Statistical modeling of copper losses in the silicate slag of the sulfide concentrate smelting process

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This article presents the results of the statistical modeling of copper losses in the silicate slag of the sulfide concentrates smelting process. The aim of this study was to define the correlation dependence of the degree of copper losses in the silicate slag on the following parameters of technological processes: SiO2, FeO, Fe3O4, CaO and Al2O3 content in the slag and copper content in the matte. Multiple linear regression analysis (MLRA), artificial neural networks (ANNs) and adaptive network based fuzzy inference system (ANFIS) were used as tools for mathematical analysis of the indicated problem. The best correlation coefficient (R2 = 0.719) of the final model was obtained using the ANFIS modeling approach.

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  • 1. Schlesinger M.E. King M.J. & Sole K.C. & Davenport W.G. (2011). Extractive Metallurgy of Copper (5th ed.). Oxford UK: Elsevier.

  • 2. Fernandez-Caliani J.C. Rios G. Martinez J. & Jimenez F.J. (2012). Occurrence and speciation of copper in slags obtained during the pyrometallurgical processing of chalcopyrite concentrates at the Huelva smelter (Spain). J. Min. Metall. Sect. B 48(2) 161–171. DOI: 10.2298/jmmb111111027f.

  • 3. Sarrafi A. Rahmati B. Hassani H.R. & Shirazi H.H.A. (2004). Recovery of copper from reverberatory furnace slag by flotation. Miner. Eng. 17 457–459. DOI: 10.1016/j.mineng.2003.10.018.

  • 4. Moskalyk R.R. & Alfantazi A.M. (2003). Review of copper pyrometallurgical practice: today and tomorrow. Miner. Eng. 16 893–919. DOI: 10.1016/j.mineng.2003.08.002.

  • 5. Shi C. Meyer C. & Behnood A. (2008). Utilization of copper slag in cement and concrete. Resour. Conserv. Recycl. 52 11151120. DOI: 10.1016/j.resconrec.2008.06.008.

  • 6. Gorai B. Jana R.K. & Premchand P. (2003). Characteristics and utilisation of copper slag – a review. Resour. Conserv. Recycl. 39 299–313. DOI: 10.1016/S0921-3449(02)00171-4.

  • 7. Jalkanen H. Vehviläinen J. & Poijärvi J. (2003). Copper in solidified copper smelter slags. Scand. J. Metall. 32 65–70. DOI: 10.1034/j.1600-0692.2003.00536.x.

  • 8. Zivkovic Z. Mitevska N. Mihajlovic I. & Nikolic Dj. (2010). Copper losses in sulfide concentrate smelting slag are dependent on slag composition. Miner. Metall. Process. 27 141–147.

  • 9. Acuna C. & Sherrington M. (2005). Slag cleaning processes: A growing concern. Mater. Sci. Forum. 475 2745–2752. DOI: 10.4028/

  • 10. Živković Ž. Mitevska N. Mihajlović I. & Nikolić Đ. (2009). The influence of the silicate slag composition on copper losses during smelting of the sulfide concentrates. J. Min. Metall. Sect. B 45 23–34. DOI: 10.2298/JMMB0901023Z.

  • 11. Goni C. & Sanchez M. (2009). Modeling of copper content variation during „El Teniente“ slag cleaning process. VIII International Conference on Molten Slags Fluxes & Salts. Santiago Chile 123–131.

  • 12. Djordjevic P. Mitevska N. Mihajlovic I. Nikolić Dj. Manasijevic D. & Zivkovic Z. (2012). The effect of copper content in the matte on the distribution coefficients between the slag and the matte for certain elements in the sulphide copper concentrate smelting process. J. Min. Metall. Sect. B 48 143–151. DOI: 10.2298/JMMB111115012D.

  • 13. Djordjevic P. Mitevska N. Mihajlovic I. Nikolic Dj. & Zivkovic Z. (2014). Effect of the slag basicity on the coefficient of distribution between copper matte and the slag for certain metals. Miner. Process. Extr. Metall. Rev. 35 202–207. DOI: 10.1080/08827508.2012.738731.

  • 14. Mitevska N. Živković Ž. & Marinković J. (2000). The influence of reverb slag composition on copper losses. J. Min. Metall. Sect. B 36 63–76.

  • 15. Sridhar R. Toguri J.M. Simeonov S. (1997). Copper losses and thermodynamic considerations in copper smelting. Metall. Mater. Trans. B 28 191–200. DOI: 10.1007/s11663-997-0084-5.

