-
DEVELOPING SIMPLE REGRESSIONS FORPREDICTING GOLD GRAVITY
RECOVERY IN
GRINDING CIRCUIT
Zhixian Xiao
A thesis submitted to theFaculty of Graduate Studies and
Research
In partial fulfillment of the requirement for the degree
ofMaster of Engineering
Department of Mining, Metals and Materials EngineeringMcGill
UniversityMontral, Canada
September 2001
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Abstract
Determining whether or not a gold gravity circuit should be
installed in a gold
plant requires a prediction of how much goId will be recovered.
This has always been a
difficult task because recovery takes place from the grinding
circulating load, in which
gold's behavior must be described.
A population-balance mode! (PBM) to predict gold gravity
recovery wasdeveloped at McGill University in 1994 (Laplante et al,
1995). The objective of thisresearch was to make this PBM user
friendly. This was achieved in two different ways.
First, the behavior of gravity recoverable gold (GRG) in
secondary ball mills andhydrocyclones was described by two
parameters, 't and R..25Ilm, and these parameters
were linked to the circulating load of ore and the fineness of
the grinding circuit
product, for easy estimation. Second, the database of
simulations produced by the PBM
was represented by two multilinear regressions (one for coarse
GRG, the other for fineGRG) linking the predicted GRG recovery to
the naturallogarithm of 't, R-25Ilm, the sizedistribution of the
GRG and the recovery effort (Re), defined as the proportion, in %,
ofthe GRG in the circulating load recovered by gravity. Re was
found to be the most
significant parameter, 't the least. The GRG size distribution,
represented either by two
(coarse GRG) or three (fine GRG) points on the cumulative
passing curve, has asignificant impact on recovery. A total of
twenty different GRG size distributions were
used to generate the simulation database.
The multilinear regressions were tested on four case studies,
and found topredict GRG recovery well within the precision with
which the GRG content can be
measured, a relative 5%. Whenever size-by-size recovery data are
available, the PBM
itself would be used; if not, the simpler regressions would be
preferred.
-
11
Rsum
Pour justifier l'installation d'un circuit gravimtrique dans un
concentrateur, ondoit, au minimum, pouvoir estimer la quantit d'or
qui sera rcupre. Cette tche est
ardue, car la rcupration se fait de la charge circulante au
broyage, dans laquelle le
comportement de l'or doit tre dcrit.
Un modle d'quilibrage de population (MEP) permettant d'estimer
larcupration gravimtrique de l'or a t dvelopp l'universit McGill en
1994
(Laplante et al, 1995). Le but de cette thse tait de rendre ce
modle convivial. Letravail s'est fait en deux tapes. D'abord, nous
avons dcrit le comportement de l'or
rcuprable par gravimtrie (ORG) dans les broyeurs boulets
secondaires et leshydrocyclones l'aide de deux paramtres, 1 et
R-25J.lm, pour ensuite faire le lien entre
ces paramtres, la charge circulante et la finesse de broyage,
afin de faciliter leur
estimation. Par la suite, nous avons reprsent la base de donnes
obtenues du MEP par
deux rgressions multilinaires (une pour l'ORG grossier, l'autre
pour l'ORG fin)faisant le lien entre la rcupration de l'ORG et le
logarithme naturel des variables
indpendantes, soient 1, R..25J.lffi, la distribution
granulomtrique de l'ORG et l'effort de
rcupration (Re), dfini comme tant le pourcentage de l'ORG de la
charge circulantequi est rcupr. De tous les paramtres, Re a le plus
d'impact et 1 le moins. La
distribution granulomtrique de l'ORG, reprsente soit par deux
paramtres pour
l'ORG grossier ou trois pour l'ORG fin, a un impact majeur sur
la rcupration, qui at dtermin en simulant la rcupration de 20
granulomtries diffrentes.
Les rgressions multilinaires, utilises pour quatre tudes de cas,
ont pu estimer
la rcupration en ORG avec une prcision au moins gale de celle
avec laquelle la
quantit d'ORG peut tre estime, soit environ 5% (relatif). Nous
recommandonsl'utilisation du MEP lorsqu'un estim de la rcupration
de l'ORG en fonction de la
taille des particules est disponible; sinon, les rgressions
doivent tre utilises.
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111
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IV
Acknowledgements
1 would like to thank Professor A. R. Laplante for his keen
insight, WIseguidance, enthusiasm and constant support during this
program. 1 'd like to thank him
for allowing me to work at my own pace and his invaluable help
in technical writing
skills and oral skills in the discussion, especially for his
correction of the thesis during
his sabbaticalleave.
1 would also like to thank Professor J. A. Finch for his
inspiring lectures andsuggestions about the presentation.
1 wish to thank my friends and colleagues in the Mineral
Processing group,
especially the Gravity Separation group: Mr. R. Langlois for his
instruction in computer
skill; Dr. Liming Huang for his valuable technical discussions
and endless help in my
daily life.
1 also wish to thank the Natural Sciences and Engineering
Research Council of
Canada for their research funding.
Last but not least, 1 extend my warmest thanks to my parents and
parents-in-Iawfor their support and encouragement, my sweet
daughter Jessica Xiao for her
cooperation and the fun she gives me and my wife for her
continued support,
encouragement and love.
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Table of Contents
Abstract
Rsum 11Zhaiyao 111
Acknowledgements IV
Table of Contents V
List of Figures VI
List of Tables Vll
List of Abbreviations Xl
v
Chapter 1: Introduction1.1 Background
1.1.1 Oravity Recoverable Oold and
Predicting the Oold Recovery
1.1.2 Oold Behaviour in Orinding Circuits
1.1.3 Advantages of Recovering Oold by Gravity
1.2 Objectives of the Study1.3 Thesis Structure
Chapter 2: Gravity Recoverable Gold: A Background2.1
Introduction
2.2 Gravity Recoverable Gold
2.2.1 ORO Potential of Ores
2.2.2 ORO Available in Streams
2.3 Unit Processes
1
1
2
3
56
7
9
9
9
10
13
15
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2.3.1 Comminution and Classification 162.3.1.1 The Breakage
Function 162.3.1.2 The Selection Function 182.3.1.3 Investigation
of Go1d's Behaviour in Comminution 182.3.1.4 Go1d's Behaviour in
Cyclone 20
2.3.2 Recovery Dnits 23
2.3.2.1 Knelson Concentrator 23
2.3.2.2 Table 26
2.3.2.3 Jigs 27
Chapter 3: Simulating Gold Gravity Recovery 323.1 Introduction
323.2 The GRG Population Balance Model 32
3.2.1 A Simplified Approach 32
3.2.2 The Full PBM 393.3 Input Data for the PBM 43
3.3.1 GRG Data (F Matrix) 433.3.2 Dnits Matrices 45
Chapter 4: Simulation Results 524.1 Introduction 524.2
Simulation Results 52
4.2.1 Basic Case Study 524.2.2 Gravity Recovery Effort 554.2.3
Impact of Operating Variables 56
4.3 Representing Results with Mu1tilinear Regressions 614.3.1
Criteria and General Approach for Representing
the Simulated Database
61
VI
-
4.3.2 Regressions for Fine and Coarse GRG Size Distributions
62
4.3.3 Comparing the Regressions and Original PBM and
Testing for Phenomenological Correctness 64
4.4 Estimation of't and R.25 ~m 694.4.1 Representing the
Grinding Circuit Design
Parameters with 't and R.25 ~m 694.4.2 Case Study 72
Chapter 5: Model Reliability and Validation 745.1 Introduction
74
5.2 Model Reliability 74
5.2.1 GRG-25~m, GRG-75~m, GRG-150~m and F Matrix 745.2.2 R-25~m
and C Matrix 775.2.3 't and B Matrix 79
5.2.4 Re and R Matrix 795.3 Model Validation 80
5.3.1 Campbell Mine Case Study 80
5.3.2 Northem Qubec Cu-Au Ore Case Study 835.3.3 Case Study:
Snip Operation 84
5.3.4 Case Study: Bronzewing Mine 86
5.4 Model Extrapolation and Applications 88
5.4.1 Model Extrapolation 88
5.4.2 Model Applications 89
Chapter 6: Conclusions and Future Work 916.1 Introduction 91
6.2 General Conclusions 91
6.3 Strengths and Weaknesses ofProposed Protocol 93
Vll
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6.5 Future Work 94
References 97
Appendix A: Breakage and selection function used for GRG and ore
103
Appendix B: Grinding matrix for GRG and ore 105
Appendix C: GRG used for simulation 110
Appendix D: An example for simulation 112
Appendix E: Database used for generation ofregressions 117
Appendix F: Regression ANOVA Table for Coarse and Fine GRG
131
Appendix G: Database for generating the relationship between 1,
R-25~m andcirculating load, fineness of grind. Regression ANOVA
Table 135
Vlll
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IX
List of Figures
Figure 2-1 Procedure for measuring GRG content with a KC-MD3
Il
Figure 2-2 Cumulative GRG recovery of three stages as function
of particle size 13
Figure 2-3 Typical partition curve for gangue, goId and GRG
21
Figure 2-4 Partition curves of the secondary cyclones ofNew
Britannia 22
Figure 2-5 Schematic cross-section of a Knelson Concentrator MD3
24
Figure 2-6 Basic Jig construction 29
Figure 2-7 Comparing size-by-size recovery of a KC and a Duplex
Jig 30
Figure 3-1 Simple circuit of gravity recovery from the baIl mill
discharge 33
Figure 3-2 Simple circuit of gravity recovery from the cyclone
underflow 35Figure 3-3 Circuit of gravity recovery from the cyclone
underflow using
a size-by-size approach 37
Figure 3-4 Recovery from the second mill discharge 40
Figure 3-5 Recovery from the cyclone underflow 41Figure 3-6
Recovery from the primary cyclone underflow 42
Figure 3-7 Normalized GRG distributions of the original data set
