Calculation and Prediction of Fugacity and Activity Coefficients in Binary Mixtures, using a Self-Regulated Fretwidth Harmony Search Algorithm
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Submitted:
Aug 12, 2015
Published:
Nov 7, 2015
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Abstract
This research article proposes the use of a novel variant of the HS algorithm (harmony search), i.e. SFHS (self-regulated fret width harmony search algorithm), for calculating and predicting fugacity and activity coefficients in binary mixtures. Parameter selection was carried out based on preliminary results with different standard test functions. Different previously reported systems were selected, at 25 ° C and 40 ° C, and at low and moderate pressure levels. Moreover, two solutes were selected: carbon dioxide and ethane. Different solvents, both polar and nonpolar, were selected with comparative purposes. Activity and fugacity coefficients were calculated using the Redlich-Kwong state equation and Lewis rule, along with the sfhs algorithm, assuming both solutes in vapor phase. Consistency of the activity coefficients was analyzed by the Redlich-Kister strategy. Results were very close to those found experimentally by other authors, and most of them did not differ in more than one percentage unit.
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Jiménez Leiva, C. C., Amaya, I., & Correa, R. (2015). Calculation and Prediction of Fugacity and Activity Coefficients in Binary Mixtures, using a Self-Regulated Fretwidth Harmony Search Algorithm. Revista Ingenierías Universidad De Medellín, 16(30), 67–95. https://doi.org/10.22395/rium.v16n30a4
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References
[1] A. Bonilla-Petriciolet, 'On the capabilities and limitations of harmony search for parameter estimation in vapor-liquid equilibrium modeling,' Fluid Phase Equilibria, no. 332, pp. 7-20, 2012.
[2] J. M. Smith, H. C. Van Ness and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, México: Mc Graw Hill, 1995.
[3] J. M. Prausnitz, Computer Calculations For High Pressure Vapor Liquid Equilibria, Prentice Hall International Series, 1968.
[4] K. Ohgaki, F. Sano and T. Katayama, 'Isothermal Vapor-Liquid Equilibrium Data for Binary Systems Containing Ethane at High Pressures,' Journal of Chemical and Engineering Data, vol. 21, no. 1, pp. 55-58, 1976.
[5] K. Ohgaki and T. Katayama, 'Isothermal Vapor-Liquid Equilibria for Systems Ethil Ether-Carbon Dioxide and Methil Acetate-Carbon Dioxide at High Pressures,' Journal of Chemical and Engineering Data, vol. 20, no. 3, 1975.
[6] K. Ohgaki and T. Katayama, 'Isothermal Vapor-Liquid Equilibrium Data for Binaryt Systems Containing Carbon Dioxide at High Pressures: Methanol-Carbon Dioxide, n-Hexane-Carbon Dioxid, and Benzene-Carbon Dioxide Systems,' Journal of Chemical and Engineering Data, vol. 21, no. 1, 1976.
[7] S. E. Fateen and A. Bonilla, 'On the performance of swarm intelligence optimization algorithms for phase stability and liquid-liquid and vapor-liquid equilibrium calculations,' Periodica Polytechnica Chemjical Engineering, vol. 59, no. 3, pp. 186-200, 2015.
[8] M. Sadeghi, H. Salami, V. Taghikhani and M. Robert, 'A comprehensive study on CO2 solubility in brine: Thermodynamic-based and neural network modeling,' Fluid Phase Equilibria, vol. 403, pp. 153-159, 2015.
[9] J. A. Lazzús, 'Optimization of high-pressure vapor-liquid equilibrium modelling of binary mixtures (supercritical fluid + ionic liquid) by particle swarm algorithm,' University of Kragujevac, Faculty of Science, vol. 73, no. 3, pp. 663-688, 2015.
[10] Z. Geem, J. Kim and G. Loganathan, 'A New Heuristic Optimization Algorithm: Harmony Search,' Simulation, no. 76, pp. 60-68, 2001.
[11] J. Contreras, I. Amaya and R. Correa, 'An improved variant of the conventional Harmony Search algorithm,' Appl. Math. Comput., no. 227, pp. 824-830, 2014.
[12] I. Amaya, J. Cruz and R. Correa, 'Harmoy Search algorithm: a variant with Self-regulated Fretwidth,' Appl. Math. Comput., no. 266, pp. 1127-1152, 2015.
[13] O. A. Hougen, K. M. Watson and R. A. Ragatz, Chemical Process Principles - Part II. Thermodynamics, New York: John Wiley & Sons, Inc., 2005.
[14] J. López, V. Trejos and C. Cardona, 'Objetive functions analysis in the minimization of binary VLE data for asymmetric mixtures at high pressures,' Fluid Phase Equilibria, no. 248, pp. 147-157, 2006.
[15] D.-Y. Peng and D. B. Robinson, 'A New Two Constant Equation of State,' Journal of Industrial and Engineering Chemistry, vol. 15, no. 1, 1976.
[16] G. Soave, 'Equilibrium constants from a modified Redlich-Kwong equation of state,' Chemical Engineering Science, vol. 27, no. 6, pp. 1197-1203, 1971.
[17] L. N. Canjar and F. S. Manning, Thermodynamic Properties and Reduced Correlations for Gases, Houston: Gulf Publishing Company, 1967.
[18] J. López, V. Trejos and C. Cardona, 'Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n alkanols,' Fluid Phase Equilibria, no. 275, pp. 1-7, 2009.
[19] A. Bharti, Prerna and T. Banerjee, 'Applicability of Cuckoo Search Algorithm for the Prediction of Multicomponent Liquid-Liquid Equilibria for Imidazolium and Phosphonium Based Ionic Liquids,' Industrial and Engineering Chemistry Research, vol. 54, no. 49, pp. 12393-12407, 2015.
