[Anyone who has any doubts at all about the utter unsustainability of modern world
capitalism and the onset of terminal crisis, should read Albert Bartlett's original
article on the meaning of exponential growth, archived at:
http://www.npg.org/reports/bartlett_index.htm
Below is Bartlett's comments on the 209th anniversary of this classic prediction of
the end of Big Oil.
Mark]
"Forgotten Fundamentals of the Energy Crisis"
by Albert A. Bartlett
University of Colorado at Boulder
Background
Around 1969, college and university students developed a major interest in the
environment and, stimulated by this, I began to realize that neither I nor the
students had a good understanding of the implications of steady growth, and in
particular, of the enormous numbers that could be produced by steady growth in
modest periods of time. On September 19, 1969 I spoke to the students of the
pre-medical honor society on "The Arithmetic of Population Growth." Fortunately I
kept my notes for the talk, because I was invited to speak to other groups, and I
gave the same talk, appropriately revised and enlarged. By the end of 1975 I had
given the talk 30 times using different titles, and I was becoming more interested
in the exponential arithmetic of steady growth. I started writing short numbered
pieces, "The Exponential Function," which were published in The Physics Teacher.
Then the first energy crisis gave a new sense of urgency to the need to help people
to gain a better understanding of the arithmetic of steady growth, and in particular
of the shortening of the life expectancy of a non-renewable resource if one had
steady growth in the rate of consumption of such a resource until the last of the
resource was used.
When I first calculated the Exponential Expiration Time (EET) of U.S. coal for a
particular rate of growth of consumption, using Eq. 6, I used my new hand-held
electronic calculator, and the result was 44 years. This was so short that I
suspected I had made an error in entering the problem. I repeated the calculation a
couple of more times, and got the same 44 years. This convinced me that my new
calculator was flawed, so I got out tables of logarithms and used pencil and paper
to calculate the result, which was 44 years. Only then did I begin to realize the
degree to which the lifetime of a non-renewable resource was shortened by having
steady growth in the rate of consumption of the resource, and how misleading it is
for leaders in business and industry to be advocating growth of rates of consumption
and telling people how long the resource will last "at present rates of
consumption."
This led to the first version of this paper which was presented at an energy
conference at the University of Missouri at Rolla in October 1976, where it appears
in the Proceedings of the Conference. In reading other papers in the Procedings I
came to realize that prominent people in the energy business would sometimes make
statements that struck me as being unrealistic and even outrageous. Many of these
statements were quoted in the version of the paper that is reprinted here, and this
alerted me to the need to watch the public press for more such statements.
Fortunately ( or unfortunately ) the press and prominent people have provided a
steady stream of statements that are illuminating because they reflect an inability
to do arithmetic and / or to understand the energy situation.
As this is written, I have given my talk on "Arithmetic, Population, and Energy"
over 1260 times in 48 of the 50 States in the 28 years since 1969. I wish to
acknowledge many constructive and helpful conversations on these topics I have had
throughout the 20 years with my colleagues in the Department of Physics, and in
particular with Professors Robert Ristinen and Jack Kraushaar, who have written a
successful textbook on energy. (Energy and Problems of a Technical Society, John
Wiley & Sons, New York City, 2nd Ed. 1993)
Reflections on the "Fundamentals" Paper Twenty Years Later
As I read the 1978 paper in 1998, I am pleased to note that the arithmetic that is
the core of the paper remains unchanged, and I feel that there are only a few points
that need correction or updating.
1) When I derived my Eq. 6 in the Appendix, I was unaware that this equation for
the Exponential Expiration Time (EET) had been published earlier by R. T. Robiscoe
(his Eq. 4) in an article, "The Effect of Growth Rate on Conservation of a
Resource." American Journal of Physics, Vol. 41, May 1973, p. 719-720. I apologize
for not having been aware of this earlier derivation and presentation of this
equation.
2) III. The world population was reported in 1975 to be 4 billion people growing
at approximately 1.9 % per year. In 1998 it is now a little under 6 billion
people and the growth rate is reported to be around 1.5 % per year. The decline
in the rate of growth is certainly good news, but the population growth won't stop
until the growth rate has dropped to zero.
