integrating short- and long-term mine planning through...
TRANSCRIPT
Integrating Short- and Long-term Mine Planning through Stochastic Optimization and
Future data-Application and Comparisons
Arja Jewbali
Newmont Mining corporation
Content
• Introduction
• Quantifying geological uncertainty
• Simulating short- scale orebody variability
• Stochastic production scheduling
• Production scheduling with simulated ‘future’ data
• Application at gold mine
• Comparisons and the value of the approach
• Conclusions
Risk in Mining: Australasian Examples
About 85% of discrepancies are due to poor understanding/modelling of the orebody being mined (After Baker and Giacomo, 1998)
1st year of production
• 60% of mines had an average rate of production LESS
THAN 70% of planned rate
• In the first year after start up, 70% of mills or
concentrators had an average rate of production LESS
THAN 70% of design capacity
• Key contributor to mining risk felt in all downstream
phases: Geology and reserves
Risk in Mining: A World Bank Survey (after Vallee, 2000)
Conventional vs Stochastic Approaches
Traditional view Unknown,
true answer
Single, often precise, wrong answer
Cashflows, cost/ounce, metal, reserves, …
Prob
abili
ty
1
Orebody Model
Single estimated model
Risk oriented view
Multiple probable models
Financial and Production Forecasts
Mine Design & Production Scheduling
Mining Process or Transfer Function
Accurate uncertainty
Prob
abili
ty
1 Accurate uncertainty quantification
Prob
abili
ty
1
Cashflows, cost/ounce, metal, reserves, …
Quantitative Models of Geological Uncertainty:
Monte Carlo or stochastic or geostatistical
conditional simulations
Quantification of Uncertainty about a Gold Deposit Monte Carlo Simulations
Lode 1502 Simulation #1
Future Drilling Data
Production sequencing with simulated grade control drilling
Mine Production Scheduling
• Short- and long- term mine production scheduling are based on exploration data
• Exploration data which does not capture the short-scale behavior of the orebody
• Grade control drilling: Available at time of mining not at the time of planning
• Integrate short scale behavior of the orebody at the time of planning with “future” grade control drilling?
• What is the value in doing so?
‘Future’ Grade Control Data
Exploration data Grade control data
Bench/Section of pit already mined out
Define relationship
Exploration data Simulate grade control data
Bench/Section of pit NOT yet mined out
Updating Existing Orebody Models with New Data
Simulated grade control drilling
Update
Stochastic Optimization & Production Scheduling
Using quantified geological uncertainty
Discounting geological risk while sequencing
A Stochastic Integer Programming Formulation
P N S P Rt t s t t s t ti i r r r r
t=1 i=1 s=1 t=1 r=1
Max E(NPV) X - ( Cu Yu + Cl Yl )∑∑ ∑∑∑
P= number of periods: 4-monthly periods for 4 years = 12 N= number of blocks: 5,626 blocks of 30 x 30 x 7.5 m S= number of simulated orebody models: 20 used R= number of targets: 2 grade and ore production
Binary variable tiE(NPV)
tiX
Expected NPV for block i mined in period t
trYu Excess amount produced compared to the target
s trCu Cost to penalize excess production
trYl Deficient amount produced compared to the target
s trCl Cost to penalize deficient production
Stochastic Integer Programming - SIP
……
Ore Grade 1 Metal …
Orebody Model 1 A production
schedule
Orebody Model 2
Orebody Model R
Ore Grade 2 Metal …
Ore Grade R Metal …
- TARGET [ ]
- TARGET [ ]
- TARGET [ ]
Deviation 1
Deviation 2
Deviation R
1 2 3
4
Managing Risk Between Periods
Met
al q
uant
ity
(100
0 K
g)
Ct=Ct-1 * RDFt-1 RDFt=1/(1+r)t
r – orebody risk discount rate
Deviations from production target
RDF – risk discounting factor
0
0.5
1
1.5
2
2.5
3
0 1 2 3 40
1 2 3
1
2
3
Periods
Application and Comparisons at a Gold Mine
• Exploration and grade control data • Variable at short distances: grade control at 5 x 7 m • Standard resource model (MIK) and “layer cake”
schedule • Reconciliations: Producing more than predicted
2000
2200
Y=99824
P1
P2 P3
P4
P5
Scheduling and Simulated ‘Future’ Data
Existing Stochastic LOM Scheduling Process
Proposed Multistage Approach with Short-scale Information
Simulation of orebody models from exploration data
Stochastic optimization and generation of production schedules
Updating of the existing orebody models with the future data
Stage 1
Quantification of risk and analysis of schedule Stage 4
Simulation of high density ‘future’ grade control information
Stochastic optimization and generation of production schedules
Stage 2
Stage 3
• Stage 1: ‘Future’ Grade Control Data
• Stage 2: Updating of Existing Simulated Models
Simulations Without and With Future Data
Y=99870
Y=99967
50200 50600
2240
2000
<0.8 0.8-1.2 1.2-1.6 1.6-2.2
>2.2
AU g/t
50600 50200
2240
2000 Y=99870
Y=99967
50200 50600
2240
2000
50600 50200
2240
2000
Based on exploration data
Based on simulated grade control data
Recoverable Reserves
Grade tonnage curve for the updated models
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8M
illio
ns
Cutoff grade g/t
Tonn
age
0
2
4
6
8
10
12
Gra
de g
/t
MIK modelSimulations
Grade tonnage curve
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8
Mill
ions
Cutoff grade g/t
Tonn
age
0.00
2.00
4.00
6.00
8.00
10.00
12.00
Gra
de g
/t
Based on exploration data
Based on simulated future grade control data
Stage 3: Stochastic Production Schedule Stage 4: Risk Analysis
Schedule (quarters) – Simulations based on Exploration Data
MIK model Average of the simulations Simulations
Mill target
Y=99824
P1
P2 Y=99824
Viability of the derived schedule given grade control information
Average of the simulations Simulations
Mill target
Schedule (quarters) – Simulations based on Simulated Future Grade Control
MIK model Average of the simulations Simulations
Mill target
Scheduling and Simulated Future Data
Mine’s Schedule
SIP & Simulated Orebody (exploration based)
SIP & Future data (grade control based)
Period (years) 2005
2007 2008 2009
1 2
4
Period (years)
2007 2008 2009
Period (years)
2006 2007
2009
1 2 3
5
Y=99824
P1
P2
P3
P4
2000
2200
Y=99824
P1
P2 P3
P4
P1
P2
P3
P5
P1
P2 P3
P5
Y=99824
P1
P2
Y=99824
P1
P2
Scheduling and Simulated Future Data
Simulations (exploration
data)
Updated simulations (future data)
Mines schedule
(future data)
Ore Tonnes (Mt)
14 18
10
Metal Tonnes (Mgrams)
52
55
38
Cumulative NPV (Million AUD)
552 560
330
Y=99824
P1
P2 P3
P4
Y=99824
P1
P2 P3
P4
P1
P2 P3
P5
P1
P2 P3
P5
Y=99824
P1
P2 Y=99824
P1
P2
Mines schedule
Exploration based schedule
Grade control based schedule
THANK YOU