The value of drilling — A chance-constrained optimization approach

The challenge of managing geological uncertainty in mine planning is central to optimizing resource extraction while minimizing risks and costs. This paper introduces a novel approach to coal mine planning by integrating chance-constrained programming to address the uncertainty inherent in mining operations. The main takeaway from this work is the demonstration that focusing on reducing the variance of high-quality coal blocks, rather than low-quality ones, can lead to better blending outcomes, higher profitability and more efficient resource utilization. The study presents a case study of a coal mining operation, using chance-constrained programming to manage the uncertainty surrounding coal property predictions, specifically the predicted coke strength after reaction (CSR). Background Coal miners, like many in resource extraction industries, face considerable uncertainty in the ore’s characteristics. Variations in coal quality, especially in properties such as CSR, crucially determine the economic feasibility of the mining process. CSR, a key measure of the strength of coke produced from coal, is particularly important in steel production, influencing blast furnace efficiency. However, geological uncertainty can cause CSR values to fluctuate, challenging mining operations to meet quality standards while managing cost-effective resource extraction strategies. Traditional methods of managing uncertainty in mine planning often involve drilling additional boreholes to gather more data on the ore’s quality. These methods, however, generally focus on reducing the variance of low-quality coal, believing that the uncertainty in poorer-quality resources should be minimized to ensure better blending outcomes. This paper challenges this traditional approach, suggesting that focusing on reducing the uncertainty of high-quality blocks of coal may provide better results by enabling more effective blending and better accommodation of low-quality materials. Chance-constrained programming offers an optimization framework that integrates probabilistic constraints to model uncertainty. In the context of this paper, chance constraints allow for the modeling of the probability that a coal blend will meet a specific CSR threshold, thus providing a more flexible, realistic approach to managing risk in the mine planning process. This paper explores the use of chance-constrained programming in determining the best locations for infill drilling. Method We describe an ore blending model which is a simplified adaptation of the model outlined in Jeuken and Kearney (2021). The model is a coal blending problem where the objective is to maximize the revenue generated from a blend of coal while ensuring that the CSR of the blended product meets a predefined minimum threshold. The model uses a time-based approach, considering a planning horizon over 24 months and incorporating a probabilistic component to account for uncertainty in CSR. We formulate the coal blending problem with constraints that include inventory management, capacity limitations, and the chance constraint for CSR. The chance constraint ensures that the CSR for the blended coal is unlikely to fall below the threshold, providing flexibility in the optimization process while maintaining product quality. Fig. 1 Plots showing (a) the ordered by a priori value of CSR, in orange, and the dollar value increase resultant of reducing the variance of that block, in gray, and (b) the ordered by a priori value of the standard deviation of CSR, in orange, and the dollar value increase resultant of reducing the variance of that block, in gray. The key decision variable in this model is the selection of drilling locations. Drilling additional boreholes reduces the uncertainty (variance) of CSR values for specific blocks of coal, thereby refining the prediction of CSR. This study evaluates different drilling strategies by solving the chance-constrained optimization problem under various scenarios. Specifically, we use two approaches to evaluate the value of drilling individual blocks of coal: (1) Given the computational complexity of solving the model for multiple blocks, the study first assesses the impact of drilling each block individually. We do this by solving separate models, each focused on a single block, and evaluating the revenue increase associated with reducing the variance in that block’s CSR. (2) We solve a linearized version of the model to select the optimal combination of drilling locations for a given number of holes. Fig. 2 Plot showing the increase in dollar value by individually drilling the 10 blocks that give the largest increase in dollar value. The couplets contain the expected value of CSR (in percent)and the standard deviation. Results The case study, based on a coal mine complex in Queensland, Australia, evaluates the impact of variance reduction on the quality of coal blends and the resulting revenue. The case study uses 108 distinct coal sources, each with unique CSR characteristics and availability across 24 months. The key property under consideration is CSR, which must exceed a minimum threshold of 67 percent. The first set of results highlights the relationship between the revenue increase and either the expected CSR value or reducing variance. In Fig. 1, we present this data, which demonstrates that the revenue increase correlates somewhat with the expected CSR value for each block and strongly with the standard deviation of the CSR value. We then use the linearized version of the model to select the optimal combination of drilling locations for 10 locations. In Fig. 2, we rank these blocks by revenue increase after variance reduction. The blocks selected for drilling exhibit high CSR values, all greater than or close to the threshold of 67 percent, and large standard deviations. Table 1 presents the cumulative use of ore as the number of blocks drilled increases. The results show that with additional drilling, the use of low-grade coal increases, while high-CSR coal use remains constant. Both of these methods challenge the conventional approach of focusing on high variance, low-CSR blocks, indicating that reducing uncertainty in high-CSR blocks enhances the ability to absorb lower-quality coal, leading to more effective blending and higher overall revenue. Discussion The results presented in this study reveal important insights into the management of geological uncertainty in coal mine planning. The most significant finding is that drilling high-quality coal with high CSR but high variance may offer more value than drilling low-quality coal with lower variance. This challenges traditional industry practices, which typically prioritize drilling low-quality blocks to reduce uncertainty. The chance-constrained programming approach used in this study offers several advantages over traditional models. The flexibility provided by chance constraints allows for the modeling of different levels of risk and offers decision-makers a more nuanced view of the trade-offs between feasibility and conservatism in the blending process. Additionally, the linearized model developed in this paper provides an efficient way to select optimal drilling locations without the need for solving multiple, time-consuming models. Conclusion This study demonstrates the value of using chance-constrained programming to optimize coal blending under uncertainty, offering a more flexible and efficient approach to mine planning. The insights from the techniques presented may challenge traditional practices and call for a rethinking of mine planning strategies. Future research could explore the application of this model in different mining contexts, including metalliferous mining, where similar challenges related to uncertainty and blending exist. By refining these methods, the potential for improving mine planning and optimizing resource extraction under uncertainty is vast. Selected reference Jeuken R, Forbes M, Kearney M (2021) Optimal blending strategies for coking coal using chance constraints. J Oper Res Soc 72(12):2690–2703

The value of drilling — A chance-constrained optimization approach

Authored by: Rick Jeuken and Michael Forbes

To view this article you must be a member of SME/UCA.

Mining Engineering’s Weekly Rundown: Episode 73

Get your SME Foundation VIP Access Conference Pass to MINEXCHANGE 2027

“Check the box” and help support the SME Foundation

Mining Engineering’s Weekly Rundown: Episode 73

Get your SME Foundation VIP Access Conference Pass to MINEXCHANGE 2027

“Check the box” and help support the SME Foundation

To view this article you must be a member of SME/UCA.

Long-term service agreements and lifecycle management programs crucial in gearless mill drive maintenance

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

Related Articles

Rare earth elements in the global economy: Usage, recovery and the quest for supply security — A review

A systematic evaluation of localization signals in the advancing openpit mine Aitik

From foundation to future: Revisiting AI integration in mining engineering education through current perspectives of students, educators and industry

Iron ore tailings reprocessing by electrostatic separation plus two-stage froth flotation

Mining Engineering’s Weekly Rundown: Episode 73

Get your SME Foundation VIP Access Conference Pass to MINEXCHANGE 2027

“Check the box” and help support the SME Foundation

Mining Engineering’s Weekly Rundown: Episode 73

Get your SME Foundation VIP Access Conference Pass to MINEXCHANGE 2027

“Check the box” and help support the SME Foundation

Use Single Sign On