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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 UniversityMontréal, 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 was
developed at McGill University in 1994 (Laplante et al, 1995). The objective of this
research 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 and
hydrocyclones 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 fine
GRG) linking the predicted GRG recovery to the naturallogarithm of 't, R-25Ilm, the size
distribution of the GRG and the recovery effort (Re), defined as the proportion, in %, of
the 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 a
significant 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 to
predict 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
Résumé
Pour justifier l'installation d'un circuit gravimétrique dans un concentrateur, on
doit, au minimum, pouvoir estimer la quantité d'or qui sera récupérée. Cette tâche est
ardue, car la récupération se fait de la charge circulante au broyage, dans laquelle le
comportement de l'or doit être décrit.
Un modèle d'équilibrage de population (MEP) permettant d'estimer la
récupération gravimétrique de l'or a été développé à l'université McGill en 1994
(Laplante et al, 1995). Le but de cette thèse était de rendre ce modèle convivial. Le
travail s'est fait en deux étapes. D'abord, nous avons décrit le comportement de l'or
récupérable par gravimétrie (ORG) dans les broyeurs à boulets secondaires et les
hydrocyclones à l'aide de deux paramètres, 1 et R-25J.lm, pour ensuite faire le lien entre
ces paramètres, la charge circulante et la finesse de broyage, afin de faciliter leur
estimation. Par la suite, nous avons représenté la base de données obtenues du MEP par
deux régressions multilinéaires (une pour l'ORG grossier, l'autre pour l'ORG fin)
faisant le lien entre la récupération de l'ORG et le logarithme naturel des variables
indépendantes, soient 1, R..25J.lffi, la distribution granulométrique de l'ORG et l'effort de
récupération (Re), défini comme étant le pourcentage de l'ORG de la charge circulante
qui est récupéré. De tous les paramètres, Re a le plus d'impact et 1 le moins. La
distribution granulométrique de l'ORG, représentée soit par deux paramètres pour
l'ORG grossier ou trois pour l'ORG fin, a un impact majeur sur la récupération, qui a
été déterminé en simulant la récupération de 20 granulométries différentes.
Les régressions multilinéaires, utilisées pour quatre études de cas, ont pu estimer
la récupération en ORG avec une précision au moins égale de celle avec laquelle la
quantité d'ORG peut être estimée, soit environ 5% (relatif). Nous recommandons
l'utilisation du MEP lorsqu'un estimé de la récupération de l'ORG en fonction de la
taille des particules est disponible; sinon, les régressions doivent être utilisées.
111
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IV
Acknowledgements
1 would like to thank Professor A. R. Laplante for his keen insight, WIse
guidance, 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 and
suggestions 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-Iaw
for 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.
Table of Contents
Abstract
Résumé 11
Zhaiyao 111
Acknowledgements IV
Table of Contents V
List of Figures VI
List of Tables Vll
List of Abbreviations Xl
v
Chapter 1: Introduction
1.1 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 Study
1.3 Thesis Structure
Chapter 2: Gravity Recoverable Gold: A Background
2.1 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
5
6
7
9
9
9
10
13
15
2.3.1 Comminution and Classification 16
2.3.1.1 The Breakage Function 16
2.3.1.2 The Selection Function 18
2.3.1.3 Investigation of Go1d's Behaviour in Comminution 18
2.3.1.4 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 32
3.1 Introduction 32
3.2 The GRG Population Balance Model 32
3.2.1 A Simplified Approach 32
3.2.2 The Full PBM 39
3.3 Input Data for the PBM 43
3.3.1 GRG Data (F Matrix) 43
3.3.2 Dnits Matrices 45
Chapter 4: Simulation Results 52
4.1 Introduction 52
4.2 Simulation Results 52
4.2.1 Basic Case Study 52
4.2.2 Gravity Recovery Effort 55
4.2.3 Impact of Operating Variables 56
4.3 Representing Results with Mu1tilinear Regressions 61
4.3.1 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 69
4.4.1 Representing the Grinding Circuit Design
Parameters with 't and R.25 ~m 69
4.4.2 Case Study 72
Chapter 5: Model Reliability and Validation 74
5.1 Introduction 74
5.2 Model Reliability 74
5.2.1 GRG-25~m, GRG-75~m, GRG-150~m and F Matrix 74
5.2.2 R-25~m and C Matrix 77
5.2.3 't and B Matrix 79
5.2.4 Re and R Matrix 79
5.3 Model Validation 80
5.3.1 Campbell Mine Case Study 80
5.3.2 Northem Québec Cu-Au Ore Case Study 83
5.3.3 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 91
6.1 Introduction 91
6.2 General Conclusions 91
6.3 Strengths and Weaknesses ofProposed Protocol 93
Vll
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 and
circulating load, fineness of grind. Regression ANOVA Table 135
Vlll
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 35
Figure 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 41
Figure 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 for
simulation (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% 55
Figure 4-2 GRG recovery as function of recovery effort with coarse,
Intermediate and fine classification 57
Figure 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 59
Figure 4-5 GRG recovery as a function of the recovery effort for fine
(Pso =75 !-lm) coarse (Pso=150 !-lm) grinding, NNX-3 sample 60
Figure 4-6 Comparison of PBM and regression for fine GRG 65
Figure 4-7 Comparing the PBM and the regression for a coarse
GRG distribution 66
Figure 4-8 Effect of GRG size distribution of GRG recovery 67
Figure 4-9 GRG recovery decreases with the increasing dimensionless
retention time in the mill 68
Figure 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 71
Figure 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 86
Figure 5-5 Measured and predicted gold gravity recoveries of the case studies 88
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 sites
Table 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 E
Table 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 GRG
Recovery 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
64
66
67
73
81
81
82
XlI
Table 5-4 Sensitive analysis of the impact of relative change of Re , 'r and R251lID 82
Table 5-5 Data used for predicting GRG recovery on Northern Québec Cu-Au Ore 83
Table 5-6 Data used for predicting GRG recovery on Snip 85
Table 5-7 Parameters used for goId recovery prediction 87
Table 5-8 Predicted and reported gold recovery of Bronzewing Mine 87
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
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 (Marsden
and House, 1992). However, no matter in which form gold exists, sorne is liberated in
grinding circuits where it accumulates because of its density and malleability (Basini et
CHAPTERONE INTRODUCTION 2
al 1991). Therefore, gravity concentration can be incorporated in the recovery
flowsheet. Dorr and Bosiqui (1950) emphasized the importance ofrecovering gold from
the 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 includes
gold 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 GRG
behaviour 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 load
once a full scale unit is installed or (b) how much goId will be recovered at steady-state
by 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 units
in 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), as
capital 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 to
reduce 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% of
capital and operating costs can thus be truncated, and the resulting flowsheet would be
environmentally more attractive, if only for political reasons. For such projects, the
economic 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 lesser
role, 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 its
gangue (Banisi, et. al. 1991); therefore, it moves slower from its natural grain size into
finer size classes than its gangue. Gold, and particularly GRG, also has a distinct
behaviour 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, at
Agnico-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). This
yielded 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 (or
their progeny) circulate between 50 and 100 times in a grinding circuit and build up to
very high circulating loads, 2000-8000%, and often leave the grinding circuit only once
they are overground (Laplante, 2000. Basini et al, 1991). Thus, in the absence of
gravity, 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 or
passivation, 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 for
gravity concentration are the ball mill discharge, the primary cyclone underflow and
perhaps the SAG mill discharge (Agar, 1992). In most gold mines, the primary gravity
concentrator usually treats part or all of the primary cyclone underflow or ball mill
discharge to recover liberated gold. The primary gravity concentrate is then upgraded
with 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 bullion
is more than 99% and is received almost immediately, while gold in flotation
concentrate 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 up
behind mill liners is minimized*; (iii) the removal of some of the gold by gravity
concentration 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 reducing
soluble 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 gold
particles 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 can
also 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 gold
directly 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 gravity
separation equipment (a Reichert cone) has resulted in significant decreases in the
consumption of reagents in the oxide flotation circuit (Venter et al, 1982). Gravity gold
recovery 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 percent
increase 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 gravity
recoverable gold (GRG) was used successfully to estimate the gold liberation of over 75
samples (Laplante et al, 1993). The main stumbling block in the application of gravity
separation 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 recovery
using multi-linear regressions. Third, the developed regressions are linked to a new
concept, the recovery effort, the Pso of gravity recoverable gold (GRG), the retention
time 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 a
population balance model.
2). To develop simple regressions for predicting GRG recovery using the gravity
recovery 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 /lm
reports to the cyclone underflow, R..25Ilm)'
3). To assess the sensitivity of predicted goId recovery to the parameters of the
PBM.
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 using
a 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 how
important 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) was
proposed by Laplante (1992) (more details will be presented in Chapter three). The
model 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 be
described 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 their
gravity 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 or
stream that can be recovered by gravity at a very low yield «1%). It includes gold that
is 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 the
benefit 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 enhanced
separation). The Kneison Concentrator (KC) has been by far the most commercially
successfui centrifuge unit used for goId recovery. It was therefore appropriate to choose
a 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 the
tailing. 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 stage
1 to 400 g/min and 5 L!min for stage 3. These correspond to optimal settings as
determined 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 the
test 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. Figure
2-2 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 size
class, the minus 20 J.lm fraction, the lower limit is arbitrarily set at a 15 J.lm). Results
are 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
100
Particle size (IJm)
4-~~~~~~~~~~~~~----I--"- stage 1
"'i-~~~~~~~~~~-~~----I""""'-stage 2
4-~'----~--~~~~~~-~~---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 extracted
and 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 maximize
GRG 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 decrease
its 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 is
less 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 nugget
effect. 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 relative
standard deviation will be Jlj";;. This describes the fundamental sampling error and
does 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. It
has been proposed (Putz, 1994) that around 10 to 50 kg of material would be sufficient
for 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 SAG
or 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 North
America 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 enables
mineraI 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 behaviour
of 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). The
relationship 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 be
normalizable. 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 order
production 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 grinding
process 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 order
with 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 oft
Sj(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 silica
by grinding approximately 50 g silica and 4.88 g (consisting of 1240 flakes) of gold
from a single size class, 850-1200 ~m, respectively in a ball mill. Before grinding, the
samples were screened to determine the initial size distribution. Grinding was then done
incrementally for total times of 15, 30, 60, 90, 150, and 210 seconds. After each
grinding 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 gold
grinds 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 tried
to 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 of
fragments in the other size classes, and c) what proportion of the progeny and unbroken
material 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 different
samples 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* -R
GRG= 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 cyclone
partition curves. The curve can be obtained by analysis of three or four of the projected
cyclone 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 and
Shu, 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, tm
1000
'---------------------_._--
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 the
simulation (more detail will be discussed in Chapter three). Plitt' s model (1976) was
also 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 the
underflow 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
10 100
Particle 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 the
world, 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 velocities
of 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. There
are 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 (it
is now using a single unit and a smaller Knelson Concentrator in the gold room). This
change 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. Since
the 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 Béliveau mill used a
Knelson MD30 to treat its flash flotation concentrate (Putz et al, 1993; Putz, 1994). The
mill 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 flash
cell (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 theoretically
averages 60 Gs. For the KC-MD3, water is injected tangentially at high pressure into
the 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 density
can 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 slurry
then fills each ring to capacity to create a concentrating bed. Compaction of the
concentrating 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 is
usually 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 finest
size 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). Many
goId 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 many
design 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 and
Harris, 1993). Because of the different forces (60 Gs for KC, IG for the table) acted on
particles, 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 Béliveau. 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 the
minus 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 are
still 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 been
installed.
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 relationship
between 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 Béliveau 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. Jigging
is 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 to
O.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 open
tank, filled with a fluid, normally water, with a horizontal jig screen near the top, and
provided 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 mechanism
and 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 to
dilate 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 acceptable
recovery and is determined by the area of sereen bed. In other words, different
capacities result in different recoveries. Jig capacity varies depending on the jig
configuration, ore feed size, and adjustments of stroke length and speed. Coarser grains
can 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 circulating
load at the expense of low stage recovery.
1000100Particle size,J,lm
-o-KC
L • Jig
100 .."........---------~
80
60 "'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 only
Vincent 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 circulating
load 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 shows
that 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 McGill
gravity research group (Laplante et al., 1994). It makes use of a population-balance
model (PBM) that represents gold liberation, breakage and classification behaviour to
simulate gold gravity recovery in a grinding circuit. In this chapter, how the PBM
makes use of the characterization of GRG and its behaviour in unit processes will be
presented. This chapter is divided into three sections. In section 3.2, the derivation of
the PBM is shown, starting from a very simple, single class model, to progress to a
three-size class model and finally the full model. A limited number of circuits are
presented 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) is
described; values for the matrices that will be used in the PBM are given in sections
3.3.1 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 a
ball mill, and the total GRG is assumed to appear in the mill discharge as F. B
represents 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 fed
to the primary recovery unit (if the full discharge is not treated). Primary and gold room
recovery can be represented separately (e.g. as P and G), but if both tailings are
combined, 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 includes
both GRG freshly liberated (i.e., F) and GRG that was present in the cyclone underflow
and 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 the
ball 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 F
that 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:
DR*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, 0.98
for 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 baIl
mill 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 and
recovered by Reichert Cones (P2 = 0.85), the concentrate is upgraded by Knelson
Concentrator. 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 and
gold 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 2
1- 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= 0.3
0.2°
0.99
°[
0.1
P= °°
°0.2
°
[
0.5
R= °°
°0.35
° o.u [
0.9
B = 0.06
0.03
°0.95
0.04
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 37
Overflow....-----,
p
Primary 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 the
exarnple above, 0.2 (20%) is in the coarse size class, 0.3 (30%) in the interrnediate size
class and 0.2 (20%) in the fine size class2, for a total GRG content of 70% (30% of the
gold in the ore in non-GRG). For the classification matrix C, shown above, we assume
that 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 the
screen oversize, whereas aIl of the GRG in the second and third size class report to the
screen undersize (henee a fraction of 0.2 of the cyclone underflow stream). For primary
recovery 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 material
transfer 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 mill
once, 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 main
diagonal 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" becomes
non-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 for
easier identification) or square matrices. With the exception of the B matrix, the square
matrices 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= 2.596
1.932[
0.0690]D= 0.1817
0.1353
Summing X and D yields, respective1y, total goId recovery, 0.3859 (38.6%) and
the circulating load of GRG, 5.91 (591%). From the GRG recovery matrix, it can be
observed 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 before
being 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 block
diagram shown in Figure 3-4 (Laplante, Woodcock and Noaparast, 1994). As material
is ground and discharged, GRG is generated as E. A primary concentration step yields a
proportion Pi of each size class (forming a diagonal matrix P) that is then presented to a
gravity separator for upgrading. From each size class, a GRG recovery of ri (forming a
diagonal 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 returned
to 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 to
finer size classes (the lower triangular submatrix of B). Given the above description, it
can 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 size
class. 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 various
components of the model is case specifie. For example, retrofit applications will be able
to 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 gravity
circuits, where gold is recovered from the primary cyclone underflow. Figure 3-6
represents goId recovery from the primary cyclone underflow, as practiced at Casa
Berardi (CB), Québec.
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
1000100
Particle 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 simply
multiplies 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 different
size distributions, which were fitted with four parameters). The problem was corrected
by 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 each
curve, 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
100
Partide size (~m)
0+------.---.-------,-------,-----,--,--,-,--,-----="'"---""1""""-"
10
"'0
~ 80 +----~d.co+-'Q)
~ 60Q) +--------"IIl'-.-~~~
>+:ico::J 40 -+-----~-____1t:-"11<;--
E::Jocfl. 20 +----------"""-;;=-----=:;;.-lI~5O:___'k"l~""='''=_-~~---_1
Figure 3-8 Coarse and Fine GRG Size Distributions (down to 25 !lm) Used forSimulation (Hatched lines: fine GRGs; solid lines: Coarse GRGs)
3.3.2 Unit Matrices
For aU unit matrices, the overaU algorithm is a size-by-size description of the
processes. Each matrix row corresponds to a size class, typicaUy starting with +600 !lm
for size class 1 down to the -25 !lm for size class 12, the finest one.
Recovery matrices CP and R matrix)
P and R are diagonal matrices, expressing the recovery of GRG in size class i of
the primary gravity unit (P) and gold room (R). Recovery usually can be set when
designing a gravity circuit by the selection and size of concentration equipment.
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 primary
stage 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) and
the 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 a
simple equation 3-11 of the type (Austin et. al, 1984):
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 47
Hl! 0 0 0 0
H 21 H 22 0 0 0
M d = H 31 H 32 H 33 0 0 *M Equation 3-12f
0
H n1 H n2 H n3 H n4 H nn
Each Hjj (on the main diagonal) is the fraction which remains in the original size
class j. the terms Hij (i>j) below each mail diagonal Hjj are the fraction which enter the
finer size class i from the original size class j. The assumption that no material can exit
the 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<j).
The finest size class (the -25 !-Lm fraction) was included in the matrix to model
its gravity recovery. This is atypical. When modeling the breakage of ore, the mass in
the finest fraction (the "pan") is not explicitly modeled, since it cannot be ground in a
finer size class, and is calculated by mass balance conservation. However, when
modeling GRG breakage, (i.e. not total gold), sorne of the GRG in the finest size class
becomes unrecoverable due to over-grinding. In this work, the assumption used by
Laplante et al (1995) that 98% of the GRG in the finest size class remains GRG in the
discharge will be used (i.e. Hnn = 0.98). The same assumption is used for the second
finest size class.
The elements Hij in the grinding matrix B are function of the breakage and
selection functions of the material and the residence time distribution in the mill --Hij =
j(Si*'t, bij). The formula shown below are used to calculate the elements Hij of matrix B
for plug flow and perfectly mixed residence time distributions, respectively:
Equation 3-13
Equation 3-14
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 48
For this work, the residence time distribution is assumed to follow Weller's
RTD which consists of one plug flow, one large perfect mixer and two small perfect
mixers, with 10% in the plug flow, 70% in the large perfect mixer and 10% in each of
the two small perfect mixers.
B =T * [I+S i * 'ts] -2 * [I+S i * 'tlrl * exp[-Si * 'tpd *rI Equation 3-15
where
T, rI are linear transformation matrices
'tpf, 'tl, 'ts are residence time of plug flow, large, small perfect mixer, respectively.
The selection function of GRG is based on the findings of Banisi, Laplante and
Marois (1991) at Golden Giant. They found that at the coarser end of grinding, 850
1200 !lm, the selection function of gold was twenty times lower than that of the ore, and
that in the finer range, 37-53 !lm, it was six times lower. Other selection function values
can be calculated assuming a log-linear function with particle size. This link between
GRG and gangue grinding kinetics was used to generate B matrices for gangue that
correspond to the B matrices for GRG.
The breakage function, b ij , used in this simulation is that from the Golden Giant
Mine (it is assumed that the breakage function for aIl GRG is the same) (Noaparast,
1997).
Typical values of B grinding are shown in Table 3-2, for a dimensionless mean
retention time of unity, which corresponds to the original survey at Golden Giant Mine
(Banisi, 1990). The high values on the diagonal matrix suggest that even the coarsest
GRG has a low probability of being "selected" for grinding, which is the case with a
high circulating load of ore, say above 500%. It will be lower with lower circulating
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 49
loads, but rarely below 0.75. The probability of survival of the -25 !-Lm and the 25-37
!-Lm fractions is arbitrarily set at 0.98, as previously discussed.
Table 3-2 Typical B Matrix for GRG
Size, 600- 425- 300- 212- 150- 106- 75- 53- 37- 25- -25
J..lID 850 600 425 300 212 150 106 75 53 37600 .945425 .036 .954300 .004 .031 .960212 .003 .004 .027 .966150 .002 .002 .003 .023 .971106 .002 .002 .002 .002 .020 .97575 .001 .001 .001 .002 .002 .017 .97953 .001 .001 .001 .001 .001 .002 .014 .97937 .001 .001 .001 .001 .001 .001 .001 .014 .97525 .000 .001 .000 .001 .001 .001 .001 .001 .010 .980-25 .001 .001 .001 .002 .002 .001 .002 .002 .002 .007 .980
In this work, different B matrices are first obtained by changing "C from 0.5 to 3,
to reflect different grinding conditions. The pre-corrected grinding matrix is computed
with the input values of "C, breakage (bij) and selection function (Si) of the material in a
baIl mill simulation, using two Basic language programs called BALLDATA and
BALLMILL developed by McGill gravity research group. The final grinding matrix B
(corrected grinding matrix B) is then corrected by using the work of Noaparast to take
into account the losses from GRG to non-GRG due to smearing, overgrinding or
excessive flaking, using the factors shown in Table 2-1. The columns of the corrected
grinding matrix B for GRG SUffi up to less than unity.
Classification CC Matrix)
C is a key component in estimating goId recovery because fine GRG grinds very
slowly, and is therefore primarily removed from the grinding circuit either to the
cyclone overflow or in the gold gravity concentrate. Unfortunately, the database for
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 50
GRG partition curves is fragmentaI, as is the link between the partition curve of GRG
and that of its gangue. As a result, the generation of partition curves both for GRG and
its gangue can only be generated if sorne assumptions are made. It is understood that
further plant work will be necessary to validate the approach used here, and to extend it
to coarser grinds (the existing data covers mostly grinds of 65% to 85% passing 75 j.lm).
Plitt's model was used to represent the partition curves of GRG and its gangue.
Table 3-3 shows the parameters used to generate the partition curves of GRG
and its gangue used in this work. Figure 3-9 shows the resulting partition curves. The
following assumptions are made: Cl) the bypass fraction is set at 25% for all partition
curves, (2) separation sharpness increases with increasing corrected Dso, from 1.1 to 1.2
for GRG and 2.0 to 2.5 for its gangue, and (3) the ratio of corrected Dso of GRG and its
gangue varies from 1:6 to 1:9, increasing with decreasing cut size.
The partition curves of Figure 3-9 will first serve to assess how sensitive GRG
recovery is to classification, and will be refined as the industrial database is expanded.
AlI in all, although it seems that the approach proposed for the generation of GRG
partition curve lacks a good database, it is in agreement with generally observed trends
(i. e. decreasing separation sharpness at fine size). It will also provide the framework for
a future thorough fundamental study of this problem.
