FACULTY OF TECHNOLOGY

UTILIZING FROTH PHASE BEHAVIOUR AND

MACHINE VISION TO INDICATE FLOTATION

PERFORMANCE

Senni Uusi-Hallila

Master’s thesis

Degree Programme in Process Engineering

April 2014

ABSTRACT

FOR THESIS University of Oulu Faculty of Technology Degree Programme (Bachelor's Thesis, Master’s Thesis) Major Subject (Licentiate Thesis)

Degree Programme in Process Engineering

Author Thesis Supervisor

Uusi-Hallila, Senni Josefiina Paavola, M. (D.Sc.), Leiviskä, K. (Prof.)

Title of Thesis

UTILIZING FROTH PHASE BEHAVIOUR AND MACHINE VISION TO INDICATE FLOTATION

PERFORMANCE Major Subject Type of Thesis Submission Date Number of Pages

Automation Master’s Thesis 1.4.2014 85 p., 16 App.

Abstract

Flotation is one of the most well-known mineral separation methods. In flotation process hydrophobicity of the

solids is manipulated in order to separate the valuable minerals from the gangue. It is highly complex process

because many simultaneous sub-processes and interactions occur within the system. It is essential to have a good

understanding and representation of the flotation phenomena in order to design control strategies.

Modern physical froth stability measures have an intrusive nature and therefore they are not practical to provide a

continuous online froth stability measurement. Unlike these measures, machine vision is able to measure the key

aspects of the froth owing to its non-intrusive nature. Several physical, statistical and dynamical features of froth

surface are possible to measure with the machine vision techniques.

The objective of this work was to understand the froth phase behavior better which indicates the flotation

performance. Literature review of flotation and measurements used in flotation were performed. Image analysis

methods were listed and, regarding to the importance of the froth stability, dynamical features of the froth image

analysis were investigated more closely. A primary batch flotation test-work was carried out in University of Oulu.

The main batch flotation experiments were executed in University of Cape Town with the wide range of operating

conditions. Video captures were analyzed with statistical methods and dependencies between FrothSense™ data

and concentration data were discovered. Furthermore, PLS model was formed from FrothSense™ data and process

measurements in order to predict water recovery, copper grade and copper recovery.

Online measurements obtained from FrothSense™ with wide range of operating conditions can be used for soft

sensors. Soft sensors can estimate the stability of the froth with the robust predictions.

Additional Information

Preface

This thesis was carried out at University of Oulu and University of Cape Town

between March 2013 and March 2014. Thesis was a part of MineSense project

which aim was to reduce the environmental impact of the mineral beneficiation

processes and to increase their productivity.

Kauko Leiviskä (Prof.) and Marko Paavola (D.Sc.) from University of Oulu were

supervisors of this work. They gave me the chance to work in this interesting

project collaborated with University of Cape Town. Cyril O’Connor (Prof.) and

Kirsten Corin (D.Sc.) from University of Cape Town gave me the assignment for

this work and supervised me in the experimental part. I would like to express my

gratitude for all of them for their guidance, instructions and support during this

work. I would also like to thank Nikolai Vatanski from Outotec for his advises

and for borrowing FrothSense™ camera.

I want to thank the staff of Centre for Minerals Research, especially Moegsien

Southgate, and the staff of Oulu Mining School for helping me to execute the

experiments. Lastly, I would like to thank my family and friends for great

support, compassion and patience. Special thanks to my dad.

Contents

Abstract

Preface

Contents

1 Introduction ................................................................................................................. 7

2 Flotation ........................................................................................................................ 9

2.1 Introduction ........................................................................................................... 9

2.2 Measurements ..................................................................................................... 12

2.2.1 Introduction ................................................................................................. 12

2.2.2 Pulp levels in cells ....................................................................................... 13

2.2.3 Air flow rates ............................................................................................... 13

2.2.4 Slurry flow rates .......................................................................................... 15

2.2.5 Elemental assaying ...................................................................................... 15

2.2.6 Density .......................................................................................................... 16

2.2.7 Reagent addition ......................................................................................... 16

2.2.8 Eh, pH and conductivity ............................................................................ 17

2.2.9 Gas dispersion ............................................................................................. 18

2.2.10 Machine vision ........................................................................................... 19

2.3 Control ................................................................................................................. 20

3 Image analysis ........................................................................................................... 23

3.1 Physical features ................................................................................................. 24

3.1.1 Edge detection algorithms ......................................................................... 25

3.1.2 Watershed algorithms ................................................................................ 25

3.1.3 Froth color .................................................................................................... 26

3.1.4 Other physical features............................................................................... 27

3.2 Statistical features ............................................................................................... 27

3.2.1 Fast Fourier transforms .............................................................................. 27

3.2.2 Wavelet transforms ..................................................................................... 28

3.2.3 Fractal descriptors ....................................................................................... 30

3.2.4 Co-occurrence matrices and their variants .............................................. 31

3.2.5 Texture spectrum analysis ......................................................................... 32

3.2.6 Latent variables ........................................................................................... 32

3.2.7 Interquartile range ...................................................................................... 34

3.2.8 Median .......................................................................................................... 34

4 Dynamical features ................................................................................................... 35

4.1 Mobility ................................................................................................................ 35

4.1.1 Bubble tracking ............................................................................................ 35

4.1.2 Block matching ............................................................................................ 36

4.1.3 Cluster matching ......................................................................................... 36

4.1.4 Pixel tracking ............................................................................................... 36

4.2 Stability ................................................................................................................ 37

4.2.1 Bubble burst rate ......................................................................................... 39

4.2.2 Air recovery ................................................................................................. 39

4.2.3 Solids loading .............................................................................................. 41

4.2.4 Water recovery ............................................................................................ 42

4.2.5 Flotation performance ................................................................................ 43

5 Experimental tests ..................................................................................................... 45

5.1 Batch flotation in Oulu ....................................................................................... 45

5.1.1 Experimental setup ..................................................................................... 45

5.1.2 Data analysis ................................................................................................ 46

5.2 Batch flotation in Cape Town ........................................................................... 47

5.2.1 Experimental setup ..................................................................................... 47

5.2.2 Data analysis ................................................................................................ 49

6 Results and Discussion ............................................................................................. 51

6.1 Tests in University of Oulu ............................................................................... 51

6.2 Tests in University of Cape Town .................................................................... 57

6.3 Summary .............................................................................................................. 71

7 Conclusions ................................................................................................................ 73

8 References ................................................................................................................... 74

Appendixes ............................................................................................................... 1-16

7

1 Introduction

Flotation is one of the most common mineral concentration methods where the

valuable minerals are separated from the gangue. It is based on the manipulation

of the difference in hydrophobicity of the solids. After grinding, the slurry enters

a conditioning tank where reagents (collector, frother, and auxiliary reagents)

and particles react. Next, the slurry enters the flotation tank where bubbles are

able to attach to mineral surfaces and hydrophobic valuable minerals rise up to

the froth phase and overflow into the launder while hydrophilic gangue particles

remain in the pulp phase and are recovered to the tails stream. Other

simultaneous sub-processes and interactions also occur within the system and

therefore it is a highly complex process. These sub-processes cause or influence

the breakdown of the froth. The rate of froth breakdown is referred to as the froth

stability. A high rate of recovery and poor selectivity is promoted by stable froths

due to the recovery of a higher concentrations of entrained material. Conversely,

because of lower transport and higher drainage, unstable froths promote lower

rates of recovery and good selectivity. (Morar, 2010)

Modern physical froth stability measures are not practical to provide continuous

online froth stability measurement due to their intrusive nature. Machine vision

has the potential to measure key aspects of the froth that can inform about

flotation performance owing to its non-intrusive nature. It is possible to measure

several physical, statistical and dynamical features of the froth surface with

machine vision techniques. (Morar, 2010)

A key prerequisite for designing control strategies is a good understanding and

representation of the flotation phenomena. Furthermore, information about the

process states is also a crucial factor for the control. Measurement

instrumentation, fault detection and diagnosis, soft sensors, data reconciliation,

8

pattern recognition, process and controller performance monitoring are the

important aspects in the control strategy. Grade and recovery are the two

common output variables of the flotation process that are used to describe the

targets. The grade-recovery curve (the upper bound) is used in a control task to

locate the target corresponding to maximum revenue. However, this target

moves as the upper bound, the feed characteristics, the throughput, and the metal

market prices move. (Hodouin et al., 2001)

The objective of this work is to better understand the froth phase within a batch

flotation cell in terms of froth stability and valuable mineral recovery.

Measurements used in flotation are examined and possible froth image analysis

methods are investigated, focusing on the dynamical features of the froth. Lastly

experimental batch flotation tests are executed in University of Oulu and in

University of Cape Town. Video captures obtained from tests are analyzed with

statistical methods. Also, dependencies between concentration data and online

measurements captured with FrothSense™ are discovered. Moreover, PLS

model is formed from FrothSense™ data and input variables in order to predict

water recovery, copper grade and copper recovery.

The flotation process is introduced in Section 2 where the measurements used are

listed and described. In Section 3 froth image analysis is presented in terms of

physical and statistical features. Dynamical features of image analysis are

investigated more closely in Section 4 where mobility and stability are the main

factors. The experimental tests are introduced in Section 5 where setups and data

analysis methods used in University of Oulu and in University of Cape Town are

described. In Section 6 results obtained from tests are presented and questions

that have appeared in different process stages are discussed. Finally conclusions

are made based on the information presented in Section 7.

9

2 Flotation

2.1 Introduction

After minerals liberation process (crushing, grinding and size classification), ore

is fed to conditioning tanks. Conditioning is a mechanical pretreatment of

mineral sludge where reagents are added in order that minerals would have as

beneficial conditions as possible and enough time to adjust to those reactions

which are desirable in flotation. (Hukki, 1964). Reagents used in flotation are:

Collectors. Enhance the hydrophobicity (water-hating) of the valuable

minerals and promote adhesion to air bubbles.

Frothers. They encourage the formation of a metastable froth phase that

enables the removal of particles carried by air bubbles to the surface of the

cell. They also reduce the induction time, where the collision of particles

and bubbles is allowed to found contact more rapidly.

Auxiliary Reagents. These are depressants, which promote the

hydrophilicity (water-loving) of the gangue minerals, and activators,

which promote the adsorption of reagents onto selected solids. (Yarar,

2000)

Small bubbles are introduced into flotation systems and contacted with

suspended hydrophobic metal-rich particles whilst hydrophilic gangue particles

remain within the water phase and are recovered to the tailings stream. The

bubbles rise and carry the valuable particles to the surface of the liquid, froth

phase, where they overflow into a launder. (Shean and Cilliers, 2011) Fig. 1 shows

the configuration of typical flotation cell.

10

Fig. 1. Structure of flotation cell. (Haavisto et al., 2006)

A surface-active agent (frother) is added to the pulp phase in order to get the

required formation of the froth. The addition will enhance the distribution of air

throughout the pulp and form a relatively unstable froth that would break down

rapidly for further treatment. Moreover, the surface-active agent used should not

significantly interact with the solids particles in the pulp phase when using

sulfide minerals in flotation. Water and entrained solids drain back into the pulp

by the continuous breakage of the froth lamellae. This does not include

detachment of the valuable minerals from the liquid-air interface. Entrained

solids refer to those which are caught up in the flow of water and air towards the

froth phase; it is non-selective and mostly based on the small size of particles able

to be effected by cell hydrodynamics. The stability of the froth has a huge impact

on the final grade of the valuable mineral because the recovery of the entrained

gangue is directly proportional to water recovered. However, too low froth

stability can cause a loss of valuable minerals which makes the further processing

of the material impossible. (Wiese et al., 2011)

The stability of the froth is dependent on the changes in the solution chemistry

such as frother concentration and water quality. In addition, the size and the

11

nature of the hydrophobic particles attaching at the air-water interface also effect

the stability of the froth. Consequently activators, collectors and depressants

have a significant role in froth stability. Froth stability can be increased up to a

certain intermediate contact angle by increasing particle hydrophobicity.

Additionally, particles can destabilize the froth at higher contact angles

(depending on the concentration), which leads to collapse and drainage of the

froth. Attachment of weakly hydrophobic particles at both interfaces of the

draining lamella can stabilize froth. They can also physically prevent further

draining of the film and eventual rupture, if they are packed sufficiently close.

Anyway, destabilization of froth can be caused by strongly hydrophobic particles,

which bridge the froth films. They also allow the rapid movement of the interface

across the particle surface, which results in a collapse of the bubble. These

particles can act as froth breakers again and again as long as they remain attached

at the air-water interface. Therefore they can be extremely effective destabilizers.

(Wiese et al., 2011)

The process may sound relatively simple but in reality it is highly complex due

to high number of variables that affect the flotation and the occurrence of other

simultaneous sub-processes (e.g. coalescence of bubbles, entrainment of gangue

into the froth phase, detachment of valuable particles from bubbles).

Furthermore, controlling it is very challenging because of the co-interaction

between variables. For example, if the air flow rate increases it will result in a

larger bubble size, which will consequently affect the bubble rise velocity, gas

hold up, froth depth, rate of attachment, etc. (Shean and Cilliers, 2011)

In Table 1 there is an example from a platinum flotation operation showing how

different process deviations can change the froth appearance. Furthermore,

different process deviations can cause similar changes in froth appearance. This

12

signifies how complex flotation process can be and how difficult it is to have an

effective process control. (Wright, 1999)

Table 1. List of changes in froth appearance caused by different process deviations. (Moolman

et al., 1996b)

Process deviation Froth appearance

Frother addition rate too high Froth too stable, Bubbles too small

Frother addition rate too low Froth less stable, Large bubbles formed by coalescence

Depressant flow rate too high Froth watery and runny, Low mineral loading, Small bubbles

Depressant flow rate too low Froth too viscous, Low mobility, Large bubbles

Activator flow rate too high Brittle, and mobile froth

Pulp level too high Fast and watery froth

Pulp level too low Sticky and viscous froth with low mobility

Pulp density too high Viscous froth with low mobility

Pulp density too low Watery, runny and unstable froth

Particle feed too coarse Brittle froth, Small bubbles

Particle feed too fine Stable and sticky froth, Large bubbles

Aeration rate too high Low grade, Fast froth, Large bubbles

Aeration rate too low Low recovery, Slow froth, Small bubbles

2.2 Measurements

2.2.1 Introduction

According to Laurila et al. (2002), the most important variables in flotation circuit

are:

slurry properties (density, solids content)

slurry flow rate (retention time)

electrochemical parameters/potentials (pH, Eh, conductivity)

chemical reagents and their addition rate (frothers, collectors, depressants,

activators)

pulp levels in cells

air flow rates into cells

froth properties (speed, bubble size distribution, froth stability)

particle properties (size distribution, shape, degree of mineral liberation)

mineralogical composition of the ore

mineral concentrations in the feed, concentrate and tailings (recovery, grade)

froth wash water rate (especially in flotation columns)

13

In order to achieve good process control results it may well be unnecessary to

manipulate/measure each of these variables simultaneously. Though, the effects

of each of these variables on the flotation process should be considered. (Shean

and Cilliers, 2011)

Before optimization and control can be performed, information about input

disturbances, process operating parameters and final product quality is required.

In addition, the quality of measured information largely determines the

efficiency of an implemented control system. Nevertheless, essential properties

such as liberation degree, surface chemistry, bubble size distribution, bubble

loading and other aforementioned topics remain difficult to measure and infer

even though there are available instruments to measure important parameters

such as ore composition, flow rates and less ore specific properties (e.g. pH,

density, pulp levels). (Bergh and Yianatos, 2011)

2.2.2 Pulp levels in cells

The most common methods of pulp level measurements are a float with angle

arms and capacitive angle transmitter, a float with a target plate and ultrasonic

transmitter, and reflex radar (Laurila et al., 2002). Other methods include;

hydrostatic pressure measurement (both the slurry density and air holdup in the

pulp are required to be known for an accurate measurement), microwave radar

and ultrasonic transmitter, and conductivity and capacitance (see e.g. Hamilton

and Guy, 2000). Accurate level measurement is commonly problematic because

the slurry-froth transition is not sharp and variations in slurry density and/or

very dense froth layers often exist (Laurila et al., 2002).

2.2.3 Air flow rates

There are three common methods of measuring air flow rates in flotation circuit:

differential pressure meter with venturi tube, differential pressure transmitter

14

with Pitot-tube or annubar tube and thermal gas mass flow sensor. The first two

methods are the most popular. (Laurila et al., 2002)

Differential pressure measurement with venturi tube is expensive and requires a

large space, yet it is a reliable, accurate method and produces tolerable pressure

drops. A pressure drop is the result of the tube’s ability to restrict to flow, which

is then measured and air flow rate determined. (Laurila et al., 2002)

The gas flow rate is determined in differential pressure transmitter with Pitot-

tube or annubar tube by comparing the pressure between internal pipe and static

gas. Due to the annubar element’s several measurement point it provides an

average air velocity while Pitot-tube has only one point. With differential

pressure meters problems appear as they require large space and large sections

of straight piping, which means that a fully developed flow profile is needed.

(Laurila et al., 2002)

Thermal gas mass flow measurement is based on the cooling effect of the air

flowing past the sensor that is correlated to air flow rate (Laurila et al., 2002). Fig.

2 shows the methods for measuring air flow rates.

Fig. 2. Illustration of (A) thermal gas mass flowmeter, (B) venturi tube with differential

pressure meter and (C) Pitot tube. (Shean and Cilliers, 2011)

15

2.2.4 Slurry flow rates

Slurry flow rates are measured by commonly used magnetic flow meters. The

device is based on Faraday's principle of induction and it consists of an

electromagnetic coil around an insulated length of pipe. In order to enable an

electric current, electrodes are installed at opposite sides of the pipe so the current

is generated through the flowing fluid and measuring device and thereafter the

flow rate can be determined. The modern meters take up to 30 measurements per

minute. The method used in these magnetic flow meters is non-obtrusive.

However, as solids and air bubbles decrease the performance, slurry

measurement is problematic. Furthermore, de-magnetization is required if

magnetic solids are present. (Shean and Cilliers, 2011)

Fixed or variable speed pumps, which can handle slurries, can also control slurry

flow rates. For advanced flotation control (AFC) and optimizing flotation control

(OFC) the measurement of slurry flow rates are important. (Laurila et al., 2002)

2.2.5 Elemental assaying

Elemental assays from process flow streams are provided by online X-ray

fluorescence (XRF) analyzers which are now considered standard hardware in

large scale flotation plants (Garrido et al., 2008). Most XRF machines are able to

analyze several solids contents and elements, some modern analyzers can handle

up to 24 streams allowing several points in a process to be sampled. The sampling

cycle time is between 10 and 20 min depending on how many sample points are

attached to the analyzer and the time to analyze a single sample can range from

15 seconds to a minute (Laurila et al., 2002). Detection limits are as low as 3-30

ppm and the accuracy ranges from 1 to 6% (Moilanen and Remes, 2008).

The visual and near-infrared reflectance spectroscopic analysis of process slurries

aims to be ancillary where the online assay information available from an XRF

16

analyzer is supplemented. A practically continuous online estimate of slurry

content is reported to be reached as these measurements can be taken with high

frequency as opposed to sparse XRF analysis. It is also stated that spectral

information can be used to accurately predict element contents in the slurry in

between consecutive XRF analyses. This measurement would allow rapid

identification for any process disruptions. (Haavisto et al., 2008)

Since operators do not trust the online information given by estimation models,

these analyzers are considered to be under-utilized despite the obvious benefits

of online XRF analysis. (Garrido et al., 2008)

2.2.6 Density

Flotation plants commonly use nuclear density meters as density measurement.