3) VI. In 1978 I reported that "We are currently importing one-half of the
petroleum we use." The data now indicate that, except for brief periods, this could
not have been true in 1978. The basis for my statement was a newspaper clipping
that said that the U.S. had experienced, in 1976, the first month in its history in
which more oil was imported than was produced domestically. However, the imported
fraction of the oil consumed in the U.S. has risen, and in early 1995 the news said
that the calendar year 1994 was the first year in our nation's history when we had
to import more oil than we were able to get from our ground ourselves. (Colorado
Daily, February 24, 1995)
4) IX. The paper reported that by 1973 nuclear reactors (fission) supplied
approximately 4.6 % of our national electrical power. By 1998 this had climbed to
approximately 20 % of our electrical power, but no new nuclear power plants have
been installed in the U.S. since the 1970s.
5) A table that I wish I had included in the original paper is one that would give
answers to questions such as, "If a non-renewable resource would last, say 50 years
at present rates of consumption, how long would it last if consumption were to grow
say 4 % per year?" This involves using the formula for the EET in which the
quotient ( R / r0 ) is the number of years the quantity R of the resource would
last at the present rate of consumption, r0 . The results of this simple
calculation are shown in Table I.
TABLE I
Lifetimes of non-renewable resources for different rates of growth of consumption.
Except for the left column, all numbers are lifetimes in years.
0 % 10 30 100 300 1000 3000 10,000
1 % 9.5 26 69 139 240 343 462
2 % 9.1 24 55 97 152 206 265
3 % 8.7 21 46 77 115 150 190
4 % 8.4 20 40 64 93 120 150
5 % 8.1 18 36 56 79 100 124
6 % 7.8 17 32 49 69 87 107
7 % 7.6 16 30 44 61 77 94
8 % 7.3 15 28 40 55 69 84
9 % 7.1 15 26 37 50 62 76
10 % 6.9 14 24 34 46 57 69
Example 1. If a resource would last 300 years at present rates of consumption,
then it would last 49 years if the rate of consumption grew 6 % per year.
Example 2. If a resource would last 18 years at 5 % annual growth in the rate
of consumption, then it would last 30 years at present rates of consumption. (0 %
growth)
Example 3. If a resource would last 55 years at 8 % annual growth in the rate of
consumption, then it would last 115 years at 3 % annual growth rate.
6) In the end of Section VIII of the 1978 paper I quoted Hubbert as writing in 1956
that "the peak of production of petroleum" in the U.S. would be reached between
1966 and 1971. The peak occurred in 1970. Hubbert predicted that "On a world scale
[oil production] will probably pass its climax within the order of half a
century...[2006]" My more recent analysis suggests the year 2004, while Campbell
and Laherrere predict that the world peak will be reached before 2010, (Scientific
American, March 1998, pp. 78-83) Studies by other geologists predict the peak
within the first decade of the next century. Hubbert's analysis appears thus far to
be remarkably good.
7) The "Fundamentals" paper was followed by a paper titled, "Sustained
Availability: A Management Program for Non-Renewable Resources." American Journal
of Physics, Vol. 54, May 1986, pp. 398-402. This paper makes use of the fact that
the integral from zero to infinity of a declining exponential curve is finite.
Thus, if one puts production of a non-renewable resource on a declining exponential
curve, one can always find a rate of decline such that the resource will last
forever. This is called "Sustained Availability," which is somewhat analogous to
"sustained yield" in agriculture. This paper explores the mathematics of the
options that this plan of action can give to a resource-rich nation that wants to
divide its production of a resource between domestic use and exports.
8) Many economists reject this sort of analysis which is based on the assumption
that resources are finite. A colleague in economics read the paper and later told
me that "It is all wrong." When I asked him to point out the specific errors in the
paper, he shook his head, saying, "It is all wrong."
9) The original paper dealt more with resources than with population. I feel that
it is now clear that population growth is the world's most serious problem, and that
the world's most serious population problem is right here in the U.S. The reason for
this is that the average American has something like 30 to 50 times the impact on
world resources as does a person in an underdeveloped country. (A.A. Bartlett,
Wild Earth, Vol. 7, Fall 1997, pp. 88-90)
We have the jurisdiction and the responsibility needed to permit us to address our
U.S. population problem, yet many prefer to focus their attention on the population
problems in other countries. Before we can tell people in other countries that they
must stop their population growth, we must accept the responsibility for working to
stop population growth in the United States, where about half of our population
growth is the excess of births over deaths and the other half is immigration, legal
plus illegal. This leads me to offer the following challenge:
Can you think of any problem, on any scale, From microscopic to global, whose
long-term solution is in any demonstrable way, Aided, assisted, or advanced by
having larger populations At the local level, the state level, the national level,
or globally?
Horror Stories
Here are more recent horror stories to add to those that were recounted in the
original paper.
