How General is the Hubbert Curve?
The Hubbert model of crude oil production has been shown to be able to describe several regional cases, but it is not yet generally accepted as valid for the worldwide case of oil production. The present paper shows that the model can be used to describe gneral cases in which a resource is depleted faster than it can be replaced, that is the case of biological resources. In some cases, historical fishery data can be considered relevant in order to understand the present price trends of crude oil.
By Ugo Bardi and Leigh Yaxley
This paper has been published in the proceedings of the 4th ASPO workshop, Lisbon 2005
HOW GENERAL IS THE HUBBERT CURVE? THE CASE OF FISHERIES
Ugo Bardi(1) and Leigh Yaxley(2)
(1) Association for the study of Peak Oil and Gas (ASPO) and
Dipartimento di Chimica, Università di Firenze,
(2) Society of Petroleum Engineers
Kuala Lumpur 50480, Malaysia,
The Hubbert model of crude oil production has been shown to be able to describe several regional cases, but it is not yet generally accepted as valid for the worldwide case of oil production. The present paper shows that the model can be used to describe gneral cases in which a resource is depleted faster than it can be replaced, that is the case of biological resources. In some cases, historical fishery data can be considered relevant in order to understand the present price trends of crude oil.
I. INTRODUCTION
In the 1950s, M. K. Hubbert was the first to use a symmetric bell shaped curve to fit the production trends of crude oil. The method turned out to be successful in describing the production of the 48 lower US states and in predicting its peak year (1971). There are several other regions of the world where oil production also followed a single bell shaped curve and others where a number of bell curves can be identified (1). Hubbert himself proposed that a single, symmetric bell curve could describe the global production of crude oil.
If the shape of the global oil production curve will follow Hubbert’s model, that is it will be bell shaped and symmetric, the consequences on the global economy are potentially enormous. However, doubts have been cast on the general validity of the Hubbert model (see, e.g. (2)).
As shown in (3,4) the Hubbert model can be derived from general assumptions. Nevertheless, the confidence placed on the use of a specific model ultimately derives from its successful use in describing historical cases. There is no doubt that Hubbert curves describe regional cases for crude oil and of other mineral resources, but there are no cases, so far, of a mineral resource terminally depleted worldwide.
However, since the Hubbert model is of very general applicability, it should be valid not only for mineral resources but for all cases in which a resource is depleted much faster than it can be replaced. This is the case of some biological resources, e.g. fisheries, where several examples of total, or nearly total, depletion of the resource are known in history. Cases which are especially interesting are those where a) a resource went through a complete depletion cycle b) the market for that resource was global, or at least limited to a closed economic region and c) there was no equivalent resource able to substitute the depleted one. Such cases provide a good model for the present crude oil situation. From these cases we can also obain relevant information about price trends. We show here that there are at least two historical cases (whale oil and caviar) for which price data exist. Prices show a tendency to exponential growth after the Hubbert peak.
II. HISTORICAL CASES
A complete Hubbert cycle can be observed for whale hunting in 19th century (data from ref. 5). (fig. 1).
Fig. 1 Production of whale oil and whale bone (baleen)
As reported in more detail in (6) the production curves for both whale oil and “whale bone” (or “baleen”) followed a symmetric bell shaped curve The market of whale oil was global already in 19th century and its decline was not caused, at least at the beginning, by shifting to a different resource. Here, the data have been fitted with a simple Gaussian curve which was shown to provide a good approximation for the Hubbert model (3)
The price data for whale oil (corrected for inflation (7)) are reported in fig 2 as a function of depletion. The data show a considerable upwards jump for ca. 60% depletion, i.e. some time after the Hubbert peak.
Fig 2: Whale oil price versus depletion
Another clear-cut case, similar to that of whales, is that of the Caspian sturgeon, the source of caviar. The data for worldwide sturgeon landings (8) are shown fig. 3.
Fig 3. Prices of caviar and sturgeon landings
The production data have been fitted with a Gaussian function. Inflaction corrected prices (7) show a rising exponential growth starting after the Hubbert peak. Whereas the start of the rise agrees with the whale case, the price plateau observed for whale oil is not observed for caviar. The difference can be explained considering that the plateau for whale oil prices may be due to the development of crude oil as a replacement for whale oil and its marketing some 15 years after the peak of whale oil production.
Examining fishery data, several other cases of bell shaped production curves can be found, e.g. in the fishery data of the FAO (www.fao.org). Even the the global fisheries production may be following a bell shaped curve which may have peaked in the early 1990s (9).
III. CONCLUSION
The comparison of the cases of fisheries and of mineral extraction tells us that the human pressure on the environment is causing a wide range of resources to go through a depletion cycle which follows Hubbert’s law. The case of some fisheries, sturgeon and 19th century whales, may be especially relevant for the comparison with conventional crude oil extraction. In all these cases we have a non-replaceable, or at least not easily replaceable, resource being depleted worldwide. If whale oil and caviar are a representative example of price trends for this kind of resources, we may expect the price of conventional crude oil to start an exponentially rising trend in the vicinity, or slighlty after, the Hubbert peak. The fact that such an exponential rise may have already started is an indication that we may be close, or have already passed the peak
REFERENCES
[1] Campbell, C. 2004, The Essence of Oil and Gas Depletion Multi Science Publishing Company Ltd
[2] Lynch, M. C. 2004, http://www.gasresources.net/Lynch(Hubbert-Deffeyes).htm
[3] Bardi, U. 2005. Energy Policy, Volume 33, P. 53-61
[4] Reynolds, D.B., 1999. Ecological Economics 31, 155.
Campbell, C. 2004, The Essence of Oil and Gas Depletion Multi Science Publishing Company Ltd
[5] A. Starbuck, History of the American Whale Fishery, Seacaucus, N.J. 1878, reprinted 1989
[6] Bardi, U 2004
http://www.aspoitalia.net/aspoenglish/documents/bardi/whaleoil/whalefishing2004.pdf
[7] Sahr, 2002, http://oregonstate.edu/dept/pol_sci/fac/sahr/sahr.htm
[8] Catarci, C. 2004, FAO Fisheries Circular No. 990 http://www.fao.org/documents/show_cdr.asp?url_file=/DOCREP/006/Y5261E/Y5261E00.HTM
[9] Pauly, D., Alder, J., Bennett, E., Christensen V., Tyedmers,P., Watson, R. 2003, “The Future for Fisheries”, Science, 21 november, vol 302