43
Figure 3-8 Coarse and fine GRG size distributions (down to 25
!-lm) used forsimulation (Hatched lines: fine GRGs; solid lines:
coarse GRGs) 45
Figure3-9 Partition curves of GRG and ore for the three
classification cases
(fine, intermediate, coarse) 51
Figure 4-1 GRG recovered in various size class when treating
bleeds of
5 and 12% 55Figure 4-2 GRG recovery as function of recovery
effort with coarse,
Intermediate and fine classification 57Figure 4-3 the impact of
GRG size distribution to GRG recovery 58
-
Figure 4-4 %GRG in size fractions as a function of the Pso for
the
phoenix NNX3 sample 59Figure 4-5 GRG recovery as a function of
the recovery effort for fine
(Pso =75 !-lm) coarse (Pso=150 !-lm) grinding, NNX-3 sample
60Figure 4-6 Comparison of PBM and regression for fine GRG 65Figure
4-7 Comparing the PBM and the regression for a coarse
GRG distribution 66Figure 4-8 Effect of GRG size distribution of
GRG recovery 67Figure 4-9 GRG recovery decreases with the
increasing dimensionless
retention time in the mill 68Figure 4-10 Gravity recovery as a
function of the recovery effort for fine
GRG and for coarse, medium and fine classification curves 69
Figure 4-11 't as a function of the ore circulating load and
product size 71
Figure 4-12 R-25!-lm as a function of the ore circulating load
and product size 71Figure 4-13 GRG recovery as a function ofthe
recovery effort (Cu-Au ore) 73
x
Figure 5-1 Partition curve for ore*, gold* and GRG* with a
saprolitic component 77
Figure 5-2 Campbell Mine cumulative GRG as function of particle
size 80
Figure 5-3 GRG content retained as function of particle size
84
Figure 5-4 Cumulative GRG retained in each size class for
Bronzewing Mine 86Figure 5-5 Measured and predicted gold gravity
recoveries of the case studies 88
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List of Tables
Table 2-1 Differences between GRG determination for ores and
streams
Table 2-2 Coefficient used to correct the grinding matrix
Table 2-3 Typical values of Knelson Concentrator's recovery
Table 2-4 Typical values of Shaking Table's recovery used for
simulation
Table 2-5 Evolution of the use of Jigs and KC at certain
Canadian sitesTable 2-6 Typical values of Jig' s recovery used for
simulation'
Table 3-1 Normalized GRG distributions used for the
simulation
Table 3-2 Typical B matrix for GRG
Table 3-3 Parameters used to calculate the partition curves
Table 4-1 GRG size distribution ETable 4-2 The recovery matrix
P*R
Table 4-3 Grinding matrix B (for a 't value of 1)Table 4-4
Classification matrix C (for a R..25J.lm value of82.8%)Table 4-5
Variables of regression analysis
Table 4-6 Actual and normalized GRG size distribution for Midas
sample
Table 4-7 Actual and normalized GRG size distribution for
Campbell
Table 4-8 Effect of changing product fineness from 65 to 85%
minus
at a circulating load of 250%, for Re =5%
Table 5-1 Basic data from the Campbell grinding circuit
Table 5-2 Experimental and estimated data used for predicting
GRGRecovery in Campbell Mine
Table 5-3 Predicted and reported gold recovery for Campbell
Mine
Xl
14
20
25
27
28
31
44
49
50
54
54
55
55
646667
73
81
81
82
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XlI
Table 5-4 Sensitive analysis of the impact of relative change of
Re , 'r and R251lID 82Table 5-5 Data used for predicting GRG
recovery on Northern Qubec Cu-Au Ore 83Table 5-6 Data used for
predicting GRG recovery on Snip 85Table 5-7 Parameters used for
goId recovery prediction 87Table 5-8 Predicted and reported gold
recovery of Bronzewing Mine 87
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GRG
KC
LKC
CL
PM
GRG_x
ANOVA
PBM
int.
KC-CD3
KC-CD30
Pso
g/min
g/t
Gs
Kg/min
L!min
SAG
List of Abbreviations and Acronyms
Gravity Recoverable Gold
Knelson Concentrator
Laboratory Knelson Concentrator
Circulating Load
Perfect Mixer
Gravity Recoverable Gold content below certain size
Analysis of Variances
Population-Balance Model
intermediate (used in table)
3 in Center Discharge Knelson Concentrator
30 in Center Discharge Knelson Concentrator
the particle size at which 80% of the mass passes
grams per minute
grams per tonne
times of gravity acceleration
kilogram per minute
litre per minute
semi-autogenous
Xl1l
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CHAPTERONE
CHAPTERONE
INTRODUCTION
1.1 Background
INTRODUCTION 1
Gravity concentration of gold remained the dominant mineraI
processing method
for thousands of years, and it is only in the twentieth century
that its importance
declined, with the development of the froth flotation and
cyanidation. However, in
recent years, gravity systems have been reevaluated due to
increasing flotation costs, the
environmental and health hazards associated with cyanide, and
the relative simplicity
and low cost of gravity circuits, and the fact that they produce
comparatively little
pollution. Particularly over the past twenty years, goId gravity
recovery has evolved
significantly because of the advent of the new technologies,
such as Knelson and Falcon
Concentrators.
Treatment methods for the recovery of gold from ores depend on
the type of
mineralization. Gold ores in which sulphides are largely
oxidized are best treated by
cyanidation; gold ores that contain their major values as base
metals, such as copper,lead and zinc, are generally treated by
flotation; gold that is intimately associated with
pyrite and arsenopyrite, and usually with non-sulphide gangue
mineraIs, is frequentIy
treated with the combination of flotation, sulphides oxidation
and cyanidation (Marsdenand House, 1992). However, no matter in
which form gold exists, sorne is liberated ingrinding circuits
where it accumulates because of its density and malleability
(Basini et
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CHAPTERONE INTRODUCTION 2
al 1991). Therefore, gravity concentration can be incorporated
in the recoveryflowsheet. Dorr and Bosiqui (1950) emphasized the
importance ofrecovering gold fromthe grinding circuit and advocated
gravity concentration, especially for those ores in
which a significant proportion of the goId is associated with
base metal sulphides. In
flotation and cyanidation plants, a gravity circuit is often
used within grinding circuits,
after a baIl mill discharge or cyclone underflow (Agar, 1980;
Anon, 1983).
1.1.1 Gravity Recoverable Gold and Predicting the Gold
Recovery
The term "Gravity Recoverable Gold" (GRG) is easily confused
with the term"free gold". "Free gold" refers to gold that is
readily extracted by cyanide at reasonable
grinds, typically when the ore is ground to a size of 80% below
75 Ilm. It can represent
a measure of the degree of 1iberation of the gold. "Gravity
Recoverable Gold" (GRG)refers to that portion of gold present in
ores or mill streams that can be recovered by
gravity into a very small concentrate mass 1%) under ideal
condition. GRG includesgold that is not totally liberated.
Generally, the amount of gold that can be recovered by
cyanidation is much higher than the GRG content.
The McGill University research group has already developed a
method of
characterizing GRG in an ore. The details will be discussed in
chapter two. The research
group has also proposed the use of Population-Balance Model
(PBM) to predict GRGbehaviour in grinding circuits, either with or
without gravity recovery. In this thesis, the
characterization of GRG and prediction of gravity recovery will
be presented as two
different concepts. Characterizing the GRG content of an ore is
not in itself a prediction
of how much gold will be recovered by gravity. Since GRG
accumulates in the
circulating load of grinding circuits, predicting gravity
recovery must incorporate a
description of this behaviour, as it determines how often a GRG
particle or its progeny
can be presented to a recovery unit that treats either all or
part of the circulating load.
Most methods of predicting gold gravity recovery fail to take
into account this dynamic
-
CHAPTERONE INTRODUCTION 3
component of gold recovery. For example, a pilot centrifuge unit
installed in the
circulating load of an existing circuit may weIl recover gold
effectively but its
performance reveals little about (a) how much gold will be left
in the circulating loadonce a full scale unit is installed or (b)
how much goId will be recovered at steady-stateby a full-scale,
similar recovery unit.
Earlier Knelson Concentrator applications were largely
retrofits, in plants where
gravity recovery was either not used or implemented with older
equipment, typically
jigs in North America and spirals in Australia. Retrofitting one
or many centrifuge unitsin an existing plant is generally a
low-risk, low-retum endeavor. Few operating savings
can be generated from downstream recovery circuits (e.g.
flotation, cyanidation), ascapital costs have already been sunk.
For such applications, predicting how much gold
will be recovered by gravity is often not critical.
Many green field projects, on the other hand, rely heavily on
gravity recovery toreduce the downstream processing effort,
resulting in significant savings in capital and
operating costs. For example, a gold-copper ore can be treated
by a combination of
gravity-flotation for a much lower cost than
flotation-cyanidation. As much as 25% ofcapital and operating costs
can thus be truncated, and the resulting flowsheet would be
environmentally more attractive, if only for political reasons.
