2102
Studies on Multi-Component Particle Behavior
in a Hydrocyclone Classifier—Development of a
New Mathematical Model
M Padhi, N Mangadoddy
Department of Chemical Engineering, IIT Hyderabad, Kandi (V), Sangareddy (M), Medak, India
N A.N. Mainza
Center for Mineral Research, Chemical Engineering, University of Cape Town, Cape Town, South Africa
ABSTRACT: The behaviour of multi-component particles in a hydrocyclone is not well-understood, often
overlooked in classification experiments and mathematical model development. This study aimed to explore
the behaviour of multi-density and multi-size particles during hydrocyclone classification through experiments
and Computational Fluid Dynamics (CFD) simulations. The research delved into particle and slurry behaviour,
including settling and viscosity effects, to understand particle interactions during classification involving
particles of varying densities but similar size distribution. The study examined the classification performance
in relation to the different density components and size variation of the feed. The fundamental models for
settling and viscosity were revisited to include terms representing the impact of multi-component behaviour
in a hydrocyclone environment. Using experimental data from physical classification experiments and insights
on flow characteristics for multi-component classification, a mathematical model was developed. This model,
based on a dimensionless terms approach, drew inspiration from the modified conceptual multi-component
mathematical model for hydrocyclone reported by Narasimha et al.[1]. The developed multi-component
hydrocyclone model aligns well with experimental data for component partition curve properties such as cut-
size, water recovery, and separation sharpness. Additional equations were included to describe the component
solids recovery to underflow, considering the role of density in particle deportment to product streams in the
hydrocyclone. While the model can predict multi-component classification behaviour in a hydrocyclone at an
industrial scale, it requires data for mineral ores that are not fully liberated to enhance its predictive capabilities.
Keywords: Multicomponent particles, hydrocyclone, separations, settling &viscosity, mathematical model.
INTRODUCTION
The mineral processing starts with the comminution step
to liberate the mineral components in the ore prior to con-
centration or extraction stages. The process of ore dressing
physically separates the valuable mineral-rich fraction from
the unwanted/gangue particles. Two of the key processes
involved in pre-concentration stages are comminution and
classification. Based on the estimated liberation size of the
ore, the operating parameters for the milling circuit are
optimized to ensure that ore particles that can be recovered

Previous Page Next Page

Extracted Text (may have errors)

2102
Studies on Multi-Component Particle Behavior
in a Hydrocyclone Classifier—Development of a
New Mathematical Model
M Padhi, N Mangadoddy
Department of Chemical Engineering, IIT Hyderabad, Kandi (V), Sangareddy (M), Medak, India
N A.N. Mainza
Center for Mineral Research, Chemical Engineering, University of Cape Town, Cape Town, South Africa
ABSTRACT: The behaviour of multi-component particles in a hydrocyclone is not well-understood, often
overlooked in classification experiments and mathematical model development. This study aimed to explore
the behaviour of multi-density and multi-size particles during hydrocyclone classification through experiments
and Computational Fluid Dynamics (CFD) simulations. The research delved into particle and slurry behaviour,
including settling and viscosity effects, to understand particle interactions during classification involving
particles of varying densities but similar size distribution. The study examined the classification performance
in relation to the different density components and size variation of the feed. The fundamental models for
settling and viscosity were revisited to include terms representing the impact of multi-component behaviour
in a hydrocyclone environment. Using experimental data from physical classification experiments and insights
on flow characteristics for multi-component classification, a mathematical model was developed. This model,
based on a dimensionless terms approach, drew inspiration from the modified conceptual multi-component
mathematical model for hydrocyclone reported by Narasimha et al.[1]. The developed multi-component
hydrocyclone model aligns well with experimental data for component partition curve properties such as cut-
size, water recovery, and separation sharpness. Additional equations were included to describe the component
solids recovery to underflow, considering the role of density in particle deportment to product streams in the
hydrocyclone. While the model can predict multi-component classification behaviour in a hydrocyclone at an
industrial scale, it requires data for mineral ores that are not fully liberated to enhance its predictive capabilities.
Keywords: Multicomponent particles, hydrocyclone, separations, settling &viscosity, mathematical model.
INTRODUCTION
The mineral processing starts with the comminution step
to liberate the mineral components in the ore prior to con-
centration or extraction stages. The process of ore dressing
physically separates the valuable mineral-rich fraction from
the unwanted/gangue particles. Two of the key processes
involved in pre-concentration stages are comminution and
classification. Based on the estimated liberation size of the
ore, the operating parameters for the milling circuit are
optimized to ensure that ore particles that can be recovered

