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Lab experiments using different flotation
cell geometries
Carolina Vivian de Souza
Natural Resources Engineering, master's level (120 credits)
2020
Luleå University of Technology
Department of Civil, Environmental and Natural Resources Engineering
Lab experiments using different flotation cell
geometries
by:
Carolina Vivian de Souza
Division of Minerals and Metallurgical Engineering (MiMer) Department of Civil,
Environmental and Natural Resources Engineering Luleå University of Technology
Supervisor:
Vitalis Chipakwe
Examiner:
Saeed Chehreh Chelgani
Luleå, Sweden
2020
Abstract
Due to the increasing demand for processing low-grade ores, larger volumes of material are
being processed. Therefore, the size of flotation equipment has significantly increased for the
past decades. The studies related to scale-up are and will remain to be crucial in terms of
designing larger flotation equipment. One of the most important factors for flotation scaling-
up is the “flotation rate constant”. Hence, the main aim of this investigation was to
understand the scale-up criteria when the size of different laboratory-scale cells increases,
using the Outotec GTK LabCell®. This was done by assessing the influence of impeller
speed, as a hydrodynamic variable, on the flotation performance. Recovery was found to
increase with an increase in the cell area to rotor diameter ratio. Flotation rate and recovery
increased with an increase in the impeller speed until a certain point that it eventually
decreased for the 2 l and 7.5 l cells. For the 4 l cell, the flotation rate and recovery decreased
with increasing the impeller speed. The impeller speed of 1200 rpm allowed a successful
scale-up based on the flotation rate constants and recovery when increasing the size of the
cells. Maintaining the impeller speeds constant at 1300 rpm increased the flotation rate
constants and recovery when increasing the cell size from both the 2 and 4 l cells to the 7.5 l
cell. A further increase in the impeller speed to 1400 rpm also produced the flotation rate
constants and recovery to increase as the cell size increased from both the 2 and 4 l cells to
the 7.5 l cell. However, when increasing the cell size from 2 l to 4 l, good results were also
observed for all impeller speeds. The products concentrate seem to become finer when
decreasing the cell size, with only a few exceptions. The recovery of particles larger than 38
μm was found to differ considerably less among the different scales.
Keywords: cell hydrodynamics; flotation; impeller speed; scale-up; mechanical laboratory-
scale flotation cells; flotation kinetic rate
i
Content
Introduction ......................................................................................................................................................... 1
1.2 Aim and Objectives ................................................................................................................................... 2
Literature Survey ................................................................................................................................................ 4
2.1 Flotation ...................................................................................................................................................... 4
2.2 Flotation equipment .................................................................................................................................. 8
2.2.1 Pneumatic cells ................................................................................................................................... 9
2.2.2 Mechanical cells ................................................................................................................................ 11
2.2.3 Laboratory flotation equipment ..................................................................................................... 13
2.3 Scale-up of flotation process .................................................................................................................. 17
2.3.1 Computational Fluid Dynamics (CFD) ......................................................................................... 19
2.3.2 Kinetic scale-up ................................................................................................................................ 22
2.3.3 Machine design scale-up ................................................................................................................. 28
2.4 Influence of the impeller speed and design in flotation ..................................................................... 31
2.5 Flotation of silicates ................................................................................................................................. 35
2.5.1 Commonly used reagents ............................................................................................................... 35
Materials and Methodology ........................................................................................................................... 38
3.1 Flotation equipment ................................................................................................................................ 39
3.2 Sampling and sample preparation ........................................................................................................ 41
3.2.1 Grinding and Sieving ...................................................................................................................... 41
3.2.2 Flotation reagents ............................................................................................................................. 43
3.3 Flotation tests ........................................................................................................................................... 44
Results................................................................................................................................................................. 45
4.1 Recovery assessments ............................................................................................................................. 45
4.2 Kinetic assessments ................................................................................................................................. 50
4.3 Effect of Cell Size ..................................................................................................................................... 52
4.4 Effect of Particle Size Distribution ........................................................................................................ 53
4.5 Effect of impeller speed .......................................................................................................................... 58
Discussions and Conclusions ......................................................................................................................... 60
5.1 Effect of Cell Size ..................................................................................................................................... 60
5.2 Effect of impeller speed .......................................................................................................................... 61
5.3 Effect of Particle Size Distribution ........................................................................................................ 63
5.4 Conclusions .............................................................................................................................................. 67
EIT Chapter ........................................................................................................................................................ 70
6.1 Recommendations for future work ....................................................................................................... 70
6.2 SWOT Analysis ........................................................................................................................................ 71
References .......................................................................................................................................................... 72
Appendices ........................................................................................................................................................ 76
ii
List of figures
Figure 1 Process of adsorption of a collector in a mineral surface and attachment to the air bubble
(extracted from Gupta and Yan, 2006). ............................................................................................................. 7
Figure 2 Classification of collectors (extracted from Napier-Munn and Wills, 2005). ............................... 7
Figure 3 Schematic of a Jameson cell (extracted from Silva, 2005). ............................................................... 9
Figure 4 Schematic pneumatic cell model Imhoflot (extracted from Chaves, 2006). ................................ 10
Figure 5 Schematic of a column flotation (extracted from Mesa and Brito-Parada, 2019a). .................... 10
Figure 6 Schematic of a mechanical flotation cell (extracted from Mesa and Brito-Parada, 2019). ........ 11
Figure 7 Typical flow patterns in a mechanical flotation cell (Outokumpu) (extracted from Gorain et
al., 1995). .............................................................................................................................................................. 12
Figure 8 Flotation cell designs (extracted from Chaves, 2006). ................................................................... 12
Figure 9 Impeller-stator designs. (extracted from (Chaves, 2006). ............................................................. 13
Figure 10 Schematic of a Hallimond tube (extracted from Wills & Napier-Munn, 2006). ....................... 14
Figure 11 Schematic of a laboratory bench-scale mechanical flotation equipment (extracted from Mesa
and Brito-Parada, 2019). .................................................................................................................................... 14
Figure 12 Laboratory mechanical flotation cell (extracted from Wills & Napier-Munn, 2006)............... 15
Figure 13 Denver Lab Cell D-1 flotation machine (extracted from McGill University, 2020). ................ 16
Figure 14 Trend in the flotation tank size over the last century (y-axis is on a logarithmic scale)
(extracted from Mesa and Brito-Parada, 2019a). ........................................................................................... 17
Figure 15 Power number for the diverse impellers Reynolds number (extracted from Mesa and Brito-
Parada, 2019a). ................................................................................................................................................... 29
Figure 16 Schematic of the methodology. ...................................................................................................... 39
Figure 17 Outotec GTK LabCell® flotation machine (extracted from Mattsson et al., 2019)). ................ 40
Figure 18 Outotec GTK LabCell® cells, rotor, and impellers used in this investigation. ........................ 41
Figure 19. Outotec GTK LabCell® cells dimensions for the cells used in this investigation. ................. 41
Figure 20. Particle Size Distribution for the initial sample and flotation feed. ......................................... 43
Figure 21 Cumulative recovery reached by the different cells at each impeller speed after 7 minutes of
flotation. .............................................................................................................................................................. 46
Figure 22. Cumulative recovery over time for the 2-, 4- and 7.5 l cells. ..................................................... 46
iii
Figure 23. Non-cumulative recovery over time for the 2-, 4- and 7.5 l cells. ............................................. 48
Figure 24 Cumulative water recovery for the different impeller speeds after 7 minutes of flotation. .. 49
Figure 25. Non-cumulative water recovery over time for the 2-, 4- and 7.5 l cells. .................................. 50
Figure 26 Particle size distribution of the flotation product for the 2 litre cell according to the different
impeller speeds. ................................................................................................................................................. 55
Figure 27 Particle size distribution of the flotation product for the 4 litre cell according to the different
impeller speeds. ................................................................................................................................................. 55
Figure 28 Particle size distribution of the flotation product for the 7.5 litre cell according to the
different impeller speeds. ................................................................................................................................. 56
Figure 29 Cumulative recovery for the impeller speeds of 1200-, 1300-, and 1400 rpm. ......................... 58
Figure 30 Recovery for the different impeller speeds after 1, 3, 5, and 7 minutes. ................................... 59
List of tables
Table 1 Silicates major groups (adapted from Agapito Mendes et al., 2018). ............................................ 35
Table 2 Manufacturer recommended machine parameters for the different scales (extracted from
Outotec, 2018). .................................................................................................................................................... 39
Table 3. Grinding parameters for the Ball mill and Rod mill. ..................................................................... 42
Table 4. Recoveries for the different concentrations tested using Armeen C as a collector. ................... 43
Table 5 Kinetics parameters obtained from two different kinetics models for the 2-, 4-, and 7.5 l cells at
the impeller speeds of 1200 rpm, 1300 rpm, and 1400 rpm.......................................................................... 51
Table 6 Ratios among the different cells. ........................................................................................................ 52
Table 7 Flotation rate (k) index for the scale-up between different cells and impeller speeds. .............. 53
Table 8 Recovery (R) index for the scale-up between different cells and impeller speeds. ..................... 53
Table 9 d80 for the 2-, 4-, and 7.5 litres cells at the impeller speed of 1200 rpm, 1300 rpm, and 1400
rpm....................................................................................................................................................................... 53
Table 10 d80 ratios when increasing the cell size. ......................................................................................... 54
Table 11 Kinetics parameters as a function of particle size for the different cells and impeller speeds.56
Table 12 SWOT analysis regarding the project. ............................................................................................. 71
iv
List of appendices
Appendix 1. Calculations for the predicted recovery according to the flotation rate constant for the
first-order kinetic model equation ..............................................................................................................76
Appendix 2. Calculations for the predicted recovery according to the flotation rate constant for the
second-order kinetic model equation .......................................................................................................77
Appendix 3. Linear regression for calculation of the flotation rate for the different cells and impeller
speeds using the first-order model ............................................................................................................78
Appendix 4. Linear regression for calculation of the flotation rate for the different cells and impeller
speeds using the second-order model ......................................................................................................81
Appendix 5. Cumulative Recovery of solids as a function of particle size in froth after 1-, 3-, 5-, and 7
minutes ..........................................................................................................................................................84
Appendix 6. Calculations for the flotation rate constant estimation rate as a function of particle size
for the different cells and impeller speeds using the first-order kinetic model .................................85
Appendix 7. Linear regression for calculation of the flotation rate as a function of particle size for the
different cells and impeller speeds using the first-order kinetic model ...............................................86
v
Preface
The present thesis report is the outcome of the final stage of the master’s program in
Resources Engineering – EMerald, which is jointly developed by the following
universities: Université de Liège (Belgium), Université de Lorraine (France),
Technische Universität Bergakademie Freiberg (Germany) and Luleå Tekniska
Universitet (Sweden).
This study was carried out at Luleå Tekniska Universitet. The methodology for
developing this investigation is divided into two different parts: sample preparation
and flotation tests. The sample preparation involves materials handling, grinding,
splitting, and sieving for the olivine material. Flotation tests are performed to
investigate the influence of the impeller speed, as a hydrodynamic variable, during the
scaling-up in a laboratory-scale. This influence is examined in terms of particle size,
recovery, and the flotation rate constant.
vi
Acknowledgments
I would like to give my utmost gratitude and respect for all those people who
provided me assistance, insight, and encouragement, both directly and indirectly,
whether they know of their contribution or not.
I would like to record my thank you and appreciation to Professor Saeed Chehreh
Chelgani and Vitalis Chipakwe for providing direction and encouragement throughout
this work, Tack så mycket!
To all my colleagues, professors, coordinators, friends, and all the people involved
in the Emerald Program. Thanks a lot! Special thanks to Carlos, for all the moments we
shared together, and for all the memories I will never forget. To Mari, Natália, Antônio,
Ervin, Pasindu, Vimbainashe, Anna, Luis, Ali, Neil, and Chelsea for all the chats,
understanding, forbearance, and encouragement. Without your support, this work
would not have been able to come to completion. It was a pleasure to go on this
adventure with you all!
Special gratitude to my family. To my dearest parents, Adriano and Viviane, and
sister, Lívia, for their unconditional love and support. To my grandmother, Graça, for
being the reason I am still here. Without you, I would not have had the courage to go
on and face the challenges I was thrown every day. Muito Obrigada!
I could not finish without thanking all those who have shared all these experiences
with me, contributing to all the memories and to make this an unforgettable time. To
Fredrik for being my support and safety when I most needed it in Sweden. To Nicole,
for being my guide when I could not see the light. To all my friends, in Brazil and all
around the world. Thank you very much, guys!
Lastly, to God. I owe this all to You.
Infinite thanks for the memories, trust, and friendship!
vii
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Lab experiments using different flotation cell geometries
1
Chapter 1
Introduction
Back in time, the grades of ore deposits were considerably higher, and the ore required
fewer and simpler beneficiation operations before being sent to the smelters than nowadays.
Most high-grade ore deposits have reached exhaustion, and technologies involving the
beneficiation of lower grade deposits continue to merge. Nowadays, the requirement for
treating ores with such low grade and complex mineralization increased the demand for
grinding the ore into finer size fractions to meet the liberation degree. Flotation has surged in
order to concentrate these fine particles. However, these fine particles are still problematic
material in terms of concentration.
One of the main challenges is higher throughput. Because of the increasing demand for
processing the low-grade ores, larger volumes of material are being processed. Therefore, the
size of flotation equipment has also significantly increased for the past decades. With this,
many challenges have surged in terms of equipment performance, design, and operation.
These challenges are commonly associated with problematic pulp hydrodynamics and froth
transportation (Mesa and Brito-Parada, 2019a). Thus, the studies related to scale-up are and
will remain to be crucial in terms of designing larger flotation machines. For addressing
these issues, it is important to well-understand the scaling-up process in flotation. One of the
most important factors for flotation scaling-up is the “flotation rate constant”.
The flotation rate constant (k) is the recovery that can be reached through a specific
interval of time. It is known to increase with an increase in particle size until reaching its
maximum value. After that, the flotation rate decreases associated with a further increase in
particle size (Horst, 1952).
Lab experiments using different flotation cell geometries
2
Determining the flotation rate constant has been considered in many investigations using
different methods of assessing it. The following first-order equation is usually applied. It was
first expressed by H. Garcia Zunica in 1935 (Horst, 1952).
( )
In Equation 1, r is the amount recovered, R is the original amount, t is the flotation time,
and k is the flotation constant (Horst, 1952).
The flotation rate is dependent on many flotation factors, such as mineral properties and
flotation hydrodynamic variables. Thus, all these factors can directly affect the flotation
scaling up. For that, it is important to well-understand the hydrodynamics phenomena
behind the scale-up process.
