quantification of uncertainty of geometallurgical variables in mine

Quantification of Uncertainty of Geometallurgical Variables in Mine Planning Optimisation

Exequiel Sepulveda

School of Civil, Environmental and Mining Engineering

Supervisors: Peter Dowd and Chaoshui Xu

Outline

BackgroundLiterature reviewGapsAimsConclusion

Problem

Main cause of mine project’s failure:Real production is far of estimated production

Diagnostic:Unrealistic mine planning

Sources: www.hostpph.com & smallbussines.com

Background

Expected

Reality

What (ore-waste discrimination)

When (scheduling) Where (processing)

Under technical, operative and

economic restrictions

Mine Planning Background

Source: www.im-maining.com

Planning Optimisation

Extraction sequence

Layouts: Open pit Underground

Criteria: Maximising NPV Minimising

deviation on production targets

Source: www.womp-int.com

Background

3D discretisation

Many small blocks

Each block represents many features Quality Quantity Metallurgical

response

Resource Model Background

𝑣 𝑖=𝒕𝒊∗𝒈𝒊∗𝑹∗𝑷− 𝑡𝑖∗𝑪𝑴− { 0 ,𝑖𝑓 𝑤𝑎𝑠𝑡𝑒𝑡 𝑖∗𝑪𝑷 ,𝑒𝑙𝑠𝑒}∀ 𝑖∈𝐵

max∑i∈ B

❑ 𝑣𝑖(1+𝑟 )𝑖

Goal: maximising profit for all blocks

Quantity

Quality

Processing recovery

Price

Mining cost

Optimisation FormulationBackground

Economic value of block i

Processing cost (Newman et al. 2010)

Literature Review

Uncertainty sources Financial Geological Metallurgical

Risk analysis

(Dowd, 1994; Dimitrakopoulos, 1998)

Source: www.ni.com

Financial Price, Costs Foreign interchange

rates Statistical

distributions Historical (Grobler, Elkington

& Rendu, 2011)

Lognormal (Amankwah, Larsson & Textorius, 2013)

Wiener process (Evatt, Soltan & Johnson, 2012)

Uncertainty Sources Literature Review

Source: www.agmetalminer.com

Geological Grades (quality)

Spatial correlation Geostatistical

simulations

Better quantification of uncertainty

(Dowd 1994; Dimitrakopoulos 1998) Source: www.petrowiki.org

Uncertainty Sources Literature Review

Metallurgical Recovery Rock type

Can be simulated(Suazo, Kracht and Alruiz,2010)

They are not included in current research

Uncertainty Sources Literature Review

Source: ageofempiresonline.wikia.com

Monte Carlo simulations

Distributions of Net Present Value

Risk Assessment Literature Review

(Dowd, 1994)

Stochastic optimisation Probability

distributions Objective function Restrictions

(Lagos et al., 2011; Amankwah, Larsson & Textorius, 2013) Source: www.sciencedirect.com

Risk Assessment Literature Review

Real option valuation Static NPV Without

flexibility With flexibility

Risk Assessment Literature Review

(Dimitrakopoulos & Abdel Sabour, 2007).

Gaps

Geometallurgical features

Underground mines

Mine complexity

Gaps

(1) Key geometallurgical features are missed, fixed or predefined

Rock types

Recovery

Hardness

Gaps

(2) Underground mines Several

methods Block location

change Fracturing

modelling Source: www.technology.infomine.com

Gaps

(3) Mine Complexity Multi source Multi process Stockpiles

Source: www.minesight.com

Aims

Quantification of uncertainty of geometallurgical variables Grades Rock types Recovery

Aims

New optimisation formulations Stochastic

optimisation Multi-objective

optimisation Mine complexity

Aims

Efficient algorithms Meta-heuristic algorithms

Near-to-optimal Fast computing

Handle realistic problems

Conclusion

Geometallurgical variables can improve risk assessment

Complexity (real word) Better tools for decision makers

Quantification of Uncertainty of Geometallurgical Variables in Mine Planning Optimisation

Exequiel Sepulveda

School of Civil, Environmental and Mining Engineering

Supervisors: Peter Dowd and Chaoshui Xu