Determination of binary diffusion coefficients of hydrocarbon mixtures using MLP and ANFIS networks based on QSPR method

Abstract In this article, at first, a quantitative structure–property relationship (QSPR) model for estimation of limiting diffusion coefficients of hydrocarbon liquids, D AB 0 , is developed. Particle swarm optimization variable selection (PSOvs) method, together with multi-linear regression (MLR) model, selects suitable descriptors from a pool of 1124 predefined descriptors. The MLR model is trained based on a data bank of 345 experimental binary diffusivities of hydrocarbons in infinite dilution solutions. The objective function of the optimizer for descriptor selection is the multi-variant RQK function. In addition, an artificial neural network (ANN) and an adaptive neuro-fuzzy inference system (ANFIS) are developed as two nonlinear black-box estimators of D AB 0 based on the descriptors obtained from PSOvs algorithm. The estimation results of these three QSPR models (PSO-MLR, ANN and ANFIS) are compared with five semi-empirical correlations. Furthermore, using 402 experimental binary diffusion coefficient data at different concentrations and temperatures, another multi-layer perceptron network (MLPN) is constructed to predict the diffusion coefficients of binary hydrocarbon liquid systems at various concentrations and temperatures. The input variables of this network are D AB 0 , D BA 0 , and mole fraction of the component A. Average absolute relative deviations (AARD) of the developed MLP-QSPR model for training, test, and whole data are respectively, 5.86%, 7.79%, and 6.32%. Indeed this model has less than 5% AARD for more than 50% of the data points. Also, the results of the MLP model designed to estimate the binary diffusivities of concentrated hydrocarbon mixtures show that the average absolute relative error for the whole of test and training data is 6.3%. The comparison of the developed MLP model with experimental data and some of semi-empirical correlations indicates that the suggested modeling scheme based on QSPR and MLP method has very good accuracies for estimation/prediction of liquid hydrocarbon diffusivity not only in infinite dilution but also at concentrated solutions.

[1]  Masoud Monjezi,et al.  Prediction of backbreak in open-pit blasting using fuzzy set theory , 2010, Expert Syst. Appl..

[2]  Yan-Ping Chen,et al.  Correlation of the mutual diffusion coefficients of binary liquid mixtures , 1998 .

[3]  J. Maxwell.  The Scientific Papers of James Clerk Maxwell , 2009 .

[4]  Rajamani Krishna,et al.  THE MAXWELL-STEFAN FORMULATION OF IRREVERSIBLE THERMODYNAMICS FOR SIMULTANEOUS HEAT AND MASS TRANSFER , 1979 .

[5]  K. Lucas,et al.  Correlations for prediction of diffusion in liquids , 1986 .

[6]  R. Reid,et al.  The Properties of Gases and Liquids , 1977 .

[7]  R. Wellek,et al.  Diffusion coefficients of n-heptane and n-decane in n-alkanes and n-alcohols at several temperatures , 1974 .

[8]  C. A. N. Castro,et al.  MUTUAL DIFFUSIVITY IN n-HEPTANE + n-HEXANE ISOMERS , 1987 .

[9]  Arthur W. Adamson,et al.  Diffusion in Liquid Hydrocarbon Mixtures , 1964 .

[10]  T. K. Kett,et al.  Diffusion in the solvents hexane and carbon tetrachloride , 1969 .

[11]  W. Wakeham,et al.  Mutual diffusion coefficients for binary mixtures of normal alkanes , 1982 .

[12]  D. K. Anderson,et al.  Mutual Diffusion in the Liquid System Hexane-Hexadecane , 1964 .

[13]  W. Hayduk,et al.  Liquid Diffusivities in Normal Paraffin Solutions , 1976 .

[14]  H. Y. Lo.  Diffusion coefficients in binary liquid n-alkane systems , 1974 .

[15]  E. Mclaughlin,et al.  Diffusion in binary liquid mixtures , 1969 .

[16]  Reza Eslamloueyan,et al.  A neural network-based method for estimation of binary gas diffusivity , 2010 .

