Document Type : Full article


Faculty of Chemical Engineering, Babol Noshiravani University of Technology


Two main objectives have been considered in this paper: providing a good model to predict the critical temperature and pressure of binary hydrocarbon mixtures, and comparing the efficiency of the artificial neural network algorithms and the support vector regression as two commonly used soft computing methods. In order to have a fair comparison and to achieve the highest efficiency, a comprehensive search method is used in neural network modeling, and a particle swram optimization algorithm for SVM modeling. To compare the accuracy of the models, various criteria such as ARD, MAE, MSE, RAE and R2 are used. The simulation results show that the ARD for the prediction of the true critical temperature and pressure of the binary hydrocarbon mixtures for the final optimized ANN-based model is equal to 0.0161 and 0.0387, respectively. The corressponding ARD value for the SVM-based model is equal to 0.0086 and 0.0091 for critical temperature and pressure, respectively. Simulation results show that although both models have a very high predictive accuracy, the SVM has higher learning speed and accuracy than ANN.


Main Subjects

[1]      He, M., Xin, N., Liu, Y. and Zhang, Y., “Determination of critical properties for binary and ternary mixtures of short chain alcohols and alkanes using a flow apparatus”, J. Supercrit. Fluids, 104, 19 (2015).

[2]      Wang, L., Han, K., Xia, S., Ma, P. and Yan, F., “Measurement and correlation of critical properties for binary mixtures and ternary mixtures containing gasoline additives”, J. Chem. Thermodyn., 74, 161 (2014).

[3]      Belyakov, M. Y., Gorodetskii, E. E., Kulikov, V. D., Muratov, A. R., Voronov, V. P., Grigoriev, B. A. and Volkov, A. N., “Anomalous properties of dew-bubble curves in the vicinity of liquid-vapor critical points”, Fluid Phase Equilib., 358, 91 (2013).

[4]      Poling, B. E., Prausnitz, J. M. and O'Connell, J. P., The Properties of gases and liquids, fifth edition, New York, (2001).

[5]      Najafi, H., Maghbooli, B. and Sobati, M. A., “Prediction of true critical temperature of multi-component mixtures: An extension to Chueh and Prausnitz method”, Fluid Phase Equilib., 363, 1 (2014).

[6]      Hosseini-Nasab, S. M., Manteghian, M., Sefti, M. V., Izadpanah, A. A. and Zare, M., “A neuro-fuzzy model as a predictive tool for the vapor-liquid equilibrium of binary mixtures”, Pet. Sci. Technol., 31, 68 (2013).

[7]      Ansari, H. R. and Gholami, A., “An improved support vector regression model for estimation of saturation pressure of crude oils”, Fluid Phase Equilib., 402, 124 (2015).

[8]      Najafi, H., Maghbooli, B. and Sobati, M. A., “Prediction of true critical temperature of multi-component mixtures: Extending fast estimation methods”, Fluid Phase Equilib., 392, 104 (2015).

[9]      Zhao, Y., Zhang, X., Deng, L. and Zhang, S., “Prediction of viscosity of imidazolium-based ionic liquids using MLR and SVM algorithms”, Comput. Chem. Eng., 92, 37 (2016).

[10]  Mehdizadeh, B. and Movagharnejad, K., “A comparison between neural network method and semi empirical equations to predict the solubility of different compounds in supercritical carbon dioxide”, Fluid Phase Equilib., 303, 40 (2011).

[11]  Hayer, H., Haghbakhsh, R., Keshtkari, S. and Raeissi, S., “Support vector machine and CPA EoS for the prediction of high-pressure liquid densities of normal alkanols”, J. Taiwan Inst. Chem. Eng., 45, 2888 (2014).

[12]  Lashkarbolooki, M., Hezave, A. Z. and Ayatollahi, S., “Artificial neural network as an applicable tool to predict the binary heat capacity of mixtures containing ionic liquids”, Fluid Phase Equilib., 324, 102 (2012).

[13]  Sabzevari, S. and Moosavi, M., “Density prediction of liquid alkali metals and their mixtures using an artificial neural network method over the whole liquid range”, Fluid Phase Equilib., 361, 135 (2014).

[14]  Fogel, D. B., Liu, D. and Keller, J. M., Fundamentals of computational intelligence, John Wiley & Sons, Inc., Hoboken, NJ, USA, (2016).

[15]  Hemmati-Sarapardeh, A., Shokrollahi, A., Tatar, A., Gharagheizi, F., Mohammadi, A. H., Naseri, A., “Reservoir oil viscosity determination using a rigorous approach”, Fuel, 116, 39 (2014).

