DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY...

153
DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN GRINDING CIRCUIT Zhixian Xiao A thesis submitted to the Faculty of Graduate Studies and Research In partial fulfillment of the requirement for the degree of Master of Engineering Department of Mining, Metals and Materials Engineering McGill University Montréal, Canada © September 2001

Transcript of DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY...

Page 1: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 2: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

1+1 National L1braryof Canada

Acquisitions andBibliographie Services

3QS Wellington StrNtOttawa ON K1 A 0N4canada

BibliothèQue nationaledu Canada

Acquisitions etservices bibliographiques

395. rue W..ngtonOlta_ ON K1 A 0N4can.csa

Ol.w" __

The author bas granted a non­exclusive licence alloWÎDg theNational Library ofCanada 10reproduce, loan, distnbute or seUcopies of this thesis in microform,paper or electronic formats.

The author retains ownership of thecopyright in this thesis. Neither thethesis nor substantial extracts from itmay he printed or otherwisereproduced without the author'spermission.

L'auteW' a accordé une licence nonexclusive permettant à laBibliothèque nationale du Canada dereproduire, prater, distribuer ouvendre des copies de cette thèse sousla forme de microfichelfilm, dereproduction sur papier ou sur formatélectronique.

L'auteW' conserve la propriété dudroit d'auteur qui protège cette thèse.Ni la thèse ni des extraits substantielsde celle-ci ne doivent être imprimésou autrement reproduits sans sonautorisation.

0-612-79103-3

Canad~

Page 3: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 4: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 5: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

111

rn~~~~~~wwmw~~~~~mn~W~~f!JL ~:9 1[ 1Jë ~ r»f ~~ M. JiJT ~ 1ir :E ~ fl $ :9 ~ BI t2J- 1Jt m~ ~ q)(. ïffi f»t ~~ ~ B"J ~ q)( $ * ~ me ~ - J»t il! [ïI ~t B"J I~,~~~B"J~~~~mW~~B"J~~~illrrB"J, ïffi~ ~y ~ ~ B"J fi ~ ~ ~l t2J- il 1ifB :tt!! m~.

-~m~f»t~~B"J~~~~*B"J~.~~mm~1994 !if:: 1î1f 'li:. ttl * ( LAPLANTE et al, 1995). * il" i~ X B"J 1î1f ~ ElB"J ~ ~ ~o 1ïiJ ~ ,~\ • ~ ~f *~ m B"J ~ 1im I. 'li:. fi ttl]l! ~ ~ $.m B"J *~ m. l! - 1î1f ~ § B"J ~ lm :i1 ~ r w-J 1r 00 * no ~ ~:fmB"J: ~-: ~~=$)t:f*mlJtfo7j(n1î1Ë~~~~nBI

~ ~ ~ B"J fT ~ m T w-J ~ ~ ~j( * m~. - ~ ~ 1: (7[; Jf!. Ü1:m 1ir st râJ) ,33 - ~ ~ R-25~m ( /J\ ~ 25 ~ * B"J ~ n BI ~ q)( ~* A i~ 7k n iiJi mt 3 m; mE B"J S 71'- $) . ~ T ~ ~ r»f ~IJ ~ B"J~~$, l!w-J~~~fomW~~~ B"J~~j.\.~1S7.m1ir

~œ}jtJt**~-~. ~=: ES,~\.~1~ff~mf~mr:1:fl'* ~ 89 ~ ~ ~ ~ $ 89 ~ tg J$ BI ~ m w-J ~ !l -g- ~ ,t1: ~ ~3

1r f!f(- ~ ffl ~ fll *1 ~ ~ n BI ~ q)( ~, 33 - ~ ~ m~ ~œ

f1 ~ ~ n BI ~ ~ ~)* 1~ *-. l! w-J ~ !l -g- ~ ,t1: ~ ~3 1r f!ft~ r»f r9JIJ ~ 89 ~ q)( * Éij ~ e ~ ~t ~j( 89 1t • 1:, R-25~m ,:1: n BI~~~B"J~}jt~~~~~~~~n~~*~-g.~~~ ~ @j q)( ~ n Re ~ )( ~ ~ ~ ~ :fI B"J ~ ~j.\ :1: B"J S 71'- tt, fll~~~*~m~~~*B"J~~.*~X1î1f~'li:.~,m~~ q)( ~ n ~ 13 PînJ ~ 89 @] q)( * m: JI[ =li B"J ~:I: , ïffi 1: mu ~ ~