1.2 Aim and Objectives
This investigation, as a comparative study, is going to examine the impeller speed, as a
hydrodynamic variable, and its effect on the flotation rate constant during the scaling-up in a
laboratory-scale. In the first stage of this investigation, the impeller speed would be varied
for different Outotec GTK LabCell® flotation cell sizes. This machine is a mechanical
laboratory-scale batch flotation equipment that contains 2, 4, 7.5, and 12 litres plastic cells
with its respective OK type rotors, impellers, and froth scrapers. It has only recently been
introduced to the market; therefore, not many studies have been conducted regarding its
operating conditions. The examined flotation experiments can show the influence of this
variable on the flotation rate constant when the size of these cells increases. Assessing this
influence would be an important step in defining the required impeller speed for each
flotation cell.
This will be achieved through to the fulfillment of the following objective:
Lab experiments using different flotation cell geometries
3
Objective - To provide a comparative study in order to understand the influence of the impeller
speed, as a hydrodynamic variable, during the scaling-up in a laboratory-scale. For that, the impeller
speed is varied for different Outotec GTK flotation cell sizes, in order to assess the influence
of the impeller speed when the size of these cells increases. This influence is going to be
examined in terms of particle size, recovery, and the flotation rate constant.
Lab experiments using different flotation cell geometries
4
Chapter 2
Literature Survey
2.1 Flotation
Flotation is, in practice, a separation technique capable of separating minerals based
on their surface property, which is the hydrophobicity degree. It is the most efficient
separation technique for the particle size range between 25 to 100 μm, although it differs
according to the mineral being floated (Alves dos Santos and Galery, 2018).
Froth flotation is currently the most common mineral treatment method in mineral
beneficiation, due to its technical versatility and cost-viability. It was licensed in 1906 for
the concentration of ores, but it can be additionally applied in different industrial
sectors, for example, oil sands concentration, ionic flotation, algae separation, paper
deinking, plastic reusing and water treatment (Mesa and Brito-Parada, 2019a)
Its principle is based on the surface chemistry of a material, in which hydrophobic
mineral particles are separated through attachment to gas bubbles, ascending to create a
froth layer, overflowing as the mineral-rich concentrate. The separation process consists
of scattering small bubbles of gas, mostly air, in the interior of a flotation tank, which is
also called a flotation cell. The flotation cell is filled with a mineral suspension in an
aqueous media, to give a pulp. For improving the separation process, chemical reagents
that modify surface properties of minerals can also be added in the process, acting as
collectors, frothers, or regulators (Agapito Mendes et al., 2018).
The recovery of particles within the concentrate is mainly done though: true flotation,
which is the selective attachment of a particle to an air bubble; entrainment of particles;
Lab experiments using different flotation cell geometries
5
and through aggregation, which is a physical entrapment among particles to an air
bubble within the froth (Napier-Munn and Wills, 2005).
Selective attachment of particles to bubbles is the main goal through the flotation
separation. In the true flotation, the reagents should selectively react with the surface of
target minerals. However, the effectiveness of the separation among gangue and
valuable minerals relies on the entrainment and entrapment degree, as for this case,
valuable minerals and gangue are equally likely to be recovered (Napier-Munn and
Wills, 2005). Entrainment is mostly affected by the particle size, as finer particles can
easily flow upwards due to its lower gravitational forces (Boeree, 2014). But it can also
be affected by pulp density, particle shape, and froth properties like stability, drainage,
removal rate, and residence time (Flint, 2001).
According to Wang et al. (2015), coarser particles are more likely to settle at the
bottom of the flotation cell, while the fine particles are more likely to be uniformly
dispersed in the pulp phase. In a perfect mixing system, a higher number of entrained
particles can be observed, as more material is entering the froth.
The particle size also plays an important role in the stability of the froth. The froth
zone avoids the direct transport of the pulp to the concentrate defining the quality of the
concentrate (grade) and the efficiency of the process. A stable froth increases
entrainment as the drainage degree of particles back into the pulp zone is reduced, while
an increase in residence time allows a higher degree of particle detachment before the
froth flows into the launder (Boeree, 2014).
Typically, lower recoveries are associated with finer and coarser particles. In the case
of coarser particles, it has been mostly associated with detachment. This can happen in
the froth phase or the interface between pulp and froth. For finer particles, the collision
probability is decreased due to the behaviour of particles with smaller masses, which is
to follow water streamlines, decreasing recovery. In general, the impact of particle size
Lab experiments using different flotation cell geometries
6
in flotation relies on the hydrophobicity degree, which is highly conditioned by
liberation, mineral texture, and reagent adsorption (Alves dos Santos and Galery, 2018).
All minerals are categorized in conformity to their surface properties into polar or
non-polar groups. Minerals in the non-polar group have their surface categorized by the
moderately weak molecular bonds. These have their covalent molecules adhered
together through van der Waals forces, making them hydrophobic because the non-
polar surfaces are not easily attached to water dipoles. On the other hand, minerals
belonging to the polar group have a stronger covalent or ionic surface bonding. These
are naturally hydrophilic because their surfaces easily react with water molecules,
creating a stronger bond. These surface properties can be altered through the addition of
chemical reagents (Napier-Munn and Wills, 2005).
Mineral separation is connected to the surface selective affinity, mostly modified by
the reagents. Collectors are added to the pulp to selectively improve the hydrophobicity
of the targeted minerals, which are in some cases, the material of value to be floated
(Mesa and Brito-Parada, 2019a). Its molecular structure is characterized by a covalent
molecular portion and an ionic portion, turning the collector into a surfactant, a
compound with an amphipathic structure (Agapito Mendes et al., 2018).
The molecules of a collector can be either ionising or non-ionising compounds.
Ionising collectors can be cationic or anionic. These can be complex in terms of
molecules' structure and are heteropolar. This means these are composed of a charged
polar group and an uncharged non-polar group. The non-polar group commonly
consists of a hydrocarbon chain that can be found in the form of oil in the
commencement of a flotation process, this allows the mineral surface to repel water by
covering it with a thin film. For the polar group, it can be an ionizing and hydrophilic
compound, meaning that it dissociates into ions when in water. This can be altered in
order to react with the specific surface of a mineral. This process can be seen on Figure 1,
Lab experiments using different flotation cell geometries
7
in which A shows when the collector dissolves in the aqueous phase, in B the adsorption
of a collector in a mineral surface is presented, and in C, the insertion of an air bubble
allows its attachment onto the hydrophobic surface (Gupta and Yan, 2006).
Figure 1 Process of adsorption of a collector in a mineral surface and attachment to the air bubble (extracted
from Gupta and Yan, 2006).
The classification of ionising collectors is made according to the kind of ion, anion, or
cation that creates the effect of repelling water. Figure 2 shows the different classification
for collectors (Napier-Munn and Wills, 2005).
Figure 2 Classification of collectors (extracted from Napier-Munn and Wills, 2005).
Lab experiments using different flotation cell geometries
8
The recovery of these particles happens in the froth phase. Therefore, the froth should
be stable and under control for reaching an effective separation. For an effective flotation
process, the valuable mineral surface should be, or become hydrophobic and the gangue
mineral surface should be or become hydrophilic. When the valuable minerals are
hydrophobic and extracted in the floated fraction, it is called direct flotation. The
opposite is also possible, and it is called reverse flotation, in which the gangue is floated
and extracted in the floated fraction (Napier-Munn and Wills, 2005).
Flotation processes often happen in different stages (circuits). Rougher is the first
stage, in which the concentrate is obtained together with a waste that is still rich in the
mineral ore. The concentrate from this stage goes to a cleaning process, called cleaner
stage, that allows the upgrading of the final concentrate. The waste from the rougher
and cleaner stage generally follows to the scavenger stage for the possible recovery of
valuable minerals and for obtaining a waste that is adequate for disposal. There is also
the possibility of altering the stages in a circuit according to the requirements for the
process (Agapito Mendes et al., 2018).
In order to create the appropriate conditions for an efficient flotation process,
flotation machines are required. These are carefully selected to enhance the mixing
performance for promoting particle-bubble collision and bubbles dispersion and
production (Newell, 2006).
2.2 Flotation equipment
Before entering the flotation equipment, some material dressing processes are
required to ensure the efficiency of the process, such as reducing the particle size
through grinding, desliming, and conditioning.
Lab experiments using different flotation cell geometries
9
Independent of the size, flotation equipment can be mainly grouped into mechanic
cells and pneumatic cells, however, these can also be classified as tank cells and flotation
columns (Agapito Mendes et al., 2018)
2.2.1 Pneumatic cells
In pneumatic cells, the bubbles are created by infusing the air inside the cell at high
pressure or speed. This can be done either by feeding the pulp and the air separately, as
in the flotation column (Figure 7), or it can be done as in the Jameson cell (Figure 3) in
which the pulp is injected together with the air at high pressure, intensifying the
collision among bubbles and particles (Mesa and Brito-Parada, 2019a).
Figure 3 Schematic of a Jameson cell (extracted from Silva, 2005).
Figure 4 shows a schematic pneumatic cell model Imhoflot. The conic device at the
top is to regulate the froth height. The cone is inserted or removed from the cylindric
cell, increasing or reducing the available section for the froth. Agitation is provided by
injected air, reducing pulp turbulence, which is an advantage for coarse and fine
particles flotation (Chaves, 2006).
Lab experiments using different flotation cell geometries
10
Figure 4 Schematic pneumatic cell model Imhoflot (extracted from Chaves, 2006).
Column flotation is more frequently utilized in coal, phosphates, iron ore and base
metal plants, as the cleaner stage. In this equipment, the air is usually inserted in the
base of a tall cell employing a sparging system, while the pulp is fed close to the highest
part of the column (Figure 5). This allows particles to settle due to gravity and the
bubbles to rise due to its lightness and properties. In this equipment, the column height
and the ratio between height and diameter are crucial, as the bubble-particle interaction
is dependent on the space between the region where the air is inserted and the top of the
column, where the pulp is fed (Mesa and Brito-Parada, 2019a).
Figure 5 Schematic of a column flotation (extracted from Mesa and Brito-Parada, 2019a).
Lab experiments using different flotation cell geometries
11
The main variables related to column flotation that influences the concentration
process are primarily the airflow rate, water flow rate, the height of the froth, residence
time, air hold up, bubble, and particle size, among others. These variables have a
significant influence on the grade and recovery of the mineral of interest (Silva, 2005).
2.2.2 Mechanical cells
The first cells applied in flotation were Pneumatic cells, that nowadays is not very
common and more broadly utilized in the industry for specific cases. Currently,
mechanical cells comprise the major part of flotation equipment employed worldwide.
The purpose of a flotation tank is to inject air bubbles into the pulp, to enhance the
likelihood of collision between the bubbles and the particles within the slurry, to ensure
a stable pulp-froth interface, and to provide an adequate froth removal capacity (Mesa
and Brito-Parada, 2019a).
Controlling the airflow rate, impeller speed and pulp level is vital for the
optimization of the flotation process. As presented in Figure 6, mechanical cells contain
an impeller to create a region with high turbulence aiming to maintain the particles in
suspension, to provide bubble-particle collision, and to produce and disperse the
bubbles. These can also be sub-divided into self-aerated and forced-air cells, according
to the air introduction scheme applied. Both are broadly applied in treatment plants,
although forced-air cells provide greater control of the supplied air (Mesa and Brito-
Parada, 2019a).
Figure 6 Schematic of a mechanical flotation cell (extracted from Mesa and Brito-Parada, 2019).
Lab experiments using different flotation cell geometries
12
In a mechanical cell, for an efficient flotation to occur, the number of bubbles should
be high and with a small diameter, in a way that it captures the higher number of
particles as possible. For that, an impeller is used for generating bubbles, while a stator
breaks the bubbles in an appropriate size. An example can be seen in Figure 7 (Chaves,
2006).
Figure 7 Typical flow patterns in a mechanical flotation cell (Outokumpu) (extracted from Gorain et al., 1995).
Many different cell geometries can be used, as presented in Figure 8. These can apply
different impeller-stator designs, as presented in Figure 9.
Figure 8 Flotation cell designs (extracted from Chaves, 2006).
Lab experiments using different flotation cell geometries
13
Figure 9 Impeller-stator designs. (extracted from Chaves, 2006).
The simplest cell design is the Aker model. The impeller is a turbine, and the stator is
fixed at the bottom of the cell. Outokumpu (OK type) presents a more sophisticated
impeller-stator design as presented in the previous Figure 7.
2.2.3 Laboratory flotation equipment
The equipment previously introduced is presented on the industrial scale, but due to
physical and financial aspects, trial runs and tests are commonly performed on the
laboratory scale. These are smaller and adapted flotation equipment used to reproduce
and accomplish a comparable performance to the industrial flotation procedures.
For the micro-flotation tests, either a Modified Partridge-Smith cell or a Hallimond
tube can be applied. The first contains a frit at the bottom, a straight glass tube, and a
launder. It can be used to assess the response of a mineral for a specific flotation
condition, such as pH or reagent dosage (McGill University, 2020).
Lab experiments using different flotation cell geometries
14
The schematic of a Hallimond tube can be seen in Figure 10. It contains a frit at the
bottom to allow the air to flow. It uses similar conditions to the modified Partridge-
Smith cell and also assesses the mineral response to a specific flotation condition. The
difference is that it reduces the quantity of floated particles that fall back to the pulp
through a bending shape (McGill University, 2020).
Figure 10 Schematic of a Hallimond tube (extracted from Wills & Napier-Munn, 2006).
Mechanical bench-scale laboratory cells (Figure 11) are broadly applied machines that
demonstrate to be effective for flotation tests in terms of deciding the reagents to be used
and determining the kinetic parameters for modelling (Mesa and Brito-Parada, 2019a).
Figure 11 Schematic of a laboratory bench-scale mechanical flotation equipment (extracted from Mesa and
Brito-Parada, 2019).
Lab experiments using different flotation cell geometries
15
Nonetheless, the reduced size indicates that the majority of these cells have
significant differences in impeller size, amount of stator blades, and in other physical
proportions when contrasted to industrial cells. Also, in these laboratory equipment, the
steady-state cannot be achieved, as water is constantly added while the froth overflows
in order to keep up the pulp level, resulting in a variety of mineral grade, solid, and
reagents concentration over time (Mesa and Brito-Parada, 2019a).
In mechanical batch flotation tests, the sample size usually ranges around 500 g, 1 kg,
or 2 kg sample. These are mechanically agitated and simulate a large-scale flotation
process (Figure 12). Air is introduced mainly through a hollow standpipe around the
impeller shaft. The impeller pushes the air down the standpipe, being controlled using a
valve and through the speed of the impeller. This generates bubbles that rise through
the pulp, which are after collected in the froth zone (Napier-Munn and Wills, 2005).
Figure 12 Laboratory mechanical flotation cell (extracted from Wills & Napier-Munn, 2006).
These bench-scale flotation tests are commonly done using a Denver Lab Cell D-1
machine. It contains different cells with different capacities, usually three cells with
capacities of 500 ml, 2500 ml, and 5000 ml (Figure 13) (McGill University, 2020).
Lab experiments using different flotation cell geometries
16
Figure 13 Denver Lab Cell D-1 flotation machine (extracted from McGill University, 2020).
