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Today it seems that the only thing that can be said with certainty about mining is that there is uncertainty! Managing the risks of changing commodity prices, fluctuating exchange rates and the unknown extent and quality of a geological resource challenges engineers, geologists and investors. Decisions must be made with imperfect knowledge and in the presence of economic and geological uncertainty.
Quantifying uncertainty generally requires sensitivity studies which analyse many different scenarios. While value can be realised from this approach, explicitly analysing uncertainty requires substantial time and computational effort.
A distribution is more convincing than a single number, especially when that number may not even be average. Complex non-linear processes, such as mine planning, will generally not give an average output for average input. The results are probably biased and often only a full sensitivity study will reveal the true average.
Software such as Maptek™ Vulcan™ provides comprehensive geostatistical and mine planning tools to use in tandem with sensitivity studies. Vulcan also provides efficient ways to automate workflows and vary parameters across different scenarios.
Figure 1: In all three cases, the average shown by the dotted line using conventional methods is not aligned with the average of multiple realisations.
Consider the decisions facing stakeholders in a greenfield open pit copper mining project: investors trying to decide their level of involvement and a mining engineer tasked with developing a high level long range mine plan as part of a pre-feasibility study.
After promising geophysical surveys and surface sampling, a small drilling campaign is launched and 43 holes are drilled. With so few data points the mining engineer realises that a single estimated model will most likely not deliver enough data to make informed decisions. The investors are similarly wary. It is unclear whether this deposit is worthwhile.
It is difficult to know how to proceed. The same situation will be faced in different mining decisions, such as where to put the mill, and whether expansion is a good idea.
Both mining engineer and investors understand the weakness of using an average model or an average copper price. The first step is to model the uncertainty.
Figure 2: Intersection of the probability model for revenue factor 1 with the surface. The ultimate pit crest for the estimated model is shown as a thick black line. Blocks are coloured by their probability to fall within the ultimate pit, accounting for geological and economic uncertainty.
Vulcan provides powerful tools to model geological uncertainty using conditional simulation. Mining engineers can team up with geologists and use established geostatistical workflows to generate a block model with many different equi-probable realisations of copper grade.
The models can be checked visually and statistically, and assessed for histogram and variogram reproduction. Post-processing the simulated model is easy. Summary variables such as probability above cutoff grade or variance in copper values are calculated and displayed for mine planning.
A long range mine plan is calculated for each realisation using a simple script and the Vulcan Pit Optimiser.
In effect, the engineer is using Monte Carlo simulation to transfer the geological uncertainty through the mine planning process and then synthesising the results. When this process is completed for each realisation, histograms which describe the breadth and the many possible alternatives provide greater direction than a single value.
An improved graph (figure 1) includes error bars for ore and waste tonnages. The value line is bracketed by the 10th and 90th percentiles, revealing the risk inherent in the project.
The dashed line shows the result of a standard averaging kriging workflow. This is clearly biased, despite using averages for all inputs. The histograms and pit by pit graph show that complex non-linear processes with average inputs do not give average results.
Investors can see exactly how the discounted value varies and make decisions based on the risk they consider acceptable. The mining engineer is now equipped with verifiable and robust results which enable risk-qualified decisions.
A simple block by block script can calculate the probability that a particular block is within the ultimate pit. The probability model can be used for planning and for visualising results.
The intersection of the model and topography (figure 2) clearly indicates where the ultimate pit could be, based on the underlying geological and economic uncertainty. Estimation only provides a single delineation indicated by the bold black line, but with simulation the entire spectrum is revealed. This probability model can also be used for sequencing the most likely blocks first and planning future drilling activities.
Figure 3: Simulated realisations of copper grade, with semi transparent blocks coloured by copper content.
Analysing uncertainty at an early stage allows plans to be developed which account for all possibilities. The Vulcan workflow ensures that the embedded analysis tools do most of the hard work.
In this case study, 500 realisations were generated with more than 1.7 million blocks. In total 23,000 ultimate pits were calculated by Vulcan Pit Optimiser in less than 10 hours. Ore and waste tonnage, value and other metrics can be exported into Microsoft™ Excel™ for further analysis. This process can also be automated to provide a streamlined reporting procedure.
Uncertainties in geological, economic and geotechnical parameters can be quantified and analysed, allowing for flexible plans and confident decision making.