For such projects, theeconomic and metallurgical impact of gravity
is such that reliable prediction of how
much gold will be recovered is critical. Even for projects where
gravity plays a lesserrole, predicting how much gold can be
recovered by gravity is desirable, if only to
justify the cost of gravity.
1.1.2 Gold Behaviour in Grinding Circuits
Gold's malleability and high specific gravity in grinding
circuits are unusual and
affect aIl important mechanisms: breakage, liberation and
classification. The specific
-
CHAPTERONE INTRODUCTION 4
rate of breakage (selection function) of gold is 5 to 20 times
lower than that of itsgangue (Banisi, et. al. 1991); therefore, it
moves slower from its natural grain size intofiner size classes
than its gangue. Gold, and particularly GRG, also has a
distinctbehaviour in hydrocyclones, whereby typically more than 98%
of all GRG fed to
cyclone reports to its underflow. Even below 25 !J.m, between
65% and 95% of GRG
still reports to underflows (depending on the fineness of
grind). For example, atAgnico-Eagle, despite the very high density
of the gangue (more than 50% sulphides),the Dso of gold was three
times smaller than that of the gangue (Buonvino, 1994). Thisyielded
recoveries to the underflow of 98% and more for all size classes
above 371lm.
Generally speaking, in the absence of gravity recovery gold
particles above 75 !J.m (ortheir progeny) circulate between 50 and
100 times in a grinding circuit and build up tovery high
circulating loads, 2000-8000%, and often leave the grinding circuit
only oncethey are overground (Laplante, 2000. Basini et al, 1991).
Thus, in the absence ofgravity, free gold disappears slowly from
coarser size classes through grinding, and
most of it reappears as GRG in finer size classes. In finer size
classes, grinding kinetics
is very slow, and GRG disappears much more by classification to
the cyclone overflow
(Laplante et al, 1994). This can cause losses due to
overgrinding or surface aging orpassivation, difficulties in the
estimation of the head grade or high gold inventories.
In a grinding circuit, the streams that contain a significant
portion of the gold forgravity concentration are the ball mill
discharge, the primary cyclone underflow and
perhaps the SAG mill discharge (Agar, 1992). In most gold mines,
the primary gravityconcentrator usually treats part or all of the
primary cyclone underflow or ball mill
discharge to recover liberated gold. The primary gravity
concentrate is then upgradedwith a shaking table to obtain a final
goId concentrate, which is directly smelted to
produce bullion containing 90-98% gold plus silver (Huang,
1996).
-
CHAPTERONE INTRODUCTION 5
1.1.3 Advantages of Recovering Gold by Gravity
Recovering gold from the circulating load of grinding circuits
yields significant
benefits from both design and operating perspectives: (i) the
payment for gold bullionis more than 99% and is received almost
immediately, while gold in flotationconcentrate is only paid 92-95%
three or four months later (Wells and Patel, 1991;Huang, 1996);
(ii) gold overgrinding is reduced and the amount of gold locked
upbehind mill liners is minimized*; (iii) the removal of some of
the gold by gravityconcentration can reduce the number of stages
and the lock-up of goId in the CIP plant
(Loveday et al, 1982); (iv) the overall goId recovery can be
improved by reducingsoluble losses and recovering large or slow
leaching gold particles that would otherwise
be incompletely leached (Loveday et al, 1982); (v) for
flotation, the risk of goldparticles advancing to flotation that
are too coarse to float is reduced and the floatability
may be increased because of reduced surface aging and (vi)
overall gold recovery canalso be increased by recovering gold
smeared cnte other particles or embedded by other
particles (Banisi, 1990; Darnton et al, 1992; Ounpuu, 1992).
Due to the diversity of gold ore types and performance of
gravity recovery units,
different levels of success have been reported. For example,
Goldcorp's Red Lake Mine
processes a high-grade goId ore and recovers a high proportion
(+50%) of the golddirectly from the grinding circuit with a Knelson
CD20 Concentrator that improves
leaching efficiency and helps to maintain high overall plant
recovery. The recovery of
coarse goId in the grinding circuit of the Tsumeb mill by using
high-tonnage gravityseparation equipment (a Reichert cone) has
resulted in significant decreases in theconsumption of reagents in
the oxide flotation circuit (Venter et al, 1982). Gravity
goldrecovery at the Homestake mill in the United States changed an
unacceptable overall
In South Africa, it is estimated that 8% of the gold mined is
stolen, much ofit from the holdup behind millliner
-
CHAPTERONE INTRODUCTION 6
recovery to acceptable levels and in the OK Tedi project in New
Guinea, a one percentincrease in the overall recovery was obtained
(Hinds, 1989; Lammers, 1984).
Despite the many advantages of gold gravity recovery it is
equally obvious that
not everyone is convinced of the benefits of installing and
operating a gravity
concentration circuit. The most important reason perhaps is the
lack of a reliable,
proven method for predicting, on a laboratory scale, whether or
not the ore is amenable
to gravity recovery and what the recovery of gold in a
concentrate would be if the
gravity separation were used (Gordon, 1992). A methodology for
characterizing gravityrecoverable gold (GRG) was used successfully
to estimate the gold liberation of over 75samples (Laplante et al,
1993). The main stumbling block in the application of
gravityseparation of gold appears to be the lack of a suitable
technique to predict from the
GRG data what the recovery of goId would be in a grinding
circuit. In this study, gold
gravity recovery from grinding circuits is first represented by
a population-balance
mode! (PBM). Second, the inputs of the PBM are linked to the
predicted goId recoveryusing multi-linear regressions. Third, the
developed regressions are linked to a new
concept, the recovery effort, the Pso of gravity recoverable
gold (GRG), the retentiontime in the mill and the partition curve
of GRG. These concepts are represented by
regression parameters that are easy to measure or calculate.
1.2 Objectives of the Study
The objectives ofthis study are as follows:
1). To simulate the gravity recoverable goId recovery in
grinding circuits using apopulation balance model.
2). To develop simple regressions for predicting GRG recovery
using the gravityrecovery effort (Re), the GRG content, the
dimensionless retention time in the
-
CHAPTERONE INTRODUCTION 7
mill (1") and the partition curve of GRG (the fraction of GRG
below 25 /lmreports to the cyclone underflow, R..25Ilm)'
3). To assess the sensitivity of predicted goId recovery to the
parameters of thePBM.
4). To test the reliability of the method using real case
studies.
1.3 Thesis Structure
This thesis consists of six chapters. This chapter introduces
the background of
this program, which includes briefly describing gold's behaviour
in grinding circuits,
the advantages of recovering gold from grinding circuit and the
rationale behind this
research. The objectives ofthis study and the thesis structure
are also presented here.
Chapter two provides the background on what gravity recoverable
gold (GRG)is and how to measure the GRG potential of ores and the
GRG available in the various
streams of a grinding circuit. The most relevant units for
comminution, classification
and goId recovery will be presented.
Chapter three introduces the GRG population balance model (PBM),
first usinga simplified approach, then as it is actually used to
predict gravity recovery. How to
estimate or generate the input data for the PBM will be
presented in this chapter. The
various unit matrices used in the PBM will be described at the
end of this chapter.
Chapter four introduces typical simulation results. It also
explores howimportant operating parameters affect the circulating
load and recovery of GRG. A new
concept, the gravity recovery effort, is presented. Results are
then summarized into
multilinear regressions for coarse and fine GRG. A dimensionless
grinding retention
-
CHAPTERONE INTRODUCTION 8
time, 't, and the recovery of GRG in the 25 /lm fraction to the
underflow of cyclone, K
25!1m, are then linked to the circulating load of ore and the
product size of the grinding
circuit. Finally, a case study is presented.
The reliability of the model is discussed in Chapter five.
Several case studies are
used to validate the model. Finally, mode! extrapolation and
applications are briefly
discussed.
General conclusions and suggestions for the future work are
presented ln
Chapter six.
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 9
CHAPTERTWO
GRAVITY RECOVERABLE GOLD:A BACKGROUND
2.1 Introduction
Predicting goId gravity recovery from grinding circuits has
always been a
difficult task. To address this problem, a population-balance
model (PBM) wasproposed by Laplante (1992) (more details will be
presented in Chapter three). Themodel includes the necessary
concepts of gold liberation, grinding and classification
used in the simulation in later chapter. In this chapter, sorne
of important concepts used
in the PBM will be reviewed; gravity recoverable gold (GRG)
characterization will bedescribed and GRG behaviour in comminution,
classification and recovery units
presented.
2.2 Gravity Recoverable Gold
Gravity recoverable goId (GRG) is a concept used to characterize
ores for theirgravity recoverable goId content. The amenability of
an ore to gravity recovery is the
single most important parameter to justify the installation of a
gravity circuit (Laplante,et al., 1993). Therefore, the ore must be
characterized for its gravity recovery potential,as it is ground
and progressively liberated. This is the most common definition of
GRG,
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 10
and the GRG test is designed to address this question. GRG
behaviour in ooits must also
be characterized, particularly in the units used to grind and
classify and ooits to recover
GRG. If the GRG content of an ore is to be fully used, its
behaviour in the various units
of a grinding circuit must be measured, then modeled. This is
achieved by measuring
the GRG content in the streams entering or exiting the ooits.
From this point of view,
there is a difference between characterization of GRG in an ore
and in a stream. The
characterized GRG of an ore measures a potential for gravity
recovery. The relevant
GRG content of a stream, by contrast, is the GRG content that is
already liberated and
available for gravity recovery.
