METHODOLOGY
OVERVIEW
The Enterprise Optimization Model database captures:
- block model and topography
- geo-technical zones and details
- mining dilution details
- mining costs
- processing cost, recovery, throughput
- blending constraints
- product definitions
- pricing and exchange rate protocols
- operational constraints
- mining/processing/production capital
- discount rate
at a far greater level of detail than is normally applied in life-of-mine planning. This is used as a consistent basis for both pit and schedule optimisation.
An optimisation study will be structured to suit the particular operation involved and to focus on the key business issues that need to be resolved.
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PIT AND PHASE OPTIMISATION
We use Gemcom Whittle software to generate pits and phases, applying a series of special techniques in the process.
Rather than packing complex cost, recovery and throughput formulae into Gemcom Whittle, we apply the detailed algorithms developed in the Enterprise Optimization Model to the block model(s) in our database, and transfer the block valuations only into the Gemcom Whittle “model” file.
This allows far more sophisticated models to be applied, maintains a clearer audit trail, ensures consistency with the settings that will be applied in Prober – B optimisation, and avoids bogging down Gemcom Whittle with extensive internal calculations. Gemcom Whittle software is therefore able to focus on what it does uniquely, which is applying Lerchs-Grossman with a suite of tools to control pit slopes and mining widths. Gemcom Whittle therefore runs much faster and can handle far larger models.
As a component of our integrated approach, the pit and phase optimisation must be steered by the results of the life-of-mine schedule from Prober - B. To develop pits and phases which efficiently target the desired material, it is necessary to know what cut-off grades, blends and processing path selections apply at various times. Although pit optimisation and schedule optimisation are mathematically separate operations, the feedback loop embodied in our integrated approach ensures consistency and harmonisation of the two.
It is important to understand that the best ultimate pit is rarely the Revenue Factor = 1.0 shell, and that, with feedback from the Schedule Optimisation, far better intermediate phases can be identified than just selecting lower Revenue Factor shells from the initial Gemcom Whittle pit optimisation. Applying standard Gemcom Whittle methodology is a good starting point, but we expect to improve on that considerably with our integrated approach.
SINGLE PIT SCHEDULE OPTIMISATION
Even in seemingly simple cases, our integrated approach can generate schedule results which are superior to regular techniques (including Gemcom Whittle Milawa and Cut-off Grade mechanisms) due to:
- The Prober – B optimiser controlling the scheduling of mine phases, cut-off grade, and stockpiling on a forward looking basis, considering the impact on all periods simultaneously (and blending, alternative processing paths if they are involved)
- The integrated framework provides a better basis for selecting the ultimate pit and designing intermediate pit phases.
MULTI-MINE SCHEDULE OPTIMISATION
Jeff Whittle’s development of Prober series of optimisation software started in the late 1990s by addressing the issues of multi-pit blending scheduling, so handling multiple pits is at the foundation of our capability. We have optimised models involving tens and even hundreds of pits and phases or underground mining blocks, with complex earliest start, start after, minimum lead and lag relationships and capital hurdles.
UNDERGOUND SCHEDULE OPTIMISATION
We do not generally get involved in the internal design of underground mining developments in terms of stope shapes and access development, but frequently optimise life of mine schedules for operations with multiple underground developments. By capturing the details of each underground development area or “block” and the associated infrastructure bottlenecks, the Prober – B optimiser prioritises blocks and combines them with consideration of the ore value, any blending considerations, infrastructure constraints, and capital development, and, of course, the plant characteristics and market conditions being supplied.
By iteration we can evaluate the merits of different cut-off grades for underground stope design. In some cases we can make that evaluation dynamic. In the case of block cave and sublevel cave mining, more detailed internal scheduling of capital development of draw points versus extended period of caving is possible.
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CUT-OFF GRADE OPTIMISATION
Ken Lane published his milestone work The Economic Definition of Ore: Cut-off Grades in Theory and Practice (Mining Journal Books: London) in 1988. This explained the case for using (usually) elevated cut-off grades early in the life of mine schedule, and prescribed the mathematics to calculate the optimal cut-off grade in relatively straightforward cases.
