19 October 2007


Abstract: We examined the world production of 57 minerals reported in the database of the United States Geological Survey (USGS). Of these, we found 11 cases where production has clearly peaked and is now declining. Several more may be peaking or be close to peaking. Fitting the production curve with a logistic function we see that, in most cases, the ultimate amount extrapolated from the fitting corresponds well to the amount obtained summing the cumulative production so far and the reserves estimated by the USGS. These results are a clear indication that the Hubbert model is valid for the worldwide production of minerals and not just for regional cases. It strongly supports the concept that “Peak oil” is just one of several cases of worldwide peaking and decline of a depletable resource. Many more mineral resources may peak worldwide and start their decline in the near future.
“Peaking” is commonly observed for oil production in many regions of the world (e.g. Laherrere 2005). According to Hubbert (Hubbert 1956) the production curve of crude oil and of other minerals is “bell shaped” and approximately symmetric; that is the peak occurs when approximately half of the extractable resources have been extracted. From the regional data, it is a logic step to extrapolate to worldwide production and arrive to the conclusion that a global peak (“peak oil”) will be reached. In most cases, the analyses based on the Hubbert model say that peak oil could occur within a few years from now. Since crude oil is the single major source of primary energy in the world, it is widely believed that the consequences of peaking could be important, or even disastrous.
However, there is a problem with the idea that we are close to a worldwide oil peaking: no major energy resource (oil, gas, and coal) has peaked globally so far. So, how can we know that the global case is comparable to the regional cases we know? One way to answer this question is to look at the economic and geologic mechanisms that produce peaking. The Hubbert model has been analyzed in several studies (Naill, 1972, Reynolds 1999, Bardi 2005, Holland 2007). In all these models, peaking and decline is the result of the gradual increase of the cost of production of the resource; in turn due to depletion. These costs can be seen in monetary terms, but can be measured in energy units as well. In the case of oil, this increasing cost is related to factors such as the lower success rate with oil prospecting, the necessity of exploiting smaller fields, and the higher costs of processing lower quality oil. These costs will gradually reduce profits and, therefore, reduce the willingness of operators to invest in further extraction. That will slow down the growth and, eventually, cause the peak and the successive decline. This analysis is independent on the kind of resource considered and on the global/regional conditions of extraction.

However, this interpretation is far from being accepted by everybody. Some say that many regional cases of peaking are not due to progressive depletion but to political or market factors or both (see, for instance, Engdhal, 2007 for a recent restatement of this idea). Hubbert’s model is also criticized because it doesn’t take into account prices. In the global case, it is said, increasing market prices will keep profits coming and, therefore, operators will continue investing on increasing the extraction rate; if not forever at least well beyond the midpoint. This interpretation goes back to the 1930s, (Zimmermann 1933) with the so called “functional model” of minerals extraction that had a considerable success in the later economic literature (e.g. Nordhaus 1992, Simon 1995, Adelman 2004). Recent model studies that take prices into account (Holland 2006) indicate that peaking should occur anyway, but the idea that increasing prices will invalidate the Hubbert model lingers around. Some studies, indeed, assume that oil production will never peak worldwide but, rather, reach a longlasting plateu (CERA 2006).

Theories come and go, but one thing is certain: even the most elegant theory needs to be supported by facts. If we can find historical examples of global resources that have peaked and declined following a bell shaped curve, that will strongly support the idea the Hubbert theory holds for global production. Up to last year, there was only one example of such a case reported in the literature: that of whaling in 19th century (Bardi 2006). Whales are not a mineral resource, but the whale stock behaved as a non renewable resource as whales were “extracted” (hunted) at a rate much faster than their reproductive rate. Recently, Dery and Anderson (2007) have shown that the global production of at least one mineral resource, phosphate rock, has peaked in the 1980s.

Just two cases may not be enough to prove the general validity of the Hubbert model but, here, we can report that there are many more cases of global peaking for minerals production. After an exhaustive examination of the USGS database of the world mineral production (Kelly 2006) we found at least 11 cases of minerals that show a global “bell shaped” curve with a clear peak. Peaking was evident by visual examination and it was confirmed by fitting the data using a bell shaped function. We used both gaussian and logistic derivative functions, finding very similar results. Both kinds of curves can be used to fit the Hubbert curve as shown by Bardi (2005) and by Staniford (2006). In addition, we found several more cases of minerals that may have recently peaked or be near peaking, although that is not completely certain yet.

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