Another example of a laboratory bench-scale flotation machine is the Outotec GTK
LabCell, which has adjustable air feed and impeller speed, and automatic froth scraping
mechanism. It also comes with different scale cells with its respective impellers, stators,
and scrapers (Outotec, 2018).
Continuous laboratory systems have been introduced, together with laboratory cells
that can perform at a steady state. Whereas laboratory tests permit assessing the impact
of different variables in a single unit, pilot-scale testing is crucial for plant circuit design.
These are small (ranging from 60 to 150 litres) industrial flotation tanks applied for
comparison of equipment and circuit efficiency in terms of costs and concentrate sample
sizes (Mesa and Brito-Parada, 2019a).
Nowadays, the decrease in grades and higher mining capacities has led to an increase
in the throughput of material being treated at modern industrial treatment plants.
Rather than the increase in the number of cells and banks, flotation equipment has
increased its dimensions in the interest of handling more material (Mesa and Brito-
Parada, 2019a).
Figure 14 shows the evolution in flotation tank sizes over the last century, alluding to
the maximum tank volume commercially accessible. This has been beneficial in terms of
Lab experiments using different flotation cell geometries
17
decreasing the overall capital and operating expenses. On the other hand, these bigger
and increasingly complex tanks created new challenges in its design, performance, and
operation especially in respect of pulp hydrodynamics and froth transportation (Mesa
and Brito-Parada, 2019a). With this increase in flotation cell sizes, it is important to
understand the mechanisms governing the scale-up process.
Figure 14 Trend in the flotation tank size over the last century (y-axis is on a logarithmic scale) (extracted from
Mesa and Brito-Parada, 2019a).
2.3 Scale-up of flotation process
Some mineral processing plants, when facing the issue of treating a higher
throughput, apply a different technique called process intensification. This means
studying and designing smaller reactors in order to improve transport and processing
rates, providing better control of kinetics. This enhances energy efficiency and decreases
capital costs.
This process intensification approach has been taken slow steps in terms of
application in the industrial scale. Although it seems to play a vital part within the
Lab experiments using different flotation cell geometries
18
future of mineral processing operations, it is improbable that it will be applied in froth
flotation, in terms of having reduced tanks within the near future. Based on that, scale-
up studies will most likely continue to be crucial in terms of designing larger flotation
equipment. As such, a stronger understanding of the hydrodynamics factors at variable
scales and their influence on performance is required, especially for the pulp and froth
zones in flotation tanks (Mesa and Brito-Parada, 2019a).
Previous flotation tanks were considerably small in volume (smaller than 1 m3)
(Arbiter, 2000). Today, these can be larger than 300 m3. This increase results in technical
and financial benefits, as fewer machines are required leading to reduced plant
footprint, simpler operational control, and less energy consumption. Anyhow, fluid
dynamic properties also influence the efficacy of flotation machines. The size, shape,
speed, and location of the agitating mechanism directly influence in pulp dynamics.
Also, the higher gap between the bulk of the froth and the discharge lip alter the froth
stability (Mesa and Brito-Parada, 2019a). These aforementioned factors can lead to new
challenges when it comes to scale-up to the industrial scale.
The scale-up approach in flotation studies is divided into two distinctive groups, the
kinetic scale-up and the machine design scale-up (Mesa and Brito-Parada, 2019a). The
kinetic scale-up consists of diverse methods of scaling-up the flotation model such as
kinetic parameters acquired over laboratory investigations, to anticipate the plant
performance (Gorain et al., 1998). The machine design scale-up is referred to as the study
field that analyses, in different scales, the behaviour and performance of flotation
equipment. This is done by centralizing on air injection technologies and impeller speed
and layout, taking into account the influences of hydrodynamic phenomena in the pulp
zone, and the geometrical and dynamic resemblances (Gorain et al., 1994).
A large majority of studies related to machine design scale-up focuses on pulp zones.
Therefore, there is an information gap when it comes to scientific studies and
Lab experiments using different flotation cell geometries
19
manufacturers guidelines on the scale-up of flotation tanks. The few works on this topic
centralize exclusively on hydrodynamics assessment of the pulp zone, by comparing the
Computational Fluid Dynamics (CFD) model estimations versus tests operated solely
with water. When it comes to modelling flotation tanks, this tool is sometimes applied to
evaluate flotation efficiency without integrating the froth and pulp zones (Mesa and
Brito-Parada, 2019a).
2.3.1 Computational Fluid Dynamics (CFD)
Recently, researchers have started applying CFD for modelling mechanically agitated
flotation cells for assessing the flow complexity regarding the different phases in the
interior of the cells (Koh et al., 2003). The design of flotation cells is normally done based
on empirically derived relations. When applying CFD modelling, individual finite
volumes categorizes the flotation cell in order to estimate local values of flow properties.
This provides a more detailed comprehension of the flow permitting the equipment
adjustment and operation and enhancing flotation performance (Koh and Schwarz,
2006).
Three flotation sub-processes are modelled using the collision, attachment, and
detachment approach. The particle-bubble collisions rate is estimated using a turbulent
collision model, using the local turbulent speed, the size, and the number of bubbles and
particles present in the different regions of the cell. Additionally, the collision, adhesion,
and stabilization probabilities are determined allowing the estimation of the attachment
rates. Likewise, the fluid turbulence allows the estimation of the detachment rates. These
attachment and detachment rates are applied in the CFD kinetic modelling containing
simulations of the transient population-balance eliminating the froth bubble–particle
aggregates (Koh and Schwarz, 2006).
Although CFD has been extensively studied for modelling of the flotation process,
the literature regarding its practice for the scale-up of flotation cells is still scarce (Mesa
Lab experiments using different flotation cell geometries
20
and Brito-Parada, 2019a). One of the first examples of the use of CFD in flotation
equipment design was made in 2000 in the work of Koh et al. (2000). In this work, a
standard Rushton turbine tank and a CSIRO flotation cell were contrasted regarding its
number of bubble-particle collisions per time per unit volume. The number of bubble-
particle collisions was predicted using the computed flow properties acquired from the
flow variables derivative from an Eulerian-Eulerian multiphase concept associated with
the standard k–e turbulence model (Koh et al., 2000).
Afterward, a Denver-type flotation cell was simulated using a combination of the
bubble–particle collision and attachment rates that have been introduced in a CFD
model (Koh and Schwarz, 2003). For the estimation of the bubble–particle collision
number, the Saffman, and Turner equation was used (Saffman and Turner, 1956), and
for accounting to the particles following the fluid streamlines, the Yoon and Luttrell
(1989) (Hassanzadeh et al., 2019) model was utilized. Similarly to the beforehand
mentioned work, the Eulerian–Eulerian method was applied in order to model the
multiphase in combination with the Multiphase Reference Frames (MRF) method for the
rotation of the impeller (Koh and Schwarz, 2003).
Subsequently, in 2006, the detachment rate and the attachment probability were
inserted in the CFD model. They implemented a first-order kinetic model including
different sub-processes equations. The CFX4.4 was used for determining the flotation
kinetic and the gas-liquid governing equations for a Rushton turbine tank and a CSIRO
Denver flotation cell. The flotation rate constant was estimated based on the particles
that remained within the cell. The same process was also applied in subsequent work, in
a self-aerated flotation cell, in which the gravitational force was included in the
dispersed phase equation, which leads to an increase in the detachment frequency (Koh
and Schwarz, 2006; Koh and Schwarz, 2007).
Lab experiments using different flotation cell geometries
21
Another work was produced in a modified Denver batch flotation cell using a CFD
model for predicting the flotation rate constant and for assessing the influence of the
impeller speed on the flotation performance. This work proved to be in good
qualitatively and quantitatively agreement based on the contrast among the
measurements obtained and the predicted flotation rate constants. In this case, an
Eulerian-Eulerian and a Lagrangian-Eulerian method were applied for modelling, using
a higher-order coupling manner among the different phases. This allowed researchers to
employ a full momentum among the particulate phases, using the Lagrangian-Eulerian
approach, providing better results (Koh and Smith, 2011).
Overall, incorporating numerical systems in fundamental models has proved to be
limited, which is attributed to the struggle of incorporating complex flotation sub-
processes models with the numerical modelling of high turbulent flow in the interior of
a mechanically agitated flotation cell. Therefore, inserting a partial differential equation
to the model, to estimate the free particles in the system, maximize the computational
demands.
In order to improve that, Karimi et al. (2014) developed a new methodology for the
estimation of the flotation performance using CFD modelling, considering the sub-
processes taking place through the separation, excluding the insertion of a new equation
for the number of particles. For that, the flotation rate constant is predicted using the
fundamental flotation model of Pyke et al. (2003) into the Eulerian-Eulerian framework.
It was proven that the new CFD model improved the flotation rate constant estimations
and allowed to assess the influence of the particles' hydrophobicity, impeller speed, and
gas flow rate on the flotation rate constant (Karimi et al., 2014).
The main literature focusing on a CFD model for the scale-up of flotation presents the
effect of machine scale-up for comparing the pulp behaviour in different Metso tanks
using CFD and Discrete Element Modelling (DEM). However, the air injection was not
Lab experiments using different flotation cell geometries
22
considered and not many details are presented, therefore, the whole complexity of the
system was not considered (Mesa and Brito-Parada, 2019a).
Similar industries have, however, applied CFD for equipment scale-up. An example
is the scale-up of fluidized-bed hydrodynamics in which the flow turbulence and
particle size affect the selection for the appropriate size of the cell (Knowlton et al., 2005).
Another work is regarding the scale-up of binder agglomeration processes, in which the
operating conditions are influenced in more than one process, therefore when reaching a
determined scale, it was recommended that the different processes should be split into
different staged unit operations (Mort, 2005).
Improving the predicting competencies of current models requires additional
investigations on CFD methods to model the collection zone, addressing the three
phases and 3D flotation systems. Although kinetic models have been useful for
assessing flotation performance, addressing the physical interactions among the
different phases would improve the actual limitations regarding scale-up
methodologies. Therefore, theoretical and experimental research regarding the scale-up
methods is vital in order to fill the gaps in knowledge that needs to be addressed (Mesa
and Brito-Parada, 2019a).
2.3.2 Kinetic scale-up
The fundamental goal of kinetic scale-up is to apply mathematical methods to
anticipate the performance of an industrial-scale plant in terms of concentrate grade and
recovery, through the evaluation of laboratory-scale data acquired in flotation tests
(Mesa and Brito-Parada, 2019a).
Researches related to kinetic flotation models are plenty. These are based on
simplification, as in chemical reactions, in which flotation is considered as a kinetic rate
operation (Mesa and Brito-Parada, 2019a).
Lab experiments using different flotation cell geometries
23
The subsequent ordinary differential equation is based on this assumption (Equation
2), in which C is the concentration of particles, k is the kinetic constant for the flotation
rate, and n is the reaction order (Bahrami et al., 2019).
(1)
Introducing the compartmental model for continuous flotation tanks in the kinetic
models enabled the deviation of its focus on the froth zone, redirecting it to the
collection zone. Based on that, the model splits the flotation process into a pair of
independent yet interlinked parts containing its recovery. These are the froth and the
collection zone. This is presented in Equation 3, in which the recoveries are represented
as overall recovery (R), collection zone recovery (Rc), and froth zone recovery (Rf). The
last can be represented by Equation 4, where the overall flotation rate constant is
represented by k, and the collection zone rate constant by kc (Mesa and Brito-Parada,
2019a).
(2)
(3)
In the following Equation 5, the flotation rate (k) can be estimated assuming that the
flotation of particles of diameter i follows a first-order rate reaction. R is the recovery at a
flotation time t, and R∞ is the recovery towards an infinite time (Duan et al., 2003).
(4)
The following Equations 6-9 shows other flotation kinetic models that can be used for
estimation of the flotation rate. These can be achieved considering different
simplifications and can be applied to describe the collection recovery component and the
overall recovery as in Equation 5 (Mesa and Brito-Parada, 2019a).
Lab experiments using different flotation cell geometries
24
(5)
(6)
(7)
(8)
Equation 6 is a variation of the first-order model, called the first-order model with a
rectangular distribution of flotabilities. Equation 7 is the second-order kinetic model and
Equation 8 is the Klimpel model, or also called, the second-order model with a
rectangular distribution of flotabilities (Bahrami et al., 2019). Finally, Equation 9 is called
the non-integral order equation (Merna et al., 2015).
The main objective of these models is to explain the flotation process using the kinetic
parameters, which can be, for example, the variables k and the theoretical maximum
recovery reachable considering the machine efficiency and mineral liberation, R∞. These
variables can be achieved through applying the models in the experimental data, and
accordingly, are reliant on the mineral properties, for example, its composition, particle
size distribution, liberation, operational settings, and the flotation machinery (Mesa and
Brito-Parada, 2019a).
The currently applicable kinetic models consider the froth as a simple zone in which
an experimentally determined fraction of the solid particles are rejected and returned to
the pulp zones. Therefore, performance may be considerably different among
laboratory-, pilot- and industrial-scale units, depending on froth stability, mixing
systems, and residence-times (Flint, 2001).
Finding the kinetic parameters at an industrial scale based on laboratory experiments
is not a simple operation for the different combinations of ore and machinery. The
flotation kinetics variables acquired from industrial-scale and experimental data are
Lab experiments using different flotation cell geometries
25
different. The amount of time that a particle stays in the system and the hydrodynamic
settings of the flow are not the same. This process is behind the theory of kinetic scale-up
and it has not been solved, as typical results in laboratory-scale data overpredict
industrial rates (Mesa and Brito-Parada, 2019a).
Many existing empirical methods for scaling-up kinetic variables are reliant on a
scaling factor. This factor commonly ranges from 1.5 to 3 and it can be achieved based
on the ratio between industrial and laboratory residence times. The estimation of the
plant flotation rate can be assumed as the division of the experimental flotation rate to
the scaling factor. The purpose is to accomplish an identical recovery by means of
linking the residence time required in a batch test and a continuous flotation circuit
(Mesa and Brito-Parada, 2019a).
There are many published studies related to the scaling factor application. Yianatos et
al. (2003) applied separability curves, which are the ratio between mineral recovery and
yield, for determining the comparison recovery. The scale-up factor then established
was kPlant τ = kLab t, based on the assumption of an ideal separability point for the
comparison recovery. This means having the concentrate incremental grade matching
the feed grade. For further studies, a non-dimensional scaling variable (φ) was added to
the equation in order to split the impacts of mixing and kinetic variations on the time
scale-up factor, as presented in Equation 10 (Yianatos et al., 2006).
(9)
Followed by these studies, Yianatos et al. (2010) integrated some impacts of tank
dimensions in the scale-up factor, which is now represented as ξ = Kac/KLab, in which the
real value from the plant (Kac) can be assumed from Equation 11. In this equation, the
influences of froth zone (ζ = kapp/kc), variances in cell mixing (ŋ), and solids segregation
(Ψ) are now inserted in the calculation of the apparent flotation rate constant, Kapp.
