A sensitivity analysis of kinetic characterizations in continuous flotation circuits under moderate deviations with respect to perfect mixing

• Autorzy: Vinnett Luis , Pino-Muñoz Catalina A. , Yianatos Juan , Díaz Francisco , Henríquez Felipe

Identyfikatory

DOI

10.37190/ppmp/152420

• Języki publikacji: EN

Abstrakty

EN

This paper studies the effect of moderate deviations with respect to perfect mixing on the estimated kinetic parameters in industrial flotation banks. Radioactive tracer tests and mass balance surveys were performed to characterize the mixing regimes and Cu kinetic responses. For three models (Single Rate Constant, Rectangular and Gamma), two approaches to incorporate the residence time distributions (RTD) in the kinetic characterizations of rougher banks were compared: (i) RTDs measured from the radioactive tracer tests; and (ii) pure perfect mixing in each flotation machine. The measured RTDs did not present significant bypass in the evaluated banks. In all cases, comparable model fitting was obtained with both RTD approaches, which indicates that the kinetic models add sufficient flexibility to compensate for moderate biases in the mixing regime. The studied kinetic models showed non-significant differences in the estimated maximum recoveries (R_∞), mean (k_mean) and median (k₅₀) rate constants when comparing the process modelling from measured RTDs and pure perfect mixing. However, the Gamma model was more sensitive to the RTD assumption in terms of the shapes of the flotation rate distributions. From the results, kinetic characterizations focused only on model fitting, or on R_∞ and k_mean (or k₅₀) estimations have low sensitivity to the assumption of perfect mixing when the RTDs present moderate deviations with respect to this regime. Special attention must be paid when characterizing floating components as the perfect mixing assumption may bias the shapes of the flotation rate distributions.

Słowa kluczowe

EN

flotation kinetics; residence time distribution; perfect mixing; flotation rate distribution; industrial flotation circuit

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Physicochemical Problems of Mineral Processing
• Rocznik: 2022
• Tom: Vol. 58, iss. 5
• Strony: art. no. 152420
• Opis fizyczny: Bibliogr. 25 poz., rys.

Twórcy

autor

Vinnett Luis

• Department of Chemical and Environmental Engineering, Universidad Técnica Federico Santa María, Valparaíso, Chile

• https://orcid.org/0000-0001-7173-9054

autor

Pino-Muñoz Catalina A.

• Department of Earth Science and Engineering, Imperial College London, London, United Kingdom

• https://orcid.org/0000-0001-5138-4030

autor

Yianatos Juan

• Department of Chemical and Environmental Engineering, Universidad Técnica Federico Santa María, Valparaíso, Chile

