Pit optimisation studies are useful for not only identifying a given resource, but insight into the best sequences for extraction. Jackie Gauntlett from Cement & Aggregate Consulting (Cemagg) explains some of the processes necessary to derive the most value from the resource and also make significant savings in time and investment.
A pit optimisation study determines the most valuable pit for a given resource. To undertake this study, we use Deswik.CAD mining software which utilises an algorithm known as “Pseudoflow”. The algorithm calculates the optimal pit based on the geology of a quarry deposit and the cost and revenue from each part of it to determine how it should be extracted to maximise NPV.
In order to do this, the algorithm takes into account three primary types of information:
- Geological model – converted to a block model at the appropriate resolution, typically around the size of the smallest mineable unit. The block model contains geological information such as the designation between waste and ore material types and in-situ density for each material type.
- Geotechnical parameters to inform the required mining slopes. For each block in the model, the model needs details of which blocks must be removed to uncover valuable material.
- Economic parameters – the value in dollars of each block once it has been uncovered. In the case of a waste block this will be negative and will be the cost of extraction, loading, and haulage. In the case of an ore block, the extraction, loading, and haulage costs will be offset by the value of the recovered ore, less any processing, sales, and other associated costs. Any block which can, during mining, be separated into waste and ore is given a value which reflects this.
The Pit Optimisation process generates an array of nested pit shells, also known as incremental pit shells. Each of these shells is allocated a Revenue Factor (RF) defined as: (incremental cost)/(incremental revenue). For example, at RF = 0.5, the revenue obtained from this incremental shell is equal to twice the cost outlay to realise those revenues. Similarly, at a RF = 1 pit shell, the incremental cost equals the incremental revenue for that pit shell, meaning that for that increment there are zero profits. The RF = 1 pit shell is thus known as the Maximum Economic Pit.
A key realisation here is that pit shells with RF > 1, will start destroying value because the costs start increasing more rapidly than the revenue, thus decaying your overall profits (see Figure 1, top of page).
Although the RF = 1 pit shell represents the maximum economic pit, It is important to note that it is unlikely to be the optimal pit (as defined by maximum NPV). The RF = 1 pit shell will only represent the optimal pit if there is no “time value of money” consideration (i.e. there is no cash flow discounting and the assumption is that the entire pit can be mined instantaneously (i.e. in one period / year)). As this is likely not possible, it is important to account for the time-value of money and discount the revenue from each subsequent period. Doing this means that the optimal pit is always less than RF = 1, usually in the range of RF = 0.6 to RF = 0.9.
Shallower pits with less overburden / lower costs generally optimise towards higher RF, and deeper pits with more overburden / higher costs optimise towards lower RF. During the study a number of interim pit shells between the current pit and the optimal pit may become apparent as natural pit stage shells. These can be used to stage the pit designs and resource extraction optimally.
DETERMINATION OF THE OPTIMAL PIT
The optimal pit shell is selected by determining which pit shell maximises NPV when revenue is discounted across the life of the quarry. However, it is important to note that the mining sequence employed has a significant effect on which pit shell NPV maximises at. For example, mining a pit bench-by-bench (the Worst Case approach) brings forward overburden stripping and delays access to what could be high revenue blocks at depth (thereby delaying cashflow). This delay could result in the lowered value of high value blocks due to discounting over time. Corollary, the Best Case approach would be to mine the optimal pit, shell-by-shell.
To illustrate this concept, Figure 2 shows two different approaches to the extraction of an orebody.
The Best Case approach would be one where each nested pit shell is mined to completion before starting the next. This means that waste stripping, and costs associated, are realised only when necessary to access the ore below. This is a shell-by-shell approach.
The Worst Case approach is bench-by-bench. Waste stripping is brought forward in the schedule, negatively impacting NPV.
It is not always operationally possible to mine according to the Best Case approach.
The reality is usually in between the best and worst case approaches and thus in order to select the optimal pit, it is common practice to use the average NPV of the two. Figure 3 illustrates this.
For a hypothetical deposit, the best case approach optimises very close to the pit shell representing RF = 1.00, with a discounted NPV of ~$50m. The worst case approach optimises at the pit shell representing RF = 0.73, with a discounted NPV of ~$28m. However, given that neither the best, or worst, case approaches are likely in reality an average is chosen with an RF = 0.79 and a discounted NPV of ~$35m.
Thus the RF = 0.79 pit shell should be used to define the Optimal pit and drive pit design and detailed scheduling studies.
Note that for the average case approach, the NPV begins to decrease at RF shells > 0.79. This illustrates that in order to mine incremental pit shells greater than RF = 0.79 cost outlay will exceed revenues (in discounted terms). Of course, it should be further noted that should the operation exercise excellent scheduling and mining practices, or should costs decrease or revenue increase, it is possible that the optimal pit could be at a higher RF than that which the peak of the average approach established, thereby increasing the life of the quarry. Similarly if poor mining practices are followed, or costs increase, or revenue decrease, it could optimise at a lower RF, thus decreasing life of the quarry.
STAGING EXTRACTION
A pit optimisation study can also provide insight into the best sequence of extraction to obtain the optimal pit. Figure 3 and Figure 4 shows the progression from Stage 1 (yellow) through Stage 2 (orange) and finally to the Optimal Pit Stage 3 (green).
CONSTRAINTS, LIMITATIONS OF PIT OPTIMISATION STUDIES
It cannot be emphasised enough that the outcome of a pit optimisation study is only as good as the assumptions being used. It is essential that a robust geological and geotechnical model is in place as well as a good understanding of costs and revenues. As it is likely that the understanding of these assumptions will change over time, or as the quarry responds to market forces (e.g. changes their product mix). As such, this optimisation should be periodically re-assessed.
Finally, stakeholders should be aware that a pit optimisation study is a strategic long term planning tool. It assists in the identification of where to start extraction (in the case of a greenfields site), how to progress extraction over the life of the quarry, and the maximum economic pit extent for a resource. Knowing this extent can provide crucial information with regards to tenement management or other stakeholder engagement. Further it assists in the selection of staged pit shells to guide staged pit designs and short term to long term scheduling.
Although a high level approach is created to help decide the optimal pit, the pit optimisation study does not produce a feasible life of quarry schedule. This needs to be carried out in a scheduling package once pit designs are in place. •
Jackie Gauntlett is the principal economic geologist for Cement & Aggregate Consulting (aka Cemagg). For more information, email jackie.gauntlett@cemagg.com or visit cemagg.com
This article also appears in the February issue of Quarry Magazine.