Lab experiments using different flotation cell geometries
26
Yet, none of these studies considers the influences of entrainment, the detachment of
particles during sampling, and further influences of the froth zone, for example, liquid
drainage and transport phenomena.
(10)
Gorain et al. (1998) suggested the following Equation 12 for the representation of k. In
this equation, kc = P.Sb, where P is a non-dimensional variable dependent on the ore
properties, is called the floatability index. And the bubble surface area is represented by
Sb (Sb = 6 Jg/d32), in which Jg is the gas superficial velocity in cm/s, while d32 is the bubble
Sauter mean diameter in mm. This scale-up process model was developed with the
intention of decoupling the ore properties (P) from the operational parameters and the
flotation machinery design (Sb), so it is only dependent on Sb.
(11)
Later researches suggested what is shown in Equation 13. That is an empirical
equation for Sb that considers the hydrodynamic effects associated with the impeller
design and operational settings, ignoring some aspects such as tank size and shape. In
this equation, the constants a = 123, b = 0.44, c = 0.75, d = − 0.10 and e = − 0.42 come from
the analysis of experimental data, while the peripheral speed of the impeller is
represented by Ns, the aspect ratio among the impeller’s diameter and height is
represented by As and the particle size of the feed is represented by P80 (Mesa and Brito-
Parada, 2019a).
(12)
To add the entrainment mechanisms in these studies, Welsby et al. (2010) proposed
the following Equation 14. In this equation, the degree of entrainment is represented by
Lab experiments using different flotation cell geometries
27
ENT, Rw represents the concentrates water recovery, i is the size class and j the liberation
class.
(13)
Lately, two non-dimensional variables (EVF and æ) were added by Amini et al. (2016)
to improve the scale-up model competences. These are shown in Equation 15 and
Equation 16. EVF is the Effective Volume in Flotation and it is the portion among the
volume of the cell in which ε (the turbulent kinetic energy dissipation rate) is bigger than
0.1 m2/s3 and the entire volume of the cell. For Equation 16, æ represents the
hydrodynamic factor. The fluid kinematic viscosity in cm2/s is represented by ν, and n is
predicted based on various flotation experiments ranging in the operational settings.
(14)
(15)
The previously mentioned kinetic scale-up models rely on deterministic models.
These have received many critiques over time, due to its industrial application and
estimation capacity. Consequently, probabilistic models have been suggested and
investigated. These states that k is the effect of merging the bubble-particle collision (Pc),
attachment (Pa), and detachment (Pd) probabilities, as presented in Equation 17, in which
Z is the collision rate (Schuhmann, 1942).
(16)
Pyke et al. (2003) presented a model that has been applied in the design of a CFD
kinetic model. This is shown in Equation 18, where the gas flow rate is Qg, the volume of
reference is Vr, the density of the solids is given by ρs (g/cm3 ), the density of the liquid is
given by ρl (g/cm3) and the fluid turbulent speed by ui (cm/s).
Lab experiments using different flotation cell geometries
28
(17)
Although many studies related to the mechanisms of flotation, multiphase flotation is
a complex system that is still not entirely explained by those models. Kinetic models are
primarily focused on the pulp zone events because the froth zone is not a kinetic process
(Mesa and Brito-Parada, 2019a).
2.3.3 Machine design scale-up
The objective of machine scale-up in flotation is to allow the conversion of laboratory-
scale to industrial-scale with the smallest interference on its efficiency. That can be
accomplished by describing the influence of machinery design, shape, and size on
flotation performance. However, this is a challenging procedure as flotation phenomena
comprise many micro-, meso- and macro-scale unrelated processes. Therefore,
similitude factors and non-dimensional analysis have been applied for simplification of
the process (Mesa and Brito-Parada, 2019a).
For the process of stirred tank scale-up, the distinct phases are combined in a
turbulent zone, and the focus is to scale-up just the pulp zone. This process includes the
development of a larger system that is expected to accomplish a mixing quality that is
equal to the experimental one (Mesa and Brito-Parada, 2019a).
As seen in Figure 15, the power spent by the diverse impellers can be calculated
based on the Reynolds number and Power number. The following Equation 19 and
Equation 20 were suggested by Arbiter (2000) and it considers the Power number and
the power per volume (P/V) as fixed. It is done by changing the rotor diameter (D) and
rotational velocity (N).
(18)
(19)
Lab experiments using different flotation cell geometries
29
Figure 15 Power number for the diverse impellers Reynolds number (extracted from Mesa and Brito-Parada,
2019a).
Equation 21 shows the nominal shear rate, in which δ is a rotor-stator scale-
independent variable that represents the shear gap width. Based on some studies, for a
scale-up process, the nominal shear rate should be kept as constant. However, this
statement just addresses the liquid phase agitation phenomena, ignoring the existence of
solids and air bubbles in a flotation process (Mesa and Brito-Parada, 2019a).
(20)
Some examples of nondimensional variables suggested for the development of froth
flotation tanks are: the Reynolds number (Re) that assess to the turbulence in the system,
and it is represented by Equation 22; the Power number (Np), which is associated to the
torque and inertial forces required to spin the impeller at a certain rate, and it is
represented by Equation 23; the Frode number (Fr) which is the ratio between the inertial
and gravitational forces, and it is represented by Equation 24; the Zwietering constant
(S) that is related to the impeller nature and geometry, and it is represented by Equation
25; and the airflow number (Na, also called air capacity number - Ca) represented by
Lab experiments using different flotation cell geometries
30
Equation 26. In these equations, ρ is the density of the pulp, µ and ν are the dynamic and
kinematic viscosity, respectively.
The power spent by the impeller is given as P and the gravitational speed is given as g.
Reimp is the Reynolds number produced by the different impeller types, ρl is the liquid
phase average density and ρs is the solid phase average density. Njs is the lowest
agitation velocity where all the particles achieve the total suspension. The particle size
mean is given by dp, the mass ratio between suspended solids and liquid is represented
as X, and the gas inflow rate by Qg (Mesa and Brito-Parada, 2019a).
(21)
(22)
(23)
(24)
(25)
A typical flotation scale-up practice, in terms of examining the gas injection and
bubble creation, is to maintain constant the connections among gas and liquid flow rate,
and tank diameter, as presented in Equation 27 (Arbiter et al., 1976).
(26)
The previously examined researches focus on different strategies for equipment
design scale-up. The different procedures have been implemented each for a specific
tank and at different operating settings. Based on that, there is a lack of additional
investigations for comparing the different scale-up systems, in both theoretical and
experimental aspects (Mesa and Brito-Parada, 2019a).
Lab experiments using different flotation cell geometries
31
It is also important to mention that all the previously mentioned methods related to
nondimensional variables can only be applied to get a comparable particle suspension
and agitation, meaning that there is still a lack of proof that these are related to
achieving similar metallurgical effectiveness. Also, the froth zone presents several
complexities that must be analysed for anticipating its performance (Mesa and Brito-
Parada, 2019a).
According to Newell (2006), if the chemical conditions within the cells of different
scale are constant, and geometric similitude applies, the scale-up of the flotation process
should be governed by hydrodynamic factors. These are the volumetric flow rate of gas
and the impeller speed.
2.4 Influence of the impeller speed and design in flotation
Mechanical cells are highly turbulent vessels in which a significant amount of energy
is present for permitting the collision of small particles with the rising bubbles. The main
function of the impeller is to keep particles in suspension, create and disperse bubbles,
and to promote bubble-particle collision. Additionally, it can produce a more turbulent
environment, affecting froth stability (Wang et al., 2015). These are usually installed in a
rotor-stator system, in order to produce high shear rates and turbulence. A turbulent
system can be responsible for either a good collection of fines but also for an increase in
detachment of particles from the bubble at larger particle sizes (Flint, 2001).
The impeller provides air to the flotation system producing bubbles at the bottom of
the cell, mixing the pulp, and avoiding particle sedimentation. It breaks the air bubbles
producing smaller bubbles offering an environment that permits the bubble-particle
collision within the slurry (Silva et al., 2018). Although it is a crucial parameter in
flotation, it also has a negative impact as it can generate excessive turbulence within the
cell. The turbulence of the pulp is strongly dependent on the impeller size and shape.
Lab experiments using different flotation cell geometries
32
Impellers are usually classified according to its mixing properties into axial, radial, or
mixed flow. Axial impellers are commonly applied in solids suspension and radial
impellers for dispersion of gas (Rushton turbine, for example). Generally, the impeller
design is associated with the flotation tank design. In industrial-scale flotation systems,
most impellers have a flat disc design associated with distinct blade shapes, commonly
adopting a half-spherical rotor design. These are generally installed as a rotor-stator
system, which is a high-speed rotor attached closely to a stator (which is fixed) allowing
the production of high shear rates and a turbulent system (Kauppila, 2019).
The following Equation 28 can be used to calculate the impeller tip speed, in which ω
is the impeller tip speed (m/s), D the is rotor diameter (m) and N is the rotation speed
(1/s) (Kauppila, 2019):
(27)
Additionally, the power input can be used for addressing the impact of the impeller
speed on flotation kinetics, independent from the shape of the impeller. Practically, an
improve in flotation can be observed when moving from lower power input to higher
power input. However, this could lead to an unstable flotation system as a result of
increasing turbulence. The following Equation 29 shows the relation between the rotor
power input (P, in W), the full mass of the fluid (m, in Kg), and the energy dissipation
rate (ε), which is a parameter that defines the real energy input to the slurry mass. An
increase in the impeller speed leads to an increase in the energy dissipation among the
flotation cell, increasing the bubble-particle probability of collision. This is advantageous
for finer particles, as these are less likely to attach to the air bubble due to its size
(Kauppila, 2019).
(28)
Lab experiments using different flotation cell geometries
33
The different mineral types and size distributions require specific hydrodynamic
conditions for flotation. This regulates the particles recovered and consequently, the
flotation rate of recovery. This highlights the importance of particle size analysis prior
and posterior to flotation. Usually, the flotation rate increases for finer particles and
decreases for coarser particles with an increase in the impeller speed. This can also be
associated with the energy input, as the flotation rate is more likely to improve for
particles in between the fines and coarse size range, with an increase in the energy input
(Kauppila, 2019).
There are 3 main zones associated to flow conditions in a flotation cell: the turbulent
zone, the quiescent zone, and the froth zone. The froth zone is responsible for the final
recovery achieved. Its recovery is directly connected to the energy input, as an increase
in the energy input leads to an unstable froth zone thus reporting a lower recovery
(Kauppila, 2019).
Another important variable is the Power number (Np), which is described as the ratio
among dissipated energy as shear and the energy applied for bulk flow production. As
an example, it can be improved through applying a lower cell aspect ratio, lower
impeller speed, and a larger impeller-stator arrangement leading to an increase in the
area with greater turbulence zone (Kauppila, 2019). This is presented in Equation 24.
According to Amini et al. (2016) in a laboratory-scale flotation cell (5 litres, for
example), increasing the impeller speed leads to a decrease in bubble size up to a critical
speed, in which the impeller speed will no longer be able to reduce the bubble size.
Consequently, an increase in the surface area of the bubble can be observed. This allows
a better bubble-particle collision probability, increasing the flotation rate. However, for
bigger cells (60 litres, for example), the same pattern might not be observed. In this case,
bubble size keeps constant independent from the impeller speed. This can be explained
by better contact between the bubble and particle due to the increase in turbulence.
Lab experiments using different flotation cell geometries
34
According to Horst (1952), at slower impeller speeds, there are less disruptive forces
within the cell, allowing particles to attach to the bubble, as the film formed around the
bubble is not as resistant to penetration by a moving particle.
When considering higher impeller speeds, more energy is expected to be placed in
the system, therefore, more bubbles should be produced. In the case of a constant
airflow rate, more bubbles are then expected to be present in the system with an increase
in the impeller speed, and the size of these bubbles are expected to be smaller. The
inferred bubble speed is expected to increase with an increase in the impeller speed.
Therefore, it becomes harder for smaller particles to attach with a bubble. This is
explained because the inertia of small particles is not enough for permitting them to
penetrate the film formed by the laminar flow of fluid around the bubble and to form a
particle-bubble aggregate. Smaller particles that attach to a bubble are, however, more
likely to reach the surface than coarse particles (Horst, 1952).
However, according to Zhang (1989), a high increase in the impeller speed can lead to
an environment with excessive turbulence, therefore, reducing the recovery of coarser
particles, due to entrainment of fine particles and detachment of coarser particles.
According to Rahman et al. (2012), the existence of fine particles is also vital for the
coarse particles to subsist in the froth. The presence of fine particles in the froth reduces
bubble coalescence, giving stability to the froth though preserving a higher bubble
surface area throughout the froth zone. On the other hand, coarser particles are more
likely to break the thin films leading to froth collapse and destabilization. The presence
of finer particles could, therefore, create a rigid and strong structure, preventing the
coarser particles to leave the froth.
Lab experiments using different flotation cell geometries
35
2.5 Flotation of silicates
Silicates are the most abundant minerals in the lithosphere. Its flotation is
considerably complex as it has six different classes according to its crystalline structure,
these are presented in Table 1. For each of these classes, a different collector is used in
flotation. Each group has a different chemical arrangement, containing silica (Si) and
oxygen (O). The difference between the structures allows the formation of different
minerals.
Table 1 Silicates major groups (adapted from Agapito Mendes et al., 2018).
Major group Structure Chemical formula Example
Nesosilicates isolated silicon tetrahedra [SiO4]4−
olivine
Sorosilicates double tetrahedra [Si2O7]6−
epidote, melilite group
Cyclosilicates rings [SinO3n]2n−
tourmaline group
Inosilicates single chain [SinO3n]2n−
pyroxene group
Inosilicates double chain [Si4nO11n]6n−
amphibole group
Phyllosilicates sheets [Si2nO5n]2n−
micas and clays
Tectosilicates 3D framework [AlxSiyO(2x+2y)]x−
quartz, feldspars, zeolites
2.5.1 Commonly used reagents
The main reagents used in the flotation of silicates are amines and carboxylic acids.
Amine is a cationic collector that binds with water to form products of substitution of
the ammonium hydroxide. It is a weak base that can be classified according to the
number of alkyl radicals into primary, secondary, or tertiary amines. The reactions are
based on the alkalinity, with protonation occurring in the acidic and moderately alkaline
pH range.
Fatty amines, such as coco amine, are the product of fatty acids ammonolysis. The
reaction produces primary amines with the chain length associated with the different
mixtures of compounds used. Amines usually function as a collector and a frother,
Lab experiments using different flotation cell geometries
36
therefore frothers are not very common in the flotation process of silicates (Agapito
Mendes et al., 2018).
Nesosilicates have the isoelectric point with the pH ranging from 4 to 8, meaning that
the amount of negative charges is equal to the number of positive charges. Minerals
from this group tend to float better using anionic collectors such as sodium oleate, as it is
insensitive to pH. It was observed through the analysis of zeta potential, infrared
spectroscopy, and micro flotation studies, that the adsorption of anionic collectors in
silicate minerals happen through chemisorption for a pH higher than the isoelectric
point, and through physisorption for a pH lower than the isoelectric point. Olivine has
the chemical formula of (Mg, Fe)2SiO4, and the isoelectric point at the pH of 4.1 (Chaves,
2006).
