Modeling of VLE and LLE Systems by using Thermodynamic model with ANFIS Structures and GMDH Type-Neural Network

Document Type : Chemistry Article

Authors

Abstract

Study of vapor - liquid and liquid – liquid Equilibrium plays an important role in the design, optimization and control of separation processes. In this research phase equilibrium of binary systems (1-propanol, water and 1-propanol, ethyl acetate) also ternary systems (water, ethylene glycol, 2-ethyl 1- hexanol and water, ethylene glycol, 1- heptanol) using thermodynamic models of NRTL and UNIQUAC were studied. Also Adaptive Nero-Fuzzy Inference System (ANFIS) and group method of Data handling (GMDH-type neural network) were used for modeling of systems. The VLE graphs (temperature based on mole fraction of vapor-liquid phases) for binary systems and LLE graphs for ternary systems at various temperatures by thermodynamics models were drawn. Accuracy of thermodynamic models, ANFIS model and GMDH type-Neural Network for the binary and ternary systems studied and compared with experimental data. Comparison of results shows that NRTL models have good fitness with the experimental data and the minimum error is related to the ANFIS Statistical model.

Keywords

Main Subjects


 
[1] Englezos, P., Kalogerakis, N., and Bishnoi, P.R. (1990) “Simultaneous regression of binary VLE and VLLE data”. Fluid phase equilibria, Vol.61, pp.1-15.
[2] Bollas, G.M., Barton, P.I., and Mitsos, A. (2009) “Bilevel optimization formulation for parameter estimation in vapor–liquid (–liquid) phase equilibrium problems”. Chemical Engineering Science, Vol.64, pp.1768-1783.
[3], Costa, A., da Silva, F., and Pessoa, F. (2000) “Parameter estimation of thermodynamic models for high-pressure systems employing a stochastic method of global optimization”. Brazilian Journal of Chemical Engineering, Vol.17, pp.349-354.
[4] Steyer, F. and Sundmacher, K. (2005) “VLE and LLE data set for the system cyclohexane+ cyclohexene+ water+ cyclohexanol+ formic acid+ formic acid cyclohexyl ester”. Journal of Chemical & Engineering Data, Vol.50, pp.1277-1282.
[5] Holland, J.H. (1992) “Genetic algorithms”. Scientific american, Vol.267, pp.66-72.
[6] Holland, J.H., (1973) “Genetic algorithms and the optimal allocation of trials”. SIAM Journal on Computing, Vol.2, pp.88-105.
[7] Silva, C. and Biscaia, E. (2003) “Genetic algorithm development for multi-objective optimization of batch free-radical polymerization reactors”. Computers & Chemical Engineering, Vol.27, pp.1329-1344.
[8] Kasat, R.B. and Gupta, S.K. (2003) “Multi-objective optimization of an industrial fluidized-bed catalytic cracking unit (FCCU) using genetic algorithm (GA) with the jumping genes operator”. Computers & Chemical Engineering, Vol.27, pp.1785-1800.
[9] Beasley, D., Martin, R., and Bull, D. (1993) “An overview of genetic algorithms: Part 1. Fundamentals”. University computing, Vol.15, pp.58-58.
[10] Alvarez, V., et al. (2008) “Parameter estimation for VLE calculation by global minimization: the genetic algorithm”. Brazilian Journal of Chemical Engineering, Vol.25, pp.409-418.
[11 Wisniak, J., Fishman, E., and Shaulitch, R. (1998) “Phase equilibria in the systems oxolane+ octane and methyl 1, 1-dimethylethyl ether+ hex-1-ene”. Journal of Chemical & Engineering Data, Vol.43, pp.304-306.
[12] Coto, B., Pando, C., and Renuncio, J.A. (2000) “Prediction of phase equilibria for binary and ternary mixtures involving tert-butyl methyl ether and tert-amyl methyl ether”. Industrial & engineering chemistry research, Vol.39, pp.767-774
[13 Ghanadzadeh, H., et al. (2010) “(Liquid+ liquid) equilibria for ternary mixtures of (water+ propionic acid+ organic solvent) at T= 303.2 K”. The Journal of Chemical Thermodynamics, Vol.42, pp.267-273.
[14], Renon, H. and Prausnitz, J.M. (1968) “Local compositions in thermodynamic excess functions for liquid mixtures”. AIChE journal, Vol.14, pp.135-144.
[15 Abrams, D.S. and Prausnitz, J.M. (1975) “Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems”. AIChE Journal, Vol.21, pp.116-128.
[16] Ketabchi, S., et al. (2010) “Estimation of VLE of binary systems (tert-butanol+ 2-ethyl-1-hexanol) and (n-butanol+ 2-ethyl-1-hexanol) using GMDH-type neural network”. The Journal of Chemical Thermodynamics, Vol.42, pp.1352-1355.
[17] Ghanadzadeh, H., Ganji, M., and Fallahi, S. (2012) “Mathematical model of liquid–liquid equilibrium for a ternary system using the GMDH-type neural network and genetic algorithm”. Applied Mathematical Modelling, Vol.36, pp.4096-4105.
[18] Murti, P. and Van Winkle, M. (1958) “Vapor-liquid equilibria for binary systems of methanol, ethyl alcohol, 1-propanol, and 2-propanol with ethyl acetate and 1-propanol-water”. Industrial & Engineering Chemistry Chemical and Engineering Data Series, Vol.3, pp.72-81.
[19] Ghanadzadeh, H., Taki, T. (2016) “liquid-liquid extraction of ethylene glycol from an aqueous solution”. 17th International Symposium on Solubility phenomena and related Equilibrium processes, Geneva, Swiss, July   24-29.
[20] Ivakhnenko, A. and Ivakhnenko, G. (1995) “The review of problems solvable by algorithms of the group method of data handling
(GMDH)”. Pattern Recognition And Image Analysis C.C Of Raspoznavaniye Obrazov I Analiz Izobrazhenii, Vol.5, pp.527-535.
[21] Nariman-Zadeh, N. and Jamali, A. Pareto genetic design of GMDH-type neural networks for nonlinear systems. in Proceedings of the International Workshop on Inductive Modelling, Czech Technical University, Prague, Czech Republic. 2007. Citeseer.
[22] Zadeh, L.A. (1965) “Fuzzy sets”. Information and control, Vol.8, pp.338-353.
[23] Jang, J.-S. (1993) “ANFIS: adaptive-network-based fuzzy inference system”. IEEE transactions on systems, man, and cybernetics, Vol.23, pp.665-685.
[24] Jamali, A., et al. Robust Pareto design of ANFIS networks for nonlinear systems with probabilistic uncertainties. in Innovations in Intelligent Systems and Applications (INISTA), 2011 International Symposium on. 2011. IEEE.