"Forgotten Fundamentals of the Energy Crisis"

by Albert A. Bartlett

University of Colorado at Boulder


The question of how long our resources will last is perhaps the most important question that can be asked in a modern industrial society.  Dr. M. King Hubbert, a geophysicist now retired from the United States Geological Survey, is a world authority on the estimation of energy resources and on the prediction of their patterns of discovery and depletion.  Many of the data used here come from Hubbert's papers.7 - 10   Several of the figures in this paper are redrawn from figures in his papers.  These papers are required reading for anyone who wishes to understand the fundamentals and many of the details of the problem. 

Table IV

United States crude oil (lower 48 states).

Ultimate total production (Ref. 7)         190 
Produced to 1972                           96.6 
Percent of ultimate total production  
produced to 1972 (Ref.7)                   50.8% 
Annual production rate 1970                3.29 

Units are 109 barrels 

(1 barrel  =  42 U.S. gal.  =  158.98 L).


Let us examine the situation in regard to production of domestic crude oil in the U.S. Table IV gives the relevant data.  Note that since one-half of our domestic petroleum has already been consumed, the "petroleum time" in the U.S. is 1 minute before noon!  Figure 1 shows the historical trend in domestic production (consumption) of crude oil.  Note that from 1870 to about 1930 the rate of production of domestic crude oil increased exponentially at a rate of  8.27 % / yr  with a doubling time of 8.4 yr.  If the growth in the rate of production stopped and the rate of production was held constant at the 1970 rate, the remaining U.S. oil would last only  (190 - 96.6) / 3.29  =  28 yr!  We are currently importing one-half of the petroleum we use.  If these imports were completely cut off and if there was no growth in the rate of domestic consumption above the 1970 rate, our domestic petroleum reserves would last only 14 yr!  The vast shale oil deposits of Colorado and Wyoming represent an enormous resource.  Hubbert reports that the oil recoverable under 1965 techniques is  80 x 109  barrels, and he quotes other higher estimates.  In the preparation of Table V, the figure  103.4 x 109  barrels was used as the estimate of U.S. shale oil so that the reserves used in the calculation of column 4 would be twice those that were used in the calculation of column 3.  This table makes it clear that when consumption is rising exponentially, a doubling of the remaining resource results in only a small increase in the life expectancy of the resource. 

Figure 1. History of U.S. crude oil production (semilogarithmic scale). 

Redrawn from Hubbert's Figure 12, Reference 7.


A reporter from CBS News, speaking about oil shale on a three-hour television special feature on energy (August 31, 1977) said, "Most experts estimate that oil shale deposits like these near Rifle, Colorado, could provide more than a 100-yr supply."  This statement should be compared with the figures given in column 4 of Table V.  This comparison will serve to introduce the reader to the disturbing divergence between reassuring statements by authoritative sources and the results of simple calculations. 

Anyone who wishes to talk about energy self-sufficiency for the United States (Project Independence) must understand Table V and the simple exponential calculations upon which it is based.

Table V.

Exponential expiration time (EET) in years of various estimates of U.S. oil reserves for different rates of growth of annual production.  Units are 109 barrels.  This table is prepared by using Eq. (6) with  r0  =  3.29  X  109  barrels/yr.  Note that this is domestic production which is only about one half of domestic consumption!  Column 1 is the percent annual growth rate.  Column 2 is the lifetime (EET) of the resource which is calculated using  R  =  190  -  96.6  =  93.4  as the estimated oil remaining in the lower 48 states.  Column 3 is the lifetime (EET) calculated  R  =  93.4  +  10  to include the Alaskan oil.  Column 4 is the lifetime (EET) calculated using  R  =  93.4  +  10  +  103.4  =  206.8  to include Alaskan oil and a hypothetical estimate of U.S. oil shale. 

  Col.1(%)     Col.2(yr)   Col.3(yr)    Col.4(yr) 

  Zero          28.4        31.4         62.8 
  1%            25.0        27.3         48.8 
  2%            22.5        24.4         40.7 
  3%            20.5        22.1         35.3 
  4%            19.0        20.4         31.4 
  5%            17.7        18.9         28.4 
  6%            16.6        17.7         26.0 
  7%            15.6        16.6         24.1 
  8%            14.8        15.7         22.4 
  9%            14.1        14.9         21.1 
  10%           13.4        14.2         19.9


Fig. 2.  History of world crude  
oil production  
(semilogarithmic scale). 

Redrawn from Hubbert's Figure 6, Reference 7.

