National University of Science and Technology MISIS (Moscow, Russia):

Shekhirev D. V., Associate Professor, Candidate of Engineering Sciences, Senior Researcher, shekhirev@list.ru

Deviations of actual material flotation kinetics from a theoretical model may have varied interpretations. Both formal methods for describing kinetic curves and methods related to the actual process phenomenology are used. The currently accepted methods for describing this inhomogeneity through the distribution of particles over the flotation rate are often reduced to kinetic curve approximations. At the same time, there is a trend toward minimizing the number of parameters requiring numerical values to be identified. It is partly due to the instability of the solution under minor changes in the initial data. This limits the applications of the calculated floatability spectra when analyzing the behavior of reagents, evaluating dressability, and modeling flotation circuits. The paper substantiates a working method for calculating a continuous piecewise-constant type of floatability distribution. A discretization method has been developed for the initial equation of the kinetics of an inhomogeneous material, to be subsequently used to identify the spectrum. The boundary flotation intensity values have been substantiated for a piecewise-constant representation of that spectrum. A stable algorithm for calculating material distribution by floatability for various actual products has been developed. It is shown that the spectrum may be sufficiently detailed by increasing the number of ranges in the piecewise-constant representation of the density function for the floatability distribution. Examples are given of floatability spectra calculations for actual materials and their application for the analysis of dressability and design of processing circuits. A computer program has been developed for establishing the floatability spectra and designing respective processing circuits. Its main interfaces are shown in the article.

1. Rubinshtein Yu. B., Filippov Yu. A. Kinetics of flotation. Moscow: Nedra, 1980. 375 p.
2. Beloglazov K. F. Regularities of the flotation process. Moscow: Metallurgizdat, 1947. 144 p.
3. Bogdanov O. S., Maksimov I. I., Podnek A. K., Yanis N. A. Theory and technology of ore flotation. 2^ed. Moscow: Nedra, 1990. 363 p.
4. Inue T., Imaitsumi T. Some aspects of flotation kinetics. VIII International congress on mineral processing. Vol. 2. Leningrad, 1969. pp. 386–398.
5. Bu X., Wang X., Zhou Sh., Li B., Zhan H., Xie G. Discrimination of six flotation kinetic models used in the conventional flotation and carrier flotation of –74 μm coal fines. ACS Omega. 2020. Vol. 5, Iss. 23. pp. 13813–13821.
6. Vinnetta L., Waters K. E. Representation of kinetics models in batch flotation as distributed first-order reactions. Minerals. 2020. Vol. 10. DOI: 10.3390/min10100913.
7. Saleh A. M. A study on the performance of second order models and two phase models in iron ore flotation. Physicochemical Problems of Mineral Processing. 2010. Vol. 44. pp. 215–230.
8. Muayad A. Shihab, Mohammed A. Dhahir, Hamad K. Mohammed. Kinetic study of air bubbles–cetyltrimethylammonium bromide (CTAB) surfactant for recovering microalgae biomass in a foam flotation column. International Journal of Technology. 2020. Vol. 11, Iss. 3. pp. 440–449.
9. Nikolaev A. A., Konyrova A., Goryachev B. E. A study on the mineralization kinetics of an air bubble in a suspension of activated and non-activated sphalerite. Obogashchenie Rud. 2020. No. 1. pp. 26–31. DOI: 10.17580/or.2020.01.05
10. Vinnetta L., Waters K. E. Comparison of different methodologies to estimate the flotation rate distribution. Minerals Engineering. 2019. Vol. 130. pp. 67–75.
11. Oosthuizen D. J., Craig I. Flotation modelling based on floatability distributions regressed from routine data. IFAC-PapersOnLine. 2018. Vol. 51, Iss. 21. pp. 105–110.
12. Goryachev B. E., Kyaw Zay Ya, Nikolaev A. A., Polyakova Yu. N. Peculiarities of sphalerite flotation by butyl potassium xanthate and sodium dithiophosphate in lime medium. Tsvetnye Metally. 2015. No. 11. pp. 14–19. DOI: 10.17580/tsm.2015.11.02.
13. Smailov B. B. Development of a method for assessing the washability and modeling of flotation schemes for processing refractory lead-zinc ores: diss. abstract for the degree of Candidate of Engineering Sciences. Moscow, 2018. 24 p.
14. Bragin V. I., Burdakova E. A., Usmanova N. F., Kinyakin A. I. Comprehensive assessment of flotation reagents by their influence on metal losses and flotation selectivity. Izvestiya Vuzov. Tsvetnaya Metallurgiya. 2021. No. 5. pp. 4–12.
15. Alexandrova T. N., Romashev A. O., Kuznetsov V. V. Development of a methodological approach to establishing the floatability of finely disseminated sulfides. Obogashchenie Rud. 2020. No. 2. pp. 9–14. DOI: 10.17580/or.2020.02.02
16. Mukhina T. N., Marchevskaya V. V. Improvement of the flotation regime for low-sulfide platinum-metal ores of the Kola Peninsula. Obogashchenie Rud. 2018. No. 4. pp. 20–27. DOI: 10.17580/or.2018.04.05.
17. Tikhonov O. N. Patterns of effective separation of minerals in the processes of mineral processing. Moscow: Nedra, 1984. 207 p.
18. Tikhonov A. N. On the solution of incorrectly set tasks and the regularization method. Doklady Akademii Nauk SSSR. 1963. Vol. 151, No. 3. pp. 501–504.