Radioactive isotope emits gamma radiation and the density can be determined

from a prior calibration after the attenuation of the radiation by the slurry is

measured. This method is non-obtrusive to the process flow. It is often infeasible

to use a nuclear density meter due to the air bubbles in the slurry and the choice

of location in the process is an important aspect. Furthermore, density can be now

measured by some on-stream XRF analyzers. Density measurements are used in

mass balance calculations and control is normally performed in the grinding

circuits. (Laurila et al., 2002)

2.2.7 Reagent addition

There is a variety of alternative equipment to be used for maintaining or setting

reagent addition rates industrially. The apparently insignificant amounts that

needed to be added (often measured in milliliters per minute) and the large

selection of different reagents (with their own chemical attributes and properties)

are the main reasons for this. A common method is a simple on-off type dosing

system which periodically opens a valve allowing reagent to enter the process.

17

To ensure that the correct amount is added, regular checks are essential and

hence this method can be very inaccurate. A more accurate method is metering

pumps, yet they require regular maintenance and are costly. Pumps are

particularly used if costs of the reagents are of importance or volumes to be

added are very small. (Laurila et al., 2002)

2.2.8 Eh, pH and conductivity

Information about the surface chemistry of the particles in the slurry is given by

measurements of activity of the (solvated) hydrogen ion (pH), electrochemical

potential (Eh) and conductivity. Moreover, they determine directly and non-

intrusively what is occurring chemically within the flotation cell. Electrochemical

property is usually measured by pH, which is related logarithmically to

hydronium ion concentration in solution. Ion selective electrodes are used for the

measurement, although they are easily contaminated by active substances in the

slurry which often makes measurement problematic. However, washing of the

electrodes and regular maintenance can be performed since sampling systems

are often used for pH measurement. (Laurila et al., 2002)

Complimentary or similar information is provided when conductivity

measurement is used instead of, or in conjunction with, pH measurement. In

highly aerated systems the use of conductivity meters should be avoided. Instead,

for highly alkaline solutions they are more suitable and are generally cheaper.

Studies (see e.g. Bennett et al., 2002) have been performed where froth density

and flow regimes are determined by conductivity measurements. (Shean and

Cilliers, 2011)

Owing to the difficulty of achieving an appropriate response of electrode probes

when maintaining them on plants, Eh measurement is considered to be too

18

problematic. In that case, further research is required concerning the choice of

material in Eh probes. (Woods, 2003)

2.2.9 Gas dispersion

Gas dispersion is a collective term for bubble size, superficial gas flow rate and

gas hold-up distribution. Three different instruments, which are used for

measuring these variables are presented. (Gomez and Finch, 2007)

Superficial gas velocity measurement sensor consists of a vertically positioned

tube which collects bubbles as the lower end is partly sunken in the pulp zone.

An orifice valve is installed on the continuous versions’ air outlet. It takes time

for the steady-state pressure to be reached and measured, when air is allowed

out of the orifice valve. The volumetric air flow rate is then inferred and

volumetric air flow rate per unit cross sectional area of cell (𝐽𝑔) calculated from

the previous calibration. A range of orifice valves needed to suit all gas velocities

bring out difficulties with the design as the froth builds up within the system.

(Gomez and Finch, 2007)

Maxwell’s model, where the concentration of a non-conducting dispersed phase

is related to the conductivities of the continuous phase and the dispersion, is the

basis for the gas hold-up measurement sensor. Consequently two measurements

are required in separate vessels: the conductivity of the aerated pulp is measured

in one vessel and the conductivity of the air free pulp is measured in the other.

Maxwell’s model is solved and the gas hold-up is estimated by using the ratio of

these measurements. In order to ensure that no bubbles enter the vessel, care is

required when selecting the opening sizes of the syphon; otherwise the method

ensures continuous measurement. (Gomez and Finch, 2007)

19

The bubble size distribution, found in the pulp phase, is measured by a bubble

size measurement sensor. A sample is channeled into a sloped viewing chamber

after it is drawn from the pulp via a tube, and exposed to a pre-set light source.

Image analysis is used to capture the continuous flow of bubbles. It is difficult to

establish the accuracy of the measurement; however the method continues to be

improved and is widely used. (Gomez and Finch, 2007)

Fig. 3. Schematics of (A) gas velocity, (B) gas hold-up and (C) bubble size measurement devices

(Gomez and Finch, 2007).

2.2.10 Machine vision

In machine vision, cameras are positioned above flotation cells to capture digital

images of the froth surface. Control actions can be performed after several froth

features are extracted from these images. Features can be categorized by physical,

statistical and dynamical properties. Several methods exist for extracting

different features and/or variables within each category. For example, bubble size,

which belongs to the physical category of froth, can be extracted by using

watershed algorithms or by detecting bubble edge. Different methods used for

feature extraction are listed in Table 2. (Shean and Cilliers, 2011)

20

Problems may appear when physical features are used for control purposes:

The surface bubbles of flowing froths are commonly observed to be

considerably larger than in the layers right below. (The predominant

portion of the volume is formed by the lower layers, which overflows into

the launder.)

The surface film size distribution have been observed not to be necessarily

representative of bubble size distribution in the underlying froth layer by

some researchers while other researchers have determined a method to

relate them together.

Larger bubbles are often over-segmented and smaller bubble sizes under-

segmented by the watershed method. (Aldrich et al., 2010)

It is common procedure for operators to regulate and control flotation by visual

inspection of the froth surface in mineral process industry. There is a significant

effect on recovery and grade which can be related to the structure of froths. Based

on the appearance of the froth the implementation and development of machine

vision was an attempt to automate and refine the control of the flotation circuit.

It is possible to measure froth velocity online by numerous commercial machine

vision systems and the measurement is very useful in the implementation of

AFC/OFC. The faster dynamics of machine vision as compared to XRF

technology allows for better predictive flotation AFC/OFC models to be created.

(Shean and Cilliers, 2011)

2.3 Control

The first studies on the automatic control of flotation circuit were published after

the first online devices for the measurement of mineral contents of flotation

slurries became available approximately two decades ago. Subsequently early

optimism changed into disappointing realization that it is very difficult to

21

develop effective systems. The flotation process is difficult to control due to the

wide variety of process disturbances caused by the variation in operating

procedures and changes in mineral characteristics. The performance of the plant

is subject to changes in surface properties, flow rates, shapes and size

distributions of particles, compositions and densities. Furthermore, common

contributory sources of disturbances are errors in actuators and measurements,

and the malfunctioning of equipment. (Moolman et al., 1996b)

The bottleneck in mineral process control is that without a minimum amount of

information on the process states, the final product quality, and the input

disturbances the material properties control and optimization cannot be

performed. The quality of the information used impact on the operating strategy

efficiency as it is the input to the real-time control and optimization algorithms,

and as the knowledge encapsulated in the models is built by it (i.e. the basis of

the control strategy). The quality of the ore-specific and less ore-specific

measurements depends heavily upon the maintenance programs. (Bergh and

Yianatos, 2011)

Flotation control has three objectives:

Because of the disturbances, the frequency and severity of erratic

operation are minimized in order to stabilize a flotation process at the

desired level

Appointed grade or recovery set-points are achieved

The economic performance of the process in maximized

A common flotation control system is shown in Fig. 4. The most important part

in the control sheet is the on-stream analyzers (OSA), though it is expensive to

purchase and maintain these instruments. Significant delays in measurement of

10 to 20 minutes are caused due to the OSAs which are usually designed to

22

analyze process flows collected from many flotation circuits. The relationship

between the performance of flotation circuits and froth visual characteristics is a

well-known fact, thus process operators often have heuristic rules applied to the

relation between visual appearance of flotation and the corresponding corrective

operating actions. Therefore conventional OSA-based control schemes have

considered froth appearances in flotation control through machine vision, i.e.

froth-based flotation control. Low capital and maintenance costs and fast

sampling rate are a few of the main advantages of machine vision solutions.

Though, only few results have been reported of the tested machine vision

solutions (e.g. ACEFLOT (DICTUC S.A.), Frothmaster™ (Outotec), and

JKFrothcam (JKTech)) in real flotation plants. (Liu and MacGregor, 2008)

Fig. 4. A common scheme of a flotation control, where a chemical analysis of ore composition

of process streams is provided by on-stream analyzers (OSAs). (Liu and MacGregor, 2008)

23

3 Image analysis

The recovery and grade of valuable minerals in the concentrate are considerably

affected by the structure of froth developed on the pulp surfaces. Process

operators know these effects well. Thus, they classify froth types into different

categories each of which has a typical operating strategy. Though, conditions

associated with more subtle structures in the froth may be impossible for process

operator to diagnose as well as being able to control the system with consistent

reliability. (Moolman et al., 1996a)

A single image can be seen as a three dimensional array of data, which is

demonstrated in Fig 5. When color is not considered, the array is changed into a

matrix of pixel intensities. However, if the images are black and white the array

will be binary. High-dimensional arrays of data, including thousands of

wavelengths, are formed when hyperspectral images are captured. In Fig. 5 the

matrix of pixel intensities alongside with three spectral features (RGB = red, green

and blue) establish the digital image. Depending on the resolution, the size of the

array changes: the range can be from a few thousands to a few million pixels. The

state of the flotation circuit can be analyzed from these series of images. (Aldrich

et al., 2010)

Fig. 5. Three dimensional array of a digital images’ data. (Aldrich et al., 2010)

24

Different types of froth features can be extracted from the images. Extractions can

be categorized into physical, statistical and dynamical features, where the last-

mentioned class of features is derived from a sequence of images unlike the first

two classes. These features can be extracted by different analytical methods

which are given in Table 2. (Aldrich et al., 2010)

Table 2. Overview of feature extraction from froth images. (Aldrich et al., 2010)

Type Froth variables or features Methods used

Physical Bubble size and shape Edge detection

Watershed

Color RGB levels (color spectrum)

Statistical FFT coefficients FFT analysis

Wavelet coefficients Wavelet analysis

Textural variables Localized pixel intensities

Co-occurrence matrix variables Co-matrix methods

Fractal descriptors Fractal analysis

Latent variables Principle component analysis

Neural network models

Dynamic Mobility Bubble tracking

Block matching

Pixel tracing

Stability Average pixel

Bubble dynamics

3.1 Physical features

The bubble shapes and bubble size distributions of the froth alongside with the

color of the froth (the type and then quantity of mineral loading on bubbles can

be indicative by this) are the physical features of the froth. When using a method

in which the image is segmented so that the individual bubble films on the froth

surface are explicitly identified, physical features can be solved directly. The

shape of bubbles is commonly analyzed by edge detection algorithms. In this case

the image is segmented by detecting sharp transitions in the pixel intensities of

the image. The watershed algorithm is also used for analyzing the shape of

bubbles. (Aldrich et al., 2010)

25

3.1.1 Edge detection algorithms

In classical edge detection functions the gradients of pixel intensities between

bubbles in froth image are found to be too small in order to be detected reliably.

In addition, further confounding of classic methods is wished due to the large

white spots or specularities on the top of the bubble formed of the gradients of

the pixel intensities. Consequently, valley edge detection and valley edge tracing

can be used for the segmentation of froth images. (Wang et al., 2003)

The main idea in valley edge detection is to disregard the edges of the texture on

a bubble and focus on the detection of valley edges between the bubbles. First

noise is filtered out from the images. This is followed by evaluation of possible

edge candidates from the image pixels by inspecting if they are at the lowest

point in valleys in certain directions. After that a cleanup procedure (which is

based on valley edge tracking) is executed in order to ensure that no gaps are

between valley edges. Compared to the previous methods, this is more reliable

and orders of magnitude faster when segmenting froth images. (Wang et al., 2003)

Another proposed image segmentation method is based on iterative application

of identification of local minima in pixel intensities, followed by borderline

thinning. After that bubble diameters can be calculated. For larger bubble sizes,

this method is more accurate: the increased computational time isn’t taken into

account so it works better with higher resolution like the other algorithms too.

(Citir et al., 2004)

3.1.2 Watershed algorithms

A simulation of water rising from different points is the morphological approach

for watershed algorithms. Fig. 6 illustrates this approach. Points a, c and e are

minima and b and d are maxima. Points a and e are identified as starting points,

markers, and d as a watershed point because it does not flood from these two

26

markers. Hence, regional maxima are identified in by locating trends in pixel

intensities along different borderlines. The positions of the markers play

evidently a critical role in the performance of method though it is not as

dependent on uniform illumination as the other approaches. Therefore

preprocessing, where the marker image is determined, is of critical importance.

Each bubble represents a localized reflection, often as a result of camera

illumination and therefore they can be used as bubble markers. Another robust

method was proposed in this context (see Sadr-Kazemi and Cilliers, 1997), where

construction of markers is based on histogram equalization, correction and

reconstruction of images. Both the extraction of bubble size and shape

distributions was eased by using this method. (Aldrich et al., 2010)

Fig. 6. The watershed algorithm used for froth image segmentation. (Aldrich et al., 2010)

3.1.3 Froth color

Through extraction of the hue, saturation and intensity (HIS), red, green and blue

(RGB) or hue, saturation and values (HSV) from color images, the froth color can

be defined. Useful information on the bubble loading could be given by this

particularly when the minerals loaded have a distinguishable color. (Aldrich et

al., 2010)

27

3.1.4 Other physical features

Other physical features, apart from the bubble color and shape, of the froth may

also offer beneficial information on the flotation circuit, e.g. the use of a load

algorithm to measure the mineral coverage of the bubbles (see e.g. Kaartinen et

al., 2002). Discovery made at the zinc flotation circuit of the Pyhäsalmi mine in

Finland is the basis of this method which proves that bright spots or total

reflectance did not occur on the top of bubbles with a high mineral load. Instead,

black windows were observed on the top of these bubbles: an indication of poor

bubble loading is attained with this proportion of black windows on their tops.

(Aldrich et al., 2010)

3.2 Statistical features

3.2.1 Fast Fourier transforms

Images can be analyzed and transformed in the frequency domain with the Fast

Fourier Transformation (FFT) method. An image is decomposed into its sine and

cosine component when using this important image processing tool. The input

image is the spatial domain equivalent and the output after transformation

represents the image in the Fourier or frequency domain. Each point in the

Fourier domain image signifies a singular frequency contained in the spatial

domain image. (Fisher et al., 2003)

Digitalized images, which are matrices of grey level pixels intensities, 𝑥(𝑛1, 𝑛2)

can be converted from the grey-scale or spatial domain to the spectral domain,

𝒳(𝜔1, 𝜔2) by Fast Fourier Transform (FFT) according to Eq. 1. (Aldrich et al., 2010)

𝒳(𝜔1, 𝜔2) = ∑ ∑ 𝑥(𝑛1, 𝑛2)𝑒−𝑗𝜔1𝑛1𝑒−𝑗𝜔2𝑛2

∞

−∞

Eq. 1

∞

−∞

28

The amplitude associated with the complex exponential in Eq. 1, where ω1 and

ω2 are the frequency components associated with the Fourier transform, is

represented by X(ω1,ω2) which is the two-dimensional discrete-space Fourier

transform of x(n1,n2). With Eq. (2) the image is then reassembled. (Aldrich et al.,

2010)

𝑥(𝑛1, 𝑛2) = ∫ ∫ 𝒳(𝜔1, 𝜔2)𝑒𝑗𝜔1𝑛1𝑒𝑗𝜔2𝑛2𝑑𝜔1𝑑𝜔2

𝜋

−𝜋

Eq. 2𝜋

−𝜋

Although the two-dimensional discrete-space function representing the image,

𝑥(𝑛1, 𝑛2) , can be real, 𝒳(ω1, ω2) is commonly convoluted as seen in Eq.1.

Consequently, the features used to represent the froth can be obtained from the

coefficients of the power spectrum, P(ω1, ω2), which is defined to enforce real

number values according to Eq. (3) (Aldrich et al., 2010)

P(ω1, ω2) = |𝒳(ω1, ω2)|2 Eq. 3

For example, the sum of the coefficients has been correlated in the power

spectrum with the average bubble sizes of froth images obtained from a copper

flotation plant (see Moolman et al., 1995b). Fourier transforms (unlike wavelet)

are not able to decompose signals with respect to both frequency and space (or

time), therefore they have not been used extensively in froth image analysis.

(Aldrich et al., 2010)

3.2.2 Wavelet transforms

The main idea of wavelets is to convolve the image 𝑥(𝑛1, 𝑛2) with a high and a

low pass filter related with a mother wavelet and after that downsample

afterwards. These four images, each one half the dimensions of the original

image, generated from the mother image correspond a high pass filter applied in

a vertical direction and the low pass filter applied in the horizontal direction (LH),

29

a high pass filter applied in both horizontal and vertical directions (HH), a high

pass filter applied in a horizontal direction and the low pass filter applied in the

vertical direction (HL) and a low pass filter applied in both directions (LL). While

the other images are detail images, LL is generally assigned as the approximation

image because it is a low pass version of the mother image. (Aldrich et al., 2010)

For each LL, i.e. approximation image, the above procedure can be repeated at

each resolution 2𝑗 , using a dyadic scale. As before, this gives four images

standing for 𝒲2𝑗ℎ , 𝒲

2𝑗𝑣 , 𝒲

2𝑗𝑑 and 𝒜𝑗2, where h (horizontal), v(vertical), d(diagonal)

and 𝒜(approximation) respectively conform to HL,LH,HH and LL as illustrated

in Fig. 7. (Aldrich et al., 2010)

Mother image can be reconstructed from {𝒲2𝑗ℎ , 𝒲

2𝑗𝑣 , 𝒲

2𝑗𝑑 } and 𝒜𝑗2, for j=1,2,…, J,

if the If wavelets are applied up to a scale of 2𝐽.

Fig. 7. Graphical demonstration of the decomposition procedure of the 2D-discrete wavelet

transform. (Murguía et al., 2013)

In order to summarize the features are extracted from images by using wavelets.

The Froebenius norm is commonly exploited as a statistic. (Aldrich et al., 2010)

30

The Frobenius norm is a matrix norm A which is defined as the square root of the

sum of the absolute squares of its elements as seen in Eq. 4. (Weisstein, 2014)

‖𝐴‖𝐹 = √∑ ∑|𝑎𝑖𝑗|2

𝑛

𝑗=1

𝑚

𝑖=1

Eq. 4

Discrete wavelet transforms in a two-dimensional discrete form are readily

implemented to images. Bharati et al. (2004) presented indications that they are

more computationally efficient and robust to varying illumination conditions

than segmentation algorithms. (Aldrich et al., 2010)

3.2.3 Fractal descriptors

Image descriptors and described important features from objects represented in

image encapsulate values of relevant information extracted from images. These

descriptors were classically used in texture analysis where reduced set of values

described the whole texture image. Few authors (Mandelbrot (1968), Carlin (2000)

and Russ (1994)) observed that many objects found in nature had characteristics

intrinsic to fractals, like self-similarity and advanced levels of complexity.