Gravity Recoverable Gold (GRG) refers to the portion of gold in
an ore orstream that can be recovered by gravity at a very low
yield 1%). It includes gold thatis totally liberated, as well as
gold in particles that are not totally liberated but with such
density that they report to the gravity concentrate. Conversely,
it excludes fine,
completely liberated gold that is not recovered by gravity
because of the improper
characteristics such as shape factor and size or gold contained
in gold carriers in such
small quantities that the specific gravity of the particle is
not affected. Information
about the GRG in an ore or stream can be used for different
purposes: if gravity
concentration exists in the circuit, the GRG information can be
used to either determine
if the circuit is optimized or assist in its optimization. If
there is no gravity
concentration in the existing circuit, the amount and size
distribution can be used as one
of factors to justify whether a gravity concentration circuit
should be installed and thebenefit of installing it.
2.2.1 GRG Potential of Ores
Despite advances in competing technologies, gravity
concentration remains an
attractive option due to its low capital and operation cost,
even at the beginning of the
third millennium. This continued interest has spurred research
in new technologies,
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 11
most of which rely on separation in centrifugaI field (sometimes
called enhancedseparation). The Kneison Concentrator (KC) has been
by far the most commerciallysuccessfui centrifuge unit used for
goId recovery. It was therefore appropriate to choosea Iaboratory
scaie KC to measure GRG content.
The procedure is shown in Figure 2-1.
Samples
(50 kg)
45-55% -751!m
-~l~
tailing
Main tail
tailing
stage 3
stage 1
850 to -20 I!m
850 to -20 I!m
Pulverizing +105 I!m
stage 2
conc.
r6
Figure 2-1 Procedure for Measuring GRG Content with a KC-MD3
The test is based on the treatment of a sample mass of typically
50-70kg with a
KC-MD3. Usually, three stages are used: for the first stage, the
representative ore
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 12
sample is crushed and pulverized to 100% -850 J.lm and then
processed with a 7.5 cm
KC-MD3. The entire concentrate is screened from 20 to 600 J.lm
and each size fraction
fire-assayed for extraction. The same procedure is performed on
a 600g sample of thetailing. For the second stage, the tailing of
stage 1 are split, and approximately a 27kg
sub-sample is ground in rod mills to a finer size, 45-55% -75
J.lm, and processed with
the KC-MD3 unit. The third stage repeats the above process with
the tailing of stage 2,
usually a mass of 24 kg, ground to 80% -75 /lm. Both
concentrates and 600 g samples
of the tailing are screened and assayed as for stage 1. The
assays of the three
concentrates and the tailing of stage 3 are used to estimate the
ORO content. The tailing
assays of stage 1 and 2 are used to estimate stage recovery and
assess assaying
reproducibility.
The Knelson tests are carried out at feed rates and fluidization
water flow rates
adjusted to match the feed size distribution, typically 1200
g/min and 7 L!min for stage1 to 400 g/min and 5 L!min for stage 3.
These correspond to optimal settings asdetermined by extensive test
work with both gold ores and synthetic feeds, but must be
adjusted for gangue density (Laplante, et al., 1996, Laplante,
et al., 1995). Because thetest is optimized in laboratory, it
yields the maximum amount of ORO; actual plant
ORO recoveries will be lower because of limitations in equipment
efficiency and in the
usual approach of processing only a fraction of the circulating
load.
Results are normally presented as size-by-size recoveries for
each stage and
overall recovery. By plotting the cumulative retained recovery
as a function of particle
size, from the coarsest to the finest size class, a graphie
presentation is obtained. Figure2-2 shows the results of a test for
sample from the Campbell mill feed (Balmertown,Ontario) (Laplante,
1999). For stage 1, recovery cumulates to 33% (for the finest
sizeclass, the minus 20 J.lm fraction, the lower limit is
arbitrarily set at a 15 J.lm). Resultsare also cumulated from stage
1 to stage 3, from 33%, the amount of ORO recovered
after one stage, to 68%, the total ORO content.
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 13
1000~ 1 Ji i
100Particle size (IJm)
4-~~~~~~~~~~~~~----I--"- stage
1"'i-~~~~~~~~~~-~~----I""""'-stage 24-~'----~--~~~~~~-~~---1--'-
stage 3
100~ 900~Q) 80>0 700! 60C)0::: 50C)
40Q).::: 30-..!!!
~ 20E~ 100
010
'--~-~~~~~~~~~~~~-~~~~~---~-~-
Figure 2-2 Typical Cumulative Gold Recovery of a GRG Test as a
Function of
Particle Size
2.2.2 GRG Available in Streams
For measuring the GRG content in streams, representative samples
are extractedand processed with a KC-MD3 operated to maximize
gravity recovery. As only GRG
that is already liberated is of importance, no grinding is used,
and each sample is
processed only once to simplify the procedure and minimize the
risk of recovering non-GRG. Putz (1994) and Vincent (1997) also
used a modified procedure to maximizeGRG recovery for difficult
separations, typically with high-density gangue. Typically,
a finer top size is used, or, for finer feeds, silica flour is
added to the sample to decreaseits overall specifie density.
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 14
There are several other laboratory methods to measure the GRG
content of a
stream. AH methods "recover" GRG in a concentrate stream.
TraditionaHy,
amalgamation has been the conventional methods of measuring GRG,
but the health
risk associated with the use of mercury has prompted commercial
and research
laboratories to discontinue its use. More recently other units,
such as the Mozley
Laboratory Separator, the superpanners or lab flotation ceHs,
have been used. Most
methods yield irreproducible results, often not enough mass is
used or not aH the GRG
is recovered.
Table 2-1 summanzes the difference between the ore and stream
GRG
determination.
Table 2-1 Differences between GRG Determination for Ores and
Streams
Ore Characterization Stream Characterization
Objective: Objective:To measure how much To measure how much
GRG is liberated as the ore is GRG is already liberatedground to
finalliberation size in streams
Procedure: Procedure:Sequentialliberation and Removal of +850
/lm fraction,
recovery at 100% -850 /lm, recovery of GRG in a single stage
from50% -75 /lm and 80% -75 /lm -850 /lm fraction. Procedure
modifiedMinimum mass used: 24 kg for high s.g. samples
Product Treatment: Product Treatment:AH three concentrates and
Same as the one of ore
600 g sample of three tailings characterization, but for
singleare screened from 20 to 600 /Jm concentrate and tailing
products
The GRG content of streams and performance of gravity units have
been
difficult to evaluate for a number of reasons. One of the
reasons is that slurry sampling
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 15
is an essential tool for the job but is error prone, especially
when GRG is present, as it isless likely to be uniformly dispersed
in the flowing slurry. Precision and accuracy are
difficult to achieve due to the occasional occurrence of coarse
gold, called the nuggeteffect. Therefore, when sampling, great care
must be taken to obtain a truly
representative sample of adequate mass. Large samples are often
required to make the
assessment ofgold content statistically sound (Putz, 1994.
Woodcock, 1994.)
For the purpose of estimating the minimum sample mass needed to
achieve a
glven accuracy, the occurrence of GRG can be assumed to follow a
Poisson
distribution. Consider a sample that contains n gold flakes on
average. Actual samples
will indeed average n gold flakes, but with a standard deviation
of j;;. The relativestandard deviation will be Jlj";;. This
describes the fundamental sampling error anddoes not include
assaying and screening errors or systematic errors stemming
from
inappropriate sampling methodology. For the same grade and mass,
finer feeds yield an
increasing number of gold particles and thus a lower fundamental
sampling error. If all
the coarse goId particles could be removed, assayed separately,
then recombined
mathematically with the grade of the material from which the
coarse particles were
removed, the error associated with the overall grade of the
sample would be lower. Ithas been proposed (Putz, 1994) that around
10 to 50 kg of material would be sufficientfor plant stream samples
and the maximum size class for which reliable GRG content
information could be thus generated would generally be below
850/-lm. Actual sample
size requirements vary according to gold grade and the size
distribution of GRG.
2.3 Unit Processes
Usually, gold gravity circuits are inserted in grinding circuits
consisting of SAGor rod mill for primary grinding and ball mills
for the secondary grinding, and
cyclopacks for classification. In most plants gold is recovered
most frequently from
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 16
cyclone underf1ows, and less frequently from baIl mill
discharges. Knelson
Concentrators are most frequently used for primary recovery,
although jigs in NorthAmerica and spirals in Australia were more
common sorne twenty years ago. Primary
concentrates are generally upgraded to smelting grade by shaking
tables, although more
recently intensive application is gaining acceptance, with
automated units such as
Oekko's In-Leach reactor and AngloOold's Modified Acacia
process. In this section,
more details about the above gravity units and their modeling
will be given.
2.3.1 Comminution and Classification
BalI mills are the only comminution units studied thus far with
the ORO
approach. The study of a grinding operation as a rate process
has becorne a well-
established practice (Kelsall et al., 1973a, 1973b; Hodouin et
al., 1978). It enablesmineraI processors to simulate the grinding
process more accurately. It can dramatically
facilitate control and optimization of the grinding circuits.
Usually, the development
and refinement of baIl mill models use the concepts of breakage
and selection functions.
Due to its malleability, gold behaves differently than other
mineraIs in baIl mill or
grinding circuits. Banisi (1990) investigated in a laboratory
mill the grinding behaviourof gold by means of breakage and
selection functions and contrasted it with that of
silica.