Table VI gives statistics on world production of crude oil.  Figure 2 shows the historical trend in world crude oil production.  Note that from 1890 to 1970 the production grew at a rate of  7.04 % / yr, with a doubling time of 9.8 yr.  It is easy to calculate that the world reserves of crude oil would last 101 yr if the growth in annual production was halted and production in the future was held constant at the 1970 level.  Table VII shows the life expectancy (EET) of world crude oil reserves for various rates of growth of production and shows the amount by which the life expectancy is extended if one adds world deposits of oil shale.  Column 4 is based on the assumption that the available shale oil is four times as large as the value reported by Hubbert.  Note again that the effect of this very large hypothetical increase in the resource is very small.  Figure 3 shows a dramatic graphical model from Mario Iona that can be used to represent this growth.11  When consumption grows  7 % / yr  the consumption in any decade is approximately equal to the sum of all previous consumption as can be seen by the areas representing consumption in successive decades.  The rectangle ABDC represents all the known oil, including all that has been used in the past, and the rectangle CDFE represents the new discoveries that must be made if we wish the  7 % / year  growth to continue one decade, from the year 2000 to 2010!  

Table VI. 

World crude oil data. Units are 109 barrels.

Ultimate total production (Ref.7)        1952 
Produced to 1972                         261 
Percent of total production produced  
to 1972 (Ref. 7)                         13.4 % 
Annual Production rate 1970              16.7 

Note that a little more than 1/8 of the world's oil has been consumed.  The "world petroleum time" is between 2 and 3 min before noon, i.e. we are between 2 and 3 doubling times from the expiration of the resource.

From these calculations we can draw a general conclusion of great importance.  When we are dealing with exponential growth we do not need to have an accurate estimate of the size of a resource in order to make a reliable estimate of how long the resource will last. 

Table VII. 

Life expectancy in years of various estimates of world oil reserves for different rates of growth of annual production.  Units are 109 barrels.  This table is prepared by using Eq. (6) with  r0  =  16.7  X  109  barrels / yr.  Column 1 is the percent annual growth rate of production.  Column 2 is the EET of the resource calculated using  r  =  1691  as the estimate of the amount of the remaining oil.  Column 3 is the EET calculated using  R  =  1691  +  190  =  1881  representing crude oil plus oil shale.  Column 4 is the EET calculated using  R  =  1691  +  4 (190)  =  2451  which assumes that the amount of shale oil is four times the amount which is known now.

  Col. 1(yr)    Col. 2(yr)    Col. 3(yr)    Col. 4(yr) 

  Zero           101            113            147  
  1%             69.9           75.4           90.3 
  2%             55.3           59.0           68.5 
  3%             46.5           49.2           56.2 
  4%             40.5           42.6           48.2 
  5%             36.0           37.8           42.4 
  6%             32.6           34.1           38.0 
  7%             29.8           31.2           34.6 
  8%             27.6           28.8           31.8 
  9%             25.7           26.8           29.5 
 10%             24.1           25.1           27.5


A friend recently tried to reassure me by asserting that there remained undiscovered under our country at least as much oil as all we have ever used.  Since it has been about 120 yr since the first discovery of oil in this country, he was sure that the undiscovered oil would be sufficient for another 120 yr.  I had no success in convincing him that if such oil was found it would be sufficient only for one doubling time or about a decade. 


As the reader ponders the seriousness of the situation and asks, "What will life be like without petroleum?" the thought arises of heating homes electrically or with solar power and of traveling in electric cars.  A far more fundamental problem becomes apparent when one recognizes that modern agriculture is based on petroleum-powered machinery and on petroleum-based fertilizers.  This is reflected in a definition of modern agriculture: "Modern agriculture is the use of land to convert petroleum into food." 

Item: We have now reached the point in U.S. agriculture where we use 80 gallons of gasoline or its equivalent to raise an acre of corn, but only nine hours of human labor per crop acre for the average of all types of produce.12 

Think for a moment of the effect of petroleum on American life.  Petroleum has made it possible for American farms to be operated by only a tiny fraction of our population; only 1 American in 26 lived on a farm in 1976.  The people thus displaced from our farms by petroleum-based mechanization have migrated to the cities where our ways of life are critically dependent on petroleum.  The farms without the large number of people to do the work are also critically dependent on petroleum-based mechanization.  The approaching exhaustion of the domestic reserves of petroleum and the rapid depletion of world reserves will have a profound effect on Americans in the cities and on the farms.  It is clear that agriculture as we know it will experience major changes within the life expectancy of most of us, and with these changes could come a major further deterioration of world-wide levels of nutrition.  The doubling time (36 - 42 yr) of world population (depending on whether the annual growth rate is 1.9 % or 1.64 %) means that we have this period of time in which we must double world food production if we wish to do no better than hold constant the fraction of the world population that is starving.  This would mean that the number starving at the end of the doubling time would be twice the number that are starving today.  This was put into bold relief by David Pimentel of Cornell University in an invited paper at the 1977 annual meeting of AAPT-APS (Chicago, 1977):  

    As a result of overpopulation and resource limitations, the world is fast losing its capacity to feed itself... More alarming is the fact that while the world population doubled its numbers in about 30 years the world doubled its energy consumption within the past decade.  Moreover, the use of energy in food production has been increasing faster than its use in many other sectors of the economy. 