Therefore the fractal dimension concept was employed as a descriptor for object

of the real world represented in images. Manoel et al. (2002) suggested the use of

a set of values extracted from the fractal dimension measure process, instead of

the fractal dimension as a unique descriptor, to characterize an image. Bruno et

al. (2008) defined a concept of fractal descriptors as being a set of values extracted

from fractal geometry methods and used to characterized artifact in an image,

like textures, contours, shapes and so. (Florindo and Bruno, 2012)

With Fractal descriptors, self-similarity is noted in the bubble size distributions

of the froth images. The area distribution of the bubbles on the froth surface

31

follows a power law distribution if the bubbles can be identified at different

scales. (Aldrich et al., 2010)

An example of self-similarity is represented in Fig. 8. Even though the same

object in different images do not share the common image properties such as

colors, textures, edges, they can share a similar geometric layout of local internal

self-similarities. (Shechtman and Irani, 2007)

Fig. 8. Self-similarity of circle in different images. (Shechtman and Irani, 2007)

3.2.4 Co-occurrence matrices and their variants

Co-occurrence matrices are used for the calculation of the second order statistic.

A grey level co-occurrence matrix (GLCM) uses the relationship between two

groups which are usually two neighboring pixels in the original image. One pixel

is compared to another in the digital image. Three parameters are observed when

one pixel wants to compute the GLCM of the image matrix: the length of

translation, the angle of displacement and the number of grey-levels in the image.

The number of grey-levels defining the image determines the size of the GLCM

matrix. The number of computations can be reduced by rescaling the image in a

lower version using less grey-levels than in the original version. In order to

obtain information characterizing the texture of the analyzed image, some

textural features must be extracted after GLCM is computed. According to

Haralick (1979) and Hall-Beyer (2004) the most relevant textural features

extracted from GLCM are contrast, entropy, correlation, inverse different

moment, angular second moment and variance. (Bartolacci et al., 2006)

32

3.2.5 Texture spectrum analysis

Texture spectrum analysis is used to extract features by scanning the image with

a nine pixel-matrix as shown in Fig 9. The eight neighboring pixels can have three

different values: less than, equal to or greater than the value of the pixel in the

center. This will give 6561 (= 38 ) combinations. The texture spectrum of the

image is created by the indices of these combinations (texture unit numbers).

Holtham and Nguyen (2002) investigated the use of texture spectrum analysis

combined with pixel tracing to evaluate the froth surface. It has also been

implemented to JKFrothCam™ software. (Aldrich et al., 2010)

Fig. 9. Texture spectrum analysis for feature extraction from froth images. (Aldrich et al., 2010)

3.2.6 Latent variables

Latent variables are divided into four different sections: principal component

analysis, Hebbian learning, multilayer perceptrons and cellular neural networks.

Multivariable image analysis is based on Principal Component Analysis (PCA)

where stacks of congruent images or three dimensional data-arrays are

represented with geometrical coordinates (two dimensions) and with a spectral

coordinate (one dimension). (Aldrich et al., 2010)

Multiresolutional multivariate image analysis (MR-MIA) is based on PCA and it

is used for RGB color images of the froth to extract textural and color information.

33

This information of mineral composition in the froth is then used to provide a

compact representation of the health of the froth. (Liu et al., 2005)

In general, Hebbian algorithm is used for extracting features from images and

then the original images can be reconstructed as a weighted sum of components.

(Aldrich et al., 2010)

A sparse coding method based on a generalization of the generalized Hebbian

algorithm (GGHA) can be used for finding features corresponding to the

poisoning phenomenon in a flotation cell. (Hyötyniemi and Ylinen, 2000)

The most common latent variable approach is the neural networks. In the first

method demonstrated by Moolman et al. (1995a) multilayer perceptrons (in the

form of auto-associative neural networks or auto-encoders) provide a natural

means to extract features from froth images. The idea of this method is that first

the image is sampled or processed by converting the two- or higher- dimensional

array into a single vector. After that it is passed to the neural network, which

attempts to reconstruct the vector by passing the data through a bottleneck layer

that basically extracts latent variables or features from image. In another method

demonstrated by Estrada-Ruiz and Perez-Garibay (2009) a multilayer perceptron

is used to relate the bubble illumination intensities to the size distributions of the

bubbles. The disadvantage of multilayer perceptrons is that neural networks

with multiple hidden layers can be challenging to train and may not yield

consistent or robust results. (Aldrich et al., 2010)

Usually a finite number of locally interconnected nonlinear process units, that

collectively can show promising behavior, construct cellular neural networks.

Generally the cells are like a grid because they are defined in a 2-dimensional

Euclidean geometry. Jeanmeure and Zimmerman (1998) and Zimmerman et al.

34

(1996) demonstrated applications where these networks have been used for their

ability to fast process froth images. (Aldrich et al., 2010)

3.2.7 Interquartile range

Interquartile range (IQR) is a robust estimate of the spread of data. Changes in

the upper and lower 25 % of the data do not have an effect on it so possible

outliers are left out. Therefore it is more representative than the standard

deviation as an estimate of the spread of the body of the data. (The MathWorks,

Inc., 2014)

3.2.8 Median

Median is “middle” value of a sample. Moreover, it can be found by arranging

observations from lowest to highest value and picking the middle one in case

there is an odd number of observations, or calculating the average value of the

two central ones in case there is an even number of observations. Median is less

sensitive to outliers than the mean. (Weisstein, 2014)

Next, dynamical features of the froth are discussed. Compared to the above, the

focus is on analyzing sequences of images instead of extracting features from

single one.

35

4 Dynamical features

With dynamic features, the movement or dynamic behavior of the froth is

captured by designed descriptors. This includes the froth stability (bubble burst

rate, fraction of air overflowing or some notion of the rate of change of the

appearance of the froth) as well as mobility (speed and direction of movement).

(Aldrich et al., 2010)

4.1 Mobility

Due to the smoothness of the images and the effects of bubbles bursting and

merging, motion estimation in froths may be problematic. Moreover, motion in

the center of flotation cell is relatively stagnant whereas near the edge of the cell

it is rapid where the froth overflows into the launder. However, an average

motion is calculated for the froth as a whole. (Aldrich et al., 2010)

4.1.1 Bubble tracking

Bubble motion analysis means tracking the motion of the localized reflections of

the light on the bubble surfaces. A motion vector is calculated for each bubble

marker. Although, motion tracking of individual bubbles over extended periods

of time is useful, difficulties occur when calculating statistics on this information

since the movement information is extracted at irregular intervals related with

the motion of the bubbles in the image. Furthermore, predetermined sub-regions

of the froth surface occasionally require detailed mobility information. (Aldrich

et al., 2010)

36

4.1.2 Block matching

Block matching algorithms are based on the calculation of motion vectors at

regular intervals in predetermined areas of interest. In order to achieve this, the

source image is partitioned into non-overlapping block and afterwards each of

these blocks are tried to match to the corresponding block in the target image.

Then cross-correlation of each source block is performed with all the possible

overlapping target blocks in source block’s search area. While the position where

maximum cross correlation is achieved, the position of the matching block is

identified. Barbian et al. (2007) described an algorithm while using this method:

a normalized height map is created and the location of the maximum value

shows the image dislocation desired to maximize the image correlation. The cross

correlation peak measurement, i.e. the normalized peak, presents a value

between zero and unity: a low value indicates a ‘viscous’, dry froth whereas a

higher value suggest a more ‘mobile’ froth. A relation was found between the

cross correlation peak and concentrate grade. (Aldrich et al., 2010)

4.1.3 Cluster matching

With the cluster matching algorithm, two successive frames of an image sequence

are clustered depending on the position and the intensity. Cluster features such

as position, shape, intensity and average grey-scale difference are used for

matching the cluster centers between successive frames, which subsequently

gives displacement estimates. Francis (2001) concluded that motion estimation

algorithms perform comparatively poorly on froth images, though when used

for clustering they were fast. (Aldrich et al., 2010)

4.1.4 Pixel tracking

The pixel tracking algorithm is again based on correlation where a block in the

center of an image is compared with corresponding blocks in a following image.

37

The blocks with the highest correlation determine the motion vector. Since the

algorithm does not search the entire motion search space, it is fast, although

accuracy may be sacrificed in the process. (Aldrich et al., 2010)

4.2 Stability

An indication of the appearance and disappearance of bubbles from the surface

of the froth is provided with stability measurements. Stability measurements as

well as velocity measurements are based on the analysis of sequences of froth

images. The average intensity of an average image of a sequence of images was

calculated in one of the first approaches made. If the change in the images is rapid

then the average is more blurred and its intensity would approach intermediate

value. The velocity of the froth was also confounded with this crude approach;

hence various authors subsequently considered more sophisticated approaches.

In order not to confound calculations with the froth velocity, the images are first

aligned in these methods. After that the images are pair-wise subtracted from one

another and then further analyzing could be performed to the residual values.

Other methods have been proposed by several authors (Barbian et al. (2003),

Barbian et al. (2005) and Barbian et al. (2006)) where the froth stability can be

concluded from other measured features of the froth. (Aldrich et al., 2010)

Froth stability is the key driver of flotation selectivity and recovery. Nonetheless,

it is not well understood how the non-linearity of mechanisms occur within the

froth or how the mechanistic effects change across different conditions. There is

still a need to do research on the effect of the operating variables on the froth

stability behavior and its relationship to flotation performance. (Morar et al., 2012)

A lot of research has been carried out on the two-phase foam systems, hence the

effect of surfactants on bubble size, foam stability and water recovery are well

38

characterized. The nature and concentration of the surfactant along with the air

rate define the stability within a two-phase froth. Mechanisms that relate to the

two-phase foam stability are well known and factors such as liquid content and

water recovery under different conditions can be predicted using different

models. (Morar et al., 2012)

Yet, there is less knowledge of three-phase froths. Studies on the effect of solids

hydrophobicity have proven that solid particles can stabilize the froth. In

addition, high loadings and highly hydrophobic solids can override the impact

of solution stabilizing effects within the froth. Thus, the knowledge of two-phase

foam systems is insufficient as a means of understanding the froth stability

behavior due to the effects of solids. (Morar et al., 2012)

There are a number of froth stability measurement devices developed for

industrial froths, but many of them are intrusive like the column or electrical

impedance measurements. The only non-intrusive stability measurements are

based upon machine vision. (Morar et al., 2012)

The advantage of these column-based measurements, which measure the rise of

the froth surface or the froth half-life, is that they measure differential froth

stability as a function of froth height. The stability effect of changing the froth

height is useful in online froth phase modelling. Only concern is that these

methods may not scale up to the entire flotation cell because of this relationship

to froth height, which is dependent on the geometry of the froth column. (Morar

et al., 2012)

The disadvantage of the column-based measurements is that they disturb the

flow of the froth and decrease the flotation cells efficiency. Moreover, the column

system takes up a lot of space compared with the machine vision approach, so it

is not practical in smaller flotation cells. Lastly, the maintenance requirements of

39

a column-based instrument are frequent and inconvenient due to the adverse

environment of the flotation cell to any equipment with moving parts. (Morar et

al., 2012)

4.2.1 Bubble burst rate

Problems with froth stability measurements could be solved with a burst rate

measurement by basically identifying and counting bubble burst events. The

bubble burst event can be described as a physical process occurring within the

froth structure. Bubble size or any other froth structural effect will not skew the

signal of each event. (Morar et al., 2012)

Bubble burst rate behaves in a similar way as the bubble size, according to the

operators. The bubble burst rate is calculated by using speed information: the

latter image in the image pair is translated back to the same position as the first

image. The difference image between the translated image and the first image is

then calculated. Lastly, the number of pixels that exceed in value a given

threshold is counted in the difference image. (Kaartinen et al., 2006)

4.2.2 Air recovery

It is well known that froth stability and structure have a momentous role in

flotation performance. Latest studies have shown that there is a link between

changes in froth stability, as operating parameters are varied, and changes in

concentrate grade and recovery (see e.g. Barbian et al., 2005 and Barbian et al.,

2006). Air recovery, or the fraction of air entering a flotation cell that overflows

the weir as unburst bubbles, was used for froth stability quantification in these

studies. (Hadler and Cilliers 2009)

The air rate entering the cell has been an important factor in determining the

flotation performance in recent studies (see e.g. Cooper et al., 2004). Control of

40

the air addition to a bank, or air profile, has an effect on the metallurgical

performance of the bank which has been highlighted in these studies. (Hadler

and Cilliers 2009)

There are two key parameters which the air recovery (𝛼) measure depends on.

The first one is either the superficial gas velocity (𝐽𝑔) through the flotation cell or

the measurement of the amount of air flowing into the cell (𝑄𝑎) discounting the

air lost to the tails. Usually the air flowing into the cells is measured for air input

into forced aerated mechanical flotation cells. A commonly used method for the

superficial gas velocity measurement is a probe inserted through the froth into

the pulp. (Morar et al., 2012)

The second one is the volumetric flow rate of the froth recovered to the launder

( 𝑉𝑓𝑟𝑜𝑡ℎ,𝑟𝑒𝑐 ). In order to determine this parameter, three variables must be

measured: the velocity of the top surface of the froth (𝑣𝑓 ) (measured using a

machine vision method), the height of the froth flowing over the weir (𝐻𝑓𝑟𝑜𝑡ℎ,𝑤𝑒𝑖𝑟)

(measured either manually or using a range meter located above the start of the

launder) and the length of the weir (𝐼𝑤𝑒𝑖𝑟). Hence, the following equation is used

for determining the air recovery. (Morar et al., 2012)

𝛼 =𝑉𝑓𝑟𝑜𝑡ℎ,𝑟𝑒𝑐

𝐽𝑔=

𝑉𝑓𝑟𝑜𝑡ℎ,𝑟𝑒𝑐

𝑄𝑎=

𝑣𝑓 ∙ 𝐻𝑓𝑟𝑜𝑡ℎ,𝑤𝑒𝑖𝑟 ∙ 𝐼𝑤𝑒𝑖𝑟

𝑄𝑎 Eq. 5

The volume taken up by solids and water within the froth is not accounted for in

this measure, which utilizes the volume of the froth recovered. While the majority

of the volume is occupied by air, the state of the froth determines how the

proportion of the air making up the froth varies. Usually, froths with large

bubbles are comprised of less water than froths with smaller bubbles. (Morar et

al., 2012)

41

There is a relationship between air recovery and froth stability. It is shown that

an initial increase in air flow rate make the froth more stable, whereas at high air

rates the froth become less stable and a drop in air recovery can be observed. Fig.

10 illustrates this peak in stability with increasing aeration. (Barbian et al., 2006).

Fig. 10. Peak in Air recovey. (Cilliers, 2009)

4.2.3 Solids loading

In order to understand the relationship between operating parameters and froth

stability/flotation performance it is important to consider the bubble solids

loading. The rigidity of the bubble shell increases and a tightly bound

hydrophobic particle layer (retards drainage) forms, when particles are attached,

resulting in a more stable froth. It is found (and confirmed theoretically in 2D

and 3D), that a higher concentration of particles resulted in a more effective

stabilization mechanism (see e.g. Morris et al., 2008). (Hadler and Cilliers, 2009)

The solids loading can be measured by sampling a single bubble on the froth

surface using a microscope slide, from which the area of the bubble “print” and

mass of the solids can be determined. After that the calculation of solids loading

42

(or mass of attached particles) per unit can be performed. (Hadler and Cilliers,

2009)

Ventura-Medina et al. (2004) have shown that if air flow rate is increased in a

single cell there will be a decrease in solids loading. Moreover, it was found that

the attachment of particles decreased movement down the bank in a bank of four

cells (see Hadler et al., 2006). There is a relationship between solid loading and

concentrate grade. Higher solids loading indicates more selective separation.

(Hadler and Cilliers, 2009)

4.2.4 Water recovery

In order to optimize reagent performance in large scale plants, test work is first

done with batch flotation experiments. However, the results of these tests can

seldom be correlated with the behavior of the particular reagent in full-scale trials.

The most common reason for this is that the changes in the froth stability brought

about by the change in reagent suite are not taken into account in batch flotation

tests. It is problematic to find a measurement that can be used to define froth

stability. What makes it difficult is that the particles entering the froth during

flotation are changing continuously. Hence, parameters such as equilibrium froth

height, froth drainage rates and dynamic froth index are rather impossible to

measure accurately during the limited time of collection. Therefore, water

recovery can be used as an indication of and variations in froth stability: if the

flotation cell is operated at a constant froth height the water recovered for each

concentrate can be measured. Another advantage of this method is that the

entrained mass is directly related to the water mass recovered. Therefore the

entrained mass can be used to decouple the gangue reporting to the concentrate

by entrainment from that recovered by true flotation. (Wiese et al., 2011)

43

4.2.5 Flotation performance

A low air recovery and the bursting of bubbles before overflowing the weir are

consequences for very low air flow rates, where lower froth mobility

compromises the stabilizing effect of high particle attachment. Under low air

flow rates fewer gangue particles entrain, therefore high concentrate grade is

enhanced under these conditions. Furthermore, the drainage of unattached

particles increases with high bursting rate, which means improvement in

selectivity but increase in drop-backs. A low overall recovery is a result of a low

recovery of unattached valuable particles, though a high flow rate of attached

solids is obtained. (Hadler and Cilliers, 2009)

On the other hand, the froth becomes unstable at very high air flow rates, which

results in low solids loading. Though a high flow of bubble surface across the

weir is ensured by the high overflow velocity, the low loading leads to a low flow

rate of attached solids. Entrainment of unattached particles (both gangue and

valuable) increases when the aeration rate is high. This results in lower

concentrate grade. Additionally, a higher overall recovery is obtained with high

rates of aeration due to the recovery of unattached valuable particles. (Hadler

and Cilliers, 2009)

As a result of a stable and mobile froth, together with the stabilization of the

bubbles by the attached particles, a high flow rate of attached solids is obtained

at the medium air flow rate, which corresponds to the peak in air recovery. When

comparing the lower air rate to the medium air rate, it is found that more

unattached particles are entrained which contributes to a higher overall recovery

of valuable ore. Moreover, a higher concentrate grade is obtained at medium air

flow rate than at the high air flow rate. When the froth is at the peak in stability

the highest recovery is achieved, with only a minor decrease in concentration

grade compared to the low rate of aeration. Consequently, flotation performance

44

can be improved by achieving the peak where the froth is stable. (Hadler and

Cilliers, 2009)

45

5 Experimental tests

The aim of the tests using batch flotation was to develop an understanding of the

froth phase in the terms of froth stability and valuable mineral recovery. Primary

tests were done in University of Oulu and the ore used was from Pyhäsalmi Mine.

The main tests were performed in University of Cape Town with a typical

Merensky ore.

5.1 Batch flotation in Oulu

5.1.1 Experimental setup

Tests done in Oulu were primary testing and the objective was to find out the

best frequency for the video capturing, to get to know MATLAB®’s video and

image capturing analysis tools and to get directional results.

The flotation procedure method defined by University of Cape Town (see

Appendix 1) was applied to batch flotation with few changes. Oulu Mining

School’s minipilot mineral beneficiation plant was used for particle size

reduction and conditioning. The applied process conditions, such as chemical

solutions, are presented in Appendix 2. The actual experiments were carried out

using 2.5 l batch flotation cell setting air flow rate to 2 l/min throughout the test.

The measurement equipment consisted of area scan camera (Basler scA1000-

30gc), led-lights, power supply for the lights, computer and computer software

to capture video image and to adjust image features. The camera was mounted

3.5 cm above the froth and it captured an area of 32.5×24 mm. The resolution of

the camera was 1032×778. The program used for video capturing saved the video

clips in 150-frame-Audio Video Interleave (AVI) files. Batch flotation test

environment is shown in Fig. 11.