  • 16. Li u J. Gui W. Xie Y. & Yang C. (2014). Dynamic modeling of copper flash smelting process at a Smelter in China. Appl. Math. Model. 38(7–8) 2206–2213. DOI:

  • 17. Liu J. Gui W. Xie Y. & Jiang Z. (2013). Solving the Transient Cost-Related Optimization Problem for Copper Flash Smelting Process with Legendre Pseudospectral Method. Mater. Trans. 54(3) 350–356. DO I: 10.2320/matertrans.M2012350.

  • 18. Živković Ž. Mihajlović I. & Nikolić Đ. (2009). Artificial neural network method applied on the nonlinear multivariate problems. Serb. J. Manag. 4 143–155.

  • 19. Živković Ž. Mihajlović I. Djurić I. & Štrbac N. (2010). Statistical modeling of the industrial sodium aluminate solutions decomposition process. Metall. Mater. Trans. B 41 1116–1122. DOI: 10.1007/s11663-010-9407-z.

  • 20. Kalina J. (2014). On robust information extraction from high-dimensional data. Serb. J. Manag. 9(1) 131–144. DOI: 10.5937/sjm9-5520.

  • 21. Azlan Hussain M. (1999). Review of the applications of neural networks in chemical control – simulation and online implementation. Artif. Intell. Eng. 13 55–68. DOI: 1016/S0954-1810(98)00011-9.

  • 22. Bloch G. & Denoeux T. (2003). Neural networks for process control and optimization: two industrial applications. ISA Trans. 42 39–51. DOI: 10.1016/S0019-0578(07)60112-8.

  • 23. Chehreh Chelgani S. & Jorjani E. (2009). Artificial neural network prediction of Al2O3 leaching recovery in the Bayer process – Jajarm alumina plant (Iran). Hydrometallurgy 97 105–110. DOI: 10.1016/j.hydromet.2009.01.008.

  • 24. Jang J.S.R. (1993). ANFIS: Adaptive-network based fuzzy inference system. IEEE Trans. Syst. Man Cybern. Syst. 23 665–685. DOI: 10.1109/21.256541.

  • 25. Savic M. Mihajlovic I. & Zivkovic Z. (2013). An ANFIS-based air quality model for prediction of SO2 concentration in urban area. Serb. J. Manag. 8 25–38. DOI: 10.2139/ssrn.2257533.

  • 26. Karami A. & Afiuni-Zadeh S. (2012). Sizing of rock fragmentation modeling due to bench blasting using adaptive neuro-fuzzy inference system and radial basis function. Int. J. Min. Sci. Technol. 22 459–463. DOI: 10.1016/j.ijmst.2012.06.001.

  • 27. Han Y. Zeng W. Zhang X. Zhao Y. Sun Y. & Ma X. (2013). Modeling the relationship between hydrogen content and mechanical property of Ti600 alloy by using ANFIS. Appl. Math. Model. 37 5705–5714. DOI: 10.1016/j.apm.2012.11.008.

  • 28. Fragiadakis N.G. Tsoukalas V.D. & Papazoglou V.J. (2014). An adaptive neuro-fuzzy inference system (ANFIS) model for assesing occupational risk in the shipbuilding industry. Safety Sci. 63 226–235. DOI: 1016/j.ssci.2013.11.013.

  • 29. Mihajlović I. Đurić I. & Živković Ž. (2014). ANFIS based prediction of the aluminum extraction from boehmite bauxite in the Bayer process. Pol. J. Chem. Tech. 16(1)103–109. DOI: 10.2478/pjct-2014-0018.

  • 30. Moroney R.N. (1998). Spurious of virtual correlation errors commonly encountered in reduction of scientific data. J. Wind. Eng. Ind. Aerod. 77&78 543–553.

  • 31. Demuth H. & Beale M. (2002). Neural Network Toolbox for Use with MATLAB Handbook. The MathWorks Inc. Natick MA.

  • 32. Jang J.S.R. Sun C.T. & Mizutani E. (1997). Neuro-Fuzzy and Soft Computing – A Computational Approach to Learning and Machine Intelligence. Prentice Hall Cambridge MA.

  • 33. Subashini L. & Vasudeven M. (2012). Adaptive neuro-fuzzy inference system (ANFIS) – based models for predicting the weld bead width and depth of penetration from the infrared thermal image of the weld pool. Metall. Mater. Trans. B 43 145–154. DOI: 10.1007/s11663-011-9570-x.

  • 34. Takagi T. & Sugeno M. (1985). Fuzzy identification systems and its application to modeling and control. IEEE Trans. Syst. Man Cybern. Syst. 15 116–132. DOI: 10.1109/tsmc.1985.6313399.

  • 35. MATLAB V.7.1 (2007). The MathWorks Inc. Natick MA.

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