44

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2.2. Development of New Group Contributions. Having defined the database, the chemical structures of all of the studied compounds are analyzed with much attention, using an algorithm that compares the chemical groups to define the most efficient contributions for evaluation of the parachor property. Consequently, 40 functional groups have been found to be more efficient for representation/prediction of the parachor of pure compounds. The functional groups used in this study are presented in Table 1. In addition, a table of their numbers of occurrences in the investigated compounds is presented as Supporting Information. These chemical groups are used as the proposed model parameters. 2.3. Optimization of Group Contributions Using an Artificial Neural Network. The first calculation step—and perhaps the most significant one—is to search for a relationship between the chemical functional groups and the desired physical properties. The simplest method for this purpose is an assumption of the existence of a multilinear relationship between these groups and the desired property (here, the parachors). This technique is similar to the method used in most of the classical group contribution methods. Several calculations show that application of the mentioned methodology for the current problem brings about poor results. Consequently, a nonlinear mathematical method of the Artificial Neural Network (ANN) is preferred and investigated.1448 ANNs are extensively used in various scientific and engineering problems,1448 e.g., calculations/estimations of physical and chemical properties of different pure compounds and investigation of the phase behaviors of complex thermodynamic systems (e.g., dissociation conditions of semiclathrate hydrates).1448 These capable mathematical tools are generally applied to study the complicated systems.1448 Theoretical explanations about the neural networks can be found elsewhere.45 Using the Artificial Neural Network toolbox of the MATLAB software (Mathworks, Inc.), a three-layer Feed Forward Artificial Neural Network (FFANN) is developed for the problem. The typical

Figure 2. Comparison between the represented/predicted results of the developed method and the experimental values13 of the parachor parameters of the investigated pure chemical compounds. 5819



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Table 2. Statistical Parameters of the Presented Models statistical parameter

value

Training Set

Table 3. Average Absolute Deviations of the Obtained Results from Experimental Values13 for Various Chemical Families

The Model

squared correlation coefficient, R2

0.996

average absolute deviation, %AADa

1.2%

standard deviation error

252.5

mean square error

235.9

Nb

183

chemical family

Validation Set

AAD%

1-alkenes

1.9

acetates

0.1

aldehydes

0.1

aliphatic ethers

0.4

alkylcyclohexanes alkylcyclopentanes

0.7 1.5 0.4


1.000

alkynes

average absolute deviation, %AADa standard deviation error

1.0% 221.8

aromatic alcohols

0.5

aromatic amines

0.1

mean square error

13.2

aromatic esters

0.2

Nb

22

C, H, NO2 compounds

0.0

Test Set

cycloaliphatic alcohols

0.0 2.1 1.3


1.3%

cycloalkanes cycloalkenes


92.9

dialkenes

2.3

19.3

dimethylalkanes

0.7

22

diphenyl/polyaromatics

1.4

ethyl and higher alkenes

0.6

squared correlation coefficient, R

2

mean square error b

N

0.998

Training þ Validation þ Test Set

inorganic halides

2.0

ketones

0.3

239.9

methylalkanes methylalkenes

0.3 0.7

mean square error

193.4

Nb

multiring cycloalkanes

0.1

227

n-alkanes

2.6

n-alkylbenzenes

1.5

naphthalenes

1.2


0.997


1.2%


a b %AAD = (100/N) ∑N i |(Rep(i)/Pred(i) Exp(i))|/Exp(i). Number of data points.

structure of a 3FFANN is schematically presented in Figure 1. The capabilities of this type of ANN have been demonstrated in previous works.1448 All the functional groups, and the properties values, of pure compounds are normalized between 1 and þ1, to decrease computational errors. This can be performed using maximum and minimum values of the numbers of each functional group over all of the investigated compounds for input data and using maximum and minimum values of the parachors for output parameters. Later, the database is divided into three subdata sets, including the “Training” set, the “Validation” set, and the “Test” set. In this work, the “Training” set is used to generate the ANN structure, the “Validation (Optimization)” set is applied for optimization of the model, and the “Test (Prediction)” set is used to investigate the prediction capability and validity of the obtained model. The process of dividing the database into three sub-datasets is performed randomly. For this purpose, proportions of ∼80%, ∼10%, and ∼10% of the main dataset are randomly selected for the “Training” set (∼183 compounds), the “Validation” set (∼22 compounds), and the “Test” set (∼22 compounds). The effect of the percent allocation of the three sub-datasets from the database on the accuracy of the ANN model has been studied elsewhere.48 The ANN model is generated by determination of the weight matrices and bias vectors.1448 As shown in Figure 1, there are two weight matrices and two bias vectors in a 3FFANN: W1 and W2, and b1 and b2, respectively.1448 These parameters should be obtained by minimization of an objective function. The objective

organic/inorganic compounds

6.2

other aliphatic acids

0.0

other alkanes other alkylbenzenes

0.8 0.9

other amines, imines

0.2

other condensed rings

3.9

other hydrocarbon rings

0.7

other inorganics

1.1

other monoaromatics

0.6

other polyfunctional C, H, O

0.1

polyfunctional C, H, O, halide polyfunctional C, H, O, N

0.0 0.1

polyfunctional esters

0.0

polyfunctional nitriles

0.1

silanes/siloxanes

2.0

sulfides/thiophenes

0.1

terpenes

0.4

function used in this study is the sum of squares of errors between the outputs of the ANN (represented/predicted properties) and the target values (experimental parachors). This minimization is performed using the LevenbergMarquardt (LM)45 optimization algorithm. There are also more-accurate optimization methods other than this algorithm; however, they need much more convergence time. In other words, the more accurate the optimization, the more time is needed for the algorithm to converge to the global 5820



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Figure 3. Estimated and experimental parachor values of n-alkanes vs the number of carbon atoms.