[16]  dos Santos, L. C., Tavares, F. W., Ahón, V. R. R. and Kontogeorgis, G. M., “Modeling MEA with the CPA equation of state: A parameter estimation study adding local search to PSO algorithm”, Fluid Phase Equilib., 400, 76 (2015).

[17]  Panda, S. and Padhy, N. P., “Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design”, Appl. Soft Comput., 8, 1418 (2008).

[18]  Hassan, R., Cohanim, B., de Weck, O. and Venter, G., “A comparison of particle swarm optimization and the genetic algorithm”, In: 46th AIAA/ASME/ASCE/AHS/ASC Struct. Struct. Dyn. Mater. Conf., American Institute of Aeronautics and Astronautics, Reston, Virigina, (2005).

[19]  Poli, R., Kennedy, J. and Blackwell, T., “Particle swarm optimization”, Swarm Intell., 1, 33 (2007).

[20]  Kennedy, J. and Eberhart, R., “Particle swarm optimization”, Proceeding of ICNN’95 - Int. Conf. Neural Networks, IEEE, n.d., pp. 1942-1948.

[21]  API, Technical data book- Petroleum refining, (1997).

[22]  Hicks, C. P. and Young, C. L., “Gas-liquid critical properties of binary mixtures”, Chem. Rev., 75, 119 (1975).

[23]  Belyakov, M. Y., Gorodetskii, E. E., Kulikov, V. D., Voronov, V. P. and Grigoriev, B.A., “Scaled equation of state and specific thermodynamic behavior of near-critical methane-pentane binary mixture”, Fluid Phase Equilib., 418, 44 (2016).

[24]  Nesterova, T. N., Vostrikov, S. V., Nesterov, I. A., Nazmutdinov, A. G. and Sosin, S. E., “Critical and maximum temperatures of coexistence of liquid and gas phase in hydrocarbons binary mixtures, I: Critical (vapour–liquid) temperatures of alkane binary mixtures”, Fluid Phase Equilib., 368, 14 (2014).

[25]  Teja, A. S. and Smith, R. L., “Critical properties of thermally unstable substances from mixture data”, AIChE J., 33, 1560 (1987).

[26]  Han, K., Xia, S., Ma, P., Yan, F. and Liu, T., “Measurement of critical temperatures and critical pressures for binary mixtures of methyl tert-butyl ether (MTBE)+alcohol and MTBE+alkane”, J. Chem. Thermodyn., 62, 111 (2013).

[27]  Vostrikov, S. V., Nesterova, T. N., Nesterov, I. A., Sosin, S. E. and Nazmutdinov, A. G., “III. Study of critical and maximum temperatures of coexistence of liquid and gas phase in hydrocarbons binary mixtures of aromatic hydrocarbons with alkanes and cycloalkanes”, Fluid Phase Equilib., 377, 56 (2014).

[28]  Wang, G., Qin, Z., Liu, J., Tian, Z., Hou, X. and Wang, J., “Critical properties of the reacting mixture in the alkylation of benzene with propene”, Ind. Eng. Chem. Res., 42, 6531 (2003).

[29]  Liu, T., Fu, J. -Y., Wang, K., Gao, Y. and Yuan, W. -K., “Gas-liquid critical properties of ethylene + benzene”, J. Chem. Eng. Data, 46, 809 (2001).

[30]  Jones, I. W. and Rowlinson, J. S., “Gas-liquid critical temperatures of binary mixtures, Part 2”, Trans. Faraday Soc., 59, 1702 (1963).

[31]  Horstmann, S., Fischer, K. and Gmehling, J., “Experimental determination of critical data of mixtures and their relevance for the development of thermodynamic models”, Chem. Eng. Sci., 56, 6905 (2001).

[32]  Singh, H., Lucien, F. P. and Foster, N. R., “Critical properties for binary mixtures of ethane containing low concentrations of n –Alkane”, J. Chem. Eng. Data, 45, 131 (2000).

[33]  Liu, J., Qin, Z., G. Wang, G., Hou, X. and Wang, J., “Critical properties of binary and ternary mixtures of hexane + methanol, hexane + carbon dioxide, methanol + carbon dioxide, and hexane + carbon dioxide + methanol”, J. Chem. Eng. Data, 48, 1610 (2003).

[34]  Nieto, P. G., García-Gonzalo, E., Fernández, J. A. and Muñiz, C. D., “Hybrid PSO–SVM-based method for long-term forecasting of turbidity in the Nalón river basin: A case study in Northern Spain”, Ecological Engineering, 73, 192 (2014).