Short‑term schedule optimization with nonlinear blending models for improved metallurgical recovery in mining

Traditional linear approaches oversimplify the complexities of ore blending. Adopting nonlinear blending models in mining and mineral processing is critical to enhancing prediction accuracy and allowing optimization regarding nonadditive variables, such as metallurgical recovery. This study implements a simulated annealing algorithm in short-term mine planning that seeks to optimize the metal recovery by considering how to blend the ore in the mine better. Two nonlinear metallurgical recovery models are used as inputs to the algorithm to represent synergistic and antagonistic blending. The results of the case study demonstrate that the optimized schedule exhibits improvements in both blending behaviors when contrasted with conventional linear-based scheduling plans. Background When natural or deliberate blending occurs, it is often assumed that the blended material’s average property, termed the effective property, is the mass or volume-weighted average of each component property. However, the averaging behavior of nonlinear variables may differ significantly. The nonlinearity may be explained by one material’s greater influence over the other, leading to an effective property greater than the average of its components. From the perspective of blending, this behavior is called synergistic blending. In the opposite case, when the lower-value component has more influence on the mixture, the effective property is lesser than the linear average. This behavior is called antagonistic blending. Blending neutral occurs when the effective property is equal to the weighted average. Figure 1 illustrates the possible blending behaviors, where there are N = 6 material components, each with a different property value p. Their weighted linear average p– is 0.77. When the components are blended, the effective property value (peff) depends on the blending behavior. Metallurgical recovery presents nonlinear behavior. Its prediction at the block scale poses challenges as a block is never processed in isolation, but in a blending unit (the set of blocks processed together). Consequently, conventional mine planning conceived based on block-scale estimations operates under biased predictions regarding metallurgical recovery. The proper metallurgical recovery of a block is only assessed after estimating the effective recovery of its blending unit which, in turn, depends on the set of blocks scheduled together in the mine plan. This study shows how a mine plan can be optimized considering nonlinear metal recovery blending. Fig. 1 Illustration of blending cases when there is mixingbetween blocks with different property values. Methods Imagine a 2D mining face discretized into regularly shaped blocks, each assigned an estimated grade. The blocks’ coordinates along the Easting and the Northing are represented by the ix, iy index, starting from left to right and south to north directions. The problem consists of scheduling the blocks to maximize the global metallurgical recovery: that is, the total metal recovered after processing all the blocks. The mixtures, crucial to this optimization, comprise blocks grouped according to the temporal sequence of their extraction. The variable representing the plant feeding order for each amalgamated mixture is the blending unit (bu). The range of blending units is denoted as bu = 1, … , BU, where BU stands for the overall number of blending units. The mass of a blending unit is the cumulative sum of the masses of its constituent blocks, and its effective recovery is contingent upon the recoveries of its composing blocks, as delineated by the blending model. Fig. 2 Scheduling of blending units in (a) synergistic and (b) antagonistic cases. The scheduling constraints revolve around (1) operational accessibility to ore blocks and (2) shovel movement. The initial constraint constitutes a fixed hard constraint, delineated by a “free face” precedence. Establishing a 45-degree precedence, to mine a block at the (ix, iy) index, the three blocks in the opposite direction of mining — indexed as (ix − 1, iy − 1), (ix, iy − 1) and (ix + 1, iy − 1) — must have been extracted in a prior or concurrent period. This condition is contingent on the mining direction, which progresses from south to north. Conversely, the shovel movement constraint is a more flexible, soft constraint. Considering an illustrative case study, where two different mining faces must be mined simultaneously, two schedules were performed for three scenarios. The first schedule is a standard schedule, which consists of a zigzag pattern, beginning in the bottom-left corner of each mining face. The second schedule is the optimal one provided by the algorithm. Regarding the scenarios, the first, second and third scenarios consisted of considering blending neutral, synergistic and antagonist models, respectively. Results In the blending neutral scenario, both standard and optimum schedules result in a total metal recovery of 6.21 mass units out of the 240 units of ore mass. Considering a synergistic scenario, the optimized schedule yielded up to 6.51 mass units of metal against 6.45 provided by the standard schedule, an increase of up to 0.93 percent. Considering an antagonistic scenario, the optimized schedule yielded up to 5.93 mass units of metal against 5.80 provided by the standard schedule, resulting in an improvement of up to 2.24 percent. Figures 2a and 2b illustrate the optimized schedules for these scenarios. Discussion For the neutral blending model, any conceivable schedule would result in a consistent metal recovery of 6.21 mass units, as the scheduling does not impact the global recoverable metal. In both synergistic and antagonistic scenarios, there were differences between the standard and the optimized schedules. In the synergistic blending, the algorithm maximized variability among blocks in each blending unit, while in antagonistic blending it minimized the variability within each BU. This variability is linked to variables affecting metallurgical response, with effective metallurgical recovery dependent on grade and metallurgical recovery of each block. Conclusions Conventional mine planning uses the mining block estimated value of a variable, ignoring the blended properties of the mixture. The illustration case demonstrated that ignoring the impact of the blending behavior of the metal recovery variable introduces bias into the expected global metal recovery value in any given schedule. Also, considering nonlinear behavior enables schedule optimization. A simulated annealing algorithm was developed to schedule blocks and cluster them into optimal blending units. In both synergistic and antagonistic blending scenarios, the optimized schedule produced superior outcomes regarding total recoverable metal. References A list of all references is available in the full paper.

Short‑term schedule optimization with nonlinear blending models for improved metallurgical recovery in mining

Authored by: Pedro Henrique Alves Campos, João Felipe Coimbra Leite Costa, Vanessa Cerqueira Koppe, Marcel Antônio Arcari Bassani and Clayton Vernon Deutsch

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