harnessing uncertainty for orebody modelling and strategic mine planning

7/31/2019 Harnessing Uncertainty for Orebody Modelling and Strategic Mine Planning

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Roussos Dimitrakopoulos

Canada Research Chair in

Sustainable Mineral Resource Development and

Optimization under Uncertainty

Department of Mining, Metals and Materials Engineering

Keynote speech to AMEC Internal conference, Vancouver, November

Harnessing Uncertainty for

Orebody Modelling and Strategic Mine Plann


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Overview

The economic side of uncertainty

Models of geological uncertainly Limits of traditional mine design optimization

Shifting the paradigm: Stochastic mine planning

Using uncertainty to improve project performance

Conclusions - Uncertainty is great!


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Uncertainty Matters:

The Economic Side of Uncertainty

Changing the way we do thing


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Risk in Mining: A World Bank Survey

60% of mines had an average rate of production LESS THAN

of planned rate

In the first year after start up, 70% of mills or concentrators haaverage rate of production LESS THAN 70% of design capacit

Key contributor to mining risk felt in all downstream phases:Geology and rese


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Many managers believe that uncertainty is a problemand should be avoided..

you can take advantage of uncertainty. Yourstrategic investments will be sheltered from its advers

effects while remaining exposed to its upside potentiaUncertainty will create opportunities and value.

Once your way of thinking explicitly includesuncertainty, the whole decision-making framework

changes. Martha Amram and Nalin Kulatilakain Real Options

Uncertainty is not a Bad Thing


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Real Options vs DCF View of Value

C

urrentAssetValue

Future

Gold Price

$0

$-

$+ Real Options View:

Current Value ofOption to Produce

Traditional DCF View

(now or never)

No productionNPV = 0

ProductionNPV > 0

Contingent DecisPayoff Functio

(future price know


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Accurate Uncertainty Assessment Needed

Unknown,trueanswer

Reserves

Accurateuncertaintyestimation

Single,oftenprecise,wrong

answer

Reserves

Probability

1

The goal of technical evaluation should be to strive for accurate assessment of uncertainty, not a single precisanswer


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Mining Project Valuation

Orebody Model

Mine Design

Production Scheduling

Financial and

ProductionForecasts

Traditional view

Unknown,trueanswer

Sofpr

wan

Reserves

Prob

ability

1

Single estimatedmodel

Risk oriented view

Accur

uncertestima

Reserves

Probability

1Accur

uncertestima

Reserves

Probability

1Multiple probable

models

Mining Process orTransfer Function


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Quantitative Models of Geological Uncertainty

Stochastic or geostatisti

conditional simulation


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Information aboutthe deposit

Actual but unknown

mineral deposit Probable models ofthe deposit

Describing the Uncertainty about

a Mineral Deposit


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Model characteristics:

o Large number of blocks

o Multiple domainso Resource classes with specific sample selection criteria

A gold lo

Describing the Uncertainty about a Gold Depos


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Lode 1502Simulation #1


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Moving Forward in Optimization:

Limits of Traditional Mine Design

Using Models of Uncertai


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Risk Analysis in a Mine Design

Objective

Quantify the impact of grade uncertainty to tonnage, grades, m

and net present value - net present vnalue vs risk exposure

Mine Design(Scenario)

Multiplesimulations

Distribution of

outcomesfor a scenario

Mine Design(Scenario X)

Methodology

.

.

.

O Pit Mi D i d


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Intermediate pushbacks

Pit Limit

Open Pit Mine Design andProduction Scheduling


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Pit Shells

NP

V

(m$,i=8%)

5

10

15

20

25

0 5 10 15 20 25 30 35 40 45

Stochastic Orebodie

Conventional

Probabil

0

Limits of Traditional Modelling

The expected project NPV has only2 4% probability to be realised


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First 2 years ofproduction Final year likely to b

negative cash flow

Limits of Traditional Modelling

Discounted Cash Flow

-5

-3-1

1

3

5

7

9

0 2 4 6 8 10 12 14

Production Period (1/4 Year)

Cash

Flow(m

$p.a.)

0


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Probabilities on Pit Limits

Pit limitdetermined

conventionally

100% probability of falli

within the pit for a given

metal price

This is Not


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This is Not ...


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Moving Forward .. Step 1

Exploring existing technolog

P t W k O Pit Mi D i


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Min acceptable ret

Upside

DownsideDCF

Pit design1 2

Value

Past Work Open Pit Mine Design

Upside Potential / Downside Risk

Upside or Avg[ ]( *Downside Value M AR probability=



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Upside Potential (m$) Downside Potential (

CB-1 CB-2 CB-3 CB-1 CB-2 C

2.3

1.3

2.4

2.9

Pit Design

2.41

2.1

2.43

2.40

0.0

-0.78

0.0

0.0

-0.079

-0.15

-0.022

-0.16

12

6

4

21.8

1.6

1.9

1.2

-

-

-

-0


Upside Potential / Downside Risk


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Moving Forward .. Step 2

Re-writing optimizers

Models of Uncertainty in Optimization


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Integer Programming

An objective function

Maximise (c1x11+c2x2

1+. )

Subject to

c1x11

+c2x21

+.

b1

c1x1p+c2x2p+. bp

c4

c1 c2 c3

Period 1

Period p

Orebody mod

c = constant

X11 = binary variab

Models of Uncertainty in Optimization

Stochastic Integer Programming


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The objective function now ..Maximise (s11x1

1+s21x21+. s12x1

1+s22x21+.)