autor

Díaz Francisco

• Trazado Nuclear e Ingeniería, Santiago, Chile

autor

Henríquez Felipe

• Minera Los Pelambres, Antofagasta Minerals, Salamanca, Chile

Bibliografia

• ABKHOSHK, E., KOR, M., REZAI, B., 2010. A study on the effect of particle size on coal flotation kinetics using fuzzy logic, Expert Syst. Appl. 37(7), 5201-5207.
• AI, G., YANG, X., LI, X., 2017. Flotation characteristics and flotation kinetics of fine wolframite, Powder Technol. 305, 377-381.
• BU, X., XIE, G., PENG, Y., 2017a. Interaction of fine, medium, and coarse particles in coal fines flotation, Energy Sources A: Recovery Util. Environ. Eff. 39(12), 1276-1282.
• BU, X., XIE, G., PENG, Y., GE, L., NI, C., 2017b. Kinetics of flotation. order of process, rate constant distribution and ultimate recovery. Physicochem. Probl. Miner. Process. 53, 342-365.
• BOEREE, C.R., 2014. Up-scaling of froth flotation equipment. M. Sc. Thesis. Delft University of Technology.
• DOWLING, E.C., KLIMPEL, R.R., APLAN, F.F., 1985. Model discrimination in the flotation of a porphyry copper ore. Miner. Metall. Process. 2, 87-101.
• EK, C., 1992. Flotation Kinetics, Innovations in Flotation Technology. Springer Dordrecht, The Netherlands, 183-210.
• GARCIA-ZUÑIGA, H., 1935. La recuperación por flotación es una función exponencial del tiempo. Boletín Minero, Sociedad Nacional de Minería 47, 83-86.
• GHARAI, M., VENUGOPAL, R., 2016. Modeling of flotation process—an overview of different approaches. Miner. Process. Extr. Metall. Rev., 37(2), 120-133.
• HUBER-PANU, I., ENE-DANALACHE, E., COJOCARIU, D.G., 1976. Mathematical models of batch and continuous flotation. Flotation–A. M. Gaudin Memorial, 675-724.
• IMAIZUMI, T., INOUE, T., 1963. Kinetic considerations of froth flotation. Proceedings of the 6th International Mineral Processing Congress, Cannes. 581–593.
• KAHANER, D., MOLER, C.B., NASH, S., FORSYTHE, G.E., 1988. Numerical Methods and Software. Prentice Hall, Englewood Cliffs, N.J.
• KELLY, E.G., CARLSON, C.E., 1991. Two flotation models: resolution of a conflict. Miner. Eng. 4 (12), 1333–1338.
• YEKELER, M., SÖNMEZ, İ., 1997. Effect of the hydrophobic fraction and particle size in the collectorless column flotation kinetics, Colloids Surf. A Physicochem. Eng. Asp. 121(1), 1997, 9-13.
• POLAT, M., CHANDER, S., 2000. First-order flotation kinetics models and methods for estimation of the true distribution of flotation rate constants, Int. J. Miner. Process. 58(1-4), 145-166.
• QAREDAQI, M., SHIRAZI, H.H.A., ABDOLLAHI, H., 2012. Comparison of Yianatos and traditional methods to determine kinetic rate constants of different size fractions in industrial rougher cells. Int. J. Miner. Process. 106, 65-69.
• SALDAÑA, M., NEIRA, P., FLORES, V., MORAGA, C., ROBLES, P., SALAZAR, I. 2021. Analysis of the Dynamics of Rougher Cells on the Basis of Phenomenological Models and Discrete Event Simulation Framework. Metals 11(9), 1454.
• SCHUHMANN JR, R., 1942. Flotation Kinetics. I. Methods for steady-state study of flotation problems. J. Phys. Chem. 46, 891-902.
• VÉDRINE, H., BROUSSAUD, A., CONIL, P., DE MATOS, C., 1991. Modelling the Flotation Kinetics of a Polymetallic Sulphide Ore, SME Annual Meeting, Denver, Colorado, USA.
• VINNETT, L., YIANATOS, J., FLORES, S., 2016. On the mineral recovery estimation in Cu/Mo flotation plants. Miner. Metall. Process. 33, 97-106.
• VINNETT L, WATERS K.E., 2020. Representation of Kinetics Models in Batch Flotation as Distributed First-Order Reactions. Minerals 10(10), 913.
• VINNETT, L., GRAMMATIKOPOULOS, T., EL-MENSHAWY, A.H., WATERS, K.E., 2022. Justifying size-by-size flotation rate distributions from size-by-association kinetic responses, Powder Technol. 395, 168-182.
• WILLS, B., NAPIER-MUNN, T., 2006. Wills’ Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery. (7th ed.), Butterworth-Heinemann, Oxford.
• WOODBURN, E.T., LOVEDAY, B.K., 1965. The effect of variable residence time on the performance of a flotation system. Journal of the Southern African Institute of Mining and Metallurgy 65, 612-628.
• YIANATOS, J., BERGH, L., VINNETT, L., PANIRE, I., DIAZ, F., 2015. Modelling of residence time distribution of liquid and solid in mechanical flotation cells, Miner. Eng. 78, 69-73.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).