[17]  M. Larrañaga,et al.  Determination of molecular diffusion coefficient in n-alkane binary mixtures: empirical correlations. , 2012, The journal of physical chemistry. B.

[18]  A. Akgerman,et al.  Diffusion coefficients for binary alkane mixtures to 573 K and 3.5 MPa , 1987 .

[19]  Don W. Green,et al.  Perry's Chemical Engineers' Handbook , 2007 .

[20]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[21]  Ross Taylor,et al.  Multicomponent mass transfer , 1993 .

[22]  Roberto Todeschini,et al.  Handbook of Molecular Descriptors , 2002 .

[23]  F. Gharagheizi,et al.  QSPR approach for determination of parachor of non-electrolyte organic compounds , 2011 .

[24]  F. Gharagheizi,et al.  A QSPR model for prediction of diffusion coefficient of non-electrolyte organic compounds in air at ambient condition. , 2012, Chemosphere.

[25]  Svetoslav H. Slavov,et al.  Quantitative correlation of physical and chemical properties with chemical structure: utility for prediction. , 2010, Chemical reviews.

[26]  Masoud Rahimi,et al.  Developing a feed forward neural network multilayer model for prediction of binary diffusion coefficient in liquids , 2012 .

[27]  C. Wilke,et al.  Correlation of diffusion coefficients in dilute solutions , 1955 .

[28]  L. Rodwin,et al.  Diffusion in the System Cyclohexane—Benzene , 1965 .

[29]  M. T. Tyn,et al.  Diffusion coefficients in dilute binary liquid mixtures , 1975 .

[30]  R. Todeschini,et al.  Detecting bad regression models: multicriteria fitness functions in regression analysis , 2004 .

[31]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[32]  Diffusion coefficient prediction of acids in water at infinite dilution by QSPR method , 2012, Structural Chemistry.

[33]  T. K. Kett,et al.  Ternary isothermal diffusion and the validity of the Onsager reciprocal relations in nonassociating systems , 1969 .

[34]  F. Gharagheizi,et al.  Estimation of molecular diffusivity of pure chemicals in water: a quantitative structure–property relationship study , 2009, SAR and QSAR in environmental research.

[35]  D. K. Anderson,et al.  Mutual Diffusion in Nonideal, Nonassociating Liquid Systems , 1964 .

[36]  H. P. Hutchison,et al.  Diffusion coefficients and densities for binary organic liquid mixtures , 1971 .

[37]  P. Lyons,et al.  Transport properties of liquid n-alkanes , 1969 .

[38]  A. Sahgal,et al.  Ethylene solubility and diffusivity in hexane-dodecane and ethylene glycol-butanol solutions , 1979 .

[39]  Knut Baumann,et al.  Cross-validation as the objective function for variable-selection techniques , 2003 .

[40]  Walter Hayduk,et al.  Correlations for prediction of molecular diffusivities in liquids , 1982 .

[41]  E. Neau,et al.  Diffusion Coefficients of Aromatic Compounds at Infinite Dilution in Binary Mixtures at 298.15 K , 2007 .

[42]  D. Bosse,et al.  Prediction of Diffusion Coefficients in Liquid Systems , 2006 .

[43]  F. Gharagheizi.  Determination of Diffusion Coefficient of Organic Compounds in Water Using a Simple Molecular-Based Method , 2012 .

[44]  A. Akgerman,et al.  High-temperature diffusion, viscosity, and density measurements in n-eicosane , 1987 .

[45]  N. Wakao,et al.  Binary Diffusion Coefficients of Organic Compounds in Hexane, Dodecane, and Cyclohexane at 303.2-333.2 K and 16.0 MPa , 1994 .

[46]  Kunal Roy,et al.  Some case studies on application of “rm2” metrics for judging quality of quantitative structure–activity relationship predictions: Emphasis on scaling of response data , 2013, J. Comput. Chem..

[47]  Kobra Zarei,et al.  Predicting infinite dilution activity coefficients of hydrocarbons in water using ant colony optimization , 2010 .