2.3.1.1 The Breakage Function
When a single brittle particle breaks into smaller pieces, a
range of particle sizes
will be produced. Conceptually, the breakage function, bij, is a
mathematical description
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 17
of the fragments distribution into a number of size classes. It
is defined as the
proportion of material which appears in size class i when broken
once in size class j.The cumulative breakage function, Bij , is the
proportion of broken material which, upon
single breakage from size class j, is finer than size class i
(Austin et al., 1971). Therelationship between breakage function
and cumulative breakage function is defined by:
bij = Bij - B (i+l)j i>j
When the fragment distribution is geometrically similar for all
size classes, the
breakage function is defined as normalizable; otherwise, it is
called non-normalizable
(Austin, et al., 1971a). In most simulations the breakage
function is assumed to benormalizable. Although it appears that
this assumption is not very realistic, it has been
found that most simulators are not sensitive to this
simplification (Laplante et al, 1985).In the simulation of this
paper the breakage functions for the gold and gangue are
assumed to be normalizable.
Many methods have been proposed to estimate the breakage
function. Herbst
and Fuerstenau (1968) have devised a laboratory method whose
basis is that zero orderproduction of fines should be apparent.
Dividing its rate constant for each size i by the
selection function ofthe original size class j yields the value
Bij;
B=F;!l S
J
j=l toi-l
where Bij is the cumulative breakage function, Fi is the fines
production rate constant of
size class i and Sj is the selection function of original size
class j (the parent class).
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 18
2.3.1.2 The Selection Function
The selection function or specific rate of breakage is a measure
of grindingprocess kinetics. In other words, it is an indication of
how fast the material breaks.There is ample experimental evidence
that batch grinding kinetics follows first orderwith respect to the
disappearance of material from a given size class due to
breakage
(Kelly et al., 1982):
dM;(t) =-Set) *M(t)dt 1 1
where
Mj(t) : mass in size class i after a grinding time oftSj(t):
rate constant for size class i (fI)
The rate constant has been described as the "selection function"
by early investigators
(Herbst et al., 1968).
2.3.1.3 Investigation of Gold's Behavior in Comminution
Banisi (1990) compared the breakage and selection functions of
gold and silicaby grinding approximately 50 g silica and 4.88 g
(consisting of 1240 flakes) of goldfrom a single size class,
850-1200 ~m, respectively in a ball mill. Before grinding,
thesamples were screened to determine the initial size
distribution. Grinding was then doneincrementally for total times
of 15, 30, 60, 90, 150, and 210 seconds. After eachgrinding
increment, the samples were screened for 20 minutes to determine
the size
distribution and then returned to the mill for the next
cycle.
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 19
After the calculation and analysis of the breakage and selection
function of goId
and silica, Banisi found that grinding of single size class of
goId and silica in a baIl mill
followed tirst order kinetics. The selection function of silica
was more than four times
that of gold. Further investigating at plant scale (Golden Giant
Mine) found that goldgrinds six to twenty times slower than its
gangue. Although Banisi's work was
important to identify the behavior of gold, there were still
sorne potential improvements.
Noaparast (1996) investigated the breakage and recoverability of
gold. He triedto generate a characterization of how goId fragments
and their progeny respond to
gravity recovery. To understand the grinding and recoverability
of gold, Noaparast
measured a) the rate of disappearance from the parent class, b)
the distribution offragments in the other size classes, and c) what
proportion of the progeny and unbrokenmaterial is gravity
recoverable. Actually, the tirst concept corresponds to the
selection
function, the second to the breakage function, and the third is
more important when
simulating the GRG recovery in grinding circuit. A basic
methodology was developed
based on three steps, namely the isolation of GRG, its
incremental grinding and
recovery. First, samples were processed with a LKC to maximize
and isolate GRG in
certain size classes. Second, each sample was first combined
with silica sand of the
same size class to a total mass of 200 g. Material was then
incrementally ground in mill.
After each increment, the ground product was dry screened and
aIl material other than
that in the original size class was set aside and replaced with
silica sand, to make up the
original 200 g for the next increment. Third, after incremental
grinding, aIl samples
were mixed and silica from the initial size class was added to
obtain a 3 kg sample. The
sample was then processed with a KC-MD3 to recover GRG. Based on
the differentsamples tested, it was found that most of the gold in
the original size class remains
gravity recoverable; even when broken to finer size classes.
Generally gravity
recoverability decreased the finer the parent size class, or for
the progeny classes much
finer than the parent class. Finally, based on the modified
Rosin-Rammler equation, a
equation was obtained to model the gold recoverability of each
size class:
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND
[
( X )4]-0693* -RGRG = 98.5 * 1-e' 22
20
Where X is geometric mean size of size class (!lm)
This equation yields the GRG data shown in Table 2-2, used to
model GRG
recovery in grinding circuit. A column matrix that includes the
data in Table 2-2 is used
to correct each element of the breakage matrix below the main
diagonal.
Table 2-2 Coefficient used to correct the grinding matrix
Size C1ass
(flm) -25" +25-37 +37-53 +53-75 +75-106 +106-150 +150-212
+212
RaRG 0.371 0.895 0.985 0.985 0.985 0.985 0.985 0.985
(* means size of the -25 !lm assumed to be 20 !lm)
2.3.1.4 Gold's Behavior in Cyclones
Gold's behavior in grinding circuits, both in comminution and
classification
units, is the result of its malleability and specifie gravity,
which combine to yield high
circulating loads. For gold or GRG classification, the only data
available are cyclonepartition curves. The curve can be obtained by
analysis of three or four of the projectedcyclone streams,
typically the underfiow, overfiow, and one or two feeds. Each
sample
is processed with KC-MD3 to determine GRG content. Studies in
various mills
(Laplante, Liu and Cauchon, 1989; Banisi, Laplante and Marois,
1991; Laplante andShu, 1992; Putz, Laplante and Ladoucer, 1993;
Woodcock, 1994; Putz, 1994) have
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 21
shown that the partition curve of GRG is above that of the ore.
A typical gold, GRG and
ore partition curve is shown in Figure 2-3 (Laplante, 2000).
-1100
80
LI.. 60-~0- 40~0
20
010 100
Partiela Size, tm1000
'---------------------_._--
Figure 2-3 Typical Partition Curve for Gangue, Gold and GRG
Clearly, most goId and GRG, even below 25 /lm, still report to
the cyclone
underflow. This explains why very large circulating loads build
up, especially in the
fine size classes, which exhibit slower grinding kinetics.
However, there is still
considerable uncertainty as to how the partition curve of goId
or GRG in the fine size
range is affected by parameters such as rheology or the cut-size
of gangue. Although
much remains to be done to understand the factors affecting
gold's behavior in
cyclones, a link between GRG and ore (i.e. gangue) partition
curves was used in thesimulation (more detail will be discussed in
Chapter three). Plitt' s model (1976) wasalso used to calculate the
full partition curve of GRG.
Ci = R f + (l-Rf)*{ l-exp [-O.693*(d/dso) m}
Where
Ci is fraction of material in size class i which reports to the
underflow
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 22
Rf is bypass which is mass fraction of cyclone feed water
recovered in theunderflow stream (it is usually called bypass)di is
characteristic particle size of size class i
dso corrected cut size
m sharpness of separation coefficient
Although the partition curves of GRG and ore can be calculated
with the above
parameters, there are still sorne problems. Part of the problem
is that the traditional
approach to estimate Dsoc cannot be used for GRG, because
recoveries for GRG in the
finest size class, typically the minus 25 !-lm fraction, tend to
be very high, 70 to 90%. In
this case they are around 40%, thus, no "8' curve is generated.
Figure 2-4 shows the
coarsest classification ever documented for GRG, at the New
Britannia Mill. Note that
although the ore partition curve fits Plitt's model weIl, that
of GRG and gold is very
difficult to fit, with no clear "8" shape and a bypass fraction
that does not equal that of
the gangue.
u.-::::>.8'#.
100908070605040302010o
10 100Particle Size, j.Jm
--Gold
-tr- GRG
1000
Figure 2-4 Partition Curves of the Primary Cyclones of New
Britannia
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 23
2.3.2 Recovery Units
2.3.2.1 Knelson Concentrator
The Knelson Concentrator is an innovative centrifugaI separator
commissioned
in the early 1980s. With successful installations in major gold
producing regions of theworld, it has become the most widely used
unit to recover GRG. One unique feature of
the Knelson Concentrator is its groove construction and
tangential fluidization water
flow in the separating bowl, which partially fluidizes the
concentrate bed. As a result,
the unit can achieve high GRG recovery over a wide size range,
typically 20 to 850 flm,with recovery falling around below 25 to 37
flm, due to low terminal settling velocitiesof finer particles and
the relatively short retention times used in the unit.
Although the standard Knelson Concentrator is designed as a
roughing
concentrator for gold ores, it can be used in slightly different
ways. First and foremost,
it can be used to recover gold from the main circulating load of
grinding circuits. Thereare many successful industrial applications
for KC to recover gold in grinding circuits.
For example, in 1995, the Campbell gold mill at Ontario
installed two Knelson
Concentrator CD 76 cm to replace the existing jigs in a rod/ball
mill grinding circuit (itis now using a single unit and a smaller
Knelson Concentrator in the gold room). Thischange has increased
gravity recovery from 35% to 50%, which translates into
economic value through a reduced gold inventory in the plant
process and an ability to
increase mill throughput. Second, it can be used to treat flash
flotation concentrates.
