footprint and economic envelope calculation for block/panel caving
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Footprint and Economic Envelope Calculation for Block/Panel CavingTRANSCRIPT
Footprint and Economic Envelope Calculation for Block/Panel Caving Mines Under Geological Uncertainty Emilio Vargas, CSIRO Chile , Delphos Universidad de Chile Nelson Morales, Delphos-AMTC, Universidad de Chile Xavier Emery, AMTC, Universidad de Chile
Introduction
• Traditional underground mine planning methods are based upon deterministic data, therefore plans and decisions may not be robust.
• Including the uncertainty in the resource model and risk analysis in early stages of the project allows making better decisions.
Methodology
1. Develop a procedure for calculating the economic outline of a block/panel caving mine (deterministic case).
2. Generate block model scenarios of the deposit
3. Validate the procedure results against existing tools.
4. Assess geological uncertainty impact on the outline by running the procedure over the scenarios.
PCBC Geovia
Scope
• Strategic mine planning.
• The envelope calculation is applicable for a Block/Panel Caving mine.
• The geological uncertainty is incorporated using conditional geostatistical simulations of a real orebody.
• Dilution is modelled using Laubscher’s approach
Footprint and Outline Computation
Algorithm 1/3
Block Model
Footprint Envelope
• Ultimate Pit Algorithm
MineLink
Algorithm 2/3
Footprint
• For each level:
– Calculate position discounted profit
– Calculate economic value, tonnage and area
• Find optimum level
Validate results with PCBC
3.85
4.32
3.17
3.78
3.95
4.52
3.78
2.30
Ore
co
lum
n
Surf
ace
Algorithm 3/3
Economic Envelope (Outline)
• Cut block model given the economic footprint data
• Compute different slope precedence depending on the level
• Calculate outline using an inverse ultimate pit algorithm
• Post-process the envelope to smooth
the outline
Generation of scenarios
Dataset and parameters
Parameter Value
Number of Blocks 2,340,000
Block Dimensions [m] 10x10x10
Levels 80
Minimum Level [m] 2,755
Maximum Level [m] 3,545
15
50
m
990 m
80
0 m
Parameter Value Cu Price [US$/t] 2.5
Selling Cost [US$/t] 0.35
Mine Cost [US$/t] 10
Processing Cost [US$/t] 16.1
Recovery 87%
Density [ton/m3] 2.7
Maximum Column Height [m] 300
Minimum Column Height [m] 100
Productivity [tpd] 200
Utilization [days/yr] 200
Draw Point Area [m2] 225
Slope angle 45°- 60°- 90°
Generation of scenarios
• Geological scenarios were generated using the turning bands algorithm (Isatis©)
– Input: 12,000 samples
– Output: 1,000 scenarios + kriging
• Dilution is integrated using Laubscher’s model – HIZ: 100 [m]
– HOD: 300 [m]
– Dilution Entry: 60%
– Not considered for validation
Validation
Footprint Validation
• PCBC vs MineLink
• There is a maximum difference of
10% between MineLink and PCBC (depends on the simulated model)
• This difference does not impact the final decision about the optimal level
0
100
200
300
400
500
600
700
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
1 7 13 19 25 31 37 43 49 55 61 67 73 79
Acc
um
ula
ted
To
nn
age
[MTo
n]
Acc
um
ula
ted
Val
ue
[MU
SD]
Level number
Accumulated Footprint Value and Tonnage by Level
Valor Script Valor PCBC Tonelaje Script Tonelaje PCBC
Impact of the Geological Uncertainty
Footprint Results
• For each simulated block model the optimum footprint is calculated over all levels.
Worst
66
0 [m
]
550 [m]
Average
67
0 [m
]
600 [m]
Best
15
50
[m]
990 [m]
Kriging
62
0 [m
]
510 [m]
Impact on the Level Selection
Kr
0
20
40
60
80
100
120
140
160
180
200
1 7 13 19 25 31 37 43 49 55 61 67 73
Fre
qu
en
cy
Economic Level distribution (Footprint)
Level [m] Level n°
Envelope Results • The shape and value of the envelope vary due to geological
uncertainty and the placement of the footprint
300
[m
]
30
0 [m
]
300
[m
]
Kriging Best Average Worst
Kr
0
50
100
150
200
250
300
Fre
qu
en
cy
Economic Value [MUSD]
Envelope Economic Value Histogram
Kr
0
50
100
150
200
250
300
350
Fre
qu
en
cy
Copper Grade [%]
Envelope Mean Grade Histogram
BM91 - Level: 2755 BM304 - Level: 3095 BM386 - Level: 2755
BMKr - Level: 3255
Risk Analysis
Envelope Results • Risk analysis
Value at Risk (1,000 scenarios)
Pessimist Optimist
1% 3% 5% 5% 3% 1% Expected Value
(1,000 scenarios) Kriging
Economic Value [MUSD] 575 781 889 2,408 2,516 2,717 1,646 1,445
Tonnage [Mton] 56 75 84 218 228 246 151 106
Area Footprint [m2] 78,520 102,460 115,380 293,980 306,520 330,840 204,484 141,800
Mean Grade [%] 0.801 0.819 0.829 0.979 0.991 1.013 0.902 0.964
5%
5%
0
50
100
150
200
250
300
Fre
qu
en
cy
Envelope Economic Distribution [MUSD]
Envelope Economic Value Distribution
Conclusions
• The kriging grade scenario has one of the worst accumulated footprint economic value for almost all levels.
• Given the 1,000 scenarios, to find the economic footprint in the first level has a probability of 20%, and a 17% near the 50th level, meanwhile to find it in upper levels has a very low probability.
• The economic envelope found using the kriged block model has an economic value below the expected value of the 1,000 scenarios.
Conclusions
• Given the risk analysis, with a 5% risk the economic value of the outline could be 46% less or more than the expected value for the pessimist or optimist scenario respectively (760 MUSD).
• The production level should be placed at the deepest level, which is more likely to be the economic level and the envelope value is near the expected value, better than the kriging’s model result.
• A risk approach in early stages of a mine project allows to take a better decision in terms of the upside and downside potential.
References
• Dimitrakopoulos R., 2011, ‘Stochastic Optimization For Strategic Mine Planning: A Decade of Developments’.
• Diering T., 2000, ‘PC-BC: A Block Cave Design and Draw Control System’.
• Elkington T., Bates L. and Richter O., 2012, ‘Block Caving Outline Optimisation’.
• Diering T., Richter O. and Villa D., 2008, ‘Block Cave Production Scheduling Using PCBC’.
• Vargas M., Morales N. and Rubio E., 2009, ‘A short term mine planning model for open-pit mines with blending constraints’.
• Emery X., Lantuéjoul C., 2006, ‘TBSIM: A computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method’.
• Vielma J., Espinoza D. and Moreno E., 2009, ‘Risk control in ultimate pits using conditional simulations’.
Footprint and Economic Envelope Calculation for Block/Panel Caving Mines Under Geological Uncertainty Emilio Vargas, CSIRO Chile, Delphos Universidad de Chile Nelson Morales, Delphos-AMTC, Universidad de Chile Xavier Emery, AMTC, Universidad de Chile
Corresponding author: [email protected]
MineLink details delphos.dmi.uchile.cl