46

Fig. 11. Set-up of the batch flotation test done in Oulu.

5.1.2 Data analysis

The aim was to determine the ideal frequency for capturing short videos using

different frequencies (10 Hz, 15 Hz, 20 Hz and 25 Hz) from four different phases

of flotation. Time span between phases was ten minutes (see Appendix 2) and

froth was scrapped into a pan every 15 seconds. Video captures were imported

to a Simulink model and every images’ pixel’s intensities were saved as a three

dimensional matrices (𝑖, 𝑗, 𝑘). These matrices were composed of nine spots in

area ‖𝑖 × 𝑗‖, which described an image, and increasing k, which described the

time. Fig. 12 illustrates how the matrices were formed and shows the dimensions.

Matrices were formed for all four phases (4 × 150 images). After that statistical

methods, median and interquartile range (IQR), were used to analyze how pixels’

intensities of these matrices changed between different phases. Finally one pixel

was chosen (𝑖 = 355, 𝑗 = 471) to see its normal probability and how its intensity

changes between different phases. Results of these are shown in Section 6.

47

Fig. 12. Three-dimensional matrix formed from video capture.

5.2 Batch flotation in Cape Town

5.2.1 Experimental setup

Merensky ore flotation procedure was applied to the experiments done in the

University of Cape Town. This flotation procedure of University of Cape Town

is seen in Appendix 1. The experiments were operated in batch mode

maintaining constant froth level and air flow-rate throughout each test-run.

Concentrates were collected by scraping the froth into a collecting pan every 15

seconds. Time span between collecting pans were two, four, six and eight

minutes, giving a total of 20 minutes flotation time. Water and mass recoveries

were calculated from these four concentrates. Samples of feed, concentrates and

tailings were analyzed by X-ray fluorescence (XRF) spectrometer. An ore typical

of the Merensky reef was used for the flotation. Reagents were Dow 250 as a

frother, Sodium Isobutyl Xanthate (SIBX) as a collector and Stypres 504 (guar) as

a depressant. Experimental design of batch flotation test is seen in Table 3.

48

The equipment used were; three-liter modified Leeds flotation cell, area scan

camera (Basler scA1000-30gc), MATLAB®’s Image Acquisition Toolbox™,

FrothSense™ camera and ACTVision© software from Outotec, computer,

separate hard disc and spot lights. Image Acquisition Toolbox™ captured color

video from the area scan camera with frequency of 15 Hz. The resolution of the

camera was 1032×778 and the area of the captured video was 125.5×96 mm.

ACTVision© software captured froth-factors, such as bubble diameter, velocity

and color, from FrothSense™ camera to an Excel sheet. Both cameras were

mounted 20 cm above the froth. Set-up of the batch flotation is seen in Fig. 13.

Float data of each experiment is seen in Appendix 4-10.

Fig. 13. Set-up of batch flotation test in University of Cape Town.

49

Table 3. Experimental design of batch flotation test in University of Cape Town.

Test Froth height

(cm) Frother (g/ton)

Collector (g/ton)

Depressant (g/ton)

Air (l/min) Run number

1 2.5 30 100 0 7 5, 6, 7, 8

2 2.5 40 100 0 7 1, 2, 3, 4

3 2.5 45 100 0 7 9, 10

4 2.5 45 100 0 10 27, 28

5 2.5 50 100 0 10 11, 12

6 2.5 45 100 100 10 23, 24

7 2.5 50 100 100 10 25, 26

8 2.5 60 100 100 10 21, 22

9 2.5 45 100 300 10 15, 16

10 2.5 50 100 300 10 17, 18

11 2.5 60 100 300 10 19, 20

12 7 50 100 0 10 13, 14

5.2.2 Data analysis

One of the video captures (Run number 25) was imported to Simulink where

three-dimensional matrices of pixel intensities were formed to workspace. First

nine pixels were chosen from the image (𝑖 × 𝑗) and then 10-second video clip (𝑘 =

0: 150) was imported to workspace. This was performed for each four flotation

phases (C1, C2, C3 and C4). Next, same statistical methods as in Oulu, median

and interquartile range (IQR), were used to analyze how pixels’ intensities

changed between each phase. Normal distribution of one pixel was plotted for

each phase and changes of pixel intensity between different phases were

analyzed. Results of these can be seen in Section 6.

Next step was to analyze data what FrothSense™ had captured. Data of bubble

diameter, total velocity and RGB values were transferred from Excel to

MATLAB® where every experiment was cut into two-, four-, six- and eight-

minute clips. These clips corresponded to the concentrates scrapped from the

froth. Data clips were scaled and medians of these clips were calculated and

plotted against the corresponding water recoveries, copper recoveries and

copper grades. The results are presented in the following Section 6.

50

Next Partial Least Squares (PLS) regression modelling was used to analyze the

correlations found between froth-factors (velocity, intensity and bubble diameter)

and concentration variables (water recovery, copper grade and copper recovery).

The following steps were used in the analysis:

1. The data was divided into two groups: training data and test data. At least

one run from each of the different flotation tests were chosen to the

training data. The rest of the runs were used as test data.

2. All the data (froth-factor data, concentration data, and process variables)

were scaled.

3. The froth-factor data and process variables were fitted into the

concentration data for a range of features using a PLS model. Both

measured and predicted values were used for forming features. Used

features and in the PLS models are listed in Table 4. The final model was

the one with smallest squared error. (Kaartinen et al., 2005)

Table 4. Features of PLS models.

Measured feature

Name Model for Used

values Output Used features and their transforms

Diameter X1 Water recovery Measured A [X1 X2 X3 X4 X5 X6 (X4/X3) (X2/X3²)]

Color X2

Velocity X3 Copper grade Measured B1 [X1 X2 X3 X4 X5 X6 (X3^0.5) (1/Y1)]

Frother X4 Predicted B2 [X1 X2 X3 X4 X5 X6 (X3^0.5) (1/A)]

Depressant X5

Air flow rate X6 Copper recovery Measured C1 [(Y2²/Y1) (1/Y1²) (1/Y1^0.5) (Y2) (Y1) (Y2/Y1)]

Water recovery Y1 Predicted C2 [(B2²/A) (1/A²) (1/A^0.5) (B2) (A) (B2/A)]

Copper grade Y2

Copper recovery Y3

51

6 Results and Discussion

6.1 Tests in University of Oulu

Pixel’s intensity value was studied for each frequency and phase. Fig. 14 shows

changes of an intensity of a pixel intensity captured at 10 Hz frequency. In Fig.

15 is shown the normal probability plot of the intensities of the same pixel.

Fig. 14. Pixel intensities in different phases captured at 10 Hz frequency.

0 50 100 1500

0.1

0.2

0.3

0.4

0.5First Phase

Pix

el In

tensity

Time

0 50 100 1500

0.1

0.2

0.3

0.4

0.5Second Phase

Pix

el In

tensity

Time

0 50 100 1500

0.1

0.2

0.3

0.4

0.5Third Phase

Pix

el In

tensity

Time

0 50 100 1500

0.1

0.2

0.3

0.4

0.5Fourth Phase

Pix

el In

tensity

Time

52

Fig. 15. Normal probability of one pixel captured at 10 Hz frequency.

Fig. 16 shows intensity values of one pixel with the same position as before

measured using 25 Hz frequency. Normal probability plots were also plotted for

the same pixel (Fig. 17).

Fig. 16. Pixel intensities in different phases captured at 25 Hz frequency.

0.05 0.1 0.15 0.2 0.25 0.3

0.003

0.010.02

0.05

0.10

0.25

0.500.75

0.90

Data

Pro

babili

ty

First Phase

0.04 0.06 0.08

0.003

0.010.02

0.05

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0.500.75

0.90

Data

Pro

babili

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Second Phase

0.04 0.06 0.08 0.1 0.12

0.003

0.010.02

0.05

0.10

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0.90

Data

Pro

babili

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Third Phase

0.05 0.1 0.15

0.003

0.010.02

0.05

0.10

0.25

0.500.75

0.90

DataP

robabili

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Fourth Phase

0 50 100 1500

0.1

0.2

0.3

0.4

0.5First Phase

Pix

el In

tensity

Time

0 50 100 1500

0.1

0.2

0.3

0.4

0.5Second Phase

Pix

el In

tensity

Time

0 50 100 1500

0.1

0.2

0.3

0.4

0.5Third Phase

Pix

el In

tensity

Time

0 50 100 1500

0.1

0.2

0.3

0.4

0.5Fourth Phase

Pix

el In

tensity

Time

53

Fig. 17. Normal probability plots of a pixel captured at 25 Hz frequency.

When comparing pixel’s intensity at different frequencies, it is seen that lower

frequencies’ pixel intensity variation is slightly bigger (see Fig. 14 and Fig. 16).

Additionally, the latter phases’ pixel intensity variation is greater than in the

former phases. One reason for this might be the movement of the bubbles.

Smaller bubbles in the latter phase move faster around the flotation cell due to

the turbulence caused by the rotor. Consequently, the intensity changes as per

the by-passing bubbles. Also the bubble burst rate is higher in the latter phase

and therefore intensity changes more rapidly.

There is a lot of variety in normal probability plots obtained with the frequencies.

With the higher frequencies the intensities are not as normally distributed than

with the lower frequencies. In all cases, the intensities do not seem to follow

normal distribution.

Following figures show boxplot of the IQR of the pixels’ intensities from four

different flotation phases captured in preliminary batch tests in University of

Oulu. In Fig. 18 frequency of the video clip was 10 Hz and in Fig. 19 it was 25 Hz.

0.05 0.1 0.15

0.003

0.010.02

0.05

0.10

0.25

0.500.75

0.90

Data

Pro

babili

ty

First Phase

0.03 0.04 0.05 0.06 0.07

0.003

0.010.02

0.05

0.10

0.25

0.500.75

0.90

Data

Pro

babili

ty

Second Phase

0.04 0.06 0.08 0.1 0.12 0.14

0.003

0.010.02

0.05

0.10

0.25

0.500.75

0.90

Data

Pro

babili

ty

Third Phase

0.05 0.1 0.15

0.003

0.010.02

0.05

0.10

0.25

0.500.75

0.90

DataP

robabili

ty

Fourth Phase

54

Fig. 18. IQR of pixels’ intensities in four different process phases obtained in batch flotation

tests in University of Oulu at video capture frequency of 10 Hz. Phase 1 lasted 0-10 min, phase

2 10-20 min, phase 3 20-30 min, and phase 4 30-40 min, respectively.

Fig. 19. IQR of pixels’ intensities in four different phases obtained in batch flotation tests in

University of Oulu at 25 Hz frequency. Phase 1 lasted 0-10 min, phase 2 10-20 min, phase 3 20-

30 min, and phase 4 30-40 min, respectively.

0

0.01

0.02

0.03

0.04

0.05

0.06

1 2 3 4Phase (Time)

Inte

nsity

10Hz IQR

0

0.01

0.02

0.03

0.04

0.05

0.06

1 2 3 4Phase (Time)

Inte

nsity

25Hz IQR

55

Medians of the same data groups were also calculated and compared using

boxplots. Fig. 20 shows the medians of pixel’s intensities in four different phases

at 10 Hz frequency. In Fig. 21 the applied frequency was 25 Hz.

Fig. 20. Medians of pixels’ intensity values in different process phases at 10 Hz frequency.

Phase 1 lasted 0-10 min, phase 2 10-20 min, phase 3 20-30 min, and phase 4 30-40 min,

respectively.

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1 2 3 4Phase (Time)

Inte

nsity

10Hz Median

56

Fig. 21. Medians of pixels’ intensity values in different process phases at 25 Hz frequency.

Phase 1 lasted 0-10 min, phase 2 10-20 min, phase 3 20-30 min, and phase 4 30-40 min,

respectively.

Interquartile ranges and medians obtained with different frequencies (15 Hz and

20 Hz) were next compared to each other. As shown by Fig. 18 and Fig. 19, the

IQR varies between the frequencies and phases. So do in median figures (Fig. 20

and Fig. 21). Based on the boxplots, both the median and IQR are incapable of

separating the different flotation phases reliably, since the confidence intervals

seem to be overlapping in most of the cases (Fig. 18 – 21). Especially, the

confidence intervals of the higher frequencies cover more each other than those

of the lower frequencies.

Lower frequencies might filter the video capture and therefore frequency used in

experiments should be chosen carefully. For example, the phenomena in the too

low frequencies do not capture all the bubble bursts. On the other hand, too high

frequencies tend to miss out images or copy the same image several times

because computer is not fast enough to save all the sharp images coming along

the cables.

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1 2 3 4Phase (Time)

Inte

nsity

25Hz Median

57

Usually there are biggest bubbles in first process phase and in the following

phases the size decreases. Furthermore, there are more white spots (reflection of

illumination on the top of the bubble) in the image when froth has more small

bubbles than big bubbles. Hence, the pixel intensity values should have increased

as flotation progressed. In this case, the pixel’s intensities should have increased

as the flotation progresses, but that did not happen (see Fig. 18 – 21). The reason

might be in the insufficient illumination, which results in dark video captures

from which these white spots cannot be captured. Other reason might be the

movement of the bubbles. Namely, due to turbulence caused by rotor made the

bubbles move fast around the flotation cell. Consequently, the intensity changes

as per the by-passing bubbles.

6.2 Tests in University of Cape Town

The same methods as above were used for analysing a video clip captured during

the experiments at University of Cape Town. Normal probability plots of a pixel’s

intensity in the four flotation phases are presented in Fig. 22. Time-series of the

values in all the phases are presented in Fig. 23.

58

Fig. 22. Normal distribution of one pixel intensity values captured in run number 25 batch

flotation tests in University of Cape Town.

Fig. 23. Pixel intensities in different phases captured at 25 Hz frequency

The intensity follows normal distribution better in the latter flotation phases as

seen in Fig. 22. Higher pixel intensity values slightly deviate from the normal

distribution. Fig. 23 shows that pixel intensity of former flotation phase vary

0.2 0.4 0.6 0.8 1

0.003

0.010.02

0.05

0.10

0.25

0.500.75

0.90

Data

Pro

babili

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First Phase

0.4 0.6 0.8

0.003

0.010.02

0.05

0.10

0.25

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0.90

Data

Pro

babili

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Second Phase

0.2 0.4 0.6 0.8

0.003

0.010.02

0.05

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0.90

Data

Pro

babili

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Third Phase

0.4 0.6 0.8

0.003

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0.05

0.10

0.25

0.500.75

0.90

DataP

robabili

ty

Fourth Phase

0 50 100 1500

0.2

0.4

0.6

0.8

1

First Phase

Pix

el In

tensity

Time

0 50 100 1500

0.2

0.4

0.6

0.8

1

Second Phase

Pix

el In

tensity

Time

0 50 100 1500

0.2

0.4

0.6

0.8

1

Third Phase

Pix

el In

tensity

Time

0 50 100 1500

0.2

0.4

0.6

0.8

1

Fourth Phase

Pix

el In

tensity

Time

59

more than the latter phase. Also intensities of latter phases are higher than the

former ones.

Next, the same statistical methods as above (IQR and meidan) were used for

analysing the video clip. Fig. 24 shows how the median of pixels’ intensities

changes in four flotation phases.

Fig. 24. Median of pixels’ intensities in four different flotation phases (C1, C2, C3, C4) captured

in run number 25 batch flotation tests in University of Cape Town. Phase C1 lasted 0-2 min,

phase C2 2-6 min, phase C3 6-12 min, and phase C4 12-20 min, respectively.

Interquartile range of the pixels’ intensities in four flotation phases are seen in

Fig. 25. Again, phases are presented in the same order as the flotation progressed.

C1 C2 C3 C4

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Phase (Time)

Inte

nsity

60

Fig. 25. IQR of pixels’ intensities in four different flotation phases captured in run number 25

batch flotation tests in University of Cape Town. Phase C1 lasted 0-2 min, phase C2 2-6 min,

phase C3 6-12 min, and phase C4 12-20 min, respectively.

As seen in Fig. 24, pixel intensities increased as the flotation progressed. This

means the images become brighter, which indicates that the amount of small

bubbles with a reflection of illumination on the top of them increases in every

flotation phase. Fig. 25 shows how interquartile ranges of pixels’ intensities also

increase as flotation progress, though the last phase has slightly smaller values

than the third phase. This might be the result of filtering, because IQR leaves out

changes in the upper and lower 25 % of the data.

Pixel intensities in video captures obtained during the experiments at University

of Oulu stayed mostly under 0.2 (see Fig. 14 and Fig. 16) whereas intensity values

in video captures obtained during the experiments at University of Cape Town

varied from 0.1 to 1 (see Fig. 23). Median and IQR values of pixels’ intensities in

four different flotation phases captured in tests in University of Cape Town

increased as the flotation progressed (see Fig. 24 and Fig. 25) whereas same

statistical values of pixels’ intensities in four different flotation phases captured

C1 C2 C3 C4

0.05

0.1

0.15

0.2

0.25

0.3

Phase (Time)

Inte

nsity

61

in tests in University of Oulu varied between phases (see Fig. 18-21). The reason

for these significant differences in statistical results is that the experimental

conditions and setups were notably different. Because the tested statistical

metrics worked in different ways in different environments, they are not practical

solutions.

Next, data obtained from FrothSense™ camera (Outotec) will be analyzed and

compared to the flotation data. Main focus of the flotation experiments is on

monitoring water recovery, copper grade and copper recovery. Additionally,

some other flotation variables, such as gangue recovery, has been monitored (for

a complete list refer to Appendix 3-16). Water recovery describes the froth

stability as explained in Section 4.2 and copper is the recovered value mineral.

Each concentrate (see Appendix 3-16) responds differently to the changing

conditions in the flotation cell as reagent is used up and the froth becomes less

stable. Therefore all the data is presented cumulative in order to show the total

effect of the whole flotation.

Fig. 26 shows mass and water recoveries of each of the flotation condition (see

Appendix 3-16). Each point in the curve corresponds to the collected concentrate

at the different flotation phase (C1, C2, C3 and C4). As mentioned before, mass

and water recovery are presented cumulatively.

62

Fig. 26. Cumulative mass and water recovery of each flotation test.

As seen in Fig. 26, the lack of water and solids recovery indicates that the froth is

highly unstable at the low frother dosages. As depressant is added the mass

recovery drops because the depressant prevents solids from becoming

hydrophobic and therefore less particles attach to the bubbles and entrain. When

frother dosage is increased water recovery increases because the frother enables

the removal of particles carried by air bubbles to the surface of the cell (entrained

mass is directly related to the water mass recovered) and allows the collision of

particles and bubbles to found contact more rapidly.

When depressant dosage is 300 g/t, the same amount of solids is recovered

regardless of the frother dosage. This implies entrainment conditions.

In the following figures, tests are categorized into four different groups: each

group has the same dosage of the depressant and air flow rate. This is performed

in order to make figures easier to read. The dosage of the depressant together

with the air flow rate were the clearest factors to classify different groups, which

can also be seen in Fig. 26. Table 5 shows how the groups were categorized.

63

Table 5. Symbols and their corresponding depressant dosage and air flow rate.

Copper grade and copper recovery to their corresponding water recovery are

presented in Fig. 27.

Fig. 27 Copper grade and copper recovery plotted against their corresponding water recovery.

See Table 5 for the key.

It can be seen that there is a dependency between copper grade and water

recovery and also copper recovery and water recovery (Fig. 27). All groups

follow the same pattern. When the depressant dosage is high the copper grade

reaches best values, though copper recovery is decreased. The best recoveries are

obtained when the depressant is not present.

