Sunday, September 26, 2010

Refining the Peak Oil Rosy Scenario Part 2: A trip down memory lane with MK Hubbert

A young Marion King Hubbert attending a technocracy conference cir. 1933—from (image 17 of 18).

Hubbert, was THE pioneering giant that brought attention to peak oil—peak fossil fuels really.  Hubbert recognized that fossil fuels (coal, oil, natural gas) are non-renewing resources, at least on the time scale of human civilization.  Hubbert also recognized that mankind was using these fossil fuels at an exponential rate such that the amounts being used were doubling every few decades.  

Hubbert did his seminal work in the area of peak oil theory in the 1950's and 60's.  He tried to warn America, and the world, about its consequences. Unfortunately for us, he failed, in that the powers that be failed to listen, and now the consequences are right around the corner.

Hubbert's work and predictions were roundly criticized and rejected when they first came out, and still today they are largely ignored by the main stream media and the government, although there are some recent signs of awaking.

How did Hubbert make his estimate in 1956?

In March 1956, Hubbert presented his paper, “NUCLEAR ENERGY AND THE FOSSIL FUELS” at the spring meeting of the Southern District Division of Production American Petroleum Institute held at the Plaza Hotel in San Antonio Texas.  He predicted that the rate of oil production in the USA would peak in 1965.  Almost as an after thought he mentioned as a secondary prediction 1970 as the peak.  He also predicted global peak oil production in 2000. 

How did Hubbert actually arrive at these predictions?  

In the paper Hubbert showed a semi-logarithmic  plot of US crude oil production versus time in years.   

Hubbert commented:

Crude-oil production from 1880 until 1930 increased at the rate of 7.9 percent per year, with the output doubling every 8.7 years.
These facts alone force one to ask how long such rates of growth can be kept up. How many periods of doubling can be sustained before the production rate would reach astronomical magnitudes? That the number must be small can be inferred from the fact that after n doubling periods the production rate will be increased by a factor of 2n. Thus in ten doubling periods the production rate would increase by a thousandfold; in twenty by a millionfold. For example, if at a certain time the production rate were 100 million barrels of oil per year - the U.S. production in 1903 - then in ten doubling periods this would have increased to 100 billion barrels per year. No finite resource can sustain for longer than a brief period such a rate of growth of production; therefore, although production rates tend initially to increase exponentially, physical limits prevent their continuing to do so.
Hubbert well understood what the implications of such exponential growth in the oil production rate meant:
...., petroleum has been produced in the United States since 1859, and by the end of 1955 the cumulative production amounted to about 53 billion barrels. The first half of this required from 1859 to 1939, or 80 years, to be produced; whereas, the second half has been produced during the last 16 years.

To extrapolate this growth curve, Hubbert recognized that the rate of production (P), equals the change in the quantity of oil (dQ) per change in unit of time (dt) is given by the differential equation: 

P = dQ/dt

and, that the total cumulative amount of oil that can be produced (Qmax) is given by the total area (integral) under the curve from a plot of dQ/dt versus t from the beginning of production (t=0) to the end of production (t=¥):
Hubbert showed this relationship in general:

Hubbert then looked for estimates of Qmax, the ultimate amount of recoverable crude oil in the USA, by surveying estimates from a number of expert sources (p. 15-17):
In the case of the United States, Weeks' estimate of 110 billion barrels (based upon production practices of about 1948) was for the land area. The United States Geological Survey (1953) has estimated potential offshore reserves of the United states, based upon the productivity of comparable adjacent land areas, to be ... 15 billion barrels...the California. Division of Mines has estimated the offshore reserves of California to be 4 billion barrels. Combining this with the U.S. Geological Survey estimate for Louisiana and Texas gives ... 20 billion.   The production record of the past two decades, due in part to improved recovery practices, indicates that Week’s figure ... may also be somewhat low.  This has accordingly been increased to 130 billion, giving a total ultimate potential reserve of 150 billion barrels of crude oil for both the land and offshore areas of the United States

Although arrived at independently, this figure is in substantial agreement with Pratt's (1956, p. 94) figure of 170 billion barrels for the total liquid hydrocarbons of the United States. .... As of January 1, 1956, the proved reserves of crude oil were 30.0 billion barrels, while those of total liquid hydrocarbons was 35.4 billion barrels. Applying this ratio to Pratt’s figure of 170 billion barrels of liquid hydrocarbons gives 144 billion barrels of crude oil.
Armed with the above equations, the estimated growth rate in production from his semi-logarithmic plot, and, the estimated total recoverable crude oil (150 billion barrels), Hubbert drew a bell-shape curve that corresponded to these data and then over-laid this onto the existing crude oil production data plus proven reserves data for the USA:

Hubbert summarizes and concludes:  
... shown in Figure 21 a graph of the production up to the present, and two extrapolations into the
future. The unit rectangle in this case represents 25 billion barrels so that if the ultimate potential production is 150 bullion barrels, then the graph can encompass but six rectangles before returning to zero. Since the cumulative production is already a little more than 50 billon barrels, then only four more rectangles are available for future production. Also, since the production rate is still increasing, the ultimate production peak must be greater than the present rate of production and must occur sometime in the future. At the same time it is impossible to delay the peak for more than a few years and still allow for the unavoidable prolonged period of decline due to the slowing rates of extraction form depleting reservoirs.

