Open Pit Mine Planning Using Sirnulated Gold Grades J. Michael Anderson A thesis submitted to

244 Pages·2001·17.48 MB·English

Open Pit Mine Planning Using Sirnulated Gold Grades
J. Michael Anderson
A thesis submitted to the Department of Mining Engineering
in conformity with the requirements for the
degree of Master of Science (Engineering)
Queen's University
Kingston, Ontario, Canada
December, 1999
Copyright O J. Michael Anderson, 1999
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ABSTRACT
Gold is a metal with a relatively high market value and therefore the effect
of emors in grade estimation, or material dassification, on a company's cash flow
are magnified. In deposits where the mineralization is erratic, estimation and
classification becomes increasingly diffiwlt. This adds to the risk of a project and
greatly affects mine planning as well as overafl project viability.
A relatively new and unexplored estimation technique known as stochastic
modeling or simulation is slowly gaining acceptanœ by mine planners. Unlike other
estimation methods that atternpt to produœ one 'besf' estimate for each point within
a property, simulation takes into account the enor involved with each estimate and
delivers multiple, equally probable estimates to the mine planner. These multiple
estimates allow for examination of the distrikition of the grade at any point, and help
to faalitate better classification of the material iocated there.
This thesis examines the simulation technique and looks at how it can be
used to delineate ore and waste. Classical approaches will be investigated to act
as a cornparison.
ACKNOWLEDGEMENTS
I would like to thank Mr. William Allan of Cameco Gold Corporation, Mr
Alan Hill of Barrick Gold Corporation, Mr. John Keyes of Battle Mountain Gold
Corporation, and Mr. Walter Segsworth of Homestake Mining Corporation and
Queen's University for their financial support throughout my studies at Queen's. I
am grateful for the case study information provided to me by Mr. Joseph Bayliss
of lnversiones Mineras del Inca.
I would also like to express my appreciation to Professor Garston
Blackwell and the rest of the staff and students of the Queen's Mining
Department for their advice and support.
TABLE OF CONTENTS
CHAPTER PAGE
ABSTRACT i
..
ACKNOWLEDGEMENTS II
CURRICULUM VlTA iii
TABLE OF CONTENTS iv
LlST OF TABLES vii
LIST OF FIGURES viii
1. O INTRODUCTION
2.0 RESOURCE MODELING AND ESTIMATION
2.1 RESOURCEJRESERVE DEFINITIONS
2.2 BLOCK MODEL CONCEPT
2.3 SAMPLING, ASSAYING AND GEOLOGICAL LOGGING
2.3.1 Sampling
2.3.2 Assaying
2.3.3 Geological Logging
2.4 VARIOGRAPHY
2.5 ESTIMATION METHODS
Traditional Mefhods:
2.5.1 Polygonal Estimation
2.5.2 Inverse Distance Power Method
Geostafisfical Estimation Mefhods:
2.5.3 Ordinary Kriging
2.5.4 Multiple lndicator Knging
3.0 STOCHASTIC MODELiNG AND SIMULATION
3.1 PROBABILITY DISTRIBUTIONS
3.2 SEQUENTIAL INDICATOR SIMULATION
3.3 RESULTS OF SIMULATIONS
3.3.1 Grade Tonnage Curves
3.4 USlNG SIMULATION RESULTS
3.4.1 Averaging
3.4.2 Probabifity
3.4.3 Loss Function
3.5 ORUWASTE DELlNEATlON
3.6 CONCLUSIONS
-
4.0 SOFTWARE INTRODUCTION
4.1 REASONS FOR WRlTlNG SOFTVVARE
4.2 CHOICE OF PROGRAMMING LANGUAGE
-
4.2.1 AutoCAD Linking Via DXF Files
4.3 SOFTWARE OVERVIEVV FOR RESEARCH AND
INDUSTRY
4.4 INPUT AND OUTPUT FILE FORMATS
4.4.1 Points File Format
4.4.2 Simulation File Format
4.4.3 Loss Function File Format
4.5 THE PROGRAMS
4.5.1 ProbPlot Program
4.5.2 VARMAP Program
4.5.3 Data Viewer Program
4.5.4 SISIM Program
4.5.5 Ore Gridder Program
5.0 INTRODUCTION TO CASE STUDY
5.1 THE MINE
5.1.1 Ownership/Location
5.1.2 Geology
5.1.3 Mining Method
5.1.4 Mining Equipment
5.1 -5 Crushing and Heap Leach
5-1.6 Gold Production
5.2 TEST OF SIMULATION
5.2.1 Obstacles to Testing
5.2.2 Testing Method
5.2.3 Analyang the Results
5.3 CASE STUDY CONCLUSIONS
6.0 CONCLUSIONS
6-1 RECOMMENDATIONS FOR FUTURE WORK
REFERENCES
APPENDIX A
A0 VARIOGRAPHY
A.1 VARIANCE
A.2 RELATIVE AND INDICATOR VARlOGRAMS
A.2.1 Relative Variograms
A.2.2 Indicator Variograms
A.3 CREATING A ROSE DIAGRAM
A4 CREATlNG A VARIOGRAM MAP
A.5 COMBlNlNG IT ALL INTO ONE VARIOGRAM
B.0 ESTIMATION METHODS
BA POLYGONAL ESTIMATION METHOD