It is possible to calculate an absolute upper limit to the amount of crude oil the earth could contain.  We simply assert that the volume of petroleum in the earth cannot be larger than the volume of the earth.  The volume of the earth is  6.81 x 1021 barrels, which would last for  4.1  x  1011 yr if the 1970 rate of consumption of oil held constant with no growth.  The use of Eq. (6) shows that if the rate of consumption of petroleum continued on the growth curve of  7.04 % / yr  of Fig. 2, this earth full of oil will last only 342 yr! 

It has frequently been suggested that coal will answer the U.S. and world energy needs for a long period in the future.  What are the facts? 

Table VIII. 

United States coal resource. 

Ultimate total production (Ref. 7) 
       High estimate                             1486 
       Low estimate                              390 
Produced through 1972  
       (My estimate from Hubbert's Fig. 22)      50 
Percent of ultimate production produced  
through 1972  
Percent of high estimate                         3% 
Percent of low estimate                          13% 
Coal resource remaining  
        High estimate                            1436 
        Low estimate                             340 
Annual production rate, 1972                     0.5 
Rate of export of coal, 1974                     0.06 
Annual production rate, 1974                     0.6 
Annual production rate, 1976                     0.665
Units are 109 metric tons.


Table VIII shows data on U.S. coal production that are taken from several sources. Figure 4 shows the history of coal production in the U.S.  Note that from 1860 to 1910, U.S. coal production grew exponentially at  6.69 % / yr  (T2  =  10.4 yr).  The production then leveled off at  0.5 x 109 tons / yr which held approximately constant until 1972 whereupon the rate started to rise steadily.  Coal consumption remained level for 60 yr because our growing energy demands were met by petroleum and natural gas.  In early 1976 the annual coal production goals of the U.S. government were 1.3 billion tons for 1980 and 2.1 billion tons for 1985.  The 1976 production is now reported to have been 0.665 billion tons and the current goal is to raise annual production to a billion tons by 1985.13  From these data we can see that the Ford administration's goals called for coal production to increase on the order of  10 % / yr  while the Carter administration is speaking of growth of production of approximately  5 % / yr. 

Fig. 4.  History of U.S. coal production (semilogarithmic scale).  Redrawn from Hubbert's Fig. 10, Ref. 7.  In the upper right, the crosses in the steep dashed curve show the coal production goals of the Ford Administration, and the circles in the lower dashed curve show the production goals of the Carter Administration.  From the close of the American Civil War to about the year 1910, coal production grew at a steady rate of 6.69% / yr.  If this growth rate had continued undiminished after 1910, the small estimate of the size of U.S. coal reserves would have been consumed by about 1967 and the larger estimate of the size of the reserves would have been consumed by about the year 1990! 

Table IX shows the expiration times (EET) of the high and the low estimates of U.S. coal reserves for various rates of increase of the rate of production as calculated from the equation for the EET [Eq. (6)].  If we use the conservative smaller estimate of U.S. coal reserves we see that the growth of the rate of consumption will have to be held below  3 % / yr if we want coal to last until our nation's tricentennial.  If we want coal to last 200 years, the rate of growth of annual consumption will have to be held below 1 % / yr! 

One obtains an interesting insight into the problem if one asks how long beyond the year 1910 could coal production have continued on the curve of exponential growth at the historic rate of  6.69 % / yr  of Fig. 4.  The smaller estimate of U.S. coal would have been consumed around the year 1967 and the large estimate would have expired around the year 1990.  Thus it is clear that the use of coal as an energy source in 1978 and in the years to come is possible only because the growth in the annual production of coal was zero from 1910 to about 1972! 


Now that we have seen the facts let us compare them with statements from authoritative sources.  Let us look first at a report to the Congress.  