With due regard for these considerations, it is almost impossible to draw the production curve based upon an assumed ultimate production of 150 billion barrels in any manner differing significantly from that shown in Figure 21, according to which the curve must culminate at about 1965 and then must decline at a rate comparable to its earlier rate of growth.
Almost as an after-thought, it seems to me, Hubbert briefly considers the alternative scenario, represented as the second dashed line in Figure 21 above:
If we suppose the figure of 150 billion barrels to be 50 billion barrels too low - an amount equal to eight East Texas oil fields - then the ultimate potential reserve would be 200 billion barrels. The second of the two extrapolations shown in Figure 21 is based upon this assumption; but it is interesting to note that even then the date of culmination is retarded only until about 1970.
Analogous methods were used to arrive at his estimate of a global peak in oil production in the year 2000.

Hubbert was well aware that improvements in oil recovery techniques could also increase the “known reserves.”  That is, if previously you only could recover 33% of the oil in a well and then a new process allows you to recover 45%, then your known reserves have increased by  36% (i.e., 100x45/33).  Hubbert, however, also recognized that implementation of such “secondary recovery” techniques was very slow and therefore would not substantially affect the peak production date.

Of course, history has shown that oil production in the USA actual reached its maximum in 1970, for which Hubbert is given credit for predicting:

Looking at this paper as a whole, however, I don’t think that Hubbert’s intention really was to predict the exact year of peak oil production, and if anything, that year would have been 1965, not 1970.  Rather, I think that Hubbert was trying to show that, for the then existing exponentially increasing rate of production, and the known reserves, peak oil (and other fossil fuel) production would soon be reached.  Even if the known reserves were off by 50 billion barrels, that would only delay the peak by five years from 1965 to 1970, Hubbert suggested.  It turns out that Hubbert was much closer to the truth that what many gave him credit for back in 1956. 

I mentioned that Hubbert drew a "bell-shaped" curve (Hubbert's Figure 21, shown above) based on the estimate of Qmax, the total recoverable crude that equal 150 billion barrels and knowing the shape of the growth rate in production as well as knowing the boundary conditions: at both t=0 and at t=∞, dQ/dt =0.  That is, at the beginning and end, the production rate is zero.

But exactly what was the form of this bell-shaped curve?  The 1956 article is silent, other than this rather cryptic comment from Hubbert:
With due regard for these considerations, it is almost impossible to draw the production curve based upon an assumed ultimate production of 150 billion barrels in any manner differing significantly from that shown in Figure 21, according to which the curve must culminate at about 1965 and then must decline at a rate comparable to its earlier rate of growth.
Years later in his 1980 presentation, Techniques of prediction as applied to the production of oil and gas (hereinafter "Techniques"), Hubbert also comments about this curve (now Figure 6):
The curves drawn in Figure 6 were not based upon any empirical equations or any assumptions regarding whether they should be symmetrical or asymmetrical; they were simply drawn in accordance with the areal constraints imposed by the estimates, and the necessity that the decline be gradual and asymptotic to zero. The strength of this procedure lies in the insensitivity of its most important deduction, namely the date of the peak-production rate, to errors in the estimate of Q. As 'Figure 6 shows, an increase in the lower estimate of 150 billion barrels by one-third delays the date of peak production by only about 5 years, or to about 1971. If the lower figure were doubled to 300 billion barrels, the date of the peak-production rate would still be delayed only to about 1978. "Techniques" p. 41 and 43
And, in a question period of that same presentation, in response to a question about the assumed symmetry of his bell-shaped curves, Hubbert states
Your statement that all of my curves are symmetric is not entirely correct. I have stated explicitly that the complete-cycle curve of production of an exhaustible resource in a given region has the following essential properties: The rate of production as a function of time begins at zero. It then increases exponentially during a period of development and later exploration and discovery.  Eventually the curve reaches one or more maxima, and finally, as the resource is depleted, the curve goes into a negative-exponential decline back to zero. There is no requirement that such a curve be symmetrical or that it have only a single maximum. In small regions such a curve can be very irregular, but in a large area such as the United States or the world these irregularities tend to smooth out and a curve with only a single principal maximum results. If such curves are also approximately symmetrical it is only because their data make them so.

In my figure of 1956, showing two complete cycles for U.S. crude-oil production, these curves were not derived from any mathematical equation. They were simply tailored by hand subject to the constraints of a negative-exponential decline and a subtended area defined by the prior estimates for the ultimate production. Subject to these constraints, with the same data, I suggest that anyone interested should draw the curves himself. They cannot be very different from those I have shown. "Techniques"  p. 138-139
Despite Hubbert's statements, I think that it pretty obvious that Hubbert did indeed assume a symmetric curve—that is, that the "negative-exponential decline" would mirror the exponential increase during development.  At least that is what his curve in Figure 21 of the 1956 presentation depicts. Indeed, Hubbert assumption is explicit in his statement cited above that:
the curve must culminate at about 1965 and then must decline at a rate comparable to its earlier rate of growth.   
However, one could imagine any number of different shapes on the decline side, such that the area under curve still equals Qmax.  For instance, consider these red and green curves overlayed onto Hubberts plots:

I might not have them scaled properly to give the assumed Qmax of 150 billion barrels, but, I think that they make the point that other shapes of decline curves are indeed possible.   

Perhaps Hubbert would have called these alternatives, "completely irrational to the semi-rational," or, he may have argued that these are not "very different from those I have shown."  We will never know.  Either way, however, from the standpoint of predicting the rate of decline in oil production, after the peak in production is reached, it is good to keep in mind that showing the decline curve as having a mirror-image to the growth curve is just an assumption.  

Indeed, I contend that it is just this kind of assumption that leads to the kind of rosy scenario view of peak oil that I discussed in Part 1.  We need a better model.

1 comment:

  1. Very interesting article, I was wondering about the mathematical form of the curves. I think Hubbert might have made the point that your red and green curves still show approximately the same peak (in time).


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