mine planning under uncertainty - ceermin€¦ · 26 miningmath software operational schedule +...
TRANSCRIPT
Mine Planning under Uncertainty
Alexandre Marinho
March/2013 1
www.miningmath.com
2
The Oil and Gas Industry
http://www2.emersonprocess.com/siteadmincenter/PM%20Roxar%20Documents/Reservoir%20Management%20Software/Roxar%20Software%20Solutions%20Brochure.pdf http://www.youtube.com/watch?v=WAvp6OhArrA
3
The Oil and Gas Industry
http://www.youtube.com/watch?v=WAvp6OhArrA
4
Workflow
www.miningmath.com
? ?
? ? ?
5
Project Evaluation
www.miningmath.com
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Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
6
Dealing with Probabilities
www.miningmath.com
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
Average
Min/Max
7
Overestimation
www.miningmath.com
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
Estimated
Min/Max
8
Underestimation
www.miningmath.com
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
Estimated
Min/Max
9
How is your mine going to perform?
www.miningmath.com
?
10
Kriging (Estimation) = Weighted Averages
www.miningmath.com
5%
7%
12%
15%
8%
11
Independent of adjacent blocks
www.miningmath.com
5%
7%
12%
15%
9%
12
Overall Consequences - Smoothing Effect
www.miningmath.com
0
5
10
15
20
25
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Fre
quency
(%
)
Grade
Sample points
Estimated points
13
Applying a Cutoff - Overestimation
www.miningmath.com
0
5
10
15
20
25
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Fre
quency
(%
)
Grade
Sample points
Estimated points
Waste classified
as ore C
UTO
FF
14
Applying a Cutoff - Underestimation
www.miningmath.com
0
5
10
15
20
25
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Fre
quency
(%
)
Grade
Sample points
Estimated points
Ore classified
as waste
CU
TO
FF
15
Non-linear Transfer Function - Example
www.miningmath.com
Scenarios
1
2
4
f(x) = x²
1² = 1
2² = 4
4² = 16
Average
21/3 = 7
x
x x²
16
Averaging Inputs
www.miningmath.com
Scenarios
1
2
4
f(x) = x²
2.3² = 5.4
Average
7/3 = 2.3
17
The Flaw of Averages - Dr. Sam Savage
www.miningmath.com
Average In Average Out
E(x²) = 7.0 ≠ 5.4
(E(x))² ≠ E(x²)
http://www.youtube.com/watch?v=j3zKgAetG5k
18
The Flaw of Averages - Dr. Sam Savage
www.miningmath.com
http://www.youtube.com/watch?v=j3zKgAetG5k
19
Averaging Inputs in Mining
www.miningmath.com
Scenarios
Estimation
Schedule
(figures from Leite and Dimitrakopoulos, 2009)
20
Mine Planning under Uncertainty
www.miningmath.com
Scenarios
Estimation
Schedule
(figures from Leite and Dimitrakopoulos, 2009)
0
5
10
15
20
25
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Fre
quency
(%
)
Grade
Simulated Points
Sample Points
21
Generate Scenarios
www.miningmath.com
22
Understand Where You Are
www.miningmath.com
?
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0
50
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200
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
Estimated
Min/Max
-150
-100
-50
0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
Estimated
Min/Max
23
Adjust Your Expectations
www.miningmath.com
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0
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200
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
Conventional
Min/Max
Stochastic
Min/Max
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-50
0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Cum
ula
tive N
et Pre
sen
t V
alu
e (
M$
)
Periods
Estimated
Min/Max
24
Optimize Under Uncertainty
www.miningmath.com
25
Step Forward
26
MiningMath Software
Operational Schedule + Ultimate Pit + Multiple Destinations
+ Cutoff Optimization + Risk Analysis
3,0
4,0
5,0
6,0
7,0
8,0
1 2 3 4 5 6 7 8 9
Ore
Pro
du
ctio
n (
t)
Mill
ion
s
Period
Average
P10 and P90
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 C
um
ula
tive
NP
V (
$)
Mill
ion
s Period
Average
P10 and P90
(same dataset from Leite 2008, Albor 2010 and Marinho 2013)
