Metallic Mineral Resources in the Twenty-First Century: II. Constraints on Future Supply

Supplying worldwide demand of metallic raw materials throughout the rest of this century may require 5–10 times the amount of metals contained in known ore deposits. This demand can be met only if mineral deposits containing the required masses of metals, in excess of present day ore reserves, exist in the Earth’s crust. It is, by definition, not known whether or not such mineral deposits exist. On the basis of the statistical distribution of metal tonnages contained in known ore deposits, however, it is possible to place constraints on the size distribution of the deposits that must be discovered in order to meet the expected demand. A nondimensional analysis of the distribution of metal tonnages in deposits of 20 metals shows that most of them follow distributions that, although not strictly lognormal, share important characteristics with a lognormal distribution. Chief among these is the observation that frequency falls off symmetrically and geometrically with deposit size, relative to a median deposit size that is approximately equal to the geometric mean deposit size. An immediate consequence of this behavior is that most of the metal endowment is concentrated in deposits that are several orders of magnitude larger than the median deposit size, and that are much rarer than the most common deposits that cluster around the median deposit size. The analysis reveals remarkable similarities among the statistical distributions of most of the metals included in this study, in particular, the fact that distribution of most metals can be fully described with essentially the same value (about 2–3) of the scale parameter, σ, which is the only parameter needed to describe the behavior of a normalized lognormal variable. This observation makes it possible to derive the following general conclusions, which are applicable to most metals—both scarce and abundant. First, it is unlikely that undiscovered mineral deposits of sizes comparable to those that contain most of the known metal endowment exist in sufficient quantities to supply the expected worldwide demand throughout the rest of this century. Second, if the expected demand is to be met, one must hope that very large deposits, perhaps up to one order of magnitude larger than the largest known deposits, exist in accessible portions of the Earth’s crust, and that these deposits are discovered.