B. 1.1 Search Range
8.2 INVERSE DISTANCE POWER METHOD
6.2.1 Quadrant Search
8.3 ORDINARY KRlGlNG
B.3.1 Unbiasedness Condition
8.3.2 Minimizing Error Variance
8.3.3 Block Kfiging and Discretkation Points
8.3.4 Applying the Theory
B.4 MULTIPLE INDICATOR KRlGlNG
8.5 SEQUENTIAL INDICATOR SIMULATION
vii
LIST OF TABLES
TABLE PAGE
2.1 Vanogram Thresholds and Parameters
2.2 Indicated Variogram Thresholds and Parameters
3-1 Random Selection from Probabilities
3.2 Simulations for Ore Grade, Dilution and Ore Loss
3.3 Example Loss Function
3.4 Classification Methods for the Sample Blast
5-1 Reconciliation Factors Before Simulation lntroduced
5.2 Reconciliation Factors After Simulation lntroduced
5.3 Basic Statistics for "Reality"
5.4 Statistics for the Various Estimation Methods
5.5 Statistics for 'Ore' (20 .5 @t)
5.6 Statistics for Estimation of 'Ore' (20 .5 glt)
5.7 MAE and MSE Values
5.8 Over and Under Estimation of 'Ore' (20 .5 glt)
5.9 Misclassification Using Averaging, Probability and Loss Function
Methods
A 1 lndicator Variogram Thresholds and Parameters
A.2 Scaled Distances for Creating a Rose Diagram
B-1 Sample Grades and Distances
B.2 Threshold Values and Grades
B.3 Threshold Probabilities
viii
LIST OF FIGURES
FIGURE PAGE
2.1 Contoured Blasthole Grades 12
2.2 Classification System 15
2.3 Block Mode1 Concept 16
2.4 Gy's Safety Line (after Gy, 1979) 22
2.5 Histogram of Blasthole Values 27
2.6 Grouping Pairs 30
2.7 Rose Diagram 32
2.8 Variogram Map 33
2.9 Modeled Variogram 35
2.1 0 Nested Variogram Modeling 36
2.1 1 Polygon Estimation Method Realization 40
2.1 2 Hi stogram of Polygonal Values 41
2.1 3 Inverse Distance Squared Estimation Method Realization 43
2.1 4 Hi stogram of Inverse Distance Squared Values 45
2.1 5 Ordinary Kriging Estimation Method Realization 49
2.1 6 Histogram of Ordinary Mged Values 50
2.1 7 Histogram of MlK Values 53
2.1 8 Multiple lndicator Krigirig- E. stimation Method Realization 54
3.1 Cumulative Probability Distribution 58
3.2 Linear Interpolation from Random Number 60
3.3 Simulation #1 62
3.4 Simulation #2 63
3.5 Simulation #3 64
3-6S imulation #4 65
3.7 Simulation #5 66
3.8 Simulation #6 67
3.9 Simulation #7 68
Simulation #8 69
Simulation #9 70
Simulation #lO 71
Histogram of Simulation Values 72
Histogram of Average of Simulations 74
Grade-Tonnage Curve for Different Estimation Methods 76
Grade-Tonnage Curve for Sample Data and Estimation Groups 78
Average of Al1 Simulations 81
Probability of Being Ore 84
Grade-Tonnage Curve for Different Confidence Levels 85
Example Loss Function 87
Digging Boundary for Averaging Method 92
Digging Boundary for Probability Method 93
Digging Boundary for Loss Fundion Method 94
4.1 Computerized Estimation/Classfication System
4.2 PTS File
4.3 SIM File
4.4 LFF File
4.5 Flowchart Symboi Legend
4.6 ProbPlot Program Flowsheet
4.7 ProbPlot Main Screen
4.8 VARMAP Program Flowsheet
4.9 VARMAP Main Screen
Data Viewer Program Flowsheet
Data Viewer Opening Screen
"Dispiay Parameters" Screen
Viewing Screen
"Contour Parameters" Screen
SlSlM Prograrn Flowsheet - Part 1
-
SISIM Program Flowsheet Part 2
-
SISIM Program Flowsheet Part 3
SlSlM Parameter lnput Screen #1
SlSlM Parameter lnput Screen #2
SlSlM Parameter lnput Screen #3
Ore Gridder Prograrn Flowsheet
Ore Gridder Program Main Screen
5.1 Gold Price During the 1990's
5.2 1740 Bench, Composited Blastholes
5.3 1745 Bench, Composited Blastholes
5.4 1750 Bench, Composited Blastholes
5.5 Bench 1750, Polygonal Estimate
5.6 Bench 1750, Inverse Distance Squared Estirnate
5.7 Bench 1750, Ordinary KrÏging Estimate
5.8 Bench 1750, Multiple lndicator Kriging Estimate
5.9 Bench 1750, 'Best' Simulation Estimate
5.1 0 Bench 17 50, Worst' Simulation Estimate
5 11 Bench 17 50, Average of Simulations
5.12 OverlUnder-Estimatinn for Various Probability Cutoffs
From Fig 2.8 Variogram Map
5.1 3 Polygonal Method Variogram Map
5.14 Inverse Distance Squared Method Variogram Map
5.1 5 Ordinary Kn'ging Method Variogram Map
5.1 6 Multiple Indicator Knging Method Variogram Map
5.1 7 Individual Simulation Van'ogram Map
A.1 Pairing Data
A2 Variogram Map for lndicator Threshold #1
A.3 Variogram Map for lndicator Threshold #2