, Volume 70, Issue 12, pp 2893–2899 | Cite as

A RQPSO Algorithm for Multiphase Equilibrium Calculation in the KIVCET Process

  • Jiadong Li
  • Yanpo Song
  • Ping ZhouEmail author
  • Ji Ma
  • Zhuo Chen
  • Liyuan Chai
Multiphase Flows in Materials Processing


The prediction of phase configurations and the optimization of operating parameters in the metallurgical process are normally achieved by the multiphase equilibrium calculation (MEC), which is formulated as a constrained optimization problem based on the principle of Gibbs free energy minimization. A revised quantum-behaved particle swarm optimization (RQPSO) algorithm has been proposed to solve the optimization problem using three-part improved strategies. Based on the KIVCET smelting characteristics, a MEC model for the KIVCET process is established and solved using the RQPSO algorithm. The calculated and industrial data of the lead grade are 96.20% and 96.33%, respectively, those of the matte grade are 19.39% and 19.68%, and the mass fractions of Pb in the predicted and industrial matte are 3.96% and 3.34%, respectively. The calculated results of the phase configuration are consistent with the actual production data, which indicates that the MEC model and RQPSO algorithm are accurate and reliable.



We would like to express our gratitude to Project supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 61621062).

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Y.I. Sannikov, M.A. Liamina, V.A. Shumskij, Y.A. Grinin, and M.V. Radashin, CIM Bull. 91, 76 (1998).Google Scholar
  2. 2.
    L.V. Slobodkin, Y.A. Sannikov, Y. A. Grinin, M.A. Lyamina, V.A. Shumskij, and N.N. Ushakov, Lead-Zinc 2000 Symposium, PA, USA, 687–692 (2000).Google Scholar
  3. 3.
    J.L. Wang, X.C. Wen, and C.F. Zhang, Trans. Nonferrous Met. Soc. China 25, 1633 (2015).CrossRefGoogle Scholar
  4. 4.
    L. Bai, M.H. Xie, Y. Zhang, and Q. Qiao, J. Cleaner Prod. 159, 432 (2017).CrossRefGoogle Scholar
  5. 5.
    W.B. White, J. Chem. Phys. 28, 751 (1958).CrossRefGoogle Scholar
  6. 6.
    G.P. Rangaiah, Fluid Phase Equilib. 187, 83 (2001).CrossRefGoogle Scholar
  7. 7.
    F. Jalali, J.D. Seader, and S. Khaleghi, Comput. Chem. Eng. 32, 2333 (2008).CrossRefGoogle Scholar
  8. 8.
    G.I. Burgos-Solórzano, J.F. Brennecke, and M.A. Stadtherr, Fluid Phase Equilib. 219, 245 (2004).CrossRefGoogle Scholar
  9. 9.
    H. Zhang, J.A. Fernández-Vargas, G.P. Rangaiah, A. Bonilla-Petriciolet, and J.G. Segovia-Hernández, Fluid Phase Equilib. 310, 129 (2011).CrossRefGoogle Scholar
  10. 10.
    N. Henderson, J.J.R. de Oliveira, H. Souto, and R. Pitanga Marques, Ind. Eng. Chem. Res. 40, 6028 (2001).CrossRefGoogle Scholar
  11. 11.
    Y.S. Teh and G.P. Rangaiah, Chem. Eng. Res. Des. 80, 745 (2002).CrossRefGoogle Scholar
  12. 12.
    D.V. Nichita and S. Gomez, Chem. Eng. J. 152, 251 (2009).CrossRefGoogle Scholar
  13. 13.
    A. Azimifar and S. Payan, Appl. Therm. Eng. 101, 79 (2016).CrossRefGoogle Scholar
  14. 14.
    A. Kabouche, A. Boultif, A. Abidi, and N. Gherraf, Fluid Phase Equilib. 336, 113 (2012).CrossRefGoogle Scholar
  15. 15.
    J. Sun, B. Feng, and W.B. Xu, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753), Portland, USA, 325–331 (2004).Google Scholar
  16. 16.
    J. Sun, W.B. Xu, and B. Feng, Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems, Singapore, 111–116 (2004).Google Scholar
  17. 17.
    T.Y. Liu, L.C. Jiao, W.P. Ma, J.J. Ma, and R.H. Shang, Knowl. Based Syst. 101, 90 (2016).CrossRefGoogle Scholar
  18. 18.
    K. Hassani and W.-S. Lee, Appl. Soft Comput. 41, 66 (2016).CrossRefGoogle Scholar
  19. 19.
    T. Liu, L. Jiao, W. Ma, and R. Shang, Commun. Nonlinear Sci. 44, 167 (2017).CrossRefGoogle Scholar
  20. 20.
    R. Logesh, V. Subramaniyaswamy, V. Vijayakumar, X.-Z. Gao, and V. Indragandhi, Future Gener. Comput. Syst. 83, 653 (2017).CrossRefGoogle Scholar
  21. 21.
    D. Wang and S. Yuan, Simul. Model Pract. Th. 69, 1 (2016).CrossRefGoogle Scholar
  22. 22.
    J. Sun, W. Fang, X.J. Wu, V. Palade, and W.B. Xu, Evol. Comput. 20, 349 (2012).CrossRefGoogle Scholar
  23. 23.
    J. Liu, J. Sun, and W.B. Xu, International Conference on Advances in Natural Computation, Xi’an, China, 959 (2006).Google Scholar
  24. 24.
    K. Deb, Comput. Method Appl. M. 186, 311 (2000).CrossRefGoogle Scholar
  25. 25.
    Q.M. Wang, X.Y. Guo, S.S. Wang, L.L. Liao, and Q.H. Tian, Trans. Nonferrous Met. Soc. China 27, 2503 (2017).CrossRefGoogle Scholar
  26. 26.
    Y. Liang and Y. Che, Inorganic Thermodynamic Data Manual, Northeastern University Press, Shenyang (1993).Google Scholar
  27. 27.
    P. Tan, C. Zhang, and R. Zhang, J. Cent. South Univ. Technol. 27, 543 (1996).Google Scholar
  28. 28.
    J.L. Wang, C.F. Zhang, and W.H. Zhang, J. Central South Univ. (Sci. Technol.) 43, 429 (2012).Google Scholar
  29. 29.
    J.L. Wang, W.H. Zhang, and C.F. Zhang, China J. Nonferrous Met. 21, 2953 (2011).Google Scholar

Copyright information

© The Minerals, Metals & Materials Society 2018

Authors and Affiliations

  1. 1.School of Energy Science and EngineeringCentral South UniversityChangshaChina
  2. 2.Hunan Key Laboratory of Energy Conservation in Process IndustryChangshaChina
  3. 3.Institute of Environmental Science and Engineering, School of Metallurgy and EnvironmentCentral South UniversityChangshaChina
  4. 4.Chinese National Engineering Research Center for Control and Treatment of Heavy Metal PollutionChangshaChina

Personalised recommendations