2448 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
and a sensitivity analysis was applied to evaluate the impact
of the selection of different sets of flotation intervals on the
R∞-f(k) estimations. The key findings of this study are sum-
marized as follows:
• The SFR model presented poor model fitting when
studying the entire dataset, with the Gamma model
leading to the lowest mean squared error.
• The SFR R∞-k pairs were more sensitive to changes
in the selection of flotation times at laboratory scale.
The rate constants were particularly sensitive to the
first two flotation intervals (t =0.5 min and t =1.5
min, respectively).
• The Rectangular and Gamma R∞-f(k) estimations
were significantly more stable that those observed
for the SFR model. However, the Rectangular f(k)
estimation also proved to be sensitive to the first
time-recovery datapoint. The location, dispersion,
and shapes of the estimated Gamma f(k)s were not
critically affected by changes in the selection of flota-
tion intervals.
• The higher stability of the Rectangular and Gamma
R∞-f(k) estimations, under different flotation inter-
vals in the experimental design, proved to lead to
lower variabilities when scaling-up laboratory results
to a continuous operation.
These findings demonstrated the relevance of adequate
experimental designs to improve the robustness of kinetic
characterizations and to reduce uncertainties in the recov-
ery predictions at large scale. The sensitivity analysis pre-
sented here is considered necessary to validate or discard
kinetic models or tests, especially when they are remarkably
sensitive to moderate changes in the flotation intervals.
ACKNOWLEDGMENTS
Funding for process modelling was provided by ANID,
FONDECYT Project (Initiation) 11240125, and
Universidad Técnica Federico Santa María Project
PI_LIR_23_02.
REFERENCES
Amelunxen, P., LaDouceur, R., Amelunxen, R., Young, C.,
(2018). A phenomenological model of entrainment
and froth recovery for interpreting laboratory flotation
kinetics tests. Minerals Engineering 125, 60–65.
Bergh, L., Yianatos, J., &Bravo, G. (2018). On-line moni-
toring of a pilot flotation rougher circuit by using PCA
models. IFAC Papers Online, 335–340.
Bu, X., Xie, G., Peng, Y., Ge, L., &Ni, C. (2017). Kinetics
of flotation. Order of process, rate constant distribu-
tion and ultimate recovery. Physicochem. Probl. Miner.
Process, 342–365.
Finch, J. A., &Dobby, G. S. (1991). Column flotation: A
selected review. Part I. International Journal of Mineral
Processing, 343–354.
García-Zuñiga, H. (1935). Flotation recovery is an expo-
nential function of time. Bol. Soc. Mac. Min, 47,
83–86.
Gharai, M., &Venugopal, R. (2015). Modeling of Flotation
Process—An Overview of Different Approaches.
Mineral Processing and Extractive Metallurgy Review,
120–133.
Huber-Panu, I., Ene-Danalache, E., &Cojocariu, D.
(1976). Mathematical models of batch and continuous
flotation. In: Fuerstenau, M.C. Ed., Flotation, A.M.
Gaudin Memorial Volume, vol. 2, AIME, New York,
675–724.
Imaizumi, T., &Inoue, T. (1963). Kinetic consideration of
froth flotation. In: Proceeding of the 6th International
Mineral Processing Congress, Cannes, 581–593.
Klimpel, R. (1980). Selection of chemical reagents for flo-
tation. In: Mullar, A.L., Bhappu, R.B. (Eds), Mineral
Processing Plant Design, 2nd edn. AIME, New York,
907–934.
Murhula, E., Hashan, M., &Otsuki, A. (2022). Effect of
Solid Concentration and Particle Size on the Flotation
Kinetics and Entrainment of Quartz and Hematite.
Metals, 13, 53.
Napier-Munn, T. J. (2012). Statistical methods to com-
pare batch flotation grade-recovery curves. Minerals
Engineering, 70–77.
Ni, C., Bu, X., Xia, W., Peng, Y., &Xie, G. (2018). Effect
of slimes on the flotation recovery and kinetics of coal
particles. Fuel, 159–166.
Ofori, P., O’Brien, G., Hapugoda, P., &Firth, B. (2014).
Distributed flotation kinetics models – A new imple-
mentation approach for coal flotation. Minerals
Engineering, 77–83.
Rao, B. V. (2023). Chaptar 10—Froth flotation and its
modeling aspects. Rajendran, S., Murty, C.V.G.K.
(Eds.), 365–436.
Ross, V., (2019). Key aspects of bench flotation as a geo-
metallurgical characterization tool. Journal of the
Southern African Institute of Mining and Metallurgy
119, 361–367.
Sandoval-Zambrano, G., &Montes-Atenas, G. (2012).