Table 3-3 Parameters Used to Calculate the Partition Curves
Coarse Classification Intermediate Classification Fine ClassificationParameters
GRG Ore GRG Ore GRG Ore
dso(llm) 14.1 80.0 10.1 68.0 8.5 60.0
m 1.2 2.5 1.1 2.3 1.1 2
Rr % 25 25 25 25 25 25
R.2Sum % 73.8 26.6 82.8 28.1 87.2 30.6
CHAPTER THREE SIMULATING GOLD GRAVITY RECOVERY 51
....... Medium GRG
1000
- - -- Fine GRG
--Fine Ore
--Medium Ore
- - - - Coarse GRG
100
Particles Size (IJm)
100 ~-----~---=-""-~.-~.~'''''...'~~._._~._~.~~---------,.// ~_;";", A
90 / /' 1./,..,/ 4f
80 1-
•70 +----------f-I---I--______i
60 +---------f--I'---I-~--_____I
--Coarse Ore50 +--------7-+--->~-______i
40 +------7'-;~<----_____I
30 +--------:;......-:~==--------j
20 +------~----------I
10+----o +--~-~'-----'----'-'--L--L-'L-'-'-+-1-==:;===:;::::==>=::;:=::=:::::;=:::;::::;'
10
Figure 3-9 Partition Curves of GRG and Ore for the Three Classification Cases(Fine, Intermediate, Coarse)
CHAPTER FOUR
CHAPTER FOUR
SIMULATION RESULTS 52
SIMULATION RESULTS
4.1 Introduction
In this chapter, a basic case study of simulation and typical simulation results are
shown in section 4.2.1. A new concept, the gravity recovery effort (Re), is introduced in
section 4.2.2. Section 4.2.3 explores the extent to which operation parameters affect the
GRG circulating load and recovery. Section 4.3 presents how the output of the model
can be represented by multilinear regressions for coarse and fine GRG distributions.
Section 4.4 links the grinding and classification of the gangue to the dimensionless
grinding time parameter 't and the percent of GRG in -25 /-lm reported to the underflow
of cyclone (R-25f.lm), as a means of back-calculating these parameters (from the
circulating load of ore and the Pgo of the grinding circuit). Finally, a case study is
presented.
4.2 Simulation Results
4.2.1 Basic Case Study
Consider the gravity recovery circuit shown in Figure 3-4, which recovers gold
from the ball mill discharge. The GRG size distribution, E, is shown in Table 4-1. The
size-by-size primary recovery matrix P and goId room recovery R of Tables 2-4 and 2-5
will be used for the basic case simulation. The product of P*R, shown in Table 4-2, is
multiplied by the fraction of the ball mill discharge bled to gravity recovery to describe
CHAPTER FOUR SIMULATION RESULTS 53
the complete gravity circuit. In the simulation, this fraction will vary from 2% to 25%
(the treated fraction used in Table 4-2 is 12%).
Table 4-1 GRG Size Distribution ESize class +25 +37 +53 +75 +106 +150 +212 +300 +425 +600
(!lm) -25 -37 -53 -75 -106 -150 -212 -300 -425 -600GRG
Content % 20.0 10.0 15.0 10.0 15.0 12.0 9.0 4.0 4.0 1.0 0
Table 4-2 The Recovery Matrix P*R (for a Bleed of 12%)
Size -850 -600 -425 -300 -212 -150 -106 -75 -53 -37 -25(!lm) +600 +425 +300 +212 +150 +106 +75 +53 +37 +25
+600 0.046 0 0 0 0 0 0 0 0 0 0+425 0 0.059 0 0 0 0 0 0 0 0 0+300 0 0 0.070 0 0 0 0 0 0 0 0+212 0 0 0 0.075 0 0 0 0 0 0 0+150 0 0 0 0 0.082 0 0 0 0 0 0+105 0 0 0 0 0 0.089 0 0 0 0 0+75 0 0 0 0 0 0 0.090 0 0 0 0+53 0 0 0 0 0 0 0 0.085 0 0 0+38 0 0 0 0 0 0 0 0 0.079 0 0+25 0 0 0 0 0 0 0 0 0 0.062 0-25 0 0 0 0 0 0 0 0 0 0 0.043
Table 4-3 Grinding Matrix B (for a 't value of 1)
Size -850 -600 -425 -300 -212 -150 -106 -75 -53 -37 -25(!lm) +600 +425 +300 +212 +150 +106 +75 +53 +37 +25
+600 0.919 0 0 0 0 0 0 0 0 0 0+420 0.057 0.932 0 0 0 0 0 0 0 0 0+300 0.008 0.048 0.943 0 0 0 0 0 0 0 0+212 0.004 0.007 0.004 0.952 0 0 0 0 0 0 0+150 0.003 0.003 0.006 0.034 0.960 0 0 0 0 0 0+105 0.002 0.003 0.003 0.004 0.029 0.967 0 0 0 0 0+75 0.002 0.002 0.002 0.002 0.004 0.024 0.972 0 0 0 0+53 0.001 0.001 0.002 0.002 0.002 0.003 0.020 0.977 0 0 0+38 0.001 0.001 0.001 0.001 0.002 0.001 0.003 0.017 0.981 0 0+25 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.013 0.964 0-25 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.002 0.006 0.98
CHAPTER FOUR SIMULATION RESULTS 54
Table 4-4 Classification Matrix C (for a R 251lm value of 82.8%)
Size -850 -600 -425 -300 -212 -150 -106 -75 -53 -37 -25(Ilm) +600 +425 +300 +212 +150 +106 +75 +53 +37 +25
+600 1 0 0 0 0 0 0 0 0 0 0+420 0 1 0 0 0 0 0 0 0 0 0+300 0 0 1 0 0 0 0 0 0 0 0+212 0 0 0 1 0 0 0 0 0 0 0+150 0 0 0 0 1 0 0 0 0 0 0+105 0 0 0 0 0 1 0 0 0 0 0+75 0 0 0 0 0 0 1 0 0 0 0+53 0 0 0 0 0 0 0 0.996 0 0 0+38 0 0 0 0 0 0 0 0 0.977 0 0+25 0 0 0 0 0 0 0 0 0 0.927 0-25 0 0 0 0 0 0 0 0 0 0 0.828
The corrected B matrix is shown in Table 4-3. The mean retention time used to
calculate B is 't' = 1 (i.e. the B matrix derived from the original Golden Giant data).
The C matrix shown in Table 4-4 and Figure 3-9 was obtained at a R251lm value
of 82.8% ("average" GRG classification) and a sharpness value, m, of 1.1.
Figure 4-1 shows how much GRG is recovered from each size fraction for the
intermediate GRG size distribution, when 5 and 12% of the mill discharge is bled to
gravity recovery. The recovery in the coarser size classes is low because there is very
little coarse GRG in the ore, whereas in the fine size classes, the GRG recovery is lower
due to the poor unit recovery of fine GRG (very apparent in Table 4-2). The drop at the
53-75 /-lm size fraction is due to the low GRG content of this specifie size class
compared to that of the adjacent classes.
CHAPTER FOUR SIMULATION RESULTS 55
1000
-8-12%B1ElErl
---+- 5% B1ElErl
100
Partide Size, IJm
16 --r--"'~~-~~~~~--~~~~~~~-.~ 14 +---------,1111~--__1~ 12 +-----llllk:---+.P-'\:----\----1
~ 10 +----*,.......J------\=\---=============---I8 8 +-------jLJ-----~-"r--------__lIDa::: 6 +--------f--r-------\rt---------I
~4+---it'-~------------.:l~---------i(9 2 -+-- ~----------"~'r<_---_1
O+-----r--..,--..,...-r-r--r-r..,.....,---r----r---;-~~_r_r_I
10
Figure 4-1 GRG Recovery When Treating Bleeds of 5 and 12% (Data ofTables 4-1~4-4)
Figure 4-1 shows that when the bleed increases from 5 to 12%, the absolute
increase in gravity recovery is relatively constant between 25 and 212 /lm, but is lower
above 212 /lm and higher below 25 /lm. These results are linked to the GRG transfer
mechanisms, mosdy grinding at coarse size and classification at fine size.
4.2.2 Gravity Recovery Effort
Before showing the impact of operating variables, a new concept, the gravity
recovery effort (Re), is now introduced first because of its effectiveness to represent the
effect of the gravity circuit on overall GRG recovery (Laplante and Xiao, 2000). The
gravity recovery effort (Re) is defined as the product of the circulating load1 treated by
1 If the mill discharge is treated, the portion of the mill discharge treated is used.
CHAPTER FOUR SIMULATION RESULTS 56
the primary gravity unit, the recovery of this unit, and gold room recovery. For
example, if a circulating load of 10% is treated, with a primary recovery of 50%, and a
gold room recovery of 90%, the gravity recovery effort (Re) is equal to 10%*50%*90%
= 4.5%. When simulating with the PBM, the gravity recovery effort (Re) can be
calculated by summing the amount of GRG in the ball mill discharge (or cyclone
underflow when recovering from there) and that recovered in the various size fractions,
and taking the ratio of the two sums:
X is equal to [1-BC*(1 - PR)r1 *E and D to PR*[I-BC*(l-PR)r1*E (Eq.3.8).
4.2.3 Impact of Operating Variables
Figure 4-2 shows, for the basic case study, GRG recovery as function of Re for
the three partition curves of Figure 3-9. GRG recovery increases with increasing Re,
being roughly proportional to the 10garithm of Re (the curves are slightly parabolic). For
the coarse classification, GRG recovery is 41 % at a recovery effort of 2%; when the
recovery effort is increased fivefold to 10.4%, GRG recovery increases to 68.7%. For
other classifications, the absolute GRG recovery increase is almost the same, as the
three lines almost are paralle1. The range of recovery effort of Figure 4-1, from 2% to
12%, corresponds to the range of actual plant operation.
CHAPTER FOUR SIMULATION RESULTS 57
100:::R --+-Coarse0 80~ 1 Classification(J) 1
> 60 --e--- intermediate00 Oassification(J) 400:::(9 -Ir-Fine0::: 20 Oassification(9
01 10 100
Recovery Effort, 0/0
Figure 4-2 GRG Recovery as Function of Recovery Effort with Coarse,Intermediate and Fine Classification
GRG recovery is affected by classification. For example, at a recovery effort of
5.3%, GRG recovery is 67% for the fine classification, 64% for the intermediate
classification, and 58% for the coarse classification. The difference is essentially linked
to the two finest size classes, which are the most likely to report to the cyclone
overflow.
CHAPTER FOUR SIMULATION RESULTS 58
'*1:C~~ 60 -1-~~~~~~~-------;;;;;;lIIIt'==-~~~~~-jo~ --+- Coarsesta::: 40 +-~--~~~~IIIIf""'!.~~~---1
c> GRGa:::c> 20 --- Rnest
GRG
10 100
O+--.....---.--.,.--,--r--r-.,....,....,---.;:==;::~::::;::::::;:~
1
~covery Blort, %
Figure 4-3 Impact of GRG Size Distribution to GRG Recovery
The GRG size distribution affects its recovery. Figure 4-3 shows, for the
operating conditions of the case study, the link between recovery effort and GRG
recovery for the coarsest and finest of the GRG size distributions (of the database 20
GRGs). When processing 10% of ball mill discharge, the recovery effort is 5.4% for
the finest GRG and GRG recovery is 37.1%; for the coarsest GRG, the recovery effort
is slightly higher, 6.2%, but GRG recovery jurnps to 85.2%. Figure 4.3 also shows that
the impact of Re is more significant for the finest GRG distribution, and virtually linear.
For the coarsest GRG, linearity is clearly lost at high Re values.
Beside the primary recovery, the goId room recovery also has a significant effect
on overaU goId recovery based on the actual plant practice and the simulation results.
Gold room recoveries of 50% to 97% were measured by the McGill research group
(Laplante, 2000). When gold room recovery decreases, Re also decreases and so does
the GRG recovery. A survey of GRG content in goId room table tailings from fifteen
plants shows that almost aU of the gold particles in the -150 /-lm fraction were liberated
(Laplante, Huang and Harris, 2000). This would indicate that variations in observed
CHAPTER FOUR SIMULATION RESULTS 59
goId room recovery are much more a function of practice than mineralogy. It also
means that improving gold room performance is important, and not only possible, but
also easily achieved.
The effect of grind size on GRG recovery can also be important because of
liberation (Laplante, 2000). Figure 4-4 illustrates how the GRG content in each size
class increases at progressively finer size (i.e. for the three stages of the GRG test), for a
--+--25
-11-25-37
-I1r-37-53
-.;A:-.... 53-75
-:*-75-106
-106-150
-+-150-212
-212-300
-300-425
~425-600
--m-- 600-8501000100
Particle size (j..Im)
13 ~---'------~'12 +-------
11 ~-----~---------!10 +-----------")(i::--\------""'\~-----~I
(99
O:::8+----------=~----"~-\-~----j(9::i 7 j-------+;;...-~-\--~r_'~--I
~6-1----------~....---~-------l
ü5+--------------"I;:1~--__j'#. 4 -1----------------'\:---'----1
3+-------
2 t-------~~==_-.1+------l...I:::===L..t:=:===:::::I..J-----Io -t--...,.---,--r-..,....,...-r-r-n--.....,..---,---,--r-r'-r-rri
10
Figure 4-4 %GRG in Size Fractions (legend in f.lm) as a Function of the Pso for thePhoenix NNX3 Sample
gold-copper ore. As expected, the GRG content in the coarsest size classes liberates at
coarse grind and does not increase with decreasing Pso, whereas the amount in the finer
size classes does. The finest size class, the minus 25f.lm fraction, shows the most
CHAPTER FOUR SIMULATION RESULTS 60
significant increase, from 3% to 12%. With more GRG liberated, the potential for
recovering GRG is higher.
100
80>-CI) 60>0Co)CI) 400:: ~CoarseC) 200:: --.-FineC)
~ 00
1 10 100
Recovery Effort, %
Figure 4-5 GRG Recovery as a Function ofthe Recovery Effort for Fine (Pso =751J.m) and Coarse (Pso= 150 IJ.m) Grinding, NNX-3 Sample
This information can then be used to model GRG recovery. Fine
classification!grinding was modeled with 't = 1 and R 25Jlm = 87%, whereas coarse
classification!grinding used values of't and R 25Jlm of 0.5 and 73%, respectively. The
amount of GRG is, in both cases, obtained from Figure 4-4. Figure 4-5 shows GRG
recovery at the two grinds and recovery efforts of 4%, 8% and 16%. GRG recovery
increases with increasing recovery effort for both grind sizes. The GRG recovery of the
finer grind/classification is slightly higher (10% to 13%) at the three recovery efforts.
The increase in recovery is only modest, because the finer grind liberates mostly fine
GRG, which is difficult to recover. The effect of the recovery effort is more significant
at fine grind, which releases fine GRG recovered more effectively at a higher recovery
effort (16%).
CHAPTER FOUR SIMULATION RESULTS 61
4.3 Representing Results with Multilinear Regressions
4.3.1 Criteria and General Approach for Representing the Simulated
Database
The final multilinear regressions can be represented by the following response
function:
where
RGRG is the recovery of total GRG
b i are regression coefficients
Xi are independent or synergetic variables (described below)
The independent variables of the multilinear regressions include Re, because of
its obvious link to gravity recovery, as weIl as 't, R-25~m and points of the GRG size
distribution, expressed as cumulative % passing (GRG_x) (-x means below size class x).
The five GRG distributions of Table 3-1 (including the fine and coarse GRG of
Figure 4-3) were first used to generate a database of 845 simulations using the PBM.
Microsoft's Excel© was used to generate multi-linear regressions. A number of
regressions were initially performed with a large different number of independent first
and second order terms and synergetic variables, in a step-wise fashion. Both the
independent variables and their natural logarithm were tested as independent variables,
and the latter retained because of their better fit. Variables that were not significant at
99% were deleted, as were variables that were significant but could be deleted without
increasing the lack of fit significantly. This yielded a first regression equation with a
standard error of 1.7%. The summary output and ANOVA are shown in appendix F
(page 131).
CHAPTER FOUR SIMULATION RESULTS 62
Although this first regression equation was found to fit the five original GRG
size distributions weIl, it fared poorly when validated with other GRG distributions.
Worse, for sorne distributions, the predicted effect was contrary to phenomenological
logic-- i.e. a finer size distribution would yield a higher GRG recovery. The poor fit was
traced to the use of only five different GRG size distributions in the original data set,
which were fitted with four parameters (t, Re, R-25j.lm, GRG_x), effectively leaving only
one degree of freedom for the effect of GRG size distribution. This rather obvious
shortcoming had been obscured by the rather large data set, which gave the regression
in excess of 800 degree of freedom. As a result, it was found necessary to add additional
simulations with different GRG size distributions to increase the regressions' reliability
and phenomenological correctness.
4.3.2 Regressions for Fine and Coarse GRG Size Distributions
A total of twenty GRG size distributions (shown in Figure 3-5) were used, split
into two sets, fine and coarse GRG. The multi-linear regressions were also performed
again with a large number of independent variables that include the first and second
order terms and synergetic terms. FinaIly, variables that were significant at 99% and
could not be deleted without significantly increasing the lack of fit were retained. It
was found that the separate regressions yielded a better fit than the original regression
with fewer parameters. Table 4-5 shows which variables were retained in the final
regression equations (aIl as naturallogarithms).
CHAPTER FOUR SIMULATION RESULTS 63
Table 4-5 Variables of Regression Analyses
Dependent Variable Independent VariablesRe Re *'t R-25/lm 't GRG-25/lm GRG-75/lm GRG.15O/lm
Fine GRGs(RfGRG) X X X X X X X
Coarse GRGs(RcGRG) X X X X X X
where
RfGRG and RcGRG are the GRG recoveries of fine and coarse GRG Slze
distributions, respectively.
GRG.25Ilm is the cumulative GRG content below 25 j..lm, in %
GRG-75Ilm is the cumulative GRG content below 75 j..lm, in %
GRG-1501lm is the cumulative GRG content below 150 j..lm, in %
The summary output and ANOVA for fine and coarse GRG regressions are
shown in Appendix F. The two regression equations are, for the fine GRG size
distribution data set,
RfGRG = -233.09 + 17.l0*ln (Re) +3.61 *ln (Re)*ln ('t)+60.71 *ln (R..25 /lm)-11.92*ln ('t)-4.34*ln (GRG-25 f!m) -57.77*ln (GRG-75 f!m) +55.51 *ln (GRG.150 f!m)
and for the coarse data set,
RcGRG = -65.4 + 15.59*ln (Re) +5.49*ln (Re)*ln ('t)+37.81 *ln (R.25 f!m)-17.26*ln ('t)-30.04*ln (GRG_75 /lm) +12.67*ln (GRG.150 J.!m)
The coarse GRG regression has a poorer fit than the fine GRG regression
because of the increased range in size distributions, as apparent from Figure 3-8 in
Chapter 3.
CHAPTER FOUR SIMULATION RESULTS 64
The parameters have minimum t values of 8.07 and 18.57 for the coarse and fine
regressions, respectively. More importantly, the very small number of parameters now
used to represent the effect of particle size makes both regressions more robust. In fact,
each parameter is now phenomenologically consistent, and as is the difference in
numerical value of corresponding parameters in the two regressions. For example, both
regressions predict that the effect of the gravity recovery effort is strongly positive (the
most significant parameter in both cases---the highest t value), but more so for fine
ORO size distributions. The only synergetic parameter predicts that when grinding is
intense (i.e. a high 't value), the recovery effort becomes more important (to recover the
coarse ORO before it grinds). The third parameter predicts that the finer the
classification (the higher R..251Jlll)' the higher the ORO recovery, especially for fine ORO
size distributions. The fourth parameter predicts that the higher the retention time in the
ball mill, the lower the ORO recovery is, but more so for coarse ORO size distributions.
The remaining parameters characterize the effect of the ORO size distribution, and all
predict that as the amounts of fine increases or coarse decreases, ORO recovery
decreases.
4.3.3 Comparing the Regressions and Original PBM and
Phenomenological Correctness
Figure 4-6 compares the fine regression and actual simulation (PBM), using the
ORO size distribution of a Battle Mountain sample (Mid-Midas sample). Table 4-6
shows the actual and normalized ORO size distributions. It is assumed that 't is equal to
0.7 and R..251lm to 74%. The line represents the regression equation, and the points
represent the PBM results. The fit is good.
CHAPTER FOUR SIMULATION RESULTS 65
Table 4-6 Actual and Normalized GRG Size Distribution for Mid-Midas Sample
Size class -25 +25 +37 +53 +75 +106 +150 +212 +300 +425 +600(/lm) -37 -53 -75 -106 -150 -212 -300 -425 -600
Actua1 GRGContent % 18.6 11.2 13.4 9.7 9.3 4.6 1.2 1.0 0.2 0.10 0.10
NormalizedGRG% 26.8 16.1 19.3 14.0 13.4 6.6 1.7 1.4 0.3 0.14 0.14
...
1--- //
/r----------• PBM
- Regression I--~
70
~ 60o
~ 50(1)
~ 40(,)
~ 30
~ 20
C) 10
o1 10
Recovery Effort, %
100
Figure 4-6 Comparing the PBM and Regression for Fine GRG
(Mid-Midas Sample)
Campbell Mine's GRG was used to compare the PBM and the regression
equation for coarse GRG. Table 4-7 shows its actual and normalized GRG size
distribution. Values of 3 for 't and 87.2% for R_251lm are used.
Figure 4-7 shows that the fit is not as good as for the fine regression, as the
coarse regression underestimates GRG recovery by 1 to 2%. Because the fit of the
coarse GRG regression is not as good (mean lack-of-fit of 2.4% compared to 1.9% for
fine GRG), this result is not unexpected. The lack-of-fit is certainly within the accuracy
of the PBM and the GRG test, which is estimated at 5% relative.
CHAPTER FOUR SIMULATION RESULTS 66
Table 4-7 Actual and Normalized GRG Size Distribution for Campbell Mine Sample
Sîze class -25 +25 +37 +53 +75 +106 +150 +212 +300 +425 +600(/lm) -37 -53 -75 -106 -150 -212 -300 -425 -600
Actual GRGContent % 10.4 6.6 7.7 5.7 6.7 5.2 5.6 5.7 5.5 2.1 5.6
NormalizedGRG% 15.6 9.9 11.5 8.5 10.0 7.8 8.4 8.5 8.2 3.1 8.4
A~J&Y
Y/~
--_.•A PBM
- Regression
90
80
?ft. 70
~ 60CI)
~ 50u& 40
C) 30lX:C) 20
10
a1 10
Recovery Effort, %
100
Figure 4-7 Comparing the PBM and the Regression for a Coarse GRG Distribution
(Sample from Campbell mine)
The fit of the regression equation depends on the value of the independent
parameters chosen. For example, for the above example, the fit improves if't is lowered
to 2.3 to 2.5, but lowering 't further worsens the fit.
CHAPTER FOUR SIMULATION RESULTS 67
10 100
Recovery Effort, %
";!. 00 +----------.-----------1
~ 00 +-------~---;;/I;=-----------I>o~ 40
0:::C> 30 -1-------7/----
0::: ~~gi~ffiGC> 20 -;------------[
-Ir-RnerGRG10 +---------------'=======~
O+---,...--..,..-r--r--r--r-r...,....,-----r--...,---r--.-..,.....,.-,--.,--t
1
Figure 4-8 Effect of GRG Size Distribution on GRG Recovery (Original GRG: 27%
-25 j.tm and 76% minus 75 j.tm; finer GRG: 32% -25 j.tm and 81 % minus 75 j.tm)
Figure 4-8 shows what happens if the GRG content is made finer, in this case
(the Mid-Midas GRG size distribution was used) an increase of the % cumulative
passing 25 j.tm from 27 to 32% and the % passing 75 j.tm from 76% to 81 %. GRG
recovery decreases by 3 to 5%, depending on the recovery effort.