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XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2101
Harden, P.W., 2002. Garnet. In: Industrial Minerals
Handy Book IV A Guide to Markets, Specifications,
and Minerals-A Global Geology. Industrial Minerals
Information Ltd., London, UK, pp. 186–192.
Jones, G. 2009. Mineral sands – an overview of the industry.
In: Dominy, S.C. (Ed.), Proceedings 7th International
Mining Geology Conference. The Australasian Institute
of Mining and Metallurgy, Melbourne, pp. 213–222.
Pistorius, P.C. 2008. Ilmenite smelting: the basics. J. South
Afr. Inst. Min. Metall. 108:35–43.
Rahman, M.A., Tardio, J., Bhargava, S.K., Zaman, M.N.,
Hasan, A.S.M.M., Torpy, A., Pownceby, M.I. 2019.
Comparison of the chemistry and mineralogy of ilmen-
ite concentrates sourced from fluvial (Brahmaputra
River) and beach placer (Cox’s Bazar) deposits,
Bangladesh. Ore Geology Reviews. 117:1–10.
Rahman, M.A., Biswas, P.K., Zaman, M.N., Miah, M.Y.,
Hossain, T. and Imamul Huq, S.M. 2012.
Characterisation of the sand of Brahmaputra river
of Bangladesh. Bangladesh Journal of Scientific and
Industrial Research. 47:167–172.
Rahman, M.A., Pownceby, M.I., Haque, N., Bruckard, W.J.,
Zaman, M.N., 2014. Characterisation of titanium-
rich heavy mineral concentrates from the Brahmaputra
River basin, Bangladesh. Trans. Inst. Min. Metall. B,
App. Earth Sci. 123:222–233.
Rahman, M.A., Pownceby, M.I., Haque, N.,
Bruckard, W.J., Zaman, M.N. 2016. Valuable heavy
minerals from the Brahmaputra River sands of
Northern Bangladesh. Trans. Inst. Min. Metall. B,
App. Earth Sci. 125(3):174–188.
Rahman, A., Pownceby, M.I., Tardio, J., Haque, N.,
Bruckard, W., Torpy, A. and Zaman, M.N. (2020)
Compositional and textural variation in ilmenite
concentrates sourced from Brahmaputra river sands,
Bangladesh: implications for TiO2 production. In:
Proceedings IMPC 2020: XXX International Minerals
Processing Congress, Cape Town, South Africa, 18–22
October 2022, 60–69.
Rietveld, H.M. 1969. A profile refinement method for
nuclear and magnetic structures. J. Appl. Crystallogr.
2:65–71.
Torpy A., Wilson N., MacRae C., Pownceby M., Biswas
P., Rahman M. and Zaman M. 2018. Deciphering the
complex mineralogy of river sand deposits through
clustering and quantification of hyperspectral x-ray
maps. Microsc and Microanal. 26(4):768–792.
Wilson, N., MacRae, C. and Torpy, A. 2008. Analysis of
combined multi-signal hyperspectral datasets using a
clustering algorithm and visualisation tools. Microsc
Microanal. 14(2):764–765.