    It is clear, particularly in the case of coal, that we have ample reserves.... We have an abundance of coal in the ground.  Simply stated, the crux of the problem is how to get it out of the ground and use it in environmentally acceptable ways and on an economically competitive basis... At current levels of output and recovery these reserves can be expected to last more than 500 years.14 

Here is one of the most dangerous statements in the literature.  It is dangerous because news media and the energy companies pick up the idea that "United States coal will last 500 years" while the media and the energy companies forget or ignore the important caveat with which the sentence began, "At current levels of output . . ."  The right-hand column of Table IX shows that at zero rate of growth of consumption even the low estimate of the U.S. coal resource "will last over 500 years."  However, it is absolutely clear that the government does not plan to hold coal production constant "at current levels of output." 

Table IX. 

Lifetime in years of United States coal (EET).  The lifetime (EET) in years of U.S. coal reserves (both the high and low estimate of the U.S.G.S.) are shown for several rates of growth of production from the 1972 level of 0.5 (x109) metric tons per year. 

          High Estimate (yr)      Low Estimate (yr)  
Zero            2872                      680 
  1%            339                       205 
  2%            203                       134 
  3%            149                       102 
  4%            119                       83 
  5%            99                        71 
  6%            86                        62 
  7%            76                        55 
  8%            68                        50 
  9%            62                        46 
 10%            57                        42 
 11%            52                        39 
 12%            49                        37 
 13%            46                        35


    Coal reserves far exceed supplies of oil and gas, and yet coal supplies only 18 % of our total energy.  To maintain even this contribution we will need to increase coal production by 70 % by 1985, but the real goal, to increase coal's share of the energy market will require a staggering growth rate.15 

While the government is telling us that we must achieve enormous increases in the rate of coal production, other governmental officials are telling us that we can increase the rate of production of coal and have the resource last for a very long time. 

    The trillions of tons of coal lying under the United States will have to carry a large part of the nation's increased energy consumption, says (the) Director of the Energy Division of the Oak Ridge National Laboratories.  "He estimated America's coal reserves are so huge, they could last ‘a minimum of 300 years and probably a maximum of 1000 years."16 

Compare the above statement of the life expectancy of U.S. coal reserves with the results of very simple calculations given in Table IX. 

    In the three-hour CBS television special on energy (August 31, 1977) a reporter stressed the great efforts that are being made to increase the rate of production of U.S. coal, and he summarized the situation in these words, "By the lowest estimate, we have enough (coal) for 200 years.  By the highest, enough for more than a thousand years." 

Again, compare the above statement with the results of simple calculations shown in Table IX. 

While we read these news stories we are bombarded by advertisements by the energy companies which say that coal will last a long time at present rates of consumption and which say at the same time that we must dramatically increase our rate of production of coal. 

    At the rate the United States uses coal today, these reserves could help keep us in energy for the next two hundred years . . . Most coal used in America today is burned by electric power plants–(which)–consumed about 400 million tons of coal last year.  By 1985 this figure could jump to nearly 700 million tons.17 

Other advertisements stress just the 500 years (no caveat): "We are sitting on half the world's known supply of coal–enough for over 500 years."18  Some ads stress the idea of self-sufficiency without stating for how long a period we might be self-sufficient.  "Coal, the only fuel in which America is totally self-sufficient."19  Other ads suggest a deep lack of understanding of the fundamentals of the exponential function. 

    Yet today there are still those who shrill (sic) for less energy and no growth... Now America is obligated to generate more energy - not less - merely to provide for its increasing population... With oil and gas in short supply, where will that energy come from?  Predominately from coal.  The U.S. Department of the Interior estimates America has 23 %  more coal than we dreamed of,  4,000,000,000,000 (trillion!) tons of it.  Enough for over 500 years.  (The non-sentences are in the original.)20 

A simple calculation of the EET based on a current production rate of  0.6 x 109 tons / yr shows that the growth in the rate of production of coal can't exceed  0.8 % / yr if the ad's 4 x 1012 tons of coal is to last for the ad's 500 yr.  However, it should be noted that the 4 x 1012 tons cited in the ad is  2.8  times the size of the large estimate of U.S. coal reserves and is 12 times the size of the small estimate of U.S. coal reserves as cited by Hubbert. 