The flotation of olivine with an amine collector is very sensitive to the pH. The
surface is negatively charged if the pH is above the isoelectric point, and therefore, the
amine attaches to the mineral surface. Besides that, there is a concentration of hydrogen
ions within the liquid and an extra amount of metal cations on the surface of the
mineral. Therefore, there is an exchange of hydrogen ions to metal cations. If the
concentration of hydrogen is small, consequently, either the ammonium ions can
exchange with the metal cations at the surface or complexes of metal-amine can be
created (Deju and Bhappu, 1967).
When using a sulfonate collector, olivine tends to float well in acidic pulps. The
recovery increases as the pH decreases. When above the isoelectric point, the recovery
starts to decrease. Also, decreasing the collector increases the hydrogen adsorption,
meaning that, when the hydrogen adsorption is minimum, there is an excess of a
collector (Deju and Bhappu, 1967).
When using the collector Armac TD, olivine does not successfully float under the
isoelectric point because both the surface and the collector ion have the same charge,
Lab experiments using different flotation cell geometries
37
resulting in electrostatic repulsion. With an increase in the pH, the collector starts to
attach to the surface of the mineral (Deju and Bhappu, 1967).
Sodium oleate (NaOL) can also be used for olivine flotation. It is a fatty acid and a
typical anionic collector characterized as a weak acid with a carboxylic functional group,
that is known for being more reactive than selective (Fang et al., 2019).
Lab experiments using different flotation cell geometries
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Chapter 3
Materials and Methodology
In this study, the impeller speed is varied for different flotation cell sizes in order to
assess the influence of this parameter on the flotation rate, particle size, and recovery
when scaling-up. Experiments can be divided into two different parts: sample
preparation and flotation tests. The sample preparation involves materials handling,
grinding, splitting, and sieving.
In general, the methodology followed in this investigation is presented in Figure 16.
For preparing the samples, dry grinding was performed for 60 kg olivine to achieve a
<106 μm particle size fraction for further flotation tests. Two laboratory mills were set
up with previously defined conditions for these tests: A Rod mill and a Ball mill. Sieving
was done using an industrial-scale rotary splitter and a Jones riffle splitter. Flotation was
performed in the Outotec GTK LabCell®.
The flotation parameters were held as constant as possible and only the influence of
impeller speed was explored by its different levels (1200 rpm, 1300 rpm, 1400 rpm) for
different cell sizes (2 l, 4 l, and 7.5 l). These were selected according to previous literature
studies and the manual machine manufacturer recommendations.
The remaining flotation parameters were held as constant as possible. Based on the
literature, the solids percentage, the airflow rate, and pH were selected and set to
specific values. For the collector concentration, flotation tests were performed on a
smaller scale.
Lab experiments using different flotation cell geometries
39
Grinding Ball Mill
Sieving Rod Mill
< 106 µm
Constant % Solids 30%
Constant pH 10
Constant Air Flow Rate 3 l/min
Collector Armeen C Coco Amine
Collector Dosage 250 g/t
2 l
4 l
7.5 l
1200 rpm
1300 rpm
1400 rpm
45 mm
60 mm
75 mm
1 minute
3 minutes
5 minutes
7 minutes
Particle Size Analysis
Flotation Kinetics (k)
Recovery
Initial
Sample
Sample
Preparation
Impeller Speeds
Rotor Diameters
Volume of Cells
Flotation
Conditions and
Flotation Tests
Froth Collection Time
Figure 16 Schematic of the methodology.
3.1 Flotation equipment
Outotec GTK LabCell® is a mechanical laboratory-scale batch flotation equipment.
For the purpose of this work, the cells used were 2-, 4- and 7.5 l using the 45-, 60-, and 75
mm rotor diameters with its respective impellers and scrapers. The manufacturer
recommended machine parameters for the different scales are presented in Table 2.
Table 2 Manufacturer recommended machine parameters for the different scales (extracted from Outotec, 2018).
Cell size (l) Rotor Diameter (mm) Rotor speed (rpm) Air flow rate (l/min)
2 45 1300 2
4 45 1800 3
7.5 60 1200 4
12 75 1450 6
Lab experiments using different flotation cell geometries
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This flotation machine is comparable to other Outotec industrial scale flotation
equipment, in terms of the design of its rotors and impellers, varying mostly in terms of
scale. The machine provides gas dispersion and addition of water for slurry suspension,
associated with adjustment of airflow rate and impeller speed. The main difference in its
froth recovery mechanism, which automatically scraps the froth (Kauppila, 2019).
Therefore, the level of slurry requires precise control to guarantee an adequate and
uniform froth recovery. Generally, this control must be manually done by adding water
to the slurry, visually, to ensure the slurry is controlled and not overflowing from the
cell. Furthermore, as the flotation test is carried on, the solid content within the slurry is
reduced due to concentrate recovery. There is no addition of feed material in the
process.
The general design of the flotation machine can be seen in Figure 17, while the cells,
rotors, and impellers used are presented in Figure 18, the respective dimensions of each
cell are presented on Figure 19.
Figure 17 Outotec GTK LabCell® flotation machine (extracted from Mattsson et al., 2019).
Lab experiments using different flotation cell geometries
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Figure 18 Outotec GTK LabCell® cells, rotor, and impellers used in this investigation.
Figure 19. Outotec GTK LabCell® cells dimensions for the cells used in this investigation.
3.2 Sampling and sample preparation
3.2.1 Grinding and Sieving
A sample of olivine with a total weight of 60 kg was initially split in an industrial-
scale rotary splitter into 20 fractions to ensure the representativeness of the sample.
Afterward, different fractions were combined for having 8 kg of samples. These were
sent to the initial step in the Rod mill and then ground by a Ball mill (Table 3).
Lab experiments using different flotation cell geometries
42
Table 3. Grinding parameters for the Ball mill and Rod mill.
Rod Mill Ball Mill
Ø300x450 mm Ø300x300 mm
Charge Rods ca. 46 kg Balls ca. 46 kg
6 x Ø45 mm 29.7 kg Ø22 mm
6 x Ø35 mm 12.6 kg Ø16 mm
6 x Ø25 mm 3.7 kg Ø12 mm
Charge volume 25% 45%
Grinding bodies
Dimensions
For the first round, the grinding times were settled as 40 minutes for each mill. The
procedure was to start with the Rod mill in a round of 40 minutes, then move the
material to the Ball mill for another 40 minutes, meaning that the feed for the Ball mill is
the material obtained from the Rod mill. The final product was extracted from the Ball
mill using a coarse wire-mesh screen. Approximately 500 g was extracted using a riffle
splitter for a sieving analysis of the product-samples.
The sieving performed for Particle Size Distribution (PSD) analysis was carried for 10
minutes each, and the equipment used was the WS Tyler® RO-TAP® RX-29-10 Sieve
Shaker 230v/50 Hz, for all dry sieving. The results of the initial sample PSD analysis are
given in the following Figure 20, in which a total of 10 sieves (1680 µm, 1180 µm, 841 µm,
595 µm, 425 µm, 300 µm, 212 µm, 149 µm, 106 µm, 75 µm, and < 75 µm, in which the top-
cut size was 1680 µm) were used for this purpose. For further sieving, the sieves 53 µm
and 38 µm were also included. The material fraction with particle size below 106 µm
were extracted and merged from the whole using manual sieving.
Lab experiments using different flotation cell geometries
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Figure 20. Particle Size Distribution for the initial sample and flotation feed.
3.2.2 Flotation reagents
For selecting the optimum collector concentration, five flotation tests were performed
in a smaller scale batch flotation device, using the same parameters pre-settled, in order
to assess the flotation response using Armeen C Coco amine (a cationic collector). The
flotation device was had 200 ml volume, the sample size for each test was 23g, therefore,
the percentage of solids for these tests was 10%.
The concentrations assessed were 100-, 150-, 200-, 250-, and 300 g/t, and their
respective recoveries after 7 minutes of flotation are presented in the following Table 4.
Based on that, the concentration of 250 g/t of Armeen C was selected for further
flotation tests. No further reagents were used for the flotation tests.
Table 4. Recoveries for the different concentrations tested using Armeen C as a collector.
Concentration (g/t) 100 150 200 250 300
Recovery (%) 2% 10% 20% 90% 79%
Lab experiments using different flotation cell geometries
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3.3 Flotation tests
After grinding the material to the required particle size (< 106 µm), the material was
split using a Jones riffle splitter into the required sample size for each cell, considering
that three samples are required for each cell. These are approximate: 995 g for the 2 l cell,
1990 g for the 4 l cell, and 3732 g for the 7.5 l cell. The percentage of solids in the slurry
was estimated at 30%, for the constant pH of 10 and the airflow rate of 3 l/min
As the material being floated is considered as a pure mineral (olivine), the objective of
these laboratory flotation tests was to understand the influence of the impeller speed on
the performance of scaling-up a flotation cell in laboratory scale. First, the collector was
added to the slurry to be conditioned. No frothers were used, as Armeen C has the
properties of a collector and frother. The slurry was then conditioned for 5 minutes in
the flotation cell, using the same impeller speed being investigated at each cycle.
The scraping cycle was settled as 1.0 second for all tests. The concentrate reported to
the froth was collected at 1-, 3-, 5- and 7 minutes. 7 minutes being the total flotation froth
collecting time. At the end of the flotation process, the samples together with the
remaining material reported to the tailings were collected in different containers,
weighted and left overnight to dry in a temperature of 110° C. After drying, the
concentrates were stored and packed in plastic bags for further PSD analysis and
weighted for further calculations on solids and water recovery.
Lab experiments using different flotation cell geometries
45
Chapter 4
Results
In this study, the main aim is to understand the scale-up criteria for the different cells
by assessing the influence of impeller speed on flotation performance. The effect of this
variable on the flotation response has been discussed on how it can be related to the
scale-up process on a laboratory scale.
4.1 Recovery assessments
The cumulative recoveries achieved by the different cells for the different impeller
speeds testes are presented in Figure 21. It can be observed that the lowest recoveries are
exhibited by the 4 litre cell, being 47.6%, 46.2%, and 44.3% the cumulative recoveries for
the impeller speeds of 1200, 1300, and 1400 rpm, respectively. The 7.5 litre cell presented
the highest cumulative recoveries of 56.6%, 73%, and 60.1% for the impeller speeds of
1200, 1300, and 1400 rpm, respectively. The 2 litre cell presented a similar progression
when compared to the 7.5 litre cell, having its highest recovery at the impeller speed of
1300 rpm. Although, in general, the cumulative recovery after 7 minutes of flotation was
substantially lower for the 2 litre cell when compared with the 7.5 litre cell. For the 2 litre
cell, the cumulative recoveries were 48.9%, 56.7%, and 50.3% for the impeller speeds of
1200, 1300, and 1400 rpm, respectively.
The time-recovery curve is a typical method of comparing the results regarding the
different cells. It gives a fast and clear image of the recovery as a function of time.
Therefore, Figure 22 shows the progression on the cumulative recovery over 1-, 3-, 5-
and 7 minutes of flotation for the impeller speeds investigated for the 2-, 4- and 7.5 l
cells.
Lab experiments using different flotation cell geometries
46
Figure 21 Cumulative recovery reached by the different cells at each impeller speed after 7 minutes of flotation.
Figure 22. Cumulative recovery over time for the 2-, 4- and 7.5 l cells.
Lab experiments using different flotation cell geometries
47
For the 2 litre cell, similar progress can be observed at the beginning of flotation for
the impeller speeds of 1300 and 1400 rpm. The cumulative recoveries for these impeller
speeds were considerably higher for the first 3 minutes of flotation (43% each). On the
other hand, for the impeller speed of 1200 rpm, the cumulative recovery for the first 3
minutes was lower (33%). Afterward, the recovery associated with the impeller speed of
1400 rpm decreased, while for 1300 rpm, it continuously increased. At 7 minutes of
flotation, for the impeller speed of 1300 rpm, the highest cumulative recovery was
obtained for this cell (56.7%).
For the 4 litre cell, the recovery was slightly higher during the first minute of flotation
for the impeller speed of 1400 rpm, afterward decreasing and reaching the lowest
cumulative recovery among the different impeller speeds for this cell (44.3%). The
cumulative recoveries associated with the impeller speeds of 1200 and 1300 rpm
presented similar results through the progress of flotation. Overall, the cumulative
recoveries presented by this cell over all impeller speeds tested did not present a
significant variation over time.
For the 7.5 litre cell, the highest cumulative recoveries among the different cells were
observed after 7 minutes of flotation for all impeller speeds tested. For the impeller
speed of 1400 rpm, the lowest cumulative recovery was observed for the first 3 minutes
of flotation (32%), and after 5 minutes, reaching a similar recovery as for the impeller
speed of 1200 rpm (46% for 1200 rpm and 47% for 1400 rpm), however, increasing
afterward though the course of flotation, reaching a cumulative recovery of 60.1% at 7
minutes, while for impeller speed of 1200 rpm the cumulative recovery at 7 minutes was
56.6%. For the impeller speed of 1300 rpm, the cumulative recovery was the highest
through the course of flotation for this cell.
Figure 23 illustrates the non-cumulative recovery regardless of the impeller speeds
investigated after 1-, 3-, 5- and 7 minutes for the 2-, 4- and 7.5 litres cells. For the first
Lab experiments using different flotation cell geometries
48
minute of flotation, the 7.5 litre cell presented the highest recovery (with an average of
20%), and the 2 litre cell presented a higher recovery (with an average of 16%) when
compared to the 4 litre cell (with an average of 9%). The average recovery after 3
minutes for the 2-, 4- and 7.5 litres cells are 23, 18, and 17%, respectively. The 2 litre cell
presented a higher recovery for the impeller speeds of 1300 and 1400 rpm (27%, and
26%, respectively), while for the 7.5 litre cell the recoveries reported for the impeller
speeds of 1300 rpm and 1400 rpm were lower (20% and 15%, respectively). However,
after 5 minutes, the average recoveries decreased. The average recovery associated with
the 2 litre cell decreased to an average of 9%, while for the 4 litre cell it was 13%. At 7
minutes of flotation, the average recovery associated with the 2 and 4 litre cells was 3%
and 7%, respectively, while for the 7.5 litre cell the average recovery was 13% at 7
minutes.
Figure 23. Non-cumulative recovery over time for the 2-, 4- and 7.5 l cells.
Lab experiments using different flotation cell geometries
49
Figure 24 illustrates the cumulative water recoveries associated with the different
cells and impeller speeds after 7 minutes of flotation. It can be observed that for the
impeller speed of 1200 rpm, the lowest water recovery was observed for the 2 litres cell.
In general, the differences between the cumulative water recoveries for the different cells
were not significant. Therefore, the non-cumulative water recovery associated with the
flotation progress was also considered, in order to understand the relationship it has
with the performance of each cell.