~ JJ PînJ m: /J\ B"J ~. . ES ft it lm :i1 HE ~ ~ B"J w-J ,~ (~t ~ fll*1 ~ ~ n BI ~ q)( ~ ïffi ~) B)t ~ ,~ (~t ~ ~œ *1 ~ ~ n BI @] 4)(~ ïffi ~) 1~ *- B"J ~ n BI ~ 4)( ~ B"J *1 }jt 71'- ~ ~t ~ B"J @] 4)( *t!1 fl JI[ =li 89 JJ PînJ. J~\ ~ fl 20 m :IF [Pl 89 m n BI ~ ~ ~ B"J~ }jt ~ ~ m ~ f~ tPJ. r: 1: pH flfi B"J ~ tg J$.

l! w-J ~ !l -g- ~ t1: ~ ~3 1.J f!f m T \2] ~ll ~ r ~ '!J1J * illfT fi ~~, ~ fi ~u ~ 'li:. :fm Bi ~~ B"J il 1ifB ,t1: il! H :tt!! Ü1: ~ r9JIJ :1:li j] m @) tHr ~ é"J *iL Ji: fI'- :fiî JiJT F ~ B"J *13 ~t *= :& 5% m: lE l21­IAJ. ~ flfi ~ 1~ ï~ *13 $. *31 ~ ~ 89 @] ~ $, r»f r9JIJ 8t BI m }j,:1: ~ 1~f f~ m; lX Z, M Jf!. ~ m 89 !l -g- ~ ,t1: @] ~3 1.J f!f ]I!m-g- ffl ~ f»f r9JIJ ~ 89 @] 4)( $ .

Page 6: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 7: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 8: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 9: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 10: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 11: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 12: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 13: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 14: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 15: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 16: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 17: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 18: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 19: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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).

Page 20: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 21: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 22: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 23: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 24: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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,

Page 25: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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,

Page 26: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 27: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 28: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 29: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 30: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 31: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 32: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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).

Page 33: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 34: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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:

Page 35: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 36: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 37: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 38: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 39: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 40: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 41: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 42: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 43: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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,

Page 44: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 45: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 46: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 47: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 48: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 49: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 50: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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:

Page 51: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 52: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 53: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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:

Page 54: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 55: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 56: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 57: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 58: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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%.

Page 59: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 60: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 61: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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):

Page 62: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 63: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 64: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 65: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 66: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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)

Page 67: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 68: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 69: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 70: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 71: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 72: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 73: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 74: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 75: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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%).

Page 76: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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).

Page 77: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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).

Page 78: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 79: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 80: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 81: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 82: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 83: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 84: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 85: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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).

Page 86: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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)

Page 87: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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?

Page 88: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 89: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 90: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 91: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 92: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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)

Page 93: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 94: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 95: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 96: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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%

Page 97: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 98: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 99: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 100: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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%

Page 101: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 102: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 103: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 104: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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_

Page 105: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 106: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 107: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 108: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 109: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 110: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 111: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 112: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

REFERENCES

References

97

1. Agar, G. E., 1992, "Assessment of Gravity Recoverable Gold", Proceedings, 25th

Ann. Meeting Canadian Mineral Processors, Ottawa, January, Paper #13.

2. Anon., 1983, "New Gold Production Method Means You Can End Health and

Pollution Dangers", Cano Mng. Journal, Vol 104, No.5, pp. 29-31.

3. Anon., 1987, "Hemlo: A North American Gold Success Story", Engineering and

Mining Journal, June, pp. 10-13.

4. Austin, L. G., Luckie, P. T., and Klimpel, R. R., 1984, "Process Engineering ofSize

Reduction: BalI Milling", Pub. SME, Littleton, CO.

5. Banisi, S., Laplante, A. R., and Marois, 1., 1991, "The behaviour of Gold in Hemlo

Mines Ltd. Grinding Circuit", CIM Bulletin, Vol. 84(955), pp. 72-78.

6. Banisi, S., 1991, "An Investigation of the Gravity Recovery of Gold", Master of

Engineering Thesis, McGill University, Montreal.

7. Bath, M. D., Duncan, A. 1., and Rudolph, E. R., 1973, "Sorne Factors Influencing

Gold Recovery by Gravity Concentration", Journal of the South African Institute of

Mining and Metallurgy, June, pp. 363-385.