When the retention time in the mill is increased, finer material and GRG are
produced. GRG recovery decreases. To illustrate this, GRG recovery was calculated by
using the regressions for a recovery effort of 5%, using the Campbell Mine and Mid
Midas GRG size distributions, at R-251lm = 74%. The GRG decrease is more significant
for the coarser Campbell GRG size distribution, as shown in Figure 4-9. Because the
range of't of Figure 4-9 is very large, from 0.6 to 4, it probably exaggerates the impact
of't in actual practice.
CHAPTER FOUR SIMULATION RESULTS 68
101
tau (dimensionless)
65 -r--'----'*' 60 +---------=
~ 55 -+-----------~Cl)
~ 50 +-----------o~ 45 -+-fineC) 40~ 35 +-L:~~:_c_o_a_rs_e____'_------~~-______;
30 4----,--......,-...,..........~!"""I'_r,__-_r__...,...........,..._.,......,....,._r_r4
0.1
Figure 4-9 GRG Recovery Decreases with Increasing Dimensionless
Retention Time in the Mill
Classification is a key variable for gravity recovery in grinding circuits. Fine
classification means that less fine GRG reports to the cyclone overflow, increasing
thereby its probability of recovery. Figure 4-10 shows the effect of classification
predicted by the regression for a fine GRG distribution (Mid-Midas). The three curves
are almost parallel with different recovery effort. The difference of GRG recovery
between coarse and fine classification in this case varies between 5 and 8%. Because
the range of classifications used in this work is relatively narrow, the impact of
classification may in fact be even greater than what is suggested in Figure 4-10.
CHAPTER FOUR SIMULATION RESULTS 69
100908070605040302010o
.-6A
~-
rw~"- Goarse-
Glass..,• Medium
Glass.)1( Fine
Glass.
1
Recovery Effort 0/0
10
Figure 4-10 Gravity Recovery as a Function of the Recovery Effort for Fine
GRG and for Coarse, Medium and Fine Classification Curves
4.4 Estimation of't and R 25J1m
4.4.1 Representing the Grinding Circuit Design Parameters with 't and
Both the PBM and the regressions use one grinding parameter, 't, and one
classification parameter, R..25~m' These two important parameters are difficult to
measure directly, as they represent concepts rather than hard measurements. To solve
this problem, the behaviour of the ore will be linked to that of GRG, and its grinding
and classification simulated to generate two variables that are well understood and
CHAPTER FOUR SIMULATION RESULTS 70
easily measured or predicted, the fineness of grind (% minus 75 Ilm in the cyclone
overflow) and the circulating load of ore. The link between the partition curve of GRG
and gangue shown in Figures 3-9 will be used to simulate the classification of gangue.
The link between the selection function of gold and that of the gangue at Golden Giant
(Banisi, 1990) will be used to mode! the ore (gangue) grinding kinetics. For each
combination of parameters of t and R..251!m for GRG, a breakage matrix and partition
curve will be determined using the above links, and then the circulating 10ad and
fineness of grind of the ore calculated. The approach requires a fresh feed size
distribution, which will be taken here as that of the primary mill at Golden Giant, as
reported by Banisi. Thus a limited database, shown in Appendix G, is generated to link
t and R..251-lm to the circulating load and fineness of grind of the ore. This database is
summarized using two multilinear regressions (details are in Appendix G):
CL = -131 + 30*ln (t) - 1.97*ln (t)*R -251!m + 75.6 *ln2 t + 4.54 * R.251-lm Equation 4-1
where
f-751!m = 44.8 + 0.458 * R -251!m +8.0*ln (t) - 1.74 * ln2 t Equation 4-2
CL is the circulating 10ad of ore, in %, and
F -751!m is the fineness of grind, as the % of ore finer than 75 /lm in the
cyclone overflow.
Figures 4-11 and 4-12 present the link between the circulating load of ore and
fineness of the cyclone overflow on one hand, and t and R..251!m on the other. Both
curves show that a finer grinding product is achieved at constant circulating 10ad by
increasing R-251-lm and 't, actions that work in opposite directions when it cornes to
gravity recovery (i.e. as 't increases GRG recovery drops; as R-25 I-lm increases GRG
recovery increases).
CHAPTER FOUR SIMULATION RESULTS 71
-+-70___ 75
-.-ao~a5
-.-90
o+---.,.............-.,.............-,---,..----r-----l
150 200 250 300 350 400 450
5
1
4+-----------------1
10)I.~
"0c:'C
<.9enQ)3..1.o--~------------l
~ E1 c: ï= ~---"'1IIII---=~~~~---:-:.Q 2
enc:Q)ECi
Circulating Load, %
Figure 4-11 't as a Function of the Ore Circulating Load and Product Size (% minus
75 /lm in the cyclone overflow)
• 70
• 75
• 80)( 85
)k 90
LL.......:::>o......
100 -r----------~--=jr____~-,
90 -+- ~=.L! -_~_~-1
80 -j--~~~_=ooA~_=___~~-j
70 -r-~~'IIIIII--_:a,.........,~~~-!1
60 ~~---------!I
50~------·
40 +--+--+--.........,..--+---+-...;
150 200 250 300 350 400 450
0/0 Circulating Load---_._----- ----_._---
Figure 4-12 R 2511m as a Function of the Ore Circulating Load and Product Size (%
minus 75 /lm in the cyclone overflow)
CHAPTER FOUR SIMULATION RESULTS 72
1: varies over a wider relative range than R..25Jlm in Figures 4-11 and 4-12 (e.g. at
a circulating 10ad of 250%, from approximately 1.2 to 2.7 vs. 66% to 88%).
Nevertheless, the effect of classification is more important, since it has higher
regression coefficients, 60.7 vs. 11.9+3.6 * ln (Re) for the fine GRGs and 37.8 vs. 17.3
+ 5.5 * ln (Re) for the coarse GRGs. Table 4-8 shows that when product fineness is
increased from 70% to 90% minus 75 /lm at a circulating load of 250%, the change in
recovery at a recovery effort of 5% due to 1: is -5% and that due to R..25Jlm is 18%. For
coarse GRGs, the difference is much smaller, -6.8% vs. +14.1%.
Table 4-8 Effect of Changing Product Fineness from 65 to 88% minus 75 /lm at a
Circulating Load of250% (1:: 1.2 to 2.7; R-25Jlm: from 66 to 88%), For Re = 5%
Regression Parameter Fine GRGs Coarse GRGs
Muitiplying 1: -11.9+3.61 *ln(Re)= -6.11 -17.26+5.49* In(Re)= -8.42
Multiplying R-25Jlm 60.71 37.81
Impact of 1: on GRG Rec. -6.11 *ln(2.7/1.2) = -5 -8.42*ln(2.7/1.2) = -6.8
Impact OfR..25Jlm on GRG +60.71 *ln(88/66) = +18.4 +37.81 *ln(88/66) = +14.1
Rec.
4.4.2 Case Stndy
A gold-copper ore is to be ground to 75% -75 /lm, using a SAG mill / baIl mill
circuit with a circulating load of 250%. The feed averages 2 g/t, 60% of which is GRG
with the "intermediate" size distribution (Figure 3-7, Table 3-1). What is the predicted
GRG recovery with these parameters by using the regressions and PBM?
CHAPTER FOUR SIMULATION RESULTS 73
-Regression
The first step consists in determining the appropriate grinding and classification
matrices by using equations 4-1 and 4-2 or Figures 4-11 and 4-12, yielding values of
71.5% of the -25 !lm partition curve reporting to the cyclone underflow (R-25Ilm =
71.5%) and 1.5 for the dimensionless retention time in the ball mill (r = 1.5). GRG
recovery is then generated as a function of the recovery effort using the predicted
regression for fine GRGs. In order to compare with the PBM, a 't value of 1.5 was used
to generate the grinding matrix and a R..251lm value of 71.5% was used to estimate the
classification matrix. GRG recovery as a function of recovery effort, shown in Figure
4-13, was then generated.
80 ~~~_._-------"--------,
70 +-------------...11111.-='-------------f
?fl. 60 +---------.....IIII"'------------f
~~ 50~ 40+---~~------------_____j
~ 30 +-....J......'--------r---=---~P~B:;-;M~---~ffi 20 +---------1
10 +-----------'--------------'---1
O+-----,.--.---r--,...-.,~,.._,_,---.--,....-.,...-,-.,--,-,-___!
10
Gravity Recovery Effort %
100
Figure 4-13 GRG Recovery as a Function of Re (Cu-Au ore Case study)
The regression fits the PBM well in this case. Although Figures 4-11 and 4-12
may vary slightly depending on the size distribution of the feed to the ball mill/ cyclone
circulating load, they can be used as a first approximation of't and R-25Ilm• Future work
will be needed to produce more robust estimates.
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION
CHAPTER FIVE
MODEL RELIABILITY AND VALIDATION
5.1 Introduction
74
The purpose of this chapter is threefold: first, to evaluate the reliability of the
model; second, to validate the model using actual case studies; and finally, to discuss
model extrapolation and industry application.
5.2 Model Reliability
The regression equations were developed to estimate gold recovery in grinding
circuits based on the Population-Balance Model (PBM). As shown in the previous
chapter, the regression equations can represent the PBM well for either coarse or fine
GRG distributions, well within the accuracy that is normally needed to predict gold
gravity recovery. The regression equations, however, are only as reliable as the PBM
is; the PBM, in tum, is only as reliable as its various input parameters (or matrices
derived from these parameters) are.
The GRG-25Ilrn, GRG-75Ilrn, GRG-1501lrn variables are used in the fine GRG
regression equation and only the GRG-75Ilrn, GRG-1501lrn variables in the coarse
regression. The coarser size GRG content, such as the percent passing 300 /lm, 425 /lm
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 75
and 600 /lm, was also included initially in the multilinear regression, but is not
significant. This indicates that the finer size GRG content is more important than that of
the coarser size for predicting gold recovery, as it is more difficult to recover. When the
PBM model is used, the full size distribution is used -i.e. E.
Reliability first requires reproducibility. The reproducibility of the GRG test,
discussed in Laplante, Woodcock (1995), is conservatively estimated at a relative 5%. It
depends on the nature of the deposit (how variable it is), what is the source of the
sample (SAG feed is possibly the most difficult to sample, drill cuttings the most
reliable) and how weIl the sample extraction protocol is respected, and as such will vary
from test to test. Sampling problems can be virtually eliminated between the
complementary tail and feed grades of the test by using 600 g of tails for the screening
step followed by pulverizing the +105 /lm fractions, but assaying remains a source of
uncertainty. By comparison with amalgamation and mineralogical results, Woodcock
(1994) concluded that the GRG test recovered an of the GRG in the ore. At the final
grind of 80% -75 /lm, as Httle as 3% and as much as 97% of the gold has been
recovered (Laplante, 2000), which is an indication that the test recovers only GRG and
aIl of the GRG.
An additional source of uncertainty stems from the relatively high weight
recovery of the three stages, typically 0.1-0.15% for stage 1 and about 0.3% each for
stages 2 and 3. Woodcock (1994) thought that the high yield can lead to an over
estimation of the amount of GRG by 5% when low-grade sulfide ores are being
processed. He suggested that the solution for those ores where the yields of stage 2 and
3 were above 1% and the sulphide content below 5% is to use no less than 18 kg of feed
for the third stage (typically 24 kg is now used). Recent work (Laplante, 2001) suggests
that approximately 4 to 6% of the sulphides are recovered when a low-grade sulphide
sample is processed, which implies that 4 to 6% of the gold associated with the
sulphides would also be recovered as gold in goId carriers. The weight recovery of
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 76
stage 1 is now further lowered by cleaning the five coarsest size classes of the
concentrate using a hydrosizer, which further reduces weight recovery to 0.3 to 0.04%
(Laplante, 2001). The hydrosizer concentrate is examined microscopically to assess
potential liberation problems. Whenever the GRG is largely liberated, much of the
uncertainty is dispelled. Examining concentrates from well over 20 samples has shown
startling difference in liberation, from virtually totally liberated to totally unliberated
(but with a significant gold content). These differences most certainly have an incidence
on how much of the GRG can be recovered by gravity, but this has never been
characterized, and could impact the reliability of the test.
Because the GRG test ends at a grind of 80% -75 /lm, actualliberation of GRG
in a grinding circuit may differ. It is suspected that preferential classification of GRG
bearing particles to the cyclone underflow would achieve better liberation that the test at
equivalent grind, and may produce slightly more GRG, to compensate for gold carrier
recovery discussed in the previous paragraph.
Many GRG standard tests have been completed using the Knelson Concentrator
with duplicated sample, such as with the sample from Louvicourt Mine, Alumbrera
(Laplante, 2000) and Alaska-Juneau (Woodcock, 1994), to test the reproducibility.
Generally, duplicate tests yield very similar results (the curves of the cumulative GRG
recovery as a function of particle size are very close). When head grade is significantly
different, GRG content may vary, typically in the coarse size range. This is consistent
with the observation often made that gravity recovery increases with head grade. This
attests to the overall reproducibility of the results obtained from GRG standard test, but
suggests that accurate modeling should take head grade into account when its impact on
GRG content is significant. It also suggests that a representative sample for GRG
should be one that has a representative head grade.
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 77
5.2.2 R 25f1ID and C Matrix
R..251lm is used in the regression equations to represent the classification matrix of
GRG used in PBM. The behaviour of gold in the cyclone(s) is very important for GRG
recovery. In aH the grinding circuit surveys analyzed by the McGill University research
group, about 98% to 99% of aH GRG fed to a cyclone reports to its underflow, unless it
is a primary cyclone in a two-stage classification circuit. GRG below 25 f.lm still
reports to cyclone underflow in a proportion ranging between 75 and 95% (Laplante,
2000). It is also confirmed by an plant data generated by the McGill group that GRG
above 37 f.lm overwhelmingly reports to the cyclone underflow. UsuaHy, a typical gold
partition curve, shown in Figure 2-3, shows that nearly 100% of GRG above 53 f.lm in
the cyclone feed reports to the cyclone underflow. However, there is still considerable
uncertainty as to how the partition curve of goId below 37 f.lm is affected by parameters
such as rheology or the cut size of gangue.
---+- Ore*
-El-- Gold*
---+- GRG*
-)(- Ore
~Gold
--e--- GRG
1000100
100 ~-........~~~M~~"'-.î90 -+----------,11W'C--.----j<ry------i ,------,
80 -t------"Â'rf------,--f----x-------I
70 -+----~_f__----+---f-------I
60 -+-------f----j~--------I
5040 -+-------v"-7'L-------~1
30 -+---------,~---------I
20 +--~~~~~~~~~~I10 '-------'
0-+---'----'--'--'--'-"-'-'+---'---'--l.-c......J.....J..........,
10
LI.-:::)S~o
Particle Size, IJm
Figure 5-1 Partition Curve for Ore*, Gold* and GRG* with a Saprolitic Component
(Data of Fig. 2-3 obtained from a paraHelline without saprolite has been included)
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 78
Figure 5-1, which cornes from the parallel circuit from which Figure 2-3 was
generated (and incorporates its data), but includes a large proportion of saprolite in the
feed, shows that the same ore in the presence of a phase that significantly increases
apparent viscosity, the gold curve can be different in the finer size range, especially
below 25 Ilm (although here GRG recovery is comparable). More work is required to
address the effect of rheology.
For simulation, to err on the cautious side, the GRG below 37 Ilm reporting to
the cyclone underf10w has been conservatively decreased from what has been observed
thus far, as discussed in section 2.3.1.4.
Another significant source ofuncertainty is the use of coarse grinds, such as Psos
of 100 to 200 Ilm, common in Australia but atypical in Canada, where most of the
existing database was generated. As a result, the relationship between the amount of
GRG below 25 Ilm reporting to the cyclone underf10w and the circulating load, the
fineness of grind (% ore below 75 Ilm to the overf1ow) is ambiguous, especially at
coarse grind. For example, in Figure 4-12 at 70% -75 Ilm, the recovery of GRG to the
cyclone underf10w at a circulating load of 250% is pegged at 66%. This is overly
conservative, as sorne of the earlier work at Camchib (Liu, 1989) suggested a GRG
recovery of 88% for the -37 Ilm fraction at a fineness of 66% -75 Ilm. Laplante and
Shu (1992) reported that at the same plant, the recovery to the underf10w of total gold
below 25 Ilm was 69%, which would imply a much higher GRG amount reporting to
the cyclone underf1ow. Therefore, at coarse grinding and classification, more plant
surveys are needed to refine estimates of the partition curve, especially in the finest size
classes.
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION
5.2.3 't and B Matrix
79
The B matrix in the PBM was replaced by 't in the regression equations. As
mentioned in chapter four, B was generated from the selection function of gold, which
is difficult to measure. The correction factors proposed by Banisi (1990) were used to
derive a selection function for gold and ore. Grinding kinetics (breakage and selection
function) also affect GRG recovery, but to a lesser extent than classification (see the
discussion in section 4.2.3). 't can affect GRG recovery more for coarse GRGs (i. e.
with faster grinding kinetics) or at low recovery effort.
Of particular concern is the role of the GRG grinding kinetics in grinding
circuits whose configuration is drastically different from that of Golden Giant, where
the feed to the first grinding loop (primary cyclones and secondary baIl mill) was
relatively fine, 5% retained at 600 !-Lm. Recent exploratory work in a South African
mill, where single stage SAG milling is used, suggests much higher values of't for the
same fineness (Laplante, 2001).
5.2.4 Re and R Matrix
Even though the effect of Re is only logarithmic, it remains the most significant
regression variable -i.e. the most critical in predicting GRG recovery accurately. There
are two sources ofuncertainty in estimating Re.
First, it is known that the efficiency of primary units such as semi-batch
centrifuges is significantly affected by operating conditions, such as gangue specifie
gravity, rotating velocity, screen and the feed rate (Laplante and Ling, 1998). For
example, the existing database does not include enough data from operations that use
high feed rates to maximize goId production at the expense of stage recovery and that
use high rotating velocity to recovery efficiently the fine GRG. Further, for recently
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 80
developed or modified units, such as 30-in and 48-in KC with new mner cone
geometries and Falcons SB-2I and SB-38, few or no plant surveys are available. These
units now dominate the field of gold gravity recovery, because of new projects or
retrofits. Therefore, the existing database is in critical need of being updated for
estimating Re.
Second, large differences in gold room recovery have been observed, and impact
directly on Re. The range in performance indicates that sorne gold rooms are superbly
operated, whereas others are loosing a significant amount of GRG, even though it has
already been upgraded into a very small mass.
5.3 Model Validation
5.3.1 Campbell Mine Case Stndy
100
80(!)c::: 60(!)(J)
40>:.;::::;~ 45.5% -75 f.lm::J 20E::J 15.8% -25 f.lm() 0- 1 1 ! 1111_~0
10 100 1000
Partide Size, ~m
Figure 5-2 Campbell Mine Cumulative GRG as Function of Particle Size
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 81
The tirst model validation case will be the Campbell mine. A standard GRG test
was performed, yielding a GRG content of 66.8%. Figure 5-2 shows the normalized
cumulative GRG content (100%) as function ofparticle size. Because the GRG content
above 150 /lm is 36.7% (100%-63.3%), which is over 25%, the coarse regression
equation will be used to predict recovery. The Camchib ore is similar to Campbell in its
low sulphides content, which makes it possible to estimate primary recovery within
reasonable limits from Knelson performance at Camchib. Table 5-1 shows the basic
data used, which was obtained from mill personnel (Bissonnette, 2001). The treated
circulating load is 20%, primary recovery is 60% (Vincent, 1997) and gold room
recovery is 90% (a small Knelson is used to recover tine gold from the table tailing).
Re, the product of all three, is equal to 10.8%. Based on circulating load of 250% and
the tineness of grinding of 80% -75 /lm, the dimensionless retention time in the mill
was estimated to be 1.7 and the R.25J.lm to be 78%. All the parameters used to predict
recovery are shown in Table 5-2.
Table 5-1 Basic Data from the Campbell Grinding Circuit
Circulating Fineness of Circulating Primary GoldLoad Grinding Load Treated Recovery Room
Recovery
250% 80%-75/lm 20% 60% 90%
Table 5-2 Experimental and Estimated Data Used for Predicting GRG Recovery inCampbell Mine
Recovery Dimensionless GRG Content GRG ContentEffort Retention Time R 25 f!m Below 751lm below 150llm
Re 1:
10.8% 1.7 78% 45.5% 63.3%
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION
Table 5-3 Predicted and Reported Oold Recovery for Campbell Mine
Predicted Predicted ReportedGRG Gold Gold
Recovery Recovery Recovery
72.1% 48.2% 50%
82
With the data from Table 5-2, the regression equation predicts a ORO recovery
of 72%, which corresponds, at a ORO content of 66.8%, to a gold recovery of 48.2%,
which is slightly below the gold gravity recovery of 50% reported when the ORO
sample was extracted (Table 5-3). Oravity recovery has since dropped, because of
lower head grades.
The accuracy of predicted gold recovery depends on the estimation of't and R_25
Ilm. Table 5-4 shows the impact of relative changes of ±1O%, ±20% and ±50% in three
parameters of Re, 't and R..25Ilm• Within the ranges tested the most significant parameter
is R_251lm (because of its high value in Table 5-2, only lower values were explored). This
confirms the need to investigate ORO classification further.
Table 5-4 Sensitivity Analysis of the Impact of Relative Change of Re, 't and R..251lm
Change Range Re 't R_251lm RGRG % Rgo1d %%
+ 10% 11.88~9.72 1.7 78 73.9~70.2 49.3~46.9
Re +20% 12.96~8.64 1.7 78 75.5~68.0 50.4~45.4
+50% 16.2~5.4 1.7 78 79.6~59.3 53.2~39.6
+ 10% 10.8 1.87~1.53 78 71.7~72.5 47.9~48.5
't +20% 10.8 2.04~1.36 78 71.3~73.0 47.7~48.8
+50% 10.8 2.55~0.85 78 70.4~75.0 47.0~50.1
-10% 10.8 1.7 70.2 71.3 47.6R..251lm -20% 10.8 1.7 62.4 66.8 44.6
-50% 10.8 1.7 39 49.1 32.8
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION
5.3.2 Northern Québec Cu-Au Ore Case Study
83
A northem Québec Cu-Au mill, first operated at 10,000 t/d, was recently
expanded to 15,000 t/d. Two GRG tests yielded a GRG content of 54%. After
normalizing to 100%, around 25% of the GRG is finer than 25 !Jm, 59% than 75 !Jm
and 82% than 150 !Jm (i.e. it belongs to the fine GRG range). A plant report indicated
that 22% of circulating load was fed to Knelson Concentrator after screening. Screen
efficiency was assumed to be 80%. The feed rate to six 30-in Knelson Concentrators
was 25 t/h, and primary and goId room GRG recovery was assumed to be 50%, yielding
a recovery effort of 7.9%. The circulating load of grinding circuit was 250% at 10,000
t/d and the fineness of grinding was 70% -75 !Jm, from which 't and R..25 /lm values of 1.2
and 66% were estimated, respectively. AH the data used to predict gold recovery are
shown on the Table 5-5.