[20] J. Fernández-Vargas, A. Bonilla-Petriciolet and J. Segovia-Hernández, 'An improved ant colony optimization method and its application for the thermodynamic modeling of phase equilibrium,' Fluid Phase Equilibria, no. 353, pp. 121-131, 2013.
[21] V. Bhargava, S. Fateen and A. Bonilla-Petriciolet, 'Cuckoo Search: A new nature-inspired optimization method for phase equilibrium calculations,' Fluid Phase Equilibria, no. 337, pp. 191-200, 2013.
[22] A. Kabouche, A. Boultif, A. Abidi and N. Gherraf, 'Interaction parameter estimation in liquid-liquid phase equilibrium modeling using stochastic and hybrid algorithms,' Fluid Phase
Equilibria, no. 336, pp. 113-121, 2012.
[2] J. M. Smith, H. C. Van Ness and M. M. Abbott, Introduction to Chemical Engineering Thermodynamics, México: Mc Graw Hill, 1995.
[3] J. M. Prausnitz, Computer Calculations For High Pressure Vapor Liquid Equilibria, Prentice Hall International Series, 1968.
[4] K. Ohgaki, F. Sano and T. Katayama, 'Isothermal Vapor-Liquid Equilibrium Data for Binary Systems Containing Ethane at High Pressures,' Journal of Chemical and Engineering Data, vol. 21, no. 1, pp. 55-58, 1976.
[5] K. Ohgaki and T. Katayama, 'Isothermal Vapor-Liquid Equilibria for Systems Ethil Ether-Carbon Dioxide and Methil Acetate-Carbon Dioxide at High Pressures,' Journal of Chemical and Engineering Data, vol. 20, no. 3, 1975.
[6] K. Ohgaki and T. Katayama, 'Isothermal Vapor-Liquid Equilibrium Data for Binaryt Systems Containing Carbon Dioxide at High Pressures: Methanol-Carbon Dioxide, n-Hexane-Carbon Dioxid, and Benzene-Carbon Dioxide Systems,' Journal of Chemical and Engineering Data, vol. 21, no. 1, 1976.
[7] S. E. Fateen and A. Bonilla, 'On the performance of swarm intelligence optimization algorithms for phase stability and liquid-liquid and vapor-liquid equilibrium calculations,' Periodica Polytechnica Chemjical Engineering, vol. 59, no. 3, pp. 186-200, 2015.
[8] M. Sadeghi, H. Salami, V. Taghikhani and M. Robert, 'A comprehensive study on CO2 solubility in brine: Thermodynamic-based and neural network modeling,' Fluid Phase Equilibria, vol. 403, pp. 153-159, 2015.
[9] J. A. Lazzús, 'Optimization of high-pressure vapor-liquid equilibrium modelling of binary mixtures (supercritical fluid + ionic liquid) by particle swarm algorithm,' University of Kragujevac, Faculty of Science, vol. 73, no. 3, pp. 663-688, 2015.
[10] Z. Geem, J. Kim and G. Loganathan, 'A New Heuristic Optimization Algorithm: Harmony Search,' Simulation, no. 76, pp. 60-68, 2001.
[11] J. Contreras, I. Amaya and R. Correa, 'An improved variant of the conventional Harmony Search algorithm,' Appl. Math. Comput., no. 227, pp. 824-830, 2014.
[12] I. Amaya, J. Cruz and R. Correa, 'Harmoy Search algorithm: a variant with Self-regulated Fretwidth,' Appl. Math. Comput., no. 266, pp. 1127-1152, 2015.
[13] O. A. Hougen, K. M. Watson and R. A. Ragatz, Chemical Process Principles - Part II. Thermodynamics, New York: John Wiley & Sons, Inc., 2005.
[14] J. López, V. Trejos and C. Cardona, 'Objetive functions analysis in the minimization of binary VLE data for asymmetric mixtures at high pressures,' Fluid Phase Equilibria, no. 248, pp. 147-157, 2006.
[15] D.-Y. Peng and D. B. Robinson, 'A New Two Constant Equation of State,' Journal of Industrial and Engineering Chemistry, vol. 15, no. 1, 1976.
[16] G. Soave, 'Equilibrium constants from a modified Redlich-Kwong equation of state,' Chemical Engineering Science, vol. 27, no. 6, pp. 1197-1203, 1971.
[17] L. N. Canjar and F. S. Manning, Thermodynamic Properties and Reduced Correlations for Gases, Houston: Gulf Publishing Company, 1967.
[18] J. López, V. Trejos and C. Cardona, 'Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n alkanols,' Fluid Phase Equilibria, no. 275, pp. 1-7, 2009.
[19] A. Bharti, Prerna and T. Banerjee, 'Applicability of Cuckoo Search Algorithm for the Prediction of Multicomponent Liquid-Liquid Equilibria for Imidazolium and Phosphonium Based Ionic Liquids,' Industrial and Engineering Chemistry Research, vol. 54, no. 49, pp. 12393-12407, 2015.
[20] J. Fernández-Vargas, A. Bonilla-Petriciolet and J. Segovia-Hernández, 'An improved ant colony optimization method and its application for the thermodynamic modeling of phase equilibrium,' Fluid Phase Equilibria, no. 353, pp. 121-131, 2013.
[21] V. Bhargava, S. Fateen and A. Bonilla-Petriciolet, 'Cuckoo Search: A new nature-inspired optimization method for phase equilibrium calculations,' Fluid Phase Equilibria, no. 337, pp. 191-200, 2013.
[22] A. Kabouche, A. Boultif, A. Abidi and N. Gherraf, 'Interaction parameter estimation in liquid-liquid phase equilibrium modeling using stochastic and hybrid algorithms,' Fluid Phase
Equilibria, no. 336, pp. 113-121, 2012.