Mathematical model of agitator for sulfuric-acid zinc leaching as a control object

This study focuses on mathematical modeling of one of the main finishing processes in production of metal zinc from roasted products. With this end in view, the theory of leaching kinetics was addressed with a view to approximating the mathematical description by a standard autocontrol link. This is required for the design and setting of systems for automated control of leaching. The mathematical model rests upon the assumption that metal zing recovery in leaching is governed by the kinetic equation of zinc oxide–sulfuric acid reaction. In the first approximation, kinetics is described using a first-order equation and an equation of material balance in agitator. As a result, a differential equation of the process is derived, as well as a transition curve is plotted and highly accurate approximated using the equation of inertia link of autocontrol. From the theoretical description of the process flow, the equation of zinc recovery in leaching is obtained. Integrating the concentration variation equation allows approximating the mathematical model of leaching at sufficient accuracy by the first-order inertia link, which makes the framework for the design of autocontrol system for leaching.

Leonov R. E., Patrakov S. S. Mathematical model of agitator for sulfuric-acid zinc leaching as a control object. MIAB. Mining Inf. Anal. Bull. 2021;(11-1):366—373. [In Russ]. DOI: 10.25018/0236_1493_2021_111_0_366.

Leonov R. E.¹, Cand. Sci. (Eng.), Associate Professor, Professor at the Automation and Computer Technologies Department, e-mail: lnprep2011@yandex.ru;
Patrakov S. S.¹, Master’s Degree Student in Automatic control, Automation and Computer Technologies Department;
¹ Ural State Mining University, Yekaterinburg, Russia.

1. Akhtamov F. E., Nishonov B. U. On the issue of zinc cake processing. Theory and technology of metallurgical production. 2016; (1): 69—72. [In Russ].

2. Zaitseva, N. A., Ivanova, I. V., Samigullina, R. F., Rotermel, M. V., Krasnenko, T. I. Synthesis, crystal and thermal properties of solid solution Zn2−2xCu2xSiO4 with willemite structure. Russ. J. Inorg. Chem. 2019; (64). [In Russ]. DOI:10.1134/S0036023619010224

3. Kozin, V. Z., Komlev, A. S. Lumpy products testing. MIAB. Mining Inf. Anal. Bull. 2020; (3—1): 410—421. [In Russ]. DOI: 10.25018/0236—1493—2020—31—0—410— 421.

4. Amdur A. А., Pavlov V. V., Fyodorov S. A. Flotation of dispersed gold drops in melts as an element of technological scheme of enrichment. MIAB. Mining Inf. Anal. Bull. 2020; (3—1): 399—409. [In Russ]. DOI: 10.25018/0236—1493—2020—31—0—399—409

5. Hassan Koohestani, Elahe Sadat Khatami, Kazem Babaei Comparative investigation of leaching of zinc from wastes of the zinc alloy production process. Mineral Processing and Extracting Metallurgy. 2019; pp.1—7. DOI: 10.1080/25726641.2019.1660506

6. Zatonskiy A. V., Bovykin K. V., Asadulin R. R., Golubeva E. V. Development and testing of industrial technology for lead cake carbonization. Russ. J. Non-ferr. Met. 2015; (5): 55—58. [In Russ].

7. Yakornov S. A., Panshin A. M., Kozlov P. A., Ivakin D. A., Golubeva E. V. Development of technology for hydrometallurgical processing of waelz-oxide to obtain carbonized lead cake. Metallurgist. 2017; (10): 60—66. [In Russ].

8. Klyain S. E., Kozlov P. A., Naboychenko S. S. Zinc extraction from crude ore. Yekaterinburg, UGGU-UPI Publ. 2009; p. 492. [In Russ].

9. Amdur A. M., Fyodorov S. A., Matushkina A. N., Apakashev R. A. Behaviour of the gold dispersed drops in the ore on being heated. Russ. J. Non-ferr. Met. 2016; (2): 3–6. [In Russ]. DOI: 10.17580/nfm.2016.02.01

10. Vatolin, N. A., Amdur, A. M. The effect of thermal coal destruction on the reduction of iron oxides from concentrates. Proceedings of the Russian Academy of Sciences. 463 (5), 556. [In Russ].