Table 5-5 Data Used for Predicting GRG Recovery on Northem Québec Cu-Au Ore
Recovery Dimensionless Gold GRG GRG GRGEffort Retention R.2511m Room Content Content Content
Re Timet Recovery Below Below below25um 75um 150llm
7.9% 1.2 66% 50% 25% 59% 82%
The fine GRG regression equation predicts a GRG recovery of 50.9% and a gold
recovery was 27.5%, very close to the measured gravity goId recovery of 28%. The
smaH difference can be explained by factors such as gravity circuit availability and
incomplete liberation of the GRG in the original tests.
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 84
100 1000
Particle Size (IJm)
After plant expansion to 15,000 t/d, the circulating load increased to 350% and
the fineness of grind dropped to 68.5% minus 75 !lm. Only 12% of circulating load is
now fed to the Knelson Concentrators, whose feed rate is approximately 35 t/h, at a
screen efficiency of 70%. Because the Knelsons are fed at a higher throughput of a
coarser product, their recovery was lowered to 40%. At a gold room recovery of 89.3%,
this yields a Re yale of 3.0% (=70%*40%* 12%*89.3%). Based on the circulating load
and the fineness of grind, a"[ value of 0.8 and 1L251-lm value of 71 % were estimated from
Equation 4-1 and Equation 4-2. The fine GRG regression equation predicts a total GRG
recovery of 41.3%, which corresponds to a gold recovery of22.3%. The measured gold
recovery is 23%, nearly the same as the predicted gold recovery.
5.3.3 Case Stndy: Snip Operation
At Snip, the gravity circuit consisted of a duplex jig treating the entire discharge
of a first baIl mill operated in closed circuit with one cyclone. Operations ceased when
the ore body was mined out.
~~---------'-------------------,
~ 100 -,--------~---__:E::::........,r:::: 90 ---t-------
~ 80 -I--------~~----__lD:: 70 -1--------~'---_____\_'~I!"f9t.~~r_____t
C) 60 -1-------.....;::::-----------1
~ 50 ---t-------59.1% -75 ID~ 40 -I----~--F--------=~--'-"-----'--"~~__l
:t:3 30 -I----~---------__l~ 20 -1--------'.--::;;;;;r-------------1
E 10 -+---------="lffl--01ii~::4ot_.._....___-____I
c3 0 +--...,....--,.....,........--r-t""'I""'t'"l""---r-.,--.,..-,.....,......,.~
10
Figure 5-3 Snip GRG Content Retained as Function of Particle Size
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 85
The GRG content of 57.8% (Vincent, 1997) has been normalized to 100% in
Figure 5-3. It belongs to the fine GRG size distribution set.
The grinding circuit used a ball mill with a circulating load range that varied
significantly, usually between 100% and 400%; the circulating load will be set to 250%.
The fineness of grinding was 75% passing 75 Ilm. Based on the above data, '[' is
estimated to be 1.5. Figure 4-2 in Vincent's thesis shows that 91 % of GRG below 25
Ilm reported to the cyclone underflow. Note that Figure 4.12 would predict a much
lower value of 71 %. From the jig and table recovery matrices used by Vincent (1997),
jig recovery ranged from 2% to 4%; the full circulating load was used. Table recovery
was measured at 80% at the lower jig yield and recovery and 60% at the higher jig yield
and recovery. Therefore, the range ofrecovery effort is between 1.6% (100%*2%*80%)
and 2.4% (100%*4%*60%). With these data (shown in Table 5-6), the fine GRG
regression equation predicts a GRG recovery from 41.3% to 48.8%, which corresponds
to a total goId recovery range from 23.8 to 28.1%. The reported gold recovery in year
1993,24.9%, is located in the range ofpredicted recovery, but the recovery of 36.8% in
1994 and 1995, is above the range.
Table 5-6 Data Used for Predicting GRG Recovery on Snip
Recovery Dimensionless Table GRG GRG GRGEffort Retention R..251lm Content Content Content
Re Time 't Recovery Below Below Below251lm 751lm 150llm
1.6-2.4% 1.5 90% 60-80% 20.5% 59.1% 83.7%
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION
5.3.4 Case Study: Bronzewing Mine
86
The Bronzewing GRG test yielded a GRG content of 88%, in the coarse GRG
data set. The cumulative GRG retained in each size class is shown in Figure 5-4.
The fineness of grinding circuit is 80% -75 /lm and the circulating load is around
250% (AMlRA P420A General Industry Survey, 2000), yielding a R.25~m of 77% and a
't value of 1.7.
100 -,--
"0i
ID 80 -1c::'(ti 59.5% -150 f.lm.....ID {
0::: 60 -1ID>:.;:;rn 40:::J
E:::J() 20~0
010 100 1000
Particle Size, I-Im
Figure 5-4 Cumulative GRG retained in each size class for Bronzewing Mine
The three 30-in Knelson Concentrators treat 29% of the circulating load with a
GRG recovery assumed to be 50% (on account of the coarseness of the feed). Gold
room recovery is assumed to be 85% (coarse gold is easily recovered in a two-stage
circuit, but no scavenging of fine gold is practiced). The recovery effort is equal to
12.4% (= 29% * 50% * 85%). Table 5-7 shows the data used for prediction. The
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 87
predicted GRG recovery, gold recovery and reported gold recovery are shown in Table
5-8. The relatively large range of reported gravity recovery covers the estimated
recovery, and suggests either a variable GRG content or unsteady operation (most likely
in the goId room).
Table 5-7 Parameter Used for Gold Recovery Prediction
Recovery Dimensionless GRG Content GRG ContentEffort Retention Time R25!im Below 751-lm Below 15Ol-lm
Re 't
12.4% 1.7 78% 32.2% 59.5%
Table 5-8 Predicted and Reported Gold recovery of Bronzewing Mine
Predicted Predicted ReportedGRG Gold Gold
Recovery Recovery Recoveryl
84.3% 74.1% 70-80%(1: from the AMlRA P420A General Industry Survey, 2000)
Figure 5-5 compares the measured and predicted recovery of the four case
studies (two case studies, the Cu-Au mill and Snip, yielded two points, and Bronzewing
yielded a range of measured recoveries). The agreement between measured and
predicted recoveries is good, the most significant difference being for the higher
recoveries of 1994 and 1995 at Snip, where the model actually under-predicted gravity
recovery. This study is based on a single measurement of jig performance based on
samples that were not extracted by the McGill research team. Disagreement for this
case study would have been higher if the R.25jlm value used had been estimated from
Figure 4-12.
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 88
100
•
80604020
'#. 100~Q.) 80>0()Q.)
600::""00 40<.9
""0Q.)- 20.2
""0Q.)1-
0a..0
11
LMeasured Gold Recovery, %
Figure 5-5 Measured and Predicted Gold Gravity recoveries of the Case Studies
5.4 Model Extrapolation and Application
5.4.1 Model Extrapolation
The model offers significant potential for extrapolation.
First, the model can be extrapolated to similar applications with operating
conditions outside those from which the simulate database was derived. This would fit
relatively small variations requiring simple adjustments, such as recovery from the
cyclone underflow, two-stage classification, harder ores, single stage milling or
secondary ball milling with a very coarse product. The PBM can easily handle these
changes, but the fundamental parameters 't and R Z5 f.lm would be estimated differently.
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 89
Second, the PBM needs to be extended to different applications such as recovery
from secondary regrind loads and "extreme recovery" -i.e. gravity circuits used as sole
or main recovery methods. Recovery efforts in such applications can exceed 20% and
GRG content often exceed 90%. It is expected that sorne of the simplifying
assumptions used that proved acceptable with modeling recovery efforts between 1 and
12% would probably no longer be valid. Regrind applications represent the opposite
end of the spectrum, with lower recovery efforts, low circulating loads of GRG, and a
relative1y low GRG content. The main impediment to this application of the PBM is the
absence of a regrind application database.
Third, the PBM could eventually be applied to different mineraIs that circulate
in grinding circuits, such as platinum group e1ements (PGEs, especially when in
metallic species), or other recovery methods from grinding circuits, the most obvious of
which is flash flotation. In a recent paper (2001), Duchesne et al. report on the
performance of flash flotation at the Louvicourt Mine concentrator, where gold
recovery by flash flotation greatly exceeds the GRG content when two flash cells are
used, and easily matches the GRG content with a single flash flotation cell. The
circulating load of goId (most of it GRG) significantly drops when the flash cells are
turned on, especially below 150 !lm (GRG above 150 !lm does not float well, as
reported by Putz and al., 1993). It is clear that the ability of fine GRG to circulate and
be presented to the flash unit contributes significantly to its ability to float gold
successfully even with a low retention time.
5.4.2 Model Applications
Sorne applications have been discussed elsewhere. Laplante et al. discussed
(1995) an optimization application at Camchib and a retrofit application at Casa
Berardi. The multilinear regressions, when coupled with the fast estimation of"C and R_
CHAPTER FIVE MODEL RELIABILITY AND VALIDATION 90
251lm, make greenfield applications much easier, and open the door for the optimization
of the recovery effort, as illustrated in Laplante et al. (2001) for a copper-gold ore. The
sensitivity analysis reported in Table 5-4 suggests that even at the greenfield stage the
methodology is accurate enough provided 't can be estimated with a 50% accuracy and
Re with a 20% accuracy. These accuracies can be achieved with the existing database,
and should be bettered, as the database grows. The uncertainty in K251lm may have
more impact on predicted recovery, and will require an extension of the existing
database, particularly at coarse grind.
The regression equations can also be used to quickly investigate "what if'
scenarios. For example, low gold prices often result in increases in throughput at
coarser grind. This results in changes in 't, K251lm and Re that aH contribute to a
decrease in gold recovery.
CHAPTERSIX
CHAPTERSIX
CONCLUSIONS AND FUTURE WORK 91
CONCLUSIONS AND FUTURE WORK
6.1 Introduction
The recovery of goId by gravity from grinding circuits differs from virtually all
other gravity recovery approaches. Its stage (or unit) recoveries are low, typically 1 to
5%, but overall recoveries are generally in the 25 to 60% range, because individual gold
particles are presented many times to the primary recovery unit. Although full-scale
recovery is difficult to predict from bench-scale tests, a novel methodology, using a
Population-Balance Model (PBM) that represents the behavior of goId both in the
traditional units of the grinding circuit and the units specifically used for gravity
recovery, was proposed to estimate gold recovery (Laplante et al, 1995). The focus of
this thesis was to present how to generate the equations to replace the PBM, test their
phenomenological correctness and validate them. The general conclusions are presented
in section 6.2. Following that, the strengths and the weaknesses of the protocol are
presented in sections 6.3. Finally, future work is discussed in section 6.4.
6.2 General Conclusions
The gravity recovery effort (Re), the GRG size distribution, the dimensionless
retention time in ball mill Ct) and the partition curve of GRG in the grinding circuit
(represented by R..25Ilm) all have a significant effect on the GRG recovery. Regression
CHAPTERSIX CONCLUSIONS AND FUTURE WORK 92
equations were generated to predict gold recovery, which was found proportional to the
natural logarithm of the recovery effort (Re), 1 and R.25j..lm. These last two parameters
were then linked to two fundamental design parameters of the grinding circuit, the
circulating load and the product size (the fineness of grind). The regression equations
derived from the PBM were shown to be phenomenologically correct, as weIl as
providing a very good fit to the database generated by the PBM. The most significant
term of the regressions is the recovery effort, which affects the recovery of coarse and
fine GRG in a similar way: GRG recovery is proportional to ln (Re) multiplied by a
constant that is equal to 15.6 to 17.1, with a minor correction for 1. Thus doubling Re
results in an increase of approximately Il% in GRG recovery, for the range of Re
investigated. A limited number of case studies have demonstrated that the protocol
yields very satisfactory predictions when compared to measured gold recoveries.
The effect of the GRG size distribution is also significant, and can be described
reasonably weIl with two to three points on the size distribution curve, again using
naturallogarithm terms.
Industry can benefit immediately from the results of this approach. These
benefits apply to a broad spectrum of gold recovery prediction: simulations with the
regressions can assist at the design stage to rationalize the size of gravity circuit or
during production to optimize its operation. Whether the actual PBM is used or its
simpler regression surrogate, 1 and R.25j..lm can be estimated rapidly and satisfactory for
most applications, particularly when the primary mill precedes the grinding loop where
recovery is located.
CHAPTERSIX CONCLUSIONS AND FUTURE WORK 93
6.3 Strengths and Weaknesses of the Proposed Protocol
The advantages of the proposed protocol are its low cost, small sample
requirement (for the GRG test) and the ease with which the goId recovery can be
predicted. Perhaps its most important benefit is that it quickly yields information about
the total GRG and goId recovery because it links the two fundamental parameters 't and
R-251lm to the circulating load and product fineness (whether design or actual). This
implicit linkage between the behavior of gold and that of the ore in the grinding circuit
also contributes to the robustness of the approach.
The standard errors of the regressions for fine and coarse GRG are 1.9% to
2.4%, respective1y (relative to the total GRG content), weIl within the error range of
GRG test itse1f, conservatively estimated at 5% (relative to the total GRG content). The
GRG test has been extensively validated, and is highly reproducible when sample are
extracted with the proper protocol and the ore itse1f not highly variable.
The regression equations can predict the total GRG recovery weIl, but the size
by-size information that the PBM can provide is then lost. Whilst this is not likely to be
the best approach when trying to optimize an existing gravity circuit, it is particularly
useful at the design stage, when much of the information needed for the PMB is
mlssmg.
Chapter five discusses that the GRG below 25 /lm reported to the cyclone
underflow is affected by other factors, such as the rheology (viscosity) of the pulp, but
the estimation of K251lm does not include these factors. It is not known at this time
whether extreme changes in rheology can affect GRG and its gangue in different ways,
i.e. such that the re1ationship between their cut-sizes or partition curves is modified.
CHAPTERSIX CONCLUSIONS AND FUTURE WORK 94
Finally, the regression equations were developed for a very specifie overall
recovery curve (i.e. GRG recovery vs. particle size). This relationship is known to
change from unit to unit, and even the same unit (e.g. Knelson Concentrator) is known
to give different relationships depending on the specifie feed rate and gangue density.
The validation exercise of Chapter 5 suggests that as long as the recovery effort is
reasonably estimated, overall GRG recovery will also be estimated with reasonable
accuracy. The linear relationship between GRG recovery and ln (Re) limits the impact
of the error on Re: a 10% error in Re, for example, results in only a 1.7% error in GRG
recovery. However, additional validation is required to increase the level of confidence
of the regressions.
6.4 Future Work
Future work is largely driven by the weaknesses identified in the prevlOUS
section.
The partition curve of GRG has a very important effect on the GRG recovery,
especially below 37 /lm. A database that would add both accuracy and reliability to the
link between ore and GRG classification has yet to be generated. In particular, the
following questions could be asked: is this link independent of rheology? (i.e. is the
classification of GRG and rock affected in a similar way?) Should the specifie gravity
of the GRG species and its gangue be taken into account? What is the true shape of the
partition curve of GRG?
The link of grinding kinetics between the gold and ore is based on a single case
study at Golden Giant (Banisi, 1990). Breakage and selection functions are known to
vary from ore to ore (i.e. gangue). They are key factors in determining the circulating
load and fineness of ore in grinding circuit, two important parameters for accurately
CHAPTERSIX CONCLUSIONS AND FUTURE WORK 95
predicting gold recovery. Obviously more work is needed in this area. In particular, the
effect of ore hardness (or toughness) should be taken into account. The link between
the grinding kinetics of GRG and its gangue is not readily generated, as reliable data
can only be extracted from grinding circuits without gravity recovery, but with a high
GRG content.
The relationship between 't and R..25 mfl on one hand, and the circulating load and
final product size, on the other, was produced from limited data (again, based on
Banisi's work). There is evidence that the 't values thus generated are inaccurate when
single stage grinding is used, and indeed in Chapter 5, a correction factor was applied.
Should this correction factor be based on the size distribution of the fresh feed, whether
a coarsely or finely crushed product? This question is relevant, as single stage SAG
milling is the South African standard, whereas Australian practice has long relied on
fine crushing and single stage ball milling grinding.
Because a number of platinum group element (PGE)-bearing mineraIs are dense
enough to accumulate in the circulating load of grinding circuit (as observed in the mills
of Inco Ltd. and Falconbridge in the Sudbury basin), it is worth to exploring how the
proposed methodology could be adapted to platinum/palladium grinding circuits. First,
one could evaluate if the GRG standard test protocol is suitable for the PGE ores, and
what additional mineralogical information is required. Next, the differences in the
classification and breakage behaviour of PGE-bearing mineraIs and their gangue could
be investigated. By focusing on gravity recoverable PGEs and their behaviour in
grinding circuits, the potential for gravity recovery could be explored (Laplante, 2000).
Although the McGill University gravity research group has measured the
performance of GRG units for more than ten years, there is no comparable database for
the performance of flash flotation units, in which the behavior of gold is difficult to
predict. Observation at Louvicourt Mine, MSV, Lucien Béliveau (Putz et al., 1993) and
CHAPTERSIX CONCLUSIONS AND FUTURE WORK 96
Chimo mine (Laplante, 2000) confirmed that the flash flotation is more appropriate than
gravity recovery when the GRG content is low and fine, because of the high circulating
load and good floatability of GRG below 150 !lm. Thus the recovery prediction
methodology could be applied, provided a recovery matrix can be generated to represent
the flash flotation. Non-GRG recovery can also be substantial in flash flotation
concentrates, and would also require sorne modeling. Recovery data could possibly be
generated using a database of existing flash units, but may require the use of a pilot unit.
This could represent a completely novel application of the GRG methodology.
