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Peak minerals: What can we learn from the history of mineral economics and the cases of gold and phosphorus?


The objective of this paper is to provide a conceptual and empirical historic analysis of applications, misunderstandings, and fallacies surrounding the Hubbert curve, the U-shaped production curve of a commodity, and peak minerals. We show that the ultimate recoverable resources (URR) cannot be predicted by fitting a symmetric curve to the data of past (historic) production for any commodity on a global scale. Without knowledge of the URR, it is not possible to determine the peak production time. For well-confined areas, in the case of a supply market, it might be possible today to construct a satisfactory Hubbert curve and to determine peak production. For phosphate, the case of Nauru Island is a good example, but so far, it is not possible for any commodity worldwide. URR comprise past production, presently known reserves, and future reserves developed from resources (known, but uneconomic at present) and parts of the geopotential (not yet known, but by geological reasoning and technological innovations, reserves can be expected to be discovered). The concept of reserves is a dynamic one, determined by economic conditions, technological developments, etc. The reserves of today can be the resources of tomorrow and vice versa. These factors also influence production curves. Therefore, it is not justified to interpret every peak as caused by geological constraints. In most cases so far, peak curves are demand driven and not at all influenced by geological availability. In only a very few cases (like the curve for the lower 48 states of the USA for oil by Hubbert in 1956 or gold production in South Africa), they are supply driven, i.e., true Hubbert curves. Gold showed four peaks in the twentieth century. Since gold mining is “money mining,” there is always a demand for gold. Therefore, the causes for the peak development must be economic ones with no influence of physical-production demand factors, purely supply factors—a model case to study. We also show how the kind of commodity, government regulations, technologies, and commodity prices influence U-shaped production curves. For phosphate, we show that a peak cannot be predicted with the present base of knowledge. We face a reserve-to-consumption ratio of higher than 300, which is higher than for every major commodity and at least 10 times the length of innovation cycles in the mineral industry. If we take the dynamic nature of reserves into account, we doubt that it is very meaningful to discuss the reliability of reserve and resource data. Instead, under the aspect of long-term future supply and a postulated right to know based on the universal right to feed oneself in dignity, the geopotential of phosphorus as the source of future reserves and resources should be regularly examined by an international scientific body.

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  1. Unfortunately, in the international literature, the term “resources” is used with two meanings: resources without established economic viability (now called resources sensu stricto) and total resources comprising everything from reserves to geopotential, also meaning thus far unknown reserves and resources (sensu stricto).

  2. FOB means free on board a ship, normally exporting the product. In the following, we speak about both marketable phosphorus rock (PR-M) granulate with a concentration of about 30% P2O5 and phosphate rock (PR-Ore) with varying grades.


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The authors thank James R. Rustad for updating the Hubbert linearization function for US Oil and World Oil production, Elaine Ambrose for critically reading the paper and making numerous suggestions for improvements, and Bernhard Geissler, Doris Homberg-Heumann, Annegret Tallig, Sandro Schmidt, and Georg Wellmer for helping with the figures.

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Correspondence to Friedrich -W. Wellmer.

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F.-W. Wellmer was the former president of the Federal Institute of Geosciences and Natural Resources

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Wellmer, F.W., Scholz, R.W. Peak minerals: What can we learn from the history of mineral economics and the cases of gold and phosphorus?. Miner Econ 30, 73–93 (2017).

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  • Peak minerals
  • Hubbert curves
  • Production curves
  • Ultimate recoverable resources (URR)
  • Reservers
  • Geopotential
  • Demand driven Hubbert curves
  • Supply driven Hubbert curves
  • Lasky's law
  • Feedback control cyle of mineral supply
  • Recycling outlook
  • Innovation cycles