8. Brittan, M. 1. and Van Vuuren, E. J. J., 1973, "Computer Analysis, Modeling and

Optimisation of Gold Recovery Plants of the Angol American Group" African

Institute of Mining and Metallurgy, Vol. 73, No. 7, pp. 211-220.

9. Buonvino, M., 1994, "The Falcon CentrifugaI Concentrator" Master of Engineering

Thesis, McGill University, Montreal.

10. Burt, R. O., 1984, "Gravity Concentration Technology", Amsterdam: Elsevier

Publishers.

Il. Chyi, L.L. and J.H. Crocket, 1976, "Partition of Platinum, Palladium, Iridium and

Gold among Coexisting MineraIs from the deep Ore Zone", Strathcona mine. Sudbury,

Ontario, Economic Geology, Vol. 71, pp. 9.

Page 113: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

REFERENCES 98

12. Darnton, R, Lloyd, S., and Antonioli, M. A, 1992, "Gravity Concentration: Research,

Design and Circuit Performance at Montana Tunnels", Rando1 Go1d Forum,

Vancouver'92, March 25-27.

13. Douglas, J. K. E., and Moir, AT., 1961, "A Review of South African Gold

Recovery Practice", Trans. th Commonwealth Min. and Met. Congress,

Johannesburg. Vol. III, pp. 171-193.

14. DOIT, J. V. N., and Bosqui, F. L., 1950, "Cyanidation and Concentration of Gold and

Silver Ores", 2nd edition, New York, McGraw Hill.

15. Finch, J. A, 1984, "Modeling a Fish-hook in Hydrocyclone Selectivity Curves",

Powder Technology, Vol. 36, pp. 127-129.

16. Finch, J. A, Laplante, A R. and Leung, J. 1988, " The SPOC Manual --- Chapter 4

Modeling and Simulation: Modeling and Simulation Methodology for Ore and Coal

Processes", CANMET, Energy, Mines and Resources Canada, pp. 1-45.

17. Graham, P. R., 1989, "Following the Gold Through Manhattan's Gravity Circuit by

Size Distribution and a Floatation Method of Processing Gravity Concentrates",

SME Annual Meeting, Las Vegas, Nevada, February 27 - March 2.

18. Guest, R. N., Dunne, R. C., 1985, "An Evaluation of Gravity Separator by Use ofa

Synthetic Ore", Journal of the South African Institute of Mining and Metallurgy,

June, Vol. 85, No. 6, pp. 121-125.

19. Herbst, J. A, Lo, Y. C., and Bohrer, 1. E., 1987, "Increasing the Capacity of a

Phosphate Grinding with the Aid of Computer Simulation", MineraIs &

Metallurgical Processing, Vol. 4, No. 3, August, pp. 155-160.

20. Hinds, H. L., Trautman, L. L., and Ommen, R. D., 1989, "Homestake's Improved

Gravity Recovery Circuit", SEM Annual Meeting, Las Vegas, Nevada, February 27

-March2.

21. Hodouin, D., Bérubé, M. A, and Everell, M. D., 1978, "Modeling in Industrial

Grinding Circuits and Applications in Design", CIM Bull., September, pp. 138-145.

Page 114: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

REFERENCES 99

22. Huang, L., 1996, "Upgrading of Gold Gravity Concentrates --- A Study of the

Knelson Concentrator" Ph.D. Thesis, McGill University, Montreal, pp.42-53.

23. Kelsall, D. F., Stewart, P. S. B., and Weller K. R, 1973, "Continuous Grinding in a

Small Wet BalI Mill, Part V. A study of the Influence of Media Shape", Powder

Technol., Vol. 8, pp. 291-299.

24. Klimpel, R R., and Austin, L. G., 1984, "Simulation of a Mill Grinding Copper Ore

by Scale-up of Laboratory Data", Proc., Mintek 50, Johannesburg, South Africa.

25. Knelson, B. V., 1988, "CentrifugaI Concentration and Separation of Precious

Metals", 2nd International Conference on Gold Mining, Vancouver, Nov., pp.303­

317.

26. Knelson, B. V., 1990, "Development and Economie Application of Knelson

Concentrator in Low Grade Alluvial Gold Deposits", The AusIMIM 1990 Annual

Conference, Rotorua, New Zealand, 18-21 March, pp. 123-128.

