Article pubs.acs.org/est
Peak Nothing: Recent Trends in Mineral Resource Production James R. Rustad* Corning Incorporated, One Science Center Drive SP TD 01-1, Corning, New York 14831, United States S Supporting Information *
ABSTRACT: The Hubbert-type analysis used to analyze the production history of oil is applied here to other raw materials. Many resources commonly thought of as being close to “peaking” such as lithium, helium, copper, and the rare earth elements, show no evidence of logistic behavior at any point in their production histories. Although many resources have exhibited logistic behavior in the past, many now show exponential or superexponential growth. In most cases, the transition has occurred in the last ten to twenty years.
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INTRODUCTION Underpinning the recent focus on sustainability is the assumption that, for many raw materials, resource depletion is imminent.1 The degree of concern has been compounded by increasing public awareness of Hubbert’s logistic analysis of oil production trends.2 In the Hubbert model, the consequences of resource depletion are apparent not near the end of production, but immediately after the peak of production where falling supply meets rising demand. In such a context, the era of depletion is widely thought to have begun already. Applied initially to oil, the logistic approach can shed light on the reserves of other elements.
cumulative production equals the total amount of the resource available, Qtot, and P/Q goes to zero. Yearly primary world production histories for a number of nonrenewable resources have been compiled by the United States Geological Survey.4 These data P(nΔt) = (ΔQ(nΔt)/ Δt) (where n is an integer and Δt is one year) may be analyzed within the logistic model by plotting cumulative production Q(nΔt) on the x-axis and the fractional growth rate P(nΔt)/ Q(nΔt) on the y-axis. Yearly production has been normalized by current (2009) cumulative production to keep the units dimensionless from material to material.
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RESULTS AND DISCUSSION P/Q versus Q plots are given for oil (world and U.S.-only, Figure 1) and for a variety nonrenewable mineral resources (Figure 2). Data for worldwide oil production from 1930 to 2005, shown in Figure 1a were obtained from ref 3., data for USA oil production shown in Figure 1b are taken from ref 5. Data on mineral resources plotted in Figure 2 are taken from ref 4. For the data in ref 4, prehistorical production is taken to be zero. This assumption has negligible effect on cumulative production values greater than 10% of the current cumulative production. Thus the independent variable ranges between 0.1 and 1, i.e., from 10% of the current cumulative production to the current cumulative production (2008−2009 in most cases). As shown in Figure 1, the history of world oil production could be interpreted as passing through an early superexponential phase of growth up to about 1973, followed by a first logistic trend from about 1973 to about 1983 pointed at an apparent Qtot of approximately 0.7−0.8 of current cumulative production (current cumulative production is ∼1000 gigabarrels). This phase is followed by a second logistic trend from the early 1980s to the present, pointing to a second Qtot of approximately twice the current cumulative production.
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METHODS The logistic equation, as applied to resource production, is written
dlnQ (t )/dt = s[1 − (Q (t )/Q tot)]
(1)
where t is time, Q(t) is the cumulative production, Qtot is the total amount of the resource available, and s is a parameter which can be interpreted as the initial rate of production at t = 0. For a nearly infinite resource (Q(t)/Qtot ≪ 1), this equation reduces to the familiar equation for exponential growth. An important idea in eq 1 is to convert the yearly production to a fractional production rate, by dividing the yearly production by the cumulative production. If we let P = dQ/dt eq 1 can be rewritten in the form P/Q = s − (s/Qtot)Q . A plot of P/Q on the y axis versus Q on the x-axis is a straight line with slope −s/ Qtot, y intercept s, and x intercept Qtot.3 It is important to keep in mind that, in this formulation, cumulative production has replaced time as the independent variable. If the production of a given resource is increasing exponentially, a P/Q versus Q plot gives a flat line, indicating that the fractional growth rate is a constant percent per year, independent of cumulative production. If the production is logistic, P/Q starts at some initial rate at Q = 0 and decreases linearly with cumulative production until the resource is exhausted. At this point, © 2012 American Chemical Society
