Optimising mine capacity
Richard Quarmby, an experienced Chemical Engineering and Metallurgical Consultant, proposes an innovative method for determining how best to exploit a mineral deposit.
Studies for mineral deposits can be expensive and time-consuming. While scoping studies may take only a few months to execute, pre-feasibility and bankable feasibility studies – with their demand for ever-increasing levels of accuracy – typically take much longer, necessitating much in-fill drilling for the resource definition as well as detailed engineering design and costing for the mining and processing disciplines. It is, therefore, critical to know the throughput before embarking on such a costly exercise.
A correctly-sized mine study that avoids wasting time and money on non-optimal scenarios would be beneficial to companies and host countries alike, who are keen to expedite mine development and generate revenue as soon as possible.
When sizing a mine, the default answer has often been inferred from a deemed market-desired annual production rate or reasonable life-of-mine (LoM). But when this is deemed inappropriate, additional expense and delays ensue as alternatives are evaluated.
A new take
The approach proposed is relevant to projects at any stage of development prior to construction that have a published resource statement. Aspects of mine development are evaluated in terms of their impact on an associated base case financial model. The method uses simplified procedures to estimate capital and operating costs, strip ratios and resultant feed grades across a range of scenarios. Managers are able to compare different options at a glance, making it easier to see where an optimal solution lies.
The output table can be Net Present Value (NPV) as seen in Figure 1, Internal Rate of Return (IRR), plus several other such entities or ratios deemed useful for decision-making.
The basis for the following example is an open-pit gold project for which a feasibility study has already been published, but the technique used can be tailored to suit a commodity of choice.
The aim is to create a set of results that will provide a visual representation from which a valid comparison can be made across a range of scenarios. Once a throughput selection has taken place using this technique (termed the Q-method) and the subsequent full feasibility study is generated, along with its detailed financial model, the final result will improve.
Operating costs (opex)
Opex is typically divided into three disciplines:
General and administration (G&A)
Each is made up of contributing items, which can be classified as a fixed or variable cost. Occasionally, an item consists of both and is split. Unit operating costs for differing throughputs are then calculated.
Resource to reserve conversion
This aspect of modelling is crucial because so many parameters are affected. For every pit shell and selected cut-off grade the ore reserve or mineable resource and plant feed grade will change, as will the total amount of material to be mined, the amount of waste and resultant strip ratio.
Group of nested pit shells – supplied by a Mine Planner typically using a proprietary software package such as Whittle/Gemcom Four-X Analyser.
Amount of pure waste tonnes and total tonnes within each shell – from the same source.
Grade-tonnage versus cut-off grade (CoG) curve for the resource - supplied by the Resource Manager.
Nature of the orebody - The orebody is assumed to be uniformly described by the grade-tonnage versus CoG curve.
Split of Ore and Waste – For each pit shell, the amount of pure waste and total grade-bearing ore is determined. After a cut-off grade is selected, the grade-tonnage versus CoG chart is used to calculate how much of the grade-bearing ore reports to the plant with the balance becoming waste. The plant feed grade is then read from the same chart.
Prestrip - for the base-case throughput the ratio (pre-strip tonnes / total tonnes) remains constant for each pit shell. Also, the resultant strip required is directly proportional to the throughput.
Scheduling and Stockpiling - None.
Financial and optimisation model
A financial model represents the base case. Typical outputs include:
LoM and payback period
Grade and recovery data
The simplified model spreads the production, costs and revenue evenly across the LoM, as determined by the plant capacity and the available reserve. This provides a quick yet reasonable evaluation for comparison purposes.
The optimisation procedure manipulates the base case by scaling it across a range of scenarios. The output comprises a results page for each selected pit shell and gold price. At a glance, one sees the effect of plant throughput and CoG on a number of parameters, for example IRR, seen in Figure 2.
No single metric from the many useful measures depicted is considered adequate to make a throughput decision. Rather judicious inspection of all seems proper, given the practical constraints in place in terms of capital raising, desired returns, a logical mine life (range of LoM seen in Figure 3), payback period, etc.
The curve of maximum NPV is depicted in Figure 4. At some point the increase in returns seems outweighed by the increase in capital requirements as confirmed in the NPV/Capital Ratiomax curve in Figure 5. It seems reasonable to call for detailed study to be undertaken at an ‘optimum’ throughput of 2.0 Mtpa.
Certain simplifying assumptions prevent the Q-Method from being judged a panacea for each discrete option – instead, it stands effective as a meaningful assessment across a wide range.
When a company defines an orebody that extends into the depths, they hope to exploit it in such a way as to maximise profit to shareholders. So how big does one make the pit, or rather how deep and how fast does one treat it? The ruling price of the commodity, plus the grade within the ore, defines its monetary value. But also to be taken into account are the associated operating costs of treating this unit of ore. A financial model will pull all of this together, but will also include the capital costs required to build the mine. These are substantial and naturally dependent on how fast one wishes to treat the ore. The greater the capacity, the greater the associated cost of the mine fleet, the pre-strip and the process plant. Thus the selection of throughput is absolutely crucial to governing the ultimate profitability of the mine.
Effect of throughput on capex, opex and ore reserve
Throughput affects opex where the fixed portion leads to a decrease (if high throughput) or increase (if low throughput) in unit costs. The variable portion varies directly with throughput therefore when expressed as a unit cost will remain constant. Capex implications are relatively straightforward, with higher costs being associated with higher throughputs. It is determining the amounts of ore and waste that becomes more intricate as they change with throughput and selected pit shell. Ore is classified as being above a cut-off value, representative of its operating cost at a ruling commodity price, which in turn is dependent upon the selected throughput. Thus there will always be a proportion of grade-bearing material that will be reclassified as waste, since it would be uneconomical to treat. This proportion of waste within a shell will increase as the selected throughput decreases, since the cut-off grade increases with increased opex. Naturally, the resultant feed grade of the ore to the process plant also changes and in this instance will increase, though there will be fewer tonnes reporting there.
Capital costs (capex)
Extensive use is made of factoring in the capital cost estimation using techniques well described in the known literature such as the Lang factor (1947), the six-tenths rule for scaling by Williams (1969) and the refinement to this equation suggested by Guthrie (1970). The generic scaling equation is given by:
Simply stated, an item of twice the capacity should cost considerably less
than double the cost of the original equipment. A remarkable level of accuracy has been demonstrated with this method.
With that said, some aspects of a mine design don’t change significantly with capacity whereas others change proportionately.
Ideally, each individual item contributing to the capex figure should have an appropriate factor assigned to it. Alternatively, items can also be grouped into areas, such as infrastructure, process plant, mining fleet, pre-strip and sustaining capital, and then an approximate factor applied to each. Further refinements can also be made to this factor whether scaling up or down.
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