Flash flotation can recover gold bearing sulphide mineraIs from
hard-rock ores. Sincethe product of flash flotation from the
circulating load of grinding circuits contains a
significant amount of GRG, gravity recovery of the GRG from
these products before
smelting has been increasingly accepted. For example, the Lucien
Bliveau mill used a
Knelson MD30 to treat its flash flotation concentrate (Putz et
al, 1993; Putz, 1994). Themill was then moved to the Chimo mine,
and recovery from the flash flotation
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 24
concentrate was then supplemented by a second Knelson treating a
bleed from the
cyclone underflow, for coarser gold (+300 !lm) that would not
readily float in the flashcell (Zhang, 1998).
Separation in the Knelson Concentrator is based on the
difference in centrifugaI
forces exerted upon gold and gangue particles and on the
fluidization of injected water.It utilizes the principles of
hindered settling and a centrifugaI force that
theoreticallyaverages 60 Gs. For the KC-MD3, water is injected
tangentially at high pressure intothe rotating concentrating cone
through a series of fluidization holes to keep the bed of
heavy particles fluidized (Figure 2-5). The feed is introduced
as slurry whose densitycan be up to 70% to the base of the rotating
inner bowl through the stationary feed tube
(called downcomer).
Feed
'l~'lils
COllC't,::utrate
Figure 2-5 Schematic cross-section of a Knelson Concentrator
MD3
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 25
When the slurry reaches the bottom of the cone, it is forced
outward and up the
cone wall depending on the size and specifie gravity by
centrifugaI force. The slurrythen fills each ring to capacity to
create a concentrating bed. Compaction of theconcentrating bed is
prevented by the fluidizing water that enters tangentially into
the
concentrate bed opposite to the rotation, at a flow rate
controlled to achieve optimum
fluidization. Under the effect of centrifugaI force and water
fluidization, high specifie
gravity particles such as gold are then retained in the
concentrating cone. Gangue
particles are washed out of the inner bowl due to their low
specifie gravity. When a
concentrating cycle is completed, the feed must be stopped or
diverted, then
concentrates are flushed from the cone into the concentrate
launder (Knelson et al.,1994). For the small units (e.g. KC-MD3 and
KC-MD7.5), concentrate removal isusually accomplished by releasing
the inner bowl from the outer bowl and washing the
concentrate out. For larger units, concentrate removal can be
achieved automatically by
mechanically flushing the concentrate to the concentrate launder
through the multi-port
hub.
For this work, size-by-size recovenes for a KC-MD 30 generated
at mme
Camchib will be used (Vincent, 1997). These are shown in Table
2-3.
Table 2-3 Typical Values of Knelson Concentrator's Recovery
Size 25 37 53 75 106 150 212 300 425 +600
(/lm) -25 -37 -53 -75 -106 -150 -212 -300 -425 -600
RKC 0.6 0.65 0.72 0.75 0.78 0.77 0.73 0.68 0.65 0.58 0.48
Generally, Knelson size-by-size recoveries are relatively size
independent: it is
frequent to observe a ratio of 1.5:1 to 3:1 in the recovery of
the coarsest to the finestsize classes. This ratio usually
increases with increasing feed rate and gangue specifie
gravity.
-
CHAPTER 2
2.3.2.2 Table
GRAVITY RECOVERABLE GOLD: A BACKGROUND 26
The shaking table is perhaps the most metallurgically efficient
form of gravity
concentrator, being used to treat the smaller, more difficult
streams, and to produce final
concentrates from the products of other forms of gravity system
(Wills, 1997). ManygoId plants use a shaking table to upgrade
Knelson concentrates, achieving recoveries
that vary between 40% and 95%.
A shaking table consists of a slightly inc1ined deck on to which
the feed is
introduced at the feed box and distributed along part of the
upper edges and spread over
the riffled surface. Wash water is distributed along the balance
of the feed side from the
launder. The table is vibrated longitudinally cause the
partic1es to "crawl" along the
deck parallel to the direction of motion. Thus the motion causes
the partic1es move
diagonally across the deck from the feed end and finally to fan
out according to their
size and the density. The larger lighter partic1es are washed
into the tailing launder
while the smaller, denser partic1es riding highest towards the
concentrate launder. Sorne
fines, inc1uding fine GRG, are immediately washed into the tail
discharge upon feeding
(Putz, 1994).
Sivamohan and Forssberg (1985b) have reviewed the significance
of manydesign and operating variables. The separation on a shaking
table is controlled by a
number of operating variables, such as wash water, feed pulp
density, deck slope,
amplitude, and feed rate. Partic1e shape and size range play an
important role in the
table separation. There is sorne confusion as to what the table
is most capable of
recovering, but the work of Huang (1996) c1early shows that most
gold losses are fine,liberated goId that can be recovered with a KC
MD-3. Sorne of the lost gold is flaky,
and generally reports in the middling fraction, generally
intermingled with pyrite. Much
of this goId will not be recovered well by gravity, because it
is not fully liberated. This
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 27
pattern appears to hold irrespective of the nature of the table
surface, flat, riftled or
grooved.
When usmg a conventional shaking table to process KC
concentrates, a
significant fraction of the finer gold may be lost to the table
tails (Huang, Laplante andHarris, 1993). Because of the different
forces (60 Gs for KC, IG for the table) acted onparticles,
incomplete liberation particles and gold flakes. Thus, the table
tailings that
contain significant amounts of GRG should be recycled to the KC
for scavenging to
recover more GRG, as practiced at Lucien Bliveau. The shaking
table recovery data
used for simulation in Chapter 3 are shown in Table 2-4. It
shows that in the finest size
class the recovery is much lower than that of other size
classes. Although recovery
drops significantly with decreasing particle size, it remains
relatively high even for theminus 25-llm fraction, typically above
50%.
Table 2-4 Typical Values ofShaking Table's Recovery Used for
Simulation
Size 25 37 53 75 106 150 212 300 425 +600(~m) -25 -37 -53 -75
-106 -150 -212 -300 -425 -600
%Rt 60 80 90 95 96 96 94 92 90 85 80
2.3.2.3 Jigs
Jigs used to be the recovery unit of choice for gold in North
America. Sorne arestill used, although they have been replaced by
Knelson Concentrator in a large number
of plants. Table 2-5 lists a selected number of Canadian sites
where jigs have beeninstalled.
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 28
At plant start-up, most recent mill designs have incorporated
Knelson units. Jigs
are discussed here because they offer, at low yield, a much
different relationshipbetween GRG recovery and particle size.
Table 2-5 Evolution of the Use of Jigs and KC at Certain
Canadian Sites
Case 1 Case 2 Case 3
Casa Berardi Campbell Mine Jolu
Golden Giant MSV, Dome Mine, Snip Operation
Lucien Bliveau Est Malartic
Mine Camchib Sigma
Case 1: Jigs used at start-up, then removed; KC installed
later.
Case 2: Jigs used and then replaced by KC.
Case 3: Jigs used until mine shut-down
The jig is one of the most widely applied gravity concentrating
devices. Jiggingis the process of sorting different specifie
gravity mineraIs in a fluid by stratification,
based on the movement of a bed of particles. The particles in
the bed are arranged by
the stratification in layers with increasing specifie gravity
from the top to the bottom.
The jig is normally used to concentrate relatively coarse
material, from 200 mm toO.lmm. When the specifie gravity difference
is large, good concentration is possible
over a wider size range (Wills, 1997), which explains its
earlier role in gold recovery.
The basic construction of a jig is shown in Figure 2-6.
Essentially it is an opentank, filled with a fluid, normally water,
with a horizontal jig screen near the top, andprovided with a
spigot in the bottom, or hutch compartment, for concentrate
removal.
The jig also includes means to continuously receive raw ore
feed, a drive mechanismand methods of separating the stratified bed
into two or more product streams (Burt,
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 29
1984). The jig bed consists of layer of coarse, heavy particles
called ragging. In the jig,separation of mineraIs of different
specifie gravity occurs in a fluidized bed by a
Tailing
Jig bed
Ragging
Jig Screen
Concentrate
Discharge spigot
Figure 2-6 Basic Jig Construction
pulsating current of water which produces stratification. On the
upstroke the bed of
ragging and slurry are normally lifted as a mass, and then
dilated as the velocity
decreases, while the suction stroke slowly closes the bed. The
purpose of jigging is todilate the bed of material so that the
denser and smaller particles penetrate the
interstices of the bed.
Jig capacity is described as the optimum throughput that
produces an acceptablerecovery and is determined by the area of
sereen bed. In other words, different
capacities result in different recoveries. Jig capacity varies
depending on the jigconfiguration, ore feed size, and adjustments
of stroke length and speed. Coarser grainscan usually be fed in
larger volumes than fine grains in relation the area of the jig
bed.
-
CHAPTER 2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 30
For gold, jigs are generally used as the primary recovery unit
to treat the full circulatingload at the expense of low stage
recovery.
1000100Particle size,J,lm
-o-KCL Jig
100 .."........---------~8060 "'l-~~~~~~~~~.._______~
40
20
o+---IIBIIIBMeil-=tl;:10
Figure 2-7 Comparing Size-by-Size Recovery of a Knelson
Concentrator and a
Duplex Jig (Based on Putz, 1994, and Vincent, 1997)
Both Putz (1994) and Vincent (1997) have studied jig circuits,
although onlyVincent generated size-by-size GRG recovery data. Both
reported very low stage
recoveries, about 2%. Overall gravity recoveries were in both
cases in the forties,
because (a) the full circulating load was treated and (b) the
amount of GRG circulatingload was around 2000% (Le. 2%* 2000%/100%
= 40%). Table 2-6 shows the size-by-size recoveries that will be
used for simulation (from Vincent, 1997). Figure 2-7 showsthat
compared to KC, the relative effect of partic1e size on recovery is
extremely high.
