Reflections on the ASPO-USA Logo

By Al Bartlett

The ASPO-USA annual meeting in Denver in October 2009 was memorable for me. The meeting gave me the opportunity to meet old friends and to make a number of new friends. But most important were the many high-quality presentations of data and of interpretations. However, I did have a few idle moments and I found myself looking at the logo for ASPO-USA which was prominently displayed in a large poster on the stage of the ballroom. And I was thinking about what the logo means. The logo pictures the Earth as a transparent spherical tank of petroleum that is half full. There is a drilling rig at the Earth’s north pole with a pipe going down into the petroleum that fills the southern hemisphere of the half-full Earth.

Questions Come to Mind

This led me to think of an example that I used to use in my talk, “Arithmetic, Population and Energy.” Suppose the Earth is a spherical tank filled with petroleum;

1) How long would this quantity of petroleum last “at current rates of production?”
2) How long would this quantity of petroleum last if, starting with today’s production rate, we have a constant 7% annual growth in production until all the petroleum in the spherical tank
was consumed? (It’s a matter of record that the average growth rate of world petroleum production for one hundred years from about 1870 to 1970 was approximately 7% per year.)
3) What time is it when the petroleum reserves are half consumed, as shown in the logo?

Data

Here are the data that are used to make the estimates.

Volume of the Earth; = 1.083 10(21) meters cubed

= 2.862 10(23) gallons (less than half of Avogadro’s Number; remember your chemistry?)
= 6.814 10(21) barrels (42 gallons each).

This volume is 6.814 with the decimal point moved 21 places to the right, or 6,814,000,000,000,000,000,000 barrels!

Current rate of world petroleum production, approximately:

= 80 10(6) barrels per day (mb/d)
= 80 million barrels per day)
= 29.2 10(9) barrels per year (bb/y)

Answers to the Questions

The answer to Question #1 is found easily:
Expiration Time = 6.814 10(21) barrels / 29.2 10(9) barrels per year

= 2.33 10(11) years = 233 billion years!

This is about sixteen times as long as the estimated age of the universe!

The answer to Question #2 requires us to use a formula for the life expectancy of a resource when production grows steadily until the last bit of the resource is produced.

(It is completely unrealistic to assume that you could have steady growth in the rate of production of a resource until the last bit of the resource was produced, after which the rate of production would fall suddenly to zero, so why bother with the calculation? The central philosophy of the economies of developed nations, in particular of the United States, is to achieve the impossible; namely to have steady growth forever, so we need to know where steady growth would lead us. The Hubbert Curve with the rate of production rising to a peak and then falling to zero is a much more realistic assumption for the path of production vs. time.)

(I won’t bother you here with the derivation of the following equation for the expiration time, T(E) of a finite resource when production is growing steadily at some rate such as 7% per year.)

T(E) = (1/k) ln[(kR/r) + 1]

Where T(E) is the expiration time in years,
k is the percent growth per year divided by 100;

(For 7% per year, k =0.07 per year.)
ln[ ] is the natural logarithm of the quantity in brackets
R is the size of the presently remaining resource in barrels
r is the current rate of production of the resource in barrels per year

We note that these calculations are not difficult. They are done with a simple hand-held scientific calculator costing less than $20.

Let’s introduce T(P) as the number of years the resource would last “at present rates of production” which is R/r = T(P), so our equation above becomes:T(E) = (1/k) ln[(k x T(P)) +1]

Using the given numbers for a spherical Earth full of oil,

T(E) = (1/0.07) ln[(0.07 x 2.33 10(11)) +1]
T(E) = 336 years!

The a spherical tank of oil the size of the Earth would last about 233 billion years “at present rates of consumption” or about 336 years if consumption grew steadily 7% per year from its present rate until all of the resource was consumed!

Let’s look at a less extreme example. Suppose a resource would last 90 years “at present rates of production;” T(P) = 90 years. Then with 7% annual growth in production the resource would last;

T(E) = (1/0.07) ln[ (0.07 x 90) + 1] = 28.4 years

Both examples are unrealistic because they assume that one could have steady growth in the rate of production until the last bit of the resource was produced. This never happens.
Again, we can ask, why bother with such unrealistic calculations? It is common to hear journalists and others tell people that we have enough petroleum to last for 40 years “at present rates of production.” This datum is often interpreted to mean that we don’t have to worry about running out for 40 years. At the same time that we hear how long a resource will last “at present rates of production” we are hearing learned non-scientists telling us that we have to have growth in the rates of production in order to meet the growing demand. As is demonstrated in these two examples, the growth will significantly shorten the calculated life-expectancy of the resource.

These two examples are dramatic demonstrations of the unrecognized conflict between the life expectancy “at present rates of production” and the goals of our society to have steady continuous growth—forever.

The third question refers to the example of the bacteria in a bottle. Bacteria grow by doubling; one bacterium divides to become two, the two divide to become four, the four become eight, sixteen, etc. Suppose you had bacteria that doubled this way every minute. Suppose you put one of these bacteria in an empty bottle at 11:00 AM and then observed that the bottle was full at 12:00 noon. Now here’s our case of ordinary steady growth (they double every minute, so we are observing a steady growth rate of 100% per minute).

This tape can be played forward or backward. If the bottle is full at 12:00 noon and you take out half of the remaining objects every minute, the numbers are the same as with growing bacteria, doubling every minute until they fill the bottle.

Question: At what time was the bottle half full?
Answer: 11:59 AM, because they double every minute.

Conclusion

So when we see the ASPO-USA logo with the spherical earth half full of petroleum, the time of this snapshot is 11:59; one minute to twelve or one doubling time away from the production of the last bit of the resource.

The ASPO-USA logo is perhaps designed to represent the fact that, world-wide, we have produced approximately a trillion barrels of oil and the remaining reserve is approximately another trillion barrels of oil. This is a situation where we have produced half of the resource (or when the bottle is half full), the time is one minute before 12:00 noon!”

That’s the time depicted in the ASPO-USA logo. There will be a quiz over this material at the next meeting. (I’m just kidding.)

Dr. Albert A. Bartlett, professor emeritus of physics at the University of Colorado in Boulder, has delivered versions of his famous talk—“Forgotten Fundamentals of the Energy Crisis”—to 1780 audiences world-wide during the last 40 years. Albert.Bartlett@Colorado.EDU

(Note: Commentaries do not necessarily represent ASPO-USA’s positions; they are personal statements and observations by informed commentators.)