Sequencing ore extraction to control blend quality with uncertainty in the geological model
Industry representative: Adam Ghandar, Schneider Electric, Australia
Moderators: Winston Sweatman, Massey University, New Zealand; Kevin White, University of South Australia
Mine scheduling is the task of determining the best material to supply to a processing plant in order to hit production targets, subject to a number of physical, logical, and capacity constraints. This includes determining mining sequences for excavators to follow and selecting material to draw from stockpiles to service the processing plant. On extraction, material can either be processed directly or stockpiled for processing at a later time. An overall stockpiling plan is required.
A geological model specifies quality attributes of material in the ground such as chemical composition, ore hardness, and friability. The material to potentially be extracted is nominally partitioned into a set of blocks of predetermined regular dimensions. Each block is assumed to have consistent overall attributes. However, this model has a level of uncertainty associated with it. The geological model is built upon core samples. Due to the expense of drilling, not every block is sampled, and the uncertainty in estimates of the mineral content tends to increase for blocks that are further from the nearest core sample. The study group’s primary aim was to consider the impact of this uncertainty and how an awareness of uncertainty could be used to improve the optimisation and management of the extraction.
The problem is to optimise the extraction sequence and processing plant feed in order to meet planned production targets. During extraction, more accurate information about the attributes of each block becomes available. There should be consideration of the use of this information to determine a modified schedule that deviates from the mine plan in order to maximise the chance of hitting quality targets. The planning method must be scalable to work with tens of thousands of distinct “blocks” of material in the geological model.
During mining, the blocks of material are drilled, blasted, excavated and loaded into trucks. The order of extraction is constrained in a number of ways. For an open cut mine, each block to be extracted must first be uncovered if it is not already at the surface. This is taken to mean that the block above and the eight blocks surrounding the block above must all be extracted before the nominated block.
The extracted blocks are either processed immediately, stockpiled for later use, or discarded. There are a number of stockpiles, differentiated by quality. This means that the average quality of material delivered to be processed can be moderated by judicious reclamation from stockpiles.
The demand for ore from the mine is expressed in terms of builds. The builds reflect customer demand for the mine product and may form part or all of a shipment at the port. Each build is a specified tonnage of material with given minimum percentages of certain ore types and maximum percentages of undesirable elements. The challenge for mine scheduling is to sequence the extraction of blocks to meet, or exceed, the quantity and quality constraints of the set of current builds.
The study group considered two mine management approaches with regards uncertainty:
- planning production at the level of whole builds in advance in a manner that maximises their likelihood of meeting quality specifications, and
- planning production within each build so that adaptation or online replanning is facilitated.
The group was provided with a large historical data set by the industry representative. Each block in the data set is 25 metres square with a height of 5 metres. The block record describes the location of the block, and estimates of its total tonnage and content by percentage weight of various minerals and degrading elements. More accurate information about the composition of the block, obtained after extraction, is also recorded in the data.
Graphical analysis by the group provided an insight into the distribution that the mineral content of a mine might take. There is some natural spatial segregation among the blocks and this facilitated the study of subsets of the data. Precedence graphs for the extraction of blocks were constructed. Feasible extraction sequences can be generated from these and compared.
A mixed integer programming (MIP) model was formulated. The aim of the model is to select suitable blocks with which to construct a build, in minimum time. Although the actual order of excavation is not considered in this model, it is constrained to ensure that the chosen blocks are uncovered if necessary. Other constraints included a penalty on excessive movement of the excavators (diggers). After excavation of the ore, some truckloads are sent for immediate processing, while others are stockpiled or discarded. The limiting resource in the MIP is the excavators, which typically constitute the production bottleneck in a mine. The initial model is nonlinear, but linearisation strategies have been investigated.
Possible sources of variability in estimates were identified. These include the position of the sample holes and specifically the distance of a block from a sample hole. The core samples are typically at the nodes of a rectilinear grid and 100 metres apart in both directions. This means that some blocks are 50 metres or more from the nearest sample. The quality of ore may be associated with greater variability as some high quality ore, for example iron, is found in concentrated seams. There may also also be a discontinuity in strata where there is a geological change in the nature of the rock. Making use of a combination of such effects, the data set was supplemented with a plausible measure of the uncertainty.
A typical build has both quality and quantity specifications. The operator plans to meet this from a collection of specific blocks. In practice the variability in content of the blocks may require emendations, perhaps making use of the stockpiles, but these are to be minimised.
The group postulated the notion of a “correction cone” (or “feasibility cone”) for the average quality of a build as it is assembled. The idea of the cone is that large deviations from the target quality can be tolerated in the early stages of the build, but that the average must converge as the build progresses. The natural tendency to convergence due to averaging will at times need to be supplemented by diversion of an extreme block away from processing to a stockpile. A block of significantly high or low quality may be tolerated in the early stages of a build, but rejected if considered later on.
A simulation model considered the management of materials arriving directly from excavation at the processing plant. Blocks that are too extreme in quality for the current build are replaced by an equal tonnage of material from an appropriately chosen stockpile. In all cases the average build quality converges, and rates of replacement vary from 10% to 35%. By modelling this build further insight was gained into the process.
As noted above, the characteristics of some blocks are more uncertain than others. Intuitively, it seems that the ultimate quality of a build could be better controlled by including high uncertainty blocks first and then proceeding to blocks of low uncertainty. This is called a “decreasing uncertainty” strategy. Another simulation model was built and tested on synthetic data. The model supports the hypothesis that if there is any choice about the order in which selected blocks are processed then a decreasing uncertainty strategy yields a higher probability of meeting the build quality target.
Using the uncertainty estimates for mineral content in a mine will lead to a more efficient use of the resource in terms of running costs and requirements for capital equipment. Ideas for how this may occur were explored at the MISG to begin addressing this challenging project.