27. Laplante, A R, 1987, "Mineralogy and Metallurgical Performance of Various

Gold-Copper Ores of the Chibougamau Area, Québec", Proc. Intern. Symp. on Gold

Metallurgy, Eds. R. S., Salter, D. M. Wysouzil, G. W. Mcdonald, Winnipeg, Aug.,

pp.l41-155.

28. Laplante, A R, 1984, "Plant Sampling and Balancing for Gold Ores", 1st Intern.

Symp. Precious on metals recovery, Reno, June, paper V.

29. Laplante, AR., 1999, Course Notes, "Modeling and Control of Mineral Processing

Systems", Mining and Metallurgical Engineering Department, McGill University.

September, pp. 10-65.

30. Laplante, A. R, 2001, Course Notes, "Mathematical Application in the Mineral

Processing Industry", Mining and Metallurgical Engineering Department, McGill

University. January, pp. 95-140.

31. Laplante, AR., Finch, 1. A, and deI Villar, R, 1987, "Simplification of the

Grinding Equation for Plant Simulation", Trans. Inst. Min. Metall. (London), Sect.

C., June, Vol. 96, pp. C 108-112.

Page 115: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

REFERENCES 100

32. Laplante, A R., Liu, L., and Cauchon, A, 1990, "Gold Gravity Recovery at the Mill

of Les Mines Camchib Inc., Chibougamau, Quebec", Proceedings, Process

Mineralogy Symp., Las Vegas, Feb. 1989, Eds. W. Petruk, R. D. Hagni, S. Pignolet­

Brandom and D. M. Hausen, pp. 247-258.

33. Laplante, AR., Putz, A, and Huang, L., 1993, "Sampling and Sample Processing

for Gold Gravity Circuits", Proceedings, Professional Development Seminar on

Gold Recovery by Gravity, McGill University, May, Montreal.

34. Laplante, A. R., Putz, A., Huang, L., and Vincent, F., 1994, "Practical

Considerations in the Operations of Gold Gravity Circuits", Proceedings, 26th Ann.

Meet. Canadian Mineral Processors, Ottawa, January, Paper #23.

35. Laplante, A. R., Woodcock, F., and Noaparast, M., 1994, "Predicting Gold

Recovery by Gravity", Proceedings, Annual Meeting of SME, Albuquerque, Paper

94-158.

36. Laplante, A R., Shu, Y., and Marois, 1., 1994, "Experimental Characterization of a

Laboratory CentrifugaI Separator", Submitted to the Canadian Metallurgical

Quarterly.

37. Laplante, A R, 2000, "Simulating the Effect of Grind Size and Recovery Effort on

the Gravity Recovery of Gold for Six Battle Mountain Ore Samples" Technical

Report, Corrected Version, McGill University, November.

38. Laplante, A. R, 1999 "Report on the Characterization of Gravity Recoverable Gold

in a Sample of Ore from the Campbell Mine", Technical Report, McGill University,

March.

39. Laplante, A R, 2001 "Report on the Characterization of Gravity Recoverable Gold

in a Sample of Kemess #1 Ore", Technical Report, McGill University, January.

40. Loveday, B. K., and Forbes, J. E., 1982, "Sorne Considerations in the Use of

Gravity Concentration for the Recovery of Gold", Journal of the South African

Institute of Mining and Metallurgy, May, pp. 121-123.

Page 116: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

REFERENCES 101

41. Marsden, 1., and House, L, 1992, "The Chemistry of Gold Extraction", First

published in 1992 by Ellis Horwood Limited, England, pp. 45-92.

42. Noaparast, M., 1997, "The Behavior of Malleable Metals in Tumbling Mills."

Master of Engineering Thesis, McGill University, Montréal.

43. Narayanan, S. S., 1987, "Modeling the Performance of Industrial BalI Mills Using

Single Particle Breakage Data", International Journal of Mineral Processing, Vol.

20, No. 776, Dec., pp. 114-120.

44. Ounpuu, M., 1992, " Gravity Concentration of Gold from Base Metal Flotation

Mills". Proceedings, 24th Meet. Canadian Mineral Processors, Ottawa, Jan., Paper

#10.

45. Plitt, L. R, 1976, "A Mathematical Model of the Hydrocyclone Classifier", CIM

Bull., Vol. 69, No. 776, Dec., pp. 114-123.

