2112 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
In the Rsi modelling, Rf is chosen from the single aver-
age density component classification model developed
by Narasimha et al (2012) [29] shown in equation 14.
For practical usage, one needs to calibrate the constants
using experimental data performed on the ore or material
involved in the classification. The constant Kw in Rf equa-
tion, is a function of particle properties like density. For
the bi component mixture of magnetite and silica, the con-
stants were found to be 61.8 and 38.79 for magnetite and
silica, respectively. However, the constant Kw was observed
to be dependent mainly on the hydrocyclone dimensions,
and need to be refitted for different hydrocyclone designs.
For the three small hydrocyclones used in separating a
bi-component mixture of magnetite and silica, the values
for Kw were found to be 0.31, 0.1, and 0.009 for 2-inch,
3-inch, and 4-inch, respectively.
CONCLUSIONS
The natural ores having multicomponent characteristics
i.e., liberated particles consists of multiple sizes and den-
sities are identified to have component wise performance
efficiencies. The insights from experimental data and CFD
simulations illustrates the interaction of various proportion
of components during classification process. In addition,
the operating conditions such as inlet pressure, solids con-
centration effect is also observed to be significant during
the multicomponent classification.
The multicomponent mathematical model for cut size
prediction is developed by extending the single compo-
nent model of Narasimha et al. 2014 [2]. Inputs from the
CFD studies on the bi-component separation mechanism
in terms of multi-component particle rheology, settling
velocities and the segregation phenomena are utilized to
develop the new multi-component classification model.
The proposed multi-component model can predict the
component-wise cut size, solids recovery, and alpha reason-
ably close to the experimental data and found them within
30% error except for the sharpness of separation.
• Compared to the previous single averaged density-
based models, this new alpha equation showing an
improved accuracy with the standard error of 3.38 in
validation.
• The relative error for the feed flow rate, cut size, sepa-
ration sharpness, and solids recovery equations for
both overall and components were 13.1, 15.35, 18.3,
and 21.68, respectively.
• The present model includes the very first attempt
to present the solids recovery model in the empiri-
cal form. Model validation with additional data is
attempted and found reasonably close to the literature
output data. The standard error between experimen-
tal and model estimated of overall, silica, and magne-
tite solids recovery are found as 6.3 with R2 values for
respective particles as 12.5, 23.9, and 16.3.
Compared to the previously proposed single component-
based models, the newly proposed model accounts for the
component proportion factor. Hence, the predictions can
be done for a wide range of concentrations &component
combinations.
ACKNOWLEDGMENT
The authors would like to express their sincere thanks
to DST-SERB, India (EMR/2016/00378/046), IIT
Hyderabad and the Ministry of education for the funding
and resources support to undertake the current research
work. The authors would like to thank the expert technical
advice and discussions in collaboration with the Centre for
Minerals Research, University of Cape Town.
REFERENCE
[1] M. Narasimha, A.N. Mainza, P.N. Holtham, M.S.
Powell, M.S. Brennan, A semi-mechanistic model of
hydrocyclones -Developed from industrial data and
inputs from CFD, Int. J. Miner. Process. 133 (2014)
1–12. doi: 10.1016/j.minpro.2014.08.006.
[2] M. Narasimha, J. Crasta, T. Sreenivas, A.N. Mainza,
Performance of hydrocyclone separating bi-com-
ponent mixture, 27th Int. Miner. Process. Congr.
(2014) 1–10.
[3] a Mainza, M.S. Powell, B. Knopjes, A compari-
son of different cyclones in addressing challenges in
the classification of the dual density UG2 platinum
ore, J. South African Inst. Min. Metall. 105 (2005)
341–348.
[4] M. Padhi, M. Kumar, N. Mangadoddy, Understanding
the Bi-component Particle Separation Mechanism in
a Hydrocyclone Using CFD Model, Ind. Eng. Chem.
Res. 59 (2020) 11621–11644. doi: 10.1021/acs.
iecr.9b06747.
[5] M. Padhi, N. Mangadoddy, T. Sreenivas, T. Reddy
Vakamalla, A.N. Mainza, Study on Multi-Component
Particle Behaviour in a Hydrocyclone Classifier Using
Experimental and Comutational Fluid Dynamics
Techniques, Sep. Purif. Technol. 18 (2019) 115–698.
doi: 10.1016/j.seppur.2019.115698.
[6] K.R. Weller, U.J. Sterns, E. Artone, W.J. Bruckard,
Multicomponent models of grinding and classifica-
tion for scale-up from continuous small or pilot scale
circuits, Int. J. Miner. Process. 22 (1988) 119–147.
doi: 10.1016/0301-7516(88)90060-9.
