Impacts of grade distribution and economies of scale on cutoff grade and capacity planning

Strategic mine planning focuses on cutoff grade selection, capacity planning and block sequencing. Despite significant knowledge accumulated, potential value can be added to mineral sourcing by addressing various aspects. A case study on a metallic deposit with a lognormal grade distribution examines if grade/metal distribution influences cutoff grade selection. Six data sets with different shape and scale factors, but the same ore tonnage and metal quantity, are analyzed. Results indicate deposits with lower shape and scale factors are more sensitive to metal price and discount rate changes. The study also investigates the effect of economies of scale (EoS) on project value, focusing on the ratio of variable cost to total cost (capacity factor). Two regression analyses are conducted for optimal capacity planning and cutoff grade selection. The first shows capacity planning is highly sensitive to the EoS of mining and mineral-processing costs, with grade variability and metal distribution being negligible. In the second analysis, grade variability and EoS of mineral processing costs are vital for cutoff grade selection. Introduction Three major problems of mine planning are capacity planning, cutoff grade selection and block sequencing. In current practice, cutoff grades and sequencing are optimized for given mining and processing capacities. Naturally, the results can be optimal for given capacities only. However, whether these capacities are optimal is not known. It is worth noting that there is one optimal mining and processing capacity, fitting metal heterogeneity and continuity in a deposit to maximize the project’s net present value (NPV). In the mine planning context, an optimal cutoff grade cannot be calculated without optimal capacities, and optimal capacities cannot be calculated without an optimal cutoff grade. Therefore, these problems should be optimized simultaneously to maximize the economic value harvested from a mining operation. Fig. 1 The effect of EoS on processing recovery. The EoS significantly impacts cutoff grade and capacity planning. As capacities increase, operating costs decrease but annual head grade may reduce. Mining operations have increased capacities to cut costs, but lower head grades can outweigh these savings if the discount rate is low. Capacity increases can lead to negative outcomes, such as lower recovery and metal loss (Fig. 1). Therefore, the tradeoff between benefits from larger capacities and associated losses should be investigated [1]. This paper investigates two variables to find the best configuration of capacity and cutoff grade: (a) grade distribution type in the deposit and its parameters, and (b) the effect of EoS. Methods This study predicts ore-waste amounts based on statistical features derived from grade tonnage histograms. As the grades of metallic deposits often exhibit lognormal distribution, this research focuses on lognormal distribution. The lognormal distribution is characterized by the shape factor, σ, and scale factor, μ. Shape and scale factors are the standard deviation and mean of the logarithm of a normal distribution, respectively. These factors on grade tonnage and grade-metal distributions profoundly influence cutoff grade selection and capacity planning. Furthermore, the magnitude of EoS (the steepness of the curve) governs fixed- and variable-cost proportions in the total operating cost of an operation. It is a basic equation, as seen in Eq. (1), which predicts the cost related to a processing capacity based on a known cost-capacity relation: Cost 2 = Cost 1 (Capacity 2 / Capacity 1) k (1) where k denotes the magnitude of EoS. Called the capacity factor, k is used to measure the magnitude of EoS as follows: k = variable cost / total cost (2) A lower k results in a steep cost-capacity curve, meaning the fixed-cost proportion is higher than the variable-cost proportion. On the other hand, a flatter cost-capacity curve means the variable-cost proportion is higher than the fixed-cost proportion, resulting in a higher k value. Therefore, the effect of EoS decreases when k increases. This research employs three different k parameters: k1, k2 and k3. They represent the variable proportion of mineral-processing, mining and capital costs, respectively. The research tests different cost-capacity relationships to find the optimum processing capacity. To this end, the simultaneous cutoff grade and capacity planning model is implemented (detailed model is available in the full paper). Case study and discussion The grade-tonnage histogram of a gold deposit was used to test the proposed model, with six fictitious gold deposit data sets generated for benchmarking. Despite identical material and metal quantities, the model found different cutoff grades due to varying skewness and kurtosis. Tests on price and discount rate show that orebodies with smaller shape and scale factors are more sensitive to cutoff grade changes, while those with higher factors offer more flexible strategies for different financial scenarios. Moreover, combinations of three k1, three k2, three k3, five shape factors and three discount rates were generated. Based on the simultaneous cutoff grade and capacity planning model, optimum configurations were plotted as surface plots, analyzing the effects of the capacity factor on capacity planning (Fig. 2). Results show that the steepness of the surface plot for k2 (Fig. 2a), which is for the variable-cost proportion of mining cost, is higher than the steepness of the surface plots for k1 and k3 (Figs. 2b and 2c). Results show that processing capacity and cutoff grade are influenced by grade distribution and EoS. Processing capacities are affected by the EoS of the mining and mineral-processing systems, and cutoff grade is affected by grade distribution and the EoS of the mineral-processing system. For capacity planning, the effect of the cost structure of mining operations is higher than that of the cost structure of mineral-processing operations. Interestingly, the effect of grade variability is almost negligible, which means that capacity planning is only dependent on variable-fixed cost proportions. In addition, the cutoff grade gets larger with higher shape and scale factors. Finally, as the proportion of variable cost of mineral-processing costs increases, the optimal cutoff grade also increases. Conclusion This research aims to demonstrate (1) the effects of ore and metal distribution within a deposit and (2) EoS on capacity planning and cutoff grade selection. Based on the proposed model, it is found that higher shape and scale factors of both grade-tonnage and grade-metal distributions result in higher optimal cutoff grades and higher NPVs. Furthermore, the results show that while the effect of the EoS of mineral processing systems is noticeable on cutoff grade selection, the EoS of mining systems is more effective in capacity planning. In addition, while the impact of grade variability is relatively senseless on the capacity planning, it is profoundly critical for cutoff grade selection. ■ Selected reference Balci M, Kumral M (2022) Building an innovation strategy and culture on the structural characteristics of the mining industries. Resour Policy 78:102936

Impacts of grade distribution and economies of scale on cutoff grade and capacity planning

Authored by: Mehmet Balci and Mustafa Kumral

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