Figure 24 Cumulative water recovery for the different impeller speeds after 7 minutes of flotation.
Considering the non-cumulative water recovery over time (Figure 25), it can be
observed that the 2 litre cell presented its highest water recovery during the first minute
of flotation for all impeller speeds investigated, with an average of 25 %, while for the 4
and 7.5 litres cells, the average was 17% and 21% at the same time, respectively. After 3
minutes of flotation, the water recoveries associated with the 2 and 4 litres cells
increased to an average of 31% and 32%, respectively. Afterward, water recoveries
decreased for all cells. After 7 minutes, the 7.5 litre cell presented the highest water
recovery, with an average of 22%. For the 2 and 4 litres cells, the water recoveries were
the lowest, with an average of 7% and 11%.
Lab experiments using different flotation cell geometries
50
Figure 25. Non-cumulative water recovery over time for the 2-, 4- and 7.5 l cells.
4.2 Kinetic assessments
The mechanisms governing flotation in the system assessed in this work are not
completely known. Therefore, in order to calculate the kinetic flotation rate for each of
the tests conducted, the results of the flotation tests at different conditions were
associated with different kinetic models using linear regression.
According to Horst (1952), the best way of finding the reaction order is to apply
different equations for determining the one with the best fit to describe the reaction.
Therefore, in order to evaluate the flotation rate from the experimental results, Equation
5 and Equation 7 were used. Equation 5 is addressed as the first-order model equation,
while Equation 7 is the second-order kinetic model.
For that, each equation was rearranged isolating ‘kt’. Equation 5 and Equation 7 were
rearranged as Equation 30 and Equation 31, respectively. Afterward, the ‘A’ term of each
Lab experiments using different flotation cell geometries
51
equation was plotted versus the flotation time. Based on these equations, the linear
regression was obtained, and the flotation rate constant ‘k’ was determined as the slope
of the resulting linear regression.
(29)
(30)
The predicted recovery using each equation was calculated based on the ‘k’ obtained
through the linear regression. The detailed results from these calculations are presented
in Appendix 1 and Appendix 2. The linear regressions for each cell at the different
impeller speeds, using the first-order model and the second-order model are
respectively presented in Appendix 3 and Appendix 4.
The respective flotation rate (k) for the 2-, 4- and 7.5 l cells, with its respective R2 for
the two rate model equations, are presented in Table 5. Both models presented a good fit
to the experimental results. Therefore, the first-order rate model was selected for
assessing the flotation rate.
Table 5 Kinetics parameters obtained from two different kinetics models for the 2-, 4-, and 7.5 l cells at the
impeller speeds of 1200 rpm, 1300 rpm, and 1400 rpm.
Impeller Speed
Cell k (min⁻¹) R² k (min⁻¹) R² k (min⁻¹) R²
2 liters 0.08 0.98 0.11 0.89 0.08 0.81
4 liters 0.10 0.98 0.09 0.98 0.08 0.99
7.5 liters 0.10 1.00 0.17 0.99 0.12 0.99
Impeller Speed
Cell k (min⁻¹) R² k (min⁻¹) R² k (min⁻¹) R²
2 liters 0.13 1.00 0.19 0.93 0.13 0.84
4 liters 0.14 0.99 0.13 0.99 0.12 1.00
7.5 liters 0.18 0.99 0.39 0.93 0.22 0.96
Classical first-order model
1200 rpm 1300 rpm 1400 rpm
Second-order kinetic model
1200 rpm 1300 rpm 1400 rpm
Lab experiments using different flotation cell geometries
52
The results revealed a higher flotation rate constant in the 7.5 litre cell for all impeller
speeds (0.1, 0.17, 0.12 for the impeller speeds of 1200-, 1300-, and 1400 rpm). This cell is
also associated with the highest recoveries. For the impeller speed of 1200 rpm, the
lowest flotation rate constant is attributed to the 2 litre cell (0.08), while for the impeller
speeds of 1300 rpm and 1400 rpm, the lowest flotation rate constant is associated to the 4
litre cell (0.09 and 0.08, respectively).
For the 2 litre cell, it is possible to observe an increase in flotation rate for the impeller
speed of 1300 rpm when compared to the impeller speed of 1200 rpm and 1400 rpm. The
same progress is observed for the 7.5 litre cell. For the 4 litre cell, the flotation rate did
not present a significant increase or decrease for the different impeller speeds.
4.3 Effect of Cell Size
The dimensions of the cells used in this study are not systematic. The cell height to
area ratio is the same for the 2 and 7.5 l cells (0.05), therefore, flotation is expected to
present the same progress for these cells (Table 6). The 4 l cell has a higher ratio of 0.06.
This increases the distance that the particles must travel to where the froth is collected,
at the top of the cell. The cell area to rotor diameter ratio deviates for the different cells.
The 4 l cell presents the lower ratio, followed by the 2 l and 7.5 l cells.
Table 6 Ratios among the different cells.
2 l 4 l 7.5 l
0.05 0.06 0.05
5.3 5.1 5.6
Cell Height / Cell Area
Cell Area / Rotor Diameter
Ratios
Cell
Table 7 and Table 8 presents the recovery and flotation rate indexes for the different
cells and impeller speeds. Based on that, it is possible to observe that by increasing the
cell area to rotor diameter ratio, the flotation rate constant and recovery also increases
for these cases.
Lab experiments using different flotation cell geometries
53
Table 7 Flotation rate (k) index for the scale-up between different cells and impeller speeds.
Impeller speed 1200 rpm 1300 rpm 1400 rpm
k Cell 4 L / K Cell 2 L 1.15 0.80 0.99
k Cell 7.5 L / K Cell 4 L 1.08 1.97 1.48
k Cell 7.5 L / K Cell 2 L 1.25 1.57 1.47
Table 8 Recovery (R) index for the scale-up between different cells and impeller speeds.
Impeller speed 1200 rpm 1300 rpm 1400 rpm
R Cell 4 L / R Cell 2 L 0.97 0.81 0.88
R Cell 7.5 L / R Cell 4 L 1.19 1.58 1.36
R Cell 7.5 L / R Cell 2 L 1.16 1.29 1.19
4.4 Effect of Particle Size Distribution
Table 9 shows the d80 of the product for the different cells and impeller speeds
addressed in this work. In general, for the 7.5 litre cell, the particle size increased with an
increase in the impeller speed, while for the 4 litre cell, the particle size decreased for the
impeller speed of 1300 rpm and increased for the impeller speed of 1400 rpm. For the 2
litre cell, the particle size decreased with an increase in the impeller speed.
Table 9 d80 for the 2-, 4-, and 7.5 litres cells at the impeller speed of 1200 rpm, 1300 rpm, and 1400 rpm.
Impeller speed Cell 2l Cell 4l Cell 7.5 l
1200 rpm 88 90 75
1300 rpm 81 80 88
1400 rpm 82 87 87
d 80
When increasing the cell size from the 2 litre cell to the 4 litre cell, the d80 ratio for the
different impeller speeds did not present a large variation (Table 10). Therefore, the
particle size among these cells, if considering only the d80, did not present a significant
change when increasing the cell size. The same is observed when increasing the cell size
from the 2 and 4 litres cell to the 7.5 litre cell for the impeller speeds of 1300 rpm and
1400 rpm. For the impeller speed of 1200 rpm, the d80 ratio was slightly lower, meaning
the particle size among these cells presented the highest variation regarding the d80.
Lab experiments using different flotation cell geometries
54
Table 10 d80 ratios when increasing the cell size.
Impeller Speed
d80 (4 L) / d80 (2 L)
d80 (7.5 L) / d80 (2 L)
d80 (7.5 L) / d80 (4 L)
0.85 1.09 1.06
0.83 1.10 1.00
1200 rpm 1300 rpm 1400 rpm
1.02 0.99 1.06
To distinguish the different particle sizes in the following sections, the fraction
between 106 µm and 75 µm is addressed as the coarse particle size fraction. For
addressing the fine particle size, only the fraction below 38 µm is considered. The
remaining fractions are addressed as medium size particles (-75µm + 38µm).
Figure 26 shows the particle size distribution for the 2 litre cell at the different
impeller speeds. Based on that, it is possible to observe the effect of a higher impeller
speed regarding the particle size distribution. For the impeller speed of 1400 rpm, the
presence of finer particles (-38 µm) is higher when compared to the impeller speeds of
1200 rpm and 1300 rpm.
The 4 litre cell did not present similar results when going from the impeller speeds of
1200 rpm and 1300 rpm to 1400 rpm. The results from this cell show that for the impeller
speed of 1400 rpm, there is a higher concentration of coarse particles, whereas, for the
impeller speeds of 1200 rpm and 1300 rpm, the variations in particle size are not
considered high, presenting a slightly higher concentration of coarse and medium size
particles (
Figure 27).
For the 7.5 litre cell, in general, a similar pattern in terms of particle size distribution
is observed for all impeller speeds (
Figure 28). However, when considering the size-by-size distribution at each flotation
time, many discrepancies are observed among the different impeller speeds and cell
sizes.
Lab experiments using different flotation cell geometries
55
Figure 26 Particle size distribution of the flotation product for the 2 litre cell according to the different impeller
speeds.
Figure 27 Particle size distribution of the flotation product for the 4 litre cell according to the different impeller
speeds.
Lab experiments using different flotation cell geometries
56
Figure 28 Particle size distribution of the flotation product for the 7.5 litre cell according to the different
impeller speeds.
The experimentally determined variation of the flotation rate constant as a function of
particle size for the different impeller speeds is presented in Table 11. For the
determination of the flotation rate constant, the first order kinetic model was applied
according to Equation 5, in which the cumulative recovery of solids after 1, 3, 5 and 7
minutes was obtained for each size fraction. The detailed calculated values are presented
on the Appendix 5 and Appendix 6. Based on the rearranged Equation 30, the graphic
representations presented in Appendix 7 were obtained, in which the slope of each
curve is a measure of the flotation rate for the size fractions of: -38 µm, +38 -75 µm, and
+75 µm. These size fractions will be addressed as coarse (+75 µm), fines (-38 µm) and
medium size (+38 -75 µm) particles.
Table 11 Kinetics parameters as a function of particle size for the different cells and impeller speeds.
Impeller Speed ( RPM )
Particle Size ( µm ) < 38 + 38 - 75 > 75 < 38 + 38 - 75 > 75 < 38 + 38 - 75 > 75
Cell 2 L 0.32 0.05 0.16 0.07 0.06 0.44 0.35 0.06 0.08
Cell 4 L 0.31 0.07 0.12 0.38 0.06 0.13 0.08 0.05 0.19
Cell 7.5 L 0.36 0.07 0.15 0.29 0.09 0.43 0.42 0.08 0.24
Impeller Speed ( RPM )
Particle Size ( µm ) < 38 + 38 - 75 > 75 < 38 + 38 - 75 > 75 < 38 + 38 - 75 > 75
Cell 2 L 0.90 0.94 0.94 0.69 0.86 0.97 0.92 0.81 0.80
Cell 4 L 0.94 0.97 0.89 0.95 0.97 0.97 0.94 0.99 1.00
Cell 7.5 L 0.99 0.98 0.90 0.81 0.99 0.99 0.85 1.00 0.98
Flotation rate constant (k)
1200 1300 1400
R ²
1200 1300 1400
Lab experiments using different flotation cell geometries
57
Based on that, it is possible to observe that at the lowest impeller speed of 1200 rpm,
the flotation rate constant is higher for the particle size of -38 µm, followed by +75 µm
and +38 -75 µm. For this impeller speed, the 2 litre cell presented a higher number of fine
particles for the first minute of flotation, then reporting a larger number of coarse
particles and medium-size particles through the course of flotation. For the 4 litre cell,
the particles larger than 53 µm have a higher concentration for the first 3 minutes of
flotation. After that, a considerably high number of fine particles is observed until 7
minutes of flotation. The 7.5 litre cell presented a considerably high number of coarse
particles only for the first minute of flotation, followed by slightly equal particle size
distribution recovered at 3 minutes of flotation. After 5 minutes, a higher number of
medium size and coarse particles is observed.
At an increased impeller speed of 1300 rpm, the flotation rate constant increases for
the particle size of +75 µm for the 2 litre cell. For this cell, a higher number of coarse
particles and medium size particles are present through all the course of flotation. The
7.5 litre cell also presented its highest rate for the particle size of +75 µm, although also
having a higher rate for the -38 µm size fraction. This cell also presented a higher
concentration of coarse particles through all the course of flotation, except at 7 minutes,
in which the particle sizes are more equally recovered. For the 4 litre cell the highest rate
was observed for the particle size of -38 µm. For this cell, more fines were recovered
during the first minute of flotation, and afterward, coarser and medium-size particles
were recovered. Overall, the lowest flotation rates observed for the impeller speed of
1300 rpm are for the particle size of +38 -75 µm in all cases.
When the impeller speed is further increased to 1400 rpm, the flotation rate constant
increases for small particle sizes for both the 2 and 7.5 litre cells. For the 4 litre cell, the
flotation rate constant increased with particle size, therefore, bubble-particle stability
apparently becomes more important. In general, for all the cells, a slightly equal size
Lab experiments using different flotation cell geometries
58
distribution was presented over the course of flotation, except that the 2 litre cell that
presented a higher recovery of fine particles.
4.5 Effect of impeller speed
From the experimental results regarding the effect of impeller speed on the recovery,
Figure 29 shows that, in general, the impeller speed of 1300 rpm presented the highest
variations in the overall recovery between the different cells. The lowest recoveries, in
general, were observed at the impeller speeds of 1200 rpm and 1400 rpm.
Figure 29 Cumulative recovery for the impeller speeds of 1200-, 1300-, and 1400 rpm.
Considering the non-cumulative recoveries for the different impeller speeds, it is
possible to see that for the impeller speed of 1200 rpm, after the first minute of flotation,
the highest variation in flotation recovery is observed (Figure 30), with an average of
14%. After 3 minutes, the variations in recovery were relatively low for all the cells.
For the impeller speed of 1300 rpm, a large variation in recovery was observed after
the first minute of flotation, with an average of 14%, which is related to the low recovery
associated with the 4 litre cell when compared to the other cells. After 5 minutes, the
average recovery decreased to an average of 11% and 8% after 7 minutes, presenting a
Lab experiments using different flotation cell geometries
59
high variation as the recovery associated with the 7.5 litre cell was considerably higher
at this time (15%).
For the impeller speed of 1400 rpm, the recovery did not present a high variation on
its average value for the first 5 minutes of flotation (with an average ranging from 12%
to 18%). After 7 minutes, the average recovery decreased to 7%.
Figure 30 Recovery for the different impeller speeds after 1, 3, 5, and 7 minutes.
