lab experiments using different flotation cell geometries

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

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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

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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

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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

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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

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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!

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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).


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:


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.


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;


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


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,


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).


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.


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).


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).


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).


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).


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).


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).


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).


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


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


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


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


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).


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


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).


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).


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


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


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.


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


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).


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


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)


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


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).


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.


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)


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.


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.


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,


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,


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).


38

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.


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


40

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).


41

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).


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.


43

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%


44

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.


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.


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.


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


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.


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%.


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


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


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.


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.


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.


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.


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


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


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


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.


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.


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


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.


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


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.


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


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


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


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,


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.


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.


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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contributing factors and modelling in flotation. Miner. Eng. 70, 77–91.


Welsby, S.D.D., Vianna, S.M.S.M., Franzidis, J.P., 2010. Assigning physical significance to

floatability components. Int. J. Miner. Process. 97, 59–67.

https://doi.org/10.1016/j.minpro.2010.08.002

Yianatos, J.B., Bergh, L.G., Aguilera, J., 2003. Flotation scale up: Use of separability curves.

Miner. Eng. 16, 347–352. https://doi.org/10.1016/S0892-6875(03)00024-4

Yianatos, J.B., Henríquez, F.H., Oroz, A.G., 2006. Characterization of large size flotation cells.

Miner. Eng. 19, 531–538. https://doi.org/10.1016/j.mineng.2005.09.005

Zhang, J.-G., 1989. Factors affecting the kinetics of froth flotation.

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


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


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


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


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



+ 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



+ 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



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


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


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


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


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


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


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


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


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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lab experiments using different flotation cell geometries

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