This inspired Jeff Whittle’s development of Opti-cut software in the mid 1990’s, which is now embodied in the Gemcom Whittle software package (we use Prober – B for this purpose now).
Cut-off grade calculations are not straightforward. As well as involving some detailed trade-offs between mining cost and the benefit of higher head grades in the current period, consideration must be given to the opportunity cost of the effect on future periods and the reduction on the overall life of the operation. Stockpiling possibilities complicate the calculations further.
Implicit in Prober – B is detailed cut-off grade optimisation. Through a process of “grade banding”, blocks are grouped by rock-type within a phase into bands of like material. The appropriate definition of “like material” depends on the case at hand, and what can be identified as the key value driver to the particular operation (which can change over time). This can be metal grades, combinations of grades, Net Smelter Return or Net Value per tonne or per meter cubed, or banding by other important criteria including throughput characteristics or the block’s consumption of particular constrained processing inputs (acid, power, oxygen etc).
Identifying the appropriate grade banding basis to support the cut-off grade mechanism is a key part of an optimisation study and requires significant experience and insight.
The Whittle Consulting Prober – B optimiser calculates optimal cut-off grades, by mine phase, rock type and period:
- for multiple pits, multiple rock types, multiple elements, alternative processing paths, multiple products, considering characteristics other than just metal grades
- in scenarios involving changing metal prices, costs, recoveries, and throughputs over time
- simultaneously controlling the pit/phase/underground mining schedule by component
- considering stockpile and reclaim opportunities with the different mining cost, reclaim/rehandle cost and potential change in recovery
- and adjusting the product specification and mix accordingly where this is flexible.
The Whittle Consulting Prober - B is the ultimate cut-off grade optimiser.
INTEGRATED MINING AND PROCESSING OPTIMISATION
Mining and processing optimisation should not be approached separately, as one affects the other and there is an opportunity to have them work in unison to realise the maximum value.
At one level, the plant operating cost, recovery and throughput capacity will influence the size of the ultimate pit, the mining schedule, optimal cut-off grades, stockpiling and blending strategies, so the mining plan needs to be re-optimised for each potential plant configuration. Likewise the plant needs to be optimised to suit the nature of the feed that the mine can deliver based on the characteristics of the ore body, mining methods, mining selectivity and grade control practices
At a much deeper level, it is common that a particular plant can be run at a range of combinations of:
- recovery versus throughput
- recovery versus operating cost
- recovery versus the concentration or purity of the product (which may feed further downstream plant)
and these relationships could be varied over the life of the operation if required.
This presents an additional lever for generating value. Just as the optimal cut-off grade applied when mining will vary over the life-of-mine, so too will the trade-off between recovery and the other parameters.
If the recovery curve data is available, then Whittle Consulting can develop plans which exploit these flexibilities, and produce a mine and processing strategy which is superior to the fixed-configuration case.
Understanding these issues at a conceptual level is one thing, but performing the actual calculations to determine the right result requires sophisticated specialised capabilities and software.
BLENDING OPTIMISATION
Many types of plant can only operate, or achieve better results (in terms of cost, throughput or recovery) when the feed from various sources are combined to meet certain criteria. This might be metal grade ranges but could be other characteristics like hardness, particle size, density, viscosity, etc. With some characteristics the blend may perform better in the processing plant than the average of the individual components – a synergy being created.
Sensitivity to blend may exist at the mine’s mill/concentrator, at the company’s leach, smelter or refinery, or at the customer’s plant (in which case the product characteristic will have boundaries or rewards/penalties prescribed in the contract).
This creates an opportunity to combine material that is otherwise out of specification, to make a blend that is acceptable or superior to the individual components. From an analytical point of view this is challenging as it means that material in different locations and periods (if stockpiling is possible) can be combined to increase value.
Whittle Consulting’s Prober B software optimises the blends, and does so simultaneously with mining schedule, cut-off grades, processing path selection, production etc. Blending outcomes are part of the feedback loop to pit and phase optimisation in our integrated approach.