Lab experiments using different flotation cell geometries
60
Chapter 5
Discussions and Conclusions
5.1 Effect of Cell Size
The geometrical aspect of different cells can affect the hydrodynamic conditions of the
flotation system. It can alter the rising speed of bubbles and transport distance of the
floatable material. A large cell height to area ratio locates the impeller and the mixing zone
further away from the top of the cell and consequently reduces the turbulence in the
upper part of the cell. A low cell height to area ratio reduces the turbulence around the cell
walls and consequently lead to a higher risk of solids sedimentation in these areas (Boeree,
2014). A change in the impeller size and design also affects the flow and turbulence in the
flotation cell (Shen et al., 2019).
The effect of cell size on the flotation kinetics and recovery was investigated by altering
the impeller speed and rotor diameter on different laboratory-scale cells. As presented in
Table 6 Ratios among the different cells. the dimensions of the cells are not systematic. The cell
height to area ratio is the same for the 2 and 7.5 l cells, therefore, flotation is expected to
present the same progress for these cells, although the 2 l cell presented a lower
cumulative recovery in comparison to the 7.5 l cell, both cells presented a similar trend.
The cell area to rotor diameter ratio also deviates for the different cells. As the cell area
to rotor diameter ratio increases, the recovery also tends to increase. A higher ratio made
the turbulence conditions more appropriate for the 7.5 l cell. Therefore, the size of the
turbulence zone seems to play an important role as it is expected to increase as the rotor
size increases.
Lab experiments using different flotation cell geometries
61
The kinetic study was also developed to have a better understanding of the effect of
these variables on the flotation rate. Based on that, both the 2 and 4 l cells presented lower
flotation rates for the impeller speeds of 1300 rpm and 1400 rpm when compared to the 7.5
l cell. Therefore, increasing the cell area to rotor diameter ratio increases the flotation rate
constant for these cases. By keeping a constant impeller speed of 1200 rpm, a successful
scale-up is achieved based on the recovery and flotation rate constants when increasing
the size of the cells. Effective scale-up results were also observed when increasing the cell
size from 2 l to 4 l for all the impeller speeds tested.
According to Mattsson et al. (2019), a decrease in the flotation rate is expected for this
equipment as the cell size increases. However, this is highly dependent on the rotor
diameter, as for a high rotor diameter to the cell diameter ratio, the flotation rate constant
tends to increase.
The laboratory cell size and rotor diameter together with the operating conditions have
a significant effect not only on the flotation rate constant but also on the recovery. Based
on that, the impeller speed should be carefully selected once it appears to have an impact,
not only on the flotation rate constants but also on the achievable recoveries. The
following section will address the effect of this variable on the flotation performance.
5.2 Effect of impeller speed
An extensive variety of commercial laboratory flotation machine designs are available
nowadays. Mechanical cells contain an impeller to create a region with high turbulence
aiming to maintain the particles in suspension, to provide bubble-particle collision, and to
produce and disperse the bubbles (Wang et al., 2015). Accordingly, the gas dispersion
conditions in the cell are altered. According to Newell and Grano (2006), both the recovery
and flotation kinetics, in general, increases with an increase in the impeller speed, as an
increase in turbulence increases the number of particle-bubble collisions. However, at high
Lab experiments using different flotation cell geometries
62
impeller speeds, turbulence is too high, therefore, a plateau and eventual decrease in
recovery and flotation rate may be possible. This is associated with an increase in
detachment of coarse particles and instability in the froth zone.
To evaluate the effect of impeller speed on the flotation performance for the different
cells in the Outotec-GTK LabCell, the impeller speed was set at three levels, corresponding
to 1200 rpm, 1300 rpm, and 1400 rpm.
The metallurgical responses show an increase in the flotation rate and recovery as the
impeller speed increased from 1200 rpm to 1300 rpm for the 2 l and 7.5 l cells. A further
increase in the impeller speed to 1400 rpm decreased both the recovery and flotation rates
for these cells. Differently, for the 4 l cell, the highest recovery and flotation rate was
observed at the impeller speed of 1200 rpm, then a decrease in both recovery and flotation
rate was observed associated with an increase in the impeller speed.
In general, the flotation rate and recovery increased with an increase in the impeller
speed until a certain point that it eventually decreased for the 2 l and 7.5 l cells. For the 4 l
cell, the flotation rate and recovery decreased with increasing the impeller speed. From
the dimension ratios presented in Table 6, the 4 l cell had the lowest cell area to rotor
diameter ratio and the highest cell height to area ratio, which affected the turbulence
conditions and consequently, the recovery and flotation kinetics.
The recovery of mineral particles through entrainment is also affected by the impeller
speed. A turbulent regime in a mechanical flotation cell can produce a modification in the
suspension of solids and the pulp density in the section under the pulp-froth interface,
destabilizing the lower zones of the froth and affecting the overall flotation performance
(Mesa and Brito-Parada, 2019b). According to Akdemir and Sönmez (2003), an increase in
the impeller speed can lead to an increase in recovery through entrainment. This can also
be associated with an increase in water recovery, as more minerals are entrained to the
concentrate.
Lab experiments using different flotation cell geometries
63
The water recovery is an important variable to consider. It is the amount of water
recovered within the concentrate. It can influence the recirculating load, entrainment of
particles, and residence times. The water flow is commonly recognized as responsible for
particle transportation via entrainment (Flint, 2001).
The recovery associated with the 4 l cell for the first minute of flotation was
considerably low when compared with the 2 and 7.5 l cells, for all impeller speeds. The
same was observed for water recovery. According to Mattsson et al. (2019), the control of
the froth level and the water addition during flotation can influence in flotation behaviour
for this equipment. Therefore, the low recovery associated with the 4 l cell in the first
minute could also be associated with the manual addition of water for keeping the froth
level up and it could have influenced the flotation performance for this cell.
The 2 and 7.5 l cells presented a considerably high water recovery for the first 3
minutes and after 5 minutes of flotation, respectively. By increasing the amount of water, a
higher quantity of solids is suspended into the froth phase, which can lead to entrainment
of solids being recovered in the concentrate (Wang et al., 2015). Entrainment is mostly
affected by the particle size, as finer particles can easily flow upwards due to its lower
gravitational forces (Boeree, 2014). Therefore, the influences of the particle size
distribution will be addressed in the following section.
5.3 Effect of Particle Size Distribution
The 2 l cell at the impeller speed of 1400 rpm reported more fine particles (-38 µm) than
for the impeller speeds of 1200 rpm and 1300 rpm. Considering that the impeller speed of
1400 rpm was the highest speed tested, the results for the 2 l cell suggests it could have a
relation with the excessively turbulent environment for this cell at the impeller speed of
1400 rpm. A high increase in the impeller speed can lead to an environment with excessive
Lab experiments using different flotation cell geometries
64
turbulence, therefore, reducing the recovery of coarser particles, due to entrainment of
fine particles and detachment of coarser particles.
The low recoveries associated with the 4 l cell could somehow be related to an unstable
froth as the impeller speed required for this cell is expected to be lower than those tested
in this study. In general, the 4 l cell did not present a considerable number of fine particles
on its concentrate, except for the impeller speeds of 1200 rpm and 1300 rpm, in which a
higher recovery of fine particles was reported after 7 minutes and at the first minute of
flotation, respectively. For these impeller speeds, the 4 l cell had its highest recoveries.
Coarser particles are more likely to break the thin films leading to froth collapse and
destabilization. The presence of fine particles in the froth reduces bubble coalescence,
giving stability to the froth though preserving a higher bubble surface area throughout the
froth zone, creating a rigid and strong structure, preventing the coarser particles to leave
the froth. Hence, the presence of fine particles could have enhanced the froth stability for
these impeller speeds, which affected the cumulative recovery for the 4 litre cell.
The 7.5 l cell, in general, did not report a significant recovery of fine particles (-38 µm)
for all impeller speeds, presenting a slightly higher concentration of coarse and medium
size particles. However, the d80 of this cell seemed to increase with an increase in the
impeller speed.
Based on the differences that have been identified between the different cells. One of
the main differences was found in the behaviour of fine particles. The products
concentrate seem to become finer when decreasing the cell size, with only a few
exceptions. The recovery of particles larger than 38 μm was found to differ considerably
less among the different scales. According to Boeree (2014), larger cells can present to have
zones of fine particle segregation below the froth phase. Based on that, the recovery and
flotation kinetics of fine particles should be better for the smaller cells.
Lab experiments using different flotation cell geometries
65
Another possibility would be a better recovery of fine particles in the 2 l cell when at
the impeller speed of 1400 rpm, but the time-recovery figures showed that the final
recovery is better in the 7.5 l cell. This also indicates the flotation performance. If it was the
case of equal flotation performance, the concentrates should present similar particle size
distributions curves, once the feed material is the same.
The flotation rate constants for each particle size presented on Table 11 indicates that
the flotation rate is, in general, higher for both the finer (-38 µm) and coarser fractions (+75
µm). This relationship was observed for all the cells at the impeller speed of 1200 rpm. At
a higher impeller speed, the different cells presented a different behaviour. According to
Newell (2006), the stability efficiency can influence in the process for the different particle
sizes and impeller speeds, therefore, for coarser particles, particle detachment can be
significant.
At a higher impeller speed, it is expected that more bubbles are produced, once the air
flow rate is constant. Also, the bubbles are expected to be smaller. The particles speed
increases with an increase in the impeller speed and it becomes harder for the finer
particles to attach to the bubble. The inertia of finer particles is sometimes insufficient to
allow the particles to penetrate the film formed by the laminar flow of fluid around the
bubble to form a bubble-particle aggregate.
The flotation rate is expected to increase with an increase in particle size. However,
according to the experimental results, the flotation rate decreases when increasing the
particle size from –38 µm to +38 –75 µm for the different impeller speeds and remained
slightly constant for the particle fraction of +38 –75 µm when considering the different cell
sizes.
At the impeller speed of 1200 rpm, the flotation rate presented the same trend of results
for the different cells, reaching its highest values for the particles size fraction of -38 µm,
followed by a decrease for the particle size fraction of +38 –75 µm and slightly increasing
Lab experiments using different flotation cell geometries
66
for the particle size fraction of +75 µm. At a slower impeller speed, the disruptive forces
within the cell are lower, and the film formed by the laminar flow does not offer a very
high resistance to penetration by a moving particle. The inertia of the particles is also
insufficient for providing the bubble-particle attachment. Therefore, the finer particles that
attach to the bubble are more like to reach the surface when compared to the coarser
particles, which explains the fact that at a lower impeller speed, the flotation rate is
expected to remain fairly constant or decrease as the particle size increases as indicated by
the results.
The decrease in the flotation rate was also observed at a higher impeller speed of 1400
rpm. For the 2 litre and 7.5 litre cells, the flotation rate decreased as particle size increased
when considering the particle size fraction of –38 µm and +75 µm. The probability of
bubble-particle attachment increases with an increase in the particle size as before, but the
probability of the bubble-particle aggregate reaching the surface decreases. This could be
due the fact that the disruptive forces increase with an increase in the impeller speed.
Although the inertia of the particles increases with an increase in the impeller speed, the
disruptive forces overcome this, as it is harder for a large particle to remain attached to a
bubble when compared with a finer particle.
The 4 litre cell presented a different trend. For this cell, the flotation rate increased as
the particle size increased for the impeller speed of 1400 rpm and decreased as the particle
size increased for the impeller speed of 1300 rpm. However, as previously discussed, the 4
litre cell did not present its better performance for any of the tests, suggesting that the
impeller speeds tested generated an excessive turbulence for this cell, and a lower impeller
speed might be required.
The impeller speed of 1300 rpm was responsible for the best performance for the 2 litre
and 7.5 litre cells. The flotation rate increases as the particle size increases. The 7.5 litre cell
had a higher flotation rate for the particle size fraction of –38 µm when compared to the 2
Lab experiments using different flotation cell geometries
67
litre cell. As the best performance was reached for these cells at this impeller speed, the
optimum conditions provided the appropriate environment for the finer and coarser
particles to reach the surface as a bubble-particle aggregate. Also, the inertia of the
particles has enough magnitude to penetrate the film formed by the laminar flow of fluid
around the bubble and attach to the bubble at this impeller speed.
A comparison of the variation of the flotation rate constant with particle size for the 2
litre and 7.5 litre cells shows that regardless the impeller speed, for the particle size
fraction of –38 µm, the flotation rate constants in the 2 litre cell is always lower than those
in the 7.5 litre cell. For the particle size fraction of +75 µm the flotation rate constants are
slightly stable and only presents to be lower for the 2 litre cell at the impeller speed of 1400
rpm.
5.4 Conclusions
In this study, the main aim was to understand the scale-up criteria for the different cells
by assessing the influence of impeller speed on the flotation performance, under the
condition of constant airflow rate. The effect of this variable on flotation responses was
discussed on how it can be related to the scale-up process. Each criterion tested involved
varying the impeller speed as the cell volume, and hence impeller diameter was increased.
Recovery was found to increase with an increase in the cell area to rotor diameter ratio.
A higher ratio made the turbulence conditions more appropriate for the 7.5 l cell.
Therefore, the size of the turbulence zone seems to play an important role as it is expected
to increase as the rotor size increases.
In general, the flotation rate and recovery increased with an increase in the impeller
speed until a certain point that it eventually decreased for the 2 l and 7.5 l cells. For the 4 l
cell, flotation rate and recovery decreased with increasing the impeller speed, suggesting
that a decrease in impeller speed might be required. The low recovery associated with the
Lab experiments using different flotation cell geometries
68
4 l cell in the first minute could also be associated with the manual addition of water for
keeping the froth level up and it could have influenced the flotation performance for this
cell.
The impeller speed of 1200 rpm allowed a successful scale-up based on the flotation
rate constants and recovery when increasing the size of the cells. Maintaining the impeller
speeds constant at 1300 rpm increased the flotation rate constants and recovery when
increasing the cell size from both the 2 and 4 l cells to the 7.5 l cell. A further increase in
the impeller speed to 1400 rpm also produced the flotation rate constants and recovery to
increase as the cell size increased from both the 2 and 4 l cells to the 7.5 l cell. However,
when increasing the cell size from 2 l to 4 l, it was possible to achieve similar scale-up
results for all impeller speeds.
Considering that with the impeller speed of 1400 rpm for the 2 l cell, more fines were
recovered, this could have a relation with the excessively turbulent environment for this
cell, which can lead to entrainment of fine particles and detachment of coarser particles.
For this speed, recovery also decreased.
The 7.5 litre cell presented the highest recoveries for all impeller speeds. This is further
evidence that turbulence was not fully developed in the smaller cells. Thus, products
concentrate seem to become finer when decreasing the cell size, with only a few
exceptions, indicating that entrainment of fine particles and detachment of coarser
particles may play a role. The recovery of particles larger than 38 μm was found to differ
considerably less among the different scales.
The results show that, there is some scatter in the size-by-size flotation rate constants,
suggesting that experimental errors are at least in part responsible for the variation seen in
the data. Another possible reason could be the variations in bubble velocity with varying
the cell size. Another factor that can contribute to this is the entrainment of fine particles,
Lab experiments using different flotation cell geometries
69
as it could lead to the differences in the flotation rate constant for fine particles, both
between cells of different sizes, and for the same cells at different impeller speeds.