Subject tos11x1

1+s21x21+. b1

s11x1p+s21x2p+. b1

s12x1p+s22x2

p+. b1

s1rx1p+s2rx2

p+. b1


Simulated model 1Simulated model 2

Simulated model r

Period 1

Period p

s41

s11 s21 s31

s41

s11 s2

1 s

s41

s1

1 s2

1

s41

s1n s2n


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Uncertainty Will

Create Opportunities and Val

Higher NPV for less risk

Base Case:


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Base Case:Geological Risk Assessment of Ore Produc

Uncertainty in Ore Production - Base Case Schedule

13.9% 13.5%

8.7%

18.2%

12.7% 12.4% 12.5%10.8% 11.4%

12.4%10.4%

12.3%

9.0%

11.9%14.5%

12.3% 12.9%

Mt

Mt

Mt

Mt

Mt

Mt

Mt

Mt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Period

OreProdu

ction

0%

10%

20%

30%

40%

50%

60%

70%

A v e r a g eDeviation ( % )

Avrg. Deviation

Target Ore ProductionMaximum Ore

Expected OreMinimum Ore

Risk based: Assessment in Ore Production


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Risk-based: Assessment in Ore Production

Uncertainty in Ore Production - Risk-based Schedule

0.5%3.0%

1.2% 0.7%3.5%

1.9%0.2%

2.7% 1.6%0.0% 0.6% 0.4% 0.1% 0.0% 0.7%

Mt

Mt

Mt

Mt

Mt

Mt

Mt

Mt

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Period

OrePro

duction

0%

10%

20%

30%

40%

50%

60%

70%

AverageD

eviation(%)

Avrg. DeviationTarget Ore Production

Maximum Ore

Expected Ore

Minimum Ore

Uncertainty is Good: Base case vs Risk-ba


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2001 2003 2005 2007 2009 2011 2013 2015

Dif ference 28%

Risk-Based

Traditional and Ri

Traditional Expected

N

PV

Year

y

Multistage combinatorial optimization


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Uncertainty is Good:

Discounting Geological Ris

The discounting goes alongwith production sequenc

SIP Production Scheduling Model


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Objective function

SIP - Production Scheduling Model

Part

Part

Part

Par

Ut t t

*i iii 1- E{(NPV) }MC s= +M

tt

s ss 1+ (SV) (P) q=

P Nt t

iit 1 i 1Max [ E{(NPV) } b= =

Mty ty tyty

su l slus 1- )](c d c d= +

Mill & dump

Stockpile inpu

Stockpile outpu

Risk management

Stochastic Integer Programming - SIP


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g g g

OreGrade 1Metal

OrebodyModel 1

A productionschedule

Orebody

Model 2

Orebody

Model R

OreGrade 2Metal

Ore

Grade RMetal

- TARGET

- TARGET

- TARGET

Deviation 1

Deviation 2

Deviation R

123

4

Cross-Sectional Views of the Schedules


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Cross Sectional Views of the Schedules

SIP Whittle Four-X

1

2345

6

Periods

Managing Risk Between Periods


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0

0.5

1

1.5

2

2.5

3

0 1 2 3 40

1 2 3

1

2

3

Metalquanti

ty

(1

000Kg)

Periods

Ct

=Ct-1

* RDFt-1 RDFt=1/(1+r)t

r orebody risk discount rate

Managing Risk Between Periods

Deviations from metal production target

RDF risk discounting factor

Case Study on a Large Gold Mine


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Orebody risk discounting rate 20 %

Cost of shortage in ore production 10,000 /t

Cost of excess ore production 1,000 /tCost of shortage in metal production 20 /gr

Cost of excess metal production 20 /gr

Number of simulated orebody models 15

The SIP specific information

y g

Deviations from Production Targets


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1 2 3 4 5 6

Periods

0

- 4

Metalq

uantity

(100

0Kg)

- 8

- 12

- 16

- 20

Metal Production

SIP mo

WFX

6Stockpiles Profile


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0Tonnes(million

)

1 2 3 4 5 6

2

4

6

Available ore atthe end of eachperiod

1 2 3 4 5 6Periods

0Tonnes(m

illion)

1

23 Ore taken out

from thestockpile

4

5

SIP mod

WFX

Uncertainty is Good: Traditional vs Risk-Bas


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1 2 3 4 5 6 Periods0

200$(million

)

400

600

800

1000

SIP model WFX

Cumulative NPV values

SIP model WFXAverage NPV values


$723 M

Risk Based

$609 M

TraditionalDifference = 17%

Geological RiskDiscounting=20%

Some conclusions


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. uncertainty is (not) a problem and should be avoided

you can take advantage of uncertainty.

.uncertainty will create opportunities and value.

once your way of thinking explicitly includes uncertainthe whole decision-making framework changes.

We need:

Stochastic mine planning and NEW mathematical mod

And


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It is all about good people:

Education and training in a long term se

And


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Please join us!

harnessing uncertainty for orebody modelling and strategic mine planning

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