Symbol Name Depressant dosage (g/t) Air flow rate (l/min) Run numbers

O Circle 0 7 1, 2, 4, 5, 6, 8, 10

* Asterisk 0 10 12, 28

□ Square 100 10 22, 23, 26

Diamond 300 10 15, 18, 19

-200 0 200 400 6000

2

4

6

8

10

12

14

16

Cumulative Water Recovery

Copper

Gra

de

-200 0 200 400 60020

30

40

50

60

70

80

90

Cumulative Water Recovery

Cum

ula

tive C

opper

Recovery

64

In the following three figures (Fig. 28, Fig. 29, Fig. 30) the froth-factors (velocity,

intensity and bubble diameter) captured with FrothSense™ camera are

compared to the corresponding water recovery. The water recovery increases as

the flotation proceeds.

Fig. 28. Velocity of the froth and corresponding water recovery. See Table 5 for the key.

When the water recovery is high, the velocity of the froth is low, as seen in Fig.

28. This implies that as the flotation proceeds the movement of the froth slows

down. In the beginning of the flotation, when there are bigger bubbles in the froth,

it moves faster. Movement of the froth is highest at 7 l/min air low rate when the

depressant is not used. There are smaller bubbles as the dosage of the depressant

is high (see Fig. 30) and the movement of the froth is low (see Fig. 28). This might

be an outcome of destabilization: as depressant is present, it will prevent small

particles becoming hydrophobic which usually stabilizes the froth (see Section

2.1).

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26-50

0

50

100

150

200

250

300

350

400

450

Velocity

Cum

ula

tive W

ate

r R

ecovery

65

Fig. 29. Intensity of the froth and corresponding water recovery. See Table 5 for the key.

Fig. 29 shows there is not clear relation between water recovery and intensity of

the froth even though wide range of operating conditions were performed. Minor

linearity can be seen when the air feed rate is 7 l/min and depressant dosage is 0

g/ton: the intensity values decreased as the flotation progressed. Most of the

intensity values are between 0.30-0.45. As seen in Fig. 24, the intensity increased

as the flotation progressed. However, here intensities stay at a certain range.

These two different measurements were obtained from two different cameras.

Both of the cameras use different algorithms to calculate intensity values.

Therefore, the results are not comparable.

0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7-50

0

50

100

150

200

250

300

350

400

450

Intensity

Cum

ula

tive W

ate

r R

ecovery

66

Fig. 30. Bubble diameters of the froth and corresponding water recovery. See Table 5 for the

key.

The median diameter of the bubbles decreases as the flotation proceeds as seen

in Fig. 30. As the feed of air is increased or as depressant is added, the variation

of the bubble diameter becomes smaller. Consequently, the biggest bubble

diameters are obtained when the air feed rate is 7 l/min and depressant dosage is

0 g/ton and the smallest diameters when air feed rate is 10 l/min and depressant

dosage is 300 g/ton.

Next Partial Least Squares (PLS) regression modelling was used to analyze the

correlations found between froth-factors and concentration variables.

Fig. 31 shows the fit for the training and test data to the measured water recovery.

Only measured values of the process variables were used for the modelling. The

coefficient of determination (R-Squared) is 0.9217 for the training data and 0.8448

for the test data. Consequently, the fit for both datas in the PLS analyzis shows

significant certainty in the prediction.

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55-50

0

50

100

150

200

250

300

350

400

450

Bubble Diameter

Cum

ula

tive W

ate

r R

ecovery

67

Fig. 31. Measured water recovery (Reference) and a model with measured values for training

and test data. See Table 4 in Section 5.2.2 for information about the used features in the model.

In the following Fig. 32 is shown the fit for the training and test data to the

measured copper grade. Here, only measured values were used for creating

model A whereas in the case of model B predicted values of water recovery were

used. The coefficient of determination is 0.8641 for the model A and 0.7869 for

the model B when analyzing the fit for the training data to the measured copper

grade. Furthermore, when observing test data’s fit, model A’s coefficient of

determination is 0.8454 and model B’s is 0.6625. As expected, model A works

better than model B in both cases. However, the difference between model with

measured values and model with predicted values is only slight. Thus, the

prediction of copper grade is quite accurate with PLS analysis.

0 10 20 30 40 50 60-200

0

200

400

600

Sample number

Wate

r re

covery

Training Data

Reference

Model

0 5 10 15 20 25 30 35 400

200

400

600

Sample number

Wate

r re

covery

Test Data

Reference

Model

68

Fig. 32. Measured copper grade (Reference), model with measured water recovery (Model A)

and model with predicted water recovery (Model B) for training and test data. See Table 4 in

Section 5.2.2 for information about the used features in the model.

Measured copper recovery, model of copper recovery with measured values

(model A) and model of copper recovery with predicted values (model B) for

training and test data are shown in Fig. 33. The coefficient of determination for

model A in training data is 0.8361 and 0.6704 for model B. Thus, model A and

model B have only minor difference between the predictions of copper recovery.

Therefore, prediction of copper recovery is fairly accurate. For test data, model

A’s coefficient of determination is 0.1677 and model B’s -0.0280. Poor coefficient

of determination values might be a result of outliers in the test data. This can be

seen in Fig. 33’s test data part where reference line’s copper recovery drops at 28th

data point. Neither model A nor model B follow the decrease in copper recovery.

0 10 20 30 40 50 60-10

0

10

20

Sample number

Copper

gra

de

Training Data

Reference

Model A

Model B

0 5 10 15 20 25 30 35 40-5

0

5

10

15

Sample number

Copper

gra

de

Test Data

Reference

Model A

Model B

69

Fig. 33. Measured copper recovery (Reference), model with measured water recovery and

copper grade (Model A) and model with predicted water recovery and copper grade (Model B)

for training and test data. See Table 4 in Section 5.2.2 for information about the used features

in the model.

Fig. 34 shows the surface predicted by the copper recovery model, which was

formed from the information of training data, predicts water recovery, copper

grade and copper recovery. The red dots in the figure present the measured

values of concentration variables while the black dots present the predicted

values. As seen in the figure, both measured and predicted values follow the

surface of the model.

0 10 20 30 40 50 600

50

100

Sample number

Copper

recovery

Training Data

Reference

Model A

Model B

0 5 10 15 20 25 30 35 4020

40

60

80

100

Sample number

Copper

recovery

Test Data

Reference

Model A

Model B

70

Fig. 34. Surface plot of the behavior of the model for training data. Red dots are measured

values of water recovery, copper grade and copper recovery, whereas predicted values of them

are mark as the black dots.

The performance of the model with the test data is shown in Fig. 35. Again, the

red dots present the measured values of concentration variables and the black

dots present the predicted values. It is seen that some of the data points deviate

from the surface. These data points are the possible outliers observed before (see

Fig. 33). It is also possible that the training data is not representative or the

selected features do not capture the dependency between the variables

unambiguously.

The uncertainty seen in all of the models could be at least partially explained with

accuracy of measurement timing. The FrothSense™ camera was switched on

before flotation process was put into operation. Therefore there was a small delay

before the true measurements were captured. Although, this was taken into

account when choosing the froth-factor values from the excel file and transferring

them to MATLAB®, a possible minor error can reflect to the PLS modelling.

0

0.5

1

1.5

0

0.5

1

1.520

30

40

50

60

70

80

90

Copper gradeWater Recovery

Copper

recovery

)

71

Other sources of errors are inaccuracies in measurements (camera and manual

from the concentrates).

Fig. 35. Surface plot of the behavior of the model for test data. Red dots are measured values

of water recovery, copper grade and copper recovery, whereas predicted values of them are

mark as the black dots.

6.3 Summary

It is clear that water recovery, copper grade and copper recovery can be predicted

with PLS regression model. Furthermore, if water recovery can be determined,

copper grade and copper recovery could be estimated. On the other hand, if

water recovery is estimated with PLS model, which is formed from froth-factors

and process variables, the stability of the froth could be predicted. Moreover, PLS

model could be used as a controller that stabilizes the froth.

Further analyzing of the data is needed in order to find the best model and the

most effective features describing the model. Alternatively principal component

0

0.5

1

1.5

0

0.5

1

1.520

30

40

50

60

70

80

90

Copper gradeWater Recovery

Copper

recovery

)

72

regression (PCR) could be used for modelling. Moreover, feature selection could

be more accurate and also a larger set of transformation of features could be used.

Kaartinen et al. (2006) found a clear correlation between the mean intensity of the

red color channel and the final concentrate grade. Therefore more research could

be done to find dependencies between red color and concentration data. Lastly,

different validation methods (e.g. leave-one-out cross-validation) could be used

for optimizing the model.

73

7 Conclusions

The aim of this work was to have a better understanding of the froth phase with

in a batch flotation cell. A literature review of flotation and measurements used

in flotation was performed. Also froth image analysis methods were listed. With

regards to the importance of the froth stability, dynamical features of the froth

image analysis were investigated more closely. Tests were carried out in

University of Oulu and in University of Cape Town. Video captures were

analyzed with statistical methods and dependencies between FrothSense™ data

and concentration data were discovered. Furthermore, PLS model was formed

from FrothSense™ data and process conditions in order to predict water recovery,

copper grade and copper recovery.

Online measurements obtained from FrothSense™ can be used for soft sensors

to predict water recovery, copper grade and copper recovery (wide range of

operating conditions). Moreover, the stability of the froth can be estimated with

the robust predictions of concentration data obtained from soft sensors.

Therefore, it is possible to use developed models as a mineral beneficiation

process control to stabilize the froth and disturbance rejection.

The data obtained from the batch flotation tests in University of Cape Town and

introduced in this work can be used for further study. The studies could address

the feature selection, different model structures, cross-validation and

dependencies between red color and concentration data.

74

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Appendix 1

MERENSKY ORE FLOTATION PROCEDURE

Mill 1kg ore to 60% passing 75µm at 66 % solids in a laboratory scale mill.

Mill with e.g. 10ml (100g/ton) collector solution.

Transfer to 3L flotation cell and make up to 35 % solids.

Synthetic plant water used throughout and pulp level controlled manually.

Maintain a froth level of 2cm.

Collect 40 ml feed sample using a 50ml disposable syringe

0 min Add depressant at required dosage using a disposable syringe or

a pipette, e.g. 20ml (200g/ton)

2 min Add frother using a micro syringe, e.g. 40µl (40g/ton)

3 min Turn air on and maintain at a flow rate of 7 L/min throughout

test

5 min Collect C1 (2 min)

9 min Collect C2 (4 min)

15 min Collect C3 (6 min)

23 min Collect C4 (8 min)

Collect concentrates by scraping froth into collecting pan every 15 seconds.

At end, turn off gas.

Collect a 40ml tailings sample using a 50ml disposable syringe

Empty, rinse and clean flotation cell into tailings bucket

*Adjust conditioning times if no depressant is used.

**Copper sulphate, depressants and powdered collectors made up as 1% solutions in

volumetric flasks using distilled water (1g in 100ml).

Appendix 2

Process conditions

Feed flowrate 0.0149 l/s

Air flowrate 2.00 l/min

Flotation cell 2.50 l

Volume of slurry 2.00 l

Density 1.2680 kg/dm3

Chemicals flowrate

Dosfroth (0.1 %) 0.2050 ml/s

Xanthate (0.5 %) 0.4050 ml/s

ZnSO4 (1.5 %) 0.2083 ml/s

Particle size distribution

Screen opening (μm)

Weight of fraction with

sieve (g) Weight of sieve (g)

Weight of fraction (g)

Cumulative weight (g)

Weight percent

(%)

Cumulative weight percent

(%) Ore pass

percent (%)

+250 255 253.9 1.1 1.1 0.307865 0.307865 99.69214

125 263.9 255.6 8.3 9.4 2.322978 2.630842 97.36916

90 268.3 255.2 13.1 22.5 3.666387 6.297229 93.70277

63 290.9 251.4 39.5 62 11.05514 17.35236 82.64764

45 314 254.3 59.7 121.7 16.70865 34.06101 65.93899

32 319.6 239.6 80 201.7 22.39015 56.45116 43.54884

-32 509.5 353.9 155.6 357.3 43.54884 100 0

Phase Time

1 00:00-00:01

2 00:10-00:11

3 00:20-00:21

4 00:30-00:31

Appendix 3

RUN NUMBER 1 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 9,08 12,74 13,90 10,19 16,84 921,95 17,72 18,48

Frother 40 g/ton PAPER 3,26 3,27 3,25 3,23 3,25 11,00 3,54 3,33

Collector 100 g/ton CONC. 5,82 9,47 10,65 6,96 13,59 910,95 14,18 15,15

Depressant 0 g/ton B + H2O 553,05 546,47 544,74 544,85

Air 7L BOTTLE 489,14 398,59 348,72 159,44

Height 2.5cm H20 63,91 147,88 196,02 385,41

D + C + H20 291,91 346,63 404,93 585,05

DISH 215,80 173,30 174,00 176,85

C + H20 76,11 173,33 230,93 408,20

H20 REC. 6,38 15,98 24,26 15,83

RUN NUMBER 2 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 7,28 12,45 16,52 13,59 21,06 938,57 18,02 16,79

Frother 40 g/ton PAPER 3,56 3,38 3,47 3,16 3,49 10,61 3,18 3,21

Collector 100 g/ton CONC. 3,72 9,07 13,05 10,43 17,57 927,96 14,84 13,58

Depressant 0 g/ton B + H2O 489,14 398,59 348,72 553,29

Air 7L BOTTLE 382,89 241,20 127,89 182,33

Height 2.5cm H20 106,25 157,39 220,83 370,96

D + C + H20 328,42 352,80 431,71 585,10

DISH 215,80 173,30 174,00 176,85

C + H20 112,62 179,50 257,71 408,25

H20 REC. 2,65 13,04 23,83 26,86

RUN NUMBER 3 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 6,33 11,61 15,86 13,59 18,89 939,62 18,14 20,18

Frother 40 g/ton PAPER 3,23 3,16 3,46 3,30 3,23 11,03 3,35 3,54

Collector 100 g/ton CONC. 3,10 8,45 12,40 10,29 15,66 928,59 14,79 16,64

Depressant 0 g/ton B + H2O 543,63 544,05 539,28 559,56

Air 7L BOTTLE 437,73 404,62 315,69 158,00

Height 2.5cm H20 105,90 139,43 223,59 401,56

D + C + H20 326,98 332,45 431,67 609,35

DISH 215,80 173,30 174,00 176,85

C + H20 111,18 159,15 257,67 432,50

H20 REC. 2,18 11,27 21,68 20,65

RUN NUMBER 4 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 6,81 13,46 14,38 11,60 19,00 933,51 18,68 18,08

Frother 40 g/ton PAPER 3,25 3,33 2,58 2,70 3,18 10,90 2,82 2,84

Collector 100 g/ton CONC. 3,56 10,13 11,80 8,90 15,82 922,61 15,86 15,24

Depressant 0 g/ton B + H2O 437,73 404,62 515,22 539,86

Air 7L BOTTLE 330,37 234,51 263,87 87,28

Height 2.5cm H20 107,36 170,11 251,35 452,58

D + C + H20 329,93 371,53 460,87 658,42

DISH 215,80 173,30 174,00 176,85

C + H20 114,13 198,23 286,87 481,57

H20 REC. 3,21 17,99 23,72 20,09

Appendix 4

RUN NUMBER 5 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 6,83 12,61 12,58 8,17 18,11 942,90 18,21 16,76

Frother 30 g/ton PAPER 3,30 3,36 2,85 2,74 3,25 11,13 2,82 2,71

Collector 100 g/ton CONC. 3,53 9,25 9,73 5,43 14,86 931,77 15,39 14,05

Depressant 0 g/ton B + H2O 542,76 544,44 555,44 555,80

Air 7L BOTTLE 422,59 345,83 246,46 142,22

Height 2.5cm H20 120,17 198,61 308,98 413,58

D + C + H20 301,41 394,80 511,41 604,57

DISH 175,27 173,30 174,00 176,85

C + H20 126,14 221,50 337,41 427,72

H20 REC. 2,44 13,64 18,70 8,71

RUN NUMBER 6 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 4,03 9,66 10,93 10,40 18,09 950,89 15,55 17,20

Frother 30 g/ton PAPER 2,78 2,70 2,84 2,71 2,83 11,18 2,89 3,45

Collector 100 g/ton CONC. 1,25 6,96 8,09 7,69 15,26 939,71 12,66 13,75

Depressant 0 g/ton B + H2O 422,59 345,83 529,16 560,49

Air 7L BOTTLE 352,94 167,11 154,56 141,72

Height 2.5cm H20 69,65 178,72 374,60 418,77

D + C + H20 245,39 367,42 568,33 613,11

DISH 175,27 173,30 174,00 176,85

C + H20 70,12 194,12 394,33 436,26

H20 REC. -0,78 8,44 11,64 9,80

RUN NUMBER 7 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 6,90 10,15 11,53 9,60 16,94 940,31 18,48 16,07

Frother 30 g/ton PAPER 3,37 3,31 2,71 2,65 3,34 10,69 2,69 2,68

Collector 100 g/ton CONC. 3,53 6,84 8,82 6,95 13,60 929,62 15,79 13,39

Depressant 0 g/ton B + H2O 558,13 540,27 536,14 559,72

Air 7L BOTTLE 435,01 339,43 243,05 178,27

Height 2.5cm H20 123,12 200,84 293,09 381,45

D + C + H20 305,01 390,41 489,33 576,53

DISH 175,27 173,30 174,00 176,85

C + H20 129,74 217,11 315,33 399,68

H20 REC. 3,09 9,43 13,42 11,28

RUN NUMBER 8 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 6,60 9,85 10,06 10,65 14,80 939,19 17,71 17,42

Frother 30 g/ton PAPER 2,74 2,75 2,74 2,79 2,66 10,65 2,67 2,84

Collector 100 g/ton CONC. 3,86 7,10 7,32 7,86 12,14 928,54 15,04 14,58

Depressant 0 g/ton B + H2O 435,01 558,88 566,13 557,75

Air 7L BOTTLE 330,31 340,96 271,79 175,77

Height 2.5cm H20 104,70 217,92 294,34 381,98

D + C + H20 286,80 409,46 484,28 582,98

DISH 175,27 173,30 174,00 176,85

C + H20 111,53 236,16 310,28 406,13

H20 REC. 2,97 11,14 8,62 16,29

Appendix 5

RUN NUMBER 9 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 17,07 18,70 16,40 13,57 20,24 950,99 18,94 20,87

Frother 45 g/ton PAPER 4,92 4,91 4,94 4,86 5,00 11,18 4,87 4,78

Collector 100 g/ton CONC. 12,15 13,79 11,46 8,71 15,24 939,81 14,07 16,09

Depressant 0 g/ton B + H2O 557,47 563,48 465,42 534,95

Air 7L BOTTLE 468,72 443,78 270,41 215,65

Height 2.5cm H20 88,75 119,70 195,01 319,30

D + C + H20 299,14 349,14 422,54 612,38

DISH 175,23 173,05 176,77 249,86

C + H20 123,91 176,09 245,77 362,52

H20 REC. 23,01 42,60 39,30 34,51

RUN NUMBER 10 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 13,83 18,19 17,22 14,11 20,29 925,16 20,38 17,63

