The Endogenous Reserve Frontier: Cut-off Grade, Capacity, and Sequencing in Resource-to-Reserve Conversion

Deep beneath the earth's surface, vast quantities of rock contain valuable metals, but not all of that rock is considered a mineable asset. In the world of mining, a distinction is drawn between a geological resource, which is simply the total amount of mineralized material known to exist, and a mineral reserve, which is the specific portion of that material that can be profitably extracted under current conditions. This difference is not merely a matter of counting rocks; it is a complex economic calculation involving the price of the metal, the cost of digging and processing it, and the time it takes to bring it to the surface. For decades, economists and engineers have treated the size of a mine's reserve as a fixed starting point, a static number that dictates how fast a mine should operate. However, this view overlooks a critical reality: the decision of what counts as a reserve is made before the mine opens, and that decision depends heavily on the order in which the rock is removed.

Juan Ignacio Guzmán, an economist at the Pontificia Universidad Católica de Chile, has developed a new way of looking at this problem. His research challenges the idea that reserves are a fixed geological input. Instead, he argues that the amount of ore a mine plans to extract is a flexible outcome, determined by how the mine is sequenced. The central question he addresses is simple yet profound: does the order in which a mine processes its rock change the total amount of rock it is worth mining? To answer this, he built a mathematical model that connects three usually separate ideas: the grade of the ore (how rich it is in metal), the size of the processing plant, and the schedule for digging. His work reveals that the answer depends entirely on whether the mine can pick and choose its rock or if it must process a mixed blend.

In many real-world mining operations, the rock cannot be picked up and sorted with perfect precision. Due to the shape of the deposit, the need to remove waste rock first, or the limitations of the machinery, a mine often has to process a steady stream of mixed material. This is what Guzmán calls a "stationary blended feed." In this scenario, if a mine decides to include a lower-quality, marginal piece of rock in its plan, that rock takes up valuable time in the processing plant. Because the plant has a limited capacity, every hour spent processing a low-value rock is an hour that a higher-value rock cannot be processed. This creates a hidden cost: by adding the marginal rock, the mine delays the processing of the richer, more profitable rock. Because money today is worth more than money in the future, this delay reduces the total value of the project. Consequently, to make the project profitable, the mine must set a higher standard for what it considers "ore." It must exclude the marginal rock that would otherwise slow down the richer rock. In this blended world, the mine's reserve is smaller than the total amount of positive-value rock available, because the act of including the extra rock hurts the value of the rest.

However, Guzmán's model also explores a different, more ideal scenario: perfect descending-margin selectivity. Imagine a mine that can access its rock in a perfect order, processing the richest, most valuable rock first and saving the marginal, lower-value rock for the very end. In this case, adding a marginal piece of rock to the plan does not displace or delay any of the richer rock. The marginal rock simply waits its turn at the back of the line. Since it does not push back the cash flows from the better rock, it does not create a timing penalty. In this ideal world, the mine can include every single piece of rock that has any positive value, regardless of how long it takes to reach it. The reserve boundary stays at the basic break-even point, and the mine can extract a much larger portion of the geological resource.

The paper demonstrates that the difference between these two scenarios is not about the geology itself, but about the technology and constraints of the mine. Two mines could sit on top of the exact same rock formation with the exact same distribution of metal grades. If one mine is constrained by the need to blend its feed or follow a strict digging order, it will declare a smaller reserve. If the other mine has the flexibility to sequence its extraction perfectly, it will declare a larger reserve. The research shows that the "reserve" is not a fixed geological fact, but a derived economic stock that changes based on how the mine is planned.

To test how this works in the real world, Guzmán applied his model to the Copper Mountain mine in British Columbia, using public data on its reserves and resources. The mine reported proven and probable reserves of 367 million tonnes, with an additional 138 million tonnes of resources that were not yet classified as reserves. By fitting a mathematical curve to this data, the model simulated what would happen under the two different sequencing rules. Under the realistic assumption of a blended feed, the model matched the reported reserve of 367 million tonnes. But when the model assumed the mine could perfectly sequence its rock, the amount of economically viable ore jumped to nearly 503 million tonnes. Crucially, the size of the processing plant did not need to change much to accommodate this extra rock; instead, the mine would simply operate for a longer period of time. The extra rock would be processed later, extending the life of the mine rather than requiring a bigger factory.

This finding has significant implications for how we understand mineral supply. For years, analysts have often used a fixed ratio to estimate how much of a geological resource will eventually become a mineable reserve. Guzmán's work suggests this approach is flawed because it ignores the sequencing constraints that actually determine the reserve size. If a mine has limited flexibility in how it digs, a large portion of the resource may never be included in the economic plan, even if the metal is there and the price is right. Conversely, improvements in mining technology that allow for better sequencing or more flexible blending could unlock vast amounts of additional supply without discovering new deposits. The study concludes that the "reserve frontier" is not a static line drawn on a map, but a dynamic boundary that shifts with the mine's ability to manage its schedule and capacity.

The research also clarifies the role of time in mining economics. In the blended scenario, the longer a mine plans to operate, the more valuable the time penalty becomes, pushing the cut-off grade higher and shrinking the reserve. In the perfect sequencing scenario, time does not penalize the reserve size; it only affects the size of the plant and the duration of the operation. This distinction explains why some mines might appear to have a smaller reserve relative to their resources, not because the rock is poor, but because the mine's design forces it to be selective. The paper does not claim to solve every problem in mine planning, nor does it provide a new way to estimate the exact reserves of a specific company. Instead, it offers a clear theoretical framework that explains why reserves vary and highlights that the order of extraction is just as important as the price of the metal or the cost of digging. By recognizing that reserves are a result of planning choices rather than just geological facts, economists and engineers can better predict how much metal will actually reach the market and how changes in technology or infrastructure might alter that supply.