46. Putz, A., Laplante, A. R., and Ladouceur, G., 1993, "Evaluation of a Gravity Circuit

in a Canadian Gold Operation", Proceedings, Randol Gold Forum, Beaver Creek,

September, pp. 145-149.

47. Putz, A., 1994, "An Investigation of the Gravity Recovery of Gold", Master of

Engineering Thesis, McGill University, Montreal.

48. Richards, R H., and Locke, C. E., 1940, "Text Book of Ore Dressing", McGraw

Hill, pp. 50-78.

49. Sabelin, T., 1. Iwasaki and K.J. Reid, 1986, "Platinum Group MineraIs in the Duluth

Complexioned their Beneficiation Behaviours", Skilling Mining Review, Minnesota

Mining Symposium, Jan., pp. 25.

50. Spring, R, Larsen, C., and Mular, A., 1988, "The SPOC Manual --- Chapter 4.1

Industrial BalI Mill Modelling: Documented Application of the Kinetic Model",

CANMET, Energy, Mines and Resources Canada, pp. 1-20.

51. Spiller, D. E., 1983, "Gravity Separation of Gold - Then and Now", Mining

Yearbook, pp.79-81.

Page 117: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

REFERENCES 102

52. Vincent, F., 1997, "A Comparison of Knelson Concentrator and Jig Performance for

Gold Recovery" Master of Engineering Thesis, McGill University, Montreal, pp.

70-79.

53. Volborth, A and M.I Pasecznyk, 1984, "Platinum, Palladium, Rhenium, Sulphide and

Graphite Mineralization in the Stillwater Complex of Montana - an Illustrated

Description", Applied Mineralogy, Metall. Soc. of AIME, Feb. pp. 15.

54. Wills, B. A, 1997, "Mineral Processing Technology", 5th Edition, Pergamon Press,

Oxford, pp. 300-435.

55. Woodcock, F., and Laplante, AR., 1993, " A Laboratory Method to Measure Free

Gold Content", Proceedings, Randol Gold Seminar, Beaver Creek, September, pp.

151-155.

56. Woodcock, F., 1994, "Use of a Knelson Unit to Quantify Gravity Recoverable Gold

in an Ore Sample", Master of Engineering Thesis, McGill University, Montreal, pp.

1-121.

57. Xiao, Z., Laplante A R., 2001, "Predicting Gold Gravity Recovery in Grinding

Circuits: Parametric Estimation and Representation of Results" Proceedings,

Conference ofMetallurgists 2001, Toronto.

58. Xiao, J., 1998, "Testing a New Gold CentrifugaI Concentrator" Master of

Engineering Thesis, McGill University, Montreal, pp. 4-25.

59. Yalcin, T., Lachapell, D., and Hmidi, N. 2001, "Simulation of the Grinding Circuit

at St Andrew Goldfield Ltd's Stock Mine Mill", Proceedings, 3ih Ann. Meet.

Canadian Mineral Processors, Ottawa, January, Paper #41.

60. Zhang, B., 1997, "Recovering Gold from High Density Gangues with Knelson

Concentrators" Master of Engineering Thesis, McGill University, Montreal, pp. 63­

68.

Page 118: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

AppendixA

Breakage and Selection Function

Used for GRG and Ore

103

Page 119: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 120: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

Appendix B

Grinding Matrix for GRG and Ore

105

Page 121: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 122: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 123: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 124: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 125: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

Appendix C

GRGs Used for Simulation

110

Page 126: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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.

Page 127: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

Appendix 0

An Example of Simulation

112

Page 128: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 129: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 130: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 131: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 132: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

Appendix E

Database Used forGenerating Regressions

117

Page 133: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 134: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 135: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 136: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 137: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 138: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 139: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 140: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 141: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 142: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 143: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 144: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~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

Page 145: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

~ %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

Page 146: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

Appendix F

Regression ANOVA

Table For Coarse and Fine GRG

131

Page 147: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 148: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 149: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 150: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

Appendix G

Database for Generating the Relationship

between 't, R 251lm and Circulating Load,

Fineness of Grind.

Regression ANOVA Table

135

Page 151: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 152: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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

Page 153: DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY ...digitool.library.mcgill.ca/thesisfile34000.pdf · DEVELOPING SIMPLE REGRESSIONS FOR PREDICTING GOLD GRAVITY RECOVERY IN

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