Correlation of vapour liquid equilibria of binary mixtures using artificial neural networks

Abstract

Abstract: In this paper, a back propagation artificial neural network (BP-ANN) model is presented for the simultaneous estimation of vapour liquid equilibria (VLE) of four binary systems viz chlorodifluoromethan-carbondioxide, trifluoromethan-carbondioxide, carbondisulfied-trifluoromethan and carbondisulfied-chlorodifluoromethan. VLE data of the systems were taken from the literature for wide ranges of temperature (222.04—343.23K) and pressure (0.105 to 7.46MPa). BP-ANN trained by the Levenberg-Marquardt algorithm in the MATLAB neural network toolbox was used for building and optimizing the model. It is shown that the established model could estimate the VLE with satisfactory precision and accuracy for the four systems with the root mean square error in the range of 0.054—0.119. Predictions using BP-ANN were compared with the conventional Redlich-Kwang-Soave (RKS) equation of state, suggesting that BP-ANN has better ability in estimation as compared with the RKS equation (the root mean square error in the range of 0.115—0.1546).

Key words: vapour liquid equilibria, artificial neural networks, refrigerant

摘要： In this paper, a back propagation artificial neural network (BP-ANN) model is presented for the simultaneous estimation of vapour liquid equilibria (VLE) of four binary systems viz chlorodifluoromethan-carbondioxide, trifluoromethan-carbondioxide, carbondisulfied-trifluoromethan and carbondisulfied-chlorodifluoromethan. VLE data of the systems were taken from the literature for wide ranges of temperature (222.04—343.23K) and pressure (0.105 to 7.46MPa). BP-ANN trained by the Levenberg-Marquardt algorithm in the MATLAB neural network toolbox was used for building and optimizing the model. It is shown that the established model could estimate the VLE with satisfactory precision and accuracy for the four systems with the root mean square error in the range of 0.054—0.119. Predictions using BP-ANN were compared with the conventional Redlich-Kwang-Soave (RKS) equation of state, suggesting that BP-ANN has better ability in estimation as compared with the RKS equation (the root mean square error in the range of 0.115—0.1546).

关键词: vapour liquid equilibria;artificial neural networks;refrigerant

Hajir Karimi, Fakhri Yousefi. Correlation of vapour liquid equilibria of binary mixtures using artificial neural networks[J]. .

Hajir Karimi, Fakhri Yousefi. 运用人工神经网络关联二元混合物中气液相平衡[J]. CIESC Journal.

References

1 Petersen, R., Fredenslund, A., Rasmussen, P., “Artificial neural networks as a predictive tool for vapor liquid equilibrium”, Comput. Chem. Eng., 18, s63—s67(1994).
2 Guimaraes, P.R.B., McGreavy, C., “Flow of information through an artificial neural network”, Comput. Chem. Eng., 19(S1), 741—746 (1991).
3 Sharma, R., Singhal, D., Ghosh, R., Dwivedi, A., “Poten-tial applications of artificial neural networks to thermo-dynamics: Vapour-liquid equilibrium predictions”, Com-put. Chem. Eng., 23, 385—390(1999).
4 Ganguly, S., “Prediction of VLE data using radial basis function network”, Comput. Chem. Eng., 27, 1445—1454(2003).
5 Urata, S., Takada, A., Murata, J., Hiaki, T., Sekiya, A., “Prediction of vapor-liquid equilibrium for binary sys-tems containing HFEs by using artificial neural network”, Fluid Phase Equilib., 199, 63—78(2002).
6 Mohanty, S., “Estimation of vapour liquid equilibria for the system carbon dioxide-difluoromethane using artifi-cial neural networks”, Int. J. Refrig., 29, 243—249(2006).
7 Mohanty, S., “Estimation of vapour liquid equilibria of binary systems, carbon dioxid-ethyl caproate, ethyl caprylate and ethyle caprate using artificial neural net-works”, Fluid Phase Equilib., 235, 92—98(2005).
8 Rai, P., Majumdar, G.C., Das Gupta, S., De, S., “Predic-tion of the viscosity of clarified fruit juice using artificial neural network: A combined effect of concentration and temperature”, J. Food Eng., 68, 527—533(2005).
9 Bouchard, C., Grandjean, A., “A neural network correla-tion for variation of viscosity of sucrose aqueous solu-tions with temperature and concentration”, Lebensm-Wiss. U. -Technol., 28, 157—159(1995).
10 Laugier, S., Richon, D., “Use of artificial neural net-works for calculating derived thermodynamic quantities from volumetric property data”, Fluid Phase Equilib., 210, 247—255(2003).
11 Potukuchi, W., Wexler, A.S., “Predicting vapor pressures using neural networks”, Atmos. Environ., 31, 741—753(1997).
12 Shyam, S.S., Oon-Doo, B., Michele, M., “Neural net-works for predicting thermal conductivity of bakery products”, J. Food Eng., 52, 299—304(2002).
13 Rumelhart, D.E., Hinton, G.E., Williams, R.J., “Learning representations by backpropagation errors”, Nature, 323, 533—536(1986).
14 Hagan, M.T., Menhaj, M., “Training feedforward net-works with the Marquardt algorithm”, IEEE Trans. Neu-ral Networks, 5(6), 989—993(1994).
15 Minai, A.A., Willams, R.D., “Acceleration of back-propagation through learning rate and momentum adaptation”, In: the 1st International Joint Conference on Neural Networks, 676(1990).
16 Haralambous, C., “Conjugate gradient algorithm for effi-cient training of artificial neural networks”, IEEE Proc., 139(3), 301—310(1992).
17 Karimi, H., Ghaedi, M., “Simultaneous determination of thiocyanate and salycilate by a combined UV-spectro-photometric detection principal component artificial neural network”, Ann. Chim., 96, 657—667( 2006),
18 Fausett, L., “Fundamentals of Neural Networks: Archi-tectures, Algorithms and Applications”, Printice-Hall, New Jersey (1994).
19 Roth, H., Peters-Gerth, P., Lucas, K., “Experimental va-por-liquid equilibria in the systems R22-R23, R22-CO2, CS2-R22, R23-CO2, CS2-R23 and their correlation by equations of state”, Fluid Phase Equilib., 73, 147—166(1992).
20 Arbib, A. M., The Handbook of Brian Theory and Neural Networks, The MIT Press, Massachusetts, 15—20(2002).
21 Christov, M., Dohrn, R., “High-pressure fluid phase equi-libria. Experimental methods and systems investigated (1994—1999)”, Fluid Phase Equilib., 202, 153—218(2002).
22 Soave, G., “Equilibrium constants from a modified Redlich-Kwong equation of state”, Chem. Eng. Sci., 27, 1197—1203(1972).

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