Previous Page Next Page

Extracted Text (may have errors)

XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2101
Harden, P.W., 2002. Garnet. In: Industrial Minerals
Handy Book IV A Guide to Markets, Specifications,
and Minerals-A Global Geology. Industrial Minerals
Information Ltd., London, UK, pp. 186–192.
Jones, G. 2009. Mineral sands – an overview of the industry.
In: Dominy, S.C. (Ed.), Proceedings 7th International
Mining Geology Conference. The Australasian Institute
of Mining and Metallurgy, Melbourne, pp. 213–222.
Pistorius, P.C. 2008. Ilmenite smelting: the basics. J. South
Afr. Inst. Min. Metall. 108:35–43.
Rahman, M.A., Tardio, J., Bhargava, S.K., Zaman, M.N.,
Hasan, A.S.M.M., Torpy, A., Pownceby, M.I. 2019.
Comparison of the chemistry and mineralogy of ilmen-
ite concentrates sourced from fluvial (Brahmaputra
River) and beach placer (Cox’s Bazar) deposits,
Bangladesh. Ore Geology Reviews. 117:1–10.
Rahman, M.A., Biswas, P.K., Zaman, M.N., Miah, M.Y.,
Hossain, T. and Imamul Huq, S.M. 2012.
Characterisation of the sand of Brahmaputra river
of Bangladesh. Bangladesh Journal of Scientific and
Industrial Research. 47:167–172.
Rahman, M.A., Pownceby, M.I., Haque, N., Bruckard, W.J.,
Zaman, M.N., 2014. Characterisation of titanium-
rich heavy mineral concentrates from the Brahmaputra
River basin, Bangladesh. Trans. Inst. Min. Metall. B,
App. Earth Sci. 123:222–233.
Rahman, M.A., Pownceby, M.I., Haque, N.,
Bruckard, W.J., Zaman, M.N. 2016. Valuable heavy
minerals from the Brahmaputra River sands of
Northern Bangladesh. Trans. Inst. Min. Metall. B,
App. Earth Sci. 125(3):174–188.
Rahman, A., Pownceby, M.I., Tardio, J., Haque, N.,
Bruckard, W., Torpy, A. and Zaman, M.N. (2020)
Compositional and textural variation in ilmenite
concentrates sourced from Brahmaputra river sands,
Bangladesh: implications for TiO2 production. In:
Proceedings IMPC 2020: XXX International Minerals
Processing Congress, Cape Town, South Africa, 18–22
October 2022, 60–69.
Rietveld, H.M. 1969. A profile refinement method for
nuclear and magnetic structures. J. Appl. Crystallogr.
2:65–71.
Torpy A., Wilson N., MacRae C., Pownceby M., Biswas
P., Rahman M. and Zaman M. 2018. Deciphering the
complex mineralogy of river sand deposits through
clustering and quantification of hyperspectral x-ray
maps. Microsc and Microanal. 26(4):768–792.
Wilson, N., MacRae, C. and Torpy, A. 2008. Analysis of
combined multi-signal hyperspectral datasets using a
clustering algorithm and visualisation tools. Microsc
Microanal. 14(2):764–765.

XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2103
downstream are prepared. However, irrespective of the
controlled parameters the material properties also have sig-
nificant effect on the separation and grinding efficiencies.
Due to the varying liberation status of different compo-
nents after grinding, density differences arise in the particle
system. The particles with varying sizes and density classes
result in a multicomponent particle system.
In the past, limited studies have been attempted to
understand the multi-density particle behaviour during the
classification process in hydrocyclones [1–4]. Most of these
studies have observed a significant change in the cut-size
and solids recovery to the underflow for its’ components
compared with the overall mixture behaviour. The changes
in in performance is attributed to the particle density dif-
ference compared to the overall or average mixture density.
However, it is not clear how the interaction of different
density components affects the separation of particles dur-
ing classification in a hydrocyclone. Some notable studies
involving the behaviour of components in hydrocyclones
include Cho [5] who focused on describing the classifica-
tion of binary, ternary and quaternary component mixtures
of minerals such as coal, limestone, magnetite, and quartz
in the laboratory and pilot-scale hydrocyclone. Narasimha
et al. [2], proposed a conceptual multi-component hydro-
cyclone model by extending a single density component
mathematical model developed by the same workers.
Mainza et al.[3] studied the deportment of chromite and
silica components in the UG2 platinum ore. Recently Padhi
et al. [4,5] performed physical experiments and computa-
tional simulations using CFD which showed that differ-
ent density components do not act independently during
classification in a dual component system, even when they
are fully liberated and proposed the particle displacement
mechanism to describe the interaction of lighter and heavier
components inside the hydrocyclone.
Attempting to understand the complex nature of par-
ticle separation in the hydrocyclone has occupied research-
ers for a long time several mathematical models have been
developed using different approaches over the past four
decades [6–9]. The two commonly used models are (Plitt
et. Al, 1976) [10] and (Nageswarao, 1978) [11], which have
been incorporated into the MODSIM [12] and JKSimMet
simulator [13,14]software, respectively. These models are
successfully used in grinding circuit simulations worldwide.
Recently the authors have developed and implemented an
improved hydrocyclone model in JKSimMet latest ver-
sion[1]. Although some of the existing mathematical mod-
els can describe hydrocyclone classification performance
for the ore’s single average density, their predictions for
ores with wide differences in the component densities are
usually poor. It is important to ensure that fine particles
deport to the overflow and coarse particles to the underflow
in process plants. In several instances like lead/zinc regrind
circuits, coal partitioning, or UG2 platinum ore (Upper
group 2 platinum ore, South Africa), single averaged density
hydrocyclone models are unable to predict the classification
performance well because of the multi-density occurrence
in the ores. Since the principle of separation in a hydrocy-
clone is driven by centrifugal forces and settling, particle
density is an important property. It can’t be ignored in the
model meant for the classification applications that involve
ores with significantly different component densities.
In this study, an attempt to understand the multi-
component particle behaviour and the interactions inside
the flow system is made using the physical experiments and
simulations utilizing computational fluid dynamics tech-
nique. The multi-density suspension properties, such as vis-
cosity and the hindered settling velocity are studied. These
properties are used in the multicomponent mathematical
model equations describing the separation performance
parameters such as cut-size, flow rate, solids recovery, and
sharpness of separation.
METHODOLOGY
Hydrocyclone Laboratory Experiments
The classification experiments were performed using 2, 3
and 4-inch diameter hydrocyclones a custom-made labo-
ratory scale test rig. A schematic of the test rig and pho-
tographs of the experimental set up are same as described
in Padhi et al., (2019) [5]. The design specifications of the
hydrocyclones used are given in Figure 1. The test rig has
a 200 litres sump and is set up to collect the slurry from
the overflow and underflow streams. It is equipped with
a Warmen 5 HP model pump to deliver the feed slurry
suspension to hydrocyclone. The slurry mixture is pre-
pared in the sump to meet the selected hydrocyclone feed
requirements for the test. To ensure the uniform mixing
of slurry suspension in the system, one part of the slurry
from the pump delivery line goes to bypass/recirculation.
The bypass line is utilized to regulate the operating pres-
sure for the hydrocyclone. The preliminary hydrocyclone
experiments were performed using only water, followed
by a slurry composed of different proportions of magne-
tite and quartz in the mixtures. The particle size distribu-
tions of quartz and magnetite were analysed and are given
in Figure 2. The d63.2 for silica and magnetite from the size
analysis performed were 44 and 37 microns, respectively.
The lower and upper size bound for magnetite and quartz
is recorded as 0.406–1500 and 1.15–1500 microns, respec-
tively. In these experiments, an attempt was made to keep

Previous Page Next Page

Extracted Text (may have errors)

XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2103
downstream are prepared. However, irrespective of the
controlled parameters the material properties also have sig-
nificant effect on the separation and grinding efficiencies.
Due to the varying liberation status of different compo-
nents after grinding, density differences arise in the particle
system. The particles with varying sizes and density classes
result in a multicomponent particle system.
In the past, limited studies have been attempted to
understand the multi-density particle behaviour during the
classification process in hydrocyclones [1–4]. Most of these
studies have observed a significant change in the cut-size
and solids recovery to the underflow for its’ components
compared with the overall mixture behaviour. The changes
in in performance is attributed to the particle density dif-
ference compared to the overall or average mixture density.
However, it is not clear how the interaction of different
density components affects the separation of particles dur-
ing classification in a hydrocyclone. Some notable studies
involving the behaviour of components in hydrocyclones
include Cho [5] who focused on describing the classifica-
tion of binary, ternary and quaternary component mixtures
of minerals such as coal, limestone, magnetite, and quartz
in the laboratory and pilot-scale hydrocyclone. Narasimha
et al. [2], proposed a conceptual multi-component hydro-
cyclone model by extending a single density component
mathematical model developed by the same workers.
Mainza et al.[3] studied the deportment of chromite and
silica components in the UG2 platinum ore. Recently Padhi
et al. [4,5] performed physical experiments and computa-
tional simulations using CFD which showed that differ-
ent density components do not act independently during
classification in a dual component system, even when they
are fully liberated and proposed the particle displacement
mechanism to describe the interaction of lighter and heavier
components inside the hydrocyclone.
Attempting to understand the complex nature of par-
ticle separation in the hydrocyclone has occupied research-
ers for a long time several mathematical models have been
developed using different approaches over the past four
decades [6–9]. The two commonly used models are (Plitt
et. Al, 1976) [10] and (Nageswarao, 1978) [11], which have
been incorporated into the MODSIM [12] and JKSimMet
simulator [13,14]software, respectively. These models are
successfully used in grinding circuit simulations worldwide.
Recently the authors have developed and implemented an
improved hydrocyclone model in JKSimMet latest ver-
sion[1]. Although some of the existing mathematical mod-
els can describe hydrocyclone classification performance
for the ore’s single average density, their predictions for
ores with wide differences in the component densities are
usually poor. It is important to ensure that fine particles
deport to the overflow and coarse particles to the underflow
in process plants. In several instances like lead/zinc regrind
circuits, coal partitioning, or UG2 platinum ore (Upper
group 2 platinum ore, South Africa), single averaged density
hydrocyclone models are unable to predict the classification
performance well because of the multi-density occurrence
in the ores. Since the principle of separation in a hydrocy-
clone is driven by centrifugal forces and settling, particle
density is an important property. It can’t be ignored in the
model meant for the classification applications that involve
ores with significantly different component densities.
In this study, an attempt to understand the multi-
component particle behaviour and the interactions inside
the flow system is made using the physical experiments and
simulations utilizing computational fluid dynamics tech-
nique. The multi-density suspension properties, such as vis-
cosity and the hindered settling velocity are studied. These
properties are used in the multicomponent mathematical
model equations describing the separation performance
parameters such as cut-size, flow rate, solids recovery, and
sharpness of separation.
METHODOLOGY
Hydrocyclone Laboratory Experiments
The classification experiments were performed using 2, 3
and 4-inch diameter hydrocyclones a custom-made labo-
ratory scale test rig. A schematic of the test rig and pho-
tographs of the experimental set up are same as described
in Padhi et al., (2019) [5]. The design specifications of the
hydrocyclones used are given in Figure 1. The test rig has
a 200 litres sump and is set up to collect the slurry from
the overflow and underflow streams. It is equipped with
a Warmen 5 HP model pump to deliver the feed slurry
suspension to hydrocyclone. The slurry mixture is pre-
pared in the sump to meet the selected hydrocyclone feed
requirements for the test. To ensure the uniform mixing
of slurry suspension in the system, one part of the slurry
from the pump delivery line goes to bypass/recirculation.
The bypass line is utilized to regulate the operating pres-
sure for the hydrocyclone. The preliminary hydrocyclone
experiments were performed using only water, followed
by a slurry composed of different proportions of magne-
tite and quartz in the mixtures. The particle size distribu-
tions of quartz and magnetite were analysed and are given
in Figure 2. The d63.2 for silica and magnetite from the size
analysis performed were 44 and 37 microns, respectively.
The lower and upper size bound for magnetite and quartz
is recorded as 0.406–1500 and 1.15–1500 microns, respec-
tively. In these experiments, an attempt was made to keep