1) The Rocky Mountain News of October 6, 1993 reported that: Shell Oil Co. said
"... it planned to spend $1.2 billion to develop the largest oil discovery in the
Gulf of Mexico in the past 20 years. The discovery ... has an estimated ultimate
recovery in excess of 700 million barrels of oil and gas." The 700 million barrels
of oil sounds like a lot -- until you note that at that time the U.S. consumption
was 16.6 million barrels / day, so that this "largest oil discovery in the Gulf of
Mexico in the past 20 years" would supply the needs of the U.S. for only 42
days!
2) The headline in the Wall Street Journal for July 18, 1986 proclaimed that "U.S.
Oil Output Tumbled in First Half as Alaska's Production Fell Nearly 8%." In the
body of the story we read that the chief economist for Chevron Corporation observes
that, "The question we can't answer yet is whether this is a new trend or a quirk."
The answer to his question is that it is neither; it is an old trend! It is exactly
what one expects as one goes down the right side of the Hubbert Curve.
3) Another headline on the front page of the Wall Street Journal (April 1, 1997)
said: "Four Decades Later, Oil Field Off Canada is Ready to Produce. Politics,
Money and Nature Put Vast Deposit on Ice; Now It Will Last 50 Years: Shot in the
Arm for U.S." In the body of the story we read that:
The Hibernia field, one of the largest oil discoveries in North American in decades,
should deliver its first oil by year end. At least 20 more fields may follow,
offering well over one billion barrels of high-quality crude and promising that a
steady flow of oil will be just a quick tanker-run away from the energy-thirsty East
Coast.
Total U.S. oil consumption in 1996 was about 18 million barrels a day. Do the
long division and one sees that the estimated "one billion barrels of high-quality
crude" will supply the needs of the U.S. for just 56 days! This should be compared
with the "50 Years" in the headline.
4) In the Prime Time Monthly Magazine (San Francisco, September 1995) we find an
article, "Horses Need Corn" by the famous radio news broadcaster Paul Harvey. He
emphasizes the opportunity we have to make ethanol from corn grown in the U.S. and
then to use the ethanol as a fuel for our cars and trucks: "Today, ethanol
production displaces over 43.5 million barrels of imported oil annually, reducing
the U.S. trade balance by $645 million. . . For as far ahead as we can see, the
only inexhaustible feed for our high horsepower vehicles is corn."
There are two problems with this:
A) The 43.5 million barrels must be compared with the annual consumption of motor
gasoline in the U.S. In 1994 we consumed 4.17 billion barrels of motor vehicle
gasoline. (Annual Energy Review, 1994, DOE / EIA 0384(94), p. 159) The ethanol
production is seen to be approximately 1 % of the annual consumption of gasoline
by vehicles in the U.S. So one would have to multiply corn production by a factor
of about 100 just to make the numbers match. An increase of this magnitude in the
farm acreage devoted to the production of corn for ethanol would have profound
negative dietary consequences.
B) It takes energy (generally diesel fuel) to plow the ground, to fertilize the
ground, to plant the corn, to take care of the corn, to harvest the corn, and then
more energy is needed to distill the corn to get ethanol. So it turns out that in
the conventional production of ethanol, the finished gallon of ethanol contains less
energy than was used to produce it ! It's an energy loser! The net energy of this
"energy source" is negative!
5) The Clinton administration, in a "Draft Comprehensive National Energy Strategy"
(February 1998) talks about America's oil as being "abundant," (pg. 4) and it
advocates "promoting increased domestic oil ... production" (pg. 2) to reverse this
downward trend in U.S. oil production. The peak of the Hubbert Curve of oil
production in the U.S. was reached in 1970 and we are now well down the right side
of the Curve. The Draft Strategy calls for "stabilization of domestic oil
production" (pg. 12) which is explained in "Strategy 1" (pg. 12) "By 2005, first
stop and then reverse the decline in domestic oil production." The Hubbert Curve
rises and falls in a manner like that of a Gaussian Error Curve, and once one is
over the peak, one can put bumps on the downhill side, but except for such "noise,"
the trend after the peak is always downhill. A large national effort might reverse
the decline in U.S. oil production for a year or two, but it hardly plausible to
propose to "stabilize" domestic oil production for any extended period of time. It
almost seems as though the U.S. Department of Energy has not studied the works of
Hubbert, Campbell & Laherrere, Ivanhoe, Edwards, Masters and other prominent
petroleum geologists.
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