In the Rsi modelling, Rf is chosen from the single aver-
age density component classification model developed
by Narasimha et al (2012) [29] shown in equation 14.
For practical usage, one needs to calibrate the constants
using experimental data performed on the ore or material
involved in the classification. The constant Kw in Rf equa-
tion, is a function of particle properties like density. For
the bi component mixture of magnetite and silica, the con-
stants were found to be 61.8 and 38.79 for magnetite and
silica, respectively. However, the constant Kw was observed
to be dependent mainly on the hydrocyclone dimensions,
and need to be refitted for different hydrocyclone designs.
For the three small hydrocyclones used in separating a
bi-component mixture of magnetite and silica, the values
for Kw were found to be 0.31, 0.1, and 0.009 for 2-inch,
3-inch, and 4-inch, respectively.
CONCLUSIONS
The natural ores having multicomponent characteristics
i.e., liberated particles consists of multiple sizes and den-
sities are identified to have component wise performance
efficiencies. The insights from experimental data and CFD
simulations illustrates the interaction of various proportion
of components during classification process. In addition,
the operating conditions such as inlet pressure, solids con-
centration effect is also observed to be significant during
the multicomponent classification.
The multicomponent mathematical model for cut size
prediction is developed by extending the single compo-
nent model of Narasimha et al. 2014 [2]. Inputs from the
CFD studies on the bi-component separation mechanism
in terms of multi-component particle rheology, settling
velocities and the segregation phenomena are utilized to
develop the new multi-component classification model.
The proposed multi-component model can predict the
component-wise cut size, solids recovery, and alpha reason-
ably close to the experimental data and found them within
30% error except for the sharpness of separation.
• Compared to the previous single averaged density-
based models, this new alpha equation showing an
improved accuracy with the standard error of 3.38 in
validation.
• The relative error for the feed flow rate, cut size, sepa-
ration sharpness, and solids recovery equations for
both overall and components were 13.1, 15.35, 18.3,
and 21.68, respectively.
• The present model includes the very first attempt
to present the solids recovery model in the empiri-
cal form. Model validation with additional data is
attempted and found reasonably close to the literature
output data. The standard error between experimen-
tal and model estimated of overall, silica, and magne-
tite solids recovery are found as 6.3 with R2 values for
respective particles as 12.5, 23.9, and 16.3.
Compared to the previously proposed single component-
based models, the newly proposed model accounts for the
component proportion factor. Hence, the predictions can
be done for a wide range of concentrations &component
combinations.
ACKNOWLEDGMENT
The authors would like to express their sincere thanks
to DST-SERB, India (EMR/2016/00378/046), IIT
Hyderabad and the Ministry of education for the funding
and resources support to undertake the current research
work. The authors would like to thank the expert technical
advice and discussions in collaboration with the Centre for
Minerals Research, University of Cape Town.
REFERENCE
[1] M. Narasimha, A.N. Mainza, P.N. Holtham, M.S.
Powell, M.S. Brennan, A semi-mechanistic model of
hydrocyclones -Developed from industrial data and
inputs from CFD, Int. J. Miner. Process. 133 (2014)
1–12. doi: 10.1016/j.minpro.2014.08.006.
[2] M. Narasimha, J. Crasta, T. Sreenivas, A.N. Mainza,
Performance of hydrocyclone separating bi-com-
ponent mixture, 27th Int. Miner. Process. Congr.
(2014) 1–10.
[3] a Mainza, M.S. Powell, B. Knopjes, A compari-
son of different cyclones in addressing challenges in
the classification of the dual density UG2 platinum
ore, J. South African Inst. Min. Metall. 105 (2005)
341–348.
[4] M. Padhi, M. Kumar, N. Mangadoddy, Understanding
the Bi-component Particle Separation Mechanism in
a Hydrocyclone Using CFD Model, Ind. Eng. Chem.
Res. 59 (2020) 11621–11644. doi: 10.1021/acs.
iecr.9b06747.
[5] M. Padhi, N. Mangadoddy, T. Sreenivas, T. Reddy
Vakamalla, A.N. Mainza, Study on Multi-Component
Particle Behaviour in a Hydrocyclone Classifier Using
Experimental and Comutational Fluid Dynamics
Techniques, Sep. Purif. Technol. 18 (2019) 115–698.
doi: 10.1016/j.seppur.2019.115698.
[6] K.R. Weller, U.J. Sterns, E. Artone, W.J. Bruckard,
Multicomponent models of grinding and classifica-
tion for scale-up from continuous small or pilot scale
circuits, Int. J. Miner. Process. 22 (1988) 119–147.
doi: 10.1016/0301-7516(88)90060-9.