When we view the range of creative information that is offered to the public we cannot wonder that people are confused.  We may wish that we could have rapid growth of the rate of consumption and have the reserves of U.S. coal last for a large number of years, but very simple calculations are all that is needed to prove that these two goals are incompatible.  At this critical time in our nation's history we need to shift our faith to calculations (arithmetic) based on factual data and give up our belief in Walt Disney's First Law: "Wishing will make it so."21 

On the broad aspects of the energy problem we note that the top executive of one of our great corporations is probably one of the world's authorities on the exponential growth of investments and compound interest.  However, he observes that "the energy crisis was made in Washington."  He ridicules "the modern-day occult prediction" of "computer print-outs" and warns against extrapolating past trends to estimate what may happen in the future.  He then points out how American free-enterprise solved the great "Whale Oil Crisis" of the 1850s.  With this single example as his data base he boldly extrapolates into the future to assure us that American ingenuity will solve the current energy crisis if the bureaucrats in Washington will only quit interfering.22   It is encouraging to note that the person who made these statements in 1974, suggesting that the energy crisis was contrived rather than real, has now signed his name on an advertisement in Newsweek Magazine (Sept. 12, 1977) saying that, "Energy is not a political issue.  It's an issue of survival. Time is running out."  However, the same issue of Newsweek Magazine carried two advertisements for coal which said: "We've limited our use of coal while a supply that will last for centuries sits under our noses... Coal–can provide our energy needs for centuries to come." 

Carefully read this ad by the Edison Electric Institute for the Electric Companies telling us that: "There is an increasing scarcity of certain fuels.  But there is no scarcity of energy.  There never has been.  There never will be.  There never could be. Energy is inexhaustible."  (Emphasis is in the original.)23  We can read that a professor in a school of mining technology offers "proof" of the proposition: "Mankind has the right to use the world's resources as it wishes, to the limits of its abilities . . ."24  

We have the opening sentence of a major scientific study of the energy problem: "The United States has an abundance of energy resources; fossil fuels (mostly coal and oil shale) adequate for centuries, fissionable nuclear fuels adequate for millennia and solar energy that will last indefinitely."25  We can read the words of an educated authority who asserts that there is no problem of shortages of resources: "It is not true that we are running out of resources that can be easily and cheaply exploited without regard for future operations."  His next sentence denies that growth is a serious component of the energy problem, "It is not true that we must turn our back on economic growth"(emphasis is in the original).   Three sentences later he says that there may be a problem: "We must face the fact that the well of nonrenewable natural resources is not bottomless."26  He does suggest that lack of "leadership" is part of the problem. 

We have a statement by Ralph Nader, "The supply of oil, gas, and coal in this country is enormous and enough for hundreds of years.  It is not a question of supply but a question of price and profits, of monopolies and undue political influence."27 

Expert analysis of the problem can yield unusual recommendations.  We have the opening paper in an energy conference in which a speaker from a major energy company makes no mention of the contribution of growth to the energy crisis when he asserts that: "The core of the energy problem both U.S. and worldwide [is] our excessive dependence on our two scarcest energy resources - oil and natural gas."  For him continued growth is not part of the problem, it is part of the solution! More energy must be made available at a higher rate of growth than normal – in the neighborhood of 6 percent per year compared to a recent historical growth rate of 4 percent per year.28 

The patient is suffering from cancer, and after a careful study, the doctor prescribes the remedy; give the patient more cancer.  Here is a second case where cancer is prescribed as the cure for cancer.  The National Petroleum Council in its report to the energy industry on the energy crisis: observed that "Restrictions on energy demand growth could prove (to be) expensive and undesirable. . . The Council ‘flatly rejected' any conservation-type measures proposing instead the production of more energy sources domestically and the easing of environmental controls."29 

Study this statement carefully: "Energy industries agree that to achieve some form of energy self-sufficiency the U.S. must mine all the coal that it can."30  The plausibility of this statement disappears and its real meaning becomes apparent when we paraphrase it: "The more rapidly we consume our resources, the more self-sufficient we will be."  David Brower has referred to this as the policy of "Strength through Exhaustion." 31 This policy has many powerful adherents.  For example, on the three-hour CBS television special on energy (Aug. 31, 1977) William Simon, energy adviser to President Ford said: "We should be "trying to get as many holes drilled as possible to get the proven (oil) reserve . . ." 

Is it in the national interest to get and use these reserves as rapidly as possible?  We certainly get no sense of urgency from the remarks of the Board Chairman of a major multinational energy corporation who concludes the discussion "Let's Talk Frankly About Energy" with his mild assessment of what we must do.  "Getting on top of the energy problem won't be easy.  It will be an expensive and time-consuming task.  It will require courage, creativeness and discipline . . ."32 

If one searches beyond the work of Hubbert for an indication of others who understand the fundamental arithmetic of the problem one finds occasional encouraging evidence.33  However, when one compares the results of the simple exponential calculations with news stories, with statements from public officials, and with assertions in advertisements of the energy companies it is hard to imagine that this arithmetic is widely understood.  

The arithmetic of growth is the forgotten fundamental of the energy crisis.  

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