Errors in the estimation of size-by-liberation flotation
rate constants. Minerals Engineering, 1–10.
and a sensitivity analysis was applied to evaluate the impact
of the selection of different sets of flotation intervals on the
R∞-f(k) estimations. The key findings of this study are sum-
marized as follows:
• The SFR model presented poor model fitting when
studying the entire dataset, with the Gamma model
leading to the lowest mean squared error.
• The SFR R∞-k pairs were more sensitive to changes
in the selection of flotation times at laboratory scale.
The rate constants were particularly sensitive to the
first two flotation intervals (t =0.5 min and t =1.5
min, respectively).
• The Rectangular and Gamma R∞-f(k) estimations
were significantly more stable that those observed
for the SFR model. However, the Rectangular f(k)
estimation also proved to be sensitive to the first
time-recovery datapoint. The location, dispersion,
and shapes of the estimated Gamma f(k)s were not
critically affected by changes in the selection of flota-
tion intervals.
• The higher stability of the Rectangular and Gamma
R∞-f(k) estimations, under different flotation inter-
vals in the experimental design, proved to lead to
lower variabilities when scaling-up laboratory results
to a continuous operation.
These findings demonstrated the relevance of adequate
experimental designs to improve the robustness of kinetic
characterizations and to reduce uncertainties in the recov-
ery predictions at large scale. The sensitivity analysis pre-
sented here is considered necessary to validate or discard
kinetic models or tests, especially when they are remarkably
sensitive to moderate changes in the flotation intervals.
ACKNOWLEDGMENTS
Funding for process modelling was provided by ANID,
FONDECYT Project (Initiation) 11240125, and
Universidad Técnica Federico Santa María Project
PI_LIR_23_02.
REFERENCES
Amelunxen, P., LaDouceur, R., Amelunxen, R., Young, C.,
(2018). A phenomenological model of entrainment
and froth recovery for interpreting laboratory flotation
kinetics tests. Minerals Engineering 125, 60–65.
Bergh, L., Yianatos, J., &Bravo, G. (2018). On-line moni-
toring of a pilot flotation rougher circuit by using PCA
models. IFAC Papers Online, 335–340.
Bu, X., Xie, G., Peng, Y., Ge, L., &Ni, C. (2017). Kinetics
of flotation. Order of process, rate constant distribu-
tion and ultimate recovery. Physicochem. Probl. Miner.
Process, 342–365.
Finch, J. A., &Dobby, G. S. (1991). Column flotation: A
selected review. Part I. International Journal of Mineral
Processing, 343–354.
García-Zuñiga, H. (1935). Flotation recovery is an expo-
nential function of time. Bol. Soc. Mac. Min, 47,
83–86.
Gharai, M., &Venugopal, R. (2015). Modeling of Flotation
Process—An Overview of Different Approaches.
Mineral Processing and Extractive Metallurgy Review,
120–133.
Huber-Panu, I., Ene-Danalache, E., &Cojocariu, D.
(1976). Mathematical models of batch and continuous
flotation. In: Fuerstenau, M.C. Ed., Flotation, A.M.
Gaudin Memorial Volume, vol. 2, AIME, New York,
675–724.
Imaizumi, T., &Inoue, T. (1963). Kinetic consideration of
froth flotation. In: Proceeding of the 6th International
Mineral Processing Congress, Cannes, 581–593.
Klimpel, R. (1980). Selection of chemical reagents for flo-
tation. In: Mullar, A.L., Bhappu, R.B. (Eds), Mineral
Processing Plant Design, 2nd edn. AIME, New York,
907–934.
Murhula, E., Hashan, M., &Otsuki, A. (2022). Effect of
Solid Concentration and Particle Size on the Flotation
Kinetics and Entrainment of Quartz and Hematite.
Metals, 13, 53.
Napier-Munn, T. J. (2012). Statistical methods to com-
pare batch flotation grade-recovery curves. Minerals
Engineering, 70–77.
Ni, C., Bu, X., Xia, W., Peng, Y., &Xie, G. (2018). Effect
of slimes on the flotation recovery and kinetics of coal
particles. Fuel, 159–166.
Ofori, P., O’Brien, G., Hapugoda, P., &Firth, B. (2014).
Distributed flotation kinetics models – A new imple-
mentation approach for coal flotation. Minerals
Engineering, 77–83.
Rao, B. V. (2023). Chaptar 10—Froth flotation and its
modeling aspects. Rajendran, S., Murty, C.V.G.K.
(Eds.), 365–436.
Ross, V., (2019). Key aspects of bench flotation as a geo-
metallurgical characterization tool. Journal of the
Southern African Institute of Mining and Metallurgy
119, 361–367.
Sandoval-Zambrano, G., &Montes-Atenas, G. (2012).
Errors in the estimation of size-by-liberation flotation
rate constants. Minerals Engineering, 1–10.