Frother 45 g/ton PAPER 4,76 4,64 4,87 4,94 4,87 11,22 4,87 4,79

Collector 100 g/ton CONC. 9,07 13,55 12,35 9,17 15,42 913,94 15,51 12,84

Depressant 0 g/ton B + H2O 468,72 443,78 549,59 546,40

Air 7L BOTTLE 357,37 319,09 334,90 232,41

Height 2.5cm H20 111,35 124,69 214,69 313,99

D + C + H20 311,04 347,07 442,50 608,55

DISH 175,23 173,05 176,77 249,86

C + H20 135,81 174,02 265,73 358,69

H20 REC. 15,39 35,78 38,69 35,53

RUN NUMBER 11 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 25,78 21,15 16,50 14,73 18,90 942,62 20,09 19,07

Frother 50 g/ton PAPER 4,94 4,93 4,94 4,81 4,91 11,27 4,91 4,93

Collector 100 g/ton CONC. 20,84 16,22 11,56 9,92 13,99 931,35 15,18 14,14

Depressant 0 g/ton B + H2O 302,21 319,00 489,40 528,41

Air 10L BOTTLE 225,34 230,03 310,37 240,89

Height 2.5cm H20 76,87 88,97 179,03 287,52

D + C + H20 344,69 359,12 429,09 606,96

DISH 175,23 173,05 176,77 249,86

C + H20 169,46 186,07 252,32 357,10

H20 REC. 71,75 80,88 61,73 59,66

RUN NUMBER 12 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 25,59 22,33 18,89 14,09 19,74 934,81 20,70 19,47

Frother 50 g/ton PAPER 4,84 4,93 4,99 4,83 4,88 11,01 5,13 4,92

Collector 100 g/ton CONC. 20,75 17,40 13,90 9,26 14,86 923,80 15,57 14,55

Depressant 0 g/ton B + H2O 506,22 501,78 490,00 562,92

Air 10L BOTTLE 411,50 395,25 343,87 279,53

Height 2.5cm H20 94,72 106,53 146,13 283,39

D + C + H20 360,93 389,38 416,98 601,69

DISH 175,23 173,05 176,77 249,86

C + H20 185,70 216,33 240,21 351,83

H20 REC. 70,23 92,40 80,18 59,18

Appendix 6

RUN NUMBER 13 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 0,00 9,42 11,27 10,20 21,20 958,48 18,35 18,37

Frother 50 g/ton PAPER 0,00 5,04 5,07 4,72 5,08 11,36 4,81 3,53

Collector 100 g/ton CONC. 0,00 4,38 6,20 5,48 16,12 947,12 13,54 14,84

Depressant 0 g/ton B + H2O 0,00 571,57 566,95 572,29

Air 10L BOTTLE 0,00 437,95 223,63 180,26

Height 7.00cm H20 0,00 133,62 343,32 392,03

D + C + H20 0,00 312,80 532,73 651,77

DISH 0,00 173,06 176,80 249,87

C + H20 0,00 139,74 355,93 401,90

H20 REC. 0,00 1,74 6,41 4,39

RUN NUMBER 14 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 0,00 5,44 11,67 9,77 19,68 945,07 21,46 18,47

Frother 50 g/ton PAPER 0,00 2,80 5,14 4,94 3,35 11,09 4,93 4,73

Collector 100 g/ton CONC. 0,00 2,64 6,53 4,83 16,33 933,98 16,53 13,74

Depressant 0 g/ton B + H2O 0,00 437,95 511,95 510,80

Air 10L BOTTLE 0,00 328,53 188,69 128,26

Height 7.00cm H20 0,00 109,42 323,26 382,54

D + C + H20 0,00 284,97 512,92 639,44

DISH 0,00 173,06 176,80 249,87

C + H20 0,00 111,91 336,12 389,57

H20 REC. 0,00 -0,15 6,33 2,20

RUN NUMBER 15 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 11,38 6,45 6,27 6,50 19,41 958,59 22,44 19,46

Frother 45 g/ton PAPER 5,06 4,95 5,06 4,84 4,95 11,00 4,84 5,13

Collector 100 g/ton CONC. 6,32 1,50 1,21 1,66 14,46 947,59 17,60 14,33

Depressant 300 g/ton B + H2O 479,77 547,94 527,64 526,95

Air 10L BOTTLE 397,36 467,83 353,82 216,40

Height 2.5cm H20 82,41 80,11 173,82 310,55

D + C + H20 336,15 299,81 387,02 603,76

DISH 175,24 173,09 176,85 249,87

C + H20 160,91 126,72 210,17 353,89

H20 REC. 72,18 45,11 35,14 41,68

RUN NUMBER 16 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 10,08 6,97 6,35 6,73 19,72 961,07 18,39 21,45

Frother 45 g/ton PAPER 4,97 4,96 4,99 4,93 4,98 10,87 5,00 5,03

Collector 100 g/ton CONC. 5,11 2,01 1,36 1,80 14,74 950,20 13,39 16,42

Depressant 300 g/ton B + H2O 397,36 467,83 353,82 495,27

Air 10L BOTTLE 312,84 394,06 205,79 262,20

Height 2.5cm H20 84,52 73,77 148,03 233,07

D + C + H20 307,44 292,00 364,46 530,31

DISH 175,24 173,09 176,85 249,87

C + H20 132,20 118,91 187,61 280,44

H20 REC. 42,57 43,13 38,22 45,57

Appendix 7

RUN NUMBER 17 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 11,68 6,63 6,80 7,20 18,88 950,96 21,32 21,90

Frother 50 g/ton PAPER 4,86 4,91 5,00 5,02 5,01 11,22 5,00 4,97

Collector 100 g/ton CONC. 6,82 1,72 1,80 2,18 13,87 939,74 16,32 16,93

Depressant 300 g/ton B + H2O 312,84 394,06 505,16 479,41

Air 10L BOTTLE 253,37 334,41 390,27 224,25

Height 2.5cm H20 59,47 59,65 114,89 255,16

D + C + H20 323,92 290,71 358,24 567,18

DISH 175,24 173,09 176,85 249,87

C + H20 148,68 117,62 181,39 317,31

H20 REC. 82,39 56,25 64,70 59,97

RUN NUMBER 18 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 11,42 6,76 6,66 7,01 18,60 970,28 17,67 18,68

Frother 50 g/ton PAPER 4,97 4,96 4,98 5,04 5,01 10,98 4,88 4,94

Collector 100 g/ton CONC. 6,45 1,80 1,68 1,97 13,59 959,30 12,79 13,74

Depressant 300 g/ton B + H2O 253,31 334,41 340,27 501,35

Air 10L BOTTLE 178,54 249,15 220,90 231,15

Height 2.5cm H20 74,77 85,26 119,37 270,20

D + C + H20 330,91 316,19 408,24 575,07

DISH 175,24 173,09 176,85 249,87

C + H20 155,67 143,10 231,39 325,20

H20 REC. 74,45 56,04 110,34 53,03

RUN NUMBER 19 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 14,48 6,47 6,26 7,06 17,18 971,63 16,69 19,69

Frother 60 g/ton PAPER 4,93 4,84 4,73 4,83 5,03 11,30 5,02 4,99

Collector 100 g/ton CONC. 9,55 1,63 1,53 2,23 12,15 960,33 11,67 14,70

Depressant 300 g/ton B + H2O 522,65 517,34 523,54 504,84

Air 10L BOTTLE 439,65 424,96 374,32 247,39

Height 2.5cm H20 83,00 92,38 149,22 257,45

D + C + H20 413,06 335,19 400,74 590,23

DISH 175,27 173,08 176,80 249,86

C + H20 237,79 162,11 223,94 340,37

H20 REC. 145,24 68,10 73,19 80,69

RUN NUMBER 20 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 13,38 6,51 6,42 7,64 18,01 955,41 16,50 16,93

Frother 60 g/ton PAPER 4,71 4,92 4,82 4,85 4,93 11,03 4,43 4,55

Collector 100 g/ton CONC. 8,67 1,59 1,60 2,79 13,08 944,38 12,07 12,38

Depressant 300 g/ton B + H2O 439,65 424,94 374,32 507,91

Air 10L BOTTLE 348,02 352,52 233,37 219,25

Height 2.5cm H20 91,63 72,42 140,95 288,66

D + C + H20 402,24 309,57 404,12 643,50

DISH 175,27 173,08 176,80 249,86

C + H20 226,97 136,49 227,32 393,64

H20 REC. 126,67 62,48 84,77 102,19

Appendix 8

RUN NUMBER 21 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 19,63 15,37 16,46 15,76 17,62 945,05 16,48 15,85

Frother 60 g/ton PAPER 4,50 4,90 5,03 4,90 4,58 11,40 5,13 4,87

Collector 100 g/ton CONC. 15,13 10,47 11,43 10,86 13,04 933,65 11,35 10,98

Depressant 100 g/ton B + H2O 348,02 352,52 511,13 527,92

Air 10L BOTTLE 233,50 239,47 299,73 157,35

Height 2.5cm H20 114,52 113,05 211,40 370,57

D + C + H20 411,20 407,23 521,81 741,20

DISH 175,27 173,08 176,80 249,86

C + H20 235,93 234,15 345,01 491,34

H20 REC. 106,28 110,63 122,18 109,91

RUN NUMBER 22 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 19,81 14,76 15,08 16,93 19,01 924,19 19,57 15,72

Frother 60 g/ton PAPER 5,04 4,93 5,22 5,24 5,07 11,13 5,13 5,08

Collector 100 g/ton CONC. 14,77 9,83 9,86 11,69 13,94 913,06 14,44 10,64

Depressant 100 g/ton B + H2O 526,38 460,36 527,78 546,60

Air 10L BOTTLE 412,76 351,64 340,17 190,71

Height 2.5cm H20 113,62 108,72 187,61 355,89

D + C + H20 406,92 394,47 475,86 739,38

DISH 175,27 173,08 176,80 249,86

C + H20 231,65 221,39 299,06 489,52

H20 REC. 103,26 102,84 101,59 121,94

RUN NUMBER 23 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 15,17 14,13 13,86 13,54 16,98 939,83 13,83 14,05

Frother 45 g/ton PAPER 4,91 5,07 4,94 4,79 4,73 10,96 4,82 4,88

Collector 100 g/ton CONC. 10,26 9,06 8,92 8,75 12,25 928,87 9,01 9,17

Depressant 100 g/ton B + H2O 538,38 513,57 472,19 542,98

Air 10L BOTTLE 433,82 398,11 259,96 208,76

Height 2.5cm H20 104,56 115,46 212,23 334,22

D + C + H20 341,50 365,10 464,55 657,41

DISH 175,29 173,08 176,84 249,87

C + H20 166,21 192,02 287,71 407,54

H20 REC. 51,39 67,50 66,56 64,57

RUN NUMBER 24 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 13,98 14,96 14,73 14,50 16,18 948,23 17,42 14,24

Frother 45 g/ton PAPER 4,69 4,90 5,03 5,02 4,83 11,26 4,81 4,98

Collector 100 g/ton CONC. 9,29 10,06 9,70 9,48 11,35 936,97 12,61 9,26

Depressant 100 g/ton B + H2O 433,82 398,11 501,61 521,26

Air 10L BOTTLE 325,58 286,07 310,96 219,49

Height 2.5cm H20 108,24 112,04 190,65 301,77

D + C + H20 334,54 371,09 453,55 639,09

DISH 175,29 173,08 176,84 249,87

C + H20 159,25 198,01 276,71 389,22

H20 REC. 41,72 75,91 76,36 77,97

Appendix 9

RUN NUMBER 25 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 18,51 15,19 15,10 14,09 16,38 951,49 11,20 16,67

Frother 50 g/ton PAPER 4,92 4,85 5,06 4,91 4,73 11,29 4,96 4,72

Collector 100 g/ton CONC. 13,59 10,34 10,04 9,18 11,65 940,20 6,24 11,95

Depressant 100 g/ton B + H2O 325,58 286,07 502,54 533,03

Air 10L BOTTLE 195,42 174,60 302,67 187,50

Height 2.5cm H20 130,16 111,47 199,87 345,53

D + C + H20 398,61 389,46 477,54 688,95

DISH 175,29 173,08 176,84 249,87

C + H20 223,32 216,38 300,70 439,08

H20 REC. 79,57 94,57 90,79 84,37

RUN NUMBER 26 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 18,19 14,87 14,58 15,16 15,68 946,23 19,71 16,44

Frother 50 g/ton PAPER 4,81 4,99 4,80 4,93 4,84 10,98 5,13 5,08

Collector 100 g/ton CONC. 13,38 9,88 9,78 10,23 10,84 935,25 14,58 11,36

Depressant 100 g/ton B + H2O 195,42 174,60 527,55 464,14

Air 10L BOTTLE 86,36 94,62 330,71 126,85

Height 2.5cm H20 109,06 79,98 196,84 337,29

D + C + H20 379,32 353,41 472,20 691,82

DISH 175,29 173,08 176,84 249,87

C + H20 204,03 180,33 295,36 441,95

H20 REC. 81,59 90,47 88,74 94,43

RUN NUMBER 27 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 23,30 23,25 18,79 14,12 15,75 930,05 16,96 15,16

Frother 45 g/ton PAPER 4,79 4,99 4,95 4,86 4,92 10,88 4,83 5,09

Collector 100 g/ton CONC. 18,51 18,26 13,84 9,26 10,83 919,17 12,13 10,07

Depressant 0 g/ton B + H2O 541,08 537,45 488,55 517,08

Air 10L BOTTLE 426,03 389,47 271,63 191,07

Height 2.5cm H20 115,05 147,98 216,92 326,01

D + C + H20 364,99 419,53 486,90 660,85

DISH 175,25 173,07 176,79 249,87

C + H20 189,74 246,46 310,11 410,98

H20 REC. 56,18 80,22 79,35 75,71

RUN NUMBER 28 C1 C2 C3 C4 FEED TAILS TAILS2 TAILS3

C + PAPER 22,13 23,28 19,19 13,60 16,88 919,57 12,82 14,55

Frother 45 g/ton PAPER 5,22 5,04 5,01 5,00 5,16 11,07 5,01 4,84

Collector 100 g/ton CONC. 16,91 18,24 14,18 8,60 11,72 908,50 7,81 9,71

Depressant 0 g/ton B + H2O 426,03 389,47 489,23 513,31

Air 10L BOTTLE 298,79 234,81 288,18 139,03

Height 2.5cm H20 127,24 154,66 201,05 374,28

D + C + H20 363,33 421,19 456,85 692,02

DISH 175,25 173,07 176,79 249,87

C + H20 188,08 248,12 280,06 442,15

H20 REC. 43,93 75,22 64,83 59,27

Appendix 10

Run no.

Reagents

Sample

Time,

Mass

Water

Cum

C

umAve cum

Std devStd error

Ave cum w

Std devStd error

Copper

Copper

Cum

Copper

Copper

AveStd dev

Std errorAve

Std devStd error

Nickel

Nickel

Cum

Nickel

Nickel

AveStd dev

Std errorAve

Std devStd error

SulphurSulphur

Cum

.Sulphur

SulphurAverage

Std devStd error

Average

min

Pull, gR

ec, gM

ass, gW

ater, gM

ass, gR

ec, g%

Mass

Copper

Grade

Rec

Copper grade

Copper rec

%M

assN

ickelG

radeR

ecN

ickel gradeN

ickel rec%

Mass

SulphurG

radeR

ecoveryS grade

S recovery

Mass

%%

%%

Mass

%%

%%

Mass

%%

%%

1Frother 40

C1

25,82

6,385,82

6,384,05

1,210,60

22,761,68

0,848,91

51,8651,86

8,9155,79

10,931,89

0,9545,29

8,584,29

5,1329,85

29,855,13

14,553,89

0,830,42

7,794,54

2,2717,20

100,10100,10

17,2024,64

16,331,82

0,9115,19

Collector 100

C2

49,47

15,9815,29

22,3613,33

1,570,79

30,014,67

2,341,86

17,6269,48

4,5474,76

5,350,59

0,2974,30

2,011,00

5,3550,66

80,525,27

39,264,99

0,260,13

31,295,96

2,9810,80

102,28202,38

13,2449,81

12,590,73

0,3738,17

Depressant 0

C3

610,65

24,2625,94

46,6225,31

0,920,46

42,0411,00

5,500,41

4,3273,80

2,8479,40

3,020,18

0,0980,09

1,050,52

3,0632,59

113,104,36

55,154,48

0,100,05

52,941,72

0,865,60

59,64262,02

10,1064,48

9,880,37

0,1956,31

Air 7LC

48

6,9615,83

32,9062,45

34,451,39

0,6952,71

17,458,73

0,241,65

75,452,29

81,182,28

0,130,07

82,491,02

0,511,47

10,25123,36

3,7560,15

3,840,12

0,0661,66

1,290,65

3,2422,55

284,578,65

70,038,42

0,310,16

65,06

F973,18

0,1093,15

0,22210,11

0,33325,04

T910,95

0,0214,94

0,0766,48

0,12109,31

T214,18

0,02

0,260,08

1,200,13

1,82

T315,15

0,02

0,290,09

1,360,13

1,98

Cc+Tt

0,09692,94

0,211205,09

0,418406,34

Mass Bal

99,7797,61

125,01

2Frother 40

C1

3,722,65

3,722,65

10,4939,02

39,0210,49

42,00

3,6013,39

13,393,60

6,1913,60

50,5950,59

13,6011,28

Collector 100

C2

9,0713,04

12,7915,69

3,2129,09

68,115,33

73,315,41

49,0762,46

4,8828,88

10,7097,05

147,6411,54

32,91

Depressant 0

C3

13,0523,83

25,8439,52

0,476,13

74,242,87

79,904,05

52,80115,26

4,4653,29

7,1693,44

241,089,33

53,74

Air 7LC

410,43

26,8636,27

66,380,24

2,5176,75

2,1282,60

1,8819,58

134,843,72

62,344,58

47,77288,85

7,9664,39

F992,65

0,0875,42

0,19189,10

0,32317,65

T927,96

0,0214,66

0,0769,42

0,14128,06

T214,84

0,020,26

0,09

1,350,22

3,25

T313,58

0,020,22

0,081,08

0,121,56

Cc+Tt

0,09492,91

0,218216,31

0,452448,56

Mass Bal

123,19114,39

141,21

3Frother 40

C1

23,10

2,183,10

2,1810,84

33,6033,60

10,8435,63

3,4710,74

10,743,47

5,0017,30

53,6353,63

17,3010,21

Collector 100

C2

48,45

11,2711,55

13,454,09

34,5468,15

5,9072,25

5,1343,38

54,134,69

25,2011,20

94,64148,27

12,8428,24

Depressant 0

C3

612,40

21,6823,95

35,130,55

6,7874,93

3,1379,44

4,4955,68

109,804,58

51,137,53

93,37241,64

10,0946,02

Air 7LC

48

10,2920,65

34,2455,78

0,282,88

77,812,27

82,492,49

25,61135,41

3,9563,05

4,9751,14

292,788,55

55,76

F994,26

0,0881,02

0,20197,56

0,33329,10

T928,59

0,0215,51

0,0870,12

0,15137,43

T214,79

0,02

0,250,08

1,170,21

3,08

T316,64

0,02

0,290,09

1,440,28

4,59

Cc+Tt

0,09594,32

0,216214,77

0,528525,11

Mass Bal

116,42108,71

159,56

4Frother 40

C1

3,563,21

3,563,21

13,4747,95

47,9513,47

47,76

3,3611,97

11,973,36

5,4217,20

61,2361,23

17,2014,63

Collector 100

C2

10,1317,99

13,6921,20

2,8929,25

77,205,64

76,885,76

58,3270,29

5,1331,82

11,20113,46

174,6912,76

41,73

Depressant 0

C3

11,8023,72

25,4944,92

0,404,76

81,963,22

81,623,81

44,99115,28

4,5252,18

6,8480,71

255,4010,02

61,01

Air 7LC

48,90

20,0934,39

65,010,23

2,0584,00

2,4483,66

2,2119,67

134,953,92

61,094,25

37,83293,23

8,5370,04

F988,10

0,0879,79

0,20193,07

0,33327,06

T922,61

0,0215,04

0,0870,90

0,16143,93

T215,86

0,020,26

0,09

1,390,13

2,01

T315,24

0,020,27

0,091,41

0,142,07

Cc+Tt

0,102100,41

0,224220,92

0,424418,64

Mass Bal

125,84114,42

128,00

Appendix 11

Run no.