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AppendixA
Breakage and Selection Function
Used for GRG and Ore
103
Table A-1 Breakage Function for GRG
104
Size (IJm)+425 0.75+300 0.08 0.75+212 0.04 0.08 0.75+150 0.037 0.04 0.08 0.75+106 0.026 0.037 0.04 0.08 0.75+75 0.019 0.026 0.037 0.04 0.08 0.75+53 0.0135 0.019 0.026 0.037 0.04 0.08 0.75+37 0.0093 0.0135 0.019 0.026 0.037 0.04 0.08 0.75+25 0.0092 0.0093 0.0135 0.019 0.026 0.037 0.04 0.08 0.75
Table A-2 Breakage Function for Ore
Size (IJm)+425 0.44+300 0.17 0.44+212 0.08 0.17 0.44+150 0.06 0.08 0.17 0.44+106 0.048 0.06 0.08 0.17 0.44+75 0.038 0.048 0.06 0.08 0.17 0.44+53 0.030 0.038 0.048 0.06 0.08 0.17 0.44+37 0.024 0.030 0.038 0.048 0.06 0.08 0.17 0.44+25 0.019 0.024 0.030 0.038 0.048 0.06 0.08 0.17 0.44
Table A-3 Selection Function for GRG and Ore
Size (IJm) 1 Si GRG Si Orel
+600 0.0863 1.194+425 0.0719 0.868+300 0.0598 0.63+212 0.0497 0.457+150 0.0414 0.332+106 0.0344 0.241+75 0.0286 0.175+53 0.0238 0.127+37 0.0197 0.091+25 0.0162 0.065
Appendix B
Grinding Matrix for GRG and Ore
105
Grinding Matrix for GRG
Table 8·1: RTD: Tau = O.S, ( PF=O.OS Ts=O.OS TL=0.3S)
106
Size (IJm) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.9582 0 0 0 0 0 0 0 0 0 0
+425 0.0305 0.9650 0 0 0 0 0 0 0 0 0
+300 0.0039 0.0257 0.9708 0 0 0 0 0 0 0 0
+212 0.0018 0.0032 0.0215 0.9756 0 0 0 0 0 0 0
+150 0.0016 0.0015 0.0026 0.0180 0.9796 0 0 0 0 0 0
+106 0.0011 0.0013 0.0012 0.0021 0.0151 0.9830 0 0 0 0 0
+75 0.0009 0.0010 0.0011 0.0010 0.0018 0.0126 0.9858 0 0 0 0
+53 0.0006 0.0007 0.0008 0.0009 0.0009 0.0015 0.0106 0.9882 0 0 0
+37 0.0004 0.0004 0.0005 0.0006 0.0007 0.0007 0.0012 0.0088 0.9902 0 0
+25 0.0004 0.0004 0.0004 0.0005 0.0005 0.0006 0.0006 0.0010 0.0073 0.9919 0
-25 0.0006 0.0009 0.0011 0.0013 0.0014 0.0016 0.0018 0.0020 0.0025 0.0081 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table 8-2: RTD: Tau = O.S, (PF=O.OS Ts=O.OS TL=0.S6)
Size (IJm) +6001 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.9344 0 0 0 0 0 0 0 0 0 0
+425 0.0471 0.9449 0 0 0 0 0 0 0 0 0
+300 0.0066 0.0399 0.9538 0 0 0 0 0 0 0 0
+212 0.0029 0.0053 0.0336 0.9614 0 0 0 0 0 0 0
+150 0.0025 0.0024 0.0043 0.0282 0.9677 0 0 0 0 0 0
+106 0.0018 0.0021 0.0019 0.0035 0.0237 0.973 0 0 0 0 0
+75 0.0013 0.0015 0.0018 0.0016 0.0029 0.0199 0.9774 0 0 0 0
+53 0.0009 0.0010 0.0012 0.0015 0.0014 0.0024 0.0167 0.9812 0 0 0
+37 0.0008 0.0008 0.0009 0.0010 0.0012 0.0011 0.0019 0.0139 0.9844 0 0
+25 0.0005 0.0005 0.0006 0.0007 0.0008 0.0010 0.0009 0.0016 0.0116 0.9872 0
-25 0.0012 0.0016 0.0019 0.0021 0.0023 0.0026 0.0031 0.0033 0.0040 0.0128 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table 8-3: RTD: Tau = 1.0 (PF=0.10 Ts=0.10 TL=0.70)
Size (IJm) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.9190 0 0 0 0 0 0 0 0 0 0
+425 0.0576 0.9318 0 0 0 0 0 0 0 0 0
+300 0.0085 0.0489 0.9428 0 0 0 0 0 0 0 0
+212 0.0036 0.0069 0.0413 0.9521 0 0 0 0 0 0 0
+150 0.0031 0.0030 0.0056 0.0348 0.9599 0 0 0 0 0 0
+106 0.0023 0.0026 0.0025 0.0045 0.0293 0.9665 0 0 0 0 0
+75 0.0017 0.0019 0.0022 0.0020 0.0037 0.0246 0.9719 0 0 0 0+53 0.0011 0.0014 0.0015 0.0018 0.0017 0.0030 0.0207 0.9766 0 0 0
+37 0.0009 0.0010 0.0012 0.0013 0.0015 0.0014 0.0025 0.0173 0.9806 0 0
+25 0.0007 0.0006 0.0008 0.0009 0.0010 0.0013 0.0012 0.0020 0.0144 0.9840 0
-25 0.0015 0.0019 0.0021 0.0026 0.0029 0.0032 0.0037 0.0041 0.0050 0.0160 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table B-4: RTD: Tau = 1.5, (PF=O.15 Ts=O.15 TL=1.05)107
Size (I..Im) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251+600 0.8898 0 0 0 0 0 0 0 0 0 0+425 0.0765 0.9068 0 0 0 0 0 0 0 0 0+300 0.0126 0.0655 0.9215 0 0 0 0 0 0 0 0+212 0.0052 0.0102 0.0558 0.9341 0 0 0 0 0 0 0+150 0.0044 0.0043 0.0082 0.0473 0.9446 0 0 0 0 0 0
+106 0.0032 0.0037 0.0035 0.0067 0.0400 0.9536 0 0 0 0 0+75 0.0023 0.0026 0.0031 0.0029 0.0054 0.0337 0.9611 0 0 0 0+53 0.0017 0.0019 0.0022 0.0026 0.0024 0.0044 0.0285 0.9675 0 0 0+37 0.0012 0.0014 0.0016 0.0018 0.0021 0.0020 0.0036 0.0238 0.9730 0 0+25 0.0011 0.0010 0.0011 0.0013 0.0015 0.0018 0.0016 0.0029 0.0199 0.9777 0-25 0.0020 0.0026 0.0030 0.0033 0.0040 0.0045 0.0052 0.0058 0.0071 0.0223 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table B-5: RTD: Tau = 2.0, (PF=0.20 Ts=0.20 TL=1.40)
Size (I..Im) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +531 +371 +251 -251+600 0.8474 0 0 0 0 0 0 0 0 0 0
+425 0.1031 0.8704 0 0 0 0 0 0 0 0 0+300 0.0190 0.0891 0.8904 0 0 0 0 0 0 0 0+212 0.0077 0.0153 0.0764 0.9076 0 0 0 0 0 0 0
+150 0.0063 0.0063 0.0124 0.0652 0.9221 0 0 0 0 0 0+106 0.0046 0.0053 0.0052 0.0100 0.0556 0.9346 0 0 0 0 0
+75 0.0033 0.0038 0.0043 0.0042 0.0081 0.0469 0.945 0 0 0 0+53 0.0024 0.0028 0.0032 0.0036 0.0035 0.0065 0.0398 0.9541 0 0 0+37 0.0017 0.0019 0.0022 0.0026 0.0030 0.0029 0.0053 0.0335 0.9617 0 0+25 0.0015 0.0014 0.0017 0.0019 0.0022 0.0025 0.0024 0.0043 0.028 0.9684 0-25 0.0030 0.0037 0.0042 0.00493 0.0055 0.0066 0.0075 0.0081 0.0103 0.0316 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table B-6: RTD: Tau = 3.0 (PF=0.30 Ts=0.30 TL=2.10)
Size (I..Im) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.7838 0 0 0 0 0 0 0 0 0 0+425 0.1390 0.8148 0 0 0 0 0 0 0 0 0+300 0.0306 0.1221 0.8421 0 0 0 0 0 0 0 0+212 0.0122 0.0247 0.1062 0.8661 0 0 0 0 0 0 0
+150 0.0094 0.0099 0.0199 0.0917 0.8865 0 0 0 0 0 0
+106 0.0069 0.0078 0.0081 0.016 0.0789 0.9043 0 0 0 0 0+75 0.0050 0.0057 0.0065 0.0065 0.0129 0.0674 0.9192 0 0 0 0+53 0.0037 0.0042 0.0047 0.0054 0.0054 0.0104 0.0575 0.9323 0 0 0+37 0.0026 0.0030 0.0035 0.0039 0.0045 0.0044 0.0084 0.0486 0.9434 0 0+25 0.0022 0.0020 0.0024 0.0028 0.0032 0.0038 0.0036 0.0068 0.0409 0.9531 0-25 0.0046 0.0058 0.0066 0.0076 0.0086 0.0097 0.0113 0.0123 0.0157 0.0469 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Grinding Matrix for Ore
Table B-7: RTO: Tau = O.S, (PF=O.OS Ts=O.OS TL=0.3S)
108
Size (IJm) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251+600 0.5916 0 0 0 0 0 0 0 0 0 0+425 0.1337 0.6746 0 0 0 0 0 0 0 0 0+300 0.0721 0.1149 0.7462 0 0 0 0 0 0 0 0+212 0.0411 0.0577 0.0949 0.8054 0 0 0 0 0 0 0
+150 0.0305 0.0313 0.0449 0.0759 0.8526 0 0 0 0 0 0
+106 0.0244 0.0231 0.0235 0.0342 0.0594 0.8896 0 0 0 0 0+75 0.0197 0.0185 0.0173 0.0174 0.0258 0.0455 0.9179 0 0 0 0
+53 0.0158 0.0148 0.0138 0.0129 0.0129 0.0192 0.0344 0.9394 0 0 0
+37 0.0127 0.0118 0.0111 0.0103 0.0095 0.0094 0.0142 0.0258 0.956 0 0
+25 0.0102 0.0095 0.0088 0.0082 0.0076 0.007 0.0069 0.0104 0.0189 0.9683 0
-25 0.0482 0.0438 0.0395 0.0357 0.0322 0.0293 0.0266 0.0244 0.0251 0.0317 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table B·S: RTO: Tau = O.S, (PF=O.OS Ts=O.OS TL=0.S6)
Size (IJm) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.4538 0 0 0 0 0 0 0 0 0 0
+425 0.1532 0.5489 0 0 0 0 0 0 0 0 0
+300 0.0940 0.1415 0.637 0 0 0 0 0 0 0 0
+212 0.0584 0.0793 0.124 0.7144 0 0 0 0 0 0 0
+150 0.0443 0.0463 0.0643 0.1041 0.7792 0 0 0 0 0 0
+106 0.0359 0.0345 0.0356 0.0505 0.0846 0.8319 0 0 0 0 0
+75 0.0292 0.0277 0.0264 0.0269 0.0398 0.0668 0.8735 0 0 0 0+53 0.0236 0.0224 0.0211 0.0198 0.0201 0.0295 0.0517 0.9057 0 0 0
+37 0.0192 0.018 0.017 0.0159 0.0148 0.0149 0.0221 0.0393 0.931 0 0
+25 0.0154 0.0145 0.0136 0.0127 0.0118 0.011 0.0109 0.0164 0.0292 0.95 0
-25 0.073 0.0669 0.061 0.0557 0.0497 0.0459 0.0418 0.0386 0.0398 0.05 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table B-9: RTO: Tau = 1.0 (PF=0.10 Ts=0.10 TL=0.70)
Size (IJm) +6001 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.3858 0 0 0 0 0 0 0 0 0 0
+425 0.1564 0.4829 0 0 0 0 0 0 0 0 0
+300 0.1029 0.1505 0.5766 0 0 0 0 0 0 0 0+212 0.0673 0.0897 0.1366 0.6619 0 0 0 0 0 0 0
+150 0.0519 0.0547 0.0746 0.1181 0.7353 0 0 0 0 0 0
+106 0.0425 0.0412 0.0429 0.0599 0.0981 0.7984 0 0 0 0 0
+75 0.0348 0.0333 0.0318 0.0328 0.0468 0.0789 0.8456 0 0 0 0+53 0.0284 0.027 0.0256 0.0242 0.0247 0.0358 0.0619 0.8842 0 0 0
+37 0.0231 0.0218 0.0206 0.0194 0.0182 0.0184 0.027 0.0477 0.9149 0 0+25 0.0186 0.0177 0.0166 0.0156 0.0145 0.0135 0.0135 0.0202 0.0357 0.938 0
-25 0.0883 0.0812 0.0747 0.0681 0.0624 0.055 0.052 0.0479 0.0494 0.062 1Sum 1 1 1 1 1 1 1 1 1 1 1
Table 8-10: RTD: Tau = 1.5, (PF=0.15 Ts=0.15 TL=1.05)
109
t
Size (IJm) 1 +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.2668 0 0 0 0 0 0 0 0 0 0
+425 0.1495 0.3596 0 0 0 0 0 0 0 0 0
+300 0.1131 0.1565 0.4571 0 0 0 0 0 0 0 0
+212 0.0822 0.1059 0.153 0.5526 0 0 0 0 0 0 0
+150 0.0665 0.0707 0.0935 0.1408 0.6400 0 0 0 0 0 0
+106 0.0558 0.0550 0.0580 0.0787 0.123 0.7169 0 0 0 0 0
+75 0.0468 0.0452 0.0439 0.0458 0.0637 0.1034 0.7813 0 0 0 0
+53 0.0387 0.0372 0.0356 0.0342 0.0353 0.0501 0.0839 0.8336 0 0 0
+37 0.0318 0.0304 0.029 0.0275 0.0261 0.0267 0.0386 0.0663 0.876 0 0
+25 0.0258 0.0248 0.0234 0.0222 0.0209 0.0197 0.0199 0.0292 0.0507 0.9092 0
-25 0.1230 0.1147 0.1065 0.0982 0.091 0.0832 0.0763 0.0709 0.0733 0.0908 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table 8-11: RTD: Tau = 2.0, (PF=0.20 Ts=0.20 TL=1.40)
Size (IJm) +212 +150 +1061 +75 1 +5311 +3711 +2511 -251
+600 0.1921 0 0 0 0 0 0 0 0 0 0
+425 0.1344 0.2755 0 0 0 0 0 0 0 0 0
+300 0.1132 0.1508 0.3695 0 0 0 0 0 0 0 0
+212 0.0089 0.1127 0.1567 0.4672 0 0 0 0 0 0 0
+150 0.0759 0.0812 0.1048 0.1520 0.5616 0 0 0 0 0 0
+106 0.0657 0.0654 0.0694 0.0920 0.1392 0.6485 0 0 0 0 0
+75 0.0562 0.0548 0.0538 0.0567 0.0771 0.1214 0.7240 0 0 0 0
+53 0.0473 0.0458 0.0441 0.0428 0.0447 0.0623 0.1014 0.7872 0 0 0
+37 0.0393 0.0379 0.0364 0.0347 0.0333 0.0344 0.0489 0.0821 0.8401 0 0
+25 0.0322 0.0311 0.0296 0.0282 0.0268 0.0254 0.0259 0.0375 0.0640 0.8817 0
-25 0.2348 0.1448 0.1357 0.1264 0.1173 0.1080 0.0998 0.0932 0.0959 0.1183 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Table 8-12: RTD: Tau = 3.0 (PF=0.30 Ts=0.30 TL=2.10)
ISize (IJm) II +60011 +42511 +30011 +21211 +15011 +10611 +7511 +5311 +3711 +2511 -251
+600 0.1080 0 0 0 0 0 0 0 0 0 0
+425 0.1029 0.1719 0 0 0 0 0 0 0 0 0
+300 0.1020 0.1287 0.2521 0 0 0 0 0 0 0 0
+212 0.0921 0.1121 0.1475 0.3441 0 0 0 0 0 0 0
+150 0.0848 0.0910 0.1136 0.1560 0.4411 0 0 0 0 0 0
+106 0.0777 0.0784 0.0839 0.1075 0.1542 0.5372 0 0 0 0 0
+75 0.0695 0.0685 0.0683 0.0727 0.0958 0.1433 0.6264 0 0 0 0
+53 0.0604 0.0591 0.0577 0.0569 0.0601 0.0812 0.1264 0.7052 0 0 0
+37 0.0515 0.0501 0.0486 0.0470 0.0458 0.0479 0.0663 0.1264 0.7741 0 0
+25 0.0430 0.0418 0.0403 0.0388 0.0372 0.0358 0.0370 0.0663 0.0864 0.8302 0
-25 0.2081 0.1984 0.1880 0.1770 0.1658 0.1546 0.1439 0.10211 0.1395 0.1698 1
Sum 1 1 1 1 1 1 1 1 1 1 1
Appendix C
GRGs Used for Simulation
110
GRGs Used for the Simulation111
Bilan1 Bilan2 Louvicourt East Malartic1 East Malartic 2
Size(lJm} GRG% Norm. % GRG% Norm. % GRG% Norm. % GRG% Norm. % GRG% Norm. %
+600 0.3 0.5 4.1 6.0 0 0.0 44.8 57.6 3.5 5.7
+420 0.4 0.7 3.5 5.1 1.4 4.1 1.1 1.4 1.9 3.1
+300 1.5 2.5 3.8 5.6 1.3 3.8 1.5 1.9 2.6 4.2
+212 1.9 3.2 1.9 2.8 1.7 4.9 2.0 2.6 3.5 5.8
+150 2.9 4.9 4.2 6.2 3.5 10.1 3.2 4.1 5.5 9.0
+106 4.5 7.6 4.3 6.3 3.7 10.7 3.7 4.8 6.5 10.6
+75 7.2 12.1 5.8 8.5 4.8 13.9 4.1 5.3 7.2 11.7
+53 6.3 10.6 5.3 7.8 4 11.6 3.8 4.9 6.7 10.9
+37 7.9 13.3 8.7 12.8 4.2 12.2 4.5 5.8 7.9 12.9
+25 7.2 12.1 8.1 11.9 3.9 11.3 2.8 3.6 4.9 8.1
-25 19.3 32.5 18.4 27.0 6 17.4 6.3 8.0 10.9 17.9
Sum 59.4 100.0 68.1 100.0 34.5 100.0 77.7 100.0 61.0 100.0
Selbaie Aelrd New Britannia William Mine David Bell
Size(lJm} GRG% Norm. % GRG% Norm. % GRG% Norm. % GRG% Norm. % GRG% Norm. %
+600 5.3 10.8 0.04 0.1 0.1 0.1 0 0.0 5.5 7.1
+420 4.8 9.8 0.12 0.2 0.2 0.3 0.3 0.5 9.1 11.8
+300 1.1 2.2 1.6 2.8 1.8 2.4 1.3 2.2 4.7 6.1
+212 0.6 1.2 2.93 5.2 1.9 2.6 1.4 2.4 3.1 4.0
+150 2 4.1 5.79 10.3 5.1 6.9 2.6 4.4 7.9 10.2
+106 3.2 6.5 4.72 8.4 7.2 9.7 3.7 6.3 7 9.1
+75 3.4 7.0 8.3 14.7 13.8 18.5 5.8 9.9 7.4 9.6
+53 3.1 6.3 4.18 7.4 12.6 16.9 6.1 10.4 5.7 7.4
+37 4.4 9.0 12.27 21.8 13.1 17.6 8 13.7 6.7 8.7
+25 2.2 4.5 11.9 21.1 8 10.8 7.3 12.5 5.5 7.1-25 18.8 38.4 4.43 7.9 10.6 14.2 22 37.6 14.7 19.0
48.9 100.0 56.28 100.0 74.4 100.0 58.5 100.0 77.3 100.0
CB'99 Bronzewing Eskay Creek Vaal River La Ronde
Size(lJm} GRG% Norm. % GRG% Norm. % GRG% Norm. % GRG% Norm. % GRG% Norm. %
+600 0.3 0.5 4.2 4.8 0.8 1.6 0.6 0.9 0 0.0+420 0.3 0.5 5.5 6.2 0.7 1.4 0.5 0.7 0.1 0.2
+300 0.8 1.3 5.5 6.2 2.8 5.6 0.8 1.2 0.9 1.8
+212 1.8 2.9 6.8 7.7 3.5 7.0 2.2 3.3 3.1 6.2
+150 4 6.4 13.8 15.6 6.4 12.9 6.3 9.4 5 10.0
+106 6.6 10.5 12.4 14.0 7.4 14.9 10.2 15.2 4.8 9.6
+75 10.4 16.5 11.6 13.1 9.2 18.5 13 19.4 6.9 13.8+53 8.9 14.1 6.6 7.5 6.3 12.7 8.6 12.8 3.6 7.2
+37 10.5 16.7 6.2 7.0 5.8 11.7 9.1 13.6 10.3 20.6+25 7 11.1 9.4 10.6 3.2 6.4 5.9 8.8 11.2 22.4-25 12.3 19.6 6.3 7.1 3.6 7.2 9.8 14.6 4.2 8.4
Sum 62.9 100.0 88.3 100.0 49.7 100.0 67 100.0 50.1 100.0
Note: %GRG means the actual measured GRG content ln an ore.%Norm. means the normalization of actual GRG content.
