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Proceedings of the XV Balkan Mineral Processing Congress, Sozopol, Bulgaria, June 12 – 16, 2013
702
THE KINETIC FLOTATION MODELLING OF CHALCOPYRITE FROM DOMESTIC ORES USING
SOFTWARE TOOLS
A. Krstev, B. Krstev, Z. Zdravev, Ferat Sala, J. Zivanovik, Z. Gocev
1University “Goce Delchev”, Faculty of Natural and Technical Sciences, Shtip, R. of Macedonia
2Mine Bucim, Radovis, R. of Macedonia
3University “Goce Delchev”, Faculty of Computer Science, Shtip, R. of Macedonia
4University Prishtina, Faculty of Geoscience, Mitrovica
ABSTRACT. To improve kinetic flotation models, many first-order flotation kinetics models with distributions of flotation rate constants were redefined so that they could
all be represented by the same set of three model parameters. As a result, the width of the distribution become independent of its mean, and parameters of
the model and the curve fitting errors, became virtually the same, independent of the chosen distribution function. In our case, investigations of the chalcopyrite ores are
carried out using the Classical model, Klimpel Model and fully mixed model. According to the experimental results obtained in laboratory, the Classical model is most
appropriate for presentation of kinetic flotation, especially by means of MATLAB modeling.
KEYWORDS: investigation, modelling, kinetic, Matlab, Bucim
INTRODUCTION
In the possible and existing equations for flotation kinetic the
assumption is such that velocity coefficient for anyonessulphide
minerals (for example chalcopyrite or galena) is the constant k. The
huge number of investigators, as A. Gupta, D.S. Јuanhad calculated
the number of group models (
grouped tests for flotation
) or
cumulative flotation from first order considering the following models:
Clasical kinetic model, I=Io[1-e-kt]
Klimpel kinetic model, I=Io[1- )]
Kelsal kinetic model, I = (io-)(1- )+ (1- )
Modified Kelsal kinetic model – Gama model from Loveday,
Innou, I=Io(1-( )P)
The mentioned kinetic models are appropriate for presentation of
the main flotation charascteristic,
the flotation kinetic
, very important
for everyone project solution or assumption for good and sure
flotation performance. According to the existing or previous kinetic
investigations for kinetic flotation (Clasical kinetic model) for different
sulphide minerals, the above mentioned models and constant k for
copper mineral will have the following equation (chalcopyrite):
I = Io [1-e-kt] = 89.25 [1 – e- 1.025xt]
According to the existing or previous kinetic investigations for
kinetic flotation (Clasical kinetic model) for different oxide - sulphide
minerals, the above mentioned models and constant k for copper
mineral will have the following equation (65% chalcopyrite and 35%
oxide minerals as cuprite, azurite, malachite):
I = Io [1-e-kt] = 73.5 [1 – e- 0.56xt]
According to the existing or previous kinetic investigations for
kinetic flotation (Clasical kinetic model) for different oxide - sulphide
minerals, the above mentioned models and constant k for copper
mineral will have the following equation (65% chalcopyrite and 35%
oxide minerals as cuprite, azurite, malachite), but with application of
process of sulphidization with Na2S, (NH4)2SO4, NH2SO4 :
I = Io [1-e-kt] = 74.2 [1 – e- 0.61xt]
Kinetic flotation modeling of chalco pyrite using software
tools
The applicatible software packete for kinetic flotation modeling in
MATLAB®(R) GUI, will be shown for concrete examples for copper
minerals flotation (chalcopyrite ores or mixed oxide – sulphide ores)
enabling appropriate tabular or graphic presentation for Clasical
kinetic model (I. Brezani, F. Zelenek), determining the constant kin
the function of the time frequency of the useful reagent addition.
Fig. 1 Kinetic presentation by Matlab
Fig. 2 Kinetic presentation by Matlab
Fig. 3 Kinetic presentation by Matlab
Proceedings of the XV Balkan Mineral Processing Congress, Sozopol, Bulgaria, June 12 – 16, 2013
703
Fig. 4 Kinetic presentation by Matlab
Fig. 5 Results in total
Comparison of the kinetic models (Classical, Klimpel andFully
mixed model) for constant
к
and flotation time
Fig. 6 Kinetic presentation by Matlab
Fig. 7 Kinetic presentation by Matlab
Fig. 8 Kinetic presentation by Matlab
Proceedings of the XV Balkan Mineral Processing Congress, Sozopol, Bulgaria, June 12 – 16, 2013
704
Tabl. 1Comparison of the kinetic models for flotation kinetic
(I%) Classical
model
Klimpel
model
Fully mixed
model
Time (s) Mineral (%) Mineral (%) Mineral (%)
60 0.5723 0.3342 0.4407
120 0.7776 0.5132 0.5901
180 0.8513 0.6157 0.6652
240 0.8777 0.6784 0.7104
300 0.8872 0.7194 0.7407
360 0.8906 0.7477 0.7623
420 0.8918 0.7682 0.7785
480 0.8923 0.7837 0.7911
540 0.8924 0.7958 0.8012
720 0.8925 0.8199 0.8223
CONCLUSION
According to the experimental results obtained in laboratory and
industrial conditions, the Classical model is most appropriate for
presentation of kinetic flotation, especially by means of MATLAB
modeling.
REFERENCES
Brezani, I. Zelenak, F., (2010). MATLAB® tool for determining first
order flotation kinetic constants., Institute of Montanneous
Sciences and Environmental Protection. Technical University of
Kosice,BERG Faculty,
Brezani, i. Zelenak, f., (2010). Matlab® tool for modeling first order
flotation kinetics., Institute of Montanneous Sciences and
Environmental Protection. Technical University of Kosice,BERG
Faculty,
Evgun L., Ekmekci Z., Gülsoy Ö., Benzur H., (2004). “Modelling and
Simulation of Grinding Circuit in Magneuli Copper Concentrator”,
Physicochemical Problems in Mineral Proceding, 38(2004), 231-
240, USA.
Krstev A. PhD Thessis, 2012.
Herbst, J. A. (1982). “The Application of Modern Control Theory to
Mineral Processing Operations”, Proceedings 12th CMMI
Congress. H. W. Glen, Editor, South Africa Inst. Min. Metall.,
Johannesburg, 779-823.
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