Reagents

Sample

Time,

Mass

Water

Cum

C

umAve cum

Std devStd error

Ave cum w

Std devStd error

Copper

Copper

Cum

Copper

Copper

AveStd dev

Std errorAve

Std devStd error

Nickel

Nickel

Cum

Nickel

Nickel

AveStd dev

Std errorAve

Std devStd error

SulphurSulphur

Cum

.Sulphur

SulphurAverage

Std devStd error

Average

min

Pull, gR

ec, gM

ass, gW

ater, gM

ass, gR

ec, g%

Mass

Copper

Grade

Rec

Copper grade

Copper rec

%M

assN

ickelG

radeR

ecN

ickel gradeN

ickel rec%

Mass

SulphurG

radeR

ecoveryS grade

S recovery

Mass

%%

%%

Mass

%%

%%

Mass

%%

%%

5Frother 30

C1

23,53

2,443,53

2,443,04

1,210,85

2,262,28

1,619,64

34,0234,02

9,6436,24

13,172,62

1,3138,71

13,516,75

5,1018,01

18,015,10

8,314,28

0,710,36

6,192,87

1,4416,30

57,5457,54

16,3011,59

17,030,76

0,3811,23

Collector 100

C2

49,25

13,6412,78

16,0810,58

1,881,33

11,275,95

4,213,74

34,5568,57

5,3773,03

6,690,92

0,4670,50

4,542,27

6,9564,32

82,326,44

38,016,09

0,490,24

29,847,15

3,5813,50

124,88182,41

14,2736,75

14,440,35

0,1833,17

Depressant 0

C3

69,73

18,7022,51

34,7819,07

2,591,83

22,8910,95

7,740,58

5,6574,22

3,3079,05

4,070,54

0,2777,67

1,370,69

4,1440,26

122,585,45

56,595,60

0,260,13

49,036,20

3,107,90

76,87259,28

11,5252,23

11,790,31

0,1648,84

Air 7LC

48

5,438,71

27,9443,49

26,051,62

1,1431,22

10,187,20

0,311,70

75,912,72

80,863,05

0,220,11

80,250,62

0,312,07

11,22133,80

4,7961,77

4,920,15

0,0858,84

3,191,59

4,5524,71

283,9910,16

57,2110,10

0,170,09

57,37

F989,15

0,0990,92

0,22216,33

0,49480,73

T931,77

0,0217,05

0,0873,98

0,16

T215,39

0,02

0,280,08

1,280,21

3,23

T314,05

0,02

0,270,09

1,250,23

3,26

Cc+Tt

0,09593,89

0,219216,60

0,502496,41

Mass Bal

103,26100,13

103,26

6Frother 30

C1

1,25-0,78

1,25-0,78

15,9819,98

19,9815,98

20,74

3,36

4,214,21

3,361,98

18,1022,63

22,6318,10

4,88

Collector 100

C2

6,968,44

8,217,66

5,9641,45

61,437,48

63,785,83

40,5444,75

5,4521,07

14,40100,22

122,8514,96

26,50

Depressant 0

C3

8,0911,64

16,3019,30

1,4311,58

73,014,48

75,805,35

43,2688,00

5,4041,44

9,1173,70

196,5512,06

42,40

Air 7LC

47,69

9,8023,99

29,100,48

3,6576,66

3,2079,59

3,6928,35

116,354,85

54,796,52

50,14246,69

10,2853,21

F990,11

0,0767,75

0,19192,58

0,33329,71

T939,71

0,0219,55

0,0983,40

0,23

T212,66

0,020,26

0,10

1,260,22

2,81

T313,75

0,020,27

0,101,36

0,233,12

Cc+Tt

0,09796,32

0,214212,34

0,468463,58

Mass Bal

142,16110,26

140,60

7Frother 30

C1

23,53

3,093,53

3,0913,49

47,6247,62

13,4946,82

4,3015,18

15,184,30

6,8716,80

59,3059,30

16,8012,94

Collector 100

C2

46,84

9,4310,37

12,523,70

25,3372,95

7,0371,72

6,8146,58

61,765,96

27,9413,10

89,60148,91

14,3632,48

Depressant 0

C3

68,82

13,4219,19

25,940,68

6,0478,99

4,1277,66

5,1645,53

107,295,59

48,538,20

72,32221,23

11,5348,26

Air 7LC

48

6,9511,28

26,1437,22

0,322,25

81,243,11

79,872,96

20,59127,88

4,8957,84

5,3036,84

258,079,87

56,29

F984,94

0,0881,57

0,20195,41

0,48474,74

T929,62

0,0217,01

0,0979,14

0,15

T215,79

0,02

0,360,10

1,530,26

4,06

T313,39

0,02

0,270,10

1,310,16

2,16

Cc+Tt

0,103101,71

0,224221,10

0,465458,46

Mass Bal

124,68113,14

96,57

8Frother 30

C1

3,862,97

3,862,97

13,5952,46

52,4613,59

51,06

4,3516,77

16,774,35

7,6116,90

65,2365,23

16,9015,51

Collector 100

C2

7,1011,14

10,9614,11

3,2423,01

75,476,89

73,467,67

54,4471,21

6,5032,33

12,7090,17

155,4014,18

36,94

Depressant 0

C3

7,328,62

18,2822,73

0,664,83

80,304,39

78,165,18

37,92109,13

5,9749,55

8,9265,29

220,7012,07

52,46

Air 7LC

47,86

16,2926,14

39,020,33

2,6082,90

3,1780,69

3,2025,11

134,245,14

60,955,51

43,31264,01

10,1062,76

F984,30

0,0987,61

0,21203,55

0,31302,18

T928,54

0,0216,16

0,0874,23

0,16

T215,04

0,020,34

0,09

1,390,14

2,08

T314,58

0,020,27

0,091,27

0,192,76

Cc+Tt

0,104102,74

0,224220,25

0,427420,67

Mass Bal

117,26108,20

139,21

Appendix 12

Run no.

Reagents

Sample

Time,

Mass

Water

Cum

C

umAve cum

Std devStd error

Ave cum w

Std devStd error

Copper

Copper

Cum

Copper

Copper

AveStd dev

Std errorAve

Std devStd error

Nickel

Nickel

Cum

Nickel

Nickel

AveStd dev

Std errorAve

Std devStd error

SulphurSulphur

Cum

.Sulphur

SulphurAverage

Std devStd error

Average

min

Pull, gR

ec, gM

ass, gW

ater, gM

ass, gR

ec, g%

Mass

Copper

Grade

Rec

Copper grade

Copper rec

%M

assN

ickelG

radeR

ecN

ickel gradeN

ickel rec%

Mass

SulphurG

radeR

ecoveryS grade

S recovery

Mass

%%

%%

Mass

%%

%%

Mass

%%

%%

9Frother 45

C1

212,15

23,0112,15

23,0110,61

2,181,54

19,205,39

3,815,43

66,0266,02

5,4371,12

6,441,42

1,0170,47

0,930,65

5,2263,45

63,455,22

28,385,19

0,040,03

24,815,05

3,5715,00

182,25182,25

15,0039,84

15,100,14

0,1036,93

Collector 100

C2

413,79

42,6025,94

65,6124,28

2,351,66

58,3910,21

7,220,50

6,9672,98

2,8178,62

3,090,39

0,2778,61

0,010,01

3,9854,90

118,354,56

52,944,68

0,170,12

51,072,65

1,876,44

88,81271,06

10,4559,26

10,380,10

0,0758,40

Depressant 0

C3

611,46

39,3037,40

104,9136,19

1,721,22

97,3910,64

7,530,21

2,3975,37

2,0281,19

2,130,17

0,1281,28

0,130,09

1,6418,83

137,173,67

61,363,74

0,110,07

60,930,61

0,433,45

39,54310,59

8,3067,90

8,220,11

0,0869,08

Air 7LC

48

8,7134,51

46,11139,42

45,131,39

0,98132,41

9,927,01

0,151,31

76,681,66

82,601,74

0,110,08

82,680,11

0,080,68

5,92143,10

3,1064,01

3,140,05

0,0363,75

0,370,26

2,6623,17

333,767,24

72,967,14

0,140,10

74,82

F1016,08

0,0775,94

0,19188,18

0,32321,08

T939,81

0,0214,38

0,0770,08

0,12

T214,07

0,02

0,240,08

1,190,12

1,63

T316,09

0,02

0,260,08

1,310,14

2,24

Cc+Tt

0,09192,83

0,220223,56

0,450457,43

Mass Bal

122,24118,80

142,47

10Frother 45

C1

9,0715,39

9,0715,39

7,4567,54

67,547,45

69,81

5,1746,86

46,865,17

21,2415,20

137,86137,86

15,2034,01

Collector 100

C2

13,5535,78

22,6251,17

0,638,50

76,043,36

78,604,55

61,67108,53

4,8049,20

7,0495,39

233,2610,31

57,55

Depressant 0

C3

12,3538,69

34,9789,86

0,222,68

78,722,25

81,372,02

24,93133,47

3,8260,50

4,1751,50

284,768,14

70,26

Air 7LC

49,17

35,5344,14

125,390,15

1,3480,06

1,8182,76

0,726,59

140,053,17

63,482,84

26,04310,80

7,0476,68

F986,43

0,0875,16

0,19187,72

0,40389,64

T913,94

0,0216,18

0,0979,60

0,13114,24

T215,51

0,020,25

0,08

1,280,10

1,50

T312,84

0,020,24

0,091,14

0,101,34

Cc+Tt

0,09896,74

0,224220,61

0,411405,31

Mass Bal

128,72117,52

104,02

11Frother 50

C1

220,84

71,7520,84

71,7520,80

0,060,04

70,991,07

0,763,44

71,6371,63

3,4475,52

3,500,09

0,0675,42

0,140,10

4,6797,24

97,244,67

41,194,55

0,170,12

40,930,37

0,2611,30

235,49235,49

11,3055,95

11,550,35

0,2553,48

Collector 100

C2

416,22

80,8837,06

152,6337,61

0,770,54

157,637,07

5,000,31

5,0676,69

2,0780,85

2,070,00

0,0080,73

0,170,12

2,7544,64

141,883,83

60,103,65

0,260,18

59,341,08

0,763,99

64,72300,21

8,1071,32

8,200,15

0,1068,67

Depressant 0

C3

611,56

61,7348,62

214,3650,34

2,431,72

228,5920,12

14,230,16

1,8878,57

1,6282,84

1,590,04

0,0382,69

0,210,15

0,738,45

150,333,09

63,682,90

0,270,19

63,050,88

0,622,75

31,79332,00

6,8378,88

6,780,07

0,0575,94

Air 10LC

48

9,9259,66

58,54274,02

59,931,96

1,38288,01

19,7813,99

0,111,10

79,671,36

84,001,35

0,020,01

83,780,31

0,220,42

4,21154,54

2,6465,46

2,500,20

0,1464,71

1,060,75

2,0220,04

352,046,01

83,646,00

0,010,01

80,10

F1019,21

0,0884,81

0,20204,25

0,40403,61

T931,35

0,0220,21

0,0874,19

0,1198,72

T215,18

0,02

0,240,09

1,300,07

1,12

T314,14

0,02

0,220,08

1,190,07

0,98

Cc+Tt

0,09394,84

0,232236,08

0,413420,92

Mass Bal

111,83115,59

104,29

12Frother 50

C1

20,7570,23

20,7570,23

3,5673,85

73,853,56

75,33

4,4391,84

91,844,43

40,6711,80

244,85244,85

11,8051,02

Collector 100

C2

17,4092,40

38,15162,63

0,305,18

79,032,07

80,612,32

40,44132,28

3,4758,58

4,1472,04

316,898,31

66,03

Depressant 0

C3

13,9080,18

52,05242,81

0,141,90

80,921,55

82,540,63

8,71140,98

2,7162,43

2,4133,50

350,396,73

73,01

Air 10LC

49,26

59,1861,31

301,990,11

0,9981,92

1,3483,56

0,373,45

144,442,36

63,961,84

17,04367,42

5,9976,56

F1015,23

0,0885,14

0,19197,77

0,34345,18

T923,80

0,0214,60

0,0870,68

0,13116,40

T215,57

0,020,26

0,08

1,260,08

1,18

T314,55

0,020,25

0,091,31

0,162,33

Cc+Tt

0,09798,04

0,222225,82

0,473479,94

Mass Bal

115,15114,19

139,04

Appendix 13

Run no.

Reagents

Sample

Time,

Mass

Water

Cum

C

umAve cum

Std devStd error

Ave cum w

Std devStd error

Copper

Copper

Cum

Copper

Copper

AveStd dev

Std errorAve

Std devStd error

Nickel

Nickel

Cum

Nickel

Nickel

AveStd dev

Std errorAve

Std devStd error

SulphurSulphur

Cum

.Sulphur

SulphurAverage

Std devStd error

Average

min

Pull, gR

ec, gM

ass, gW

ater, gM

ass, gR

ec, g%

Mass

Copper

Grade

Rec

Copper grade

Copper rec

%M

assN

ickelG

radeR

ecN

ickel gradeN

ickel rec%

Mass

SulphurG

radeR

ecoveryS grade

S recovery

Mass

%%

%%

Mass

%%

%%

Mass

%%

%%

Height 7.00cm

13Frother 50

C1

2

Collector 100

C2

44,38

1,744,38

1,743,51

1,230,87

0,801,34

0,956,40

28,0228,02

6,4033,65

6,970,81

0,5828,33

7,525,31

3,5815,66

15,663,58

8,443,83

0,350,25

6,992,05

1,459,63

42,1842,18

9,6311,22

9,820,26

0,199,29

Depressant 0

C3

66,20

6,4110,58

8,159,88

1,000,71

7,171,39

0,983,59

22,2350,25

4,7560,35

5,070,46

0,3258,75

2,261,60

4,2026,01

41,673,94

22,464,13

0,280,20

21,461,43

1,0110,40

64,48106,66

10,0828,37

9,161,30

0,9224,72

Air 10LC

48

5,484,39

16,0612,54

15,031,46

1,0310,46

2,942,08

1,548,43

58,693,65

70,483,97

0,450,32

69,890,83

0,593,79

20,7762,44

3,8933,66

4,110,31

0,2232,44

1,731,22

6,7837,15

143,818,95

38,258,50

0,640,45

34,81

F991,56

0,0879,77

0,20199,40

0,43422,40

T947,12

0,0328,60

0,13118,48

0,28

T213,54

0,02

0,340,12

1,680,25

3,37

T314,84

0,03

0,380,13

1,910,23

3,37

Cc+Tt

0,08483,27

0,187185,50

0,379375,98

Mass Bal

104,3893,03

89,01

Height 7.00cm

14Frother 50

C1

Collector 100

C2

2,64-0,15

2,64-0,15

7,5519,92

19,927,55

23,024,08

10,7710,77

4,085,54

10,0026,40

26,4010,00

7,35

Depressant 0

C3

6,536,33

9,176,18

4,5229,54

49,475,39

57,154,43

28,9539,71

4,3320,45

7,5449,24

75,648,25

21,07

Air 10LC

44,83

2,2014,00

8,382,18

10,5259,99

4,2869,31

4,3320,91

60,634,33

31,227,66

37,00112,63

8,0531,37

F978,25

0,0880,33

0,19188,41

0,45440,21

T933,98

0,0325,59

0,13117,96

0,24

T216,53

0,030,45

0,14

2,270,28

4,56

T313,74

0,030,39

0,141,92

0,243,23

Cc+Tt

0,08886,55

0,199194,22

0,367359,00

Mass Bal

107,74103,09

81,55

15Frother 45

C1

26,32

72,186,32

72,185,72

0,860,61

57,3820,94

14,818,47

53,5053,50

8,4767,61

9,110,91

0,6465,36

3,182,25

11,9175,27

75,2711,91

38,7211,90

0,020,01

35,055,18

3,6728,10

177,59177,59

28,1041,23

28,600,71

0,5039,62

Collector 100

C2

41,50

45,117,82

117,297,47

0,490,35

101,5022,34

15,802,62

3,9357,43

7,3472,58

7,640,42

0,3072,10

0,690,49

11,8017,70

92,9711,89

47,8211,88

0,010,00

45,782,89

2,0521,40

32,10209,69

26,8148,69

26,970,22

0,1549,02

Depressant 300

C3

61,21

35,149,03

152,438,76

0,390,28

138,1820,16

14,261,58

1,9159,34

6,5775,00

6,760,26

0,1874,77

0,330,23

8,3010,04

103,0111,41

52,9911,48

0,100,07

51,811,67

1,1817,20

20,81230,50

25,5353,52

25,620,13

0,0954,61

Air 10LC

48

1,6641,68

10,69194,11

10,490,29

0,21181,80

17,4112,31

0,971,61

60,965,70

77,045,81

0,150,10

77,000,05

0,033,43

5,70108,71

10,1755,92

10,190,03

0,0255,09

1,170,83

13,8022,91

253,4123,71

58,8423,50

0,290,21

60,01

F990,21

0,0987,37

0,21210,12

0,37362,42

T947,59

0,0215,82

0,0872,92

0,13

T217,60

0,02

0,320,09

1,550,19

3,27

T314,33

0,02

0,270,09

1,250,18

2,52

Cc+Tt

0,08079,13

0,196194,41

0,435430,71

Mass Bal

90,5792,52

118,84

16Frother 45

C1

5,1142,57

5,1142,57

9,7549,82

49,829,75

63,11

11,8860,71

60,7111,88

31,3929,10

148,70148,70

29,1038,00

Collector 100

C2

2,0143,13

7,1285,70

3,346,71

56,537,94

71,6111,88

23,8884,59

11,8843,73

22,1044,42

193,1227,12

49,35

Depressant 300

C3

1,3638,22

8,48123,92

1,702,31

58,846,94

74,549,81

13,3597,93

11,5550,63

18,3024,89

218,0125,71

55,71

Air 10LC

41,80

45,5710,28

169,491,07

1,9260,76

5,9176,97

3,907,03

104,9610,21

54,2611,90

21,42239,43

23,2961,18

F990,29

0,0884,01

0,20197,66

0,39386,21

T950,20

0,0215,68

0,0872,26

0,18

T213,39

0,020,25

0,09

1,260,17

2,32

T316,42

0,020,30

0,091,42

0,142,25

Cc+Tt

0,08078,94

0,195193,42

0,395391,33

Mass Bal

93,9797,85

101,33

Appendix 14

Run no.