Appendix 0
An Example of Simulation
112
Simulation of GRG Recovery with the Operation Conditions as following:RTD PF=0.05 TS=0.05 TL=0.35 C matrix (R25~m = 73.8%)
113
Treated fraction" 015
[;JI Feed
IlPrimary
IlGold Room
1GRG% Rec. % Rec. %
+600 0 0.48 0.8425 1 0.58 0.85300 4 0.65 0.9212 4 0.68 0.92150 9 0.73 0.94106 12 0.77 0.9675 15 0.78 0.9653 10 0.75 0.9537 15 0.72 0.925 10 0.65 0.815 20 0.6 0.6Sum 100.0
1matrix
+600 1 0 0 0 0 0 0 0 0 0 0425 0 1 0 0 0 0 0 0 0 0 0300 0 0 1 0 0 0 0 0 0 0 0212 0 0 0 1 0 0 0 0 0 0 0150 0 0 0 0 1 0 0 0 0 0 0106 0 0 0 0 0 1 0 0 0 0 075 0 0 0 0 0 0 1 0 0 0 053 0 0 0 0 0 0 0 1 0 0 037 0 0 0 0 0 0 0 0 1 0 025 0 0 0 0 0 0 0 0 0 1 0
-25 0 0 0 0 0 0 0 0 0 0 1
Recovery Matrix =Primary * gold room *1 matrix * Treated fraction
+600 0.0576 0 0 0 0 0 0 0 0 0 0425 0 0.0740 0 0 0 0 0 0 0 0 0300 0 0 0.0878 0 0 0 0 0 0 0 0212 0 0 0 0.0938 0 0 0 0 0 0 0150 0 0 0 0 0.1029 0 0 0 0 0 0106 0 0 0 0 0 0.1109 0 0 0 0 075 0 0 0 0 0 0 0.1123 0 0 0 053 0 0 0 0 0 0 0 0.1069 0 0 037 0 0 0 0 0 0 0 0 0.0972 0 025 0 0 0 0 0 0 0 0 0 0.0780 0
-25 0 0 0 0 0 0 0 0 0 0 0.0540
Grinding Matrix (Uncorrected)
+600 0.9582 0 0 0 0 0 0 0 0 0 0425 0.0305 0.965 0 0 0 0 0 0 0 0 0300 0.0039 0.0257 0.9708 0 0 0 0 0 0 0 0212 0.0018 0.0032 0.0215 0.9756 0 0 0 0 0 0 0150 0.0016 0.0015 0.0026 0.018 0.9796 0 0 0 0 0 0106 0.0011 0.0013 0.0012 0.0021 0.0151 0.983 0 0 0 0 075 0.0009 0.00095 0.0011 0.001 0.0018 0.0126 0.9858 0 0 0 053 0.0006 0.0007 0.0008 0.0009 0.0009 0.0015 0.0106 0.9882 0 0 037 0.0004 0.0004 0.0005 0.0006 0.0007 0.0007 0.0012 0.0088 0.9902 0 025 0.0004 0.0004 0.0004 0.0005 0.0005 0.0006 0.0006 0.00098 0.0073 0.9919 0
-25 0.0006 0.00085 0.0011 0.0013 0.0014 0.0016 0.0018 0.00202 0.0025 0.0081 11 1 1 1 1 1 1 1 1 1 1
Matrix used for correction114
+600 1 0 0 0 0 0 0 0 0 0 0425 0.985 1 0 0 0 0 0 0 0 0 0300 0.985 0.985 1 0 0 0 0 0 0 0 0212 0.985 0.985 0.985 1 0 0 0 0 0 0 0150 0.985 0.985 0.985 0.985 1 0 0 0 0 0 0106 0.985 0.985 0.985 0.985 0.985 1 0 0 0 0 075 0.985 0.985 0.985 0.985 0.985 0.985 1 0 0 0 053 0.985 0.985 0.985 0.985 0.985 0.985 0.985 1 0 0 037 0.985 0.985 0.985 0.985 0.985 0.985 0.985 0.985 1 0 025 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.895 0.98 0
-25 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.371 0.98
Grinding Matrix (Corrected) B
+600 0.9582 0 0 0 0 0 0 0 0 0 0425 0.0300 0.9650 0 0 0 0 0 0 0 0 0300 0.0038 0.0253 0.9708 0 0 0 0 0 0 0 0212 0.0018 0.0032 0.0212 0.9756 0 0 0 0 0 0 0150 0.0016 0.0015 0.0026 0.0177 0.9796 0 0 0 0 0 0106 0.0011 0.0013 0.0012 0.0021 0.0149 0.9830 0 0 0 0 075 0.0009 0.0009 0.0011 0.0010 0.0018 0.0124 0.9858 0 0 0 053 0.0006 0.0007 0.0008 0.0009 0.0009 0.0015 0.0104 0.9882 0 0 037 0.0004 0.0004 0.0005 0.0006 0.0007 0.0007 0.0012 0.0087 0.9902 0 025 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0009 0.0065 0.9721 0
-25 0.0002 0.0003 0.0004 0.0005 0.0005 0.0006 0.0007 0.0007 0.0009 0.0030 0.98Sum 0.9990 0.9989 0.9989 0.9988 0.9988 0.9987 0.9986 0.9985 0.9977 0.9751 0.9800
C Matrix
+600 1 0 0 0 0 0 0 0 0 0 0425 0 1 0 0 0 0 0 0 0 0 0300 0 0 1 0 0 0 0 0 0 0 0212 0 0 0 1 0 0 0 0 0 0 0150 0 0 0 0 1 0 0 0 0 0 0106 0 0 0 0 0 1 0 0 0 0 075 0 0 0 0 0 0 0.999 0 0 0 053 0 0 0 0 0 0 0 0.988 0 0 037 0 0 0 0 0 0 0 0 0.95 0 025 0 0 0 0 0 0 0 0 0 0.869 0
-25 0 0 0 0 0 0 0 0 0 0 0.738
I-R Matrix
+600 0.9424 0 0 0 0 0 0 0 0 0 0425 0 0.9261 0 0 0 0 0 0 0 0 0300 0 0 0.9123 0 0 0 0 0 0 0 0212 0 0 0 0.9062 0 0 0 0 0 0 0150 0 0 0 0 0.8971 0 0 0 0 0 0106 0 0 0 0 0 0.8891 0 0 0 0 075 0 0 0 0 0 0 0.8877 0 0 0 053 0 0 0 0 0 0 0 0.8931 0 0 037 0 0 0 0 0 0 0 0 0.9028 0 025 0 0 0 0 0 0 0 0 0 0.9220 0
-25 0 0 0 0 0 0 0 0 0 0 0.9460
B*C115
+600 0.9582 0 0 0 0 0 0 0 0 0 0425 0.0300 0.9650 0 0 0 0 0 0 0 0 0300 0.0038 0.0253 0.9708 0 0 0 0 0 0 0 0212 0.0018 0.0032 0.0212 0.9756 0 0 0 0 0 0 0150 0.0016 0.0015 0.0026 0.0177 0.9796 0 0 0 0 0 0106 0.0011 0.0013 0.0012 0.0021 0.0149 0.9830 0 0 0 0 075 0.0009 0.0009 0.0011 0.0010 0.0018 0.0124 0.9848 0 0 0 053 0.0006 0.0007 0.0008 0.0009 0.0009 0.0015 0.0104 0.9763 0 0 037 0.0004 0.0004 0.0005 0.0006 0.0007 0.0007 0.0012 0.0086 0.9407 0 025 0.0004 0.0004 0.0004 0.0004 0.0004 0.0005 0.0005 0.0009 0.0062 0.8447 0
-25 0.0002 0.0003 0.0004 0.0005 0.0005 0.0006 0.0007 0.0007 0.0009 0.0026 0.7232
B*C*(I-R)
+600 0.9030 0 0 0 0 0 0 0 0 0 0425 0.0283 0.8936 0 0 0 0 0 0 0 0 0300 0.0036 0.0234 0.8856 0 0 0 0 0 0 0 0212 0.0017 0.0029 0.0193 0.8840 0 0 0 0 0 0 0150 0.0015 0.0014 0.0023 0.0161 0.8788 0 0 0 0 0 0106 0.0010 0.0012 0.0011 0.0019 0.0133 0.8740 0 0 0 0 075 0.0008 0.0009 0.0010 0.0009 0.0016 0.0110 0.8742 0 0 0 053 0.0006 0.0006 0.0007 0.0008 0.0008 0.0013 0.0093 0.8720 0 0 037 0.0004 0.0004 0.0004 0.0005 0.0006 0.0006 0.0010 0.0076 0.8493 0 025 0.0003 0.0003 0.0003 0.0004 0.0004 0.0005 0.0005 0.0008 0.0056 0.7788 0
-25 0.0002 0.0003 0.0004 0.0004 0.0005 0.0005 0.0006 0.0007 0.0008 0.0024 0.6842
[I-B*C*(I-R))
+600 0.097 0 0 0 0 0 0 0 0 0 0425 -0.028 0.1064 0 0 0 0 0 0 0 0 0300 -0.004 -0.023 0.1144 0 0 0 0 0 0 0 0212 -0.002 -0.003 -0.019 0.1160 0 0 0 0 0 0 0150 -0.001 -0.001 -0.002 -0.016 0.1212 0 0 0 0 0 0106 -0.001 -0.001 -0.001 -0.002 -0.013 0.1260 0 0 0 0 075 -0.001 -0.001 -0.001 -0.001 -0.002 -0.011 0.1258 0 0 0 053 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 -0.009 0.1280 0 0 037 0.000 0.000 0.000 -0.001 -0.001 -0.001 -0.001 -0.008 0.1507 0 025 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.001 -0.006 0.2212 0
-25 0.000 0.000 0.000 0.000 0.000 -0.001 -0.001 -0.001 -0.001 -0.002 0.3158
[I-B*C*(I-R))"'
+600 10.310 0 0 0 0 0 0 0 0 0 0425 2.7444 9.402 0 0 0 0 0 0 0 0 0300 0.8887 1.9268 8.742 0 0 0 0 0 0 0 0212 0.3657 0.5577 1.4566 8.624 0 0 0 0 0 0 0150 0.2229 0.2172 0.3615 1.1430 8.249 0 0 0 0 0 0106 0.1460 0.1363 0.1348 0.2493 0.8735 7.937 0 0 0 0 075 0.1126 0.0986 0.0954 0.0975 0.1809 0.6962 7.949 0 0 0 053 0.0769 0.0711 0.0688 0.0708 0.0733 0.1318 0.5750 7.812 0 0 037 0.0422 0.0362 0.0374 0.0406 0.0424 0.0438 0.0844 0.3964 6.6337 0 025 0.0241 0.0200 0.0179 0.0199 0.0186 0.0202 0.0213 0.0374 0.1681 4.5215 0
-25 0.0122 0.0129 0.0136 0.0146 0.0144 0.0151 0.0165 0.0176 0.0180 0.0345 3.1664
O=R*[I-B*C*(I-Rlr1
116
+600 0.5939 0 0 0 0 0 0 0 0 0 0425 0.2029 0.6953 0 0 0 0 0 0 0 0 0300 0.0780 0.1691 0.7671 0 0 0 0 0 0 0 0212 0.0343 0.0523 0.1367 0.8093 0 0 0 0 0 0 0150 0.0229 0.0224 0.0372 0.1176 0.8490 0 0 0 0 0 0106 0.0162 0.0151 0.0149 0.0276 0.0969 0.8800 0 0 0 0 0
75 0.0126 0.0111 0.0107 0.0110 0.0203 0.0782 0.8928 0 0 0 053 0.0082 0.0076 0.0073 0.0076 0.0078 0.0141 0.0615 0.8349 0 0 037 0.0041 0.0035 0.0036 0.0039 0.0041 0.0043 0.0082 0.0385 0.6448 0 025 0.0019 0.0016 0.0014 0.0016 0.0014 0.0016 0.0017 0.0029 0.0131 0.3527 0
-25 0.0007 0.0007 0.0007 0.0008 0.0008 0.0008 0.0009 0.0010 0.0010 0.0019 0.1710Sum 0.976 0.979 0.980 0.979 0.980 0.979 0.965 0.877 0.659 0.355 0.171
X=[I-B*C*(I-Rlr '*F D=R*X
+600 0.0 +600 0.0425 9.4 425 0.7300 36.9 300 3.2212 40.9 212 3.8150 80.5 150 8.3106 104.8 106 11.6
75 130.1 75 14.653 89.6 53 9.637 106.0 37 10.325 49.0 25 3.8
-25 64.8 -25 3.5
Sum 711.9 Sum 69.5
Appendix E
Database Used forGenerating Regressions
117
Database Used for Generating Fine GRG Regression
~ % RGRG %R" PF %R25um No. 1% RGRG % R. PF %R-25pm 11 47.7 2.06 0.05 73.8 51 75.1 8.25 0.08 87.22 55.3 3.38 0.05 73.8 52 76.8 9.46 0.08 87.23 59.9 4.69 0.05 73.8 53 78.3 10.66 0.08 87.24 63.1 5.98 0.05 73.8 54 79.5 11.85 0.08 87.25 65.7 7.25 0.05 73.8 55 41.2 2.05 0.1 73.86 67.7 8.51 0.05 73.8 56 50.6 3.37 0.1 73.87 69.5 9.76 0.05 73.8 57 56.3 4.68 0.1 73.88 71 11.00 0.05 73.8 58 60.3 5.97 0.1 73.89 72.3 12.24 0.05 73.8 59 63.3 7.24 0.1 73.8
10 53.7 2.03 0.05 82.8 60 65.7 8.50 0.1 73.811 61.2 3.34 0.05 82.8 61 67.8 9.75 0.1 73.812 65.6 4.62 0.05 82.8 62 69.5 10.99 0.1 73.813 68.7 5.89 0.05 82.8 63 71 12.22 0.1 73.814 71.1 7.13 0.05 82.8 64 46.7 2.02 0.1 82.815 73 8.37 0.05 82.8 65 56.2 3.32 0.1 82.816 74.7 9.60 0.05 82.8 66 61.9 4.60 0.1 82.817 76.1 10.81 0.05 82.8 67 65.7 5.87 0.1 82.818 77.3 12.02 0.05 82.8 68 68.7 7.11 0.1 82.819 58 2.01 0.05 87.2 69 71 8.35 0.1 82.820 65.2 3.30 0.05 87.2 70 72.9 9.57 0.1 82.821 69.4 4.57 0.05 87.2 71 74.5 10.79 0.1 82.822 72.4 5.82 0.05 87.2 72 75.9 11.99 0.1 82.823 74.6 7.05 0.05 87.2 73 51.2 2.06 0.1 87.224 76.4 8.27 0.05 87.2 74 60 3.28 0.1 87.225 77.9 9.48 0.05 87.2 75 65.5 4.55 0.1 87.226 79.2 10.68 0.05 87.2 76 69.3 5.79 0.1 87.227 80.4 11.87 0.05 87.2 77 72.1 7.02 0.1 87.228 43.5 2.05 0.08 73.8 78 74.3 8.24 0.1 87.229 52.3 3.38 0.08 73.8 79 76.1 9.45 0.1 87.230 57.6 4.68 0.08 73.8 80 77.7 10.65 0.1 87.231 61.4 5.97 0.08 73.8 81 79 11.84 0.1 87.232 64.2 7.24 0.08 73.8 82 37.4 2.04 0.15 73.833 66.5 8.50 0.08 73.8 83 47.4 3.36 0.15 73.834 68.4 9.75 0.08 73.8 84 53.7 4.66 0.15 73.835 70.1 10.99 0.08 73.8 85 58.2 5.95 0.15 73.836 71.5 12.22 0.08 73.8 86 61.5 7.22 0.15 73.837 49.2 2.02 0.08 82.8 87 64.2 8.48 0.15 73.838 58.1 3.33 0.08 82.8 88 66.4 9.73 0.15 73.839 63.3 4.61 0.08 82.8 89 68.3 10.97 0.15 73.840 66.9 5.87 0.08 82.8 90 70 12.20 0.15 73.841 69.6 7.12 0.08 82.8 91 42.4 2.00 0.15 82.842 71.8 8.36 0.08 82.8 92 52.8 3.30 0.15 82.843 73.6 9.58 0.08 82.8 93 59.2 4.58 0.15 82.844 75.1 10.80 0.08 82.8 94 63.5 5.84 0.15 82.845 76.5 12.00 0.08 82.8 95 66.8 7.09 0.15 82.846 53.2 2.00 0.08 87.2 96 69.4 8.33 0.15 82.847 62 3.29 0.08 87.2 97 71.5 9.55 0.15 82.848 67 4.56 0.08 87.2 98 73.3 10.76 0.15 82.849 70.5 5.80 0.08 87.2 99 74.9 11.97 0.15 82.850 73 7.03 0.08 87.2 100 46.6 2.04 0.15 87.2
118
~I%~RG %R" PF %R.25H'" Il No. II%~RG %R" PF %R-25H'" 1101 56.4 3.26 0.15 87.2 151 66.5 9.44 0.3 82.8102 62.7 4.52 0.15 87.2 152 68.9 10.65 0.3 82.8103 67 5.77 0.15 87.2 153 70.9 11.86 0.3 82.8104 70.2 7.00 0.15 87.2 154 35.3 2.04 0.3 87.2105 72.7 8.22 0.15 87.2 155 45.6 3.17 0.3 87.2106 74.8 9.42 0.15 87.2 156 53.5 4.42 0.3 87.2107 76.5 10.62 0.15 87.2 157 59.2 5.66 0.3 87.2108 77.9 11.81 0.15 87.2 158 63.5 6.88 0.3 87.2109 32.9 2.02 0.2 73.8 159 66.9 8.09 0.3 87.2110 43.4 3.34 0.2 73.8 160 69.6 9.30 0.3 87.2111 50.3 4.64 0.2 73.8 161 71.9 10.50 0.3 87.2112 55.2 5.92 0.2 73.8 162 73.9 11.69 0.3 87.2113 59 7.20 0.2 73.8 163 47.4 2.065 0.05 73.8114 62 8.46 0.2 73.8 164 55.4 3.401 0.05 73.8115 64.5 9.70 0.2 73.8 165 60.4 4.719 0.05 73.8116 66.6 10.94 0.2 73.8 166 64 6.021 0.05 73.8117 68.5 12.17 0.2 73.8 167 66.8 7.313 0.05 73.8118 38 2.04 0.2 82.8 168 69.1 8.595 0.05 73.8119 48.4 3.27 0.2 82.8 169 71.1 9.869 0.05 73.8120 55.5 4.55 0.2 82.8 170 72.8 11.136 0.05 73.8121 60.5 5.81 0.2 82.8 171 74.3 12.397 0.05 73.8122 64.2 7.05 0.2 82.8 172 53.9 2.04 0.05 82.8123 67.2 8.29 0.2 82.8 173 62 3.356 0.05 82.8124 69.6 9.51 0.2 82.8 174 66.9 4.653 0.05 82.8125 71.6 10.72 0.2 82.8 175 70.4 5.936 0.05 82.8126 73.3 11.93 0.2 82.8 176 73 7.207 0.05 82.8127 41.1 2.01 0.2 87.2 177 75.2 8.47 0.05 82.8128 51.7 3.23 0.2 87.2 178 77 9.726 0.05 82.8129 58.9 4.48 0.2 87.2 179 78.6 10.975 0.05 82.8130 63.8 5.73 0.2 87.2 180 79.9 12.22 0.05 82.8131 67.5 6.95 0.2 87.2 181 58.7 2.019 0.05 87.2132 70.4 8.17 0.2 87.2 182 66.5 3.322 0.05 87.2133 72.7 9.38 0.2 87.2 183 71.2 4.606 0.05 87.2134 74.7 10.58 0.2 87.2 184 74.5 5.876 0.05 87.2135 76.4 11.77 0.2 87.2 185 77 7.135 0.05 87.2136 28.4 2.06 0.3 73.8 186 79 8.387 0.05 87.2137 38.2 3.30 0.3 73.8 187 80.6 9.632 0.05 87.2138 45.6 4.59 0.3 73.8 188 82.1 10.872 0.05 87.2139 51.1 5.87 0.3 73.8 189 83.3 12.107 0.05 87.2140 55.3 7.14 0.3 73.8 190 43.3 2.058 0.08 73.8141 58.8 8.40 0.3 73.8 191 52.5 3.394 0.08 73.8142 61.6 9.64 0.3 73.8 192 58.1 4.711 0.08 73.8143 64 10.88 0.3 73.8 193 62.2 6.013 0.08 73.8144 66.1 12.11 0.3 73.8 194 65.3 7.304 0.08 73.8145 32.1 2.01 0.3 82.8 195 67.8 8.585 0.08 73.8146 42.7 3.23 0.3 82.8 196 70 9.858 0.08 73.8147 50.4 4.49 0.3 82.8 197 71.8 11.125 0.08 73.8148 56 5.75 0.3 82.8 198 73.4 12.385 0.08 73.8149 60.3 6.99 0.3 82.8 199 49.4 2.029 0.08 82.8150 63.7 8.22 0.3 82.8 200 58.8 3.345 0.08 82.8
119
No. I%~RG %Re PF %R.25um 1 No. II%~RG %Re PF %R-25Hm 1201 64.5 4.641 0.08 82.8 251 70 11.1 0.15 73.8202 68.4 5.923 0.08 82.8 252 71.8 12.36 0.15 73.8203 71.4 7.194 0.08 82.8 253 42.6 2.007 0.15 82.8204 73.8 8.456 0.08 82.8 254 53.5 3.318 0.15 82.8205 75.8 9.711 0.08 82.8 255 60.2 4.612 0.15 82.8206 77.5 10.961 0.08 82.8 256 64.9 5.892 0.15 82.8207 79 12.205 0.08 82.8 257 68.5 7.162 0.15 82.8208 53.8 2.006 0.08 87.2 258 71.3 8.424 0.15 82.8209 63.2 3.308 0.08 87.2 259 73.6 9.679 0.15 82.8210 68.7 4.591 0.08 87.2 260 75.5 10.927 0.15 82.8211 72.4 5.86 0.08 87.2 261 77.2 12.171 0.15 82.8212 75.3 7.119 0.08 87.2 262 47.1 2.046 0.15 87.2213 77.5 8.37 0.08 87.2 263 57.4 3.277 0.15 87.2214 79.4 9.615 0.08 87.2 264 64.1 4.557 0.15 87.2215 81 10.854 0.08 87.2 265 68.7 5.824 0.15 87.2216 82.3 12.089 0.08 87.2 266 72.2 7.082 0.15 87.2217 41 2.053 0.1 73.8 267 74.9 8.333 0.15 87.2218 50.7 3.388 0.1 73.8 268 77.1 9.576 0.15 87.2219 56.8 4.704 0.1 73.8 269 78.9 10.815 0.15 87.2220 61.1 6.006 0.1 73.8 270 80.4 12.05 0.15 87.2221 64.4 7.297 0.1 73.8 271 32.8 2.024 0.2 73.8222 67 8.578 0.1 73.8 272 43.5 3.351 0.2 73.8223 69.3 9.851 0.1 73.8 273 50.7 4.664 0.2 73.8224 71.2 11.117 0.1 73.8 274 55.9 5.963 0.2 73.8225 72.9 12.378 0.1 73.8 275 60 7.252 0.2 73.8226 46.9 2.022 0.1 82.8 276 63.2 8.532 0.2 73.8227 56.9 3.336 0.1 82.8 277 65.9 9.805 0.2 73.8228 63 4.632 0.1 82.8 278 68.2 11.071 0.2 73.8229 67.2 5.913 0.1 82.8 279 70.1 12.331 0.2 73.8230 70.4 7.184 0.1 82.8 280 38.3 2.051 0.2 82.8231 73 8.446 0.1 82.8 281 49 3.289 0.2 82.8232 75.1 9.701 0.1 82.8 282 56.4 4.579 0.2 82.8233 76.8 10.95 0.1 82.8 283 61.7 5.858 0.2 82.8234 78.4 12.194 0.1 82.8 284 65.7 7.126 0.2 82.8235 51.8 2.063 0.1 87.2 285 68.8 8.387 0.2 82.8236 61.1 3.298 0.1 87.2 286 71.4 9.641 0.2 82.8237 67.1 4.58 0.1 87.2 287 73.6 10.889 0.2 82.8238 71.2 5.849 0.1 87.2 288 75.5 12.132 0.2 82.8239 74.2 7.107 0.1 87.2 289 41.5 2.022 0.2 87.2240 76.6 8.358 0.1 87.2 290 52.6 3.245 0.2 87.2241 78.6 9.603 0.1 87.2 291 60.1 4.521 0.2 87.2242 80.3 10.842 0.1 87.2 292 65.3 5.785 0.2 87.2243 81.7 12.076 0.1 87.2 293 69.2 7.042 0.2 87.2244 37.2 2.041 0.15 73.8 294 72.3 8.291 0.2 87.2245 47.5 3.374 0.15 73.8 295 74.8 9.534 0.2 87.2246 54.2 4.689 0.15 73.8 296 76.9 10.772 0.2 87.2247 58.9 5.99 0.15 73.8 297 78.6 12.006 0.2 87.2248 62.5 7.28 0.15 73.8 298 28.4 2.064 0.3 73.8249 65.5 8.561 0.15 73.8 299 38.4 3.314 0.3 73.8250 67.9 9.834 0.15 73.8 300 46 4.619 0.3 73.8