-
CHAPTER2 GRAVITY RECOVERABLE GOLD: A BACKGROUND 31
Table 2-6 Typical Values of Jig's Recovery Used for
Simulation
Size 25 37 53 75 106 150 212 300 425 +600
(/lm) -25 -37 -53 -75 -106 -150 -212 -300 -425 -600
% Rjig 0.3 0.7 1.6 2.1 3.8 4.2 5.6 9.3 10.5 10.1 18.9
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 32
CHAPTER THREE
SIMULATING GOLD RECOVERY
3.1 Introduction
A methodology to estimate gold recovery by gravity was developed
by McGillgravity research group (Laplante et al., 1994). It makes
use of a population-balancemodel (PBM) that represents gold
liberation, breakage and classification behaviour tosimulate gold
gravity recovery in a grinding circuit. In this chapter, how the
PBMmakes use of the characterization of GRG and its behaviour in
unit processes will bepresented. This chapter is divided into three
sections. In section 3.2, the derivation ofthe PBM is shown,
starting from a very simple, single class model, to progress to
athree-size class model and finally the full model. A limited
number of circuits arepresented and for each, the matrix equation
for calculating the GRG recovery is derived.In section 3.3, the
extraction of plant data for GRG (as opposed to total gold)
isdescribed; values for the matrices that will be used in the PBM
are given in sections3.3.1 and 3.3.2, respectively.
3.2 The GRG Population Balance Model
3.2.1 A Simplified Approach
Consider the following circuit in a gold plant (Figure 3-1):
fresh feed is fed to aball mill, and the total GRG is assumed to
appear in the mill discharge as F. Brepresents the proportion of
the GRG in the ball mill feed which is still gravity
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 33
recoverable in the mill discharge1 AlI or sorne of the ball mill
discharge is sent to the
primary recovery and gold room recovery units. Primary recovery
is based on the full
amount of GRG discharged from the ball mill, not that part of
the discharge actually fedto the primary recovery unit (if the full
discharge is not treated). Primary and gold roomrecovery can be
represented separately (e.g. as P and G), but if both tailings
arecombined, it is more expedient to represent their overall
recovery, R. The tailings from
the primary unit and gold room are recycled as the feed to the
cyclone, with any portion
of the mill discharge that was not treated. The overflow of
cyclone goes to the next
recovery stage, such as flotation or cyanidation. The underflow
of the cyclone is sent
back to the ball mill to regrind. C is the proportion of GRG in
the cyclone feed that
reports to the cyclone underflow.
Ove flow
c clone
'-------.. ..
.. B. ..'----' F
BalI Mill Recovery Unit and Gold Room
Figure 3-1 Simple Circuit of Gravity Recovery from the BalI Mill
Discharge
Let us define X as the amount of GRG in the ball mill discharge,
which includesboth GRG freshly liberated (i.e., F) and GRG that was
present in the cyclone underflowand was not ground into non-GRG in
the ball mill. Then gravity recovery, D, is equal to
R*X, and the GRG directed to the cyclone is (l-R)*X, of which a
proportion C is
1 The proportion is high, as gold is highly malleable and only a
small fraction is ground into non-recoverable particles
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 34
classified to the underflow of cyclone, i.e. C*(l-R)*X. This ORO
is then ground in theball mill, and a proportion B survives. Thus,
at the ball mill discharge, the amount of
ORO is equal to B*C*(1-R)*X as ORO that has "survived" grinding,
plus an amount Fthat has beenjust liberated, for a total
ofB*C*(1-R)*X + F, which is also equal to X:
Re-arranging:
X= B*C*(1-R)*X + F Equation 3-1
x F[1- B *C *(1- R)] Equation 3-2
or X = [l-B*C*(l-R)] -1* F
And the ORO recovery, D, is equal to:
D R*F[l-B*C*(1-R)] Equation 3-3
As a numerical example, let us use values of 0.8 (80%) for F,
0.95 for B, 0.98for C and 0.1 for R. The value ofR can be obtained
by taking the product ofhow much
of the circulating load is treated, how much is recovered in the
primary recovery unit,
and how much of the ORO in the primary concentrate is recovered
in the gold room.
Thus a R value of 0.1 could be obtained if 25% (0.25) of the
circulating load is treated,with a primary recovery of 50% (0.5)
and a gold room recovery of 80% (0.8).
The total ORO recovery, calculated with the above formula, is
0.494 or 49.4%.
Of a total of 80% ORO in the feed, approximately five eighth, or
49.4% of the total
gold, is recovered. These data are reasonably realistic,
although B is slightly low. This
is the simplified PBM derived for this circuit
configuration.
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 35
Consider another circuit, shown Figure 3-2 below:
Overflow,---,
KCand
GoldRoom
RD
Figure 3-2 Simple Circuit of Gravity Recovery from the Cyclone
Underflow
As ore is ground and discharged from the baIl mill, GRG is
generated as E. The baIlmill discharge is then sent to the cyclone.
The cyclone overflow goes to the recovery
circuit, and from the underflow one fourth of the circulating
load (Pl = 0.25) is bled andrecovered by Reichert Cones (P2 =
0.85), the concentrate is upgraded by KnelsonConcentrator. The
Knelson concentrate is further upgraded in the goId room. For
simplicity's sake, the Knelson and gold room recoveries are
lumped in a single
parameter, R (= 0.5). The tailings from the Reichert cones,
Knelson Concentrator andgold room are recycled to the baIl mill.
Using the same approach as for the first circuit,
the following equation is obtained, where X is the amount of GRG
in the cyclone
underflow:
Equation 3-4
Rearranging Equation 3-4 results in the following PBM for this
circuit:
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 36
P.*P*R*C*FD= 1 21- B *C *(1- ~ *P2 *R) Equation 3-5
Using the above values and equations, the GRG recovery, D, is
equal to 0.434 or
43.4%, and the circulating load X, to 4.085 or 408.5%.
Although a size-by-size approach is not used in the above PBMs,
the results
suggest that reasonable answers can be obtained for
understanding how gold gravity
recovery from a grinding circuits works.
If gold recovery from the grinding circuit needs to be
predicted, a size-by-size
approach is necessary for deriving the PBM. This approach will
now be demonstrated
with three size classes, using simple recovery from the cyclone
underflow (Figure 3-3).Part of the underflow is bled and fed to a
screen, with the screen undersize to the
primary recovery unit, and the oversize back to baIl mil!. The
concentrate from primary
recovery is treated in the gold room. Primary and gold room
recovery will be lumped in
a single recovery matrix. Material not selected for primary
recovery and the Knelson
and gold room tailings will be directed to the baIl mill for
further grinding. The relevant
matrices are shown here:
[0.2]
E= 0.30.2
0.99
[
0.1
P=
0.2
[
0.5
R=
0.35
o.u [
0.9B = 0.06
0.03
0.950.04
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 37
Overflow....-----,
pPrimary and Gold room
D +- R
Cyclone Ilr--~
BalI Mill
T L..- ..
BFresh Feed--~" .. F
Figure 3-3 Circuit of Gravity Recovery from the Cyclone
Underflow Using
a Size-by-Size Approach
The matrix E shows the amount of GRG of the ore in each size
class. In theexarnple above, 0.2 (20%) is in the coarse size class,
0.3 (30%) in the interrnediate sizeclass and 0.2 (20%) in the fine
size class2, for a total GRG content of 70% (30% of thegold in the
ore in non-GRG). For the classification matrix C, shown above, we
assumethat 100% (l.0) of the coarse GRG reports to the cyclone
underflow, as do 99% (0.99)of the interrnediate size GRG and 90%
(0.9) of the fine GRG. For primary screening, P,20% of the
circulating load is screened, and half of the coarse GRG is
rejected to thescreen oversize, whereas aIl of the GRG in the
second and third size class report to thescreen undersize (henee a
fraction of 0.2 of the cyclone underflow stream). For
primaryrecovery P, it is assumed the primary recovery units is
better at recovering coarse GRG
(50%) than GRG in the medium and finest size class (35%). AlI
the above materialtransfer matrices are diagonal, because they
represent units in which GRG is not ground
(i.e. does not migrate from one size to a finer one).
2 Column vectors that identify flows of GRG (i.e. E, Xand .Q)
are underlined for easier identification
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 38
For the grinding matrix B, it is assumed that upon going through
the ball millonce, 90% of the coarse GRG "survives" grinding, as
opposed to 95% of the
intermediate size GRG and 98% of fine GRG (these values are
found on the maindiagonal of B). Of the 10% of the coarse GRG that
breaks into finer size classes, 6%reports as GRG in the second size
class and 3% in the third (l% becomes non-GRG).Similarly, of the 5%
of the intermediate size GRG that is ground, 4% reports as fine
GRG (also 1% becomes non-GRG). The 2% of the fine GRG that
"disappears" becomesnon-GRG. With these descriptions, the grinding
matrix can be expressed as a lower
triangular matrix. Note that the matrices used are either column
matrices (underlined foreasier identification) or square matrices.
With the exception of the B matrix, the squarematrices are
diagonal, because they represent unit processes in which GRG does
not
transfer from one size class to another. The B matrix is lower
triangular, to represent the
migration of sorne of the GRG into finer size class by
breakage.
The circulating load of GRG and how much is recovered in each
size class
recovery can be derived as for the previous non-matrix
approach:
x = [I-B * C * (I-P * R)] -1 * C *E
And the GRG recovery is:
D =P * R * (I-B * C * (I-P * R)) -1 * C *E
Equation 3-6
Equation 3-7
Note that division in the scalar model becomes matrix inversion
in the matrix model.