Reagents

Sample

Time,

Mass

Water

Cum

C

umAve cum

Std devStd error

Ave cum w

Std devStd error

Copper

Copper

Cum

Copper

Copper

AveStd dev

Std errorAve

Std devStd error

Nickel

Nickel

Cum

Nickel

Nickel

AveStd dev

Std errorAve

Std devStd error

SulphurSulphur

Cum

.Sulphur

SulphurAverage

Std devStd error

Average

min

Pull, gR

ec, gM

ass, gW

ater, gM

ass, gR

ec, g%

Mass

Copper

Grade

Rec

Copper grade

Copper rec

%M

assN

ickelG

radeR

ecN

ickel gradeN

ickel rec%

Mass

SulphurG

radeR

ecoveryS grade

S recovery

Mass

%%

%%

Mass

%%

%%

Mass

%%

%%

17Frother 50

C1

26,82

82,396,82

82,396,64

0,260,19

78,425,61

3,978,07

55,0155,01

8,0767,95

8,230,24

0,1766,60

1,911,35

11,8380,68

80,6811,83

39,8911,84

0,010,00

38,332,22

1,5724,60

167,77167,77

24,6043,75

25,551,34

0,9546,68

Collector 100

C2

41,72

56,258,54

138,648,40

0,210,15

134,575,76

4,072,54

4,3859,39

6,9573,36

7,100,21

0,1572,67

0,970,69

11,6219,99

100,6711,79

49,7811,77

0,030,02

48,212,22

1,5719,60

33,71201,48

23,5952,54

24,341,05

0,7456,30

Depressant 300

C3

61,80

64,7010,34

203,3410,14

0,290,21

222,0926,51

18,751,43

2,5761,95

5,9976,53

6,140,21

0,1575,82

1,000,70

6,5111,72

112,3910,87

55,5710,88

0,010,01

53,812,49

1,7615,10

27,18228,66

22,1159,63

22,861,05

0,7463,82

Air 10LC

48

2,1859,97

12,52263,31

12,210,44

0,31278,59

21,6015,28

0,661,44

63,395,06

78,315,22

0,220,15

77,640,94

0,672,68

5,85118,23

9,4458,46

9,490,07

0,0556,56

2,691,90

8,5218,57

247,2419,75

64,4820,65

1,280,91

69,48

F985,51

0,0986,44

0,20199,76

0,37362,67

T939,74

0,0214,85

0,0768,09

0,11101,49

T216,32

0,02

0,290,09

1,410,11

1,78

T316,93

0,02

0,310,09

1,460,17

2,90

Cc+Tt

0,08280,96

0,205202,24

0,389383,46

Mass Bal

93,66101,24

105,73

18Frother 50

C1

6,4574,45

6,4574,45

8,4054,19

54,198,40

65,24

11,8476,37

76,3711,84

36,7626,50

170,93170,93

26,5049,61

Collector 100

C2

1,8056,04

8,25130,49

3,115,59

59,797,25

71,9811,40

20,5296,89

11,7446,64

20,0036,00

206,9325,08

60,06

Depressant 300

C3

1,68110,34

9,93240,83

1,552,61

62,406,28

75,126,68

11,23108,12

10,8952,04

16,3027,38

234,3123,60

68,01

Air 10LC

41,97

53,0311,90

293,860,78

1,5463,94

5,3776,98

2,765,44

113,559,54

54,6611,30

22,26256,57

21,5674,47

F997,73

0,0986,43

0,20200,44

0,33330,25

T959,30

0,0216,02

0,0769,44

0,1093,82

T212,79

0,020,25

0,09

1,210,09

1,14

T313,74

0,020,27

0,101,33

0,091,23

Cc+Tt

0,08383,06

0,208207,75

0,345344,51

Mass Bal

96,10103,64

104,32

19Frother 60

C1

29,55

145,249,55

145,249,11

0,620,44

135,9613,13

9,295,85

55,8555,85

5,8567,88

6,170,46

0,3268,28

0,570,40

10,3098,37

98,3710,30

43,9810,51

0,300,21

43,530,63

0,4517,10

163,31163,31

17,1048,76

17,100,00

0,0040,92

Collector 100

C2

41,63

68,1011,18

213,3410,72

0,650,46

201,2517,10

12,102,85

4,6460,49

5,4173,51

5,660,35

0,2573,71

0,280,20

10,9417,83

116,2010,39

51,9510,58

0,270,19

51,580,52

0,3718,70

30,48193,79

17,3357,86

17,290,07

0,0548,66

Depressant 300

C3

61,53

73,1912,71

286,5312,29

0,600,43

280,238,92

6,301,60

2,4562,94

4,9576,49

5,120,24

0,1776,53

0,060,04

7,2211,05

127,2410,01

56,8910,11

0,140,10

56,530,51

0,3615,20

23,26217,04

17,0864,81

17,180,14

0,1055,26

Air 10LC

48

2,2380,69

14,94367,22

14,800,21

0,15371,67

6,294,45

0,661,48

64,424,31

78,294,35

0,060,04

78,430,19

0,132,74

6,10133,35

8,9359,62

8,830,14

0,1059,44

0,240,17

8,6919,38

236,4215,82

70,6015,82

0,010,00

61,14

F1001,64

0,0993,70

0,22216,05

0,49490,80

T960,33

0,0214,89

0,0767,82

0,08

T211,67

0,02

0,220,10

1,130,10

1,18

T314,70

0,02

0,260,09

1,270,10

1,45

Cc+Tt

0,08282,28

0,223223,67

0,334334,89

Mass Bal

87,81103,53

68,23

20Frother 60

C1

8,67126,67

8,67126,67

6,5056,32

56,326,50

68,68

10,7292,94

92,9410,72

43,0817,10

148,26148,26

17,1033,07

Collector 100

C2

1,5962,48

10,26189,15

2,704,29

60,615,91

73,9111,04

17,55110,50

10,7751,22

18,0028,62

176,8817,24

39,46

Depressant 300

C3

1,6084,77

11,86273,92

1,372,18

62,795,29

76,576,67

10,66121,16

10,2256,16

17,5028,00

204,8817,27

45,71

Air 10LC

42,79

102,1914,65

376,110,58

1,6364,42

4,4078,56

2,406,71

127,878,73

59,279,62

26,84231,72

15,8251,69

F983,48

0,0989,15

0,20198,56

0,45439,62

T944,38

0,0215,11

0,0768,13

0,18

T212,07

0,020,22

0,09

1,080,33

3,98

T312,38

0,020,22

0,091,13

0,121,45

Cc+Tt

0,08382,00

0,219215,73

0,456448,25

Mass Bal

91,98108,64

101,96

Appendix 15

Run no.

Reagents

Sample

Time,

Mass

Water

Cum

C

umAve cum

Std devStd error

Ave cum w

Std devStd error

Copper

Copper

Cum

Copper

Copper

AveStd dev

Std errorAve

Std devStd error

Nickel

Nickel

Cum

Nickel

Nickel

AveStd dev

Std errorAve

Std devStd error

SulphurSulphur

Cum

.Sulphur

SulphurAverage

Std devStd error

Average

min

Pull, gR

ec, gM

ass, gW

ater, gM

ass, gR

ec, g%

Mass

Copper

Grade

Rec

Copper grade

Copper rec

%M

assN

ickelG

radeR

ecN

ickel gradeN

ickel rec%

Mass

SulphurG

radeR

ecoveryS grade

S recovery

Mass

%%

%%

Mass

%%

%%

Mass

%%

%%

21Frother 60

C1

215,13

106,2815,13

106,2814,95

0,250,18

104,772,14

1,514,32

65,3865,38

4,3272,29

4,330,01

0,0171,85

0,630,45

7,21109,10

109,107,21

47,357,64

0,610,43

48,531,67

1,1817,20

260,24260,24

17,2052,39

17,050,21

0,1555,81

Collector 100

C2

410,47

110,6325,60

216,9125,10

0,710,50

211,517,64

5,400,65

6,8472,22

2,8279,85

2,840,03

0,0279,17

0,960,68

2,4125,22

134,325,25

58,305,51

0,370,26

58,740,62

0,443,76

39,37299,60

11,7060,32

11,710,01

0,0164,37

Depressant 100

C3

611,43

122,1837,03

339,0935,75

1,821,29

323,3922,20

15,700,18

2,0474,25

2,0182,11

2,050,07

0,0581,46

0,920,65

0,596,71

141,043,81

61,224,06

0,360,25

61,570,50

0,351,75

20,00319,61

8,6364,34

8,770,19

0,1468,57

Air 10LC

48

10,86109,91

47,89449,00

47,021,23

0,87439,32

13,709,68

0,091,03

75,281,57

83,251,58

0,020,01

82,670,81

0,570,34

3,66144,70

3,0262,80

3,160,20

0,1463,18

0,540,38

1,0811,73

331,336,92

66,706,94

0,040,03

71,51

F1003,87

0,0877,73

0,20196,66

0,42420,62

T933,65

0,0113,26

0,0766,57

0,09

T211,35

0,02

0,180,09

1,010,16

1,79

T310,98

0,02

0,170,09

1,000,19

2,06

Cc+Tt

0,09090,44

0,230230,40

0,495496,72

Mass Bal

116,35117,16

118,09

22Frother 60

C1

14,77103,26

14,77103,26

4,3364,00

64,004,33

71,40

8,08119,31

119,318,08

49,7216,90

249,61249,61

16,9059,23

Collector 100

C2

9,83102,84

24,60206,10

0,656,36

70,362,86

78,502,31

22,72142,03

5,7759,18

3,9438,73

288,3411,72

68,42

Depressant 100

C3

9,86101,59

34,46307,69

0,212,07

72,432,10

80,810,67

6,56148,59

4,3161,92

1,8718,44

306,788,90

72,79

Air 10LC

411,69

121,9446,15

429,630,10

1,1673,59

1,5982,10

0,343,95

152,543,31

63,561,27

14,85321,63

6,9776,32

F984,29

0,0881,70

0,21205,52

0,41405,53

T913,06

0,0214,43

0,0767,69

0,15

T214,44

0,020,25

0,09

1,350,15

2,15

T310,64

0,020,18

0,090,99

0,060,68

Cc+Tt

0,09189,63

0,244239,99

0,428421,45

Mass Bal

109,72116,77

103,93

23Frother 45

C1

210,26

51,3910,26

51,399,78

0,690,49

46,566,84

4,845,42

55,6555,65

5,4262,86

5,590,23

0,1647,90

21,1614,96

8,6488,66

88,668,64

36,778,88

0,340,24

36,410,51

0,3618,00

184,68184,68

18,0049,52

20,002,83

2,0045,78

Collector 100

C2

49,06

67,5019,32

118,8919,34

0,020,02

118,260,89

0,631,18

10,6666,31

3,4374,90

3,390,05

0,0457,49

24,6317,42

3,8134,47

123,136,37

51,076,33

0,060,04

51,460,55

0,395,95

53,91238,59

12,3563,97

13,081,03

0,7359,47

Depressant 100

C3

68,92

66,5628,24

185,4528,65

0,570,40

189,726,04

4,270,32

2,8369,14

2,4578,10

2,390,08

0,0560,01

25,5818,08

1,4012,51

135,644,80

56,264,72

0,110,08

56,830,81

0,573,03

27,03265,61

9,4171,22

9,780,52

0,3765,91

Air 10LC

48

8,7564,57

36,99250,02

37,761,09

0,77260,99

15,5110,97

0,151,30

70,441,90

79,571,85

0,080,05

61,1326,07

18,440,48

4,22139,87

3,7858,01

3,690,12

0,0958,57

0,790,56

2,4321,26

286,887,76

76,927,87

0,170,12

70,12

F984,04

0,1097,66

0,22219,05

0,45439,87

T928,87

0,0113,84

0,0764,98

0,1090,84

T29,01

0,02

0,180,11

0,960,09

0,78

T39,17

0,02

0,170,11

0,980,10

0,88

Cc+Tt

0,09088,53

0,245241,11

0,379372,96

Mass Bal

90,66110,07

84,79

24Frother 45

C1

9,2941,72

9,2941,72

5,7553,40

53,405,75

32,93

9,1284,69

84,699,12

36,0522,00

204,38204,38

22,0042,03

Collector 100

C2

10,0675,91

19,35117,63

1,1511,57

64,973,36

40,073,69

37,12121,81

6,3051,85

6,2562,88

267,2613,81

54,97

Depressant 100

C3

9,7076,36

29,05193,99

0,313,01

67,982,34

41,931,35

13,06134,87

4,6457,40

2,8327,45

294,7110,14

60,61

Air 10LC

49,48

77,9738,53

271,960,13

1,2569,23

1,8042,70

0,434,05

138,923,61

59,131,39

13,18307,88

7,9963,32

F997,37

0,0987,36

0,21209,65

0,42422,88

T936,97

0,0214,15

0,0763,93

0,0981,14

T212,61

0,182,22

0,10

1,210,10

1,31

T39,26

0,020,16

0,100,96

0,272,48

Cc+Tt

0,163162,14

0,236234,94

0,488486,23

Mass Bal

185,60112,07

114,98

Appendix 16

Run no.

Reagents

Sample

Time,

Mass

Water

Cum

C

umAve cum

Std devStd error

Ave cum w

Std devStd error

Copper

Copper

Cum

Copper

Copper

AveStd dev

Std errorAve

Std devStd error

Nickel

Nickel

Cum

Nickel

Nickel

AveStd dev

Std errorAve

Std devStd error

SulphurSulphur

Cum

.Sulphur

SulphurAverage

Std devStd error

Average

min

Pull, gR

ec, gM

ass, gW

ater, gM

ass, gR

ec, g%

Mass

Copper

Grade

Rec

Copper grade

Copper rec

%M

assN

ickelG

radeR

ecN

ickel gradeN

ickel rec%

Mass

SulphurG

radeR

ecoveryS grade

S recovery

Mass

%%

%%

Mass

%%

%%

Mass

%%

%%

25Frother 50

C1

213,59

79,5713,59

79,5713,49

0,150,11

80,581,43

1,014,84

65,7565,75

4,8470,11

4,760,11

0,0870,43

0,450,32

7,54102,51

102,517,54

41,887,71

0,230,17

44,333,47

2,4518,90

256,85256,85

18,9052,80

18,650,35

0,2553,44

Collector 100

C2

410,34

94,5723,93

174,1423,60

0,470,33

173,101,47

1,040,66

6,8472,59

3,0377,41

3,010,03

0,0277,92

0,720,51

2,6727,57

130,085,44

53,145,52

0,120,09

55,523,38

2,394,44

45,91302,76

12,6562,24

12,420,33

0,2462,23

Depressant 100

C3

610,04

90,7933,97

264,9333,51

0,660,47

262,872,92

2,070,23

2,2874,88

2,2079,85

2,190,02

0,0280,38

0,750,53

0,727,23

137,304,04

56,094,10

0,080,06

58,543,47

2,461,86

18,67321,44

9,4666,08

9,290,25

0,1866,10

Air 10LC

48

9,1884,37

43,15349,30

43,210,08

0,06352,27

4,192,97

0,131,17

76,041,76

81,091,72

0,050,04

81,660,80

0,560,40

3,67140,97

3,2757,59

3,270,00

0,0060,14

3,612,56

1,2211,20

332,637,71

68,387,48

0,330,23

68,62

F1001,54

0,0989,12

0,21206,22

0,42420,65

T940,20

0,0214,67

0,0770,31

0,44

T26,24

0,02

0,130,13

0,790,13

0,80

T311,95

0,02

0,200,09

1,080,19

2,29

Cc+Tt

0,09493,77

0,244244,79

0,486486,46

Mass Bal

105,22118,71

115,64

26Frother 50

C1

13,3881,59

13,3881,59

4,6962,73

62,734,69

70,75

7,88105,37

105,377,88

46,7818,40

246,19246,19

18,4054,07

Collector 100

C2

9,8890,47

23,26172,06

0,696,80

69,532,99

78,432,54

25,07130,43

5,6157,91

3,7637,15

283,3412,18

62,23

Depressant 100

C3

9,7888,74

33,04260,80

0,232,20

71,732,17

80,910,71

6,96137,39

4,1661,00

1,8117,70

301,049,11

66,12

Air 10LC

410,23

94,4343,27

355,230,11

1,1672,89

1,6882,22

0,373,82

141,213,26

62,701,22

12,48313,52

7,2568,86

F1004,46

0,0993,55

0,23227,61

0,46458,03

T935,25

0,0214,68

0,0768,05

0,22

T214,58

0,020,24

0,08

1,230,16

2,35

T311,36

0,020,19

0,091,03

0,131,52

Cc+Tt

0,08888,65

0,224225,23

0,453455,30

Mass Bal

94,7798,95

99,40

27Frother 45

C1

218,51

56,1818,51

56,1817,71

1,130,80

50,068,66

6,133,95

73,0473,04

3,9574,24

4,070,17

0,1273,09

1,631,15

4,5283,74

83,744,52

35,294,58

0,080,06

33,981,86

1,318,76

162,15162,15

8,7647,22

10,632,64

1,8747,25

Collector 100

C2

418,26

80,2236,77

136,4035,96

1,150,81

127,7812,20

8,630,34

6,2679,30

2,1680,60

2,180,03

0,0279,63

1,370,97

2,8251,57

135,313,68

57,033,66

0,030,02

55,122,70

1,913,43

62,63224,78

6,1165,46

7,191,53

1,0865,27

Depressant 0

C3

613,84

79,3550,61

215,7549,97

0,910,64

199,8722,46

15,890,15

2,0881,38

1,6182,72

1,610,00

0,0081,83

1,260,89

0,7710,70

146,012,88

61,542,86

0,040,03

59,862,37

1,681,87

25,88250,66

4,9572,99

5,811,21

0,8673,31

Air 10LC

48

9,2675,71

59,87291,46

58,901,37

0,97267,36

34,0924,11

0,111,05

82,421,38

83,781,38

0,010,01

82,851,31

0,930,47

4,32150,33

2,5163,36

2,500,02

0,0161,62

2,461,74

1,4513,43

264,094,41

76,905,18

1,090,77

77,02

F1001,24

0,1099,61

0,24240,50

0,45451,56

T919,17

0,0215,07

0,0767,38

0,19

T212,13

0,02

0,200,09

1,090,09

1,11

T310,07

0,02

0,180,09

0,950,08

0,78

Cc+Tt

0,09898,38

0,237237,26

0,343343,40

Mass Bal

98,7698,65

76,05

28Frother 45

C1

16,9143,93

16,9143,93

4,1870,75

70,754,18

71,94

4,6478,46

78,464,64

32,6712,50

211,38211,38

12,5047,29

Collector 100

C2

18,2475,22

35,15119,15

0,366,61

77,362,20

78,662,71

49,34127,80

3,6453,21

4,3679,53

290,908,28

65,08

Depressant 0

C3

14,1864,83

49,33183,98

0,162,24

79,601,61

80,940,84

11,95139,76

2,8358,18

2,6938,14

329,056,67

73,62

Air 10LC

48,60

59,2757,93

243,250,11

0,9780,57

1,3981,92

0,484,09

143,842,48

59,891,83

15,74344,78

5,9577,14

F983,95

0,0217,12

0,21210,07

0,36353,24

T908,50

0,0215,72

0,0768,06

0,24

T27,81

0,020,15

0,11

0,840,13

1,02

T39,71

0,020,19

0,100,97

0,090,87

Cc+Tt

0,10098,35

0,244240,20

0,454446,97

Mass Bal

574,44114,34

126,54