120
~1%RaRG %R" PF %R.25~m
"No. 1/ % RaRG %R" PF %R-25~m 1
301 51.7 5.914 0.3 73.8 351 75.4 11.598 0.05 87.2302 56.2 7.2 0.3 73.8 352 34.5 2.036 0.08 73.8303 59.8 8.478 0.3 73.8 353 43.1 3.35 0.08 73.8304 62.8 9.748 0.3 73.8 354 48.7 4.637 0.08 73.8305 65.4 11.013 0.3 73.8 355 52.8 5.904 0.08 73.8306 67.6 12.272 0.3 73.8 356 56 7.152 0.08 73.8307 32.3 2.019 0.3 82.8 357 58.6 8.386 0.08 73.8308 43.2 3.246 0.3 82.8 358 60.9 9.607 0.08 73.8309 51.1 4.527 0.3 82.8 359 62.8 10.816 0.08 73.8310 57 5.8 0.3 82.8 360 64.5 12.014 0.08 73.8311 61.5 7.065 0.3 82.8 361 41.5 2.063 0.08 82.8312 65.1 8.322 0.3 82.8 362 49.9 3.284 0.08 82.8313 68.1 9.574 0.3 82.8 363 55.5 4.543 0.08 82.8314 70.6 10.821 0.3 82.8 364 59.5 5.779 0.08 82.8315 72.7 12.064 0.3 82.8 365 62.6 6.998 0.08 82.8316 35.7 2.051 0.3 87.2 366 65.1 8.201 0.08 82.8317 46.3 3.197 0.3 87.2 367 67.3 9.392 0.08 82.8318 54.4 4.463 0.3 87.2 368 69.1 10.572 0.08 82.8319 60.4 5.721 0.3 87.2 369 70.7 11.742 0.08 82.8320 64.9 6.973 0.3 87.2 370 46.2 2.034 0.08 87.2321 68.4 8.219 0.3 87.2 371 54.6 3.236 0.08 87.2322 71.3 9.46 0.3 87.2 372 60.1 4.475 0.08 87.2323 73.8 10.696 0.3 87.2 373 63.9 5.691 0.08 87.2324 75.8 11.929 0.3 87.2 374 66.9 6.89 0.08 87.2325 37.7 2.052 0.05 73.8 375 69.3 8.074 0.08 87.2326 45.6 3.37 0.05 73.8 376 71.3 9.246 0.08 87.2327 50.7 4.661 0.05 73.8 377 73 10.407 0.08 87.2328 54.4 5.931 0.05 73.8 378 74.5 11.56 0.08 87.2329 57.3 7.182 0.05 73.8 379 32.7 2.026 0.1 73.8330 59.8 8.417 0.05 73.8 380 41.6 3.336 0.1 73.8331 61.9 9.639 0.05 73.8 381 47.5 4.622 0.1 73.8332 63.7 10.85 0.05 73.8 382 51.8 5.887 0.1 73.8333 65.3 12.05 0.05 73.8 383 55.2 7.135 0.1 73.8334 44.8 2.018 0.05 82.8 384 57.9 8.368 0.1 73.8335 52.8 3.309 0.05 82.8 385 60.2 9.588 0.1 73.8336 57.7 4.57 0.05 82.8 386 62.3 10.796 0.1 73.8337 61.3 5.809 0.05 82.8 387 64 11.994 0.1 73.8338 64.1 7.03 0.05 82.8 388 39.5 2.051 0.1 82.8339 66.4 8.234 0.05 82.8 389 48.3 3.269 0.1 82.8340 68.3 9.426 0.05 82.8 390 54.2 4.525 0.1 82.8341 70 10.607 0.05 82.8 391 58.5 5.76 0.1 82.8342 71.5 11.777 0.05 82.8 392 61.7 6.977 0.1 82.8343 50.5 2.055 0.05 87.2 393 64.4 8.18 0.1 82.8344 57.7 3.263 0.05 87.2 394 66.6 9.37 0.1 82.8345 62.4 4.505 0.05 87.2 395 68.5 10.56 0.1 82.8346 65.8 5.724 0.05 87.2 396 70.2 11.72 0.1 82.8347 68.4 6.924 0.05 87.2 397 43.9 2.021 0.1 87.2348 70.6 8.11 0.05 87.2 398 52.8 3.219 0.1 87.2349 72.4 9.282 0.05 87.2 399 58.7 4.455 0.1 87.2350 74 10.445 0.05 87.2 1 4001 62.8 5.67 0.1 87.2
121
No. I%~RG %R" PF %R.25um 1 No. 1I%~RG %R" PF %R-25~m 1401 65.9 6.867 0.1 87.2 451 35.8 2.027 0.2 87.2402 68.5 8.051 0.1 87.2 452 45.2 3.143 0.2 87.2403 70.6 9.222 0.1 87.2 453 52.4 4.364 0.2 87.2404 72.4 10.383 0.1 87.2 454 57.5 5.569 0.2 87.2405 74 11.536 0.1 87.2 455 61.5 6.76 0.2 87.2406 29.7 2.008 0.15 73.8 456 64.6 7.938 0.2 87.2407 39 3.311 0.15 73.8 457 67.2 9.106 0.2 87.2408 45.3 4.592 0.15 73.8 458 69.4 10.265 0.2 87.2409 49.9 5.854 0.15 73.8 459 71.3 11.416 0.2 87.2410 53.5 7.1 0.15 73.8 460 23 2.012 0.3 73.8411 56.5 8.331 0.15 73.8 461 31.7 3.225 0.3 73.8412 59 9.549 0.15 73.8 462 38.5 4.486 0.3 73.8413 61.2 10.757 0.15 73.8 463 43.8 5.734 0.3 73.8414 63.1 11.954 0.15 73.8 464 48.1 6.968 0.3 73.8415 35.9 2.029 0.15 82.8 465 51.6 8.19 0.3 73.8416 45.3 3.239 0.15 82.8 466 54.6 9.402 0.3 73.8417 51.7 4.49 0.15 82.8 467 57.2 10.605 0.3 73.8418 56.4 5.722 0.15 82.8 468 59.4 11.798 0.3 73.8419 60 6.937 0.15 82.8 469 27.5 2.021 0.3 82.8420 62.8 8.138 0.15 82.8 470 36.6 3.14 0.3 82.8421 65.3 9.327 0.15 82.8 471 43.9 4.369 0.3 82.8422 67.3 10.505 0.15 82.8 472 49.5 5.584 0.3 82.8423 69.1 11.674 0.15 82.8 473 53.9 6.787 0.3 82.8424 40.5 2.06 0.15 87.2 474 57.5 7.979 0.3 82.8425 49.5 3.187 0.15 87.2 475 60.5 9.161 0.3 82.8426 56 4.417 0.15 87.2 476 63 10.334 0.3 82.8427 60.6 5.628 0.15 87.2 477 65.2 11.5 0.3 82.8428 64.1 6.823 0.15 87.2 478 30.9 2.042 0.3 87.2429 66.9 8.005 0.15 87.2 479 39.9 3.079 0.3 87.2430 69.2 9.175 0.15 87.2 480 47.5 4.286 0.3 87.2431 71.2 10.335 0.15 87.2 481 53.2 5.48 0.3 87.2432 72.9 11.487 0.15 87.2 482 57.6 6.663 0.3 87.2433 26.9 2.048 0.2 73.8 483 61.2 7.835 0.3 87.2434 35.8 3.277 0.2 73.8 484 64.2 8.998 0.3 87.2435 42.4 4.551 0.2 73.8 485 66.7 10.154 0.3 87.2436 47.4 5.808 0.2 73.8 486 68.9 11.302 0.3 87.2437 51.3 7.05 0.2 73.8 487 18.2 2.003 0.05 73.8438 54.5 8.279 0.2 73.8 488 22.6 2.953 0.05 73.8439 57.2 9.496 0.2 73.8 489 26.7 4.031 0.05 73.8440 59.6 10.702 0.2 73.8 490 30.1 5.078 0.05 73.8441 61.6 11.899 0.2 73.8 491 33 6.102 0.05 73.8442 32.4 2.063 0.2 82.8 492 35.6 7.109 0.05 73.8443 41.4 3.198 0.2 82.8 493 38 8.101 0.05 73.8444 48.4 4.441 0.2 82.8 494 40.2 9.081 0.05 73.8445 53.5 5.667 0.2 82.8 495 42.3 10.051 0.05 73.8446 57.5 6.878 0.2 82.8 496 44.1 11.012 0.05 73.8447 60.7 8.075 0.2 82.8 497 23.5 2.006 0.05 82.8448 63.3 9.262 0.2 82.8 498 28.3 2.869 0.05 82.8449 65.6 10.439 0.2 82.8 499 33 3.911 0.05 82.8450 67.6 11.607 0.2 82.8 500 36.8 4.924 0.05 82.8
122
~I%~RG %R., PF %R25~m /1 No. 1/ %~RG %R., PF %R-25~m 1501 40.1 5.916 0.05 82.8 551 58.8 11.389 0.08 87.2502 43 6.893 0.05 82.8 552 16.7 2.02 0.1 73.8503 45.6 7.857 0.05 82.8 553 21.1 2.907 0.1 73.8504 47.9 8.81 0.05 82.8 554 25.4 3.981 0.1 73.8505 50.1 9.576 0.05 82.8 555 28.9 5.026 0.1 73.8506 52.1 10.694 0.05 82.8 556 32 6.049 0.1 73.8507 53.9 11.627 0.05 82.8 557 34.8 7.055 0.1 73.8508 27.8 2.022 0.05 87.2 558 37.3 8.046 0.1 73.8509 32.6 2.813 0.05 87.2 559 39.5 9.026 0.1 73.8510 37.6 3.832 0.05 87.2 560 41.6 9.996 0.1 73.8511 41.6 4.824 0.05 87.2 561 43.6 10.957 0.1 73.8512 45.1 5.797 0.05 87.2 562 45.4 11.911 0.1 73.8513 48.1 6.755 0.05 87.2 563 21.5 2.018 0.1 82.8514 50.8 7.703 0.05 87.2 564 26.3 2.822 0.1 82.8515 53.2 8.642 0.05 87.2 565 31.3 3.861 0.1 82.8516 55.4 9.574 0.05 87.2 566 35.4 4.873 0.1 82.8517 57.4 10.5 0.05 87.2 567 38.8 5.865 0.1 82.8518 59.2 11.421 0.05 87.2 568 41.8 6.841 0.1 82.8519 17.3 2.035 0.08 73.8 569 44.6 7.805 0.1 82.8520 21.6 2.924 0.08 73.8 570 47 8.759 0.1 82.8521 25.9 3.999 0.08 73.8 571 49.2 9.705 0.1 82.8522 29.4 5.045 0.08 73.8 572 51.3 10.643 0.1 82.8523 32.4 6.068 0.08 73.8 573 53.2 11.576 0.1 82.8524 35.1 7.074 0.08 73.8 574 25.4 2.03 0.1 87.2525 37.6 8.065 0.08 73.8 575 30.2 2.763 0.1 87.2526 39.8 9.045 0.08 73.8 576 35.7 3.78 0.1 87.2527 41.9 10.015 0.08 73.8 577 40 4.771 0.1 87.2528 43.8 10.976 0.08 73.8 578 43.7 5.743 0.1 87.2529 45.6 11.93 0.08 73.8 579 46.8 6.702 0.1 87.2530 22.4 2.034 0.08 82.8 580 49.7 7.649 0.1 87.2531 27 2.84 0.08 82.8 581 52.2 8.589 0.1 87.2532 31.9 3.881 0.08 82.8 582 54.5 9.521 0.1 87.2533 35.9 4.893 0.08 82.8 583 56.5 10.447 0.1 87.2534 39.3 5.885 0.08 82.8 584 58.4 11.369 0.1 87.2535 42.3 6.861 0.08 82.8 585 15.9 2.049 0.15 73.8536 44.9 7.825 0.08 82.8 586 20 2.876 0.15 73.8537 47.4 8.779 0.08 82.8 587 24.4 3.947 0.15 73.8538 49.6 9.725 0.08 82.8 588 28.1 4.99 0.15 73.8539 51.6 10.663 0.08 82.8 589 31.3 6.012 0.15 73.8540 53.5 11.596 0.08 82.8 590 34.1 7.018 0.15 73.8541 26.4 2.047 0.08 87.2 591 36.6 8.009 0.15 73.8542 31.1 2.782 0.08 87.2 592 39 8.988 0.15 73.8543 36.4 3.8 0.08 87.2 593 41.1 9.958 0.15 73.8544 40.6 4.791 0.08 87.2 594 43.1 10.92 0.15 73.8545 44.2 5.764 0.08 87.2 595 44.9 11.874 0.15 73.8546 47.3 6.722 0.08 87.2 596 20.5 2.043 0.15 82.8547 50.1 7.67 0.08 87.2 597 25 2.789 0.15 82.8548 52.6 8.609 0.08 87.2 598 30.1 3.825 0.15 82.8549 54.8 9.542 0.08 87.2 599 34.3 4.835 0.15 82.8550 56.9 10.468 0.08 87.2 600 37.9 5.826 0.15 82.8
123
~I%~RG %R" PF %R.25pm Il No. II%~RG %R" PF %R-25Hm 1601 41 6.801 0.15 82.8 651 13.4 2.02 0.3 73.8602 43.8 7.765 0.15 82.8 652 17.1 2.775 0.3 73.8603 46.3 8.719 0.15 82.8 653 21.6 3.831 0.3 73.8604 48.6 9.665 0.15 82.8 654 25.4 4.864 0.3 73.8605 50.7 10.604 0.15 82.8 655 28.8 5.88 0.3 73.8606 52.6 11.537 0.15 82.8 656 31.8 6.882 0.3 73.8607 24.1 2.052 0.15 87.2 657 34.5 7.87 0.3 73.8608 28.7 2.729 0.15 87.2 658 36.9 8.849 0.3 73.8609 34.3 3.742 0.15 87.2 659 39.2 9.818 0.3 73.8610 38.8 4.731 0.15 87.2 660 41.3 10.779 0.3 73.8611 42.6 5.703 0.15 87.2 661 43.3 11.733 0.3 73.8612 45.9 6.661 0.15 87.2 662 17 2.005 0.3 82.8613 48.8 7.608 0.15 87.2 663 21.2 2.681 0.3 82.8614 51.4 8.548 0.15 87.2 664 26.5 3.702 0.3 82.8615 53.7 9.48 0.15 87.2 665 30.9 4.702 0.3 82.8616 55.9 10.407 0.15 87.2 666 34.8 5.687 0.3 82.8617 57.8 11.329 0.15 87.2 667 38.1 6.659 0.3 82.8618 14.6 2.015 0.2 73.8 668 41.1 7.62 0.3 82.8619 18.7 2.836 0.2 73.8 669 43.8 8.572 0.3 82.8620 23.2 3.902 0.2 73.8 670 46.3 9.517 0.3 82.8621 27 4.943 0.2 73.8 671 48.5 10.456 0.3 82.8622 30.2 5.964 0.2 73.8 672 50.6 11.39 0.3 82.8623 33.1 6.969 0.2 73.8 673 19.9 2.007 0.3 87.2624 35.7 7.96 0.2 73.8 674 24.2 2.617 0.3 87.2625 38.1 8.94 0.2 73.8 675 30.1 3.615 0.3 87.2626 40.3 9.91 0.2 73.8 676 34.9 4.594 0.3 87.2627 42.3 10.873 0.2 73.8 677 39.1 5.56 0.3 87.2628 44.2 11.828 0.2 73.8 678 42.6 6.514 0.3 87.2629 18.8 2.004 0.2 82.8 679 45.8 7.459 0.3 87.2630 23.3 2.744 0.2 82.8 680 48.6 8.397 0.3 87.2631 28.6 3.775 0.2 82.8 681 51.2 9.329 0.3 87.2632 32.9 4.782 0.2 82.8 682 53.5 10.255 0.3 87.2633 36.6 5.77 0.2 82.8 683 55.6 11.178 0.3 87.2634 39.9 6.745 0.2 82.8 684 37.1 2.008 0.05 73.8635 42.7 7.708 0.2 82.8 685 56.6 8.122 0.05 73.8636 45.3 8.662 0.2 82.8 686 61.9 11.58 0.05 73.8637 47.7 9.607 0.2 82.8 687 42.8 1.977 0.05 82.8638 49.8 10.547 0.2 82.8 688 62.6 7.933 0.05 82.8639 51.8 11.48 0.2 82.8 689 67.8 11.297 0.05 82.8640 22 2.011 0.2 87.2 690 47 1.951 0.05 87.2641 26.7 2.682 0.2 87.2 691 66.5 7.8 0.05 87.2642 32.5 3.69 0.2 87.2 692 71.6 11.106 0.05 87.2643 37.2 4.676 0.2 87.2 693 33.9 2 0.08 73.8644 41.2 5.646 0.2 87.2 694 55.6 8.11 0.08 73.8645 44.6 6.603 0.2 87.2 695 61.2 11.568 0.08 73.8646 47.6 7.55 0.2 87.2 696 39.3 1.964 0.08 82.8647 50.3 8.489 0.2 87.2 697 61.5 7.917 0.08 82.8648 52.7 9.421 0.2 87.2 698 67 11.28 0.08 82.8649 54.9 10.348 0.2 87.2 699 43.1 1.936 0.08 87.2650 57 11.27 0.2 87.2 700 65.4 7.781 0.08 87.2
124
~1%~RG %R" PF %R.25Hm /1 No. n% ~RG %R" PF %R-25Hm 1701 70.8 11.086 0.08 87.2 751 73.6 8.32 0.08 82.8702 32.2 1.993 0.1 73.8 752 78.1 11.961 0.08 82.8703 55 8.103 0.1 73.8 753 55.2 1.994 0.08 87.2704 60.8 11.559 0.1 73.8 754 76.7 8.228 0.08 87.2705 37.3 1.955 0.1 82.8 755 81 11.828 0.08 87.2706 60.8 7.905 0.1 82.8 756 43.4 2.036 0.1 73.8707 66.6 11.268 0.1 82.8 757 67.8 8.448 0.1 73.8708 41 1.925 0.1 87.2 758 72.9 12.154 0.1 73.8709 64.7 7.767 0.1 87.2 759 48.7 2.009 0.1 82.8710 70.4 11.072 0.1 87.2 760 72.8 8.318 0.1 82.8711 29.3 1.979 0.15 73.8 761 77.5 11.959 0.1 82.8712 53.8 8.082 0.15 73.8 762 52.4 1.988 0.1 87.2713 59.9 11.538 0.15 73.8 763 75.9 8.224 0.1 87.2714 34 1.937 0.15 82.8 764 80.4 11.824 0.1 87.2715 59.5 7.878 0.15 82.8 765 39.3 2.028 0.15 73.8716 65.7 11.24 0.15 82.8 766 66.2 8.445 0.15 73.8717 37.3 1.905 0.15 87.2 767 71.8 12.152 0.15 73.8718 63.4 7.736 0.15 87.2 768 44.2 1.998 0.15 82.8719 69.4 11.041 0.15 87.2 769 71.2 8.307 0.15 82.8720 25.9 1.957 0.2 73.8 770 76.5 11.95 0.15 82.8721 52 8.046 0.2 73.8 771 47.6 1.974 0.15 87.2722 58.7 11.501 0.2 73.8 772 74.3 8.209 0.15 87.2723 30.1 1.91 0.2 82.8 773 79.3 11.811 0.15 87.2724 57.7 7.833 0.2 82.8 774 34.6 2.014 0.2 73.8725 64.4 11.196 0.2 82.8 775 64 8.43 0.2 73.8726 33 1.875 0.2 87.2 776 70.3 12.14 0.2 73.8727 61.4 7.687 0.2 87.2 777 38.9 1.979 0.2 82.8728 68.1 10.992 0.2 87.2 778 68.9 8.283 0.2 82.8729 22.1 1.924 0.3 73.8 779 74.9 11.928 0.2 82.8730 49.4 7.98 0.3 73.8 780 41.9 1.952 0.2 87.2731 56.7 11.433 0.3 73.8 781 72 8.178 0.2 87.2732 25.5 1.872 0.3 82.8 782 77.8 11.782 0.2 87.2733 54.8 7.756 0.3 82.8 783 29.1 1.991 0.3 73.8734 62.3 11.116 0.3 82.8 784 60.6 8.391 0.3 73.8735 27.9 1.833 0.3 87.2 785 67.9 12.103 0.3 73.8736 58.4 7.603 0.3 87.2 786 32.7 1.949 0.3 82.8737 65.9 10.906 0.3 87.2 787 65.4 8.23 0.3 82.8738 50.2 2.038 0.05 73.8 788 72.4 11.876 0.3 82.8739 69.8 8.439 0.05 73.8 789 35.2 1.918 0.3 87.2740 74.2 12.145 0.05 73.8 790 68.4 8.116 0.3 87.2741 56 2.019 0.05 82.8 791 68.3 8.535 0.05 73.8742 74.9 8.319 0.05 82.8 792 74.9 8.417 0.05 82.8743 78.9 11.96 0.05 82.8 793 79.1 8.339 0.05 87.2744 60.1 2.002 0.05 87.2 794 67.1 8.528 0.08 73.8745 78 8.232 0.05 87.2 795 73.5 8.405 0.08 82.8746 81.8 11.832 0.05 87.2 796 77.6 8.324 0.08 87.2747 45.8 2.038 0.08 73.8 797 66.3 8.522 0.1 73.8748 68.6 8.446 0.08 73.8 798 72.6 8.396 0.1 82.8749 73.4 12.152 0.08 73.8 799 76.6 8.312 0.1 87.2750 51.3 2.014 0.08 82.8 800 64.7 8.508 0.15 73.8
125
~I%~RG %Re PF %R25~m /1 No. 1/ %~RG %Re PF %R-25Hm 1801 70.9 8.376 0.15 82.8 851 64.2 8.517 0.1 73.8802 74.8 8.288 0.15 87.2 852 70 8.362 0.1 82.8803 62.5 8.481 0.2 73.8 853 73.7 8.254 0.1 87.2804 68.5 8.341 0.2 82.8 854 62.7 8.494 0.15 73.8805 72.2 8.248 0.2 87.2 855 68.4 8.332 0.15 82.8806 59.1 8.431 0.3 73.8 856 72 8.219 0.15 87.2807 64.7 8.279 0.3 82.8 857 60.5 8.455 0.2 73.8808 68.2 8.178 0.3 87.2 858 66.1 8.284 0.2 82.8809 70.2 8.682 0.05 73.8 859 69.6 8.166 0.2 87.2810 76.1 8.558 0.05 82.8 860 57.2 8.387 0.3 73.8811 79.7 8.47 0.05 87.2 861 62.6 8.204 0.3 82.8812 68.8 8.666 0.08 73.8 862 66 8.077 0.3 87.2813 74.7 8.536 0.08 82.8 863 73 8.718 0.05 73.8814 78.3 8.445 0.08 87.2 864 78 8.6 0.05 82.8815 68 8.654 0.1 73.8 865 81 8.515 0.05 87.2816 73.8 8.521 0.1 82.8 866 71.6 8.712 0.08 73.8817 77.4 8.427 0.1 87.2 867 76.6 8.588 0.08 82.8818 66.3 8.629 0.15 73.8 868 79.6 8.499 0.08 87.2819 72.1 8.489 0.15 82.8 869 70.8 8.706 0.1 73.8820 75.6 8.391 0.15 87.2 870 75.7 8.578 0.1 82.8821 63.9 8.589 0.2 73.8 871 78.8 8.487 0.1 87.2822 69.6 8.44 0.2 82.8 872 69.1 8.689 0.15 73.8823 73 8.336 0.2 87.2 873 74 8.555 0.15 82.8824 60.4 8.522 0.3 73.8 874 77 8.459 0.15 87.2825 65.8 8.359 0.3 82.8 875 66.7 8.658 0.2 73.8826 69.1 8.247 0.3 87.2 876 71.6 8.514 0.2 82.8827 52.1 7.978 0.05 73.8 877 74.6 8.412 0.2 87.2828 58.4 7.769 0.05 82.8 878 63.1 8.599 0.3 73.8829 62.6 7.625 0.05 87.2 879 67.8 8.441 0.3 82.8830 51.2 7.96 0.08 73.8 880 70.7 8.331 0.3 87.2831 57.4 7.746 0.08 82.8 881 67.6 8.527 0.05 73.8832 61.5 7.598 0.08 87.2 882 74.1 8.403 0.05 82.8833 50.6 7.947 0.1 73.8 883 78.3 8.321 0.05 87.2834 56.7 7.73 0.1 82.8 884 66.4 8.52 0.08 73.8835 60.9 7.581 0.1 87.2 885 72.8 8.391 0.08 82.8836 49.5 7.919 0.15 73.8 886 76.8 8.305 0.08 87.2837 55.5 7.697 0.15 82.8 887 65.6 8.513 0.1 73.8838 59.6 7.545 0.15 87.2 888 71.9 8.318 0.1 82.8839 47.9 7.875 0.2 73.8 889 75.9 8.294 0.1 87.2840 53.8 7.464 0.2 82.8 890 64.1 8.498 0.15 73.8841 57.8 7.49 0.2 87.2 891 70.2 8.36 0.15 82.8842 45.5 7.801 0.3 73.8 892 74.1 8.269 0.15 87.2843 51.2 7.562 0.3 82.8 893 61.9 8.47 0.2 73.8844 55 7.4 0.3 87.2 894 67.8 8.325 0.2 82.8845 66.2 8.542 0.05 73.8 895 71.5 8.228 0.2 87.2846 72.2 8.396 0.05 82.8 896 58.6 8.419 0.3 73.8847 75.9 8.293 0.05 87.2 897 64.2 8.262 0.3 82.8848 65 8.528 0.08 73.8 898 67.6 8.158 0.3 87.2849 70.8 8.377 0.08 82.8850 74.5 8.27 0.08 87.2