The GRG circulating load and recovery are as follows:
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 39
[1.379]
X= 2.5961.932 [
0.0690]D= 0.1817
0.1353
Summing X and D yields, respective1y, total goId recovery,
0.3859 (38.6%) andthe circulating load of GRG, 5.91 (591%). From
the GRG recovery matrix, it can beobserved that recovery is highest
in the intermediate size class, because the coarsest size
class grinds more rapidly and is partially screened out of the
gravity circuit feed; the
circulating load and recovery is highest in the intermediate
size class; the finest size
class, despite receiving progeny from the two coarser size
classes, does not have the
largest circulating load or recovery, because a significant
proportion reports to the
cyclone overflow and its size makes gravity recovery less
effective. These trends
mirror actually circuit performance.
For the derivation of the above PBM, sorne assumptions were
made. First, the
GRG first appears at the discharge of the ball mill with the
size distribution generated
by the GRG test, E. Second, no GRG will be rejected to the
cyclone overflow beforebeing liberated. The validity of these
assumptions was discussed by Laplante et al
(1995).
3.2.2 The Full PBM
The full PBM is very similar to the three-size-class model
presented above;
typically, 10 to 12 size classes are used. Consider a grinding
circuit made of the blockdiagram shown in Figure 3-4 (Laplante,
Woodcock and Noaparast, 1994). As materialis ground and discharged,
GRG is generated as E. A primary concentration step yields
aproportion Pi of each size class (forming a diagonal matrix P)
that is then presented to agravity separator for upgrading. From
each size class, a GRG recovery of ri (forming adiagonal matrix R)
is achieved.
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 40
Ball Mill
Primary concentration
SecondaryRecovery
DGravityConcentrates
Figure 3-4 Recovery from the Second Mill Discharge
Material not presented to the gravity unit or not recovered from
all gravity units
is then classified by cyclone, a fraction Ci (forming a diagonal
matrix C) being returnedto the mill. In the mill, a fraction of the
GRG in each size class remains in the same size
class in the mill discharge (the main diagonal of Matrix B), but
sorne GRG reports tofiner size classes (the lower triangular
submatrix of B). Given the above description, itcan be derived the
same way as simple PBM as the following formula:
D = PR* [I-BC (I-PR)r1 * E Equation 3-8
where D is a column matrix of the GRG flowrate into the
concentrate for each sizeclass. Each di corresponds to the amount
of GRG recovered in size class i. The sum of
the diS gives the total GRG recovery.
This circuit is relatively common in gold plants, and will be
used to generate an
extensive database that will be summarized with multi-linear
regressions.
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 41
When simulating GRG recovery, parametric estimation for the
variouscomponents of the model is case specifie. For example,
retrofit applications will be ableto take advantage of the existing
grinding circuit to generate much of the data in a
reliable way (C and B) and validate the algorithm. Greenfield
applications will use data"borrowed" from other operations, with a
corresponding decrease in reliability. For
optimization studies, the usual approach will be used to
generate C, B, P and R from the
existing circuit, tune the model to achieve a D consistent with
observed circuit
performance, and test changes in recovery by modifying P and
C.
Although equation 3-8 is specifie to the circuit shown in Figure
3-4, similar
equations representing different circuits can readily be
derived. Figures 3-5 and 3-6
show two such circuits, represented by the folIowing equations,
respectively:
Fresh Feed
Primary
Mill
Classification
Concentrate
B
BalI Mill
...-----1. SecondaryRecovery
Cyclone
Figure 3-5 Recovery from the Cyclone Underf10w
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 42
Secondary.----~~-., Recovery
SecondaryClassification
B
First Classification
Primary
Mill Concentrate
Fresh Feed
BaU Mill
Figure 3-6 Recovery from the Primary Cyclone Underflow
D = PR * [1-BC * (I-PR)] -1 * C *E Equation 3-9
D = PR * CI* [1 + B * (I-MB) -1 * M] *E Equation 3-10
where M = (I-PR) * CI + (I - CI) * C2 Equation 3-11
where CI and C2 are two matrices that describe the partition
curves of the
primary and secondary cyclones, respectively. Figure 3-5
represents most gravitycircuits, where gold is recovered from the
primary cyclone underflow. Figure 3-6represents goId recovery from
the primary cyclone underflow, as practiced at Casa
Berardi (CB), Qubec.
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 43
3.3 Input Data for the PBM
3.3.1 GRG Data (F Matrix)
OriginaHy, five different GRG distributions, normalized to 100%
and shown in
Figure 3-7 as cumulative, were used as Ematrix (Table 3-1) in
the simulation.
-+-- very fine_fine-.- interrrediate
~coarse--.- int. less fines
1000100Particle Size, J.Il1
o+--J.---J.....J~~~~k""II-J-~10
100 iIII~~-----------,~ lCl)
~ 80 +--\-~.--\-~~~.oCl)
0::: 60 +-~-\---lIIIl~~--'..----~~~~-j~~ 40
+---~---'~~--~-----I::::JEc3 20
+-~~------'~----'~"w-~------'~~-J?ft
Figure 3-7 Normalized GRG Distributions of the Original Data
Set(1: Coarse; 2: Intermediate; 3: Fine; 4: Very Fine; 5:
Intermediate --fewer fines)
They represent different contributions of coarse and fine GRG.
Because aH final
simulation results are expressed in terms of the recovery of
GRG, as opposed to total
gold, the actual quantity of GRG is 100% for aH simulations. The
end-user simplymultiplies the GRG recovery by the GRG content to
obtain the total gold recovery. For
example, if the simulated GRG recovery is 50%, and the total GRG
content is 80%,then the total goId recovery by gravity is 40%.
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 44
Table 3-1 Normalized GRG Distributions Used for the
Simulation
Size, IJ,m Very fine Fine Intermediate Coarse int. less
fines+600 0 0 0 16 0
425-600 0 0 1 8 0300-425 0 1 4 9 2212-300 0 1 4 10 6150-212 2 3
9 12 10106-150 2 7 12 Il 1075-106 4 17 15 11 1453-75 8 15 10 8
1337-53 10 18 15 6 1425-37 22 12 10 5 23
-25 52 26 20 4 8Sum 100 100 100 100 100
First, gravity recovery was simulated for the five GRG size
distributions,
systematically varying other operating conditions, such as
classification, grinding and
the recovery matrix (details will be given in the next Chapter).
One regression mode!was then generated and found to fit the five
original GRG size distributions weIl, but
fared poody with other GRG distributions, because the five
original GRG size
distributions did not yield an adequate number of degrees of
freedom for the regression
coefficients describing the effect of the GRG size distribution
(i.e. only five differentsize distributions, which were fitted with
four parameters). The problem was correctedby using a wider
database of GRG distributions, twenty in total, aIl shown in Figure
3-8.
The last point (i.e. the contribution of the -25 /-lm fraction)
has been deleted from eachcurve, for the sake of clarity.
Further fitting efforts indicated that mode1 accuracy was
generally poor for the
coarsest size distributions. As a result, the twenty GRGs,
including the original five,
were split into two subsets, fine and coarse GRG, based on the
cumulative GRG content
coarser than 150 /lm, with a 25% transition limit between coarse
and fine GRG.
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 45
1
100) 11!
A CoarseGRGs
100Partide size (~m)
0+------.---.-------,-------,-----,--,--,-,--,-----="'"---""1""""-"
10
"'0~ 80 +----~d.co+-'Q)~ 60Q) +--------"IIl'-.-~~~>
+:ico::J 40 -+-----~-____1t:-"11
-
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 46
For the present work, the value of P*R depends on the treated
fraction of
circulating load (ball mill discharge) and the units used to
recover gold in the primarystage and gold room. It was decided to
use a single relationship between particle and
primary/gold room recovery, and to vary the proportion of the
circulating load being
treated to vary P*R, -i.e. the gravity recovery effort. This
proportion was set equal for
each size class.
The size-by-size primary and gold room recovery shown in Chapter
2 were used
for simulation. The primary recovery came from the performance
of a MD30 KC with a
conventional bowl used at Les Mines Camchib (Laplante, Liu and
Cauchon, 1990) andthe goId room recovery from generally observed
goId room practice (Huang, 1996).
Grinding (B Matrix)
The grinding B matrix is probably the most difficult to estimate
for the
simulation, because GRG particles are ground at a rate
noticeably lower than the overall
ore due to their malleability (Banisi, Laplante and Marois,
1991).
A typical population balance grinding model is one that relates
the size
distribution of the discharge of the mill, mg, to the size
distribution of the feed, mf, the
residence time distribution in the mill, the breakage function,
bij, and selection function,S. Ofthese parameters, S and bij are
the most critical. The model can be resolved into asimple equation
3-11 of the type (Austin et. al, 1984):
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CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 47
Hl! 0 0 0 0H 21 H 22 0 0 0
M d = H 31 H 32 H 33 0 0 *M Equation 3-12f0
H n1 H n2 H n3 H n4 H nn
Each Hjj (on the main diagonal) is the fraction which remains in
the original sizeclass j. the terms Hij (i>j) below each mail
diagonal Hjj are the fraction which enter thefiner size class i
from the original size class j. The assumption that no material can
exitthe mill in a size class coarser than the one in which it
entered is the reason the upper
triangle of the matrix is null (Hij=O for i
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CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 48
For this w