Optimization of Extended UNIQUAC Model Parameter for Mean Activity Coefficient of Aqueous Chloride Solutions using Genetic+PSO

Document Type : Research Paper


1 Department of Chemical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

2 Institute of Production and Recovery, Research Institute of Petroleum Industry, Tehran, Iran

3 Petroleum University of Technology, Ahwaz, Iran


In the present study, in order to predict the activity coefficient of inorganic ions, 12 cases of aqueous chloride solution were considered (AClx=1,2; A=Li, Na, K, Rb, Mg, Ca, Ba, Mn, Fe, Co, Ni). For this study, the UNIQUAC thermodynamic model is desired and its adjustable parameters are optimized with the Genetic + PSO algorithm. The optimization of the UNIQUAC model with PSO+ genetic algorithms has good results. So that the minimum and maximum electrolyte error of the whole system are 0.00044 and 0.0091, respectively. For this study, a temperature of 298.15 and a pressure of 1 is considered. Also, in this study for the electrolyte system, the Artificial bee colony (ABC) algorithm, and Imperialist competitive algorithm (ICA) has been studied. The results showed that the Artificial bee colony algorithm has a lower accuracy than the Genetic+ Particle swarm optimization (PSO) algorithm. The minimum concentration was 0.1 Molality and the maximum concentration was 3 Molality. Based on the results, the activity coefficient of LiCl, NaCl, KCl, RbCl + H2O, MgCl2, CaCl2, BaCl2, MnCl2, FeCl2, CoCl2 NiCl2 depends on the ionic strength of the electrolyte system.


[1] Hashemi SH, Hashemi SA. Prediction of scale formation according to water injection operations in Nosrat Oil Field. Modeling Earth Systems and Environment. 2020 Mar;6(1):585-9.
[2] Hashemi SH, Mousavi Dehghani SA, Dinmohammad M. Thermodynamic Prediction of Ba and Sr Sulfates Scale Formation in Waterflooding Projects in Oil Reservoirs. Journal of Mineral Resources Engineering. 22;4(2):23-37.
[3] Otumudia E, Awajiogak U. Determining the Rates for Scale Formation in Oil Wells, International Journal of Engineering Research and Applications. 2016;6(9 Part 1):62-6.
[4] Haghtalab A, Kamali MJ, Shahrabadi A. Prediction mineral scale formation in oil reservoirs during water injection. Fluid Phase Equilibria. 2014 Jul 15;373:43-54.
[5] El-Said M, Ramzi M, Abdel-Moghny T. Analysis of oilfield waters by ion chromatography to determine the composition of scale deposition. Desalination. 2009 Dec 15;249(2):748-56.
[6] Bromley LA. Thermodynamic properties of strong electrolytes in aqueous solutions. AIChE Journal. 1973 Mar;19(2):313-20.
[7] Chen CC, Evans LB. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE Journal. 1986 Mar;32(3):444-54.
[8] Hashemi SH. Thermodynamic study of water activity of single strong electrolytes. Journal of Applied and Computational Mechanics. 2017 Jun 1;3(2):150-7.
[9] Hashemi SH, Dehghani SA, Khodadadi A, Dinmohammad M, Hosseini SM, Hashemi SA. Optimization of Extended UNIQUAC Parameter for Activity Coefficients of Ions of an Electrolyte System using Genetic Algorithms. Korean Chemical Engineering Research. 2017;55(5):652-9.
[10] Hashemi SH, Dehghani SA, Dinmohammad M, Hashemi SA. Prediction of Water Activity of Electrolyte Solutions with Extended UNIQUAC Model. Journal of Chemical and Pharmaceutical Research. 2017;9(1):247-52.
[11] Hashemi SH, Mousavi Dehghani SA, Dinmohammad M, Hashemi SA. Thermodynamic prediction of anhydrite mineral deposit formation in petroleum electrolytic solutions. Nashrieh Shimi va Mohandesi Shimi Iran (NSMSI) 2018 July 4.
[12] Alhajri IH, Alarifi IM, Asadi A, Nguyen HM, Moayedi H. A general model for prediction of BaSO4 and SrSO4 solubility in aqueous electrolyte solutions over a wide range of temperatures and pressures. Journal of Molecular Liquids. 2020 Feb 1;299:112142 .
[13] Thomsen K, Rasmussen P. Modeling of vapor–liquid–solid equilibrium in gas–aqueous electrolyte systems. Chemical Engineering Science. 1999 Jun 1;54(12):1787-802.
[14] Abrams DS, Prausnitz JM. Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or completely miscible systems. AIChE Journal. 1975 Jan;21(1):116-28.
[15] Sander B, Rasmussen P, Fredenslund A. Calculation of solid-liquid equilibria in aqueous solutions of nitrate salts using an extended UNIQUAC equation. Chemical Engineering Science. 1986 Jan 1;41(5):1197-202.
[16] García AV, Thomsen K, Stenby EH. Prediction of mineral scale formation in geothermal and oilfield operations using the extended UNIQUAC model: part I. Sulfate scaling minerals. Geothermics. 2005 Feb 1;34(1):61-97.
[17] Langeveld J, Engelbrecht AP. A generic set-based particle swarm optimization algorithm. InInternational conference on swarm intelligence, ICSI. 2011 Jun (pp. 1-10).
[18] Murthy KR, Raju MR, Rao GG. Comparison between conventional, GA and PSO with respect to optimal capacitor placement in agricultural distribution system. In2010 Annual IEEE India Conference (INDICON) 2010 Dec 17 (pp. 1-4). IEEE.
[19] Ghasemi M, Ghavidel S, Rahmani S, Roosta A, Falah H. A novel hybrid algorithm of imperialist competitive algorithm and teaching learning algorithm for optimal power flow problem with non-smooth cost functions. Engineering Applications of Artificial Intelligence. 2014 Mar 1;29:54-69.
[20] Basturk B. An artificial bee colony (ABC) algorithm for numeric function optimization. InIEEE Swarm Intelligence Symposium, Indianapolis, IN, USA, 2006.
[21] Karaboga D, Basturk B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of global optimization. 2007 Nov 1;39(3):459-71. [22] Karaboga D, Basturk B. On the performance of artificial bee colony (ABC) algorithm. Applied Soft Computing. 2008 Jan 1;8(1):687-97.
[23] Stokes RH, Robinson RA. Ionic hydration and activity in electrolyte solutions. Journal of the American Chemical Society. 1948 May;70(5):1870-8.