Extrapolating phosphorus production to estimate resource reserves

Various indicators of resource scarcity and methods for extrapolating resource availability are examined for phosphorus. These include resource lifetime, and trends in resource price, ore grade and discovery rates, and Hubbert curve extrapolation. Several of these indicate increasing scarcity of phosphate resources. Calculated resource lifetime is subject to a number of caveats such as unanticipated future changes in resource discovery, mining and beneficiation technology, population growth or per-capita demand. Thus it should be used only as a rough planning index or as a relative indicator of potential scarcity. This paper examines the uncertainty in one method for estimating available resources from historical production data. The confidence intervals for the parameters and predictions of the Hubbert curves are computed as they relate to the amount of information available. These show that Hubbert-type extrapolations are not robust for predicting the ultimately recoverable reserves or year of peak production of phosphate rock. Previous successes of the Hubbert curve are for cases in which there exist alternative resources, which is not the situation for phosphate. It is suggested that data other than historical production, such as population growth, identified resources and economic factors, should be included in making such forecasts.