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substitution of tin and silver for lead in solder could double the demand for these two elements.

Elements that could experience changes in demand large enough to alter the estimated life of their reserve base include cadmium, lithium, nickel, platinum-group metals (PGMs), and tellurium. The main markets that might create this increased demand are batteries in electric and hybrid automobiles, solar cells, and catalytic surfaces. Cadmium could see the largest changes because it is a potential constituent in both batteries and solar cells. Nickel and lithium might be used in batteries, tellurium in solar cells, and PGMs in catalytic surfaces for fuel cells. Flexibility in responding to increased demand will differ for these metals, and will likely be greatest for nickel and lithium, which form deposits of their own and possibly for PGMs, which come partly from deposits of their own and partly as by-products of (largely) nickel production (Mungall and Naldrett 2008). Cadmium and tellurium are largely by-products of zinc and copper refining, respectively, and their long-term availability will depend on resources and uses of these elements. Recycling will probably be greatest for batteries, although this will help meet demand only when there is a large stock of batteries in use.

Extending the Reserve Base

As the reserve base is exhausted, society must turn to new conventional deposits or to unconventional deposits. This will probably involve a three-step process. The first step will almost certainly be to find new conventional deposits in poorly explored parts of the near-surface crust. Following this, we could seek conventional deposits at greater depths in the crust or attempt to use unconventional deposits. Available estimates of resources can be divided roughly into these three categories.

Conventional Resources in the Near-surface Crust

The stock of conventional deposits is obviously larger than those that are known. Many parts of the world have not been well explored and, even where some exploration occurred, many geologically interesting discoveries have not been adequately evaluated. Almost all of the efforts to estimate remaining conventional deposits have used information from the surface to determine what is at depth in the crust. Whether it is stated explicitly or implied, our ability to estimate resources at depth has been limited to the depth to which Earth has been explored and mined for the deposit type in question. For most deposits, this is no more than about 1 km, and therefore most currently available estimates of our resource of conventional deposits represent only this (uppermost or near-surface) part of Earth's crust. The most widely used methods for these estimates are based on two types of information: production and geological (Singer and Mosier 1981; McLaren and Skinner 1987).

Production-based estimates use information from mineral-producing operations and assume that they provide a representative sample of the region of interest, including its unexplored or unexploited parts. These data have led to two well-known global-scale relations. McKelvey (1960) showed that the degree to which commodities must be concentrated in the crust to form mineral deposits is related both to the average crustal abundance of that commodity and, fortunately, to the amount of the commodity used by society. Iron, which is used in large amounts, comes from deposits with iron concentrations that are only 5-10 times greater than its average crustal abundance. Gold, on the other hand, is used in small amounts and comes from deposits with gold concentrations that are at least 250 times greater than the average crustal abundance of about 2 ppm. Thus, elements used in large amounts are easier for Earth to concentrate into mineral deposits than those used in small amounts. In another example, Lasky (1950) showed that there is a logarithmic increase in the volume of ore for some commodities with an arithmetic decrease in grade, although DeYoung (1981) argued that it is not reasonable to extrapolate this relation to extremely low grades typical of common rocks (a point that is discussed further below). Finally, Folinsbee (1977) and Howarth et al. (1980) used a variant of Zipf's Law to suggest that individual deposits could be ranked in a way that might indicate the magnitude of undiscovered deposits.

The best known production-based approach, popularly known as Hubbert's curve, was used to estimate global oil resources and is the basis for the widely publicized "peak oil" concept (Hubbert 1962). The Hubbert's curve approach, which was first outlined by Hewett (1929), is based on the observation that global and U.S. production of oil increased slowly over a long period of time and the related assumption that, as reserves are exhausted, production will decline in a mirror image of the initial increase. Thus, knowledge of the increasing part of the curve and recognition of the peak in production allows estimation of ultimate resources. Although the peak of oil production in the U.S. has been recognized, controversy persists over whether it has been reached for world oil production (Bartlett 2000; Deffeyes 2005). There is even less agreement about peaks for metal production (Roper 1978; Petersen and Maxwell 1979; Yerramilli and Sekhar 2006), although individual countries show peaks for individual commodities (Figures 1-8 in Kesler 1994). Thus, although these methods provide interesting insights, they have not, as yet, yielded undisputed quantitative estimates of global-scale mineral resource stocks other than oil.

Geological estimates, which were refined during studies of regions proposed for inclusion in the U.S. wilderness program (Wallace et al. 2004), have provided considerably more quantitative information. These estimates are commonly based on genetic models for a specific type of mineral deposit, including information on the geologic environment in which they form. Areas where the geology is known, but there has been no mineral exploration, can then be ranked, often quantitatively, in terms of their likely endowment of undiscovered mineral deposits (Wallace et al. 2004; Singer et al. 2005a). Singer

(2008) has shown that this approach depends in part on the scale at which data are compiled and evaluated because there is an inverse relation between the size of a favorable region and the spatial density of deposits that it appears to contain. This approach can be used to estimate resources in new or unconventional deposit types as long as there is geological information on the nature and setting of such deposits.

The most widely circulated geological estimate was made by the U.S. Geological Survey for the United States (Anonymous 1998), which quantified resources of gold (4.5 x 104 tons), silver (7.9 x 105 tons), copper (6.4 x 108 tons), lead (1.8 x 108 tons), and zinc (2.5 x 108 tons) in conventional deposits to depths of about 1 km in the crust. Of these amounts, about 75-85% remains to be mined. If we assume that deposits are evenly distributed on all continents (which is not strictly correct), world resources (including mined material) amount to about 6.9 x 105 tons of Au, 1.2 x 107 tons of Ag, 9.9 x 109 tons of Cu, 2.7 x 109 tons of Pb, and 3.9 x 109 tons of Zn. These amounts are 7-20 times larger than the resource base numbers in Table 7.1.

Deeper (Ultimate) Conventional Resources

The continental crust is up to 50 km thick, and current mining reaches depths of 3.3 km. Thus, our ultimate resource of conventional deposits should be considerably larger than just the material in the upper kilometer or so of the crust. One of the few attempts to estimate resources of conventional deposits for the entire crust was made for copper using the tectonic-diffusion model of Wilkinson and Kesler (2007). The estimate is based on a calculation that forms model mineral deposits at a fixed depth in the model crust and allows each deposit to diffuse through the crust as time passes, randomly moving up, down, and sideways (stasis). The model keeps track of all deposits as they migrate through the crust. Some deposits diffuse to the model Earth's surface, whereas others move through the surface to be eroded, and still others remain buried. The model evaluates numerous possible combinations of up-down-stasis movement for the deposits and monitors when (in calculation time) the number and age-frequency distribution of deposits at the model surface best fits the actual age-frequency distribution for known deposits of that type. The model output representing this best-fit condition is then calibrated by reference to the average depth of emplacement of the deposit type of interest (derived from geological information) and the period of time represented by the age-frequency distribution.

The tectonic-diffusion estimate for copper was based on a compilation by Singer et al. (2005b), which includes age and copper contents for over 500 known porphyry copper deposits (Table 7.2). The model calculation indicates that about 1.7 x 1011 tons of copper are present in porphyry copper deposits throughout the entire Earth's crust. Porphyry copper deposits make up 57% of Earth's copper deposits, and therefore all copper deposits in the crust should

Table 7.2 Reserves and resources of copper based on estimates of Kesler and Wilkinson (2008). All amounts in metric tons; annual production, and reserve base from USGS.

Category

Tons

Years

Annual production of copper (2008)

1.56E+07

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