Modeling and forecasting complex patterns of mineral production. Gold mining in Canada

Abstract

The complex pattern of gold production in Canada, which differs from the classic Hubbert´s curve, is modeled, and a short-term forecast is made, via the Fundamental Equation of Mineral Production (FEMP). For intervals of time with a variable production to reserves ratio, a discrete piecewise version of the equation updates the reserves and the Production to Reserves Ratio (PRR) by units of time. These piecewise linear portions of the PRR correspond to sub-cycles of rising and declining production embedded in the overall history of production. This version of the FEMP allows modelling of any pattern of mineral production at a universal range of scales. The Hubbert´s linearization indicates the official account of reserves underestimates the real amount of gold resources in Canada. The equivalence between the Hubbert’s formula and the FEMP is introduced. The Hubbert curve is shown as a case study of the Fundamental Equation, featured as the product of a quadratic function of the cumulative production and a rational function of the PRR with time. The forecast for Canada’s current gold production illustrates the metal output is about to peak with an all-time record high in the near future, unless new findings or influential global economic factors are introduced (i.e., a sharp and sustained growth of gold demand from regional markets), allowing an increase of the slope of the linear function featured by the PRR of the FEMP-based model.