Received: Revised: Accepted: Published: 1903
September 2, 2011 December 12, 2011 January 5, 2012 January 5, 2012 dx.doi.org/10.1021/es203065g | Environ. Sci. Technol. 2012, 46, 1903−1906
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A flexible value of Qtot could be expected for several reasons, the most obvious being an unanticipated “sudden” discovery of fundamentally new types of reserves. Alternatively, an increase in Qtot could be driven by technological improvements in extraction technologies or changes in economic conditions that make resources recoverable at increasingly low concentrations in the earth’s crust. Copper, for example, has continually decreased in grade throughout much of its production history (until at least 1985). During this period, copper shows an approximately exponentially growing production at 3−4% per year since approximately 1940, with a somewhat subtle superexponential trend from 1945 to 1973, a logistic trend from 1973 to 1994, and a flat trend from 1994 onward. There is little evidence, however, of a continuous, technologically driven increase in Qtot . On the other hand, resources transitioning to recyclingdominated production or subject to increasingly strict environmental regulation may shift Qtot (as defined from primary production data, such as shown in Figure 2) to lower values. This may have happened in the case of the highly regulated element mercury, but does not appear to have happened in the case of lead (high secondary production and toxicity) or the toxic elements arsenic and cadmium. Individual assessment of these kinds of effects would have to be considered in more detailed materials flow analysis on a resource-by-resource level.7 The logistic analysis presented here is not meant to replace materials life-cycle analysis, but complements these more detailed studies by emphasizing a simpler, more resource-comprehensive approach. In fact, an important aspect of the Hubbert approach is that it tends to view the multitude of detailed societal and technological perturbations as being distributed on a continuum, buffeting a net result driven toward some inevitable Qtot. Although many strategic resources clearly do appear to exhibit logistic trends during their production histories, these trends have changed to exponential or even superexponential growth over the last 10−20 years. It seems unlikely that this rather pervasive change results from simultaneous innovations in extraction technologies for such disparate materials as Bi, Mo, Mn, Te, Ge, and P; more likely, it indicates a new phase of growth driven by the demands of rapidly growing economies in Asia and South America. But here again, fluctuating geopolitical factors, when viewed from the Hubbert perspective, are supposed to fall on a continuum, just as do influences from technological innovation. After all, the Hubbert model, when applied to oil production in the United States (the canonical success story of the logistic approach, see Figure 1b), passes through World War II, the oil crisis of the early 1970s, and the end of the Cold War, covers the time period between the ENIAC and the Jaguar supercomputers; and spans advances in enhanced oil recovery and drilling technologies without any major discontinuities. Isolated events are sometimes apparent in the mineral resource data. A good example is helium, which shows a clearly discernible transient perturbation due to the 1996 helium privatization act in the United States.7 Data for the mineral resources may indicate some fundamental change, occurring broadly between 1990 and 2000, in how these resources are produced and consumed on a global scale, transcending any geopolitical events or technological advances seen previously in the 20th century. It is notable that the logistic trend for oil production is stable over this time period.
Figure 1. (a) Hubbert-type analysis of world oil production, taken from ref 3, here interpreted as representing three phases of growth with distinct values of Qtot. (b) The same analysis for oil production in the U.S., data taken from ref 5.