optimum. The LM algorithm45 is the most-widely used algorithm for training, because it is robust and accurate enough to deal with the considered system.1448 In most cases, the number of neurons in the hidden layer (n) is fixed. Therefore, the main goal is to produce an ANN method that is capable of predicting the target values as accurately as possible. This step is repeated until the best ANN is obtained. Generally, and especially in FFANNs, optimizing the number of neurons in the hidden layer is more efficient, according to the accuracy of the obtained Feed Forward Artificial Neural Network (FFANN).1448

3. RESULTS AND DISCUSSION An optimized FFANN is obtained using the aforementioned procedure for representation/prediction of the parachor of 227 pure compounds. For this purpose, several 3FFANN modules are generated, assuming numbers of 150 for n (the number of neurons in the hidden layer), using the previously described procedure. The most accurate results are observed at n = 5. It should be noted that this value is not the global value, because the optimization method used to train the ANN has great effects on the obtained value.1448 Therefore, the developed three-layer FFANN has a structure of 40-5-1. The mat file (MATLAB file format) of the obtained ANN containing all of the parameters of the model is freely available from the authors upon request. Furthermore, the instruction for running the developed computer program, accompanied by an example of calculating the parachor property of a defined compound, has been presented in the Appendix. The represented/predicted parachors are compared with the experimental values in Figure 2. The statistical results obtained by the ANNGC method are reported in Table 2. As can be seen, the squared correlation coefficient (R2), the absolute average deviation (% AAD), the standard deviation error, and the root-mean-square error of the model over the “Training” set are 0.996, 1.2%, 252.5,

and 235.9, respectively; those over the “Validation (Optimization)” set are 1, 1%, 221.8, and 13.2, respectively; those over the “Test (Prediction)” set are 0.998, 1.3%, 92.9, and 19.32, respectively; and those over the main dataset are 0.997, 1.2%, 239.9, and 193.4, respectively. Furthermore, the %AAD values of the results from experimental values13 for each of the 44 chemical families are reported in Table 3. The results imply that the obtained ANN-GC method is accurate to represent/predict the parachors of the investigated pure compounds from various chemical families. For better illustration of the quality of the developed model prediction capability, the estimated and experimental parachor values of n-alkanes have been sketched as a function of the number of carbon atoms in Figure 3, and very good agreement is found. In the final analysis, we should point out that the presented model results lead to %AAD values from experimental data of more than 10%, with regard to the parachor values for five compounds. It seems that there is no relation between these compound structures and the calculated/predicted parachor values to show some weaknesses in evaluation of the property of interest for the related chemical families. Therefore, it is probable that the parachor values for these compounds are not accurate or may be somehow erroneous.

4. CONCLUSION In this communication, a group contribution-based method was presented for representation/prediction of the parachor of pure chemical compounds. The model is the result of a combination of Feed Forward Neural Networks and Group Contributions. The required parameters of the model are the numbers of occurrences of 40 functional groups in each investigated molecule. It should be noted that most of these functional groups are not available in a particular molecule simultaneously. Therefore, computation of the required parameters from chemical structure of any molecule is simple. To develop the model, the 5821


Industrial & Engineering Chemistry Research experimental parachor values from the largest available dataset13 containing 227 pure chemical compounds from various chemical families were applied. As a consequence, a reliable method was developed to represent/predict the parachors of many pure chemical compounds. However, it still has one limitation: The method has a wide range of applicability, but its prediction capability is restricted to the compounds that are similar to those used to develop the model. Application of the developed tool for compounds that are totally different than the investigated ones is not recommended, although it may be used for a rough estimation of the parachors of these types of compounds.

’ APPENDIX: INSTRUCTIONS FOR RUNNING THE PROGRAM The model is very easy to apply. One needs to just drag and drop the mat file (freely available in the Supporting Information) into the MATLAB environment (any versions) workspace. One can follow the example given below to get a response from the model step by step: Assume that one is willing to predict the parachor value of isobutane using the developed model. First, the group-contribution parameters should be defined from chemical structure of isobutane (refer to the Supporting Information). Later, drag and drop the mat file, and the following commands should be entered in the MATLAB workspace: 2 3 30 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 7 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 05 0

0

0

0

0

0

0

0

simðnet; GC’Þ The estimated parachor value is 189.99, whereas its experimental value is 191.4 (ARD% = 0.7%).

’ ASSOCIATED CONTENT

bS

Supporting Information. Spreadsheet including the number of occurrences of the 40 functional groups in all of 227 pure compounds in the main dataset, the distributions of the data in three datasets, and the obtained results. (Excel file.) This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ (33) 1 64 69 49 70. Fax: þ (33) 1 64 69 49 68. E-mail: [email protected].

’ ACKNOWLEDGMENT A.E. gratefully thanks MINES ParisTech for providing a Ph.D. scholarship. ’ REFERENCES (1) Balasubrahmanyam, S. N. Einstein, “parachor” and molecular volume: Some history and a suggestion. Curr. Sci. India 2008, 94, 1650–1658. (2) Danesh, A. PVT and Phase Behaviour of Petroleum Reservoir Fluids; Elsevier: Amsterdam, 1998. (3) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. Properties of Gases and Liquids, 5th Ed.; McGrawHill: New York, 2001.

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(48) Gharagheizi, F.; Sattari, M.; Tirandazi, B. Prediction of lattice crystal energy using enthalpy of sublimation: A group contributionbased model. Ind. Eng. Chem. Res. DOI: 10.1021/ie1001672j.

’ NOTE ADDED AFTER ASAP PUBLICATION After this paper was published online March 21, 2011, a correction was made to eq 1. The revised version was published April 5, 2011.

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Determination of Parachor of Various Compounds ... - ACS Publications

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