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Clarifying the Hubbert model

The rise in oil prices observed in 2004 has given new impetus to the debate on the availability of crude oil in the future. In particular, much of the discussion has been centered on the validity of the “Hubbert” model which assumes that global oil production will follow a bell shaped curve. A related concept is that of “Peak Oil,” a term which indicates the moment in which worldwide production will peak, afterwards to start an irreversible decline.

According to some interpretations, the recent price increases are a confirmation of the correctness of the Hubbert approach and an indication that the oil peak may be very close in time or even that it may already have taken place. Others have hotly contested this interpretation. In the debate, those who favor the Hubbert model are often branded as “pessimists” and even “catastrophists”.

By the same approach, those who disparage the Hubbert approach should be labeled as “abundantists” or “cornucopians”. Name calling, however, doesn’t solve the question of whether we are facing an irreversible decline in oil production in the near future.

The debate has often been based on partial or wrong interpretations of what is exactly the Hubbert model and what it can be used for. Before engaging in the debate, therefore, we should define what we are talking about; namely:

1. What we are trying to predict

2. How are we going to predict it

3. What is the reliability of the prediction

4. What are the consequences

1st point: What we are trying to predict. What we should be most worried about in this historical phase is the availability of cheap liquid fuels, mainly to beused for transportation. Other fossil resources, for instance natural gas and coal, may become in scarce supply in the future, but not in the short term. For liquid fuels, the definition of “cheap” is fundamental and it focuses our attention on “conventional oil” defined as a liquid which can be extracted from wells.

There are, of course, other resources out of which it is possible to extract or create liquid fuels (biomass, tar sands, shales, etc.) but this can’t be done cheaply for good physical reasons. So, it is very important to predict the availability of crude oil because a world without cheap liquid fuels would be much different than the one we are used to.

2nd point. How are we going to make the prediction. There are various ways in which it is possible to say something about the future availability of a non renewable resource. Some are extremely rough, such as the “R/P ratio”, that is the ratio of reserves to production. Nowadays, the R/P ratio for crude oil corresponds to about 40 years at the present rate of production. However, since production will be anything but constant in the future, the R/P ratio is basically useless as a forecasting tool.

Another model worth a quick mention is the classic “Hotelling Rule” which, however, has never been reported to be able to predict a historical case of production of a non renewable resource. Finally, we can mention the approach used by some economists which consists in calculating the future demand of oil and then assuming that production will be always able to match it. This approach is so obviously wrong that it doesn’t even deserve a comment.

The Hubbert model appears to be the only one which provides a structured and complete approach to forecasting the production of crude oil. It is part of the general family of models which go under the name of “Logistic”. Logistic modeling is a well known forecasting system, commonly used and reasonably effective.

In the specific case of crude oil extraction, the Hubbert model can be seen as either an empirical approach based on the observation of historical cases or as being based on some specific assumptions, that is:
1) The resource exists in a limited amount and it cannot be recycled
2) The cost of extraction is variable (e.g. because of scale factors)
3) Cheap resources will be extracted first

Given these assumptions, there are several ways to implement the Hubbert model, but the results is always a “bell shaped” production curve which goes through a maximum (the “Hubbert peak”). The curve does not have to be perfectly symmetric but it is approximately so for reasonable assumptions of the parameters. In most cases the curve is fitted to the experimental data using the “Ultimate Recoverable Resources” (URRs) as a parameter for the fitting.

This is not strictly necessary, however, and the historical production data can be fitted with similar results to a theoretical model (the Bass equation, for instance) without the need of knowing the URRs. In most cases we obtain nearly symmetric curves which go through a maximum sometime within the first decade of the 21st century. After that, we have an irreversible decline.

3rd point: reliability of the prediction. Hubbert’s model is robust (that is, it needs a limited number of parameters) and has a good predicting capability since it has been shown to be able to describe a number of historical cases. Still, it has limits.

1. The model works best for a free market situation, that is that the economic operators will extract the resource in such a way to maximize their profits. If extraction is managed by governments and affected by ideological factors, then Hubbert may not be a good model at all.

2. The model is approximate. It can’t predict oscillations due to market factors, wars, catastrophes, etc. It does predict, however, that if production strays away from the predicted curve, it will tend to return to it. This is what seems to have happened, for instance, with the oil crisis of 1973-1984.

3. The model is good for long term predictions only. It can’t predict next month’s production, and not even next year’s production. Crude oil started to be extracted about 150 years ago and it is likely that it will continue to be extracted for comparable times. Hubbert’s model describes the whole extraction cycle, but with a “resolution” which has to be considered of at least a few years.

4th point: consequences. Predicting the future is difficult and very often the predictions turn out to be wrong. Still, forecasting is done all the time and we need it in order to try to be prepared for what the future has in store for us. With all the limits inherent to forecasting, Hubbert’s model is the best we have to try to predict what will be the future availability of a critical resource: crude oil.

The prediction tells us it is going to be increasingly difficult for production to match demand in the near future and that in a few years we may be entering a phase of irreversible decline of oil production.

Many people have reacted to these predictions in manners which often can be understood only as the result of emotional factors. Some people have developed an apocalyptic interpretation of the production peak which is assumed to bring the total collapse of society (this is sometimes called the “dieoff” scenario). The consequent suggested course of action is “run for your life” e.g. stockpile food and weapons and retire on top of some remote mountain.

On the opposite side, some people tend to ignore or deny these prediction. By far and large, this attitude seems to be just a refusal to even consider the matter or, sometimes, it can be expressed as “I never heard about this Hubbert model, therefore it must be wrong.”

Occasionally, the opposition to Hubbert is more articulate and it may take two forms: 1) Hubbert is basically right, but the actual resources are underestimated; hence the peak is far away in time or 2) Hubbert is just a wrong model and there never will be a peak nor a decline. In the latter case, it doesn’t appear that these critics are able to propose serious alternative models. In all cases, the consequence of the denial of the prediction is that there is nothing to worry about. The suggested course of action is, therefore, “do nothing”.

Both these course of actions, “run for your life” and “do nothing” are the result of an emotional response and don’t represent answers to what appears more and more a real and pressing problem. The predictions obtained from the Hubbert model may not be perfect, but we ignore them at our risk and peril.

If there is no proof that the recent rises in oil prices are an indication that the peak is here, they are nevertheless worrisome considering that many past predictions based on the Hubbert model had predicted just that. If the global peak is really close in time, we are going to see the irreversible decline of the production of crude oil which will become steep a few years after the peak.

Eventually there is simple consequence of this analysis: we have to prepare the transition from crude oil to different, non fossil sources. Right now there is no energy source of price comparable to that of oil and usable for transportation. So, we should start now working on developing technological solutions. If we wait for the decline to start, the dwindling resources might make the problem much more difficult and perhaps unsolvable.

Editorial Notes: Original title: "Peak oil 2004. Run for your life or do nothing?". -LJ

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