Plots for other nonrenewable resources, shown in Figure 2, resemble, in many cases, the one for oil. An initial trend is established pointing toward some apparent Qtot′ which is then replaced by a different trend, pointing toward a new Qtot ≫ Qtot′. Plots made in 1990 for bismuth and phosphorus; 1995 for platinum, germanium, cobalt and tellurium; and 2000 for zirconium, manganese, and molybdenum would have resulted in apparent Qtot values nearly equal to current cumulative production. Subsequently, production of these resources has transitioned to exponential or superexponential growth. Several resources often popularly perceived as exhibiting “peak” or logistic behavior, such as the rare earth elements, lithium, and helium show no evidence for a finite Qtot at any point in their production histories. There is a common misconception that mineral resources are too complex to be analyzed from the point of view of the logistic equation. Nevertheless, Figure 2 shows that logistic-like trends do appear to be commonly established during extended phases of mineral production histories. However, it is equally apparent that these long-term trends can change abruptly. When viewed in the context of multiple resources, the argument for an inevitable logistic production trend for oil, pointing toward 2000 gigabarrels, becomes less convincing. One of the most important practical points of a logistic analysis is that it allows a way of estimating of Qtot which bypasses the fraught “bottom-up” approach of adding up estimated inventories and reserves. In light of the trends established for other resources, it is not prudent to take Figure 1a as definitive evidence against the USGS bottom-up estimate of 3000 gigabarrels.6 Because of the tendency of established trends to change abruptly, the logistic model cannot be used to estimate a defendable Qtot for any of the resources displayed in Figure 2. 1904
dx.doi.org/10.1021/es203065g | Environ. Sci. Technol. 2012, 46, 1903−1906
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Figure 2. Plots of P(t)/Q′(t) (in units of yr−1) versus Q′(t) for the production histories of the resources compiled in ref 4. P(t) is the production per year, and Q′(t) is the dimensionless cumulative production (cumulative production divided by the current cumulative production). REE stands for rare earth elements which are not differentiated in ref 4.
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The implications of this transition are not necessarily optimistic. Although it may be assuasive to see that it is at least possible for a logistic production history to transition to exponential growth (or point toward a larger Qtot), the fact that production of a given resource is growing exponentially does not, of course, imply that the resource is inexhaustible. Moreover, it must be kept in mind that in many cases where logistic production trends have been established, growth rates have been decreasing from 7−10% in the 1960s and 1970s to 3−5% before leveling out to exponential growth. Only for iron (and to a lesser extent, cobalt) have the recent reversals of production declines been large enough to recover earlier growth rates. It seems unlikely that Bi, Mn, P, Mo, Pt, Ti, Zr, and Ge production will ever return to their previously experienced growth rates. If the recent reversals in logistic patterns of mineral production indicate a new phase of industrialization, it will be more constrained than the previous phase, in the sense that it may be difficult to return to resource growth rates of 5−10% per year which were commonly established during the last century.
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AUTHOR INFORMATION
Corresponding Author
*Phone: 607 974 9854; fax: 607 974 3405; e-mail: rustadjr@ corning.com.
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ACKNOWLEDGMENTS The author is grateful to Profs. William Casey and Eldridge Moores of UC Davis, Dr. Les Button of Corning Incorporated, political scientist David Rustad, and two anonymous reviewers for comments on the manuscript.
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REFERENCES
(1) Sznopek, J. L.; Brown, W. M. Materials Flow and Sustainability; Fact Sheet FS-068-98; United States Geological Survey, 1998. (2) Hubbert, M. K. Nuclear Energy and the Fossil Fuels; Publication 95; Shell Development Company, Exploration and Production Research Division: Houston, TX, 1956. (3) Deffeyes, K. S. Beyond Oil; Hill and Wang: New York, 2005. (World production data provided in numerical form by personal communication from Prof. Deffeyes, with an estimate of 17 gigabarrels for cumulative pre-1930 production.) (4) Kelly, T. D.; Matos, G. R. Historical Statistics for Mineral and Material Commodities in the United States; Data Series 1401; United States Geological Survey, 2005. http://minerals.usgs.gov/ds/2005/ 140/. (5) U.S. Energy Information Administration. Petroleum. www.eia. gov/petroleum. (6) U.S. Geological Survey World Energy Assessment Team. U.S. Geological Survey World Petroleum Assessment 2000; USGS Digital DataSeries DDS-60, 2000. (7) Graedel, T. M.; Klee, R. J. Getting serious about sustainability. Environ. Sci. Technol. 2002, 36, 523−529.
ASSOCIATED CONTENT
* Supporting Information S
A .zip archive of the spreadsheets in Microsoft Excel format with numerical values for the data shown in Figures 1 and 2 (along with larger images of each chart). This information is available free of charge via the Internet at http://pubs.acs.org/. 1905
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(8) Helium Privatization Act of 1996. http://www.blm.gov/pgdata/ etc/medialib/blm/nm/programs/0/helium_docs.Par.80129.File.dat/ pl104273.pdf.
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