ALTERNATIVE PROCESSING PATHS
Some operations have more than one plant. This may be two or more concentrators with different characteristics, or, say, a leach and smelter resulting in the same or alternative products.
Just as it is necessary to determine a cut-off grade (the distinction between what is processed and what is wasted, stockpiled or left in the ground), it is necessary to determine what we refer to as a “cut-over” which is the distinction of what will go to one plant stream or the other. Like a cut-off, a cut-over may be determined on the basis of metal grades, combinations of grades, Net Value per tonne or per meter cubed, or banding by other important criteria including throughput characteristics or the block’s consumption of particular constrained processing inputs (acid, power, oxygen, etc).
It is relatively simple to calculate the preferred processing path for a particular block of material by evaluating the cost, recovery and ultimate revenue for the alternatives. However, the preferred processing path for a particular block may already be fully occupied with more competitive material at the time it is mined, creating a situation where ore parcels must compete for the limited space in processing plant. The alternatives are to:
- leave it in the ground (may not be possible if it is part of a mining sequence targeting other material)
- waste it, with loss of its potential value
- stockpile it and process it through its preferred path later, with the associated rehandling cost, potential dilution, potential change in recovery, and loss of Net Present Value due to the timing difference in the mining cost versus the margin on processing and sales revenue
- process it through its second preferred path, displacing less competitive material.
Like cut-off rules, the cut-over rules should not be fixed over time. The distribution of grade and the other characteristics generated by mining will change as the ore body is mined, so the dividing point must move to get the right proportions of feed going to each stream.
For Enterprise Optimization, all the potential process paths for each block are set up. We allow the Prober – B optimiser to decide “on-the-fly” which path the material should go to under the circumstances prevailing at that time, and the mining schedule is simultaneously modified to suit this flexibility (plus the stockpiling, blending, processing calibration, and production plans).
CAPITAL SIZING (MINING FLEET, PLANT, INFRASTRUCTURE, ETC)
When designing a new project, checking the current configuration of an existing project, or contemplating expansions, it is necessary to consider what capacity and associated capital should be provided to the various stages in the value chain. This involves trade-offs between the benefit of throughput and flexibility, versus the capital cost involved. The decision for one point in the chain will affect the others.
If there is only one part of the chain to consider .e.g. just the mining fleet, or the processing plant, it is easy enough to “bound and step”, or iterate your way to the answer. E.g. try five steps in a possible range of plant sizes, develop a full life of mine operating plan for each including capital cost involved and compare the results.
If, however, there are say three or four stages of the chain to consider (e.g. digging and loading capacity, mine haulage capacity, plant size, rail capacity) and we want a dynamic view of cut-off grades and plant throughput versus recovery to be considered in each case, then the number of iterations requiring separate fully optimised life-of-mine production plans becomes 5 x 5 x 5 x 5 i.e. totally unwieldy.
By providing information on the cost of additional capacity for the various bottlenecks in the system, the Prober – B optimiser can control these decisions simultaneously with the determination of the matching life-of-mine plan. The result to the total problem is achieved in one optimisation iteration, determining a superior result, and significantly reducing elapsed time and workload involved in the planning process.
OPTIMISING FOR UNCERTAIN MARKET SCENARIOS
Mining business planning is generally done with a profile of metal prices and input costs over time, based on the middle forecast of future commodity prices and exchange rates.
For sensitivity analysis an optimistic/upside and pessimistic/downside case may be considered.
The more advanced approach is to apply detailed price path models, which indicate on a probability weighted basis the possible patterns of future commodity prices. Ideally a sample of these can be applied in the planning modelling to develop a probability distribution of the outcome for the business (Monte Carlo).
We have demonstrated the capability to put all the elements of Enterprise Optimization into this process so that the outcomes reflect the Real Options that exist to modify the mining, processing and production plans according to the commodity prices that actually prevail. This is far superior to the approach of simply applying multiple price path scenarios to a fixed plan, presuming there can be no reaction as reality unfolds.
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