126
Database Used for Generating Coarse GRG Regression
~1%RGRG %Re PF %R.25~m 1~I%RGRG %Re PF %R-25Hm 11 72.2 2.039 0.05 73.8 51 90.2 7.903 0.08 87.22 78.6 3.126 0.05 73.8 52 91.2 9.062 0.08 87.23 82.4 4.313 0.05 73.8 53 92 10.216 0.08 87.24 84.7 5.488 0.05 73.8 54 92.6 11.365 0.08 87.25 86.4 6.654 0.05 73.8 55 62.2 2.024 0.1 73.86 87.6 7.814 0.05 73.8 56 72 3.028 0.1 73.87 88.6 8.969 0.05 73.8 57 77.5 4.428 0.1 73.88 89.4 10.121 0.05 73.8 58 81 5.629 0.1 73.89 90.1 11.27 0.05 73.8 59 83.4 6.818 0.1 73.8
10 76.4 2.041 0.05 82.8 60 85.2 7.996 0.1 73.811 82.2 3.127 0.05 82.8 61 86.5 9.167 0.1 73.812 85.5 4.312 0.05 82.8 62 87.6 10.333 0.1 73.813 87.6 5.484 0.05 82.8 63 88.6 11.493 0.1 73.814 89.1 6.648 0.05 82.8 64 66.5 2.019 0.1 82.815 90.1 7.805 0.05 82.8 65 75.8 3.201 0.1 82.816 91 8.957 0.05 82.8 66 80.9 4.419 0.1 82.817 91.7 10.105 0.05 82.8 67 84.1 5.617 0.1 82.818 92.3 11.251 0.05 82.8 68 86.2 6.802 0.1 82.819 79.1 2.039 0.05 87.2 69 87.8 7.978 0.1 82.820 84.4 3.123 0.05 87.2 70 89 9.145 0.1 82.821 87.5 4.307 0.05 87.2 71 90 10.307 0.1 82.822 89.3 5.477 0.05 87.2 72 90.8 11.463 0.1 82.823 90.6 6.639 0.05 87.2 73 70 2.076 0.1 87.224 91.6 7.793 0.05 87.2 74 78.2 3.193 0.1 87.225 92.4 8.943 0.05 87.2 75 83 4.408 0.1 87.226 93 10.089 0.05 87.2 76 85.9 5.604 0.1 87.227 93.5 11.232 0.05 87.2 77 87.9 6.787 0.1 87.228 65.6 2.011 0.08 73.8 78 89.3 7.959 0.1 87.229 74.4 3.183 0.08 73.8 79 90.5 9.125 0.1 87.230 79.3 4.391 0.08 73.8 80 91.3 10.284 0.1 87.231 82.4 5.582 0.08 73.8 81 92.1 11.438 0.1 87.232 84.5 6.762 0.08 73.8 82 56.4 2.038 0.15 73.833 86.1 7.934 0.08 73.8 83 67.5 3.239 0.15 73.834 87.3 9.099 0.08 73.8 84 74.1 4.477 0.15 73.835 88.3 10.258 0.08 73.8 85 78.3 5.695 0.15 73.836 89.2 11.414 0.08 73.8 86 81.2 6.898 0.15 73.837 69.9 2.009 0.08 82.8 87 83.3 8.09 0.15 73.838 78.2 3.179 0.08 82.8 88 85 9.273 0.15 73.839 82.7 4.385 0.08 82.8 89 86.3 10.448 0.15 73.840 85.4 5.574 0.08 82.8 90 87.4 11.617 0.15 73.841 87.3 6.751 0.08 82.8 91 60.5 2.03 0.15 82.842 88.7 7.919 0.08 82.8 92 71.4 3.227 0.15 82.843 89.8 9.08 0.08 82.8 93 77.6 4.462 0.15 82.844 90.6 10.236 0.08 82.8 94 81.5 5.677 0.15 82.845 91.4 11.388 0.08 82.8 95 84.1 6.876 0.15 82.846 72.7 2.004 0.08 87.2 96 86 8.064 0.15 82.847 80.5 3.173 0.08 87.2 97 87.5 9.243 0.15 82.848 84.7 4.376 0.08 87.2 98 88.7 10.415 0.15 82.849 87.2 5.563 0.08 87.2 99 89.7 11.581 0.15 82.850 88.9 6.737 0.08 87.2 100 63.3 2.02 0.15 87.2
127
~I%RGRG %R. PF %R25pm I~I%RGRG %R. PF %R-25pm 1101 73.8 3.215 0.15 87.2 151 81.8 9.429 0.3 82.8102 79.8 4.447 0.15 87.2 152 83.7 10.632 0.3 82.8103 83.4 5.659 0.15 87.2 153 85.2 11.827 0.3 82.8104 85.8 6.856 0.15 87.2 154 46.9 2.007 0.3 87.2105 87.6 8.041 0.15 87.2 155 59.9 3.219 0.3 87.2106 89 9.218 0.15 87.2 156 68.4 4.48 0.3 87.2107 90.1 10.387 0.15 87.2 157 74.1 5.726 0.3 87.2108 91 11.55 0.15 87.2 158 78.1 6.957 0.3 87.2109 49.5 2.046 0.2 73.8 159 81.1 8.177 0.3 87.2110 61.6 3.262 0.2 73.8 160 83.4 9.386 0.3 87.2111 69.4 4.518 0.2 73.8 161 85.2 10.587 0.3 87.2112 74.4 5.755 0.2 73.8 162 86.7 11.779 0.3 87.2113 78 6.976 0.2 73.8 163 43.4 1.911 0.05 73.8114 80.6 8.184 0.2 73.8 164 61.8 7.692 0.05 73.8115 82.6 9.382 0.2 73.8 165 66.6 11.005 0.05 73.8116 84.3 10.571 0.2 73.8 166 48.5 1.897 0.05 82.8117 85.6 11.753 0.2 73.8 167 67.2 7.586 0.05 82.8118 53.3 2.032 0.2 82.8 168 71.9 10.837 0.05 82.8119 65.5 3.243 0.2 82.8 169 52.2 1.884 0.05 87.2120 73 4.495 0.2 82.8 170 70.7 7.505 0.05 87.2121 77.7 5.727 0.2 82.8 171 75.3 10.714 0.05 87.2122 81 6.944 0.2 82.8 172 39.7 1.927 0.08 73.8123 83.4 8.148 0.2 82.8 173 60.8 7.75 0.08 73.8124 85.3 9.342 0.2 82.8 174 65.9 11.07 0.08 73.8125 86.8 10.528 0.2 82.8 175 44.6 1.908 0.08 82.8126 88 11.706 0.2 82.8 176 66 7.632 0.08 82.8127 55.9 2.019 0.2 87.2 177 71.1 10.889 0.08 82.8128 67.9 3.226 0.2 87.2 178 48.1 1.89 0.08 87.2129 75.1 4.474 0.2 87.2 179 69.6 7.544 0.08 87.2130 79.7 5.703 0.2 87.2 180 74.5 10.76 0.08 87.2131 82.8 6.917 0.2 87.2 181 37.7 1.932 0.1 73.8132 85.1 8.119 0.2 87.2 182 60.1 7.778 0.1 73.8133 86.8 9.31 0.2 87.2 183 65.5 11.104 0.1 73.8134 88.2 10.493 0.2 87.2 184 42.2 1.91 0.1 82.8135 89.3 11.668 0.2 87.2 185 65.4 7.654 0.1 82.8136 41.4 2.044 0.3 73.8 186 70.7 10.916 0.1 82.8137 54 3.271 0.3 73.8 187 45.8 1.89 0.1 87.2138 62.8 4.544 0.3 73.8 188 68.8 7.561 0.1 87.2139 68.8 5.799 0.3 73.8 189 74 10.783 0.1 87.2140 73.1 7.039 0.3 73.8 190 34.3 1.934 0.15 73.8141 76.4 8.267 0.3 73.8 191 58.8 7.816 0.15 73.8142 79 9.484 0.3 73.8 192 64.6 11.152 0.15 73.8143 81.1 10.691 0.3 73.8 193 38.7 1.906 0.15 82.8144 82.8 11.89 0.3 73.8 194 64 7681 0.15 82.8145 44.7 2.024 0.3 82.8 195 69.7 10.953 0.15 82.8146 57.6 3.243 0.3 82.8 196 41.8 1.883 0.15 87.2147 66.3 4.509 0.3 82.8 197 67.4 7.581 0.15 87.2148 72.1 5.759 0.3 82.8 198 73.1 10.812 0.15 87.2149 76.3 6.994 0.3 82.8 199 30.3 1.928 0.2 73.8150 79.4 8.217 0.3 82.8 200 57 7.845 0.2 73.8
128
~I%RGRG %R" PF %R25pm I~I%RGRG %R" PF %R-25pm 1201 63.3 11.198 0.2 73.8 251 75.4 8.044 0.15 87.2202 34.3 1.894 0.2 82.8 252 80.2 11.544 0.15 87.2203 62 7.697 0.2 82.8 253 36 1.989 0.2 73.8204 68.4 10.983 0.2 82.8 254 65.5 8.257 0.2 73.8205 37 1.868 0.2 87.2 255 71.6 11.862 0.2 73.8206 65.4 7.588 0.2 87.2 256 40.3 1.959 0.2 82.8207 71.7 10.833 0.2 87.2 257 70.1 8.134 0.2 82.8208 25.7 1.91 0.3 73.8 258 76 11.683 0.2 82.8209 54.1 7.853 0.3 73.8 259 43.2 1.935 0.2 87.2210 61.2 11.226 0.3 73.8 260 73 8.044 0.2 87.2211 29 1.87 0.3 82.8 261 78.7 11.557 0.2 87.2212 59 7.687 0.3 82.8 262 30.3 1.972 0.3 73.8213 66.2 10.991 0.3 82.8 263 62.1 8.255 0.3 73.8214 31.3 1.838 0.3 87.2 264 69.2 11.877 0.3 73.8215 62.3 7.567 0.3 87.2 265 33.8 1.935 0.3 82.8216 69.4 10.829 0.3 87.2 266 66.6 8.115 0.3 82.8217 52.2 1.982 0.05 73.8 267 73.5 11.68 0.3 82.8218 71.4 8.137 0.05 73.8 268 36.3 1.907 0.3 87.2219 75.6 11.703 0.05 73.8 269 69.4 8.014 0.3 87.2220 57.8 1.971 0.05 82.8 270 76.2 11.542 0.3 87.2221 76.1 8.051 0.05 82.8 271 42.6 1.831 0.05 73.8222 79.9 11.564 0.05 82.8 272 58.8 7.198 0.05 73.8223 61.8 1.959 0.05 87.2 273 63.1 10.241 0.05 73.8224 79.1 7.984 0.05 87.2 274 46.7 1.822 0.05 82.8225 82.7 11.461 0.05 87.2 275 63.3 7.095 0.05 82.8226 47.7 1.994 0.08 73.8 276 67.8 10.073 0.05 82.8227 70.1 8.185 0.08 73.8 277 49.7 1.81 0.05 87.2228 74.7 11.759 0.08 73.8 278 66.5 7.013 0.05 87.2229 53 1.977 0.08 82.8 279 71 9.949 0.05 87.2230 74.8 8.09 0.08 82.8 280 39 1.86 0.08 73.8231 79.1 11.61 0.08 82.8 281 57.8 7.295 0.08 73.8232 56.8 1.962 0.08 87.2 282 62.5 10.35 0.08 73.8233 77.8 8.016 0.08 87.2 283 43 1.844 0.08 82.8234 81.8 11.501 0.08 87.2 284 62.3 7.178 0.08 82.8235 45.2 1.997 0.1 73.8 285 67.2 10.168 0.08 82.8236 69.3 8.208 0.1 73.8 286 45.9 1.829 0.08 87.2237 74.2 11.787 0.1 73.8 287 65.5 7.087 0.08 87.2238 50.4 1.977 0.1 82.8 288 70.4 10.034 0.08 87.2239 74 8.107 0.1 82.8 289 37 1.87 0.1 73.8240 78.6 11.632 0.1 82.8 290 57.2 7.344 0.1 73.8241 54 1.96 0.1 87.2 291 62.1 10.409 0.1 73.8242 77 8.03 0.1 87.2 292 40.9 1.851 0.1 82.8243 81.3 11.52 0.1 87.2 293 61.7 7.22 0.1 82.8244 40.9 1.996 0.15 73.8 294 66.8 10.218 0.1 82.8245 67.7 8.237 0.15 73.8 295 43.8 1.833 0.1 87.2246 73.1 11.827 0.15 73.8 296 64.9 7.124 0.1 87.2247 45.7 1.972 0.15 82.8 297 70 10.079 0.1 87.2248 72.4 8.127 0.15 82.8 298 33.6 1.879 0.15 73.8249 77.5 11.662 0.15 82.8 299 56 7.414 0.15 73.8250 49.1 1.952 0.15 87.2 300 61.3 10.498 0.15 73.8
129
~ %RGRG %Re PF %R.2Sum 1% RGRG %Re PF %R-2Spm 1301 37.4 1.854 0.15 82.8 351 84.4 8.284 0.1 87.2302 60.6 7.277 0.15 82.8 352 77 8.436 0.15 73.8303 66 10.292 0.15 82.8 353 80.6 8.365 0.15 82.8304 40 1.832 0.15 87.2 354 82.7 8.312 0.15 87.2305 63.7 7.172 0.15 87.2 355 74.5 8.47 0.2 73.8306 69.2 10.144 0.15 87.2 356 78.1 8.389 0.2 82.8307 29.7 1.879 0.2 73.8 357 80.3 8.329 0.2 87.2308 54.3 7.478 0.2 73.8 358 70.6 8.487 0.3 73.8309 60.1 10.588 0.2 73.8 359 74.2 8.391 0.3 82.8310 33.1 1.848 0.2 82.8 360 76.4 8.321 0.3 87.2311 58.9 7.325 0.2 82.8 361 81.4 8.716 0.05 13.8312 64.8 10.364 0.2 82.8 362 85.4 8.563 0.05 82.8313 35.5 1.821 0.2 87.2 363 87.8 8.605 0.05 87.2314 62 7.21 0.2 87.2 364 79.9 8.732 0.08 73.8315 68.1 10.206 0.2 87.2 365 83.9 8.662 0.08 82.8316 25.1 1.866 0.3 73.8 366 86.3 8.61 0.08 87.2317 51.7 7.522 0.3 73.8 367 78.9 8.738 0.1 73.8318 58.3 10.688 0.3 73.8 368 83 8.664 0.1 82.8319 28 1.826 0.3 82.8 369 85.4 8.609 0.1 87.2320 56.2 7.349 0.3 82.8 370 77.1 8.742 0.15 73.8321 63 10.421 0.3 82.8 371 81.2 8.661 0.15 82.8322 30.1 1.795 0.3 87.2 372 83.6 8.601 0.15 87.2323 59.3 7.222 0.3 87.2 373 74.4 8.736 0.2 73.8324 66.2 10.248 0.3 87.2 374 78.6 8.644 0.2 82.8325 73.1 7.795 0.05 73.8 375 81 8.577 0.2 87.2326 76.9 7.727 0.05 82.8 376 70.4 8.707 0.3 73.8327 79.4 7.671 0.05 87.2 377 74.5 8.6 0.3 82.8328 71.8 7.878 0.08 73.8 378 76.9 8.523 0.3 87.2329 75.6 7.801 0.08 82.8 379 85.6 6.453 0.05 13.8330 78.1 7.738 0.08 87.2 380 87.9 6.465 0.05 82.8331 71 7.921 0.1 73.8 381 89.3 6.468 0.05 87.2332 74.9 7.838 0.1 82.8 382 84 6.685 0.08 73.8333 77.4 7.772 0.1 87.2 383 86.4 6.692 0.08 82.8334 69.5 7.982 0.15 73.8 384 87.9 6.69 0.08 87.2335 73.4 7.889 0.15 82.8 385 83.1 6.809 0.1 73.8336 75.9 7.817 0.15 87.2 386 85.5 6.812 0.1 82.8337 67.3 8.039 0.2 73.8 387 87 6.807 0.1 87.2338 71.2 7.934 0.2 82.8 388 81.4 7.001 0.15 73.8339 73.7 7.854 0.2 87.2 389 83.9 6.997 0.15 82.8340 63.9 8.08 0.3 73.8 390 85.4 6.988 0.15 87.2341 67.8 7.957 0.3 82.8 391 78.8 7.206 0.2 73.8342 70.3 7.865 0.3 87.2 392 81.4 7.193 0.2 82.8343 81.1 8.31 0.05 73.8 393 83 7.177 0.2 87.2344 84.5 8.257 0.05 82.8 394 74.9 7.414 0.3 73.8345 86.6 8.216 0.05 87.2 395 77.6 7.387 0.3 82.8346 79.6 8.368 0.08 73.8 396 79.2 7.36 0.3 87.2347 83.1 8.308 0.08 82.8348 85.2 8.262 0.08 87.2349 78.8 8.396 0.1 73.8350 82.2 8.332 0.1 82.8
130
Appendix F
Regression ANOVA
Table For Coarse and Fine GRG
131
Table F-l Summary output and ANOVA for the Five GRG Size Distribution
Summary Output
Regression Statistics
132
Multiple RR SquareAdjusted R SquareStandard ErrorObservations
ANOVA
df
0.99570.99150.99141.674845
SS MS F
RegressionResidualTotal
10 271395.49 27139.55 9685.31834 2336.98 2.80844 273732.47
Coefficients Standard Error t Stat. Lower95% Upper 95%
Intercept -350.31 8.10 -43.27 -366.20 -334.42ln(Re) 16.70 0.11 149.53 16.48 16.92ln((Re)*ln('r) 4.36 0.18 24.68 4.02 4.71ln(R.2Sllm) 80.93 1.84 43.98 77.32 84.54lnCt) -9.66 0.38 -25.21 -10.41 -8.91ln(GRG_2s) -53.19 3.99 -13.34 -61.01 -45.36ln(GRG_7s) -107.16 2.21 -48.51 -111.50 -102.83ln(GRG_30o) 456.13 14.58 31.28 427.51 484.75ln(GRG_6oo) -552.42 22.18 -24.91 -595.95 -508.90ln(GRG_2s)*ln(Re) 13.80 0.90 15.29 12.02 15.57ln(GRG_2s)*ln('t) 2.27 0.11 21.42 2.07 2.48
Table F-2 Summary Output and ANOVA for Fine GRG
Summary Output
Regression Statistics
133
Multiple RR SquareAdjusted R SquareStandard ErrorObservations
ANOVA
df
0.99240.98490.98471.924898
SS MS F
RegressionResidualTotal
7 214353.8890 3294.9897 217648.7
30621.9 8271.43.7
Coefficients Standard Error t Stat. Lower95% Upper 95%
Intercept -233.09 7.96 -29.29 -248.71 -217.47In(Re) 17.10 0.12 139.22 16.85 17.33In«Re)*ln('t) 3.61 0.19 18.57 3.22 3.99In(R..2s).lm) 60.71 0.92 65.87 58.90 62.52lnet) -11.92 0.37 -32.07 -12.65 -11.19In(GRG_2s) -4.34 0.17 -24.95 -4.68 -3.99In(GRG_7s) -57.77 0.93 -62.12 -59.59 -55.94In(GRG_1SO) 55.51 2.19 25.25 51.19 59.82
Table F-3 Summary Output and ANOVA for Coarse GRG
Summary Output
Regression Statistics
134
Multiple RR SquareAdjusted R SquareStandard ErrorObservations
ANOVA
df
0.98890.97780.97742.37396
SS MS F
RegressionResidualTotal
6 96075.57389 2185.59395 98261.16
16012.59 2849.995.62
Coefficients Standard Error t Stat. Lower95% Upper 95%
Intercept -65.40 8.10 -8.07 -81.33 -49.47In(Re) 15.58 0.21 74.76 15.18 15.99In((Re)*ln(t) 5.49 0.33 16.78 4.85 6.14In(R.25/!m) 37.81 1.71 22.13 34.45 41.17ln(-r) -17.26 0.62 -27.76 -18.48 -16.03In(GRG_75) -30.04 0.87 -34.45 -31.75 -28.32In(GRG_150) 12.67 1.43 8.84 9.85 15.49
Appendix G
Database for Generating the Relationship
between 't, R 251lm and Circulating Load,
Fineness of Grind.
Regression ANOVA Table
135
Table G-l Data for generating the relationship between fineness of grind and
% P-75/lm 't %R..25J.lm In2't
70.5 0.8 73.8 0.05072.6 1.0 73.8 076.6 1.5 73.8 0.16479.4 2.0 73.8 0.48082.9 3.0 73.8 1.20776.2 0.8 82.8 0.05078.3 1.0 82.8 082.1 1.5 82.8 0.16484.7 2.0 82.8 0.48087.8 3.0 82.8 1.20778.6 0.8 87.2 0.05080.7 1.0 87.2 084.5 1.5 87.2 0.16486.9 2.0 87.2 0.48089.8 3.0 87.2 1.207
Table G-2 Data for generating the relationship between circulating load and
%
Circulating Load 't %R-25J.lm lnt* R..25J.lm In2't
70.5 0.8 73.8 -16 0.05072.6 1.0 73.8 0 076.6 1.5 73.8 30 0.16479.4 2.0 73.8 51 0.48082.9 3.0 73.8 81 1.20776.2 0.8 82.8 -18 0.05078.3 1.0 82.8 0 082.1 1.5 82.8 34 0.16484.7 2.0 82.8 57 0.48087.8 3.0 82.8 91 1.20778.6 0.8 87.2 -19 0.05080.7 1.0 87.2 0 084.5 1.5 87.2 35 0.16486.9 2.0 87.2 60 0.48089.8 3.0 87.2 96 1.207
136
137
Table G-3 Summary output and ANOVA for generating the relationship between
fineness of grind and 't, R251lm.
Summary Output
Regression Statistics
Multiple RR SquareAdjusted R SquareStandard ErrorObservations
ANOVA
RegressionResidualTotal
df
31114
0.99840.99680.99590.353615
SS
426.011.38
427.39
MS
142.00.13
F
1135.59
Coefficients Standard Error t Stat. Lower95% Upper 95%
Intercept 20.07 1.43 14.05 16.92 23.21't 10.38 0.05 20.63 9.28 Il.49R251lm 0.58 0.02 35.35 0.54 0.61In2('t) -9.36 0.89 -10.51 -11.32 -7.40
138
Table G-4 Summary output and ANOVA for generating the relationship between
circulating load and 't, R 251lmo
Summary Output
Regression Statistics
Multiple RR SquareAdjusted R SquareStandard ErrorObservations
ANOVA
df
0.99960.99920.99902.7815
SS MS F
RegressionResidualTotal
31114
10968484.83109769.1
36561.4 4740.77.71
Coefficients Standard Error t Stat. Lower95% Upper 95%
Intercept -140.6 10.58 -13.48 -165.89 -119.33R 25 /lm 6.42 0.13 49.48 6.14 6.71In('t)*R_25 /lm -2.72 0.045 -60.66 -2.82 -2.63In2('t) 63.75 3.89 16.40 55.19 72.31