11. Weidong Xing, Man Seung Lee. Leaching of gold and silver from anode slime with a mixture of hydrochloric acid and oxidizing agents. Geosystem Engineering. 2017; no 20(4), pp.216—223. DOI: 10.1080/12269328.2017.1278728

12. Harrison Hodge, Peter C. Hayes, William Hawker, James Vaughan. The DSP concentrate sinter-leach process for aluminium and sodium recovery 2: leaching behavior. Mineral Processing and Extractive Metallurgy. 2020; pp.1—10. DOI: 10.1080/25726641.2020.1791 681

13. Matushkina A. N., Amdur A. M., Zypin E. F. Indictors of material enrichment with predominance of finely dispersed gold before and after the heat treatment, with carbonatesilicate ore being used as an example. Gorhyj Journal. 2016; (12): 9—13. [In Russ].

14. Mungall, J. E., Brenan J. M., Godel B., Barnes S. J., Gaillard F. Transport of metals and sulphur in magmas by flotation of sulphide melt on vapour bubbles. Nature Geoscience. 2015, Vol. 8, Issue 3, рр. 216—219.

15. Amdur A. M., Vatolin, N. A., Fyodorov S. A., Matushkina A. N. Behaviour of dispersed drops of gold in the porous bodies and oxide melts in the process of heating. Proceedings of the Russian Academy of Sciences. 2015, vol. 465, no.3, pp. 307—309. [In Russ]

16. Kozin, V. Z., Komlev, A. S. Combined method for the selection of samples of mineral-dressing products and the equipment for its implementation. Obogashcheniye Rud [Ore Processing]. 2019; (3): 28—32. [In Russ].

17. Kozin, V. Z., Komlev, A. S. Determination of variation coefficients of a mass fraction of components in the concentrates. Obogashcheniye Rud [Ore Processing]. 2019; (1): 28—33. [In Russ].

18. Brochot S. Sampling for metallurgical test: how the test results can be used to estimate their confidence level. XXVIII International Mineral Processing Congress. Quebec City, Canada, 2016. Paper ID 438.

19. Yong Qiao, Jiang Diao, Deman Liu, Jianfeng Yang, Dongwei Guo, Siyu Gong, Bing Xie. Dephosphorisation of steel slags by leaching with sulphuric acid. Mineral Processing and Extractive Metallurgy. 2018 no. 127(4), pp. 250—254. DOI: 10.1080/03719553.2017.1 412096

20. B. Wang, Y. L. Hao, W. Q. Chu, S. Rong, H. L. Sun Kinetics of leaching of 20CaO·13Al2O3·3MgO·3SiO2, Mineral Processing and Extractive Metallurgy. 2017; no. 126(4): 199—204. DOI: 10.1080/03719553.2016.1220448

21. Ning Peng, Bing Peng, Hui Liu, Ke Xue, Dong Chen, Dong-Hong Lin. Reductive roasting and ammonia leaching of high iron-bearing zinc calcines. Mineral Processing and Extractive Metallurgy. 2018; no. 127(1): 1—9. DOI: 10.1080/03719553.2016.1258136

22. Pelevin A. E. Obtaining hematite concentrates from hematite-magnetite ores. MIAB. Mining Inf. Anal. Bull. 2020; (3—1): 422—430. [In Russ]. DOI: 10.25018/0236—1493— 2020—31—0—422—430.

23. Pelevin A. E., Sytykh N. A. Testing of a two-stage scheme for grinding titanomagnetite ore. Obogashcheniye Rud [Ore Processing]. 2018; (2): 13—18. [In Russ]. DOI: 10.17580/ or.2018.02.03.

24. Pelevin A. E. Ways of increasing the efficiency of iron ore raw materials processing technology. Ferrous metallurgy. Bulletin of scientific, technical, and economic information. 2019, vol.75, no.2, pp.137—146. [In Russ].

25. Prokopyev S. A., Pelevin A. E., Napolskikh S.A, Gelbing P. A. Stage separation of magnetite concentrate with the use of screw separation Obogashcheniye Rud [Ore Processing]. 2018; (4): 28—33. [In Russ]. DOI: 10.17580/or.2018.04.06.