This investigation had the objective of determining empirically this influence
specifically for the Outotec GTK LabCell flotation machine. Therefore, more research is
required as the selection of cells and rotor diameters, and so as the impeller speed, are
proven to influence in the scale-up process for this machine.
Lab experiments using different flotation cell geometries
70
Chapter 6
EIT Chapter
At present, the raw materials industry is dealing with a big challenge: the continuous
exhaustion of extensive high-grade deposits is turning the current global demand for raw
materials a progressively complex exercise. Because of that, its indispensable to develop
new technologies for processing the low-grade and smaller deposits without losing
efficiency and maintaining the quality of the ore properties. Scale-up studies are and will
remain to be crucial for the optimization of mineral production.
The methodology developed in this project allows us to understand the influence of a
hydrodynamic variable (impeller speed) on the flotation performance when scaling-up. It
is expected that this study will contribute to an increasing optimization of the scale-up
processes currently available, which will be reflected in future technologies merging for
improving this process.
6.1 Recommendations for future work
Some suggestions for future works are presented in this section.
(i) Extend the scale-up work to include other hydrodynamic variables such as
the airflow rate to improve and make more accurate the flotation process.
(ii) Investigate the interactions between other hydrodynamic variables through
the scaling-up.
(iii) Optimization of the impeller speed to assist in the performance of the 4 litre
cell.
(iv) Evaluate the kinetic models considering other variables such as contact
angles, bubble velocity, and particle sizes.
(v) Test the scale-up of flotation using cells of larger volumes.
(vi) Repeat the procedure with different minerals and/or elements.
Lab experiments using different flotation cell geometries
71
6.2 SWOT Analysis
A SWOT analysis is an analytical method frequently applied to categorize the main key
features of a specific business or project: strengths, weaknesses, opportunities, and threats
(SWOT).
Table 12 SWOT analysis regarding the project.
Strengths Weaknesses
• Inexpensive process for understanding the flotation performance.
• No negative effects on the environment.
• A rapid process that can be tested several times if required.
• Estimate flotation performance at low cost and without great physical effort.
• Addressing the flotation behaviour before moving to a larger scale.
• No pre-existing published works using the same equipment.
• Time management, as a large number of samples is required for the tests.
• Large-scale tests could present some drawbacks compared to those found in laboratory experiments
Opportunities Threats
• Easy scalability
• Refining the tests to obtain more accurate results.
• Extending the idea proposed in this study to an actual mining project
• Economically feasible
• Results from the implementation of the methodology proposed in this study depend on the experience of the operator.
• Results can deviate for different mineral types and reagents.
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Appendices
Appendix 1. Calculations for the predicted recovery according to the flotation rate constant for the first-order kinetic model equation.
Impeller
Speed
t (min) -ln(1-(R/Rmax)) R (%) R (%) for k = 0.0825 -ln(1-(R/Rmax)) R (%) R (%) for k = 0.1104 -ln(1-(R/Rmax)) R (%) R (%) for k = 0.0832
1 0.17 15.8% 7.9% 0.18 16.2% 10.5% 0.19 17.0% 8.0%
3 0.39 32.6% 21.9% 0.57 43.3% 28.2% 0.56 42.7% 22.1%
5 0.55 42.3% 33.8% 0.79 54.7% 42.4% 0.68 49.5% 34.0%
7 0.67 48.9% 43.9% 0.84 56.7% 53.8% 0.70 50.3% 44.1%
Impeller
Speed
t (min) -ln(1-(R/Rmax)) R (%) R (%) for k = 0.095 -ln(1-(R/Rmax)) R (%) R (%) for k = 0.0881 -ln(1-(R/Rmax)) R (%) R (%) for k = 0.0822
1 0.08 7.8% 9.1% 0.10 9.1% 8.4% 0.10 9.6% 7.9%
3 0.32 27.7% 24.8% 0.33 27.8% 23.2% 0.27 23.8% 21.9%
5 0.53 41.0% 37.8% 0.51 40.1% 35.6% 0.46 37.1% 33.7%
7 0.65 47.6% 48.6% 0.62 46.2% 46.0% 0.58 44.3% 43.8%
Impeller
Speed
t (min) -ln(1-(R/Rmax)) R (%) R (%) for k = 0.1029 -ln(1-(R/Rmax)) R (%) R (%) for k = 0.1735 -ln(1-(R/Rmax)) R (%) R (%) for k = 0.122
1 0.21 19.2% 9.8% 0.25 22.4% 15.9% 0.19 17.0% 11.5%
3 0.42 34.2% 26.6% 0.55 42.3% 40.6% 0.39 32.1% 30.6%
5 0.61 45.7% 40.2% 0.86 57.6% 58.0% 0.63 46.6% 45.7%
7 0.84 56.6% 51.3% 1.31 73.0% 70.3% 0.92 60.1% 57.4%
Cell 7.5 L
1200 rpm 1300 rpm 1400 rpm
Cell 4 L
1200 rpm 1300 rpm 1400 rpm
1200 rpm 1300 rpm 1400 rpm
Classical first-order kinetic model
Cell 2 L
Appendix 2. Calculations for the predicted recovery according to the flotation rate constant for the second-order kinetic model equation.
Impeller
Speed
t (min) (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.1276 (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.1899 (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.1327
1 0.19 15.8% 11.3% 0.19 16.2% 16.0% 0.20 17.0% 11.7%
3 0.48 32.6% 27.7% 0.76 43.3% 36.3% 0.74 42.7% 28.5%
5 0.73 42.3% 38.9% 1.21 54.7% 48.7% 0.98 49.5% 39.9%
7 0.96 48.9% 47.2% 1.31 56.7% 57.1% 1.01 50.3% 48.2%
Impeller
Speed
t (min) (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.1393 (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.1281 (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.1171
1 0.08 7.8% 12.2% 0.10 9.1% 11.4% 0.11 9.6% 10.5%
3 0.38 27.7% 29.5% 0.39 27.8% 27.8% 0.31 23.8% 26.0%
5 0.70 41.0% 41.1% 0.67 40.1% 39.0% 0.59 37.1% 36.9%
7 0.91 47.6% 49.4% 0.86 46.2% 47.3% 0.79 44.3% 45.0%
Impeller
Speed
t (min) (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.1761 (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.3928 (R/Rmax)/(1-(R/Rmax)) R (%) R (%) for k = 0.2155
1 0.24 19.2% 15.0% 0.29 22.4% 28.2% 0.20 17.0% 17.7%
3 0.52 34.2% 34.6% 0.73 42.3% 54.1% 0.47 32.1% 39.3%
5 0.84 45.7% 46.8% 1.36 57.6% 66.3% 0.87 46.6% 51.9%
7 1.31 56.6% 55.2% 2.70 73.0% 73.3% 1.51 60.1% 60.1%
1200 rpm 1300 rpm 1400 rpm
Cell 2 L
1200 rpm 1300 rpm 1400 rpm
Cell 4 L
1200 rpm 1300 rpm 1400 rpm
Second order kinetic model
Cell 7.5 L
Appendix 3. Linear regression for calculation of the flotation rate for the different cells and impeller speeds using the first-order model.
Appendix 4. Linear regression for calculation of the flotation rate for the different cells and impeller speeds using the second-order model.
Appendix 5. Cumulative Recovery of solids as a function of particle size in froth after 1-, 3-,
5-, and 7 minutes.
Particle Size Particle Size Particle Size
(µm) 1 minute 3 minutes 5 minutes 7 minutes (µm) 1 minute 3 minutes 5 minutes 7 minutes (µm) 1 minute 3 minutes 5 minutes 7 minutes
+ 75 0.1 0.4 0.5 0.7 + 75 0.1 0.4 0.5 0.6 + 75 0.4 0.5 0.6 0.7
+ 38 - 75 0.1 0.2 0.3 0.3 + 38 - 75 0.1 0.2 0.3 0.4 + 38 - 75 0.1 0.2 0.4 0.4
- 38 0.6 0.8 0.8 0.9 - 38 0.1 0.2 0.6 0.9 - 38 0.2 0.6 0.8 0.9
Particle Size Particle Size Particle Size
(µm) 1 minute 3 minutes 5 minutes 7 minutes (µm) 1 minute 3 minutes 5 minutes 7 minutes (µm) 1 minute 3 minutes 5 minutes 7 minutes
+ 75 0.3 0.7 0.9 0.9 + 75 0.0 0.3 0.5 0.6 + 75 0.3 0.6 0.8 0.9
+ 38 - 75 0.1 0.3 0.4 0.4 + 38 - 75 0.1 0.2 0.3 0.3 + 38 - 75 0.2 0.3 0.4 0.5
- 38 0.1 0.4 0.4 0.4 - 38 0.5 0.7 0.8 0.9 - 38 0.2 0.3 0.5 0.9
Particle Size Particle Size Particle Size
(µm) 1 minute 3 minutes 5 minutes 7 minutes (µm) 1 minute 3 minutes 5 minutes 7 minutes (µm) 1 minute 3 minutes 5 minutes 7 minutes
+ 75 0.1 0.4 0.4 0.4 + 75 0.1 0.4 0.6 0.7 + 75 0.3 0.5 0.7 0.8
+ 38 - 75 0.2 0.4 0.4 0.4 + 38 - 75 0.1 0.2 0.3 0.3 + 38 - 75 0.1 0.2 0.3 0.4
- 38 0.4 0.8 0.9 0.9 - 38 0.2 0.2 0.4 0.5 - 38 0.2 0.5 0.7 0.9
Cell 2 L Cell 4 L Cell 7.5 L
1200 RPM 1200 RPM 1200 RPM
Cumulative Recovery of solids in froth after (%) Cumulative Recovery of solids in froth after (%) Cumulative Recovery of solids in froth after (%)
1300 RPM 1300 RPM 1300 RPM
Cumulative Recovery of solids in froth after (%) Cumulative Recovery of solids in froth after (%) Cumulative Recovery of solids in froth after (%)
Cumulative Recovery of solids in froth after (%) Cumulative Recovery of solids in froth after (%) Cumulative Recovery of solids in froth after (%)
1400 RPM 1400 RPM 1400 RPM
Appendix 6. Calculations for the flotation rate constant estimation rate as a function of particle size for the different cells and impeller speeds using the first-order kinetic model.
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.1 1 0.1 1.00 0.1 1 0.1 1.00 0.6 1 0.9
1.00 0.4 3 0.5 1.00 0.2 3 0.2 1.00 0.8 3 1.5
1.00 0.5 5 0.8 1.00 0.3 5 0.3 1.00 0.8 5 1.7
1.00 0.7 7 1.1 1.00 0.3 7 0.4 1.00 0.9 7 2.9
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.1 1 0.1 1.00 0.1 1 0.1 1.00 0.1 1 0.1
1.00 0.4 3 0.6 1.00 0.2 3 0.2 1.00 0.2 3 0.2
1.00 0.5 5 0.8 1.00 0.3 5 0.4 1.00 0.6 5 0.9
1.00 0.6 7 0.9 1.00 0.4 7 0.5 1.00 0.9 7 1.9
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.4 1 0.4 1.00 0.1 1 0.1 1.00 0.2 1 0.2
1.00 0.5 3 0.7 1.00 0.2 3 0.2 1.00 0.6 3 1.0
1.00 0.6 5 0.8 1.00 0.4 5 0.4 1.00 0.8 5 1.5
1.00 0.7 7 1.4 1.00 0.4 7 0.5 1.00 0.9 7 2.4
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.3 1 0.3 1.00 0.1 1 0.1 1.00 0.1 1 0.1
1.00 0.7 3 1.1 1.00 0.3 3 0.4 1.00 0.4 3 0.5
1.00 0.9 5 2.4 1.00 0.4 5 0.5 1.00 0.4 5 0.5
1.00 0.9 7 2.8 1.00 0.4 7 0.5 1.00 0.4 7 0.6
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.0 1 0.0 1.00 0.1 1 0.1 1.00 0.5 1 0.7
1.00 0.3 3 0.4 1.00 0.2 3 0.2 1.00 0.7 3 1.1
1.00 0.5 5 0.7 1.00 0.3 5 0.3 1.00 0.8 5 1.8
1.00 0.6 7 0.8 1.00 0.3 7 0.4 1.00 0.9 7 3.0
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.3 1 0.4 1.00 0.2 1 0.2 1.00 0.2 1 0.2
1.00 0.6 3 1.0 1.00 0.3 3 0.3 1.00 0.3 3 0.4
1.00 0.8 5 1.8 1.00 0.4 5 0.5 1.00 0.5 5 0.6
1.00 0.9 7 2.9 1.00 0.5 7 0.7 1.00 0.9 7 2.0
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.1 1 0.1 1.00 0.2 1 0.2 1.00 0.4 1 0.6
1.00 0.4 3 0.4 1.00 0.4 3 0.5 1.00 0.8 3 1.8
1.00 0.4 5 0.5 1.00 0.4 5 0.6 1.00 0.9 5 2.4
1.00 0.4 7 0.6 1.00 0.4 7 0.6 1.00 0.9 7 2.7
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.1 1 0.1 1.00 0.1 1 0.1 1.00 0.2 1 0.2
1.00 0.4 3 0.5 1.00 0.2 3 0.2 1.00 0.2 3 0.2
1.00 0.6 5 0.8 1.00 0.3 5 0.3 1.00 0.4 5 0.5
1.00 0.7 7 1.2 1.00 0.3 7 0.4 1.00 0.5 7 0.6
Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax)) Rmax R t (min) -ln(1-(R/Rmax))
1.00 0.3 1 0.4 1.00 0.1 1 0.1 1.00 0.2 1 0.3
1.00 0.5 3 0.7 1.00 0.2 3 0.2 1.00 0.5 3 0.7
1.00 0.7 5 1.2 1.00 0.3 5 0.4 1.00 0.7 5 1.1
1.00 0.8 7 1.8 1.00 0.4 7 0.6 1.00 0.9 7 3.0
1400 RPM
PSD Flotation Rate / Classical first-order model (n=1)
1200 RPM
1300 RPM
Cell 2 L
(+38 -75 µm) (-38 µm)
Cell 4 L
Cell 4 L
Cell 4 L
(+75 µm) (+38 -75 µm)
(+75 µm) (+38 -75 µm) (-38 µm)
(-38 µm)
(+75 µm) (+38 -75 µm) (-38 µm)
Cell 7.5 L
Cell 7.5 L
Cell 7.5 L
(+75 µm) (+38 -75 µm)
(+75 µm)
(-38 µm)
(+75 µm) (+38 -75 µm) (-38 µm)
(+75 µm) (+38 -75 µm)
(+75 µm) (+38 -75 µm)
(+38 -75 µm) (-38 µm)
(+75 µm)
(-38 µm)
(-38 µm)
Cell 2 L
Cell 2 L
Appendix 7. Linear regression for calculation of the flotation rate as a function of particle size for the different cells and impeller speeds using the first-order kinetic model.
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